mm-4913 === Subject: JSH: Why choice rules On my math blog Penny Hassett had a comment that got me to thinking and after pondering at her suggestion what others believe to be true in their disagreements with me about a certain serious mathematical issue, I concluded that infinity could help to clear the air. So I have simple examples yet again to start (believe me it gets really hard later so please pay close attention to the easy part): 7(x^2 + 3x + 2) = (7x + 7)(x + 2) and let the ring be the ring of algebraic integers. And notice that reflects CHOICE. My choice for a simple example as the 7 can be factored an INFINITY of ways!!! After all, 7(x^2 + 3x + 2) = (x + 1)(7x + 14) is ALSO just as valid mathematically, and in fact there are an infinity of possible variations all equally valid. Key here also to notice is that there are an infinity of choices FOR EVERY x, and remember the ring is the ring of algebraic integers. So far easy and there should be no disagreement with the above! Now to the hard mathematics. Now we'll TRY to assume the ring is still the ring of algebraic integers and now a harder example: 7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5b_2(x) + 2) where 7b_1(x) = a_1(x) and b_2(x) = a_2(x) + 1 and the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. Notice the b's are chosen such that when x=0, both the b's equal 0, which is to say, they are normalized. Now just like before you have human choice, and you can imagine moving that 7 around easily enough: 7(175x^2 - 15x + 2) = (5b_1(x) + 1)(5(7)b_2(x) + 14) which is just one more human choice out of infinity. And there are an INFINITY of possibilities for EVERY x. Every x has an infinite number of choices. So how does the mathematics choose? It doesn't. I did. I chose. But that's where the fights start and the arguing and the dead math journal comes into the picture as what follows from mathematical logic and the rigidity of infinity is a conclusion that is devastating emotionally to thousands of mathematicians around the world which is that there is a core error: the ring of algebraic integers gives a false result. Because now you have that one of the a's has 7 as a factor by the choice argument. But the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and at x=1, that gives a^2 - 6a + 35 = 0 and provably in the ring of algebraic integers NEITHER of the roots can have 7 as a factor and there is shown the direct contradiction. Notice the ring of algebraic integers does not fail gracefully and its error is not fixable as your alternative is to introduce some mystical force to choose out of infinity, like, maybe God? (Posters have been remarkably vague in past arguments about how a particular factor of 7 arises, often simply repeating what is taught in math classes about ways to find the factors at any particular x, but remember there are an infinity of choices for EVERY x, so the choice problem gives you infinity at every point. So who chooses? God?) But not even God can choose for you here if you go with mathematical logic. Of course, you can like so many human beings before you simply choose to believe in what you've been taught, even though it is very, very wrong. The mystical nature of the disagreement with me is remarkable but I think it's natural for human beings to turn to spirits or mystical forces in the face of something difficult to understand. That's what your ancestors did. But then you're no longer really mathematicians. James Harris === Subject: Re: JSH: Why choice rules posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) > On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. So I have simple examples yet again to start (believe me it gets > really hard later so please pay close attention to the easy part): 7(x^2 + 3x + 2) = (7x + 7)(x + 2) and let the ring be the ring of algebraic integers. And notice that > reflects CHOICE. My choice for a simple example as the 7 can be > factored an INFINITY of ways!!! After all, 7(x^2 + 3x + 2) = (x + 1)(7x + 14) is ALSO just as valid mathematically, and in fact there are an > infinity of possible variations all equally valid. Key here also to notice is that there are an infinity of choices FOR > EVERY x, and remember the ring is the ring of algebraic integers. So far easy and there should be no disagreement with the above! Now to the hard mathematics. Now we'll TRY to assume the ring is still the ring of algebraic > integers and now a harder example: 7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5b_2(x) + 2) where 7b_1(x) = a_1(x) and b_2(x) = a_2(x) + 1 and the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. Notice the b's are chosen such that when x=0, both the b's equal 0, > which is to say, they are normalized. Now just like before you have human choice, and you can imagine moving > that 7 around easily enough: 7(175x^2 - 15x + 2) = (5b_1(x) + 1)(5(7)b_2(x) + 14) which is just one more human choice out of infinity. And there are an INFINITY of possibilities for EVERY x. Every x has > an infinite number of choices. So how does the mathematics choose? It doesn't. I did. I chose. But that's where the fights start and the arguing and the dead math > journal comes into the picture as what follows from mathematical logic > and the rigidity of infinity is a conclusion that is devastating > emotionally to thousands of mathematicians around the world which is > that there is a core error: the ring of algebraic integers gives a > false result. Because now you have that one of the a's has 7 as a factor by the > choice argument. But the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and at x=1, that gives a^2 - 6a + 35 = 0 and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. Notice the ring of algebraic integers does not fail gracefully and its > error is not fixable as your alternative is to introduce some mystical > force to choose out of infinity, like, maybe God? (Posters have been remarkably vague in past arguments about how a > particular factor of 7 arises, often simply repeating what is taught > in math classes about ways to find the factors at any particular x, > but remember there are an infinity of choices for EVERY x, so the > choice problem gives you infinity at every point. So who chooses? > God?) > Here is a proof, for x = 1, that a_1(x) and a_2(x) are both not divisible by 7. Both a_1(1) and a_2(1) are roots of a^2 - 6a + 35. We can let a_1(1) = 3 + sqrt(-26), a_2(1) = 3 - sqrt(-26) Let u = -307 - 30 * sqrt(-26) and v = -307 + 30 * sqrt(-26) Then the following can be readily checked by ordinary arithmetic: (1) a_1(1)^6 / u = -109 + 12 * sqrt(-26) (2) a_2(1)^6 / v = -109 - 12 * sqrt(-26) (3) u * v = 7^6 (4) a_1(1)^6 * a_2(1)^6 / (u * v) = 15625 = 5^6. (5) u and v are both algebraic integers (6) Neither u nor v are units in the ring of algebraic integers. Further, note that because of (4) above and because 5 and 7 are coprime, you can conclude that a_1(1)^6 / u and a_2(1)^6 / v have no factors in common with 7. Conclusions: a_1(1)^6 has a factor in common with 7, namely u. a_2(1)^6 has a factor in common with 7, namely v. Neither a_1(1) nor a_2(1) are divisible by 7, since neither u nor v are units and a_1(1)*a_2(1)/(u*v) = 5^6 is coprime to 7. The key thing here is, if you have a proof contradicting this, you are contradicting not some old theorems in algebraic number theory or Galois theory. You are contradicting plain old arithmetic. If there is a problem, it goes beyond just a problem with the ring of algebraic numbers. If you are right, you have arrived at an inconsistency in all of mathematics - you have essentially proved that 1 + 1 = 3. Either that, or your proof is wrong. Which do you think is more likely? Marcus. > But not even God can choose for you here if you go with mathematical > logic. Of course, you can like so many human beings before you simply > choose to believe in what you've been taught, even though it is very, > very wrong. The mystical nature of the disagreement with me is remarkable but I > think it's natural for human beings to turn to spirits or mystical > forces in the face of something difficult to understand. That's what > your ancestors did. But then you're no longer really mathematicians. James Harris === Subject: Re: JSH: Why choice rules posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. So I have simple examples yet again to start (believe me it gets > really hard later so please pay close attention to the easy part): 7(x^2 + 3x + 2) = (7x + 7)(x + 2) and let the ring be the ring of algebraic integers. And notice that > reflects CHOICE. My choice for a simple example as the 7 can be > factored an INFINITY of ways!!! After all, 7(x^2 + 3x + 2) = (x + 1)(7x + 14) is ALSO just as valid mathematically, and in fact there are an > infinity of possible variations all equally valid. Key here also to notice is that there are an infinity of choices FOR > EVERY x, and remember the ring is the ring of algebraic integers. So far easy and there should be no disagreement with the above! Now to the hard mathematics. Now we'll TRY to assume the ring is still the ring of algebraic > integers and now a harder example: 7(175x^2 - 15x + 2) = (5(7)b 1(x) + 7)(5b 2(x) + 2) where 7b 1(x) = a 1(x) and b 2(x) = a 2(x) + 1 and the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. Notice the b's are chosen such that when x=0, both the b's equal 0, > which is to say, they are normalized. Now just like before you have human choice, and you can imagine moving > that 7 around easily enough: 7(175x^2 - 15x + 2) = (5b 1(x) + 1)(5(7)b 2(x) + 14) which is just one more human choice out of infinity. And there are an INFINITY of possibilities for EVERY x. Every x has > an infinite number of choices. So how does the mathematics choose? It doesn't. I did. I chose. But that's where the fights start and the arguing and the dead math > journal comes into the picture as what follows from mathematical logic > and the rigidity of infinity is a conclusion that is devastating > emotionally to thousands of mathematicians around the world which is > that there is a core error: the ring of algebraic integers gives a > false result. Because now you have that one of the a's has 7 as a factor by the > choice argument. But the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and at x=1, that gives a^2 - 6a + 35 = 0 and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. Notice the ring of algebraic integers does not fail gracefully and its > error is not fixable as your alternative is to introduce some mystical > force to choose out of infinity, like, maybe God? (Posters have been remarkably vague in past arguments about how a > particular factor of 7 arises, often simply repeating what is taught > in math classes about ways to find the factors at any particular x, > but remember there are an infinity of choices for EVERY x, so the > choice problem gives you infinity at every point. So who chooses? > God?) Here is a proof, for x = 1, that a 1(x) and a 2(x) are both > not divisible by 7. Both a 1(1) and a 2(1) are roots of a^2 - 6a + 35. We can let a 1(1) = 3 + sqrt(-26), a 2(1) = 3 - sqrt(-26) Let u = -307 - 30 * sqrt(-26) and v = -307 + 30 * sqrt(-26) Then the following can be readily checked by ordinary > arithmetic: (1) a 1(1)^6 / u = -109 + 12 * sqrt(-26) (2) a 2(1)^6 / v = -109 - 12 * sqrt(-26) (3) u * v = 7^6 (4) a 1(1)^6 * a 2(1)^6 / (u * v) = 15625 = 5^6. (5) u and v are both algebraic integers (6) Neither u nor v are units in the ring of > algebraic integers. Further, note that because of (4) above and because > 5 and 7 are coprime, you can conclude that a 1(1)^6 / u > and a 2(1)^6 / v have no factors in common with 7. Conclusions: a 1(1)^6 has a factor in common with 7, namely u. a 2(1)^6 has a factor in common with 7, namely v. Neither a 1(1) nor a 2(1) are divisible by 7, since > neither u nor v are units and a 1(1)*a 2(1)/(u*v) = 5^6 > is coprime to 7. The key thing here is, if you have a proof contradicting > this, you are contradicting not some old theorems in algebraic > number theory or Galois theory. You are contradicting plain > old arithmetic. If there is a problem, it goes beyond just a Nope. The same techniques you just used would work to prove that neither of the roots of x^2 + 3x + 2 = 0 has 2 as a factor--if you don't resolve the square root. Trivial. The algebra is easy but the psychology is complex as the error allows people like you to do pretend mathematics! Your very sense of self may be wrapped up in the bogus math that you do, so it's an uphill slog to get you past your denial, into the world of doing valid mathematics. James Harris === Subject: Re: JSH: Why choice rules > On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. > So I have simple examples yet again to start (believe me it gets > really hard later so please pay close attention to the easy part): > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > and let the ring be the ring of algebraic integers. And notice that > reflects CHOICE. My choice for a simple example as the 7 can be > factored an INFINITY of ways!!! > After all, > 7(x^2 + 3x + 2) = (x + 1)(7x + 14) > is ALSO just as valid mathematically, and in fact there are an > infinity of possible variations all equally valid. > Key here also to notice is that there are an infinity of choices FOR > EVERY x, and remember the ring is the ring of algebraic integers. > So far easy and there should be no disagreement with the above! > Now to the hard mathematics. > Now we'll TRY to assume the ring is still the ring of algebraic > integers and now a harder example: > 7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5b_2(x) + 2) > where > 7b_1(x) = a_1(x) and b_2(x) = a_2(x) + 1 > and the a's are roots of > a^2 - (7x-1)a + (49x^2 - 14x) = 0. > Notice the b's are chosen such that when x=0, both the b's equal 0, > which is to say, they are normalized. > Now just like before you have human choice, and you can imagine moving > that 7 around easily enough: > 7(175x^2 - 15x + 2) = (5b_1(x) + 1)(5(7)b_2(x) + 14) > which is just one more human choice out of infinity. > And there are an INFINITY of possibilities for EVERY x. Every x has > an infinite number of choices. > So how does the mathematics choose? > It doesn't. I did. I chose. > But that's where the fights start and the arguing and the dead math > journal comes into the picture as what follows from mathematical logic > and the rigidity of infinity is a conclusion that is devastating > emotionally to thousands of mathematicians around the world which is > that there is a core error: the ring of algebraic integers gives a > false result. > Because now you have that one of the a's has 7 as a factor by the > choice argument. > But the a's are roots of > a^2 - (7x-1)a + (49x^2 - 14x) = 0 > and at x=1, that gives > a^2 - 6a + 35 = 0 > and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. > Notice the ring of algebraic integers does not fail gracefully and its > error is not fixable as your alternative is to introduce some mystical > force to choose out of infinity, like, maybe God? > (Posters have been remarkably vague in past arguments about how a > particular factor of 7 arises, often simply repeating what is taught > in math classes about ways to find the factors at any particular x, > but remember there are an infinity of choices for EVERY x, so the > choice problem gives you infinity at every point. So who chooses? > God?) > Here is a proof, for x = 1, that a_1(x) and a_2(x) are both > not divisible by 7. > Both a_1(1) and a_2(1) are roots of a^2 - 6a + 35. > We can let a_1(1) = 3 + sqrt(-26), a_2(1) = 3 - sqrt(-26) > Let u = -307 - 30 * sqrt(-26) and v = -307 + 30 * sqrt(-26) > Then the following can be readily checked by ordinary > arithmetic: > (1) a_1(1)^6 / u = -109 + 12 * sqrt(-26) > (2) a_2(1)^6 / v = -109 - 12 * sqrt(-26) > (3) u * v = 7^6 > (4) a_1(1)^6 * a_2(1)^6 / (u * v) = 15625 = 5^6. > (5) u and v are both algebraic integers > (6) Neither u nor v are units in the ring of > algebraic integers. > Further, note that because of (4) above and because > 5 and 7 are coprime, you can conclude that a_1(1)^6 / u > and a_2(1)^6 / v have no factors in common with 7. > Conclusions: > a_1(1)^6 has a factor in common with 7, namely u. > a_2(1)^6 has a factor in common with 7, namely v. > Neither a_1(1) nor a_2(1) are divisible by 7, since > neither u nor v are units and a_1(1)*a_2(1)/(u*v) = 5^6 > is coprime to 7. > The key thing here is, if you have a proof contradicting > this, you are contradicting not some old theorems in algebraic > number theory or Galois theory. You are contradicting plain > old arithmetic. If there is a problem, it goes beyond just a Nope. The same techniques you just used would work to prove that neither > of the roots of x^2 + 3x + 2 = 0 has 2 as a factor--if you don't resolve the square root. > This is not true. > Trivial. > Then provide the proof, if you think you're up to it. > The algebra is easy but the psychology is complex as the error allows > people like you to do pretend mathematics! > As the King of Pretend Mathematics, you should know? > Your very sense of self may be wrapped up in the bogus math that you > do, so it's an uphill slog to get you past your denial, into the world > of doing valid mathematics. > Here's a challenge. You've said that one could prove , using the techniques marcus_b has used, that neither root of the polynomial x^2 + 3x + 2 is divisible by 2, presumably in the ring of algebraic integers. You've even said it's trivial. So, prove it. I say you can't do it. I know that I can't, I know that none of the mathematicians that I know of can prove it. But you claim it can be done, and that it is trivial. So, put your alleged mathematics where your mouth is, and provide the proof. Can't be so hard, if it's trivial. Maybe you'll get lucky! James Harris Dale === Subject: Re: JSH: Why choice rules posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) On Jul 4, 10:51pm, W. Dale Hall On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. > So I have simple examples yet again to start (believe me it gets > really hard later so please pay close attention to the easy part): > 7(x^2 + 3x + 2) = (7x + 7)(x + 2) > and let the ring be the ring of algebraic integers. And notice that > reflects CHOICE. My choice for a simple example as the 7 can be > factored an INFINITY of ways!!! > After all, > 7(x^2 + 3x + 2) = (x + 1)(7x + 14) > is ALSO just as valid mathematically, and in fact there are an > infinity of possible variations all equally valid. > Key here also to notice is that there are an infinity of choices FOR > EVERY x, and remember the ring is the ring of algebraic integers. > So far easy and there should be no disagreement with the above! > Now to the hard mathematics. > Now we'll TRY to assume the ring is still the ring of algebraic > integers and now a harder example: > 7(175x^2 - 15x + 2) = (5(7)b 1(x) + 7)(5b 2(x) + 2) > where > 7b 1(x) = a 1(x) and b 2(x) = a 2(x) + 1 > and the a's are roots of > a^2 - (7x-1)a + (49x^2 - 14x) = 0. > Notice the b's are chosen such that when x=0, both the b's equal 0, > which is to say, they are normalized. > Now just like before you have human choice, and you can imagine moving > that 7 around easily enough: > 7(175x^2 - 15x + 2) = (5b 1(x) + 1)(5(7)b 2(x) + 14) > which is just one more human choice out of infinity. > And there are an INFINITY of possibilities for EVERY x. Every x has > an infinite number of choices. > So how does the mathematics choose? > It doesn't. I did. I chose. > But that's where the fights start and the arguing and the dead math > journal comes into the picture as what follows from mathematical logic > and the rigidity of infinity is a conclusion that is devastating > emotionally to thousands of mathematicians around the world which is > that there is a core error: the ring of algebraic integers gives a > false result. > Because now you have that one of the a's has 7 as a factor by the > choice argument. > But the a's are roots of > a^2 - (7x-1)a + (49x^2 - 14x) = 0 > and at x=1, that gives > a^2 - 6a + 35 = 0 > and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. > Notice the ring of algebraic integers does not fail gracefully and its > error is not fixable as your alternative is to introduce some mystical > force to choose out of infinity, like, maybe God? > (Posters have been remarkably vague in past arguments about how a > particular factor of 7 arises, often simply repeating what is taught > in math classes about ways to find the factors at any particular x, > but remember there are an infinity of choices for EVERY x, so the > choice problem gives you infinity at every point. So who chooses? > God?) > Here is a proof, for x = 1, that a 1(x) and a 2(x) are both > not divisible by 7. > Both a 1(1) and a 2(1) are roots of a^2 - 6a + 35. > We can let a 1(1) = 3 + sqrt(-26), a 2(1) = 3 - sqrt(-26) > Let u = -307 - 30 * sqrt(-26) and v = -307 + 30 * sqrt(-26) > Then the following can be readily checked by ordinary > arithmetic: > (1) a 1(1)^6 / u = -109 + 12 * sqrt(-26) > (2) a 2(1)^6 / v = -109 - 12 * sqrt(-26) > (3) u * v = 7^6 > (4) a 1(1)^6 * a 2(1)^6 / (u * v) = 15625 = 5^6. > (5) u and v are both algebraic integers > (6) Neither u nor v are units in the ring of > algebraic integers. > Further, note that because of (4) above and because > 5 and 7 are coprime, you can conclude that a 1(1)^6 / u > and a 2(1)^6 / v have no factors in common with 7. > Conclusions: > a 1(1)^6 has a factor in common with 7, namely u. > a 2(1)^6 has a factor in common with 7, namely v. > Neither a 1(1) nor a 2(1) are divisible by 7, since > neither u nor v are units and a 1(1)*a 2(1)/(u*v) = 5^6 > is coprime to 7. > The key thing here is, if you have a proof contradicting > this, you are contradicting not some old theorems in algebraic > number theory or Galois theory. You are contradicting plain > old arithmetic. If there is a problem, it goes beyond just a Nope. The same techniques you just used would work to prove that neither > of the roots of x^2 + 3x + 2 = 0 has 2 as a factor--if you don't resolve the square root. This is not true. Trivial. Then provide the proof, if you think you're up to it. Assume for the sake of argument that x^2 + 3x + 2 = 0 is irreducible over Z. Now assume that only one root has 2 as a factor, and let x = 2y, then 4y^2 + 6y + 2 = 0, and dividing 2 off gives: 2y^2 + 3y + 1 = 0 which is also assumed to be irreducible over Z, then it cannot be true that 2 is a factor, as then the polynomial is non-monic with integer coefficients assumed to be irreducible over Z. Note that *reducibility* is the one criteria so as I noted above, if you do not resolve the square root, then the same type argument works to show that 2 is not a factor of x^2 + 3x + 2 = 0. So the argument is actuality is about reducibility. I have to note for readers who don't know that the poster W. Dale Hall is one of the posters who conspired online against my paper and is in fact THE poster who the chief editor quoted in his email to me claiming a reviewer had claimed a mistake with my paper. He didn't realize that I'd seen the material on sci.math so knew he was lying. Contacts with another editor at the now defunct journal indicate that the journal DID use two reviewers as it states but that the chief editor became convinced by the emails from the sci.math'ers that his reviewers had made a mistake!!! Posters on sci.math have repeatedly claimed without providing evidence that the journal simply lied about using two reviewers but that is unsubtantiated opinion from people with a vested interest in lying-- obviously sci.math'ers do not want to be known as journal killers. So if you didn't know, here is one of the sci.math conspirators still arguing against the result on the newsgroup. Another person known to have sent an email to the editors based on his posting on sci.math was Arturo Magidin. So he is one of the other people who was key in killing the journal. If you didn't know they were two of the key conspirators, now you do. James Harris === Subject: Re: JSH: Why choice rules > a^2 - 6a + 35 = 0 and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. Do you know what an Algebraic Integer _is_? 14 = 2 x 7 (two primes) But, dividing 14 by an arbitrary algebraic integer gives 14/(5 - sqrt(3) i) = 5/2 + 1/2 sqrt(3) i So 14 = (5 - sqrt(3) i)(5/2 + 1/2 sqrt(3) i) (the product of two arbitrary algebraics having no factors in common with 2 or 7) Any contradiction there? M === Subject: Re: Why choice rules > On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. So I have simple examples yet again to start (believe me it gets > really hard later so please pay close attention to the easy part): 7(x^2 + 3x + 2) = (7x + 7)(x + 2) trivial and let the ring be the ring of algebraic integers. And notice that > reflects CHOICE. My choice for a simple example as the 7 can be > factored an INFINITY of ways!!! After all, 7(x^2 + 3x + 2) = (x + 1)(7x + 14) 7(x^2 + 3x + 2) = 7*(x + 1)(x + 2) OK now what ? is ALSO just as valid mathematically, and in fact there are an > infinity of possible variations all equally valid. so what? your just multiplying some number by another Key here also to notice is that there are an infinity of choices FOR > EVERY x, and remember the ring is the ring of algebraic integers. So far easy and there should be no disagreement with the above! Now to the hard mathematics. Now we'll TRY to assume the ring is still the ring of algebraic > integers and now a harder example: 7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5b_2(x) + 2) where 7b_1(x) = a_1(x) and b_2(x) = a_2(x) + 1 and the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. Notice the b's are chosen such that when x=0, both the b's equal 0, > which is to say, they are normalized. and........ Now just like before you have human choice, and you can imagine moving > that 7 around easily enough: 7(175x^2 - 15x + 2) = (5b_1(x) + 1)(5(7)b_2(x) + 14) which is just one more human choice out of infinity. And there are an INFINITY of possibilities for EVERY x. Every x has > an infinite number of choices. So how does the mathematics choose? It doesn't. I did. I chose. yes, you like the 7.......... But that's where the fights start and the arguing and the dead math > journal comes into the picture as what follows from mathematical logic > and the rigidity of infinity is a conclusion that is devastating > emotionally to thousands of mathematicians around the world which is > that there is a core error: the ring of algebraic integers gives a > false result. could you make that sentance shorter? Because now you have that one of the a's has 7 as a factor by the > choice argument. But the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and at x=1, that gives a^2 - 6a + 35 = 0 and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. one 7 goes in, one 7 comes out no contridiction! Notice the ring of algebraic integers does not fail gracefully and its > error is not fixable as your alternative is to introduce some mystical > force to choose out of infinity, like, maybe God? 7 is no good. Use 19, its much better. (Posters have been remarkably vague in past arguments about how a > particular factor of 7 arises, often simply repeating what is taught > in math classes about ways to find the factors at any particular x, > but remember there are an infinity of choices for EVERY x, so the > choice problem gives you infinity at every point. So who chooses? > God?) it is the negitive root you keep missing. Negitive square root. But not even God can choose for you here if you go with mathematical > logic. Of course, you can like so many human beings before you simply > choose to believe in what you've been taught, even though it is very, > very wrong. You may call me god, several others do. The mystical nature of the disagreement with me is remarkable but I > think it's natural for human beings to turn to spirits or mystical > forces in the face of something difficult to understand. That's what > your ancestors did. your ancestors were all trolls. But then you're no longer really mathematicians. > James Harris and you're a mathematiticn now === Subject: Re: JSH: Why choice rules posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > But then you're no longer really mathematicians. James Harris Eat you delusional narcissist! Are you still trying to sell your snake oil? You are a liar, cheat and charlatan! Please get back into your self induced and drugged state and start drinking again. It was so nice not seeing your usual bull spat out in yet another incarnation. No matter because no smoke screens will fix the flaw in your brain and anything it generates. Get your head out of your ass! Have a wonderful evening! === Subject: Re: JSH: Why choice rules > On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. > Unfortunately, infinity has been called to Washington to help calculate the national debt, and isn't available for comment. === Subject: Re: JSH: Why choice rules posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. Unfortunately, infinity has been called to Washington to help calculate > the national debt, and isn't available for comment. The error I'm highlighting allows pretend mathematics as you can appear to prove just about anything with it. Fakes can run rampant in the field once they learn the system, gaining success without ever actually mathematically proving anything that is correct. Obviously for some people keeping such an error would allow them to remain in a field where they might not be able to survive without it. Such people probably wouldn't be nice either as consider, they're willing to screw over the entire human race for the narrow gain of a paycheck today, possibly knowing full well that if our mathematics is not right, our future science that depends on the correct math can't be found. These people are scum of the earth. One guess is that such people believe that the world will be ok, and it's a dog eat dog world anyway, so why shouldn't they get theirs? So they fight this result and call me names. And so with no one but me standing up for the mathematical truth they are the voice of humanity, and it becomes the case that the human race rewards its latest major discoverer with...insults. Read through this thread and understand the people many of you enable with your silence. They are your shame. James Harris === Subject: Re: JSH: Why choice rules posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) And so with no one but me standing up for the mathematical truth they > are the voice of humanity, and it becomes the case that the human race > rewards its latest major discoverer with...insults. James Harris You are a dickhead! You think you are a discoverer? What a joke! If anyone is destroying the world, it is the politicians that gave you enough welfare to go to school and allowed you to believe you got an education. That is what is destryoing the world! You delusional narcissist! === Subject: Re: JSH: Why choice rules posting-account=FK_G5goAAAAEbWGaiao8aY3ti47UN9eX 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. Learn how to write English, wit. === Subject: Re: JSH: Why choice rules posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. Learn how to write English, wit. Exactly my initial reaction... No big surprise though: his inability to express himself clearly perfectly reflects his inability to think clearly. LOL M === Subject: Re: Sign of ZERO >European didn't sail west mostly because they didn't think there was any profitable reason to do so. for much the same reason they thought the world was flat about two millenia after whatsisgreekname. Egypme no that's a jewish name === Subject: Re: Sign of ZERO <59d18$4a4d3edd$4dfacb13$6515@news.chello.nl> AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) The Hebrews were not told about the Mayans after Isaiah failed to correct their genetics. But the Mayans were told about the so-called Old World, as Quezacoatl. >European didn't sail west mostly because they didn't think there was any profitable reason to do so. for much the same reason they thought the world was flat about two millenia > after whatsisgreekname. Egypme no that's a jewish name === Subject: Re: mayans built underground tunnels connecting to other continents the cause of this is unknown. mayans have assisted in building these tunnels with the lifeforms and could thereby exchange information and gifts with civilizations on other continents. the tunnels seem to pervade throughout all continents, including antarctica. they say the tunnels are currently being used by the lifeforms for the secret reconstruction of the fourth reich. === Subject: Re: mayans built underground tunnels connecting to other continents <4b9ad$4a4dddcb$4dfacb13$13063@news.chello.nl> AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) That is unlikely. Mayans were loaned some tools for their enlightenment, but they had not developed their own technology very far. It would be more efficient to use suborbital shuttles. > the cause of this is unknown. mayans have assisted in building these tunnels > with the lifeforms and could thereby exchange information and gifts with > civilizations on other continents. the tunnels seem to pervade throughout > all continents, including antarctica. they say the tunnels are currently > being used by the lifeforms for the secret reconstruction of the fourth > reich. === Subject: Re: mayans built underground tunnels connecting to other continents on square wheels? === Subject: Re: mayans built underground tunnels connecting to other continents <4b9ad$4a4dddcb$4dfacb13$13063@news.chello.nl> posting-account=qfTKWQoAAADrbu8lwB1KpYv95yNmrUOu Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > the cause of this is unknown. mayans have assisted in building these tunnels > with the lifeforms and could thereby exchange information and gifts with > civilizations on other continents. the tunnels seem to pervade throughout > all continents, including antarctica. they say the tunnels are currently > being used by the lifeforms for the secret reconstruction of the fourth > reich. Thats one of the Secret of Brussels too, what we call here The B File about the ñSECRET PASSAGEî to unknown cities... Cities of the Fantastic from Brussels to Br.9fsel, a secret too secret to be divulged. We are ignorant of the world of the Cit.8es Obscures, but that world is not ignorant of us. === Subject: Re: mayans built underground tunnels connecting to other continents posting-account=qfTKWQoAAADrbu8lwB1KpYv95yNmrUOu Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) Wrong again those Passages are called the Labyrinth of Time http://www.youtube.com/watch?v=2clOiEPWh9k The gates to the underworld... which means the gates to the Past... In tomorrows world where technology is on the decline and swords and sorcery on the rise, a civil war in Earth's last great kingdom threatens to destroy civilization. The aggressor kingdom has unearthed ancient relics of the past that it cannot control. http://www.youtube.com/watch?v=3V8sM7Tp7NI This one describes Br.9fsel, a city strikingly like our own Brussels. The city is taken over by madmen and destroyed. At first, the city's inhabitants and rulers encourage and fund the renovation. One by one, people in Br.9fsel begin to suffer under the bizarre attack of its corporate oligarchs. Then, when it's far too late, the city realizes its doom: all that made it livable has been razed, and what's been raised makes it unlivable. The projects end, half-done or less, when the city is bled of its last Euro. Even the ground beneath their feet rebels, when its soft underground structure and protective dikes fail under the skyscrapers' mass. Never discouraged, those of the grand plans simply blame the soil for being too weak, the country for being too poor, and the city for being unworthy of such grandeur. The Man who lived 17000 years to protect his Beloved Sun... Gran'Da'Dy!!! http://www.youtube.com/watch?v=aZZyyII3 Os > Those SECRET PASSAGES are CALLED SEWERS, PIG! lmfjao! It's like a cave. You should live in one. Saul Levy > the cause of this is unknown. mayans have assisted in building these tunnels > with the lifeforms and could thereby exchange information and gifts with > civilizations on other continents. the tunnels seem to pervade throughout > all continents, including antarctica. they say the tunnels are currently > being used by the lifeforms for the secret reconstruction of the fourth > reich. Thats one of the Secret of Brussels too, what we call here The B >File about the ñSECRET PASSAGEî to unknown cities... Cities of the >Fantastic from Brussels to Br.9fsel, a secret too secret to be divulged. We are ignorant of the world of the Cit.8es Obscures, but that world is >not ignorant of us. === Subject: Re: mayans built underground tunnels connecting to other continents though you may be off track as to the city, in the vernacular of the time it's called woonhell. wonder what I'm doing in this thread anyway. just because I haven't done any proper research on this doesn't mean people have the right to either embrace or discard it as fiction. these tunnels exist. trust me. and the secret army of european resurrection is currently deploying through them. === Subject: Re: mayans built underground tunnels connecting to other continents posting-account=qfTKWQoAAADrbu8lwB1KpYv95yNmrUOu Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > though you may be off track as to the city, in the vernacular of the time > it's called woonhell. wonder what I'm doing in this thread anyway. just > because I haven't done any proper research on this doesn't mean people have > the right to either embrace or discard it as fiction. these tunnels exist. > trust me. and the secret army of european resurrection is currently > deploying through them. Believe me that this tunnels are much older than many may think... they exist since Atlantis long before the Maya's... even Hitler was seeking to proof their existence, so no they ain't science fiction... but hidden science. === Subject: Re: mayans built underground tunnels connecting to other continents AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) Human have been abandoned to their fate because of the human tendency to select leaders like Hitler. though you may be off track as to the city, in the vernacular of the time > it's called woonhell. wonder what I'm doing in this thread anyway. just > because I haven't done any proper research on this doesn't mean people have > the right to either embrace or discard it as fiction. these tunnels exist. > trust me. and the secret army of european resurrection is currently > deploying through them. Believe me that this tunnels are much older than many may think... > they exist since Atlantis long before the Maya's... even Hitler was > seeking to proof their existence, so no they ain't science fiction... > but hidden science. === Subject: Re: mayans built underground tunnels connecting to other continents posting-account=qfTKWQoAAADrbu8lwB1KpYv95yNmrUOu Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) know your Lord or you are doomed... Prepare your Silver Dirham or walk the ol' Barbary Pirate Plank... http://static.panoramio.com/photos/original/5556263.jpg On Jul 5, 3:19am, Six of Nine or Half-dozen of the Oher > Human have been abandoned to their fate because of the human tendency > to select leaders like Hitler. though you may be off track as to the city, in the vernacular of the time > it's called woonhell. wonder what I'm doing in this thread anyway. just > because I haven't done any proper research on this doesn't mean people have > the right to either embrace or discard it as fiction. these tunnels exist. > trust me. and the secret army of european resurrection is currently > deploying through them. Believe me that this tunnels are much older than many may think... > they exist since Atlantis long before the Maya's... even Hitler was > seeking to proof their existence, so no they ain't science fiction... > but hidden science. === Subject: Re: mayans built underground tunnels connecting to other continents AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) We are our own god. > know your Lord or you are doomed... Prepare your Silver Dirham or walk the ol' Barbary Pirate Plank... http://static.panoramio.com/photos/original/5556263.jpg On Jul 5, 3:19am, Six of Nine or Half-dozen of the Oher Human have been abandoned to their fate because of the human tendency > to select leaders like Hitler. though you may be off track as to the city, in the vernacular of the time > it's called woonhell. wonder what I'm doing in this thread anyway. just > because I haven't done any proper research on this doesn't mean people have > the right to either embrace or discard it as fiction. these tunnels exist. > trust me. and the secret army of european resurrection is currently > deploying through them. Believe me that this tunnels are much older than many may think... > they exist since Atlantis long before the Maya's... even Hitler was > seeking to proof their existence, so no they ain't science fiction... > but hidden science. === Subject: Re: mayans built underground tunnels connecting to other continents posting-account=qfTKWQoAAADrbu8lwB1KpYv95yNmrUOu Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) There is no power and no will but from Gran'Da'Dy the Almighty. http://www.youtube.com/watch?v=caFiSBl-zUs&feature=related On Jul 5, 9:05am, Six of Nine or Half-dozen of the Oher > We are our own god. > know your Lord or you are doomed... Prepare your Silver Dirham or walk the ol' Barbary Pirate Plank... http://static.panoramio.com/photos/original/5556263.jpg On Jul 5, 3:19am, Six of Nine or Half-dozen of the Oher Human have been abandoned to their fate because of the human tendency > to select leaders like Hitler. though you may be off track as to the city, in the vernacular of the time > it's called woonhell. wonder what I'm doing in this thread anyway. just > because I haven't done any proper research on this doesn't mean people have > the right to either embrace or discard it as fiction. these tunnels exist. > trust me. and the secret army of european resurrection is currently > deploying through them. Believe me that this tunnels are much older than many may think... > they exist since Atlantis long before the Maya's... even Hitler was > seeking to proof their existence, so no they ain't science fiction... > but hidden science. === Subject: Re: Parallel Lines Philippe 92 laid this down on his screen : > [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > > > This doesn't allow to proove anything at all. > ... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > > [...] If EF and CD are same line > > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > > > What I am trying to say is theoretically they are parallel. If they are > even a billionth of an inch apart, then they are unparallel. If I can > measure a billionth of an inch with some instrument, then I could use > the same instrument to see whether they are not a billionth of an inch > apart. > So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. Theoretically parrallel is an abstraction that you definitely > _can't measure_ Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > But that way we cannot say anything perfect. When we draw a circle, if we could measure with that instrument, we would find there is a small difference where the point finally meets at the starting point. === Subject: Re: Parallel Lines > Philippe 92 laid this down on his screen : [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ?... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > What I am trying to say is theoretically they are parallel. If they are > even a billionth of an inch apart, then they are unparallel. If I can > measure a billionth of an inch with some instrument, then I could use > the same instrument to see whether they are not a billionth of an inch > apart. So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. Theoretically parrallel is an abstraction that you definitely > ? ? can't measure Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > But that way we cannot say anything perfect. Only when you draw it, or try to measure drawn objects. > When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. Let me give you an example of where things ARE perfect. I have an equation: g = (Xa - Z)/Y Where 'a' is a variable and X,Y & Z are constants. Although I don't know what the values of X,Y & Z are, I DO know that X is a power of 2 and Y is a power of 3. That equation is that of a straight line whose slope is X/Y and intercept is -Z/Y. therefore MUST intersect the identity line f(a) = a whose slope is exactly 1. And this intersection will be the rational number Z/(X-Y). And this is true even though I don't actually know what X,Y & Z are. If I ever do find that out, I simply plug in those values and I know exactly the point where the two lines intersect. Absolute perfection. No pencils were harmed in this production. === Subject: Re: Parallel Lines > Philippe 92 laid this down on his screen : > > > > > > [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ?... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line > > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > > What I am trying to say is theoretically they are parallel. If they are > even a billionth of an inch apart, then they are unparallel. If I can > measure a billionth of an inch with some instrument, then I could use > the same instrument to see whether they are not a billionth of an inch > apart. > > So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. > Theoretically parrallel is an abstraction that you definitely > ? ? _can't measure_ > > Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. > Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > > But that way we cannot say anything perfect. Only when you draw it, or try to measure drawn objects. > When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. Let me give you an example of where things ARE perfect. I have an equation: g = (Xa - Z)/Y Where 'a' is a variable and X,Y & Z are constants. Although I don't know what the values of X,Y & Z are, > I DO know that X is a power of 2 and Y is a power of 3. That equation is that of a straight line whose slope > is X/Y and intercept is -Z/Y. therefore MUST intersect the identity line f(a) = a > whose slope is exactly 1. And this intersection will be the rational number Z/(X-Y). > And this is true even though I don't actually know > what X,Y & Z are. If I ever do find that out, I simply > plug in those values and I know exactly the point > where the two lines intersect. Absolute perfection. No pencils were harmed in this production. Ok, let me frame my explanation in a little different way. Let's consider 3 different points on the straight line CD - as I earlier mentioned - namely, X, Y and Z. Now, if the new perpendicular EF from the point E on CD intersects at those 3 points X,Y,Z, - then EF and CD have to be the same line. Since in a 2-dimensional plane, if a straight line intersects another sraight line at more than one different point, then both the straight lines are same. === Subject: Re: Parallel Lines > Philippe 92 laid this down on his screen : [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > What I am trying to say is theoretically they are parallel. If they are > even a billionth of an inch apart, then they are unparallel. If I can > measure a billionth of an inch with some instrument, then I could use > the same instrument to see whether they are not a billionth of an inch > apart. So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. > Theoretically parrallel is an abstraction that you definitely > can't measure Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. > Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > But that way we cannot say anything perfect. Only when you draw it, or try to measure drawn objects. > When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. Let me give you an example of where things ARE perfect. I have an equation: ?g = (Xa - Z)/Y Where 'a' is a variable and X,Y & Z are constants. Although I don't know what the values of X,Y & Z are, > I DO know that X is a power of 2 and Y is a power of 3. That equation is that of a straight line whose slope > is X/Y and intercept is -Z/Y. therefore MUST intersect the identity line f(a) = a > whose slope is exactly 1. And this intersection will be the rational number Z/(X-Y). > And this is true even though I don't actually know > what X,Y & Z are. If I ever do find that out, I simply > plug in those values and I know exactly the point > where the two lines intersect. Absolute perfection. No pencils were harmed in this production. Ok, let me frame my explanation in a little different way. Let's > consider 3 different points on the straight line CD - as I earlier > mentioned - namely, X, Y and Z. Now, > if the new perpendicular EF from > the point E on CD intersects at those 3 points X,Y,Z, False premise. A perpendicular of a line can only intersect at a single point. > - then EF and CD have to be the same line. A perpendicular to CD is CD? Better re-think that. > Since in a 2-dimensional plane, if a straight > line intersects another sraight line at more than one different point, > then both the straight lines are same. But not perpendicular. === Subject: Re: Parallel Lines Mensanator formulated on Saturday : > > > > > > Philippe 92 laid this down on his screen : > [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > > What I am trying to say is theoretically they are parallel. If they are > even a billionth of an inch apart, then they are unparallel. If I can > measure a billionth of an inch with some instrument, then I could use > the same instrument to see whether they are not a billionth of an inch > apart. > > So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. > Theoretically parrallel is an abstraction that you definitely > _can't measure_ > > Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. > Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > > But that way we cannot say anything perfect. > Only when you draw it, or try to measure drawn objects. > When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. > Let me give you an example of where things ARE perfect. > I have an equation: > > ?g = (Xa - Z)/Y > > Where 'a' is a variable and X,Y & Z are constants. > Although I don't know what the values of X,Y & Z are, > I DO know that X is a power of 2 and Y is a power of 3. > That equation is that of a straight line whose slope > is X/Y and intercept is -Z/Y. > > therefore MUST intersect the identity line f(a) = a > whose slope is exactly 1. > > And this intersection will be the rational number Z/(X-Y). > And this is true even though I don't actually know > what X,Y & Z are. If I ever do find that out, I simply > plug in those values and I know exactly the point > where the two lines intersect. > > Absolute perfection. > > No pencils were harmed in this production. > > Ok, let me frame my explanation in a little different way. Let's > consider 3 different points on the straight line CD - as I earlier > mentioned - namely, X, Y and Z. Now, > if the new perpendicular EF from > the point E on CD intersects at those 3 points X,Y,Z, False premise. A perpendicular of a line can only > intersect at a single point. > - then EF and CD have to be the same line. A perpendicular to CD is CD? Better re-think that. > Since in a 2-dimensional plane, if a straight > line intersects another sraight line at more than one different point, > then both the straight lines are same. But not perpendicular. You forgot my earlier post. :-) My earlier post says - ... let's say there are 2 segments of straight lines AB and CD. I draw a perpendicular from point B onto CD which intersects at, say, E. Now, from E on CD I draw another perpendicular EF. If EF and CD are same line then AB and CD are parallel. I didn't say, at that time, what I meant by same. In my last post I tried to do that. === Subject: Re: Parallel Lines posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.5006; Windows NT 5.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-mtc-td10.proxy.aol.com[400C706A] (Prism/1.2.1), HTTP/1.1 cache-mtc-ad07.proxy.aol.com[400C74C9] (Traffic-Server/6.1.5 [uScM]) > Mensanator formulated on Saturday : > Philippe 92 laid this down on his screen : > [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > What I am trying to say is theoretically they are parallel. If they are > even a billionth of an inch apart, then they are unparallel. If I can > measure a billionth of an inch with some instrument, then I could use > the same instrument to see whether they are not a billionth of an inch > apart. > So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. > Theoretically parrallel is an abstraction that you definitely > can't measure > Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. > Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > But that way we cannot say anything perfect. > Only when you draw it, or try to measure drawn objects. > When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. > Let me give you an example of where things ARE perfect. > I have an equation: g = (Xa - Z)/Y Where 'a' is a variable and X,Y & Z are constants. > Although I don't know what the values of X,Y & Z are, > I DO know that X is a power of 2 and Y is a power of 3. > That equation is that of a straight line whose slope > is X/Y and intercept is -Z/Y. therefore MUST intersect the identity line f(a) = a > whose slope is exactly 1. And this intersection will be the rational number Z/(X-Y). > And this is true even though I don't actually know > what X,Y & Z are. If I ever do find that out, I simply > plug in those values and I know exactly the point > where the two lines intersect. Absolute perfection. No pencils were harmed in this production. > Ok, let me frame my explanation in a little different way. Let's > consider 3 different points on the straight line CD - as I earlier > mentioned - namely, X, Y and Z. Now, > if the new perpendicular EF from > the point E on CD intersects at those 3 points X,Y,Z, False premise. A perpendicular of a line can only > intersect at a single point. > - then EF and CD have to be the same line. A perpendicular to CD is CD? Better re-think that. > Since in a 2-dimensional plane, if a straight > line intersects another sraight line at more than one different point, > then both the straight lines are same. But not perpendicular. You forgot my earlier post. :-) My earlier post says - ... let's say there are 2 segments of straight > lines AB and CD. I draw a perpendicular from point B onto CD which > intersects at, say, E. Now, from E on CD I draw another perpendicular > EF. If EF and CD are same line then AB and CD are parallel. I didn't say, at that time, what I meant by same. In my last post I > tried to do that. Ok, forget all that then. Now, if the lines in question are mathematically accurate, they have 0 thickness and are thus, invisible. How can you construct a perpendicular to something that's invisible? The fact that you can see the lines implies they are not mathematically accurate, thus, youe proof fails before you even pick up your compass. === Subject: Re: Parallel Lines > Mensanator formulated on Saturday : > > > > > > > Philippe 92 laid this down on his screen : > [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > > What I am trying to say is theoretically they are parallel. If they > are even a billionth of an inch apart, then they are unparallel. If I > can measure a billionth of an inch with some instrument, then I could > use the same instrument to see whether they are not a billionth of an > inch apart. > > So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. > Theoretically parrallel is an abstraction that you definitely > _can't measure_ > > Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. > Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > > But that way we cannot say anything perfect. Only when you draw it, or > try to measure drawn objects. When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. > Let me give you an example of where things ARE perfect. > I have an equation: > > g = (Xa - Z)/Y > > Where 'a' is a variable and X,Y & Z are constants. > Although I don't know what the values of X,Y & Z are, > I DO know that X is a power of 2 and Y is a power of 3. > That equation is that of a straight line whose slope > is X/Y and intercept is -Z/Y. > > therefore MUST intersect the identity line f(a) = a > whose slope is exactly 1. > > And this intersection will be the rational number Z/(X-Y). > And this is true even though I don't actually know > what X,Y & Z are. If I ever do find that out, I simply > plug in those values and I know exactly the point > where the two lines intersect. > > Absolute perfection. > > No pencils were harmed in this production. > Ok, let me frame my explanation in a little different way. Let's > consider 3 different points on the straight line CD - as I earlier > mentioned - namely, X, Y and Z. Now, > if the new perpendicular EF from > the point E on CD intersects at those 3 points X,Y,Z, > False premise. A perpendicular of a line can only > intersect at a single point. > > - then EF and CD have to be the same line. > A perpendicular to CD is CD? Better re-think that. > Since in a 2-dimensional plane, if a straight > line intersects another sraight line at more than one different point, > then both the straight lines are same. > But not perpendicular. > > You forgot my earlier post. :-) > > My earlier post says - ... let's say there are 2 segments of straight > lines AB and CD. I draw a perpendicular from point B onto CD which > intersects at, say, E. Now, from E on CD I draw another perpendicular > EF. If EF and CD are same line then AB and CD are parallel. > > I didn't say, at that time, what I meant by same. In my last post I > tried to do that. Ok, forget all that then. Now, if the lines in question are mathematically > accurate, they have 0 thickness and are thus, > invisible. How can you construct a perpendicular > to something that's invisible? The fact that you can see the lines implies they > are not mathematically accurate, thus, youe proof > fails before you even pick up your compass. Why should they have 0 thickness? all the lines are drawn with same pencil and instruments. They should be having equal thickness, whatever that may be. === Subject: Re: Parallel Lines posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.5006; Windows NT 5.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-mtc-tb03.proxy.aol.com[400C7023] (Prism/1.2.1), HTTP/1.1 cache-mtc-ad07.proxy.aol.com[400C74C9] (Traffic-Server/6.1.5 [uScM]) > Mensanator formulated on Saturday : > Philippe 92 laid this down on his screen : > [ summarized all that horrible Google like quoting ] > How do I prove 2 straight lines are parallel to each other? > This doesn't allow to proove anything at all. > ... > [measuring] something on your physical sheet of > physical paper, [] deduce Parallel at x% accuracy. > [...] If EF and CD are same line > How do you know they're the same line? What if they're > a billionth of an inch apart or have a 1 part per billion > different slope? > What I am trying to say is theoretically they are parallel. If they > are even a billionth of an inch apart, then they are unparallel. If I > can measure a billionth of an inch with some instrument, then I could > use the same instrument to see whether they are not a billionth of an > inch apart. > So the only thing you can say is they are parallel at a 1b. of an > inch accuracy > You can't then know if they are really parallel or not. > Theoretically parrallel is an abstraction that you definitely > can't measure > Theoretically means that you can proove it by pure logical deduction > from other previously known properties of your lines. > Not by measuring anything, even with an unusual very accurate > instrument able to measure less than diameter of quarks, or angle of > less than a quark seen from the border of universe. > But that way we cannot say anything perfect. Only when you draw it, or > try to measure drawn objects. When we draw a circle, if > we could measure with that instrument, we would find there is a small > difference where the point finally meets at the starting point. > Let me give you an example of where things ARE perfect. > I have an equation: > g = (Xa - Z)/Y > Where 'a' is a variable and X,Y & Z are constants. > Although I don't know what the values of X,Y & Z are, > I DO know that X is a power of 2 and Y is a power of 3. > That equation is that of a straight line whose slope > is X/Y and intercept is -Z/Y. > therefore MUST intersect the identity line f(a) = a > whose slope is exactly 1. > And this intersection will be the rational number Z/(X-Y). > And this is true even though I don't actually know > what X,Y & Z are. If I ever do find that out, I simply > plug in those values and I know exactly the point > where the two lines intersect. > Absolute perfection. > No pencils were harmed in this production. > Ok, let me frame my explanation in a little different way. Let's > consider 3 different points on the straight line CD - as I earlier > mentioned - namely, X, Y and Z. Now, > if the new perpendicular EF from > the point E on CD intersects at those 3 points X,Y,Z, > False premise. A perpendicular of a line can only > intersect at a single point. > - then EF and CD have to be the same line. > A perpendicular to CD is CD? Better re-think that. > Since in a 2-dimensional plane, if a straight > line intersects another sraight line at more than one different point, > then both the straight lines are same. > But not perpendicular. > You forgot my earlier post. :-) > My earlier post says - ... let's say there are 2 segments of straight > lines AB and CD. I draw a perpendicular from point B onto CD which > intersects at, say, E. Now, from E on CD I draw another perpendicular > EF. If EF and CD are same line then AB and CD are parallel. > I didn't say, at that time, what I meant by same. In my last post I > tried to do that. Ok, forget all that then. Now, if the lines in question are mathematically > accurate, they have 0 thickness and are thus, > invisible. How can you construct a perpendicular > to something that's invisible? The fact that you can see the lines implies they > are not mathematically accurate, thus, youe proof > fails before you even pick up your compass. Why should they have 0 thickness? Because they're defined that way: http://en.wikipedia.org/wiki/Line (geometry) Lines are an idealisation of such objects and have no width or height at all and are usually considered to be infinitely long. http://mathworld.wolfram.com/Line.html A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. > all the lines are drawn with same > pencil and instruments. They should be having equal thickness, whatever > that may be. And, therefore, are not lines in the mathematical sense. Such drawings are abstractions used to represent lines. They are useful up to a point. What you're trying to do is beyond that point. You can do absolute proofs using the algebra of lines (if you know it) as I showed in my example. But with geometry, you are restricted to the limitation of your representations === Subject: Path2Math Website posting-account=95GawAoAAAC0pscdxdnK8PKqqiYcP4C7 rv:1.9.0.11) Gecko/2009060214 Firefox/3.0.11,gzip(gfe),gzip(gfe) This website has lots of information and help for math. Have a look here http://tinyurl.com/lpm378. === Subject: Re: Do hyperspace points exist? > The fact that we cannot visualize points in spaces of dimension higher than > three has of course nothing whatsoever to do with their existence. > - Murray R. Spiegel, Vector Analysis Do 'points in spaces of dimension higher than three' have any practical > utility, or are they just a sort of metaphysical parascientific tangent of > math? Many theories seem more natural when described as operating in spaces of dimension greater than 3. For example, electric and magnetic fields can be treated as separate but related 3D fields (i.e. related by Maxwell's equations), but special relativity suggests we view them as a single field, using 4-vectors etc.. Perhaps you would consider this a practical utility? (I.e. is it a practical utility if something makes a theory easier to visualise/understand?) I don't know much about it. I read a book once that some mathematicians > concluded that the universe exists in 11 dimensions. They needed the added > dimension to describe the data. They found a solution when 11 dimensions > are used to describe the data. I think they called it 'string theory'. > They also mentioned worm holes as a mechanism for time travel to cheat the > speed of light threshold. Again, I don't know much about it. Do these > mathematicians know what they're talking about? Can they prove their ideas > in a laboratory? Well, at the moment they're just theories, as far as I know... I don't think there is any direct proof of the String theory in a laboratory. I suppose they think they're on the cutting edge right up there with > Einstein and relativity. You'd have to ask them that yourself! :-) (I suspect most scientists are much more humble than you're imagining.) Mike. === Subject: Re: Do hyperspace points exist? Well, at the moment they're just theories, as far as I know... I don't > think there is any direct proof of the String theory in a laboratory. AFAIK no feasible experimental test of string theory has even been proposed, let alone conducted; leaving aside the question of whether or not proof of anything is possible in the physical sciences, yet further off is one that would provide any evidence one way or another. -- Odysseus === Subject: Re: Do hyperspace points exist? Actually how hidden, TCP/IP itself from version 1 and up has had packet descriptions for tunnelling data chronologically as well as dimensions with these hyperspace points you speak of. They are navigated in instanciated floating points, and with the addition I made in TCP/IP 6 of automatically assigned IP (As a contributor suggestion) it is more organic. Do you know in hyperspace there can be billions of species just like us, here on what we call earth. Here is something I will puzzel you about life and exactly how much we don't see on a planet where life is supported. I will use the elephant and the mouse. When you put an elephant next to a mouse the elephant even in our dimensional view of this majestic creature is hideously scare of it. This is because dimensionally the mouse is it the elephants main preditor - that is on other layers of the primates variesty dimensionally the mouse which we see in mass as a cute fluffy thing with wiskers and a tail in other dimension hunts and kills millions of elephants in close proximity. It really make you scare of those adorable creatures we have, I am extremely scare at this point of my finches they are killers.. Mine don't mind me.. There is more information on my creative blog: http://zeslijczequaes.spaces.live.com > The fact that we cannot visualize points in spaces of dimension higher > than three has of course nothing whatsoever to do with their existence. > - Murray R. Spiegel, Vector Analysis Do 'points in spaces of dimension higher than three' have any practical > utility, or are they just a sort of metaphysical parascientific tangent of > math? I don't know much about it. I read a book once that some mathematicians > concluded that the universe exists in 11 dimensions. They needed the > added dimension to describe the data. They found a solution when 11 > dimensions are used to describe the data. I think they called it 'string > theory'. They also mentioned worm holes as a mechanism for time travel to > cheat the speed of light threshold. Again, I don't know much about it. > Do these mathematicians know what they're talking about? Can they prove > their ideas in a laboratory? I suppose they think they're on the cutting edge right up there with > Einstein and relativity. > __________ Information from ESET Smart Security, version of virus > signature database 4215 (20090704) __________ The message was checked by ESET Smart Security. http://www.eset.com > __________ Information from ESET Smart Security, version of virus signature database 4215 (20090704) __________ The message was checked by ESET Smart Security. http://www.eset.com === Subject: Radon-Nikodym derivative posting-account=qeiFoAoAAABdk5xbVoXkxvYvq-niifs1 Gecko/20090701 Ubuntu/9.04 (jaunty) Shiretoko/3.5.1pre,gzip(gfe),gzip(gfe) Hi all. I was wondering... take a Radon-Nikodym derivative $f = d mu / d nu $. Is there any condition describing when $f$ is monotone increasing? M. === Subject: Comprehensive Test Banks and solution manuals for $35 each posting-account=jy2E5goAAAB1WGwMQL1h2k61o4k7O_u4 Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Comprehensive Test Banks and solution manuals for $35 each Email me at instructors.team[at]gmail.com if you need to buy any test bank or solution manual listed below. All emails will be answered quickly. 2009 Federal Taxation - Pratt [CapitalEth] Solutions Manual & test Bank Accounting for Non-Accounting Students test bank Accounting Information Systems (6thEd) - Hall - Solutions Manual Aerodynamics for Engineers, 5E Solution manual Bertin Russ Cummings Algebra and Trigonometry 3rd Ed, and Precalculus 3rd Ed, Instructor's Solutions Manual 2008 - Beecher, Penna, & Bittinger Analysis- With an Introduction to Proof, 4-E-Instructors SM Art Through The Ages A Global Hist Vol II Test Bank complete Auditing A Business Risk Approach (6thEd) - Rittenberg [CapitalEth] Solutions Manual Auditing A Business Risk Approach (6thEd) - Rittenberg Test Bank Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Solution Manual Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Test bank Auditing Cases Interactive Learning Approach (4thEd) - Beasley - Solutions Manual Beer, Johnston & Dewolf - Mechanics Of Materials Solution Manual 3Rd Ed Biology with Mastering Biology 8E Campbell Reece ISBN -0321494334 Test Bank Bond Markets, Analysis and Strategies 6E Instructors manual Fabozzi Brock Biology of Microorganisms 12E ISBN -0132324997 Test Bank Busines statistics Decision making 7E David F Groebner Solution manual Busines statistics Decision making 7E David F Groebner test bank Business Law and the Legal Environment Jeffrey F. Beatty 5th edition Test Bank Business Law Tax And Cases (11thEd) - Clarkson [CapitalEth] TestBank Business Statistics First Course Solutions Manual Levine Calculus A Complete Course Adams - - Instructors Solution Manual College Algebra 10E Margaret L. Lial solution manual College Algebra 10E Margaret L. Lial Test bank Concepts Of Programming Languages (8thEd) - Sebesta [CapitalEth] Solutions Manual Contemporary Financial Management (11thEd) - Moyer - Solutions Manual Cornerstone Of Managerial Accounting (2ndEd) - Mowen - Solutions Manual Corporate Partnership Estate Gift Tax 2009 - Pratt - Solutions Manual Cost accounting by Hongren 13/e test bank and Solution manual Cost Accounting Canadian (4thEd) - Horngren - Test Bank Cutnell John, Physics 7th E, Instructors manual (all solutions even +odd) Data Structures Algorithm Analysis In CPP (3rdEd) - Weiss - Solutions Manual Deitel & Deitel How to Program C++ 6th E Code solutions Options, Futures and Other Derivatives John Hull 7E test bank ch 1-21 with answers Digital Electronics A Practical Approach - William Kleitz 8th ed ISM Econometric Analysis - Solutions Manual (Greene 6Th 2007) Effective Small Business Management - Norman M Scarborough 9E Test bank Electrical Machines, Drives and Power Systems - Solutions Manual Electronic Devices and Circuit Theory 9e Instructors resource manual ISBN 0132214466 Elementary Differential Equations Boundary Value (2ndEd) - Kohler - Solutions Manual Elementary Linear Algebra (6thEd) - Larson, Falvo - Solutions Manual E-Marketing 5E Strauss Frost ISBN 0136154417 Test Bank Entrepreneurial Finance (3rdEd) - Leach - Instructors Solutions Manual Exploring Microsoft Office Excel 2007, Comprehensive, 2E Test bank Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial And Managerial Acct (10thEd) - Warren - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham test bank Friendly Introduction To Analysis (2ndEd) - Kosmala - Solutions Manual Friendly Introduction to Numerical Analysis Brian Bradie Fundamentals of Communication Systems Proakis & Salehi Fundamentals of Differential Equations 7thE Nagle Snider Instructors resource manual ISBN -0321388445 Fundamentals of Engineering Electromagnetics By David K. Cheng Solutions Manual Fundamentals of Multinational Finance 3e Muffet, Stonehill Test bank Gas Dynamics John & Keith Instructors Solution Manual General, Organic, and Biological Chemistry Structures of Life, 3E Test bank Gregory - Classical Mechanics - SOLUTIONS MANUAL (Cambridge, 2006) Human Anatomy & Physiology 7E TEST BANK ISBN 0805373810 Human Anatomy & Physiology 8E TEST BANK Hydraulics in Civil and Environmental Engineering Solutions by Chadwick & Morfett Solution's Manual InstructorÍs Manual Contemporary Engineering economics 4e Park Instructor's Edition LAN Switching and Wireless CCNA Exploration Labs and Study Guide Allan Johnson EBOOK International Economics Theory and Policy 8E Krugman Obstfeld International Management Managing Across Borders and Cultures 6E Deresky Test Bank International Management Managing Across Borders and Cultures 6E Deresky Instructors manual International Marketing and Export Management 6E Albaum Introduction To Business Statistics (6thEd) - Weiers - Solutions Manual Introduction To Business Statistics (6thEd) - Weiers - Test Bank Introduction to Econometrics 2E Stock Watson Solution manual Introduction to Linear Algebra -3rd Edition - Gilbert Strang Instructors Solutions Manual Introduction To Management Accounting (14thEd) - Horngren - Solutions Manual Introduction to Management Science - Taylor 9E Solution Manual Introduction to Parallel Computing Kumar solution manual Behavior in Organizations Greenberg 9th Edition test bank Introduction to the Design and Analysis of Algorithms 2E Levitin ISBN 0321428102 Introductory Circuit Analysis 11e Boylestad Solution manual Introductory Circuit Analysis 11E Lab solutions manual Introductory Econometrics (4thEd) - Woolridge - Solutions Manual Investment Analysis & Portfolio Management, 7e by Reilly and Brown Solutions Manual Java Foundations- Introduction to Program Design and Data Structures- ES zip Java Foundations- Introduction to Program Design and Data Structures- project solutions Linear Algebra (Jim Hefferon) (2006) Solutions Manual Linear Algebra For Engineers And Scientist (1stEd) - Hardy [CapitalEth] Solutions Manual Management Accounting Anthony A Atkinson (5th Ed) ISM and TB Management Information Systems 11E Laudon 0136078907 test bank Management Information Systems Managing the Digital Firm 10th Edition by Laudon Managerial Accounting Information for Decisions 4th ed Albrite Marketing Real people Real Choices 6 e Test Bank ISBN 0136054234 Mathematical Proofs A Transition to Advanced Mathematics (2ndEd) - Chartrand - Solutions Manual Mathematical Thinking problem solving Angelo & West Instructors manual ISBN -0130144126 Microbiology with Diseases by Body System Robert W Bauman 2nd ed Instructors manual MIS Cases Decision Making wih Application Software, 4E Instructors manual and solution files Money Banking and Financial Markets Roger LeRoy Miller (3rd ed) Test bank Object Oriented Programming in C++ 4E suplement robert Lafore Operations Management 9E Jay Heizer ISBN 0131585576 Operations Management 9E Jay Heizer ISBN 0132342979 test bank Organic Chemistry 6E Wade Test Bank Parallel Programming (2ndEd) - Wilkinson [CapitalEth] Solutions Manual Partial Differential Equations And Boundary Value Problems (2nd Ed) - Asmar - Solutions Manual Physics Principles with Applications with Mastering Physics Giancoli 6E ISM Physics with Mastering Physics 3E James walker Prebles' Artforms 9E patrick Frank TESTGEN file ISBN 0136044166 Prebles' Artforms Test Bank Precalculus (4thEd) - Blitzer - Solutions Manual Prentice Hall Federal Taxation 2009 Comprehensive - Pope - Solutions Manual Prentice HallÍs Federal Taxation 22/e 2009 Corporations test bank and solution manual Prince Medical Imaging Signals and Systems Instructors manual Principles Of Foundation Engineering (6thEd) - Das - Solution Manual Principles Of Managerial Finance Brief (5thEd) - Gitman [CapitalEth] Solutions Manual Principles of Marketing 5th European edition by Kotler Instructors solution manual Principles Of Operations Management (6thEd) - Heizer [CapitalEth] Test Bank Problem Solving With CPP (7thEd) - Savitch [CapitalEth] Solutions Manual Reinforced Concrete Design - George F. Limbrunner 7th ed ISBN [CapitalEth] 0135044359 Roads to Geometry, 3/E Solutions manual Edward C. Wallace Sandler S. I. - Chemical and Engineering Thermodynamics - Solution manual Source Code Files for Programming Concepts in MATLAB 2E David M Smith Statics And Strengths Of Materials (6thEd) - Morrow - Solutions Manual Statistics 11E James T. McClave Solution manual Stats Data And Models (2ndEd) - Veaux [CapitalEth] Solutions Manual Strategic Compensation Joe Martocchio 5th ed Test Bank Strategic Management and Competitive Advantage Concepts and Cases 2E barney hesterly ISBN 0136036112 Pearson TESTGEN file Strategic Management Concepts and Cases 12E Fred David ISBN 0138132178 test bank Strategic Management TestBank Hitt 8th edition Test Bank Martini EAP 5E TestBank International economics 12th edition Carbaugh TestBank Macroeconomics Principles and Policy Baumol 10th Undergraduate Econometrics Solutions Manual - Hill, Judge and Griffiths Understanding and Managing Organizational Behavior 5E Test bank University Chemistry with Student Access Kit siska 1e test bank Wang, L. & Zhou, X. & Wei, X. - Heat conduction. Mathematical models and analytical solutions (Springer, 2008) === Subject: Transposing ETAtAhUApoeuYAhDFPnlc7Y+wrwDjlCJMcACFHXzd9B1agg++CsiReivdiAvimGV Can someone recommend a book that details algebraic terms transposing of longer equations? === Subject: JSH: Psychology of the denial of core error posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) Turns out that if you follow rigorous mathematics it is trivial to show a problem with the use of the ring of algebraic integers with a quadratic factorization that I've often given before: 7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. The primary problem here is that if you let the ring be the ring of algebraic integers, you get something never before seen in human mathematics which is a constraint on a constant factor revealed on the right hand side of 7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) which is obviously not there on the left hand side. To understand what I mean--I'm sure some posters would reply that they find it incomprehensible--consider a simpler example in the ring of integers: 7(x^2 + 3x + 2) = (7x + 7)(x + 2) where the 7 is still unconstrained, and you can in fact move it around at will, so 7(x^2 + 3x + 2) = (7x + 7)( x + 2). Now the mathematically astute of you may notice that the first example IS fixable so that you have equivalence on both sides of the equals and the 7 is unconstrained if you use normalized functions: 7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5b_2(x)+ 2) where 7b_1(x) = a_1(x) and b_2(x) = a_2(x) + 1 and the a's are still roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and the b's are normalized because they both equal 0 when x=0. NOW notice that algebra still works and the 7 is unconstrained again and you can move it around, like before: 7(175x^2 - 15x + 2) = (5b_1(x) + 1)(5(7)b_2(x)+ 14) or even divide it off completely: (175x^2 - 15x + 2) = (5b_1(x) + 1)(5b_2(x)+ 2) But now the ring of algebraic integers itself becomes the problem as unlike any other known ring in mathematics it will not allow you to do the above!!! The b's are not in general in that ring! That is because 7b_1(x) = a_1(x) means that a_1(x) has 7 as a factor which requires that one of the roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 have 7 as a factor, and you can get a contradiction with x=1, which gives a^2 - 6a + 35 = 0 as provably in the ring of algebraic integers NEITHER of the roots of that quadratic can have 7 as a factor. That's the easy algebra and it reveals that the ring of algebraic integers is mathematically distinct from ALL other known rings, including fields of course, as the problem does not emerge in anything else! The ring of algebraic integers actually blocks algebra itself, by not allowing certain algebraic operations to occur, and that is only revealed by this remarkable construct: 7(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. What happens there is that you get the unconstrained 7 on the left-- math students are normally taught to divide such factors off--which cannot in general be divided off from the right hand side ONLY in the ring of algebraic integers, which I call entanglement. The 7 is somehow trapped in place, entangled, on the right hand side! I've proven that this problem leads to the *appearance* of contradiction and allows a math practitioner to appear to prove things that are not true, or are not actually proven. With errors in mathematics you can get this odd ability to appear to prove just about anything. Ok, the math is easy. I've simplified explaining over the years and explained over and over and over again in many different ways and even had a paper published in this area with slightly more complicated cubics before I simplified to quadratics. Now that story is interesting as it reveals an amazing psychology here: publication supposedly means something in the mathematical community but when I got published sci.math'er said it meant nothing, some of them conspired on the newsgroup to attack the paper by emails and did so, panicked the editors who pulled my paper and the journal died after managing one more edition! Now rational people knowing the math, knowing the error allows people to do fake math, would get very suspicious with that story, but this particular error appears to run so deep that the bulk of the mathematical community might rather hide it than deal with it. That's because the ring of algebraic integers was introduced over one hundred years ago. The sheer volume of erroneous publications revolving around the error can defy imagination and may represent the BULK of number theory work over the last century plus encompassing the ENTIRE 20th century!!! One dead math journal under remarkable circumstance is minor with such a situation. Notice here also that practitioners in number theory with decades in the field and lots of awards or prizes have the most to lose from the revelation of the error. Graduate students as well can have serious investment in the error as imagine being one who considers his graduate thesis and realizes it's junk!!! So for years I've included math undergrads who are really in an awkward position here, as the people they rely on the most may be the most compromised but unlike professors and grads they don't have as many years or as many successes invested in wrong mathematics! And remember, for someone who believed they were brilliant or had great accomplishments this error really can cut deep emotionally as well as in many other ways. It's like it can rip their entire world apart. I have been careful in trying to figure out the best way to hopefully get some resolution here as I understand just how high emotions can run, and some of the replies I get can give readers some perspective, but make no mistake, the fight is to keep doing wrong math, and to teach it to others. So from one perspective, the professors who didn't have a chance and the grad students who didn't have a chance are victims, yes, but they are also abusers when they are teaching to new students who DO have a chance to not be taught this error, and to do number theory and start advancing it again after, oh, about a hundred years of stagnation. James Harris === Subject: Re: JSH: Psychology of the denial of core error > Turns out that if you follow rigorous mathematics it is trivial to > show a problem with the use of the ring of algebraic integers with a > quadratic factorization that I've often given before: > Trivial though it may be, it's now been a couple of years and you still have not said what the problem is. You have never said, This shows that the algebraic integers have property X, where X is impossible, or some such. You've never done it. Can you state clearly what the problem is? === Subject: Re: JSH: Psychology of the denial of core error posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt MathPlayer 2.10d; .NET CLR 1.1.4322; PeoplePal 3.0),gzip(gfe),gzip(gfe) James, I realize that this is an exercise in futility, but I am going to try to demonstrate to you why the mathematical community does not take anything you say seriously. Many of us do, however, find you marvelously entertaining. As I remarked several times already, you write very well, and you spin an absorbing, if silly, science fiction conspiracy involving mathematicians and, in particular, number theorists. Never before have we been considered so powerful. We certainly don't feel that way. I will intersperse my specific comments withing your text, where appropriate, to try to show you how mathematicians view the mathematics of what you do. I and others have done this before to little effect, but I happen to be in the mood. Beethoven's fifth is playing in my speakers, so I guess I just feel empowered or something. > Turns out that if you follow rigorous mathematics it is trivial to > show a problem with the use of the ring of algebraic integers with a > quadratic factorization that I've often given before: 7(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. This appears to be a monic polynomial of degree 2 with coefficients in Z[x]. As such, its roots would be in some sort of integral extension (this is a technical term you may look up) of Z[x] living within a field that is an extension of degree 2 over Z(x). It is not an algebraic integer. I am unfamiliar with the factorization properties of this particular extension of Z[x], but I have no reason to suppose that it is a unique factorization domain, nor do I have any idea what the structure of its unit group might be. These are interesting questions, but I don't have the time and energy right no, if ever, to try and figure this out. > The primary problem here is that if you let the ring be the ring of > algebraic integers, you get something never before seen in human > mathematics which is a constraint on a constant factor revealed on the > right hand side of 7(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) which is obviously not there on the left hand side. I simply don't know what you mean by this. As previously mentioned, a 1 and a 2 are NOT algebraic integers. If you do out the solution of the quadratic equation you presented, getting a bunch of square roots of polynomial expressions involving x, you will probably, with perhaps some effort, be able to see that the two sides are obviously equal, assuming you have done the calculation correctly. My real point is that, since you are not dealing in the ring of algebraic integers when you use this expression, you can't pull out anything very direct that you can say about the algebraic integers. The fact that you are getting confused here and have done so now for a very long time does not increase the respect you get from the mathematical community. > To understand what I mean--I'm sure some posters would reply that they > find it incomprehensible--consider a simpler example in the ring of > integers: 7(x^2 + 3x + 2) = (7x + 7)(x + 2) where the 7 is still unconstrained, and you can in fact move it around > at will, so > I have no idea what an unconstrained 7 might be. I don't even know what a constrained 7 might be. I thought it was just a number. What are you talking about? > 7(x^2 + 3x + 2) = (7x + 7)( x + 2). Now the mathematically astute of you may notice that the first example > IS fixable so that you have equivalence on both sides of the equals > and the 7 is unconstrained if you use normalized functions: 7(175x^2 - 15x + 2) = (5(7)b 1(x) + 7)(5b 2(x)+ 2) where 7b 1(x) = a 1(x) and b 2(x) = a 2(x) + 1 and the a's are still roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and the b's are normalized because they both equal 0 when x=0. Now, apparently, the b's are functions of x, since they take values when x = 0. I have never heard of an algebraic integer taking a value when x = 0. So what is going on here? > NOW notice that algebra still works and the 7 is unconstrained again > and you can move it around, like before: 7(175x^2 - 15x + 2) = (5b 1(x) + 1)(5(7)b 2(x)+ 14) or even divide it off completely: (175x^2 - 15x + 2) = (5b 1(x) + 1)(5b 2(x)+ 2) But now the ring of algebraic integers itself becomes the problem as > unlike any other known ring in mathematics it will not allow you to do > the above!!! The b's are not in general in that ring! Not only are they not in general in that ring, but, since you have defined them in terms of the a's which are in some integral extension of a polynomial ring, and so also not in the algebraic integers, this does not require 2 exlamation points. It does not even require a single exclamation point. It is commpletely obvious. What, perhaps, requires an exclamation point is that you seem to think that they should be. > That is because 7b 1(x) = a 1(x) means that a 1(x) has 7 as a factor which requires that one of the > roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 have 7 as a factor, and you can get a contradiction with x=1, which > gives Again you are setting x to a value within an algebraic integer(!!). There are other, less esoteric why the a's and b's are not algebraic integers. > a^2 - 6a + 35 = 0 as provably in the ring of algebraic integers NEITHER of the roots of > that quadratic can have 7 as a factor. Now this polynomial, where a simply represents a variable, does actually have roots that are algebraic integers. And the two roots are both divisible by the prime that lies over 7. If you studiend a little bit of algebraic number theory, a truly fascinating subject, you would know what I am talking about and why it is true. But it is totally unclear what point you are trying to make by saying this. > That's the easy algebra and it reveals that the ring of algebraic > integers is mathematically distinct from ALL other known rings, > including fields of course, as the problem does not emerge in anything > else! The ring of algebraic integers actually blocks algebra itself, by not > allowing certain algebraic operations to occur, and that is only > revealed by this remarkable construct: 7(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. What happens there is that you get the unconstrained 7 on the left-- > math students are normally taught to divide such factors off--which > cannot in general be divided off from the right hand side ONLY in the > ring of algebraic integers, which I call entanglement. The 7 is somehow trapped in place, entangled, on the right hand side! Fascinating. You have gathered together several nonsensical conceptions into one neat package here. You present 2 a's that are in a ring that most us never have studied, although many surely have, and which are surely not algebraic integers, and yet you seem to think that they should have the properties of algebraic integers. By the way, most rings do not have roots to all polynomials defined over them. The only rings with that property are algebraically closed fields. So, again, what are you on about? Then, somehow, you get this unconstrained 7, a term you don't define, which I have never heard of, and which sounds ridiculous, and tell us that it is trapped in place and actually entangled on the other side. Nice use of language, certainly, but meaningless nonsense mathemtically in this context. > I've proven that this problem leads to the *appearance* of > contradiction and allows a math practitioner to appear to prove things > that are not true, or are not actually proven. With errors in mathematics you can get this odd ability to appear to > prove just about anything. Ok, the math is easy. I've simplified explaining over the years and > explained over and over and over again in many different ways and even > had a paper published in this area with slightly more complicated > cubics before I simplified to quadratics. Now that story is interesting as it reveals an amazing psychology > here: publication supposedly means something in the mathematical > community but when I got published sci.math'er said it meant nothing, > some of them conspired on the newsgroup to attack the paper by emails > and did so, panicked the editors who pulled my paper and the journal > died after managing one more edition! Now rational people knowing the math, knowing the error allows people > to do fake math, would get very suspicious with that story, but this > particular error appears to run so deep that the bulk of the > mathematical community might rather hide it than deal with it. That's because the ring of algebraic integers was introduced over one > hundred years ago. The sheer volume of erroneous publications > revolving around the error can defy imagination and may represent the > BULK of number theory work over the last century plus encompassing the > ENTIRE 20th century!!! One dead math journal under remarkable circumstance is minor with such > a situation. Notice here also that practitioners in number theory with decades in > the field and lots of awards or prizes have the most to lose from the > revelation of the error. Graduate students as well can have serious investment in the error as > imagine being one who considers his graduate thesis and realizes it's > junk!!! So for years I've included math undergrads who are really in an > awkward position here, as the people they rely on the most may be the > most compromised but unlike professors and grads they don't have as > many years or as many successes invested in wrong mathematics! And remember, for someone who believed they were brilliant or had > great accomplishments this error really can cut deep emotionally as > well as in many other ways. It's like it can rip their entire world > apart. I have been careful in trying to figure out the best way to hopefully > get some resolution here as I understand just how high emotions can > run, and some of the replies I get can give readers some perspective, > but make no mistake, the fight is to keep doing wrong math, and to > teach it to others. So from one perspective, the professors who didn't have a chance and > the grad students who didn't have a chance are victims, yes, but they > are also abusers when they are teaching to new students who DO have a > chance to not be taught this error, and to do number theory and start > advancing it again after, oh, about a hundred years of stagnation. > No stagnation. Incredible advancement in so many ways that I could go on for quite some while. The best resolution here would be for you to realize how wrong you've been about all this and start to learn what algebraic number theory is really about. You wouldn't have the great joy of being the only human being who is onto a terrible conspiracy that must be stopped, who is being thwarted at every turn by an alliance of crazed, power-mad number theorists, but you would have the joy of learning a beautiful subject, one of many that could become accessible to you, and that joy would be a lot more grounded in reality. Achava > James Harris === Subject: Re: JSH: Psychology of the denial of core error posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) On Jul 4, 7:56pm, Achava Nakhash, the Loving Snake > James, I realize that this is an exercise in futility, but I am going to try > to demonstrate to you why the mathematical community does not take > anything you say seriously. Many of us do, however, find you I've read your reply and it fits more with the psychological aspects of this issue. Readers who are puzzled by his reply need to understand how devastating the core error is. He may actually believe he has cogent rebuttals, but he also may be faking in case later he believes he needs to say his mind snapped in his own defense. > marvelously entertaining. As I remarked several times already, you > write very well, and you spin an absorbing, if silly, science fiction > conspiracy involving mathematicians and, in particular, number > theorists. Never before have we been considered so powerful. We > certainly don't feel that way. I will intersperse my specific comments withing your text, where > appropriate, to try to show you how mathematicians view the > mathematics of what you do. I and others have done this before to > little effect, but I happen to be in the mood. Beethoven's fifth is > playing in my speakers, so I guess I just feel empowered or something. > Turns out that if you follow rigorous mathematics it is trivial to > show a problem with the use of the ring of algebraic integers with a > quadratic factorization that I've often given before: 7(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) where the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. This appears to be a monic polynomial of degree 2 with coefficients > in Z[x]. As such, its roots would be in some sort of integral > extension (this is a technical term you may look up) of Z[x] living > within a field that is an extension of degree 2 over Z(x). It is not > an algebraic integer. I am unfamiliar with the factorization That is false. Given an algebraic integer x the roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 are always algebraic integers. So readers keeping count have one obvious error from the poster to start. > properties of this particular extension of Z[x], but I have no reason > to suppose that it is a unique factorization domain, nor do I have any That is irrelevant. There is no reason to wonder or care if it is a unique factorization domain. Readers have a second error. > idea what the structure of its unit group might be. These are > interesting questions, but I don't have the time and energy right no, > if ever, to try and figure this out. There is nothing to figure out at this point. Algebraically I've given a factorization. At best you might determine if it is correct-- it is--but it's not something that should involve a serious amount of time and energy. Third error. > The primary problem here is that if you let the ring be the ring of > algebraic integers, you get something never before seen in human > mathematics which is a constraint on a constant factor revealed on the > right hand side of 7(175x^2 - 15x + 2) = (5a 1(x) + 7)(5a 2(x)+ 7) which is obviously not there on the left hand side. I simply don't know what you mean by this. As previously mentioned, Fourth error. Clearly the 7 is just some constant multiplied by the polynomial. It should be trivially removable, and that should be evident on both sides. (Um, I made a mistake here in the original post! Reverse what I said: the 7 is clearly unconstrained on the left hand side, but not so clearly free on the right hand side.) > a 1 and a 2 are NOT algebraic integers. If you do out the solution of Repeat of the original mistake as they are algebraic integers when x is an algebraic integer, trivially. I don't know if that should count as a fifth error or just a repeat of an earlier one, but then yes, such a repeat is an error. So 5 mathematical errors so far from the poster. > the quadratic equation you presented, getting a bunch of square roots > of polynomial expressions involving x, you will probably, with perhaps > some effort, be able to see that the two sides are obviously equal, There is no effort--you just plug and chug. Possibly the poster wishes to now cast doubt on the original factorization? Sixth error. > assuming you have done the calculation correctly. My real point is > that, since you are not dealing in the ring of algebraic integers when > you use this expression, you can't pull out anything very direct that Seventh error. Repeat of earlier mistake that the ring cannot be the ring of algebraic integers. > you can say about the algebraic integers. The fact that you are > getting confused here and have done so now for a very long time does > not increase the respect you get from the mathematical community. Non sequitur. And the poster after making 7 mathematical errors in his reply digresses to make an insult which is in context, ironic. > To understand what I mean--I'm sure some posters would reply that they > find it incomprehensible--consider a simpler example in the ring of > integers: 7(x^2 + 3x + 2) = (7x + 7)(x + 2) where the 7 is still unconstrained, and you can in fact move it around > at will, so I have no idea what an unconstrained 7 might be. I don't even know Eighth error. I always find it remarkable when my attempts at simple explanation are simply denied as easily as someone claiming to be confused by 2+2 = 4, but it has happened so many times over the years that I'm no longer very surprised at seeing it. You see, if no explanation is ever simple enough then the grad student or math professor whose professional research is torn into shreds by the devastating core error can pretend to himself that it still is intact. You see, they may rationalize that all they have to do is keep claiming that it doesn't make sense, no matter how often it's explained or how simply. I still think that undergrads who have NOT built a body of supposed success on the core error are the ones who will end the charade if only when they find themselves unable to generate the energy necessary to learn bogus math--no matter how much their professors and grad students beg and plead. And they may. On the darker side of this human drama some of you may see behavior from people you respected that troubles you for the rest of your lives, as they may beg, and plead, and then threaten, or even attack. Their LIVES are what they are defending in their own minds. To some of them, forcing them to see the truth is like taking something away from them, and they may behave as if they were physically threatened. James Harris === Subject: Re: Epic failure to solve a simple problem >Hi Matt. When all is said and done, Virgil's formula after correcting >various mis-copies gives alpha directly in terms of beta. Sorry about the delay in picking back up with this. However I would agree. Seems like there were many differrent ways to skin this cat, but the end results seem to work okay and were exactly what I needed. So thank you to you, Virgin and everyone else who took a look at it. All very much appreciated. Matt === Subject: Re: Epic failure to solve a simple problem And, ohhh, what a typo!! Of course, I meant 'Virgil'. I blame Richard Branson, and the fact that my ISP is hosted by one his companies.... fingers went into autopilot! === === Subject: Re: Find a polynomial with its difference >Given a polynomial P(x) and a non-zero constant a, Q(x)=P(x)-P(x-a) >should be a polynomial of lower degree. If Q(x) is given, it is >possible to find the coefficients of P(x) in terms of the >coefficients of Q(x) (with exception that the constant term of P(x) >can be arbitrary). For simplicity, let a=1. If >P(x)=a_0+a_1 x+a_2 x^2+...+a_(n+1) x^(n+1) and >Q(x)=b_0+b_1 x+b_2 x^2+...+b_n x^n, then >a_(n+1)=b_n/(n+1), a_n=b_n/2+b_(n-1)/n, >a_(n-1)=nb_n/12+b_(n-1)/2+b_(n-2)/(n-1),.... >Is there a general formula for a_i? >Are there any other method to find P(x) from Q(x)? There was a bit left out of the previous post. The Euler-Maclaurin Sum Formula is one way. The Euler-Maclaurin Sum Formula attempts to take the difference of a function back to the function; it is exact for polynomials: EM [f(x) - f(x-1)] = f(x) + C As shown in , the operator starts -1 1 1 1 3 1 5 1 7 D + - I + -- D - --- D + ----- D - ------- D + ... 2 12 720 30240 1209600 Let g(x) = f(x) - f(x-a) and h(x) = f(ax), then g(ax) = f(ax) - f(ax-a) = h(x) - h(x-1) So f(ax) = h(x) = EM g(ax) For example, suppose f(x) - f(x-3) = x^2 + x + 2, find f(x). Modulo a constant, f(3x) = EM ( 9x^2 + 3x + 2 ) = (3x^3 + 3/2x^2 + 2x) + 1/2(9x^2 + 3x + 2) + 1/12(18x + 3) = 3x^3 + 6x^2 + 5x + 5/4 f(x) = 1/9x^3 + 2/3x^2 + 5/3x + 5/4 There are other methods to sum polynomials. For some other methods see . Rob Johnson take out the trash before replying === Subject: Re: Find a polynomial with its difference <20090702.174613@whim.org> posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) Given a polynomial P(x) and a non-zero constant a, Q(x)=P(x)-P(x-a) >should be a polynomial of lower degree. If Q(x) is given, it is >possible to find the coefficients of P(x) in terms of the >coefficients of Q(x) (with exception that the constant term of P(x) >can be arbitrary). For simplicity, let a=1. If >P(x)=a 0+a 1 x+a 2 x^2+...+a (n+1) x^(n+1) and >Q(x)=b 0+b 1 x+b 2 x^2+...+b n x^n, then >a (n+1)=b n/(n+1), a n=b n/2+b (n-1)/n, >a (n-1)=nb n/12+b (n-1)/2+b (n-2)/(n-1),.... >Is there a general formula for a i? >Are there any other method to find P(x) from Q(x)? There was a bit left out of the previous post. The Euler-Maclaurin Sum Formula is one way. The Euler-Maclaurin Sum > Formula attempts to take the difference of a function back to the > function; it is exact for polynomials: EM [f(x) - f(x-1)] = f(x) + C As shown in , the > operator starts -1 1 1 1 3 1 5 1 7 > D + - I + -- D - --- D + ----- D - ------- D + ... > 2 12 720 30240 1209600 Let g(x) = f(x) - f(x-a) and h(x) = f(ax), then g(ax) = f(ax) - f(ax-a) = h(x) - h(x-1) So f(ax) = h(x) = EM g(ax) For example, suppose f(x) - f(x-3) = x^2 + x + 2, find f(x). Modulo > a constant, f(3x) = EM ( 9x^2 + 3x + 2 ) = (3x^3 + 3/2x^2 + 2x) + 1/2(9x^2 + 3x + 2) + 1/12(18x + 3) = 3x^3 + 6x^2 + 5x + 5/4 f(x) = 1/9x^3 + 2/3x^2 + 5/3x + 5/4 There are other methods to sum polynomials. For some other methods > see . Rob Johnson Given a polynomial P(x) and a non-zero constant a, Q(x)=P(x)-P(x-a) > should be a polynomial of lower degree. If Q(x) is given, it is > possible to find the coefficients of P(x) in terms of the > coefficients of Q(x) (with exception that the constant term of P(x) > can be arbitrary). For simplicity, let a=1. If > P(x)=a_0+a_1 x+a_2 x^2+...+a_(n+1) x^(n+1) and > Q(x)=b_0+b_1 x+b_2 x^2+...+b_n x^n, then > a_(n+1)=b_n/(n+1), a_n=b_n/2+b_(n-1)/n, > a_(n-1)=nb_n/12+b_(n-1)/2+b_(n-2)/(n-1),.... > Is there a general formula for a_i? > Are there any other method to find P(x) from Q(x)? > There was a bit left out of the previous post. > The Euler-Maclaurin Sum Formula is one way. The Euler-Maclaurin Sum > Formula attempts to take the difference of a function back to the > function; it is exact for polynomials: > EM [f(x) - f(x-1)] = f(x) + C > As shown in , the > operator starts > -1 1 1 1 3 1 5 1 7 > D + - I + -- D - --- D + ----- D - ------- D + ... > 2 12 720 30240 1209600 > Let g(x) = f(x) - f(x-a) and h(x) = f(ax), then > g(ax) = f(ax) - f(ax-a) > = h(x) - h(x-1) > So f(ax) = h(x) = EM g(ax) > For example, suppose f(x) - f(x-3) = x^2 + x + 2, find f(x). Modulo > a constant, > f(3x) = EM ( 9x^2 + 3x + 2 ) > = (3x^3 + 3/2x^2 + 2x) + 1/2(9x^2 + 3x + 2) + 1/12(18x + 3) > = 3x^3 + 6x^2 + 5x + 5/4 > f(x) = 1/9x^3 + 2/3x^2 + 5/3x + 5/4 > There are other methods to sum polynomials. For some other methods > see . > Rob Johnson take out the trash before replying Bonjour, Once upon a time, on this site, a guy named Carl Devor.8e > presented very nice Maple programs to solve such things. f(D) o p(x) = q(x) ,q and f(D) known. > Example: f(x+1)-f'(x) = x^2 -3 > p(x) = I/(e(D)-D) o (x^2 -3) ,stopped at D^3 > p(x) = (I-D^2/2) o x^2-3 =x^2-4 , [...] In his book on the Riemann zeta function, H. Edwards has worked-out examples with just a few terms to compute: (a) zeta(2) (b) zeta(1/2) (c) zeta(1/2 + 18i) [pages 114 to 118]. it worked. David Bernier === Subject: Re: Find a polynomial with its difference >Given a polynomial P(x) and a non-zero constant a, Q(x)=P(x)-P(x-a) >should be a polynomial of lower degree. If Q(x) is given, it is >possible to find the coefficients of P(x) in terms of the >coefficients of Q(x) (with exception that the constant term of P(x) >can be arbitrary). For simplicity, let a=1. If >P(x)=a_0+a_1 x+a_2 x^2+...+a_(n+1) x^(n+1) and >Q(x)=b_0+b_1 x+b_2 x^2+...+b_n x^n, then >a_(n+1)=b_n/(n+1), a_n=b_n/2+b_(n-1)/n, >a_(n-1)=nb_n/12+b_(n-1)/2+b_(n-2)/(n-1),.... >Is there a general formula for a_i? >Are there any other method to find P(x) from Q(x)? The Euler-Maclaurin Sum Formula is one way. The Euler-Maclaurin Sum Formula attempts to take the difference of a function back to the function; it is exact for polynomials. As shown in , the formula starts EM [f(x) - f(x-1)] = f(x) + C Let g(x) = f(x) - f(x-a) and h(x) = f(ax), then g(ax) = f(ax) - f(ax-a) = h(x) - h(x-1) So f(ax) = h(x) = EM g(ax) For example, suppose f(x) - f(x-3) = x^2 + x + 2, find f(x). Modulo a constant, f(3x) = EM ( 9x^2 + 3x + 2 ) = (3x^3 + 3/2x^2 + 2x) + 1/2(9x^2 + 3x + 2) + 1/12(18x + 3) = 3x^3 + 6x^2 + 5x + 5/4 f(x) = 1/9x^3 + 2/3x^2 + 5/3x + 5/4 There are other methods to sum polynomials. For some other methods see . Rob Johnson take out the trash before replying === Subject: Re: cheap testbanks and solution manuals posting-account=-ElNTwoAAAAfzuZhQLys-BzoNCRh395M Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) Visit www.testbankzone.com for all your TEST BANK and SOLUTION manual needs. We offer unbeatable prices paired with friendly customer support, so we assure you an experience that won't leave you disappointed! Contact us now and we will gladly provide a free sample so you can make sure that we've got what you need. www.testbankzone.com === Subject: Re: spheres within spheres <29263851.64815.1246554652001.JavaMail.jakarta@nitrogen.mathforum.org>, > You are given a sphere of diameter 20 into which you > place spheres of diameter 1. How many of these will > fit? Is the best one can do is just to give an estimate? Type sphere packing into your favorite search engine and then weed out the ones about Kepler's problem and packing spheres into cubes and chances are you'll find an answer. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: spheres within spheres <1041807.66657.1246581326489.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > You are given a sphere of diameter 20 into which you place spheres of diameter 1. How many of these will fit? Is the best one can do is just to give an > estimate? you could find the maximum limit to the number of spheres by finding the volume of the original sphere and dividing by the volume of the smaller sphere. NP-Completeness 2 May 2000 ... equivalent to a four-dimensional sphere) are provably undecidable. ... So we have this nice construction of complexity classes P and NP but we can't .... and halts within polynomial time p (n) with a yes or no answer ... === Subject: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Everything is known about the transmitted wave, i.e., the shape & phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can this be done when the noise is several orders of magnitude greater than the signal? Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >Everything is known about the transmitted wave, i.e., the shape & >phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can >this be done when the noise is several orders of magnitude greater >than the signal? > In principle, this can be done with synchronous averaging. I have a tutorial series starting here: The basic idea is that you must be able to sample the signal synchronously with the sourve (transmitted) wave. That means you need some sort of trigger signal derived directly from the source. On each trigger, you acquire some number of samples, a long enough series for your needs. Here you will want the series long enough to encompass at least one waveform cycle, since you are looking for amplitude of the overall wave. Let's say that you acquire 1024 samples per trigger. (It's generally OK to miss triggers, as long as you always start acquisition on a trigger.) Then you add those 1024 samples, one by one, into a 1024-bin accumulator. The accumulator will end up holding the average value of the waveform, assuming that the waveform is constant and the noise is not synchronous. For every doubling of the number of samples you add into the accumulator, the S/N improves by 3 dB. The overall improvement is thus determined by how long you want to wait to accumulate enough samples. This is the technique used to monitor evoked potentials in the brain. For example, the subject is presented with a series of repeating tone bursts of a given frequency, while scalp electrodes monitor brain activity. The source of the tone bursts is also the trigger for the averager. The brain response to any given burst is hopelessly buried in noise, since the scalp electrodes see all the brain activity, not just the auditory part. Only a tiny part of the total is due to the auditory response, but that part is in synchrony with the stimulus, while the rest of the brain in general is not. So after several thousand tone bursts, you can see the auditory response. This is used to test hearing in lab animals and infants who can't report what they hear. Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card! === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form <4a4decb1.1181244@news.sysmatrix.net> posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I'm not saying your approach won't work in my case but your Fig. 1 isn't exactly my situation. My noise + signal, if you could see which was which, would look like a large smooth curve with a much smaller amplitude sin curve with a similar period superimposed just above it and/or just below it. My solution was to multiply a high frequency _always positive_ wave onto the original signal. The new signal is discontinuous but it still looks and acts a lot like the original. The difference is every time the high frequency wave was zero, the entire function would be zero and only the noise would remain. The noise is smooth so it could be accurately determined by numerical regression even if the high frequency signal wasn't all that high. Once the noise is known it can be subtracted from the entire output from the receiver. The noise needs to be known to at least 4 decimal place accuracy. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > isn't exactly my situation. It is the same situation just the spectrum of the noise is different. In all of this, the game is the same because the physics is the same. To get a signal to noise ratio or signal to interference ratio larger than one, you need a bandwidth where the noise is smaller than the signal. Averaging, which is applying a narrow bandpass filter helps most for random noise. My noise + signal, if you could see which was which, would look like a > large smooth curve with a much smaller amplitude sin curve with a > similar period superimposed just above it and/or just below it. Just how similar a period? The closer the two are, the harder your job is. My solution was to multiply a high frequency _always positive_ wave > onto the original signal. Life might be simpler if you just multiplied your signal by a square wave whose value is 0 or 1. The new signal is discontinuous but it still looks and acts a lot like > the original. The difference is every time the high frequency wave was zero, the > entire function would be zero and only the noise would remain. The > noise is smooth so it could be accurately determined by numerical > regression even if the high frequency signal wasn't all that high. Once the noise is known it can be subtracted from the entire output > from the receiver. What you are describing is not noise but interference. The noise needs to be known to at least 4 decimal place accuracy. That is a tall order. > Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > > I'm not saying your approach won't work in my case but your Fig. 1 > isn't exactly my situation. It is the same situation just the spectrum of the noise is different. >In all of this, the game is the same because the physics is the >same. To get a signal to noise ratio or signal to interference ratio >larger than one, you need a bandwidth where the noise is smaller >than the signal. Averaging, which is applying a narrow bandpass >filter helps most for random noise. Note that synchronous waveform averaging is *not* a filter, and does not affect the bandwidth of the recovered signal in the least. You still get sharp transients, for example, if they were present in the original. Synchronous waveform averaging will reject any signal that is not synchronous with the trigger, not just random noise. Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card! === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form <4a4f450a.1493429@news.sysmatrix.net> posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I'm not saying your approach won't work in my case but your Fig. 1 > isn't exactly my situation. It is the same situation just the spectrum of the noise is different. >In all of this, the game is the same because the physics is the >same. To get a signal to noise ratio or signal to interference ratio >larger than one, you need a bandwidth where the noise is smaller >than the signal. Averaging, which is applying a narrow bandpass >filter helps most for random noise. > Note that synchronous waveform averaging is *not* > a filter, and does not affect the bandwidth of the > recovered signal in the least. That's also true for the squared higher frequency sin wave method of subtracting noise. A conventional filter doesn't determine the amplitude of the noise and then subtract it. A conventional filter just attenuates noise above or below a certain bandwith. If the noise is about the same frequency as the signal, then a conventional filter will not work. > You still get > sharp transients, for example, if they were > present in the original. Filters can toss information as well as noise. > Synchronous waveform averaging will reject any > signal that is not synchronous with the trigger, > not just random noise. The higher frequency sin^2 method doesn't require an average. In one application all it takes is one period of [sampling by] the high frequency wave to determine the noise as well as the signal. Using regression and integrating over even part of the period of a smooth low frequency noise wave would yield very high precision, even if the sampling rate was fairly low. > DAQARTA v4.51 > Data AcQuisition And Real-Time Analysis > www.daqarta.com Can you reduce smooth well behaved low frequency noise by 99.995%? Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > I'm not saying your approach won't work in my case but your Fig. 1 > isn't exactly my situation. >It is the same situation just the spectrum of the noise is different. >In all of this, the game is the same because the physics is the >same. To get a signal to noise ratio or signal to interference ratio >larger than one, you need a bandwidth where the noise is smaller >than the signal. =A0Averaging, which is applying a narrow bandpass >filter helps most for random noise. > Note that synchronous waveform averaging is *not* > a filter, and does not affect the bandwidth of the > recovered signal in the least. =A0 That's also true for the squared higher frequency sin wave method of >subtracting noise. A conventional filter doesn't determine the >amplitude of the noise and then subtract it. A conventional filter >just attenuates noise above or below a certain bandwith. Just a word of caution about the general scheme of subtracting noise: I suspect that variations on this have been re-invented repeatedly, since it sounds like such a great idea. The problem is that when you actually go to implement it you find the big gotcha: It totally depends upon perfect phase and amplitude matching. If you subtract a version of the noise with a slight time or phase or level shift, the performance goes downhill drastically, and can even be worse than the raw signal. In other words, it will be very hard to make this work as a robust system. Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card! === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form <4a4f450a.1493429@news.sysmatrix.net> <4a50a4d0.862735@news.sysmatrix.net> posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I'm not saying your approach won't work in my case but your Fig. 1 > isn't exactly my situation. >It is the same situation just the spectrum of the noise is different. >In all of this, the game is the same because the physics is the >same. To get a signal to noise ratio or signal to interference ratio >larger than one, you need a bandwidth where the noise is smaller >than the signal. =A0Averaging, which is applying a narrow bandpass >filter helps most for random noise. > Note that synchronous waveform averaging is *not* > a filter, and does not affect the bandwidth of the > recovered signal in the least. =A0 That's also true for the squared higher frequency sin wave method of >subtracting noise. A conventional filter doesn't determine the >amplitude of the noise and then subtract it. A conventional filter >just attenuates noise above or below a certain bandwith. Just a word of caution about the general scheme of > subtracting noise: I suspect that variations on > this have been re-invented repeatedly, since it > sounds like such a great idea. It's surprising that a quick way of explaining why it won't work hasn't appeared as is generally the case in electronics. Certainly some scholarly type somewhere has a comprehensive list of signal processing theories and equipment. > The problem is > that when you actually go to implement it you find > the big gotcha: It totally depends upon perfect > phase and amplitude matching. That's not an issue if a smooth noise has a period several times longer than the higher frequency wave. The higher frequency wave and the signal that modulates it would clearly appear w/o any synchronization. Put 5sin(1.2x) + sinxsin^2(5x) into www.wolframalpha.com The original signal sinx can be easily retrieved without knowing the phase or even the exact frequency of the modulated wave. > If you subtract a > version of the noise with a slight time or phase > or level shift, the performance goes downhill > drastically, and can even be worse than the raw > signal. In other words, it will be very hard to > make this work as a robust system. The obvious problem with the subtracting approach is the sensor must be much more precise to get a good measurement from the difference of two large numbers. If you wanted to be +/- 1% accurate and the noise was 100 times larger than the signal, then the sensor would need 4 sig fig accuracy. The period of the noise is so long, however, the sensor could rezero itself just before and just after each signal measurement. > DAQARTA v4.51 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > FREE Signal Generator > Science with your sound card! Can you eliminate 99.9975% of noise? Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > A conventional filter doesn't determine the > amplitude of the noise and then subtract it. A conventional filter > just attenuates noise above or below a certain bandwith. But your method doesn't completely eliminate the noise either. You're approximating it by interpolation, and assuming that the result is good enough. There will always be some residual error -- and that error is just the same as the residual amount of noise that a conventional filter with equivalent passband characteristics would let through. > Filters can toss information as well as noise. So can your method, since you're assuming you can interpolate between signal samples as well. To the extent that's not exactly right, you've lost information. -- Greg === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > isn't exactly my situation. > It is the same situation just the spectrum of the noise is different. Which is everything when you want to reduce noise. > In all of this, the game is the same because the physics is the > same. The math is entirely different. A smooth low frequency noise curve can be sampled fewer times over longer intervals and the result can be very accurate, especially with regression. > To get a signal to noise ratio or signal to interference ratio > larger than one, you need a bandwidth where the noise is smaller > than the signal. Convert the signal to a higher frequency wave form that still has characteristics of the original signal. > Averaging, which is applying a narrow bandpass > filter helps most for random noise. Time = money. If the average takes more than a few cycles, the result won't be any good for other reasons. > My noise + signal, if you could see which was which, would look like a > large smooth curve with a much smaller amplitude sin curve with a > similar period superimposed just above it and/or just below it. > Just how similar a period? Maybe 0.5 - 1.5. Say the sensor is getting something like 100sin(1.3t) [the noise] + sint [the signal]. I need to know the signal to 0.25% accuracy. > The closer the two are, the harder your > job is. Total control the signal should be worth something . > My solution was to multiply a high frequency always positive wave > onto the original signal. > Life might be simpler if you just multiplied your signal by a > square wave whose value is 0 or 1. What's the advantage? > The new signal is discontinuous but it still looks and acts a lot like > the original. > The difference is every time the high frequency wave was zero, the > entire function would be zero and only the noise would remain. The > noise is smooth so it could be accurately determined by numerical > regression even if the high frequency signal wasn't all that high. > Once the noise is known it can be subtracted from the entire output > from the receiver. > What you are describing is not noise but interference. > The noise needs to be known to at least 4 decimal place accuracy. > That is a tall order. If it's not possible there's a completely different approach. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > I'm not saying your approach won't work in my case but your Fig. 1 > isn't exactly my situation. > It is the same situation just the spectrum of the noise is different. Which is everything when you want to reduce noise. Not everything. > In all of this, the game is the same because the physics is the > same. The math is entirely different. A smooth low frequency noise curve >can be sampled fewer times over longer intervals and the result can be >very accurate, especially with regression. > To get a signal to noise ratio or signal to interference ratio > larger than one, you need a bandwidth where the noise is smaller > than the signal. Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. Great as long as you don't do that to the noise, too. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. Great as long as you don't do that to the noise, too. I'm still expecting some scholar to say this was done in the early 1880s. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. > Great as long as you don't do that to the noise, too. I'm still expecting some scholar to say this was done in the early > 1880s. > Bret Cahill Actually in 1918 by Edwin Armstrong. -- Jim Pennino === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. > Great as long as you don't do that to the noise, too. I'm still expecting some scholar to say this was done in the early > 1880s. Bret Cahill Actually in 1918 by Edwin Armstrong. Amplitude of the high(er) frequency wave is modulated by the signal curve. Put sinxsin^2(10x) into signal. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. > Great as long as you don't do that to the noise, too. > I'm still expecting some scholar to say this was done in the early > 1880s. > Bret Cahill > Actually in 1918 by Edwin Armstrong. Amplitude of the high(er) frequency wave is modulated by the signal > curve. Put sinxsin^2(10x) into signal. > Bret Cahill Who cares and it is irrelevant to what I posted. -- Jim Pennino === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. Great as long as you don't do that to the noise, too. > I'm still expecting some scholar to say this was done in the early > 1880s. > Bret Cahill > Actually in 1918 by Edwin Armstrong. Amplitude of the high(er) frequency wave is modulated by the signal > curve. Put sinxsin^2(10x) into signal. Bret Cahill Who cares The people who click on threads on signal recovery. > and it is irrelevant to what I posted. Feel free to start your own thread on whatever you are interested in. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. > Great as long as you don't do that to the noise, too. > I'm still expecting some scholar to say this was done in the early > 1880s. > Bret Cahill > Actually in 1918 by Edwin Armstrong. > Amplitude of the high(er) frequency wave is modulated by the signal > curve. > Put sinxsin^2(10x) into > signal. > Bret Cahill > Who cares The people who click on threads on signal recovery. > > and it is irrelevant to what I posted. Feel free to start your own thread on whatever you are interested in. > Bret Cahill Feel free to take your meds. -- Jim Pennino === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > Convert the signal to a higher frequency wave form that still has > characteristics of the original signal. Yes, certainly. *If* you have a suitable noise-free frequency band available, this is quite easy to do. No revolutionary techniques are required. Your example assumes that you do indeed have such a band available, at about 100x the original signal frequency, and wide enough to accommodate the bandwidth of your signal. In that case, the problem is easy to solve. Just modulate your signal onto a carrier somehow (you're other technique), use a filter at the receiving end to separate the carrier from the noise, and then demodulate. Although it might not seem that way, this *is* what you are effectively doing. You're just using a somewhat unconventional technique to do the filtering and demodulation. There may be simpler ways, e.g. noise, just sample the peaks and troughs of the carrier to measure its amplitude. You don't strictly need to know the exact frequency and phase of the carrier, although if you do happen to know it, you can take advantage of that to simplify any sample-oriented processing you want to do. What others are talking about concerning averaging is what you need to do if you *don't* have a noise-free band available, and you've no choice but to deal with signal and noise together in the same band. In that case, the only way to reduce noise is to reduce the receiver's bandwith *somehow*, and averaging is one way to achieve that -- and knowing the frequency and phase of your carrier is a big help, because it lets you implement a synchronous detector. But as I said, you're assuming that you *can* find a noise-free band, so you don't need averaging (except maybe over a few cycles of your carrier frequency, which is much higher than your signal frequency). -- Greg === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form <7b8ub7F22dl8nU1@mid.individual.net> posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Convert the signal to a higher frequency wave form that still has > characteristics of the original signal. > Yes, certainly. *If* you have a suitable noise-free > frequency band available, this is quite easy to do. > No revolutionary techniques are required. The situation is so common and the applications so widespread and the solution such a short distance off trail I was assuming they already had 10,000 dirt cheap off-the-shelf versions of it as they generally do in electronics. That was the reason for the OP. Someone was supposed to answer, TI sells exactly what you want in their 87WA3 series. Anyone can wire 'em up in 5 minutes. I used them for blah blah blah . . . I was expecting / hoping for more responses like the www.DAQARTA.com guy's. It was only later that I came up with the sin^2 method and that was presented mostly to clarify the OP, not to answer it. > Your example assumes that you do indeed have such > a band available, at about 100x the original signal > frequency, and wide enough to accommodate the > bandwidth of your signal. Or the squared modulated signal. > In that case, the problem is easy to solve. Just > modulate your signal onto a carrier somehow (you're > other technique), basic solutions that led me here in the first place. The one I was calling FM circumvents the noise issue altogether and has an easy to cheaper and has a much larger market. the high frequency wave. This is a critical difference. > use a filter at the receiving end > to separate the carrier from the noise, and then > demodulate. > Although it might not seem that way, this *is* what > you are effectively doing. You're just using a > somewhat unconventional technique to do the filtering > and demodulation. So I have until July 2, 2010 to file a PPA. > There may be simpler ways, e.g. > noise, just sample the peaks and troughs of the > carrier to measure its amplitude. Actually that would _not_ work. My background isn't signal processing but now I'm starting to wonder if the hold up behind the larger solution might be traceable to a hold up in electronics. > You don't strictly need to know the exact frequency > and phase of the carrier, although if you do happen > to know it, you can take advantage of that to > simplify any sample-oriented processing you want to > do. > What others are talking about concerning averaging > is what you need to do if you *don't* have a noise-free > band available, and you've no choice but to deal with > signal and noise together in the same band. In that > case, the only way to reduce noise is to reduce the > receiver's bandwith *somehow*, and averaging is one way > to achieve that -- and knowing the frequency and phase > of your carrier is a big help, because it lets you > implement a synchronous detector. > But as I said, you're assuming that you *can* find a > noise-free band, so you don't need averaging (except > maybe over a few cycles of your carrier frequency, > which is much higher than your signal frequency). Some California physicist suggested it was impossible to destroy information and recently S. Hawkings agreed. Shred and burn your notes then put the ashes on a rocket headed toward a black hole and 10^68 years from now they'll know what you were trying to hide. The same holds for DNA and your life experiences so everyone is in effect immortal. That's one very good reason to believe efforts at reducing noise / getting information will be fruitful. I don't want to wait 10^67 years for it but then again, I'm not trying to destroy it either. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >isn't exactly my situation. >It is the same situation just the spectrum of the noise is different. > Which is everything when you want to reduce noise. No, the same considerations apply. You need a bandwidth where the ratio of signal to noise meets your requirement. >In all of this, the game is the same because the physics is the >same. > The math is entirely different. A smooth low frequency noise curve > can be sampled fewer times over longer intervals and the result can be > very accurate, especially with regression. No, what you are claiming above is for noise that has a vastly different spectral content than the signal. >To get a signal to noise ratio or signal to interference ratio >larger than one, you need a bandwidth where the noise is smaller >than the signal. > Convert the signal to a higher frequency wave form that still has > characteristics of the original signal. That has no effect on the SNR since the noise gets converted too. >Averaging, which is applying a narrow bandpass >filter helps most for random noise. > Time = money. If the average takes more than a few cycles, the result > won't be any good for other reasons. If the signal is really one thousandth of the noise, and the noise is random, you need to average a million traces to get an SNR of one. This is because the SNR increases as the square root of the number of traces averaged. >My noise + signal, if you could see which was which, would look like a >large smooth curve with a much smaller amplitude sin curve with a >similar period superimposed just above it and/or just below it. >Just how similar a period? > Maybe 0.5 - 1.5. Say the sensor is getting something like 100sin(1.3t) [the noise] + > sint [the signal]. I need to know the signal to 0.25% accuracy. So you want a bandpass filter at frequency t which has skirts down 120db at 1.3t (assuming the noise signal is narrow band and that it is 1000 times the signal amplitude originally). >The closer the two are, the harder your >job is. > Total control the signal should be worth _something_. Knowing the frequency and phase is already factored in the discussion. >My solution was to multiply a high frequency _always positive_ wave >onto the original signal. >Life might be simpler if you just multiplied your signal by a >square wave whose value is 0 or 1. > What's the advantage? > You get to look at the signal 50% of the time and the noise 50% of the time to get their relative amplitudes. > >The new signal is discontinuous but it still looks and acts a lot like >the original. >The difference is every time the high frequency wave was zero, the >entire function would be zero and only the noise would remain. The >noise is smooth so it could be accurately determined by numerical >regression even if the high frequency signal wasn't all that high. >Once the noise is known it can be subtracted from the entire output >from the receiver. >What you are describing is not noise but interference. >The noise needs to be known to at least 4 decimal place accuracy. >That is a tall order. > If it's not possible there's a completely different approach. I would go after that. > Bret Cahill > === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >Everything is known about the transmitted wave, i.e., the shape & >phase angle, except the amplitude. >All that is necessary is to recover is the amplitude of the wave. Can >this be done when the noise is several orders of magnitude greater >than the signal? > In principle, this can be done with synchronous > averaging. I have a tutorial series starting > here: > the signal synchronously with the sourve > (transmitted) wave. That means you need some sort > of trigger signal derived directly from the > source. That was the plan. Complete control over and knowledge of the source wave should provide some options to recover the signal, even if the noise is orders of magnitude more than than the source wave. Kind of like the military shooting down a tank of hydrazine with a transponder on it and then claiming they took out a satellite. > On each trigger, you acquire some number > of samples, a long enough series for your needs. > Here you will want the series long enough to > encompass at least one waveform cycle, since you > are looking for amplitude of the overall wave. The system will attenuate the low frequency wave more than a high frequency wave that isn't part of the low frequency wave. Determining the amount of attenuation of the low frequency wave was, in fact, the goal. The high frequency component, however, should attenuate much like the low frequency wave if it is tracing out the low frequency wave. > Let's say that you acquire 1024 samples per > trigger. (It's generally OK to miss triggers, as > long as you always start acquisition on a > trigger.) Then you add those 1024 samples, one by > one, into a 1024-bin accumulator. The accumulator > will end up holding the average value of the > waveform, assuming that the waveform is constant > and the noise is not synchronous. > For every doubling of the number of samples you > add into the accumulator, the S/N improves by 3 > dB. The overall improvement is thus determined by > how long you want to wait to accumulate enough > samples. Maybe 5 - 7 cycles at most. At first I thought a more sophisticated version of resonant frequency, i.e., lots of different frequency waves added together, might have been a solution but there wasn't enough time to get past the transient effects. > This is the technique used to monitor evoked > potentials in the brain. For example, the > subject is presented with a series of repeating > tone bursts of a given frequency, while scalp > electrodes monitor brain activity. The source of > the tone bursts is also the trigger for the > averager. The brain response to any given burst > is hopelessly buried in noise, since the scalp > electrodes see all the brain activity, not just > the auditory part. Only a tiny part of the total > is due to the auditory response, but that part is > in synchrony with the stimulus, while the rest of > the brain in general is not. So after several > thousand tone bursts, you can see the auditory > response. This is used to test hearing in lab > animals and infants who can't report what they > hear. > Bob Masta DAQARTA v4.51 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > FREE Signal Generator > Science with your sound card! === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >The system will attenuate the low frequency wave more than a high >frequency wave that isn't part of the low frequency wave. Determining the amount of attenuation of the low frequency wave was, >in fact, the goal. The high frequency component, however, should attenuate much like the >low frequency wave if it is tracing out the low frequency wave. If the medium has different attenuation at different frequencies, emphatically no. The measured attenuation will be the attenuation at the modulating carrier frequency (complicated by sidebands) and not the attenuation of the baseline signal. Your proposed modulation (multiplying by a sin^2 waveform) is even more complex than regular filter that bit out. (Actually, to get the full solution, you'd have to compute the entire spectrum of the complex modulated signal, and run each spectral line through the transfer function of the process, then recombine. Could get messy.) If the attenuation is flat over frequency, why bother to modulate? Just measure at a high frequency, above the range of the bandlimited noise. You can't fool Mother Nature with simple tricks. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? Bret Cahill ask comp.dsp === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill Narrowing the final detection bandwidth is the only hope. If the noise spectrum is white, narrow bandwidth through averaging works. If you cannot average, there is trouble. The old lockin amplifiers used a modulation or chopping signal and a long time constant in the final filter. I had signals at times that required an hour of integration to detect. It was slow but it worked. === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? Bret Cahill Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. I forgot to mention that the signal wave form can be anything that can be generated. (sint)(sin10t)(sin10t) was possible and the frequency of the noise was about the same as the sin(t) factor, then f(t) will plot the noise every time f(t) = 0. In this case that would be ten times as often as the sin(t) factor. The noise can then be subtracted to recover the wave form. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) The sensor receives the loud noise, say, 10sin(0.7x), plus the small signal, say, sin(x ). The signal, however, can be transformed into sin (x)sin^2(100x) so the sensor receives (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 This can be viewed by pasting the entire line into www.wolframalpha.com The blue area is the signal to be extracted from the noise. It's over the noise to the left of x = pi and under the noise to the right of pi. The high frequency curve runs between the signal and the noise and maps out both curves to any precision depending on frequency and regression. Bret Cahill > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? Bret Cahill Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. I forgot to mention that the signal wave form can be anything that can > be generated. (sint)(sin10t)(sin10t) was possible and the frequency of the noise was > about the same as the sin(t) factor, then f(t) will plot the noise > every time f(t) = 0. In this case that would be ten times as often as the sin(t) factor. The noise can then be subtracted to recover the wave form. Bret Cahill- Hide quoted text - - Show quoted text - === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > The sensor receives the loud noise, say, 10sin(0.7x), plus the small > signal, say, sin(x ). The signal, however, can be transformed into sin > (x)sin^2(100x) so the sensor receives (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 What you are doing is changing the problem. You are now looking at a sin(100x) modulated by sin(x). This says the noise and the signal are independent of one another. If you can do this, make it 1000x and make you life easier. This can be viewed by pasting the entire line into www.wolframalpha.com The blue area is the signal to be extracted from the noise. It's over > the noise to the left of x = pi and under the noise to the right of > pi. The high frequency curve runs between the signal and the noise and > maps out both curves to any precision depending on frequency and > regression. > Bret Cahill >Everything is known about the transmitted wave, i.e., the shape & >phase angle, except the amplitude. >All that is necessary is to recover is the amplitude of the wave. Can >this be done when the noise is several orders of magnitude greater >than the signal? >Bret Cahill >Narrowing the final detection bandwidth is the only hope. >If the noise spectrum is white, narrow bandwidth through >averaging works. If you cannot average, there is trouble. >The old lockin amplifiers used a modulation or chopping signal >and a long time constant in the final filter. I had signals >at times that required an hour of integration to detect. It >was slow but it worked. >I forgot to mention that the signal wave form can be anything that can >be generated. >(sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. >In this case that would be ten times as often as the sin(t) factor. >The noise can then be subtracted to recover the wave form. >Bret Cahill- Hide quoted text - >- Show quoted text - === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form <4ZSdnZYVqv95-dPXnZ2dnUVZ_oqdnZ2d@posted.docknet> posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > The sensor receives the loud noise, say, 10sin(0.7x), plus the small > signal, say, sin(x ). The signal, however, can be transformed into sin > (x)sin^2(100x) so the sensor receives (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 What you are doing is changing the problem. As I pointed out above, I forgot to mention in the OP that the designer could change the signal to suit the problem. > You are now looking at a > sin(100x) modulated by sin(x). Actually it's a sin^2(100x) which is always positive. Sin100x will not work as the sign of the original signal must be preserved. For example, try pasting (10sin(0.7x) + sin(x)sin(100x)) x from 2 to 3.4 into www.wolframalpha.com How would you know the noise curve? > This says the noise and the signal > are independent of one another. Bingo! > If you can do this, make it 1000x > and make you life easier. In some situations it may be difficult to use very high frequencies. That's why regression was mentioned. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > The sensor receives the loud noise, say, 10sin(0.7x), plus the small > signal, say, sin(x ). The signal, however, can be transformed into sin > (x)sin^2(100x) so the sensor receives > (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 > What you are doing is changing the problem. As I pointed out above, I forgot to mention in the OP that the >designer could change the signal to suit the problem. > You are now looking at a > sin(100x) modulated by sin(x). Actually it's a sin^2(100x) which is always positive. Which is equivalent to 100% amplitude modulating at 200x. Square wave chopping would work, too. That's more common in synchronous detection instruments. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >The sensor receives the loud noise, say, 10sin(0.7x), plus the small >signal, say, sin(x ). The signal, however, can be transformed into sin >(x)sin^2(100x) so the sensor receives >(10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 What you are doing is changing the problem. >As I pointed out above, I forgot to mention in the OP that the >designer could change the signal to suit the problem. >You are now looking at a >sin(100x) modulated by sin(x). >Actually it's a sin^2(100x) which is always positive. > Which is equivalent to 100% amplitude modulating at 200x. Square wave chopping would work, too. That's more common in > synchronous detection instruments. John Bret apparently has decided he knows physics and signal processing better than all of us. I have no idea why he is posting since he claims we are all wrong. He seems to think the laws of physics do not apply to him. > === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > > >The sensor receives the loud noise, say, 10sin(0.7x), plus the small >signal, say, sin(x ). The signal, however, can be transformed into sin >(x)sin^2(100x) so the sensor receives >(10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 >What you are doing is changing the problem. As I pointed out above, I forgot to mention in the OP that the >designer could change the signal to suit the problem. >You are now looking at a >sin(100x) modulated by sin(x). Actually it's a sin^2(100x) which is always positive. > > > Which is equivalent to 100% amplitude modulating at 200x. > > Square wave chopping would work, too. That's more common in > synchronous detection instruments. > > John Bret apparently has decided he knows physics and signal >processing better than all of us. I have no idea why he >is posting since he claims we are all wrong. He seems >to think the laws of physics do not apply to him. > He seems to have some idea for a gedget that needs synchronous detection to do some measurement. But of course he'll never reveal what he's actually trying to do. And he won't do any research on how everybody else has been doing it for 60 years or so. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >Bret apparently has decided he knows physics and signal >processing better than all of us. I have no idea why he >is posting since he claims we are all wrong. He seems >to think the laws of physics do not apply to him. --- Cahill is nothing more than a troll who posts for attention. JF === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=0BoC1woAAADhZZOOdizvYCaBiS4MgvYE Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; InfoPath.1),gzip(gfe),gzip(gfe) What are the ïFive PillarsÍ of Islam? August 31st, 2008 time. THANK YOU What are the ïFive PillarsÍ of Islam? They are the framework of the Muslim life: faith, prayer, concern for the needy, self-purification, and the pilgrimage to Makkah for those who are able. First Pillar: Faith There is no god worthy of worship except God and Muhammad is His messenger. This declaration of faith is called the Shahada, a simple formula which all the faithful pronounce. In Arabic, the first part is la ilaha illaÍLlah - ïthere is no god except GodÍ; ilaha (god) can refer to anything which we may be tempted to put in place of God[CapitalEth] wealth, power, and the like. Then comes illaÍLlah: ïexcept GodÍ, the source of all Creation. The second part of the Shahada is Muhammadun rasuluÍLlah: ïMuhammad is the messenger of God.Í A message of guidance has come through a man like ourselves. Second Pillar: Prayer Salat is the name for the obligatory prayers which are performed five times a day, and are a direct link between the worshiper and God. There is no hierarchical authority in Islam, and no priests, so the prayers are led by a learned person who knows the Quran, chosen by the congregation. These five prayers contain verses from the Quran, and are said in Arabic, the language of the Revelation, but personal supplication can be offered in oneÍs own language. Prayers are said at dawn, noon, mid-afternoon, sunset and nightfall, and thus determine the rhythm of the entire day. Although it is preferable to worship together in a mosque, a Muslim may pray almost anywhere, such as in fields, offices, factories and universities. Visitors to the Muslim world are struck by the centrality of prayers in daily life. A translation of the Call to Prayer is: ïGod is most great. God is most great. God is most great. God is most great. I testify that there is no god except God. I testify that there is no god except God. I testify that Muhammad is the messenger of God. I testify that Muhammad is the messenger of God. Come to prayer! Come to prayer! Come to success (in this life and the Hereafter)! Come to success! God is most great. God is most great. There is no god except God.Í Once Muslims prayed towards Jerusalem, but during the ProphetÍs Imam who leads the prayer gives the sermon at the Friday noon community prayers. Third Pillar: Zakat One of the most important principles of Islam is that all things belong to God, and that wealth is therefore held by human beings in trust. The word zakat means both ïpurificationÍ and ïgrowthÍ. Our possessions are purified by setting aside a proportion for those in need, and, like the pruning of plants, this cutting back balances and encourages new growth. Each Muslim calculates his or her own zakat individually. For most purposes this involves the payment each year of two and a half percent of oneÍs capital. A pious person may also give as much as he or she pleases as sadaqa, and does so preferably in secret. Although this word can be translated as ïvoluntary charityÍ it has a wider meaning. The Prophet (SAW) said: ïEven meeting your brother with a cheerful face is charity.Í The Prophet (SAW) said: ïCharity is a necessity for every Muslim.Í He was asked: ïWhat if a person has nothing?Í The Prophet (SAW) replied: ïHe should work with his own hands for his benefit and then give something out of such earnings in charity.Í The Companions asked: ïWhat if he is not able to work?Í The Prophet (SAW) said: ïHe should help poor and needy persons.Í The Companions further asked ïWhat if he cannot do even that?Í The Prophet (SAW) said ïHe should urge others to do good.Í The Companions said ïWhat if he lacks that also?Í The Prophet (SAW) said ïHe should check himself from doing evil. That is also charity.Í Fourth Pillar: The Fast Every year in the month of Ramadan, all Muslims fast from first light until sundown, abstaining from food, drink, and sexual relations. Those who are sick, elderly, or on a journey, and women who are pregnant or nursing are permitted to break the fast and make up an equal number of days later in the year. If they are physically unable to do this, they must feed a needy person for every day missed. Children begin to fast (and to observe the prayer) from puberty, although many start earlier. Although the fast is most beneficial to the health, it is regarded principally as a method of self purification. By cutting oneself off from worldly comforts, even for a short time, a fasting person gains true sympathy with those who go hungry as well as growth in oneÍs spiritual life. Fifth Pillar: The Pilgrimage (Hajj) The annual pilgrimage to Makkah, the Hajj, is an obligation only for those who are physically and financially able to perform it. Nevertheless, about two million people go to Makkah each year from every comer of the globe providing a unique opportunity for those of different nations to meet one another. Although Makkah is always filled with visitors, the annual Hajj begins in the twelfth month of the Islamic year (which is lunar, not solar, so that Hajj and Ramadan fall sometimes in summer, sometimes in winter). Pilgrims wear special clothes: simple garments which strip away distinctions of class and culture, so that all stand equal before God. The rites of the Hajj, which are of Abrahamic origin, include circling the KaÍba seven times, and going seven times between the mountains of Safa and Marwa as did Hagar during her search for water. Then the pilgrims stand together on the wide plain of Arafa and join in prayers for GodÍs forgiveness, in what is often thought of as a preview of the Last Judgment. In previous centuries the Hajj was an arduous undertaking. Today, however, Saudi Arabia provides millions of people with water, modem transport, and the most up-to-date health facilities. The close of the Hajj is marked by a festival, the Eid al-Adha, which is celebrated with prayers and the exchange of gifts in Muslim communities everywhere. This, and the Eid al-Fitr, a feast-day commemorating the end of Ramadan, are the main festivals of the Muslim calendar. .84.84.84.84[CapitalNTi lde].84.84.84.84[Capital NTilde].84.84.84- For more information about Islam http://english.islamway.com/ http://www.islamhouse.com/ http://www.discoverislam.com/ http://www.islambasics.com/index.php http://english.islamway.com/ http://www.islamtoday.net/english/ http://www.islamweb.net/ver2/MainPage/indexe.php http://www.sultan.org/ Contact Us At Imanway.group@gmail.com === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >What are the ëFive Pillars.89 of Islam? >August 31st, 2008 >time. --- If Allah is all-powerful and knows the future, then he knows what is going to happen from moment to moment, and how we live our lives is unimportant since he will know in advance what we will do with them. On the other hand, if we can exercise free will, then Allah can't predict the future and isn't, as you claim, omniscient. I've posed this question, many times, to you people, but have not yet received a response of any kind. I don't suppose this time will be any different. JF === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form >The sensor receives the loud noise, say, 10sin(0.7x), plus the small >signal, say, sin(x ). The signal, however, can be transformed into sin >(x)sin^2(100x) so the sensor receives >(10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 >What you are doing is changing the problem. > As I pointed out above, I forgot to mention in the OP that the > designer could change the signal to suit the problem. >You are now looking at a >sin(100x) modulated by sin(x). > Actually it's a sin^2(100x) which is always positive. Sin100x will not work as the sign of the original signal must be > preserved. Sin(100x) will work just fine. To detect sin(x) just multiply the signal by sin(100x) again or, to be careful multiply by sin(100x) and also by cos(100x). This does a quadrature detection and the magnitude of the two term is independent of the phase relative to sin(100x) For example, try pasting (10sin(0.7x) + sin(x)sin(100x)) x from 2 to 3.4 into www.wolframalpha.com How would you know the noise curve? The point of using the high frequency is to remove your signal from the noise value. >This says the noise and the signal >are independent of one another. > Bingo! >If you can do this, make it 1000x >and make you life easier. > In some situations it may be difficult to use very high frequencies. That's why regression was mentioned. The physics requirements are always the same. You need to have the signal power greater than the noise power in the detection bandwidth. Any fancy processing scheme is just trying to narrow the detection bandwidth. > Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) >The sensor receives the loud noise, say, 10sin(0.7x), plus the small >signal, say, sin(x ). The signal, however, can be transformed into sin >(x)sin^2(100x) so the sensor receives (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 >What you are doing is changing the problem. As I pointed out above, I forgot to mention in the OP that the > designer could change the signal to suit the problem. >You are now looking at a >sin(100x) modulated by sin(x). Actually it's a sin^2(100x) which is always positive. Sin100x will not work as the sign of the original signal must be > preserved. Sin(100x) will work just fine. The shape and the effect of the original signal, sin x, on the rest of the system cannot be preserved if the sign of the high frequency factor alternates each cycle. > To detect sin(x) just multiply > the signal by sin(100x) again or, to be careful multiply by > sin(100x) and also by cos(100x). This does a quadrature detection > and the magnitude of the two term is independent of the > phase relative to sin(100x) For example, try pasting (10sin(0.7x) + sin(x)sin(100x)) x from 2 to 3.4 intowww.wolframalpha.com How would you know the noise curve? > The point of using the high frequency is to remove your > signal from the noise value. And this is done by first identifying the noise curve. The high frequency curve and, therefore, the entire f(t), will equal 0 on every cycle of the high frequency. Since we know when the signal is zero we know the value of the noise at that time. >This says the noise and the signal >are independent of one another. Bingo! >If you can do this, make it 1000x >and make you life easier. > In some situations it may be difficult to use very high frequencies. > That's why regression was mentioned. > The physics requirements are always the same. You need to have the > signal power greater than the noise power in the detection bandwidth. Not if you can identify the noise to 99.995% accuracy. > Any fancy processing scheme is just trying to narrow the detection > bandwidth. I didn't think the approach above was either fancy or narrowing the bandwith. Obviously, if the noise frequency is about the same as signal frequency it will necessary to end run the use of conventional filters altogether. It would be interesting to learn if and when something similar was tried. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. > All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill > Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. >I forgot to mention that the signal wave form can be anything that can >be generated. (sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. In this case that would be ten times as often as the sin(t) factor. The noise can then be subtracted to recover the wave form. >Bret Cahill I think what's happening is that you have 1. Defined the noise to be bandlimited to radian frequencies below about 1 and 2. Up-converted (modulated) the signal to have usable (recoverable) components around 10 times that frequency. So (am I allowed to say 'duh'?) a simple highpass filtering operation will remove the noise from the upconverted signal. You moved the signal to where you knew there was no noise. It's more interesting when the signal and the noise occupy the same bandwidth. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. > All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill > Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. I forgot to mention that the signal wave form can be anything that can >be generated. (sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. In this case that would be ten times as often as the sin(t) factor. The noise can then be subtracted to recover the wave form. Bret Cahill I think what's happening is that you have 1. Defined the noise to be bandlimited to radian frequencies below > about 1 The noise and the signal are both low and have about the same frequency, ~ x/2pi. There is little that can be done to change this situation. There is no time to wait more than several cycles for the result either. > and 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only thing left is the low frequency noise. Then a high pass filter can smooth out the (sin10t)(sin10t) component so something like the original signal can still be recovered after the noise is subtracted out. Alternatively traditional filters can be eliminated altogether. The signal + noise as well as the noise alone can be traced out from the high frequency signal. The noise is then subtracted from the signal + noise to recover the signal. > So (am I allowed to say 'duh'?) a simple highpass filtering operation > will remove the noise from the upconverted signal. You moved the > signal to where you knew there was no noise. Plot f(t) and it's easy to see the original signal sill exists, although in a somewhat discontinuous form. It would be interesting if this has never been done before. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. > All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill > Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. >I forgot to mention that the signal wave form can be anything that can >be generated. >(sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. >In this case that would be ten times as often as the sin(t) factor. >The noise can then be subtracted to recover the wave form. >Bret Cahill > I think what's happening is that you have > 1. Defined the noise to be bandlimited to radian frequencies below > about 1 The noise and the signal are both low and have about the same >frequency, ~ x/2pi. There is little that can be done to change this >situation. There is no time to wait more than several cycles for the >result either. > and > 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only >thing left is the low frequency noise. You are assuming the ability to high-frequency modulate the signal before the noise is added to it. So you already know what the noiseless signal looks like. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form <7cps455q5hiruv5o5nl6u39oad7smn9c72@4ax.com> posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? Bret Cahill Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. >I forgot to mention that the signal wave form can be anything that can >be generated. >(sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. >In this case that would be ten times as often as the sin(t) factor. >The noise can then be subtracted to recover the wave form. >Bret Cahill > I think what's happening is that you have > 1. Defined the noise to be bandlimited to radian frequencies below > about 1 The noise and the signal are both low and have about the same >frequency, ~ x/2pi. There is little that can be done to change this >situation. There is no time to wait more than several cycles for the >result either. > and > 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only >thing left is the low frequency noise. You are assuming the ability to high-frequency modulate the signal > before the noise is added to it. So you already know what the > noiseless signal looks like. As I said in the OP, Everything is known about the transmitted wave, i.e., the shape & phase angle, except the amplitude. This works for the same reason reading a newspaper in a foreign language is easy. You already know what they are going to say. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. > All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill > Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. >I forgot to mention that the signal wave form can be anything that can >be generated. >(sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. >In this case that would be ten times as often as the sin(t) factor. >The noise can then be subtracted to recover the wave form. >Bret Cahill > I think what's happening is that you have > 1. Defined the noise to be bandlimited to radian frequencies below > about 1 >The noise and the signal are both low and have about the same >frequency, ~ x/2pi. There is little that can be done to change this >situation. There is no time to wait more than several cycles for the >result either. > and > 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. >To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only >thing left is the low frequency noise. > You are assuming the ability to high-frequency modulate the signal > before the noise is added to it. So you already know what the > noiseless signal looks like. As I said in the OP, Everything is known about the transmitted wave, >i.e., the shape & phase angle, except the amplitude. This works for the same reason reading a newspaper in a foreign >language is easy. You already know what they are going to say. >Bret Cahill > Are you familiar with the way a lockin amplifier works? That sounds maybe like what you are doing. If you know everything about the signal but its amplitude, then you have or can construct a normalized (unity amplitude) version of it. That will positively correlate with the unknown-amplitude version of the signal but have zero correlation to random noise. Things like IR absorption spectrometers commonly chop (square wave modulate) the light source and recover the signal with a synchronous rectifier. That washes out any noise picked up in the optical path or the detector. Things like this commonly dig signals out from 1000x the noise... but slowly. If the noise is known to be bandlimited, it's a lot easier... almost cheating. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. > All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill > Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. I forgot to mention that the signal wave form can be anything that can >be generated. (sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. In this case that would be ten times as often as the sin(t) factor. The noise can then be subtracted to recover the wave form. Bret Cahill I think what's happening is that you have 1. Defined the noise to be bandlimited to radian frequencies below > about 1 >The noise and the signal are both low and have about the same >frequency, ~ x/2pi. There is little that can be done to change this >situation. There is no time to wait more than several cycles for the >result either. and 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. >To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only >thing left is the low frequency noise. > You are assuming the ability to high-frequency modulate the signal > before the noise is added to it. So you already know what the > noiseless signal looks like. As I said in the OP, Everything is known about the transmitted wave, >i.e., the shape & phase angle, except the amplitude. This works for the same reason reading a newspaper in a foreign >language is easy. You already know what they are going to say. Bret Cahill Are you familiar with the way a lockin amplifier works? form of filtering which is valuable in many situations where the noise is all over the spectrum. This is not filtering noise; it's measuring it then subtracting it. Basically the signal is brought to zero to identify the noise. Then the noise is subtracted from whatever the receiver is putting out. For an accurate signal measurement both the noise and the noise + signal output from the receiver must be known to a higher accuracy. Integrating should yield that higher accuracy but it isn't always necessary as it can work over one single higher frequency wave cycle . > That sounds > maybe like what you are doing. If you know everything about the signal > but its amplitude, then you have or can construct a normalized (unity > amplitude) version of it. That will positively correlate with the > unknown-amplitude version of the signal but have zero correlation to > random noise. Things like IR absorption spectrometers commonly chop (square wave > modulate) the light source and recover the signal with a synchronous > rectifier. That washes out any noise picked up in the optical path or > the detector. Things like this commonly dig signals out from 1000x the > noise... but slowly. If the noise is known to be bandlimited, it's a lot easier... almost > cheating. I ran it by a lawyer and he said it was completely legal. Bret Cahill === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. > All that is necessary is to recover is the amplitude of the wave. Can > this be done when the noise is several orders of magnitude greater > than the signal? > Bret Cahill > Narrowing the final detection bandwidth is the only hope. > If the noise spectrum is white, narrow bandwidth through > averaging works. If you cannot average, there is trouble. > The old lockin amplifiers used a modulation or chopping signal > and a long time constant in the final filter. I had signals > at times that required an hour of integration to detect. It > was slow but it worked. >I forgot to mention that the signal wave form can be anything that can >be generated. >(sint)(sin10t)(sin10t) was possible and the frequency of the noise was >about the same as the sin(t) factor, then f(t) will plot the noise >every time f(t) = 0. >In this case that would be ten times as often as the sin(t) factor. >The noise can then be subtracted to recover the wave form. >Bret Cahill > I think what's happening is that you have > 1. Defined the noise to be bandlimited to radian frequencies below > about 1 >The noise and the signal are both low and have about the same >frequency, ~ x/2pi. There is little that can be done to change this >situation. There is no time to wait more than several cycles for the >result either. > and > 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. >To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only >thing left is the low frequency noise. > You are assuming the ability to high-frequency modulate the signal > before the noise is added to it. So you already know what the > noiseless signal looks like. >As I said in the OP, Everything is known about the transmitted wave, >i.e., the shape & phase angle, except the amplitude. >This works for the same reason reading a newspaper in a foreign >language is easy. You already know what they are going to say. >Bret Cahill > Are you familiar with the way a lockin amplifier works? form of filtering which is valuable in many situations where the noise >is all over the spectrum. A lockin doesn't work by phase lag; it works by correlation. This is not filtering noise; it's measuring it then subtracting it. Basically the signal is brought to zero to identify the noise. Then >the noise is subtracted from whatever the receiver is putting out. That only works if the zero+measure thing is done at or above the noise's Nyquist frequency, and that is in turn only meaningful if the noise is bandlimited. And you are able somehow to turn the signal on and off at that rate. So all you need is a highpass filter. But the math algorithm you describe is about equivalent. For an accurate signal measurement both the noise and the noise + >signal output from the receiver must be known to a higher accuracy. Integrating should yield that higher accuracy but it isn't always >necessary as it can work over _one single higher frequency wave >cycle_. > That sounds > maybe like what you are doing. If you know everything about the signal > but its amplitude, then you have or can construct a normalized (unity > amplitude) version of it. That will positively correlate with the > unknown-amplitude version of the signal but have zero correlation to > random noise. > Things like IR absorption spectrometers commonly chop (square wave > modulate) the light source and recover the signal with a synchronous > rectifier. That washes out any noise picked up in the optical path or > the detector. Things like this commonly dig signals out from 1000x the > noise... but slowly. > If the noise is known to be bandlimited, it's a lot easier... almost > cheating. I ran it by a lawyer and he said it was completely legal. > I thought you *were* a lawyer. John === Subject: Re: Noise Is 3 Orders of Magnitude Greater Than A Wave Form posting-account=GQsqxgkAAABE8huAmNd_DrpbTQqYimU6 SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > That only works if the zero+measure thing is done at or above the > noise's Nyquist frequency, and that is in turn only meaningful if the > noise is bandlimited. The noise frequency is limited to about +/- 50% - 75% of the signal frequency. > And you are able somehow to turn the signal on and off at that rate. > So all you need is a highpass filter. You'ld lose the signal with a simple filter. > But the math algorithm you > describe is about equivalent. The signal is transformed to something that has a lot of the characteristics of the original signal. For example, the integral is 1/2 the integral of the original curve. The advantage is the transformed curve plots out the difference between the noise and the transformed signal. Then the noise is subtracted. That is not a conventional filter. Bret Cahill === === Subject: Counting the number of elements of a group that are not self-inverses If G is a finite group, then why does S = { x in G : x =/= x^{-1} have an even number of elements? I want to be able to prove this formally, instead of appealing to the usual hand-waving counting arguments. In particular, can an explicit bijection be constructed so as to prove the claim? Or, can we define an equivalence relation on S such that each equivalence class has an even number of elements? === Subject: Re: Counting the number of elements of a group that are not self-inverses If G is a finite group, then why does S = { x in G : x =/= x^{-1} have an even number of elements? I want to be able to prove this formally, instead of appealing to the usual hand-waving counting arguments. In particular, can an explicit bijection be constructed so as to prove the claim? Or, can we define an equivalence relation on S > such that each equivalence class has an even number of elements? HINT pair; involution... === Subject: Re: Counting the number of elements of a group that are not self-inverses posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20090630 Fedora/3.5-1.fc11 Firefox/3.5,gzip(gfe),gzip(gfe) > If G is a finite group, then why does S = { x in G : x =/= x^{-1} have an even number of elements? I want to be able to prove this formally, instead of appealing to the usual hand-waving counting arguments. There is no hand-waving in a correct counting argumeny. > In particular, can an explicit bijection be constructed so as to prove the claim? Or, can we define an equivalence relation on S > such that each equivalence class has an even number of elements? This is a *very* simple problem, specially in view of answers you've gotten for an earlier question. Do yourself a favor and think about it for whatever time it is necessary before reading to solution given to you by $RANDOM USENET USER WHO'S ALREADY DONE THE THINKING... -- m === Subject: Re: Counting the number of elements of a group that are not self-inverses > On Jul 2, 11:13pm, qsymmetry of elements? I want to be able to prove this formally, instead > of appealing to the usual hand-waving counting > arguments. There is no hand-waving in a correct counting > argumeny. In particular, can an explicit bijection be > constructed so as to prove the claim? Or, can we define an equivalence relation on S > such that each equivalence class has an even number > of elements? This is a *very* simple problem, specially in view > of answers you've gotten for an earlier question. > Do yourself a favor and think about it for whatever > time it is necessary before reading to solution given > to you by > $RANDOM_USENET_USER_WHO'S_ALREADY_DONE_THE_THINKING... And using caps to drive home your point makes you look like an ass. === Subject: Re: Counting the number of elements of a group that are not self-inverses <543503.67864.1246610391604.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20090630 Fedora/3.5-1.fc11 Firefox/3.5,gzip(gfe),gzip(gfe) > On Jul 2, 11:13pm, qsymmetry of elements? I want to be able to prove this formally, instead > of appealing to the usual hand-waving counting > arguments. There is no hand-waving in a correct counting > argumeny. In particular, can an explicit bijection be > constructed so as to prove the claim? Or, can we define an equivalence relation on S > such that each equivalence class has an even number > of elements? This is a *very* simple problem, specially in view > of answers you've gotten for an earlier question. > Do yourself a favor and think about it for whatever > time it is necessary before reading to solution given > to you by > $RANDOM USENET USER WHO'S ALREADY DONE THE THINKING... And using caps to drive home your point makes you look like an ass. Well, apparently you are not aware of standard conventions for naming environment variables... Oh well. $STANDARD USENET CLOSING -- m === Subject: Re: Counting the number of elements of a group that are not self-inverses because for every x in S, a distinct x^-1 is in S === Subject: Re: Solution to x^4+y^4 = z^2-1? > On Jul 2, 7:29am, TPiezas Hello all, Does x^4+y^4 = z^2-1 have a non-trivial soln in > the _integers_? (Note that x^4+y^4 = z^2+1 has plenty. The eqn > x^4+y^4 = z^2 has none, > so both cases are near-misses, but it seems only > the second has small > non-trivial solns.) P.S. I have checked all all {x,y} < 1000. - Titus Because x^4 + y^4 = z^4 - 1 has no solutions (all > integer solutions of > a^4 + b^4 + c^4 = d^4 have very high values, so for > c=1 it has no > solutions, forget the author), your z, not mine, > cannot be a square > number. If x^4+y^4 = z^4-1 has been proven to have no > non-trivial integer > solns, this does NOT imply that x^4+y^4 = z^2-1 has > none. (In the same > manner x^4+y^4 = z^4 does NOT reduce to x^2+y^2 = > z^2.) The question is still open. i didn't say it did, i said it implied your z cannot be a square number. please read posts you reply to properly to avoid pissing people off === Subject: Re: Solution to x^4+y^4 = z^2-1? <30985483.66879.1246587954747.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=-ACVjwoAAAAVqSiDl929-Pe1jSK2zs-Q 5.1),gzip(gfe),gzip(gfe) > On Jul 2, 7:29am, TPiezas Hello all, Does x^4+y^4 = z^2-1 have a non-trivial soln in > the integers ? (Note that x^4+y^4 = z^2+1 has plenty. The eqn > x^4+y^4 = z^2 has none, > so both cases are near-misses, but it seems only > the second has small > non-trivial solns.) P.S. I have checked all all {x,y} < 1000. - Titus Because x^4 + y^4 = z^4 - 1 has no solutions (all > integer solutions of > a^4 + b^4 + c^4 = d^4 have very high values, so for > c=1 it has no > solutions, forget the author), your z, not mine, > cannot be a square > number. If x^4+y^4 = z^4-1 has been proven to have no > non-trivial integer > solns, this does NOT imply that x^4+y^4 = z^2-1 has > none. (In the same > manner x^4+y^4 = z^4 does NOT reduce to x^2+y^2 = > z^2.) The question is still open. i didn't say it did, i said it implied your z cannot be a square number. please read posts you reply to properly to avoid pissing people off- Hide quoted text - - Show quoted text - - Titus === Subject: Re: Solution to x^4+y^4 = z^2-1? <30985483.66879.1246587954747.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=rQxmjAoAAABkK_bEn14LxyXccZYXFodO Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jul 2, 7:29am, TPiezas Hello all, Does x^4+y^4 = z^2-1 have a non-trivial soln in > the integers ? (Note that x^4+y^4 = z^2+1 has plenty. The eqn > x^4+y^4 = z^2 has none, > so both cases are near-misses, but it seems only > the second has small > non-trivial solns.) P.S. I have checked all all {x,y} < 1000. - Titus Because x^4 + y^4 = z^4 - 1 has no solutions (all > integer solutions of > a^4 + b^4 + c^4 = d^4 have very high values, so for > c=1 it has no > solutions, forget the author), your z, not mine, > cannot be a square > number. If x^4+y^4 = z^4-1 has been proven to have no > non-trivial integer > solns, this does NOT imply that x^4+y^4 = z^2-1 has > none. (In the same > manner x^4+y^4 = z^4 does NOT reduce to x^2+y^2 = > z^2.) The question is still open. i didn't say it did, i said it implied your z cannot be a square number. please read posts you reply to properly to avoid pissing people off- Hide quoted text - - Show quoted text - - Titus Oh. A sulker. I was going to suggest a brute force search among the Pythagorean quadruples as they have a parameterisation. === Subject: Re: Adams schemes posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jun 19, 5:26am, Magdalena Moczydlowska I have one probably simple question how to prove a classical > convergence for Adams method ? Maybe somebody has a pdf file with exact and detailed proof? Magdalena The usual dictum for numerical ODE methods is that convergence = consistency + stability. Proof of consistency is usually easy enough, plugging in a Taylor series expansion of the exact solution and showing that the proposed scheme's local truncation error tends to zero with decreasing step size. In this respect the explicit Adams- Bashforth and implicit Adams-Moulton methods have comparable orders of accuracy for equal numbers of terms used in the interpolation of function values (multi-step schemes). The implicit Adams-Moulton schemes have better stability than the explicit Adams-Bashforth schemes. There are predictor-corrector combinations that use the explicit forms to produce an initial guess for the (neceesarily iterative) solutions of the implicit forms. Some brief lecture notes here may be helpful, at least in providing the requisite definitions: http://www.math.ucdavis.edu/~guy/teaching/228b/lecturenotes01-15.pdf Let me know if you'd like more details about a method of a particular order. === Subject: Re: Adams schemes > I think that you do not understand me I was thinking about Adams > scheme as a multistep method. The reply to your original message was written by some one entirely uninterested in your question. The individual can be safely ignored. As to your question, I am unable to answer it. You could try posting your question to sci.math.num-analysis. Good luck. -- Michael Press === Subject: Re: Help. What is a model? Jack Marakam said > David and I are not contradicting each another. We're > both right. I've already explained in detail. > Why are you just ignoring the information I posted for your benefit? Read the posts. You do contradict each other. > By the way, I didn't use the expression mapping > function. It's > redundant. A function is a mapping; a mapping is a > function. Saying 'mapping function' doesn't give any incorrect information. I'll take your comment as intended to be quirkily humorous rather than demonstrative of an obsessive need to appear superior to every one else. > A structure is a certain kind of function. We say > that a structure is > a structure FOR a LANGUAGE. Then, given a particular > structure, we > define another function, which is a function from the > set of sentences > into {0 1} (for false, true, respectively). Then we > say a structure is > a model OF a theory iff every sentence in the theory > evaluates to true > per the function on sentences that we defined per the > structure. So > every model is a structure. And every structure is a > model since every > structure is a model of the set of valid (logically > true) sentences. So, every structure is a model and every model is a structure. If that is the case, then there terms model and structure are synonymous, and are simply different names for the same thing. Now, a structure is defined as consisting of a domain, a signature, and an interpretation function that maps every function/relation of the signature to any function/relation at all, provided the arity is the same. And you say that a structure is a model of a theory iff every sentence in the theory evaluates to true. But unless you can define what 'true' means then you haven't defined the interpretation function, and you haven't defined what a model/structure is. So without a definition of truth, model theory is as indefinable as the notion of truth. > One can indeed > define real numbers in different ways, but the > proof that there > does not exist any mapping of the naturals to the > reals depends on > real numbers being specifically defined as > infinite sums of > rationals, > such as in decimal notation. WRONG. (1) We don't (ordinarily) define reals to be > such infinite > sums. I don't know who you mean by 'we, and why that 'we' carries more authority than any other 'we'. Real numbers are commonly defined in such terms (although it is more correct to state that irrational numbers can be defined as the limiting value of infinite sums of rationals of decreasing size such as given by decimal notation). > (2) The proof of uncountability depends only > on the reals being > a carrier set for a complete ordered field. WHATEVER > definition of 'is > a real number', as long as the set of them is a > carrier set of a > complete ordered field, that set is uncountable. You say that I am wrong (note: putting 'wrong' in capital letters doesn't add anything to support that belief). You talk about ordered fields. The definition of an ordered field includes the concepts of 'greater than' and 'less than'. Evidently these concepts do not apply to all things, so a complete definition of 'greater than' and 'less than' must make it completely clear as to what things these concepts apply to. In order to define 'greater than' or 'less than' requires certain definitions of number. So the definition of an ordered field inherently includes the definition of certain properties of natural numbers - properties that generate the concept of division, which itself generates the concept of rational numbers. So the definition of an ordered field inherently defines the rational numbers. So how do you define 'less than' for the definition of an ordered field, without using a circular definition? For example, if you define 'less than' for natural numbers, you might state that a natural number a is greater than another natural number b if it is not equal to that number and if there exists a natural number c where a - b = c. That indeed gives a definition of less than, but it only applies to natural numbers. Similarly, if you define 'less than' for rational numbers, you might state that a positive rational number d is greater than another rational number e if it is not equal to that number and if there exists a positive rational number f where d - e = f. Again we have a definition of less than, which only applies to rational numbers. So how is 'less than' or 'greater than' defined for an ordered field and which applies to real numbers, without real numbers themselves first being defined? > I don't see what that has to do with the concept of > a function that > maps propositions of a formal system to truth > values of true or > false. You shouldn't be having such a difficult time with > this concept. A structure for a language is a certain kind of > function from a > certain subset of the set of symbols. Then we build > on that to provide > a certain function from the set of formulas. To say what exactly the function is, depends on the > PARTICULAR > function, just as with many ordinary functions. If I > say, f is a > function on the set of real numbers, or f is a 1-1 > function or f > is an isomorphism, I'm just telling you what KIND of > function f is; > and if we need to know the specific values for f, > then that will > depend on what specific function f is. The same for > structures. A > structure is a certain KIND of function. What it's > values are depend > on what SPECIFIC function (from among many that are > of the KIND that > we say is a structure) we are talking about. The problem I have with your explanations is that there is no definite general specification for a function for a model. And if you do not have a clear and definite specification for such a function, then how can you say that you actually have defined in general terms what a model is? I would make the analogy of having a specification for software which has some intended purpose. If it is clearly defined then there may be many ways of accomplishing the same result. So although the specification does not define any particular software program, that does not mean that it is not a clear and precise specification that can be defined in very definite terms. And since your 'definition' of a model is dependent on the notion of truth which is an indefinable notion, it is not a specification for anything at all. === Subject: Re: Help. What is a model? > The problem I have with your explanations is that > there is no definite general specification for a > function for a model. And if you do not have a clear > and definite specification for such a function, then > how can you say that you actually have defined in > general terms what a model is? Suppose I ask, if one has not specifically described a procedure to take the limit of a function, does a limit not exist? In fact, knowing the limit depends on the procedure that defines it. The model that results depends only on the distinction between a continuous function--in which case f(x)has no limit--and the behavior of f(x) near some point of the limit. > I would make the analogy of having a specification > for software which has some intended purpose. If it > is clearly defined then there may be many ways of > accomplishing the same result. So although the > specification does not define any particular software > program, that does not mean that it is not a clear > and precise specification that can be defined in very > definite terms. > And since your 'definition' of a model is dependent > on the notion of truth which is an indefinable > notion, it is not a specification for anything at all. I must have missed the part of this discussion that holds that truth is indefinable; truth is very precisely defined in mathematics. If a theorem were not a true mathematical statement, mathematics would be empty of meaning. In any case, a computing program does not model continuous functions. A computer model, therefore, is a result to arbitrary precision and not a precise specification. Tom === Subject: Re: Help. What is a model? > In any case, a computing program does not model continuous > functions. On the contrary, all computable real functions are continuous. As to the definition of truth, there is no mathematical definition of a true mathematical statement -- indeed there can be no such definition since mathematical statement is not a mathematically defined notion. In logic we do have a definition of truth for any number of mathematically defined classes of mathematical statements, e.g. those in the language of arithmetic, analysis, and so on. These definitions do not involve the notion of a mathematical theorem, since this notion again has no mathematical definition. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Help. What is a model? In any case, a computing program does not model > continuous > functions. On the contrary, all computable real functions are > continuous. As to the definition of truth, there is no > mathematical definition of > a true mathematical statement -- indeed there can be > no such > definition since mathematical statement is not a > mathematically > defined notion. In logic we do have a definition of > truth for any > number of mathematically defined classes of > mathematical statements, > e.g. those in the language of arithmetic, analysis, > and so on. These > definitions do not involve the notion of a > mathematical theorem, since > this notion again has no mathematical definition. > I find your philosophy strained and artificial. The utility of mathematics depends very much on defining the boundary conditions of truth, and the meaning of a continuous function. While it is true that all real functions are continuous, it is not helpful to qualify computable functions in that domain, when finite limits are arbitrary. The mathematical definition of theorem is true mathematical statement. If you can't reach that level in formal logic, you are not doing mathematics. Tom > -- > Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > s Logico-Philosophicus === Subject: Re: Help. What is a model? > While it is true that all real functions are continuous, it is not > helpful to qualify computable functions in that domain, when finite > limits are arbitrary. I'm unable to make anything of this sentence. Perhaps you're using real function in some sense other than the usual? > The mathematical definition of theorem is true mathematical > statement. This is not a mathematical definition at all. > If you can't reach that level in formal logic, you are not doing > mathematics. The conclusion is inescapable, no one is doing mathematics. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Help. What is a model? While it is true that all real functions are > continuous, it is not > helpful to qualify computable functions in that > domain, when finite > limits are arbitrary. I'm unable to make anything of this sentence. Perhaps > you're using > real function in some sense other than the usual? > What do you regard as the usual? > The mathematical definition of theorem is true > mathematical > statement. This is not a mathematical definition at all. > It most certainly is. > If you can't reach that level in formal logic, you > are not doing > mathematics. The conclusion is inescapable, no one is doing > mathematics. > You cannot escape that conclusion only because you've disallowed conclusion-making tools. As I claimed, the logic is strained and artificial. Tom > -- > Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > s Logico-Philosophicus === Subject: Re: Help. What is a model? > What do you regard as the usual? Just the usual: a real function is a function from reals to reals. For the common definitions of computability of such functions, any computable real function is continuous. > It most certainly is. No, The mathematical definition of theorem is true mathematical statement. is simply nonsense since the proposed definition involves the notion of a true mathematical statement which has no mathematical definition. In standard usage theorem also does not mean true mathematical statement; in standard usage a theorem is rather a mathematical statement for which a proof has been given. (In mathematical logic theorem is used also in a technical, mathematically defined sense.) -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Help. What is a model? What do you regard as the usual? Just the usual: a real function is a function from > reals to reals. For > the common definitions of computability of such > functions, any > computable real function is continuous. Then what do you mean by continuous? No mechanical algorithm can model a continuous function except to arbitrary precision. It is one thing to prove that all real functions are continuous. It is quite another to speak of a continuous function without boundary conditions--conditions which are imposed arbitrarily. My comments are addressed to the OP's topic. A model is a result to arbitrary precision of domain and boundary conditions that are freely chosen. > It most certainly is. No, The mathematical definition of theorem is true > e mathematical > statement. is simply nonsense since the proposed definition > involves the notion > of a true mathematical statement which has no > mathematical > definition. In standard usage theorem also does not mean true > mathematical > statement; in standard usage a theorem is rather a > mathematical > statement for which a proof has been given. (In > mathematical logic > theorem is used also in a technical, mathematically > defined sense.) > I don't know whose standard usage you're referring to, but we are not going to agree. Apparently, you think logicism drives mathematics. I'm afraid it's the other way around. Tom > -- > Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man > schweigen > - Ludwig Wittgenstein, Tractatus > s Logico-Philosophicus === Subject: Re: Help. What is a model? > But unless you can define what 'true' means then you haven't defined > the interpretation function, and you haven't defined what a > model/structure is. A peculiar line of thought. > So without a definition of truth, model theory is as indefinable as > the notion of truth. Why not look up the definition? -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Help. What is a model? David Ulrich said > There _is_ a precise definition of model, as a > certain function. > The definition does not specify what function that > should be. > So what? It's precisely the same to say that there is > a precise > definition of real number, namely a real number is > S(d1, d2, ...) for some sequence of digits d_1, d_2, > .... > Your complaint about the definition of model not > specifying what function we're talking about makes > exactly as much sense as complaining that the > definition > of real number does not specify what sequence d_1, > ... > we're talking about. Yes, but you are still ignoring the fact that we do have a general function that represents a real number in general, but the problem is that you have no function that is a general function for a model. I can take, for example, the real numbers 0.1234567 and 0.1234568, and thereby define a subset of real numbers, the set of all real numbers between those two values. You appear to have no comparable way of defining a subset of your set of all model functions. === Subject: a^6+b^6+c^6 = d^6+e^6+f^6 posting-account=-ACVjwoAAAAVqSiDl929-Pe1jSK2zs-Q 5.1),gzip(gfe),gzip(gfe) Hello all, 1. The smallest soln to a^k+b^k+c^k = d^k+e^k+f^k for k = 5, [24, 28, 67] = [3, 54, 62] is also good for k = 1. In fact, for an exhaustive table with terms < 1000, almost 2/3 are for k = 1,5. See table at http://www3.alpha-net.ne.jp/users/fermat/533e.html. 2. The smallest soln for k = 6, [2,17, 40] = [6, 32, 33] is also good for k = 2. For terms < 1000, an even higher percentage of almost 3/4 are for k = 2,6. See table at http://www3.alpha-net.ne.jp/users/fermat/633e.html. Why this tendency to be multi-grade for higher powers? - Titus === Subject: Re: Why choice rules > On my math blog Penny Hassett had a comment that got me to thinking > and after pondering at her suggestion what others believe to be true > in their disagreements with me about a certain serious mathematical > issue, I concluded that infinity could help to clear the air. So I have simple examples yet again to start (believe me it gets > really hard later so please pay close attention to the easy part): 7(x^2 + 3x + 2) = (7x + 7)(x + 2) trivial and let the ring be the ring of algebraic integers. And notice that > reflects CHOICE. My choice for a simple example as the 7 can be > factored an INFINITY of ways!!! After all, 7(x^2 + 3x + 2) = (x + 1)(7x + 14) 7(x^2 + 3x + 2) = 7*(x + 1)(x + 2) OK now what ? is ALSO just as valid mathematically, and in fact there are an > infinity of possible variations all equally valid. so what? your just multiplying some number by another Key here also to notice is that there are an infinity of choices FOR > EVERY x, and remember the ring is the ring of algebraic integers. So far easy and there should be no disagreement with the above! Now to the hard mathematics. Now we'll TRY to assume the ring is still the ring of algebraic > integers and now a harder example: 7(175x^2 - 15x + 2) = (5(7)b_1(x) + 7)(5b_2(x) + 2) where 7b_1(x) = a_1(x) and b_2(x) = a_2(x) + 1 and the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0. Notice the b's are chosen such that when x=0, both the b's equal 0, > which is to say, they are normalized. and........ Now just like before you have human choice, and you can imagine moving > that 7 around easily enough: 7(175x^2 - 15x + 2) = (5b_1(x) + 1)(5(7)b_2(x) + 14) which is just one more human choice out of infinity. And there are an INFINITY of possibilities for EVERY x. Every x has > an infinite number of choices. So how does the mathematics choose? It doesn't. I did. I chose. yes, you like the 7.......... But that's where the fights start and the arguing and the dead math > journal comes into the picture as what follows from mathematical logic > and the rigidity of infinity is a conclusion that is devastating > emotionally to thousands of mathematicians around the world which is > that there is a core error: the ring of algebraic integers gives a > false result. could you make that sentance shorter? Because now you have that one of the a's has 7 as a factor by the > choice argument. But the a's are roots of a^2 - (7x-1)a + (49x^2 - 14x) = 0 and at x=1, that gives a^2 - 6a + 35 = 0 and provably in the ring of algebraic integers NEITHER of the roots > can have 7 as a factor and there is shown the direct contradiction. one 7 goes in, one 7 comes out no contridiction! Notice the ring of algebraic integers does not fail gracefully and its > error is not fixable as your alternative is to introduce some mystical > force to choose out of infinity, like, maybe God? 7 is no good. Use 19, its much better. (Posters have been remarkably vague in past arguments about how a > particular factor of 7 arises, often simply repeating what is taught > in math classes about ways to find the factors at any particular x, > but remember there are an infinity of choices for EVERY x, so the > choice problem gives you infinity at every point. So who chooses? > God?) it is the negitive root you keep missing. Negitive square root. But not even God can choose for you here if you go with mathematical > logic. Of course, you can like so many human beings before you simply > choose to believe in what you've been taught, even though it is very, > very wrong. You may call me god, several others do. The mystical nature of the disagreement with me is remarkable but I > think it's natural for human beings to turn to spirits or mystical > forces in the face of something difficult to understand. That's what > your ancestors did. your ancestors were all trolls. But then you're no longer really mathematicians. > James Harris and you're a mathematiticn now === Subject: Re: A FEATURE OF POSTSCIENTISM posting-account=Lz-LbgoAAABPDavKeW-eYeobwLHD_cvQ CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > A few years ago a serious analysis of the foundations of > thermodynamics produced the conclusion that the law of entropy > increase is actually a RED HERRING: http://philsci-archive.pitt.edu/archive/00000313/ > Jos Uffink: Bluff your Way in the Second Law of Thermodynamics If such a radical criticism had been published 40-50 years ago, the > reaction of the establishment would have ben both energetic and > hostile (remember Herbert Dingle's saga for instance). In 2001 there > was no reaction, except for a few vague positive(!) references. A few months ago another serious analysis produced the conclusion that > Einstein's relativity is an ideology, not a science: http://www.informaworld.com/smpp/content~content=a909857880 > Peter Hayes: The Ideology of Relativity: The Case of the Clock > Paradox Again the reaction is silence: no hostility coming from the > establishment. The feature of Postscientism (generally, it is a > feature of Postmodernism) that explains this state of affairs consists > in the fact that official science has adopted ALL possible > alternatives and so has become unassailable. Just an example of > radical heresy advanced by official science that discourages any > genuine criticism: Paul Davies: Was Einstein wrong? Einstein's famous equation E=mc2 is > the only scientific formula known to just about everyone. The c here > stands for the speed of light. It is one of the most fundamental of > the basic constants of physics. Or is it? In recent years a few > maverick scientists have claimed that the speed of light might not be > constant at all. Shock, horror! Does this mean the next Great > Revolution in Science is just around the corner? Education in the era of Postscientism: ....the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co- exist. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS0 000690000S1000S24000001 Student understanding of time in special relativity: Simultaneity and reference frames, American Journal of Physics -- July 2001 -- Volume 69, Issue S1, pp. S24-S35 Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity HARMONIOUSLY co-exist. In Big Brother's world this would be referred to as students exercise themselves in doublethink: http://www.liferesearchuniversal.com/1984-17.html#seventeen George Orwell: Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them. The Party intellectual knows in which direction his memories must be altered; he therefore knows that he is playing tricks with reality; but by the exercise of doublethink he also satisfies himself that reality is not violated. The process has to be conscious, or it would not be carried out with sufficient precision, but it also has to be unconscious, or it would bring with it a feeling of falsity and hence of guilt. Doublethink lies at the very heart of Ingsoc, since the essential act of the Party is to use conscious deception while retaining the firmness of purpose that goes with complete honesty. To tell deliberate lies while genuinely believing in them, to forget any fact that has become inconvenient, and then, when it becomes necessary again, to draw it back from oblivion for just so long as it is needed, to deny the existence of objective reality and all the while to take account of the reality which one denies - all this is indispensably necessary. Even in using the word doublethink it is necessary to exercise doublethink. For by using the word one admits that one is tampering with reality; by a fresh act of doublethink one erases this knowledge ; and so on indefinitely, with the lie always one leap ahead of the truth. See more educational challenges offered by Einstein's 1905 false light postulate here: Pentcho Valev pvalev@yahoo.com === Subject: Re: A FEATURE OF POSTSCIENTISM > [...] I snipped the whole thing because by now most everyone knows your message/agenda. At this point I cannot help but think, What if Valev is correct? Bring on a new physics! === Subject: one posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Discussions - sci.math | Google Groups On my math blog Penny Hassett had a comment that got me to thinking and after pondering at her suggestion what others believe to be true in ...http:// Google Groups Group categories: Science and Technology > Math .... abstracts of math publications (requires subscription).http://ams.org/ mathscinet SciMath C/C++ Scientific Math LibrarySciMath C/C++ Scientific Math Library provides advanced functions in most areas of math and is available for a wide range of applications and for a variety ...http://www.scimath.com/ Welcome to SciMath MN Minnesota students are performing very well in math and science compared to students from other nations. Minnesota students were near the top in === all 4th-and ...http://www.scimathmn.org/ Sci Math FAQ Index Subject: sci.math FAQ: Which are the 23 Hilbert Problems? Maintainer: alopez- === o@neumann.uwaterloo.ca ... Subject: sci.math FAQ: e^(i Pi) = -1 Euler's formula ...http://www.faqs.org/faqs/sci-math-faq/ Open Directory - Science: Math29 Mar 2009 ... Kids and Teens: School Time: Math (311); Recreation: Humor: Science: Mathematics (24); Society: Philosophy: Philosophy of Science: ...http://www.dmoz.org/ Science/Math/Information for readers of sci.math.research Charter and useful information for this moderated research-level newsgroup .http:// www.math.uiuc.edu/sci.math.research/ Frequently Asked Questions in Mathematics The Sci.Math FAQ Team. Editor: Alex L.97pez-Ortiz ... The Math FAQ is a so-called living document, meaning that changes and updates are constantly being ...http://www.cs.uwaterloo.ca/~alopez-o/ math-faq/math-faq.html === Subject: Calculus How to type euqations here === Subject: Re: Calculus > How to type equations here a + b a plus b ab a times b a/b a divided by b a^x a to the x-th power Use ample parenthesis to avoid ambiguity. Use sufficient spaces so the equation is easy to read. Put each equation on a separate line. If equation is long break it into another line at places where the larger expressions are kept intact. integral f(x) dx the integral of f(x) with respect to x integral(a,b) f(x) dx the integral of f(x) with respect to x from a to b sum(j=1,n) a_j the sum from j = 1 to n of a_j / intersection / union A - B set difference AB set difference Tex not recommended unless it's very simple Tex. === Subject: Re: Calculus How to type euqations here See http://aah.ryan-usa.com/node15.html. -- Which of the seven heavens / Was responsible her smile / Wouldn't be sure but attested / That, whoever it was, a god / Worth kneeling-to for a while / Had tabernacled and rested. === Subject: Re: Calculus > How to type euqations here With your keyboard or if you want to get all fancy you can buy the new anal probes that read your mind directly and output the results to the computer. === Subject: Re: conundrum of Wikipedia-- no original research and lynch mob consensus and Hales withdrawal of a sham Kepler Packing proof #670 new book 2nd edition: New True Mathematics posting-account=EaHY-goAAAAAUhMOLgvAr8pNABGrrcS7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jul 3, 1:56pm, Archimedes Plutonium > My comments below as to how mathematics is politically run > by a band of politico mathematicians via a control of the > publishing of mathematics. And how even when a Counterexample > to their alleged proofs is given, that they just ignore it. In the past week I have found a counterexample to Kepler > Packing that defeats the Hales's alleged proof. I have shown > a packing that is greater than Hales's reliance on Hexagonal > Close Packing. So I take the liberty of posting Wikipedia's sort of propaganda > on this issue and their prejudice of no original research but > a continual pandering of fake math proofs. See my below comments. --- quoting Wikipedia in entirety on Kepler conjecture since > this is likely to be chitcanned in the future and where > it is impossible to retreive, so I take the liberty of preserving > this on the sci.math Usenet so that it can be seen in the future > ---http://en.wikipedia.org/wiki/Kepler conjecture Kepler conjecture > Jump to: navigation, search > Face-centered cubic packing The Kepler conjecture, named after Johannes Kepler, is a mathematical > conjecture about sphere packing in three-dimensional Euclidean space. > It says that no arrangement of equally sized spheres filling space has > a greater average density than that of the cubic close packing (face- > centered cubic) and hexagonal close packing arrangements. The density > of these arrangements is slightly greater than 74%. In 1998 Thomas Hales, currently Andrew Mellon Professor at the > University of Pittsburgh, announced that he had a proof of the Kepler > conjecture. Hales' proof is a proof by exhaustion involving checking > of many individual cases using complex computer calculations. Referees > have said that they are 99% certain of the correctness of Hales' > proof. So the Kepler conjecture is now very close to being accepted as > a theorem. > Contents > [hide] * 1 Background > * 2 Origins > * 3 Nineteenth century > * 4 Twentieth century > * 5 Hales' proof > * 6 A formal proof > * 7 Related problems > * 8 References > * 9 External links [edit] Background > Diagrams of cubic close packing (left) and hexagonal close packing > (right). Imagine filling a large container with small equal-sized spheres. The > density of the arrangement is the proportion of the volume of the > container that is taken up by the spheres. In order to maximize the > number of spheres in the container, you need to find an arrangement > with the highest possible density, so that the spheres are packed > together as closely as possible. Experiment shows that dropping the spheres in randomly will achieve a > density of around 65%. However, a higher density can be achieved by > carefully arranging the spheres as follows. Start with a layer of > spheres in a hexagonal lattice, then put the next layer of spheres in > the lowest points you can find above the first layer, and so on - this > is just the way you see oranges stacked in a shop. This natural method > of stacking the spheres creates one of two similar patterns called > cubic close packing and hexagonal close packing. Each of these two > arrangements has an average density of frac{pi}{sqrt{18}} simeq 0.74048. The Kepler conjecture says that this is the best that can be done.84no > other arrangement of spheres has a higher average density. [edit] Origins The conjecture is named after Johannes Kepler, who stated the > conjecture in 1611 in Strena seu de nive sexangula (On the Six- > Cornered Snowflake). Kepler had started to study arrangements of > spheres as a result of his correspondence with the English > mathematician and astronomer Thomas Harriot in 1606. Harriot was a > friend and assistant of Sir Walter Raleigh, who had set Harriot the > problem of determining how best to stack cannon balls on the decks of > his ships. Harriot published a study of various stacking patterns in > 1591, and went on to develop an early version of atomic theory. [edit] Nineteenth century Kepler did not have a proof of the conjecture, and the next step was > taken by German mathematician Carl Friedrich Gauss, who published a > partial solution in 1831. Gauss proved that the Kepler conjecture is > true if the spheres have to be arranged in a regular lattice. This meant that any packing arrangement that disproved the Kepler > conjecture would have to be an irregular one. But eliminating all > possible irregular arrangements is very difficult, and this is what > made the Kepler conjecture so hard to prove. In fact, there are > irregular arrangements that are denser than the cubic close packing > arrangement over a small enough volume, but any attempt to extend > these arrangements to fill a larger volume always reduces their > density. After Gauss, no further progress was made towards proving the Kepler > conjecture in the nineteenth century. In 1900 David Hilbert included > it in his list of twenty three unsolved problems of mathematics.84it > forms part of Hilbert's eighteenth problem. [edit] Twentieth century The next step towards a solution was taken by Hungarian mathematician > L.87szl.97 Fejes T.97th. In 1953 Fejes T.97th showed that the problem of > determining the maximum density of all arrangements (regular and > irregular) could be reduced to a finite (but very large) number of > calculations. This meant that a proof by exhaustion was, in principle, > possible. As Fejes T.97th realised, a fast enough computer could turn > this theoretical result into a practical approach to the problem. Meanwhile, attempts were made to find an upper bound for the maximum > density of any possible arrangement of spheres. English mathematician > Claude Ambrose Rogers established an upper bound value of about 78% in > 1958, and subsequent efforts by other mathematicians reduced this > value slightly, but this was still a long way above the cubic close > packing density of 74%. There were also some failed proofs. American architect and geometer > Buckminster Fuller claimed to have a proof in 1975, but this was soon > found to be incorrect.[1] In 1993 Wu-Yi Hsiang at the University of > California, Berkeley published a paper in which he claimed to prove > the Kepler conjecture using geometric methods. Some experts countered, > claiming he gave insufficient support for some of his claims. Although > nothing incorrect per se was found in Hsiang's work, general consensus > has been reached, concluding that Hsiang's proof is incomplete. One of > the most vocal critics was Thomas Hales, who at the time was working > on his own proof. [edit] Hales' proof Following the approach suggested by Fejes T.97th, Thomas Hales, then at > the University of Michigan, determined that the maximum density of all > arrangements could be found by minimizing a function with 150 > variables. In 1992, assisted by his graduate student Samuel Ferguson, > he embarked on a research programme to systematically apply linear > programming methods to find a lower bound on the value of this > function for each one of a set of over 5,000 different configurations > of spheres. If a lower bound (for the function value) could be found > for every one of these configurations that was greater than the value > of the function for the cubic close packing arrangement, then the > Kepler conjecture would be proved. To find lower bounds for all cases > involved solving around 100,000 linear programming problems. When presenting the progress of his project in 1996, Hales said that > the end was in sight, but it might take a year or two to complete. > In August 1998 Hales announced that the proof was complete. At that > stage it consisted of 250 pages of notes and 3 gigabytes of computer > programs, data and results. Despite the unusual nature of the proof, the editors of the Annals of > Mathematics agreed to publish it, provided it was accepted by a panel > referee's panel G.87bor Fejes T.97th (son of L.87szl.97 Fejes T.97th) reported > that the panel were 99% certain of the correctness of the proof, but > they could not certify the correctness of all of the computer > calculations. computer part of his proof in detail. The Annals of Mathematics is going ahead with publishing the > theoretical portions of Hales' proof. The computational portions will > be published in a separate journal, Discrete and Computational > Geometry. [edit] A formal proof to produce a complete formal proof of the Kepler conjecture. The aim > is to remove any remaining uncertainty about the validity of the proof > by creating a formal proof that can be verified by automated proof- > checking software such as HOL. This project is called Project FlysPecK > - the F, P and K standing for Formal Proof of Kepler. Hales estimates > that producing a complete formal proof will take around 20 years of > work. [edit] Related problems Thue's theorem > The regular hexagonal packing is the densest sphere packing in the > plane. (1890)The 2-dimensional analog of the Kepler conjecture; the > proof is elementary. The hexagonal honeycomb conjecture > The most efficient partition of the plane into equal areas is the > regular hexagonal tiling. Hales' proof (1999).Related to Thue's > theorem. The dodecahedron conjecture > The volume of the Voronoi polyhedron of a sphere in a packing of equal > spheres is at least the volume of a regular dodecahedron with inradius > 1. McLaughlin's proof, for which he received the 1999 Morgan Prize.A > related problem, whose proof uses similar techniques to Hales' proof > of the Kepler conjecture. Conjecture by L. Fejes T.97th in the 1950s. The Kelvin problem > What is the most efficient foam in 3 dimensions? This was conjectured > to be solved by the Kelvin structure, and this was widely believed for > over 100 years, until disproved by the discovery of the Weaire[CapitalEth]Phelan > structure. The surprising discovery of the Weaire[CapitalEth]Phelan structure and > disproof of the Kelvin conjecture is one reason for the caution in > accepting Hales' proof of the Kepler conjecture. Sphere packing in higher dimensions > The optimal sphere packing question in dimensions bigger than 3 is > still open. [edit] References 1. ^ Weistein, Eric W., Kepler Conjecture from MathWorld. ISBN 0-471-08601-0 > KiB)[dead link] > * Thomas C. Hales (1999) Cannonballs and Honeycombs. An elementary > exposition of the proof of the Kepler conjecture. > * T. Aste and D. Weaire The Pursuit of Perfect > Packing (Institute Of Physics Publishing London 2000) ISBN > 0-7503-0648-3 [edit] External links * Thomas Hales' home page > * Overview of Hales' proof > * Article in American Scientist by Dana Mackenzie > * Flyspeck I: Tame Graphs, verified enumeration of tame plane > graphs as defined by Thomas C. Hales in his proof of the Kepler > Conjecture --- end quotinghttp://en.wikipedia.org/wiki/Kepler conjecture--- Many of my items edited into Wikipedia in past years were > dismissed as original research. But when some mathematician > from a established university makes a claim of a proof and all there > really is is a buzz noise background and yet Wikipedia > fills the Kepler Packing Conjecture entry with Hales's offering, > saying it is 99% correct. If Wikipedia asked me, I would say > it is a forgone conclusion with the Counterexample that Hales is > touting a fakery. And an example of this hypocrisy of original research when it > comes to Archimedes Plutonium, but 99% correct when it > comes to Hales. A few weeks ago I outlined a proof that > Euclidean geometry Axiom of Betweenness contradicts the > Parallel Postulate. I showed a diagram of how the proof works: A > > | > | > | > B C You have two parallel lines and a triangle ABC. > As you can see B is a right-angle. Now as we move > C closer to B and closer and closer, since we have > the Betweenness Axiom that between any K and L > exists a M. So as you move C closer and closer, because > of that Betweenness Axiom the Dedekind limit of supremum > enters the picture and you end up with a triangle ABC > as having two right-angles. The fix is that Euclidean > Betweenness Axiom must read between any K and L > there is an M unless K and L are consecutive Reals. So here in a paragraph I give one of the most important > math proofs of our time and everyone can understand it > even nonmath people can understand it. And compare that > to Hales with a 250 page contraption that a committee has > to get together to decide whether to publish it because noone > has the foggiest of whether it is correct and where > Wikipedia says it is 99% correct. So what is the signal that the mathematics community sends > to the world. The signal is that no matter how logical or clear > one's proof or counterexample is, none of it is acceptable to the > math-politico-establishment. And the only thing acceptable to them > (mostly a bunch of gray old men), the only thing acceptable > to them is someone with a post at a major university with a > wild claim. Here I am showing how Betweenness Axiom contradicts Parallel > Postulate or showing how Corner-Edge-Hexagonal Packing is > greater than Hexagonal-alone, and just ignored. But when a > Hales trumpets a 250 arcane pages with nothing new about > packing, then the newsmedia heralds it as 99% correct. So where is the commonsense? Is mathematics as corrupt as > the halls of politics? Is mathematics more political than most > people understand? Obviously it is. If I were Hales, I would not be running away and hiding at this > moment. I would be defending his 250 pages against my > claim of a counterexample of Corner-Edge-Hexagonal is larger > of a packing than his Hexagonal-alone. Why is Hales running away and hiding? Archimedes Plutoniumwww.iw.net/~a plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies === Subject: Re: Computers, Logic, and the Single Event posting-account=-5a9CAoAAABl1C10M224pEnfD-yAElM_ .NET CLR 2.0.50727; InfoPath.1; FDM; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) I think we will find in the not-too-distant future that what we call > sentience and intelligence is a very simple side-effect of a > mathematically-modelable physical reaction - in which a knowledge of > self and its relationship to the external world is encoded. This is the point I always try to make when discussing AI on these threads with starry eyed posters who actually believe that computers are already intelligent and sentient philosopher robots are just a marketing program away from being released to the public. The knowledge of self and its relationship to the outside world are one of the key factors in differentiating between full consciousness and the current state of AI. This is not a trivial problem. Babies initially don't know that they are seperate from the rest of the universe and the process of learning this (through brain and nervous system) is one of the most traumatic experiences a human undergoes. === Subject: Re: An optimization problem > Hi Niels, > Monte Carlo approximation (not quite familiar with that technique but > in your solution it seems effective). Besides approximation, I am > actually trying to take the property of order statistics (since we are > considering a problem with ordered i.i.d. random variables) into > consideration. If some properties of C_i can be revealed, it may be > possible to approximate more accurately. > It's worth a try, but I don't think you will get much further without making > specific assumptions about the distribution. > Also, can you provide some more details about how you implement the > Monte Carlo approximation for the problem? My intuition is to generate > a large number of realizations and take the sample mean as the > theoretical mean value. I am not sure whether I understand it > Yes, that is what I meant. Here is the Python code I used. > ---------------------------------------------------------- > import random > def DISTRIBUTION(): > # replace this by any function returning random numbers with > # the right distribution > return random.random() > MCITER = 1000000 # Number of iterations of Monte Carlo method > # Note that precision increases with square root > # of this number > MAXVARS = 10 # Maximum number of variables > #################################################################### > C = [ 0.0 ] > for n in range(1, MAXVARS+1): > sum_exp = 0.0 > for iter in range(MCITER): > sample = sorted(DISTRIBUTION() for i in range(n)) > opt = min(sample[i] + C[n-i-1] for i in range(n)) > sum_exp = sum_exp + opt > C.append(sum_exp / MCITER) > print 'C_%d =' % n, C[-1] > ------------------------------------------------------- > Note that it takes a few minutes to run. > -- > Niels Diepeveen I notice that you are using the average value of equal weight for each > sample. It may be the case with uniform distribution, but will that > cause problems when the distribution of the random variables are not > uniform? No. Nothing below the ######### makes any assumptions about the distribution except that the central limit theorem applies, i.e. it must have finite variance. -- Niels Diepeveen === Subject: Re: michelson morley experiment questions > Peter, look: > Look at these preposterous situations created by the idea > of lack of simultaneiety: Preposterous to you. Obviously Special Relativity is correct, the evidence is overwhelming, > its routinely used in engineering and if it was wrong lots of things > wouldn't work (in some cases spectacularly). Just accept it as amazing. > I guess you don't understand block universe. It literally means > you are a mannikin voicing nonconsequential inanities. Well, if that is what the block Universe literally is, it is false, as I > am not literally a mannikin. > And you agree with it? > :) > Spirit of Truth With SR? Yes, of course. And I also agree that world is not flat, and that earth > revolves around the sun and not vice-versa. All well supported by > evidence. ........ ... ........ ... You are missing the point. SR gives the condition of simultaneity. That equals a blockhead universe where the future already exists. Thus you = nothing per Einstein's SR. I can assure you that you are not a nothing and do have free will....SO something is wrong in the state of SR. Spirit of Truth === Subject: Re: michelson morley experiment questions You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. Thus you = nothing per Einstein's SR. I can assure you that you are not a nothing and do have free > will....SO something is wrong in the state of SR. > Spirit of Truth I just don't remember SR addressing the subject of free will. Spirit, would you be so king as to cite appropriate literature? BTW, what's a blockhead universe? === Subject: Re: michelson morley experiment questions > You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. > Thus you = nothing per Einstein's SR. > I can assure you that you are not a nothing and do have free > will....SO something is wrong in the state of SR. > Spirit of Truth I just don't remember SR addressing the subject of free will. Spirit, would you be so king as to cite appropriate literature? BTW, what's a blockhead universe? ROTFL You are correct, Einstein did not realize it. If he had he would not have adopted LET and would have found the correct answer. Blockhead universe is the universe where you are acting out a pre-ordained event timeline that already exists. That imagined SR universe in which you are just a Robot. Spirit of Truth Spirit of Truth really been a gemius g b === Subject: Re: michelson morley experiment questions > I just don't remember SR addressing the subject of free will. > Spirit, would you be so king as to cite appropriate literature? > BTW, what's a blockhead universe? > ROTFL You are correct, Einstein did not realize it. If he had he would > not have adopted LET and would have found the correct answer. Blockhead universe is the universe where you are acting out > a pre-ordained event timeline that already exists. That > imagined SR universe in which you are just a Robot. > Spirit of Truth > So you are saying Einstein didn't have any choice... that he had to create SR and that you, Spirit don't have any choice about learning what SR really says. Pitiful, wouldn't you say? === Subject: Re: michelson morley experiment questions I just don't remember SR addressing the subject of free will. Spirit, would you be so king as to cite appropriate literature? BTW, what's a blockhead universe? > ROTFL > You are correct, Einstein did not realize it. If he had he would > not have adopted LET and would have found the correct answer. > Blockhead universe is the universe where you are acting out > a pre-ordained event timeline that already exists. That > imagined SR universe in which you are just a Robot. > Spirit of Truth So you are saying Einstein didn't have any choice... that he had > to create SR Exactly, but you need to _confront_ the fact and confronting it face up to the fact that it is nonsense and solve the matter so that lack of simultaneity is obliterated from the scientific literature so that the scientific community can again be restored to a state of respect and truth. Spirit of Truth > and that you, Spirit don't have any choice about > learning what SR really says. Pitiful, wouldn't you say? As an aside, what would be pitiful, Sam, would be an intelligent person like you burying your head in the sand. === Subject: Re: michelson morley experiment questions ROTFL You are correct, Einstein did not realize it. If he had he would > not have adopted LET and would have found the correct answer. Blockhead universe is the universe where you are acting out > a pre-ordained event timeline that already exists. That > imagined SR universe in which you are just a Robot. > Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR Exactly, but you need to _confront_ the fact and confronting it > face up to the fact that it is nonsense and solve the matter so > that lack of simultaneity is obliterated from the scientific > literature so that the scientific community can again be > restored to a state of respect and truth. > Spirit of Truth > > and that you, Spirit don't have any choice about > learning what SR really says. Pitiful, wouldn't you say? As an aside, what would be pitiful, Sam, would be an > intelligent person like you burying your head in the sand. No--you've already stated there is no free will... confronting does no good if there is no free will. According to you... you have no choice, I have no choice, Einstein had no choice, the scientific community has no choice... all cogs grinding along unable to change outcomes. === Subject: Re: michelson morley experiment questions > ROTFL > You are correct, Einstein did not realize it. If he had he would > not have adopted LET and would have found the correct answer. > Blockhead universe is the universe where you are acting out > a pre-ordained event timeline that already exists. That > imagined SR universe in which you are just a Robot. > Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR > Exactly, but you need to _confront_ the fact and confronting it > face up to the fact that it is nonsense and solve the matter so > that lack of simultaneity is obliterated from the scientific > literature so that the scientific community can again be > restored to a state of respect and truth. > Spirit of Truth > and that you, Spirit don't have any choice about > learning what SR really says. Pitiful, wouldn't you say? > As an aside, what would be pitiful, Sam, would be an > intelligent person like you burying your head in the sand. No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. Sam, not according to me. According to your religion, SR. Face up to the situation, lack of simultaneiety which means blockhead universe is bunk. Spirit of Truth === Subject: Re: michelson morley experiment questions > ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR Exactly, but you need to _confront_ the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about > learning what SR really says. Pitiful, wouldn't you say? As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. > No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. > Sam, not according to me. According to your religion, SR. This shows how little you know of science. Why do you enjoy being stupid? Face up to the situation, lack of simultaneiety which means > blockhead universe is bunk. > Spirit of Truth === Subject: Re: michelson morley experiment questions >ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR >Exactly, but you need to _confront_ the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about > learning what SR really says. Pitiful, wouldn't you say? >As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. > Sam, not according to me. According to your religion, SR. This shows how little you know of science. > Why do you enjoy being stupid? > Face up to the situation, lack of simultaneiety which means > blockhead universe is bunk. appear too unintelligent to understand truth, boy. Spirit of Truth === Subject: Re: michelson morley experiment questions > >ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR >Exactly, but you need to _confront_ the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about >learning what SR really says. Pitiful, wouldn't you say? >As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. > No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. >Sam, not according to me. According to your religion, SR. >This shows how little you know of science. >Why do you enjoy being stupid? >Face up to the situation, lack of simultaneiety which means >blockhead universe is bunk. appear too unintelligent to understand truth, boy. You come and spew nonsense and then have a childish tantrum when it is pointed out that you know nothing about science. Go ahead and cry and stomp your feet but it will not make you look like an adult. > Spirit of Truth === Subject: Re: michelson morley experiment questions >ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR >Exactly, but you need to _confront_ the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about >learning what SR really says. Pitiful, wouldn't you say? >As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. > No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. >Sam, not according to me. According to your religion, SR. This shows how little you know of science. >Why do you enjoy being stupid? >Face up to the situation, lack of simultaneiety which means >blockhead universe is bunk. > appear too unintelligent to understand truth, boy. You come and spew nonsense and then have a childish tantrum > when it is pointed out that you know nothing about science. > Go ahead and cry and stomp your feet but it will not make > you look like an adult. I guess you also think the Earth moves, dummie! Spirit of Truth === Subject: Re: michelson morley experiment questions <4a476d29$0$25358$afc38c87@news.optusnet.com.au> <4a483464$0$4046$afc38c87@news.optusnet.com.au> <69J3m.769906$yE1.198126@attbi_s21> posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) [...] > You come and spew nonsense and then have a childish tantrum > when it is pointed out that you know nothing about science. > Go ahead and cry and stomp your feet but it will not make > you look like an adult. I guess you also think the Earth moves, dummie! Spirit of Truth You think it doesn't? === Subject: Re: michelson morley experiment questions > >ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth >So you are saying Einstein didn't have any choice... that he had >to create SR >Exactly, but you need to _confront_ the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about >learning what SR really says. Pitiful, wouldn't you say? >As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. >No--you've already stated there is no free will... confronting >does no good if there is no free will. According to you... you >have no choice, I have no choice, Einstein had no choice, the >scientific community has no choice... all cogs grinding along >unable to change outcomes. >Sam, not according to me. According to your religion, SR. >This shows how little you know of science. >Why do you enjoy being stupid? >Face up to the situation, lack of simultaneiety which means >blockhead universe is bunk. appear too unintelligent to understand truth, boy. >You come and spew nonsense and then have a childish tantrum >when it is pointed out that you know nothing about science. >Go ahead and cry and stomp your feet but it will not make >you look like an adult. I guess you also think the Earth moves, dummie! > Spirit of Truth Ah yes, calling me a dummie. That is what passes for a scientific argument from you. Remember that you cranks are here for us educated people to laugh at. > === Subject: Re: michelson morley experiment questions <4a476d29$0$25358$afc38c87@news.optusnet.com.au> <4a483464$0$4046$afc38c87@news.optusnet.com.au> <69J3m.769906$yE1.198126@attbi_s21> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.7.STABLE6) >ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR >Exactly, but you need to confront the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about >learning what SR really says. Pitiful, wouldn't you say? >As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. > No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. >Sam, not according to me. According to your religion, SR. This shows how little you know of science. >Why do you enjoy being stupid? >Face up to the situation, lack of simultaneiety which means >blockhead universe is bunk. > appear too unintelligent to understand truth, boy. You come and spew nonsense and then have a childish tantrum > when it is pointed out that you know nothing about science. > Go ahead and cry and stomp your feet but it will not make > you look like an adult. > I guess you also think the Earth moves, dummie! > Spirit of Truth Stop the name calling! Pay attention and make intelligent comments. Appearances may deceive. The Poincare Conjecture reduces to a conjecture that a minumum of 9 points on the sphere arranged somewhat like this: . . . . . . . . . is the smallest simply-connected case. That the old Poincare Conjecture is false but a modified PC involving that 9 point matrix is true. This is because the Reals are discrete and have gaps in between consecutive Reals. But now notice I connect line segments to those 9 points shown above. I cannot do it even with ascii art so let me describe it. . . . forms one triangle and the next is . . . then there is . . . and finally there is . . . These four triangles leave the inside point unscathed so that this is the point that the Poincare loop shrinks to. The essence of the 4Color Mapping is that there is no fifth closed loop that can be adjacent to four closed loops that are adjacent. In other words four adjacent closed loops is the maximum. So now, let us relook at the above modified Poincare Conjecture with its surrounding four triangles of that 9 point lattice. Can you see where Poincare Conjecture has now merged as an equivalent statement as the 4 Color Mapping Problem? The minimum number of closed loops--triangles-- to satisfy Poincare Conjecture is 4, and the maximum closed loops to satisfy 4Color Mapping is of course 4. So, in essence 9 point matrix is related to adjacency maximum of 4. The essence of 4 Color Mapping is that there is never a 5th mutual adjacency, and I proved it using the Moebius theorem, but let us look at 4 Color Mapping as an alternate statement of the Poincare Conjecture. Here is 4 Color Mapping in its essence: MMMMMM MMMMMM BBJJJ BBJJJ Shown is the M country adjacent with B and J countries. So all three are mutually adjacent, meaning, each has a contact with the others. Now let us apply a 4th mutual adjacency in the form of O: MMMMMM MMMMMM BBJJJO BBJJJO OOOO Now, clearly, can you see why 4 mutual adjacency is a maximum? Can you see that a 5th is never allowed because the J country was covered over by the O country? Now here is the relevancy and relatedness to the Poincare Conjecture for the O country covering is the same as encircling of a country so that no other country can penetrate inside the covering up of J. That 4 Color Mapping is a question of the existence of a 5th mutual adjacency. And the reason you cannot have a 5th is because the 4th encircles one of the previous 3 countries. Now the Old-Poincare Conjecture says that all closed loops has a point inside for which that loop when it shrinks will always have that point inside. The New- Poincare Conjecture as outlined in this book says that the Old Poincare Conjecture is false because the points in Euclidean and Elliptic geometry are discrete with consecutive points and having gaps in between. So we need at least 9 consecutive points in such an array to have a Poincare Conjecture: . . . . . . . . . The middle point is the Poincare point where the surrounding points serve as the smallest loop. So when we shrink that loop we end up with that middle point. Now, can you see the similarity between the 4 Color Mapping and the New Poincare Conjecture? The J country above is the point in the middle of that Poincare array. In a sense, when you do the 4 Color Mapping you are doing a Poincare loop around 3 mutual adjacent countries and the 4th country that is mutually adjacent cuts off one of the other three countries by encircling it. What is the importance of these insights? Well for one it shows 4 Color Mapping is equivalent to New-Poincare Conjecture. But more important is that the 4 Color Mapping was not affected by the revelation that the points in Euclidean geometry were discrete and consecutive with holes in between consecutive Reals. The proof of 4 Color Mapping was not affected by that revelation. But the Old Poincare Conjecture was seen as false and had to be revised with a 9 point array. So here is the interesting good news about this equivalency. Since the 4 Color Mapping is a true theorem of mathematics with discrete and consecutive Reals, and if the only Poincare Conjecture that is true is the modified form where 9 point array then the 4Color Mapping in a sense destroys the Old Poincare Conjecture. So if you believe still that the Old Poincare Conjecture is true then it is contradictory to the 4 Color Mapping and that there is a 5th mutual adjacency. So can one use the Old Poincare Conjecture and devise a 5th mutual adjacency? Apparently one can do so because of the infinite downward regression of the old Betweenness axiom that given A and B is always a new C. P.S. the ironies of life are perhaps the most marvellous experiences of living. Because it was about 20 years ago that I started proving 4 Color is false and Poincare is true and here it is 20 years later that I am forced to say 4 Color was true and Poincare was false. I am saving this for future laughter and ridicule. It would be like if Wikipedia existed in the a flat planet where you fall off if you sailed at the edge. In light of the above posts of mine, that the 4Color Mapping is equivalent to a New-Poincare-Conjecture makes Wikipedia's write-up nothing but a bunch of hogwash. --- quoting Wikipedia --- http://en.wikipedia.org/wiki/Poincare conjecture (Redirected from Poincare conjecture) Jump to: navigation, search In mathematics, the Poincar.8e conjecture (French, pronounced [pw?Öka?e]) [1] is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. It began as a popular, important conjecture, but is now considered a theorem to the satisfaction of the awarders of the Fields medal. The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3- manifold). The Poincar.8e conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere. An analogous result has been known in higher dimensions for some time. For closed 2 dimensional surfaces, if every loop can be continuously tightened to a point, then the surface is a 2-sphere. The Poincar.8e conjecture attempts to determine if the same is true for closed 3- dimensional spaces. After nearly a century of effort by mathematicians, Grigori Perelman sketched a proof of the conjecture in the program of Richard Hamilton. Several high-profile teams of mathematicians have since verified the correctness of Perelman's proof. The Poincar.8e conjecture was, before being proven, one of the most important open questions in topology. It is one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution. Perelman's work survived review and was confirmed in 2006, leading to him being offered a Fields Medal, which he declined. The Poincar.8e conjecture remains the only solved Millennium problem. On December 22, 2006, the journal Science honored Perelman's proof of the Poincar.8e conjecture as the scientific Breakthrough of the Year, the first time this had been bestowed in the area of mathematics.[2] --- end quoting Wikipedia --- Archimedes Plutonium www.iw.net/~a plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies Reply[ CapitalEHat]Reply to authorForward[Capita lEHat] Rate this post: Text for clearing space . Discussion subject changed to how can we have a Poincare Conjecture equal to a... Sounds almost incredulous that the two are the same things. But the key is that both are about encircling and closing off geometrical figures. The previous illustration of 4Color Mapping: MMMMMM MMMMMM BBJJO BBJJO OOOO In order for those four countries to be 4 colorable means there is 4 mutual adjacencies and no more. If there was a 5th mutual adjacency then we lose the 4 Color Mapping. And what makes it possible is that the O country encircles the J country so that no 5th country can ever connect with J. In the Old-Poincare Conjecture we have simply-connected that a closed loop shrinks to a point. But because Reals are discrete with gaps between consecutive Reals the Old Poincare Conjecture must be false and only with some revisions can we even have a New Poincare Conjecture. A closed loop shrunk is not a singular point but an array of at least 9 consecutive points where the Poincare point is in the middle. . . . . . . . . . So how are those two pictures above the same thing? Seems incredulous that they could be the same. They are the same if we consider shrinking the 4 Color Mapping and we consider the octupuses tentacles as country mapping. So we have five countries as octupus tentacles and they meet at the end tip-- all five. So can those five country-tentacles all be mutually adjacent of those five end-tips? Well if the Old Poincare Conjecture was true then we add another country, the L country to the above diagram: LLLLLLLLLLL LMMMMMML LMMMMMML LLBBJJOLLLL LLBBJJOL LLOOOOL LLLLLLLLL They are all mutually adjacent except for the J to L countries. But if the Old Poincare Conjecture were true we shrink that entire country set and what happens is that the J and L countries now do become mutually adjacent. They become mutually adjacent because the J country becomes the point in the Old Poincare Conjecture. The New Poincare Conjecture upon shrinkage stops short of J becoming mutually adjacent because the 9 point array blocks the penetration of the L country. Having some difficulty in explaining this and so will leave it at that. It is due to the fact it is not clear flowing to me, yet. The idea is that if the Betweenness Axiom is allowed then it is the source of all this inconsistency and contradictions. That between any two A and B is always a C causes the 5 tentacles to be mutually adjacent and causes the L country to penetrate and touch the J country. - Show quoted text - Untitled to the friends of Kolmogorov.84N.L. Dreier, A.A. Malinovskii, S.A. Musatov, ..... his customary improvizations during the lecture Luzin made a conjecture ... (they discussed a series of questions arising from Poincare's problem of three geodesies). .... remaining part was divided into two almost equal parts. ... Result for query keyword(s)=theorem author= title=newblock emph Map color theorem. newblock The four-colour theorem. ..... Note that if Szpiro's conjecture is true, then Theorem~ gives a uniform bound ...... Unitary representations of classical Lie groups of equal rank with nonzero Dirac cohomology ..... On the extremal functions of Sobolev-Poincar.8e inequality ... http://nyjm.albany.edu:8000/cgi-bin/ aglimpse/19/nyjm/Http/search/j %3Ffirstyear%3D2001%26journaldir %3Dcombined%26lastyear%3D2007%26query %3Dtheorem Result for query keyword(s)=theorem author= title=The inverse mapping theorem guarantees that any surface is; a plane, ...... Our main theorem checks the conjecture for some specific groups ..... Minimal submanifolds of K.8ahler-Einstein manifolds with equal K.8ahler angles ...... Equivalence of Analytic and Sobolev Poincare Inequalities for Planar Domains ... http://nyjm.albany.edu:8000/cgi-bin/ aglimpse/19/nyjm/Http/search/j %3Ffirstyear%3D1994%26journaldir %3Dcombined%26lastyear%3D2002%26query Poincare group. The position in the transverse plane coincides with the ...... is equal to its mass and the spin of the nucleon is ...... in the nucleon, and in impact parameter space, where they enable to map the spatial ..... [111] Musatov I.V. and Radyushkin A.V., Phys. Rev. D, 61 (2000) 074027. http://arxiv.org/pdf/0711.2625 -- Martin Musatov (The above theory) http://MeAmI.org Search for the People! === Subject: Re: michelson morley experiment questions reply-type=response Importance: Normal > Peter, look: > Look at these preposterous situations created by the idea > of lack of simultaneiety: > Preposterous to you. > Obviously Special Relativity is correct, the evidence is overwhelming, > its routinely used in engineering and if it was wrong lots of things > wouldn't work (in some cases spectacularly). > Just accept it as amazing. I guess you don't understand block universe. It literally means > you are a mannikin voicing nonconsequential inanities. > Well, if that is what the block Universe literally is, it is false, as > I am not literally a mannikin. > And you agree with it? :) Spirit of Truth > With SR? > Yes, of course. And I also agree that world is not flat, and that earth > revolves around the sun and not vice-versa. All well supported by > evidence. > ......... .. > ......... .. You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. Although the future that 'already exists' is not causally linked to the present here. > Thus you = nothing per Einstein's SR. SR says nothing of the sort. > I can assure you that you are not a nothing and do have free > will.... How do you know .. how can you every possibly know? > SO something is wrong in the state of SR. No .. only with your insistence that something must be wrong === Subject: Re: michelson morley experiment questions > Peter, look: > Look at these preposterous situations created by the idea > of lack of simultaneiety: > Preposterous to you. > Obviously Special Relativity is correct, the evidence is overwhelming, > its routinely used in engineering and if it was wrong lots of things > wouldn't work (in some cases spectacularly). > Just accept it as amazing. > I guess you don't understand block universe. It literally means > you are a mannikin voicing nonconsequential inanities. Well, if that is what the block Universe literally is, it is false, as > I am not literally a mannikin. > And you agree with it? > :) > Spirit of Truth With SR? Yes, of course. And I also agree that world is not flat, and that earth > revolves around the sun and not vice-versa. All well supported by > evidence. > ......... .. > ......... .. > You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. Although the future that 'already exists' is not causally linked to the > present here. In blockhead universe there is no Cause, only blockheads. > Thus you = nothing per Einstein's SR. SR says nothing of the sort. It sure does, but you have to have a big confront to face up to it. > I can assure you that you are not a nothing and do have free > will.... How do you know .. how can you every possibly know? I am not alone. > SO something is wrong in the state of SR. No .. only with your insistence that something must be wrong Of course there is. Lack of simultaneity is the first error of SR and it is that, that put physics into a state of confusion that it still is mired in. Spirit of Truth === Subject: Re: michelson morley experiment questions reply-type=response It might be better if you consulted some standard textbook on SR, tried to work through it, and for bits you don't understand, asked in these newsgroups. If Einstein's original paper is too advanced for you, try a popular account (Einstein himself did one). HTH Peter Webb === Subject: Re: michelson morley experiment questions <4a476d29$0$25358$afc38c87@news.optusnet.com.au> <4a483464$0$4046$afc38c87@news.optusnet.com.au> <0069a4e8$0$9716$c3e8da3@news.astraweb.com> posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP Of course there is. Lack of simultaneity is the first error of SR > and it is that, that put physics into a state of confusion that it > still is mired in. > Imbecile , SR has simultaneity, it is just that it is not ABSOLUTE, like in Newtonian mechanics. === Subject: Re: michelson morley experiment questions > Of course there is. Lack of simultaneity is the first error of SR > and it is that, that put physics into a state of confusion that it > still is mired in. > Imbecile , SR has simultaneity, it is just that it is not ABSOLUTE, > like in Newtonian mechanics. That is not the point. These are the point (try to understand them): > Look at these preposterous situations created by the idea > of lack of simultaneiety: > http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node77.html > http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity%2C_time_... You will notice that one of the blockhead SRians has tried to hide them from view so that you all can continue as slaves. Well, unfortunately for them Fabric Of The Cosmos was a best seller ,and so what is _obvious_ from lack of simultaneiery cannot be hidden any more. Shame on those who would keep you all slaves! Spitir of Truth. === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <6uqe4557in0la56perimbdql9d8qe03cpl@4ax.com> posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Miller was in much the same situation as I describe. He detected > modulations in the MMX output, but totally ignored evidence > indicating that the modulations were due to terrestrial factors, > rather than having any sort of celestial origin. I don't base my opinions on what Miller may have ignored or not > ignored but rather on analysis of his data. My own analysis shows that the data in Figure 8 of his 1933 paper > contained a signal that was not an artifact of his data reduction > algorithm and so therefore had a physical cause. My analysis of his presented results leads me to conclude that > the physical cause had a celestial component. What evidence do you have to justify that assertion? Surely not Miller's spurious claim that the signals that he detected showed constant phase when plotted against sidereal time? Guided by faulty theory, Miller drew theoretical best fits through his data points in bold lines that were much more prominent than the actual data. The effect was to draw the eye of the reader away from the fact that the theoretically computed lines tended to miss the data entirely. In the following link, I examine Miller's claim that the signals he detected showed constant phase when plotted against sidereal time, thus proving a celestial origin for the signals. The plots at first look force your eye to look at his fanciful interpretation of the data, rather than the data itself. Erase Miller's fanciful fits, and the apparent constant phase vanishes. http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm Jerry === Subject: Re: michelson morley experiment questions Guided by faulty theory, Miller drew theoretical best fits >through his data points in bold lines that were much more >prominent than the actual data. The effect was to draw the eye of > the reader away from the fact that the theoretically computed >lines tended to miss the data entirely. In the following link, I >examine Miller's claim that the signals he detected showed >constant phase when plotted against sidereal time, thus proving >a celestial origin for the signals. The plots at first look >force your eye to look at his fanciful interpretation of the >data, rather than the data itself. Erase Miller's fanciful fits, >and the apparent constant phase vanishes. >http://mysite.verizon.net/cephalobus_alienus/Miller/EraseMillerLines.htm > Hmm. The bold lines are not artistically drawn lines, but are the theoretically calculated curves of how magnitude and azimuth of measured velocity would vary over 24 hours of sideral time. Due to the earth's changing velocity as it orbits the sun, different curves are required at different times of the year. If you could show that the curves were wrongly calculated you might have a point. But looking at what is presented, I can only agree with Miller that, The calculated curves fit the observations remarkably well. === Subject: miller experiment questions posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) >Guided by faulty theory, Miller drew theoretical best fits >through his data points in bold lines that were much more >prominent than the actual data. The effect was to draw the eye of > the reader away from the fact that the theoretically computed >lines tended to miss the data entirely. In the following link, I >examine Miller's claim that the signals he detected showed >constant phase when plotted against sidereal time, thus proving >a celestial origin for the signals. The plots at first look >force your eye to look at his fanciful interpretation of the >data, rather than the data itself. Erase Miller's fanciful fits, >and the apparent constant phase vanishes. >http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm Hmm. The bold lines are not artistically drawn lines, but are the > theoretically calculated curves of how magnitude and azimuth of > measured velocity would vary over 24 hours of sideral time. Due to the earth's changing velocity as it orbits the sun, different > curves are required at different times of the year. If you could show that the curves were wrongly calculated you might > have a point. You want examples of horrible mistakes in how Miller calculated his curves? YOU GOT IT! And this is just starters...I just don't have the -time- to tear apart his whole paper... Miller's data was so dirty, that he presented running averages of his data in his plots, rather than the data itself. The manner in which Miller computed his running averages introduced artifact, such as forcing the appearance of 24 hour periodicities in his running average curves when they in fact may have had none. http://mysite.verizon.net/cephalobus alienus/Miller/FakeRunningAverages.htm > But looking at what is presented, I can only agree with Miller that, > The calculated curves fit the observations remarkably well. Jerry === Subject: Re: michelson morley experiment questions posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) >Guided by faulty theory, Miller drew theoretical best fits >through his data points in bold lines that were much more >prominent than the actual data. The effect was to draw the eye of > the reader away from the fact that the theoretically computed >lines tended to miss the data entirely. In the following link, I >examine Miller's claim that the signals he detected showed >constant phase when plotted against sidereal time, thus proving >a celestial origin for the signals. The plots at first look >force your eye to look at his fanciful interpretation of the >data, rather than the data itself. Erase Miller's fanciful fits, >and the apparent constant phase vanishes. >http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm Hmm. The bold lines are not artistically drawn lines, but are the > theoretically calculated curves of how magnitude and azimuth of > measured velocity would vary over 24 hours of sideral time. Due to the earth's changing velocity as it orbits the sun, different > curves are required at different times of the year. If you could show that the curves were wrongly calculated you might > have a point. But looking at what is presented, I can only agree with Miller that, > The calculated curves fit the observations remarkably well. The calculated curves fit the actual data poorly. The actual data belies Miller's claim that the phases are constant when plotted against sidereal time. Jerry === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <6uqe4557in0la56perimbdql9d8qe03cpl@4ax.com> posting-account=1FV9tgoAAADH0azT7-mxErKgugI383zU Gecko/20081204 SeaMonkey/1.1.14,gzip(gfe),gzip(gfe) Allais and others have came to similar conclusions. Eg see: >http://allais.maurice.free.fr/English/media14-1.htm -- Surfer This conclusion is at odds with newer measurements which are far more > precise, some up to 8 or ten orders of magnitude, which show no effects. > Experiments that attempt to detect light speed anisotropy in vacuum don't work, because variation of light speed is exactly compensated for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include something to disturb the balance. Eg in Miller's experiment, the presence of air reduced the speed of light to c/n (n==refractive index of air). That was sufficient to do it. === Subject: Re: michelson morley experiment questions > Experiments that attempt to detect light speed anisotropy in vacuum > don't work, because variation of light speed is exactly compensated > for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Eg in Miller's experiment, the > presence of air reduced the speed of light to c/n (n==refractive index > of air). That was sufficient to do it. Hmmm. I suppose there might be theories that imply this, but none are commonly known, and none are mainstream. Moreover, your claim is just plain wrong -- in particular: # Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg 2489 (1974). A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of 0.025 m/s. This is about one-millionth of the Earth's orbital velocity and about 1/10,000 of its rotational velocity. Glass has a much larger index of refration than air, so your claim is CLEARLY invalid. The underlying reason is that the gas in Miller's interferometer is sensitive to quite small changes in temperature, which most definitely occurred in his measurements -- he merely constructed the world's most unwieldy thermometer. He is not alone in that.... Tom Roberts === Subject: Re: michelson morley experiment questions > >Allais and others have came to similar conclusions. >Eg see: >http://allais.maurice.free.fr/English/media14-1.htm >-- Surfer >This conclusion is at odds with newer measurements which are far more >precise, some up to 8 or ten orders of magnitude, which show no effects. > Experiments that attempt to detect light speed anisotropy in vacuum > don't work, because variation of light speed is exactly compensated > for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Eg in Miller's experiment, the > presence of air reduced the speed of light to c/n (n==refractive index > of air). That was sufficient to do it. We are all aware you idolize Cahill but his work is rejected by real scientists. > === Subject: Re: michelson morley experiment questions > Those of us who have studied physics, and have experience where your > accelerators), know that the model of relativity corresponds MUCH better > to the experiments we have performed on the world; relativity, of > course, does support and require the lack of simultaneity you have in > mind. So, what are the differences between relative simultaneity and absolute simultaneity? ********************** In absolute simultaniety if one observer sees two events as simultaneous, all will. In relative simultanaity, this is not true. Say we have a series of events taking place and several observers observing these events. It is the job of each observer to piece all the events together into a timeline with chronological order. Under relative simultaneity, each observer will report a different timeline of these events. Some events unobserved will be left out. Under absolute simultaneity, all the timelines must be equal. Does this sound about right? ********************* Yes! You have got it! > So this really comes down to your personal lack of experience, and your > extreme naivet.8e about the ability of your thoughts to control the > universe. Just because you THINK This real universe of ours does not > support lack of simultaneity does not make it so. Indeed, real > experiments show that it does. As many observers observe the interference pattern of the MMX, each observer should have no problems reporting exactly where the beams of light come from and where and when the peaks of the light beams occur. Thus, simultaneity sounds like absolute to me. ******************** No, it doesn't even sound like simultaniety, as the MMX does not explicitly address the subject of simultaniety. You are getting confused. Any interferometer should falsify any wild and unrealistic ideas claiming that the universe supports relative simultaneity. The MMX actually falsifies the Lorentz transform since it manifests relative simultaneity. Since SR is merely an interpretation to the Lorentz transform, it is falsified as well. Simultaneity must be absolute according to any experiments. *********************** That's just nonsense. If there is something you don't understand about SR, please free to ask. === Subject: Re: michelson morley experiment questions <1TT2m.10142$Dx2.7890@flpi146.ffdc.sbc.com> <4a4d6347$0$25358$afc38c87@news.optusnet.com.au> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Hmmm... I have asked the so-called experts in justifying their arguments in why the world is observed to behave in relative simultaneity. All I got are doug the manyuk (Arabic for male prostitute), Whoever the diarrhea licker, and Peter Webb the empirical idiot (according to Uncle AlÍs classification). So, if the self-styled physicists do not understand the differences between what relative simultaneity and absolute simultaneity are, why are they promoting one from the other? That is indeed bigotry with a political agenda so sickeningly sinister. === Subject: Re: michelson morley experiment questions Hmmm... I have asked the so-called experts in justifying their arguments in why the world is observed to behave in relative simultaneity. All I got are doug the manyuk (Arabic for male prostitute), Whoever the diarrhea licker, and Peter Webb the empirical idiot (according to Uncle AlÍs classification). So, if the self-styled physicists do not understand the differences between what relative simultaneity and absolute simultaneity are, why are they promoting one from the other? I already specified the difference between relative and absolute simultaneity. The concept of absolute simultaneity is that measurements of simultaneity are independent of the reference frames;in relative simultaneity these depend upon the reference frame that is used for measurements. I know SR is hard, that's life, sometimes you have to work at understanding something. === Subject: Re: michelson morley experiment questions Importance: Normal > Hmmm... I have asked the so-called experts in justifying their > arguments in why the world is observed to behave in relative > simultaneity. All I got are doug the manyuk (Arabic for male > prostitute), Whoever the diarrhea licker, and Peter Webb the empirical > idiot (according to Uncle AlÍs classification). So, if the self-styled physicists do not understand the differences > between what relative simultaneity and absolute simultaneity are, why > are they promoting one from the other? That is indeed bigotry with a > political agenda so sickeningly sinister. Do you understand the difference yourself? === Subject: Re: michelson morley experiment questions Hmmm... I have asked the so-called experts in justifying their arguments in why the world is observed to behave in relative simultaneity. All I got are doug the manyuk (Arabic for male prostitute), Whoever the diarrhea licker, and Peter Webb the empirical idiot (according to Uncle Al.89s classification). So, if the self-styled physicists do not understand the differences between what relative simultaneity and absolute simultaneity are, why are they promoting one from the other? That is indeed bigotry with a political agenda so sickeningly sinister. Despite your miserable flaming diarrhea, you still have no answer to Sagnac. You are as much a bigot as they are. === Subject: Re: michelson morley experiment questions <1TT2m.10142$Dx2.7890@flpi146.ffdc.sbc.com> <5q3o451r9tf42nq7r3u753p83jamfq6sr2@4ax.com> <4a4c8701$0$3321$afc38c87@news.optusnet.com.au> <025cc5f0$0$26243$c3e8da3@news.astraweb.com> posting-account=A_fxOQkAAAC3cvPrAtLES_UPpvsB8VF2 Trident/4.0; GTB6; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; OfficeLiveConnector.1.3; OfficeLivePatch.0.0; yie8),gzip(gfe),gzip(gfe) > {snip...} > Whatever it is. :) OK, I mean that disagreeing with the apparent illogical >ideas in SR, at least in my case, is not to do with >my human intuition disageeing with it. This real universe >of ours does not support lack of simultaneity. Spirit > You got to understand, for diehard relativists perception IS > reality. > Well, if by perception you mean what we see experimentally, yes. > You are quite free to impose your concept of simultaneity and absolute > time > and space on the Universe; you can define a privileged frame of reference > and measure simultaneity etc from within that frame. You can even call it > the ether, if you want. > But what you also have to accept is that the frame you have chosen is > completely arbitrary, and anybody else can pick a different inertial > frame > to treat as absolute. The details of which frame or reference you choose > has > absolutely no bearing on the outcome of physical experiments, and your > absolute time and space plays no role in any physical experiment. Th eproblem with your claim is that the clock second we use to measure > time has different duration in different inertial frames. In every inertial frame, a clock second for a clock at rest in that frame is > the same clock second. Noone in any inertial frame sees their own at-rest clock ticking slower than > any other observer sees their own at-rest-clock ticking. Of course, SR further says in every inertial frame, the observer will see > clocks in motion as running slower than they do when at rest. That means > that the outcome of physical experiments in different frames cannot be > compared directly. An observer in some frame S watching an experiment while it is being > performed in a different frame S' will see different results to the observer > in S' will see. But both the observer in S and the observer in S' will see > the same results when the experiment is performed at rest in their own > frames. My point is: The passage of an S frame second does not correspond to the passage of an S' clock second and thus the same numerical results for an experiment in S' frame do not correspond to the same numerical results for the same experiment in the S frame. For example a traveling clock second in the twin > scenario cannot be compared directly with a stay at home clock second. Yes it can .. look at the clocks. No it can't.....the passage of a traveling clock second does not correspond to the passage of a stay at home clock second. Therefore you cannot compared them directly. Why? Because SR claims that the passage of a traveling clock second > corresponds to the passage of less than a clock second on the stay at > home clock. Actually, you have it backwards. The travelling clock second corresponds to > more than a stay-at-home clock second. I agree...you were right. Regardless when you compare the clocks when they return, you can see the > difference in elapsed time. > Sure you can compared the clock second after it return but those clock second accumulated during the journey cannot be compared directly withthe stay at home clock seconds accumulated during the journey of the traveling clock. > I'm not sure what the point is you were trying to make.. but I don't think > you succeeded in making it.- Hide quoted text - > The point is: The same results for identical experiment in S and S' frame is a false assertion. Ken Seto === Subject: Re: michelson morley experiment questions <1TT2m.10142$Dx2.7890@flpi146.ffdc.sbc.com> <5q3o451r9tf42nq7r3u753p83jamfq6sr2@4ax.com> <4a4c8701$0$3321$afc38c87@news.optusnet.com.au> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > {snip...} > Whatever it is. :) OK, I mean that disagreeing with the apparent illogical >ideas in SR, at least in my case, is not to do with >my human intuition disageeing with it. This real universe >of ours does not support lack of simultaneity. Spirit > You got to understand, for diehard relativists perception IS > reality. > Well, if by perception you mean what we see experimentally, yes. > You are quite free to impose your concept of simultaneity and absolute > time > and space on the Universe; you can define a privileged frame of reference > and measure simultaneity etc from within that frame. You can even call it > the ether, if you want. > But what you also have to accept is that the frame you have chosen is > completely arbitrary, and anybody else can pick a different inertial > frame > to treat as absolute. The details of which frame or reference you choose > has > absolutely no bearing on the outcome of physical experiments, and your > absolute time and space plays no role in any physical experiment. Th eproblem with your claim is that the clock second we use to measure > time has different duration in different inertial frames. In every inertial frame, a clock second for a clock at rest in that frame is > the same clock second. Noone in any inertial frame sees their own at-rest clock ticking slower than > any other observer sees their own at-rest-clock ticking. Of course, SR further says in every inertial frame, the observer will see > clocks in motion as running slower than they do when at rest. That means > that the outcome of physical experiments in different frames cannot be > compared directly. An observer in some frame S watching an experiment while it is being > performed in a different frame S' will see different results to the observer > in S' will see. But both the observer in S and the observer in S' will see > the same results when the experiment is performed at rest in their own > frames. My point is: The passage of an S frame second does not correspond to > the passage of an S' clock second and thus the same numerical results > for an experiment in S' frame do not correspond to the same numerical > results for the same experiment in the S frame. > For example a traveling clock second in the twin > scenario cannot be compared directly with a stay at home clock second. Yes it can .. look at the clocks. No it can't.....the passage of a traveling clock second does not > correspond to the passage of a stay at home clock second. Therefore > you cannot compared them directly. > Why? Because SR claims that the passage of a traveling clock second > corresponds to the passage of less than a clock second on the stay at > home clock. Actually, you have it backwards. The travelling clock second corresponds to > more than a stay-at-home clock second. I agree...you were right. > Regardless when you compare the clocks when they return, you can see the > difference in elapsed time. > Sure you can compared the clock second after it return but those clock > second accumulated during the journey cannot be compared directly > withthe stay at home clock seconds accumulated during the journey of > the traveling clock. I'm not sure what the point is you were trying to make.. but I don't think > you succeeded in making it.- Hide quoted text - > The point is: The same results for identical experiment in S and S' > frame is a false assertion. Ken Seto === Subject: Re: michelson morley experiment questions > The point is: The same results for identical experiment in S and S' > frame is a false assertion. > Not the same results, in the sense of numeric answers, but the same outcomes. For example, if an observers in an inertial frame of reference calculate that two bodies will collide, observers in all frames of reference will calculate they collide. The measurements may differ, but the outcome is the same. HTH === Subject: Re: michelson morley experiment questions Importance: Normal > Those of us who have studied physics, and have experience where your > accelerators), know that the model of relativity corresponds MUCH better > to the experiments we have performed on the world; relativity, of > course, does support and require the lack of simultaneity you have in > mind. So, what are the differences between relative simultaneity and > absolute simultaneity? Say we have a series of events taking place and several observers > observing these events. It is the job of each observer to piece all > the events together into a timeline with chronological order. Under > relative simultaneity, each observer will report a different timeline > of these events. Some events unobserved will be left out. Under > absolute simultaneity, all the timelines must be equal. Does this sound about right? > So this really comes down to your personal lack of experience, and your > extreme naivet.8e about the ability of your thoughts to control the > universe. Just because you THINK This real universe of ours does not > support lack of simultaneity does not make it so. Indeed, real > experiments show that it does. As many observers observe the interference pattern of the MMX, each > observer should have no problems reporting exactly where the beams of > light come from and where and when the peaks of the light beams > occur. Of course .. the changes in simultaneity do not affect causality > Thus, simultaneity sounds like absolute to me. What things are you claiming are simultaneous? > Any > interferometer should falsify any wild and unrealistic ideas claiming > that the universe supports relative simultaneity. How would it? > The MMX actually > falsifies the Lorentz transform since it manifests relative > simultaneity. No .. Lorentz transform explain MMX results. > Since SR is merely an interpretation to the Lorentz > transform, it is falsified as well. No > Simultaneity must be absolute > according to any experiments. Why do you think that? Seems like an unsupported assertion to me . === Subject: Re: michelson morley experiment questions > when one subtracts two UNCORRELATED random variables A > and B, the sigma of the result is sqrt(sigma(A)^2+sigma(B)^2), not what > you used, sigma(A-B). > I am afraid you are being obscurantist. No. I merely stated the standard result from statistics. This is not obscurantist, this is CORRECT. But for your case you do need to read > In my scheme, A is raw data (that is signal plus noise), B is raw data > minus most of the signal. > Consequently subtracting B from A removes most of the noise while > leaving most of the signal. > Computing the standard deviation of (B-A) therefore gives the standard > deviation of the clean signal. Not true. You grossly misrepresent the errorbars. Subtracting a background cannot possibly reduce the original statistical errors in the data. Tom Roberts === Subject: Re: michelson morley experiment questions > In my scheme, A is raw data (that is signal plus noise), B is raw data > minus most of the signal. > Consequently subtracting B from A removes most of the noise while > leaving most of the signal. > Computing the standard deviation of (B-A) therefore gives the standard > deviation of the clean signal. Not true. You grossly misrepresent the errorbars. Subtracting a >background cannot possibly reduce the original statistical errors in the >data. > Of course not. However, if I remove easy to eliminate errors from the data, why should I be interested in the original statistical errors? Suppose a radio antenna is picking up 1 volt p-p of power line hum and 1 microvolt of signal. The original statistical errors would be a million times larger than the signal. But after the hum has been eliminated with a filter or tuning circuit, would those original statistical errors still be of any irrelevance? I think not. === Subject: Re: michelson morley experiment questions > Suppose a radio antenna is picking up 1 volt p-p of power line hum and > 1 microvolt of signal. > The original statistical errors [...] That is NOT a statistical error. As I keep repeating: you REALLY need to study this. Tom Roberts === Subject: Re: michelson morley experiment questions >In my scheme, A is raw data (that is signal plus noise), B is raw data >minus most of the signal. >Consequently subtracting B from A removes most of the noise while >leaving most of the signal. >Computing the standard deviation of (B-A) therefore gives the standard >deviation of the clean signal. >Not true. You grossly misrepresent the errorbars. Subtracting a >background cannot possibly reduce the original statistical errors in the >data. > Of course not. However, if I remove easy to eliminate errors from the data, why > should I be interested in the original statistical errors? Because the removal process does not magically make signal from noise. Suppose a radio antenna is picking up 1 volt p-p of power line hum and > 1 microvolt of signal. > This depends on the filter. If you are looking for 1MHz, you can do a great job. If you are looking for 61Hz (or 51Hz depending on where one is), then you are in real trouble. You need to realize that newer experiments have limited the anisotropy to a factor of a billion or so below the even claimed resolution of Miller. Therefore he is wrong and, if you get the same results, you are wrong. To think otherwise is a bad case of self delusion. > The original statistical errors would be a million times larger than > the signal. But after the hum has been eliminated with a filter or > tuning circuit, would those original statistical errors still be of > any irrelevance? I think not. > === Subject: Re: michelson morley experiment questions > > > However, if I remove easy to eliminate errors from the data, why > should I be interested in the original statistical errors? Because the removal process does not magically make signal from >noise. > You are not being logical. If the noise has been reduced, why should the original statistical errors caused by that noise, be of relevance to the remaining signal component? > > Suppose a radio antenna is picking up 1 volt p-p of power line hum and > 1 microvolt of signal. > >This depends on the filter. If you are looking for 1MHz, you can do a >great job. If you are looking for 61Hz (or 51Hz depending on where >one is), then you are in real trouble. > True. But the relevant point here is that Millers signals were mainly contaminated by much lower frequency noise, that was easy to remove. That is clearly shown by the DFTs on this page. http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ You need to realize that >newer experiments have limited the anisotropy to a factor of a billion >or so below the even claimed resolution of Miller. > Experiments that attempt to detect light speed anisotropy in vacuum don't work, because variation of light speed is exactly compensated for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include something to disturb the balance. Eg in Miller's experiment, the presence of air reduced the speed of light to c/n. Judging by the results of his experiment this was sufficient. A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments M. Consoli, E. Costanzo Eur.Phys.J.C55:469-475,2008 http://arxiv.org/abs/0804.0979 Abstract In principle, by accepting the idea of a non-zero vacuum energy, the preferred reference frame. By treating this quantum vacuum as a relativistic medium, the non-zero energy-momentum flow expected in a moving frame should effectively behave as a small thermal gradient and could, in principle, induce a measurable anisotropy of the speed of light in a loosely bound system as a gas. We explore the phenomenological implications of this scenario by considering a new class of dedicated ether-drift experiments where arbitrary gaseous media fill the resonating optical cavities. Our predictions cover most experimental set up and should motivate precise experimental tests of these fundamental issues. === Subject: Re: michelson morley experiment questions >However, if I remove easy to eliminate errors from the data, why >should I be interested in the original statistical errors? >Because the removal process does not magically make signal from >noise. > You are not being logical. If the noise has been reduced, why should > the original statistical errors caused by that noise, be of > relevance to the remaining signal component? Because you have to be very careful in what you are removing. If you remove a constant, for example, the percentage fluctuations increase. >Suppose a radio antenna is picking up 1 volt p-p of power line hum and >1 microvolt of signal. >This depends on the filter. If you are looking for 1MHz, you can do a >great job. If you are looking for 61Hz (or 51Hz depending on where >one is), then you are in real trouble. > True. But the relevant point here is that Millers signals were mainly > contaminated by much lower frequency noise, that was easy to remove. > That is clearly shown by the DFTs on this page. > http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >You need to realize that >newer experiments have limited the anisotropy to a factor of a billion >or so below the even claimed resolution of Miller. Experiments that attempt to detect light speed anisotropy in vacuum > don't work, because variation of light speed is exactly compensated > for by Lorentz contraction of the apparatus. This is Cahill and his foolishness. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Eg in Miller's experiment, the > presence of air reduced the speed of light to c/n. But remember Cahill was shown to be wrong in this by experiments done where n was much higher number. He then had to retreat to saying that somehow air was special. Cranks do that. Judging by the results of his experiment this was sufficient. Judging by the results of data analysis and later work, he was completely wrong. A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008 > http://arxiv.org/abs/0804.0979 Abstract In principle, by accepting the idea of a non-zero vacuum energy, the > preferred reference frame. By treating this quantum vacuum as a > relativistic medium, the non-zero energy-momentum flow expected in a > moving frame should effectively behave as a small thermal gradient and > could, in principle, induce a measurable anisotropy of the speed of > light in a loosely bound system as a gas. We explore the > phenomenological implications of this scenario by considering a new > class of dedicated ether-drift experiments where arbitrary gaseous > media fill the resonating optical cavities. Our predictions cover most > experimental set up and should motivate precise experimental tests of > these fundamental issues. === Subject: Re: michelson morley experiment questions <0JmdnRs3Q_LYydfXnZ2dnUVZ_tCdnZ2d@posted.docknet> posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 > Ahh, the other pair of renowed crackpots. Let me guess, what comes next, a citation from Cahill or one from Munera? Or is it back to Dayton Miller? Messrs. Consoli and Constanzo never ran their experiments. What is even more embarassing is that their theory is ALREADY refuted by the a couple of experiments: #1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg 2489 (1974). A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of 0.025 m/s. This is about one-millionth of the Earth's orbital velocity and about 1/10,000 of its rotational velocity. #2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. A repetition of the MMX with the optical paths in perspex (n = 1.49), and a laser-based optics sensitive to ~0.00003 fringe. They report a null result with an upper limit on v.bether of 6.64 km/s. Eur.J.Phys is one of the most embarassing journals, they are at par with Foundations of Physics Letters and Physica Scripta, all known to publish fringe stuff. === Subject: Re: michelson morley experiment questions > A possible theory of operation is discussed here: > Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 >Ahh, the other pair of renowed crackpots. Let me guess, what comes >next, a citation from Cahill or one from Munera? Or is it back to >Dayton Miller? Messrs. Consoli and Constanzo never ran their experiments. What is >even more embarassing is that their theory is ALREADY refuted by the >a couple of experiments: #1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg >2489 (1974). A triangle interferometer with one leg in glass. They set an upper >limit on the anisotropy of 0.025 m/s. This is about one-millionth of >the Earth's orbital velocity and about 1/10,000 of its rotational >velocity. >#2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. A repetition of the MMX with the optical paths in perspex (n = 1.49), >and a laser-based optics sensitive to ~0.00003 fringe. They report a >null result with an upper limit on v.bether of 6.64 km/s. > I elsewhere pointed out that experiments that attempt to detect light speed anisotropy in vacuum don't work, because variation of light speed is exactly compensated for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include something to disturb the balance. Depending on the degree to which that occurs or does not occur, there is opportunity for experiments to fail to detect anisotropy. But while some fail in this regard, others succeed. Eg. Figure 4 in Miller's paper shows that the velocity he obtained in 1925 was consistent with the velocity of ether drift observed by Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 and 1905. That's five examples of successful experiments. === Subject: Re: michelson morley experiment questions > Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. NONE of those are useful. They all used the algorithm that averages turns, and that essentially forces their noise to look just like they expected a signal to look. For the ones that have data available, Miller and Michelson & Morley, their statistical errors greatly exceed their signals (the latter of course did not actually report any signal, I mean the spurious signal others claim to find in their data). They are ALL useless. And this is completely independent of YOUR analysis of Miller's data. They all used the algorithm they did, not yours. Tom Roberts === Subject: Re: michelson morley experiment questions > Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. NONE of those are useful. They all used the algorithm that averages >turns, and that essentially forces their noise to look just like they >expected a signal to look. > That is an unsubstantiated assertion. It certainly did not occur with the data that Miller presented in Figure 8 of his 1933 paper, as Miller's algorithm produced amost output as my own. === Subject: Re: michelson morley experiment questions > Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. > NONE of those are useful. They all used the algorithm that averages > turns, and that essentially forces their noise to look just like they > expected a signal to look. > That is an unsubstantiated assertion. It certainly did not occur with > the data that Miller presented in Figure 8 of his 1933 paper, I repeat: A) Miller's algorithm is a comb filter that forces his noise into three frequency bins, the lowest of which is also the signal bin. The falling spectrum of his noise naturally makes it mimic the visual signature of a signal. B) the statistical errorbars of the result of Miller's algorithm are considerably larger than the signal he found. These are both mathematical assertions about his algorithm and data that are indisputable. Just LOOK at his data and his data reduction algorithm. No amount of wishful thinking on your part can change these FACTS. > as > Miller's algorithm produced amost output as my own. That is more an indictment of your method than a validation of Miller's. Tom Roberts === Subject: Re: michelson morley experiment questions posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > I repeat: > A) Miller's algorithm is a comb filter that forces his noise into > three frequency bins, the lowest of which is also the signal bin. > The falling spectrum of his noise naturally makes it mimic the > visual signature of a signal. > B) the statistical errorbars of the result of Miller's algorithm > are considerably larger than the signal he found. These are both mathematical assertions about his algorithm and data that > are indisputable. Just LOOK at his data and his data reduction > algorithm. No amount of wishful thinking on your part can change these > FACTS. as > Miller's algorithm produced amost output as my own. That is more an indictment of your method than a validation of Miller's. Tom Roberts As you know, my approach to Miller's analysis differs from your own, in that I do not question the reality of the signal, but rather focus on whether the observed signal satisfies the criteria necessary for it to be considered as having a celestial origin. The answer, of course, is a resounding NO. Miller, for example, contended that the seasonal amplitude and azimuth variations that he observed showed constant phase when plotted against sidereal time. Miller's plots in his Fig 26 at first look rather convincing, until one realizes that it is Miller's fanciful fits to the reduced data that show constant phase, not the data itself. Erase Miller's fits to the reduced data, and the apparent constant phase vanishes. http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm I only recently realized that the method that Miller used to compute his running averages of magnitude and azimuth are highly suspect. Quite obviously, Miller did not plan for his marathon observing sessions to begin and end at 0:00 - 24:00 sidereal time, yet the running averages presented in his Figures 22, 26 and 27 are continuous over the entire 0:00 - 24:00 span. The only explanation for this, is that Miller must have improperly looped the data from his observing sessions, and computed the running average across the seam between the end of an observing session and the beginning of the same session. This procedure, of course, imposes a false 24 hour periodicity into his running averages. http://mysite.verizon.net/cephalobus alienus/Miller/FakeRunningAverages.htm Somewhere in each of his plots in Figure 22 would be a pair of points representing the end of one observing session and the beginning of the same session. One point in each of his running averages must represent an improper average of data taken over 24 hours apart. Given your access to Miller's original data, might it be possible for you to identify the points where Miller performed this improper concatenation of data? This is a low priority request. We both have real work to do. Jerry === Subject: Re: michelson morley experiment questions posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.7.STABLE6) I repeat: > A) Miller's algorithm is a comb filter that forces his noise into > three frequency bins, the lowest of which is also the signal bin. > The falling spectrum of his noise naturally makes it mimic the > visual signature of a signal. > B) the statistical errorbars of the result of Miller's algorithm > are considerably larger than the signal he found. These are both mathematical assertions about his algorithm and data that > are indisputable. Just LOOK at his data and his data reduction > algorithm. No amount of wishful thinking on your part can change these > FACTS. as > Miller's algorithm produced amost output as my own. That is more an indictment of your method than a validation of Miller's. Tom Roberts As you know, my approach to Miller's analysis differs from your > own, in that I do not question the reality of the signal, but > rather focus on whether the observed signal satisfies the > criteria necessary for it to be considered as having a celestial > origin. The answer, of course, is a resounding NO. Miller, for example, contended that the seasonal amplitude and > azimuth variations that he observed showed constant phase when > plotted against sidereal time. Miller's plots in his Fig 26 at > first look rather convincing, until one realizes that it is > Miller's fanciful fits to the reduced data that show constant > phase, not the data itself. Erase Miller's fits to the reduced > data, and the apparent constant phase vanishes. > http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm I only recently realized that the method that Miller used to > compute his running averages of magnitude and azimuth are highly > suspect. Quite obviously, Miller did not plan for his marathon > observing sessions to begin and end at 0:00 - 24:00 sidereal time, > yet the running averages presented in his Figures 22, 26 and 27 > are continuous over the entire 0:00 - 24:00 span. The only > explanation for this, is that Miller must have improperly > looped the data from his observing sessions, and computed the > running average across the seam between the end of an observing > session and the beginning of the same session. This procedure, of > course, imposes a false 24 hour periodicity into his running > averages. > http://mysite.verizon.net/cephalobus alienus/Miller/FakeRunningAverages.htm Somewhere in each of his plots in Figure 22 would be a pair of > points representing the end of one observing session and the > beginning of the same session. One point in each of his running > averages must represent an improper average of data taken over > 24 hours apart. Given your access to Miller's original data, might it be possible > for you to identify the points where Miller performed this > improper concatenation of data? This is a low priority request. We both have real work to do. Jerry present a paragraph of text, then step back and absorb. Have you considered the case of P cs NP and/or P vs NP and how it/ they relate to the Michelson-Morley experiment? Being how the speed of light is for the most part dealt with effectively as a constant, despite Einstein's admission of it being (in his words) a best guess, and how P vs. NP works against Physics in terms of absolute values and the limitations of computation as it plays against reality, their may very well be more to it. The comparison of these two problems/experiments present an overlap in the possibility exists one paradox unlocks or nullifies the keys to the other. Light is energy. The absence of the ommission of light in time propels entropy and is the purest form of unintentional computation inside celestial mechanics. Consider the universe one big Turing machine and all consequences in it the result of one of two states. <[1]> The digital state of the propulsion of light. <[2]> The absence of it. In this respect the entire universe is created by the celestial binary of Let there be...not. I do not equate the entire theory of Quantum State and Evolution to be the result of an off/on switch, but rather the continuation and fluctuation of light. Beside time light exists, does it not? MeAmI.org http://MeAmI.org Seriously, so you don't get my P vs. NP theories or diatribes of loose theory, fine, but my search is better than Google for a simple fact: Google built it. I improved it. P.S. We really need some users in Africa. It is the only continent we are somewhat lagging. If you have an African based charity or cause you would like to promote, (or any ideas on how to gain presence in the continent of Africa, send an email to MeAmI@vzw.blackberry.net. MM Musatov === Subject: Re: michelson morley experiment questions >Eg. Figure 4 in Miller's paper shows that the velocity he obtained in >1925 was consistent with the velocity of ether drift observed by >Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 >and 1905. >NONE of those are useful. They all used the algorithm that averages >turns, and that essentially forces their noise to look just like they >expected a signal to look. > That is an unsubstantiated assertion. It certainly did not occur with > the data that Miller presented in Figure 8 of his 1933 paper, as > Miller's algorithm produced amost output as my own. > So you made the same mistake that Miller did. That is something you should be ashamed of. > === Subject: Re: michelson morley experiment questions posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > A possible theory of operation is discussed here: > Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 >Ahh, the other pair of renowed crackpots. Let me guess, what comes >next, a citation from Cahill or one from Munera? Or is it back to >Dayton Miller? Messrs. Consoli and Constanzo never ran their experiments. What is >even more embarassing is that their theory is ALREADY refuted by the >a couple of experiments: #1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg >2489 (1974). A triangle interferometer with one leg in glass. They set an upper >limit on the anisotropy of 0.025 m/s. This is about one-millionth of >the Earth's orbital velocity and about 1/10,000 of its rotational >velocity. >#2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. A repetition of the MMX with the optical paths in perspex (n = 1.49), >and a laser-based optics sensitive to ~0.00003 fringe. They report a >null result with an upper limit on v?ther of 6.64 km/s. > I elsewhere pointed out that experiments that attempt to detect light > speed anisotropy in vacuum don't work, because variation of light > speed is exactly compensated for by Lorentz contraction of the > apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Depending on the degree to which that occurs or does not occur, there > is opportunity for experiments to fail to detect anisotropy. But while some fail in this regard, others succeed. Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. That's five examples of successful experiments. Make it 6. #6DIRECTORY: 1887 DIRECTORY OF CLINTON, LYONS AND CHANCY: Clinton ...W., res 1015 4th st Miller, Christ, works Curtis Bros. ..... Isaac, res 527 2d ave, up-stairs Nielsen, Peter Christ, works C. Lamb & Sons, res 530 dewitt st ...http:// files.usgwarchives.org/ia/clinton/history/dir/1887m.txt === Subject: Re: michelson morley experiment questions >A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments >M. Consoli, E. Costanzo >Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 >Ahh, the other pair of renowed crackpots. Let me guess, what comes >next, a citation from Cahill or one from Munera? Or is it back to >Dayton Miller? >Messrs. Consoli and Constanzo never ran their experiments. What is >even more embarassing is that their theory is ALREADY refuted by the >a couple of experiments: >#1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg >2489 (1974). >A triangle interferometer with one leg in glass. They set an upper >limit on the anisotropy of 0.025 m/s. This is about one-millionth of >the Earth's orbital velocity and about 1/10,000 of its rotational >velocity. >#2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. >A repetition of the MMX with the optical paths in perspex (n = 1.49), >and a laser-based optics sensitive to ~0.00003 fringe. They report a >null result with an upper limit on v.bether of 6.64 km/s. I elsewhere pointed out that experiments that attempt to detect light > speed anisotropy in vacuum don't work, because variation of light > speed is exactly compensated for by Lorentz contraction of the > apparatus. You do not read very well. Perspex is not vacuum, glass is not vacuum. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Proved wrong in the experiments above. Depending on the degree to which that occurs or does not occur, there > is opportunity for experiments to fail to detect anisotropy. But while some fail in this regard, others succeed. Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. That's five examples of successful experiments. That is your delusion showing up. There is a century of newer experiments all of which show zero. You are fixated on one bad experimenter and one crank. You need to actually read what is posted. > === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP That is your delusion showing up. There is a century of newer > experiments all of which show zero. You are fixated on one bad > experimenter and one crank. You need to actually read what is > posted. > Right on. But Peter (Surfer) will go to his grave clinging to his claims. Nothing doing. === Subject: Re: michelson morley experiment questions > That is your delusion showing up. There is a century of newer > experiments all of which show zero. You are fixated on one bad > experimenter and one crank. You need to actually read what is > posted. >Right on. But Peter (Surfer) will go to his grave clinging to his >claims. Nothing doing. > Hope you are both feeling better after those rants ! Of course objectively speaking Dougs statement, There is a century of newer experiments all of which show zero. is wrong, because the century includes: 1) Miller's experiments after 1909 2) Recent experiments by Munera et alia. Eg: Observation of a Non-conventional Influence of Earth's Motion on the Velocity of Photons, and Calculation of the Velocity of Our Galaxy PIERS Proceedings, Beijing, China, March 23-27, 2009 http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5YmVpamlu Z3wxUDRiXzAxMDgucGRmfDA4MDkwNzIyNTYzOQ== 3) Other experiments. Eg by DeWitte (1991), Torr and Kolen (1981), Cahill (2006), Cahill and Stokes (2008) and Cahill (2009). === Subject: Re: michelson morley experiment questions posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) > That is your delusion showing up. There is a century of newer > experiments all of which show zero. You are fixated on one bad > experimenter and one crank. You need to actually read what is > posted. Right on. But Peter (Surfer) will go to his grave clinging to his >claims. Nothing doing. Hope you are both feeling better after those rants ! Of course objectively speaking Dougs statement, There is a century of > newer experiments all of which show zero. is wrong, because the > century includes: 1) Miller's experiments after 1909 2) Recent experiments by Munera et alia. Eg: > Observation of a Non-conventional Influence of Earth's Motion on > the Velocity of Photons, and Calculation of the Velocity of Our > Galaxy > PIERS Proceedings, Beijing, China, March 23-27, 2009http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5Y... 3) Other experiments. Eg by DeWitte (1991), Torr and Kolen (1981), > Cahill (2006), Cahill and Stokes (2008) and Cahill (2009). Wow Surfer citing Cahill? Unexpected. === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > That is your delusion showing up. There is a century of newer > experiments all of which show zero. You are fixated on one bad > experimenter and one crank. You need to actually read what is > posted. Right on. But Peter (Surfer) will go to his grave clinging to his >claims. Nothing doing. Hope you are both feeling better after those rants ! Of course objectively speaking Dougs statement, There is a century of > newer experiments all of which show zero. is wrong, because the > century includes: 1) Miller's experiments after 1909 2) Recent experiments by Munera et alia. Eg: > Observation of a Non-conventional Influence of Earth's Motion on > the Velocity of Photons, and Calculation of the Velocity of Our > Galaxy > PIERS Proceedings, Beijing, China, March 23-27, 2009http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5Y... 3) Other experiments. Eg by DeWitte (1991), Torr and Kolen (1981), > Cahill (2006), Cahill and Stokes (2008) and Cahill (2009). Wow Surfer citing Cahill? Unexpected. Hahahahahaha === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > That is your delusion showing up. There is a century of newer > experiments all of which show zero. You are fixated on one bad > experimenter and one crank. You need to actually read what is > posted. Right on. But Peter (Surfer) will go to his grave clinging to his >claims. Nothing doing. Hope you are both feeling better after those rants ! Of course objectively speaking Dougs statement, There is a century of > newer experiments all of which show zero. is wrong, because the > century includes: 1) Miller's experiments after 1909 > Peter, But you are the imbecile who will go to his grave denying that Miller's experiment is flawed. > 2) Recent experiments by Munera et alia. Eg: > Observation of a Non-conventional Influence of Earth's Motion on > the Velocity of Photons, and Calculation of the Velocity of Our > Galaxy > PIERS Proceedings, Beijing, China, March 23-27, 2009http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5Y... > I told you that you will cite Munera :-) You are so predictable, Peter. > 3) Other experiments. Eg by DeWitte (1991), Torr and Kolen (1981), > Cahill (2006), Cahill and Stokes (2008) and Cahill (2009). Cahill, of course :-) and the other crank, DeWitte :-) You will die a crackpot, Peter, nothing doing . === Subject: Re: michelson morley experiment questions > That is your delusion showing up. There is a century of newer > experiments all of which show zero. You are fixated on one bad > experimenter and one crank. You need to actually read what is > posted. >Right on. But Peter (Surfer) will go to his grave clinging to his >claims. Nothing doing. > Hope you are both feeling better after those rants ! Of course objectively speaking Dougs statement, There is a century of > newer experiments all of which show zero. is wrong, because the > century includes: 1) Miller's experiments after 1909 2) Recent experiments by Munera et alia. Eg: > Observation of a Non-conventional Influence of Earth's Motion on > the Velocity of Photons, and Calculation of the Velocity of Our > Galaxy > PIERS Proceedings, Beijing, China, March 23-27, 2009 > http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5YmVpamlu Z 3wxUDRiXzAxMDgucGRmfDA4MDkwNzIyNTYzOQ== 3) Other experiments. Eg by DeWitte (1991), Torr and Kolen (1981), > Cahill (2006), Cahill and Stokes (2008) and Cahill (2009). > The requested site is unavailable, top ing secret or wants money. === Subject: Re: michelson morley experiment questions >That is your delusion showing up. There is a century of newer >experiments all of which show zero. You are fixated on one bad >experimenter and one crank. You need to actually read what is >posted. >Right on. But Peter (Surfer) will go to his grave clinging to his >claims. Nothing doing. > Hope you are both feeling better after those rants ! Of course objectively speaking Dougs statement, There is a century of > newer experiments all of which show zero. is wrong, because the > century includes: 1) Miller's experiments after 1909 Miller's experiment is quite compatible with relativity. In spite of your not liking it, there is no signal in it and the error bars are too large to make any claim that it disagrees with zero. 2) Recent experiments by Munera et alia. Eg: > Observation of a Non-conventional Influence of Earth's Motion on > the Velocity of Photons, and Calculation of the Velocity of Our > Galaxy > PIERS Proceedings, Beijing, China, March 23-27, 2009 > http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5YmVpamlu Z 3wxUDRiXzAxMDgucGRmfDA4MDkwNzIyNTYzOQ== > We have seen this before. No temperature control, no environmental control and huge error bars. Sloppy experimental work does not overcome careful experimental work. > 3) Other experiments. Eg by DeWitte (1991), Torr and Kolen (1981), > Cahill (2006), Cahill and Stokes (2008) and Cahill (2009). Cahill is a known crank and a joke in the physics world. He started off making some silly statements about relativity and when his mistakes were pointed out, he started to claim that the effects would only be seen when n was not 1. Then there were the experiments in solids which showed him to be wrong again. He is now reduced to claiming that there is something special about gases. He also has to ignore the experiments which he does not like. I notice that you are carefully avoiding discussing the carefully done experiments which have put the anisotropy limits many orders of magnitude below those claimed by Miller. Running away from the truth does not help your arguments. === Subject: Re: michelson morley experiment questions Miller's experiment is quite compatible with relativity. In spite >of your not liking it, there is no signal in it and the error >bars are too large to make any claim that it disagrees with zero. > Doug, I don't dislike SR, but as time has passed I have become aware of evidence against it. Eg. as I pointed out earlier, I found that Miller's signals were mainly contaminated by lower frequency noise that was easy to remove. That is shown by the DFTs on this page. http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ After removing the noise, the signals have very small error bars. That is just a fact. > > 2) Recent experiments by Munera et alia. Eg: > Observation of a Non-conventional Influence of Earth's Motion on > the Velocity of Photons, and Calculation of the Velocity of Our > Galaxy > PIERS Proceedings, Beijing, China, March 23-27, 2009 > http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5YmVpamlu Z 3wxUDRiXzAxMDgucGRmfDA4MDkwNzIyNTYzOQ== > >We have seen this before. No temperature control, no environmental >control and huge error bars. > The paper reports that environmental effects were monitored and subtracted. Perhaps it could be done better, but I don't see evidence of huge error bars. === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP Miller's experiment is quite compatible with relativity. In spite >of your not liking it, there is no signal in it and the error >bars are too large to make any claim that it disagrees with zero. Doug, I don't dislike SR, but as time has passed I have become aware of > evidence against it. > Peter, You are a self-deluded idiot. This is not curable. Munera, Consoli, Cahill are crackpots that don't evem understand that modern reenactments of MMX are done with resonating cavities. This approach severely limits drif due to temperature, humidity, mechanical stress, etc. I would give you some references but you have your head heart content on your own. === Subject: Re: michelson morley experiment questions >Miller's experiment is quite compatible with relativity. In spite >of your not liking it, there is no signal in it and the error >bars are too large to make any claim that it disagrees with zero. > Doug, I don't dislike SR, but as time has passed I have become aware of > evidence against it. What evidence? Eg. as I pointed out earlier, I found that Miller's signals were > mainly contaminated by lower frequency noise that was easy to remove. Miller's data has been superceded by newer experiments which move the resolution limits down by perhaps eight orders of magnitude. This means Miller is wrong no matter how much you try to ignore reality. That is shown by the DFTs on this page. > http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ After removing the noise, the signals have very small error bars. That is just a fact. Either Miller is correct and all careful modern experiments done are wrong or Miller is wrong. You have a delusion but that is what cranks do. >2) Recent experiments by Munera et alia. Eg: >Observation of a Non-conventional Influence of Earth's Motion on >the Velocity of Photons, and Calculation of the Velocity of Our >Galaxy >PIERS Proceedings, Beijing, China, March 23-27, 2009 >http://piers.mit.edu/piersproceedings/download.php?file=cGllcnMyMDA5YmVpa mluZ3wxUDRiXzAxMDgucGRmfDA4MDkwNzIyNTYzOQ== >We have seen this before. No temperature control, no environmental >control and huge error bars. The paper reports that environmental effects were monitored and > subtracted. Sure they were. You just keep believing that. Perhaps it could be done better, but I don't see evidence of huge > error bars. Incompetence will do that. > === Subject: Re: michelson morley experiment questions Miller's data has been superceded by newer experiments which move >the resolution limits down by perhaps eight orders of magnitude. >This means Miller is wrong no matter how much you try to ignore >reality. > Hmm. You are attempting to use logic to deny facts of observation. But the contradiction you perceive can easily be resolved, by noting that in Miller's experiment the light was passing through a gas (ie air), whereas in most modern experiments the light is passing through vacuum or something other than gas. This suggests that the gas in Miller's experiment made it sensitive to absolute motion effects, while experiments that use vacuum or a dielectric other than gas, are inherently insensitive. > > That is shown by the DFTs on this page. > http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ > > After removing the noise, the signals have very small error bars. > > That is just a fact. Either Miller is correct and all careful modern experiments done >are wrong or Miller is wrong. > No. They can both be right for reasons given above. === Subject: Re: michelson morley experiment questions > This suggests that the gas in Miller's experiment made it sensitive to > absolute motion effects, while experiments that use vacuum or a > dielectric other than gas, are inherently insensitive. Why should that be so? After all, other optical phenomena depend only on the refractive index of the material. Why is absolute motion so special? Your attempt at a special plead is ridiculous without any compelling model of why gas is so special a configuration of atoms. And experiments that have gas in the optical path but took care to regulate its temperature see no absolute motion. It is only CARELESS EXPERIMENTERS that see absolute motion in gas interferometers. Moreover, in cases where it is possible, an error analysis of their data shows their conclusion is not statistically significant. A MUCH more likely reason is that gas has a VASTLY smaller heat capacity, and a larger variation of refractive index with temperature. So an interferometer with gas in its light paths is MUCH more sensitive to variations in temperature than is one with vacuum, liquid, or solid in the light paths. Experimenters who did not perform an error analysis of their data can easily be fooled. Tom Roberts === Subject: Re: michelson morley experiment questions posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) [...] > This suggests that the gas in Miller's experiment made it sensitive to > absolute motion effects, while experiments that use vacuum or a > dielectric other than gas, are inherently insensitive. Ah, there's the special plead. [...] === Subject: Re: michelson morley experiment questions >Miller's data has been superceded by newer experiments which move >the resolution limits down by perhaps eight orders of magnitude. >This means Miller is wrong no matter how much you try to ignore >reality. > Hmm. You are attempting to use logic to deny facts of observation. No, you are holding onto your delusions. Careful experiments show no effects to a resolution a billion times that of Miller. Thst means the error bars of Miller include zero. You are being a crank if you think otherwise. But the contradiction you perceive can easily be resolved, by noting > that in Miller's experiment the light was passing through a gas (ie > air), whereas in most modern experiments the light is passing through > vacuum or something other than gas. This suggests that the gas in Miller's experiment made it sensitive to > absolute motion effects, while experiments that use vacuum or a > dielectric other than gas, are inherently insensitive. You are being willingly ignorant by ignoring experiments which have tested this effect and found it does not exist. >That is shown by the DFTs on this page. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ After removing the noise, the signals have very small error bars. That is just a fact. >Either Miller is correct and all careful modern experiments done >are wrong or Miller is wrong. > No. They can both be right for reasons given above. > No. You are just being a typical crank. > === Subject: Re: michelson morley experiment questions > [about Munera et al] > The paper reports that environmental effects were monitored and > subtracted. They did not do so with sufficient accuracy. They only measured temperature with a resolution of 0.2 C [#], and a difference that large between their arms generates a fringe shift BIGGER than their signal [@]. The temperature variance in their room was MUCH larger, and they insulated the arms from the room and from each other, so such temperature variations are virtually certain to occur. [#] This comes from an earlier paper on the same experiment. [@] This comes from a simple estimate based on the details given in that previous paper. > Perhaps it could be done better, but I don't see evidence of huge > error bars. That's because you simply do not understand error analysis. Those of us who do understand error analysis know that NONE of the experiments you cite have significant signals. Tom Roberts === Subject: Re: michelson morley experiment questions Those of us who do understand error analysis know that NONE of the >experiments you cite have significant signals. > I understood enough to figure out the following. The raw data in Figure 8 of Miller's paper admittedly contains a lot of noise: http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf However, the noise is easy to remove and after doing so I get a clean signal with small error bars http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ (That is, a significant signal.) In contrast, you deliberately use the raw data to get huge error bars: http://arxiv.org/abs/physics/0608238 so you can falsely claim that the signal lacks significance. === Subject: Re: michelson morley experiment questions > In contrast, you deliberately use the raw data to get huge error bars: > http://arxiv.org/abs/physics/0608238 > so you can falsely claim that the signal lacks significance. MILLER averaged the raw data, so the statistical errorbar on his averages comes from THE RAW DATA. The signal Miller found does indeed lack significance. This is not merely my claim, this is a mathematical FACT about these data and his analysis method. Tom Roberts === Subject: Re: michelson morley experiment questions <9ny3m.11080$aX1.7265@nlpi067.nbdc.sbc.com> <8ltu459ndvq0s1g6o25cg61ikln3tsdio7@4ax.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.7.STABLE6) MeAmI.org e-meal: > In contrast, you deliberately use the raw data to get huge error bars: > http://arxiv.org/abs/physics/0608238 > so you can falsely claim that the signal lacks significance. MILLER averaged the raw data, so the statistical errorbar on his > averages comes from THE RAW DATA. The signal Miller found does indeed > lack significance. This is not merely my claim, this is a mathematical > FACT about these data and his analysis method. > Tom Roberts Tom a fact involves perceived truth. Universal truth exists beside perfection. It does not need observation to exist. What we do not understand or seek to suppress we sometimes mock or ridicule. Make an honest effort to understand. processor; Minimum ... neurosthenia diopter orthonormal Yeshua nephele 336f45402ca12ac3 Here is 0 vs. 1: (after a) a 0 vs 1 i 2 3 de 4 s tv t x la xbox 5 en 6 lil n wayne y gameplay ...a 0 vs 1 i 2 3 de 4 s tv t x la xbox 5 en 6 lil n wayne y gameplay 7 u iphone youtube uk online vegas japanese photoshop ad el ipod jones pc bloopers e 8 ...http://www.hsiinc.org/data/ en_word_wikitube.txt === Subject: Re: michelson morley experiment questions >Those of us who do understand error analysis know that NONE of the >experiments you cite have significant signals. I understood enough to figure out the following. The raw data in Figure 8 of Miller's paper admittedly contains a lot > of noise: > http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf However, the noise is easy to remove and after doing so I get a clean > signal with small error bars > http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ > (That is, a significant signal) You have made the same mistake that Miller did. The assumption you have made is that the component of the systematic drift in the frequency bin you wanted was zero. You used this simplistic method to just apply a narrowband filter to the data for bin 50 (although your plot of the DFTs shows the assumptions you made on the response of the systematic noise. The smooth values for the bins from about 30 to about 50 demonstrate your assumption. What you have ignored in Tom's paper, is that Tom did a careful model of the systematic noise. That makes all the difference in the world to the analysis. We are to compare your guess with Tom's extensive analysis. Conclusions based on guesses always take a back seat to those supported by careful analysis. In contrast, you deliberately use the raw data to get huge error bars: > http://arxiv.org/abs/physics/0608238 > so you can falsely claim that the signal lacks significance. > You need to read and try to understand what Tom did. You claim to have deliberately imply a malice that is not there. > === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP I elsewhere pointed out that experiments that attempt to detect light > speed anisotropy in vacuum don't work, because variation of light > speed is exactly compensated for by Lorentz contraction of the > apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. > Peter, You mean that all these people don't know what they are doing and that they should be consulting you in order to correct their experiments? * Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821. Uses two multi-mode lasers mounted on a rotating table to look for variations in their interference pattern as the table is rotated. Places an upper limit on any one-way anisotropy of 0.9 m/s. * Krisher et al., Phys. Rev. D, 42, No. 2, pg 731[CapitalEth]734, (1990). Uses two hydrogen masers fixed to the Earth and separated by a 21-km fiber-optic link to look for variations in the phase between them. They put an upper limit on the one-way linear anisotropy of 100 m/s. * Champeny et al., Phys. Lett. 7 (1963), pg 241. Champeney, Isaak and Khan, Proc. Physical Soc. 85, pg 583 (1965). Isaak et al., Phys. Bull. 21 (1970), pg 255. Uses a rotating M.9assbauer absorber and fixed detector to place an upper limit on any one-way anisotropy of 3 m/s. * Turner and Hill, Phys. Rev. 134 (1964), B252. Uses a rotating source and fixed M.9assbauer detector to place an upper limit on any one-way anisotropy of 10 m/s. * Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg 1767. A guided-wave test of isotropy. Their null result is consistent with SR. * T.W. Cole, ñAstronomical Tests for the Presence of an Etherî, Mon. Not. R. Astr. Soc. (1976), 175 93P-96P. Several VLBI tests sensitive to first-order effects of an .bether are described. No .bether is detected, with a sensitivity of 70 m/s. * Ragulsky, ñDetermination of light velocity dependence on direction of propagationî, Phys. Lett. A, 235 (1997), pg 125. A ñone-wayî test that is bidirectional with the outgoing ray in glass and the return ray in air. The interferometer is by design particularly robust against mechanical perturbations, and temperature controlled. The limit on the anisotropy of c is 0.13 m/s. === Subject: Re: michelson morley experiment questions > To detect light speed anisotropy the experiment has to include > something to disturb the balance. I remark that of the following 7 experiments, 6 have propagation in some non-vacuum medium: air Cialdea, Ragulsky glass Krisher et al, Ragulsky iron Champeny et al, Turner and Hill waveguide Gagnon et al BTW Ragulsky showed that it _IS_ possible to operate an interferometer in air with stable results; temperature and mechanical stability are ESSENTIAL. Tom Roberts > * Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821. Uses two multi-mode lasers mounted on a rotating table to look > for variations in their interference pattern as the table is rotated. > Places an upper limit on any one-way anisotropy of 0.9 m/s. > * Krisher et al., Phys. Rev. D, 42, No. 2, pg 731[CapitalEth]734, (1990). Uses two hydrogen masers fixed to the Earth and separated by a > 21-km fiber-optic link to look for variations in the phase between > them. They put an upper limit on the one-way linear anisotropy of 100 > m/s. > * Champeny et al., Phys. Lett. 7 (1963), pg 241. Champeney, Isaak > and Khan, Proc. Physical Soc. 85, pg 583 (1965). Isaak et al., Phys. > Bull. 21 (1970), pg 255. Uses a rotating M.9assbauer absorber and fixed detector to place > an upper limit on any one-way anisotropy of 3 m/s. > * Turner and Hill, Phys. Rev. 134 (1964), B252. Uses a rotating source and fixed M.9assbauer detector to place an > upper limit on any one-way anisotropy of 10 m/s. > * Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg > 1767. A guided-wave test of isotropy. Their null result is consistent > with SR. > * T.W. Cole, ñAstronomical Tests for the Presence of an Etherî, > Mon. Not. R. Astr. Soc. (1976), 175 93P-96P. Several VLBI tests sensitive to first-order effects of an .bether > are described. No .bether is detected, with a sensitivity of 70 m/s. > * Ragulsky, ñDetermination of light velocity dependence on > direction of propagationî, Phys. Lett. A, 235 (1997), pg 125. A ñone-wayî test that is bidirectional with the outgoing ray in > glass and the return ray in air. The interferometer is by design > particularly robust against mechanical perturbations, and temperature > controlled. The limit on the anisotropy of c is 0.13 m/s. === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > To detect light speed anisotropy the experiment has to include > something to disturb the balance. I remark that of the following 7 experiments, 6 have propagation in some > non-vacuum medium: > air Cialdea, Ragulsky > glass Krisher et al, Ragulsky > iron Champeny et al, Turner and Hill > waveguide Gagnon et al BTW Ragulsky showed that it IS possible to operate an interferometer > in air with stable results; temperature and mechanical stability are > ESSENTIAL. Tom Roberts * Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821. Uses two multi-mode lasers mounted on a rotating table to look > for variations in their interference pattern as the table is rotated. > Places an upper limit on any one-way anisotropy of 0.9 m/s. > * Krisher et al., Phys. Rev. D, 42, No. 2, pg 731[CapitalEth]734, (1990). Uses two hydrogen masers fixed to the Earth and separated by a > 21-km fiber-optic link to look for variations in the phase between > them. They put an upper limit on the one-way linear anisotropy of 100 > m/s. > * Champeny et al., Phys. Lett. 7 (1963), pg 241. Champeney, Isaak > and Khan, Proc. Physical Soc. 85, pg 583 (1965). Isaak et al., Phys. > Bull. 21 (1970), pg 255. Uses a rotating M.9assbauer absorber and fixed detector to place > an upper limit on any one-way anisotropy of 3 m/s. > * Turner and Hill, Phys. Rev. 134 (1964), B252. Uses a rotating source and fixed M.9assbauer detector to place an > upper limit on any one-way anisotropy of 10 m/s. > * Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg > 1767. A guided-wave test of isotropy. Their null result is consistent > with SR. > * T.W. Cole, ñAstronomical Tests for the Presence of an Etherî, > Mon. Not. R. Astr. Soc. (1976), 175 93P-96P. Several VLBI tests sensitive to first-order effects of an .bether > are described. No .bether is detected, with a sensitivity of 70 m/s. > * Ragulsky, ñDetermination of light velocity dependence on > direction of propagationî, Phys. Lett. A, 235 (1997), pg 125. A ñone-wayî test that is bidirectional with the outgoing ray in > glass and the return ray in air. The interferometer is by design > particularly robust against mechanical perturbations, and temperature > controlled. The limit on the anisotropy of c is 0.13 m/s. Yes, I gave Surfer the other two (Shamir and Trimmer). I also explained to him that the latest reenctments don't use conventional interferometers anymore, they use resonating cavities . To no avail, the idiot has his head stuck up his ass so far that nothing registers. BTW, I think that you could use some of the newer references to MMX executed with resonating cavities. Do you need the references? I can send them to you. === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > A possible theory of operation is discussed here: > Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 Ahh, the other pair of renowed crackpots. Let me guess, what comes >next, a citation from Cahill or one from Munera? Or is it back to >Dayton Miller? Messrs. Consoli and Constanzo never ran their experiments. What is >even more embarassing is that their theory is ALREADY refuted by the >a couple of experiments: #1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg >2489 (1974). A triangle interferometer with one leg in glass. They set an upper >limit on the anisotropy of 0.025 m/s. This is about one-millionth of >the Earth's orbital velocity and about 1/10,000 of its rotational >velocity. #2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. A repetition of the MMX with the optical paths in perspex (n = 1.49), >and a laser-based optics sensitive to ~0.00003 fringe. They report a >null result with an upper limit on v.bether of 6.64 km/s. I elsewhere pointed out that experiments that attempt to detect light > speed anisotropy in vacuum don't work, because variation of light > speed is exactly compensated for by Lorentz contraction of the > apparatus. > Peter, First of all, this is not correct, secondly, it has nothing to do with your inability to understand why MMX executed in refringent medium refutes the cranks Consoli, Cahill and Munera > To detect light speed anisotropy the experiment has to include > something to disturb the balance. > Yes, and this is being done by using test theories of SR, like Mansouri-Sexl or Standard Model Extension. You are obviously ignorant about this subject. > Depending on the degree to which that occurs or does not occur, there > is opportunity for experiments to fail to detect anisotropy. > No, there isn't. There has never been one for years. Either way, this is not relevant to your inability to understand why Consoli, Cahill and Munera are crackpots. > But while some fail in this regard, others succeed. Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. That's five examples of successful experiments. Peter, Add Miller to the list. === Subject: Re: michelson morley experiment questions > >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. > Just wanted to point out that this was not my analysis. The link > provided was from one of Surfer's posts. It looked pretty good so I > answering. > What is obviously wrong is the conclusion. For some reason, a lot of cranks have fixated on Miller's experiments. Since there is better data available now that has up to a factor of a billion or so better resolution and accuracy, Miller's mistakes are of only historical interest. His results cannot be correct since they do not agree with those experiments. > >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. Any chance you could provide a link to data for some of the other > runs, or post that data here? Nobody should complain about the use of > bandwidth considering how much is wasted on pure crap around here :) > The run we have been beating to death has obvious defects. I would > like to see others. > You should read the paper by Tom Roberts. He does a nice job in the analysis. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> posting-account=OYbTxggAAACimxHivNfPv6KRfdOPL6RK x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis of Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. Just wanted to point out that this was not my analysis. The link > provided was from one of Surfer's posts. It looked pretty good so I > answering. What is obviously wrong is the conclusion. I was looking for something a little more specific than the results don't agree with what you expect. It uses what look to be modern methods of looking at Miller's data and gets about the same result Miller did. That is quite different from what Tom got, so I thought Tom might comment. > For some reason, a lot of > cranks have fixated on Miller's experiments. Since there is better > data available now that has up to a factor of a billion or so better > resolution and accuracy, Miller's mistakes are of only historical > interest. IMO it would be better to show how Miller got some false signals than to claim no pattern ever existed in the data. Just looking at a plot of the data in fig.8 it is obvious there is a pattern there with the frequency being sought. To say that it doesn't exist is an insult to anyone that looks at the plot. I agree the pattern is not from ether drift. I suspect the pattern is from the temperture gradient of the air, and the downward trend is caused by the heating/cooling of the frame. That I consider a very plausible explaination. But to say there is no pattern..... A quick way of showing the pattern was not ether drift would be to provide a few more sets of data that didn't show such a pattern. His results cannot be correct since they do not agree > with those experiments. > That still doesn't explain the results, and it was not my point anyway. My point is that it is just as bad to see nothing where there is something as it is to see something where there is nothing. Claiming there is no pattern when one jumps out and slaps you in the face just gives more fuel to the cranks. I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. Any chance you could provide a link to data for some of the other > runs, or post that data here? Nobody should complain about the use of > bandwidth considering how much is wasted on pure crap around here :) > The run we have been beating to death has obvious defects. I would > like to see others. > You should read the paper by Tom Roberts. He does a nice job in > the analysis. > I have read Tom's paper, several times. Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: michelson morley experiment questions > >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. >Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. > I was looking for something a little more specific than the results > don't agree with what you expect. It uses what look to be modern > methods of looking at Miller's data and gets about the same result > Miller did. That is quite different from what Tom got, so I thought > Tom might comment. > You can read Tom's paper and see in detail what he did. > >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. > IMO it would be better to show how Miller got some false signals than > to claim no pattern ever existed in the data. Just looking at a plot > of the data in fig.8 it is obvious there is a pattern there with the > frequency being sought. The adjustments that Miller made required the pattern to show up. To say that it doesn't exist is an insult to > anyone that looks at the plot. I agree the pattern is not from ether > drift. I suspect the pattern is from the temperture gradient of the > air, and the downward trend is caused by the heating/cooling of the > frame. That I consider a very plausible explaination. But to say > there is no pattern..... There are also flexing issues with the rotation but that is not the point. The claim by Miller was that all the fluctuations pointed to one spot in the sky although apparently that point changed with when he reported the results. A quick way of showing the pattern was not ether drift would be to > provide a few more sets of data that didn't show such a pattern. The fastest way to show the pattern is not ether drift is to look at the experiments with a billion times his sensitivity. That is quite conclusive. His results cannot be correct since they do not agree > >with those experiments. That still doesn't explain the results, and it was not my point > anyway. My point is that it is just as bad to see nothing where there > is something as it is to see something where there is nothing. > Claiming there is no pattern when one jumps out and slaps you in the > face just gives more fuel to the cranks. > The explaination is that it is wrong. Why is of only academic interest. Nothing you say or do will have any effect on the cranks here. They are beyond reason and are all suffering from various delusions about what science is. > >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. >Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. I have read Tom's paper, several times. And what did you disagree with? >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> posting-account=OYbTxggAAACimxHivNfPv6KRfdOPL6RK x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis of Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. I was looking for something a little more specific than the results > don't agree with what you expect. It uses what look to be modern > methods of looking at Miller's data and gets about the same result > Miller did. That is quite different from what Tom got, so I thought > Tom might comment. You can read Tom's paper and see in detail what he did. > That wasn't the question. The question was what was wrong with the analysis that showed a pattern? >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. IMO it would be better to show how Miller got some false signals than > to claim no pattern ever existed in the data. Just looking at a plot > of the data in fig.8 it is obvious there is a pattern there with the > frequency being sought. The adjustments that Miller made required the pattern to show up. That is bull and you know it. Here is Tom's paper so you can look for yourself. http://arxiv.org/ftp/physics/papers/0608/0608238.pdf Fig. 8 shows the first adjustment was made after five full turns. The pattern I am talking about shows up before that first adjustment. Perhaps you would like to explain how you think that first adjustment introduced the pattern in the preceeding five turns. Or how a total of three adjustments resulted in a half turn pattern showing up in twenty full turns. >To say that it doesn't exist is an insult to anyone that looks at the plot. I agree the pattern is not from ether > drift. I suspect the pattern is from the temperture gradient of the > air, and the downward trend is caused by the heating/cooling of the > frame. That I consider a very plausible explaination. But to say > there is no pattern..... There are also flexing issues with the rotation but that is not > the point. The claim by Miller was that all the fluctuations > pointed to one spot in the sky although apparently that point > changed with when he reported the results. No, the point I have been trying to make is there is a pattern. I agree that it is not ether drift, but something caused a pattern. To claim there is no pattern when there obviously is one is not good science. > A quick way of showing the pattern was not ether drift would be to > provide a few more sets of data that didn't show such a pattern. The fastest way to show the pattern is not ether drift is to look at > the experiments with a billion times his sensitivity. That is > quite conclusive. Those new experiments are not the same experiment. An argument could be made that something about them prevents them from picking up the Tom has said many of them showed nothing. There are a few shown here with no data. http://www.scieng.flinders.edu.au/cpes/people/cahill r/Miller1933.pdf If data for a few runs was shown it would show fig.8 was a temperture related fluke. > His results cannot be correct since they do not agree >with those experiments. That still doesn't explain the results, and it was not my point > anyway. My point is that it is just as bad to see nothing where there > is something as it is to see something where there is nothing. > Claiming there is no pattern when one jumps out and slaps you in the > face just gives more fuel to the cranks. The explaination is that it is wrong. Why is of only academic interest. > Nothing you say or do will have any effect on the cranks here. They > are beyond reason and are all suffering from various delusions about > what science is. > One of the quickest ways to turn someone into a crank is to lie to them. Telling them there is no pattern when they can see a pattern in the plot without doing any analysis imediately turns them against you. Why should they believe anything you say when they have already caught you trying to put something over on them? >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. I have read Tom's paper, several times. And what did you disagree with? > The fact that in the end he found no pattern where one obviously existed. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: michelson morley experiment questions > The question was what was wrong with the > analysis that showed a pattern? Children can see faces in clouds. PATTERNS alone are not sufficient. Physics is a QUANTITATIVE science, and one must show that the patterns are statistically significant. As I said before, when computing an average one always finds an answer, but to know if that answer is significant one must examine the errorbars. And, of course, one must compute them correctly -- Miller never looked at them, and surfer computed them incorrectly. The errorbars show unequivocally that the signal Miller found is not significant. > [what did you disagree with in Tom's analysis?] > The fact that in the end he found no pattern where one obviously > existed. But the obvious pattern is not significant. Neither are those faces in clouds. Just LOOK at figure 3 of my paper -- Miller's linear assumption is VERY BAD. The variations between the points and corners are an order of magnitude BIGGER than the signal he found, and they can only be an instrumentation effect. surfer keeps insisting that the presence of an amplitude for 1/2-turn greater than the background is a signal -- figure 3 shows that is wrong, as the difference between points and corners is purely instrumental, and has a strong amplitude with frequency 1/2-turn. Tom Roberts === Subject: Re: michelson morley experiment questions > >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: >A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. >B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. >Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. >I was looking for something a little more specific than the results >don't agree with what you expect. It uses what look to be modern >methods of looking at Miller's data and gets about the same result >Miller did. That is quite different from what Tom got, so I thought >Tom might comment. >You can read Tom's paper and see in detail what he did. That wasn't the question. The question was what was wrong with the > analysis that showed a pattern? You do not believe Tom so you should do your own analysis. You tell us what the data means. >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. >IMO it would be better to show how Miller got some false signals than >to claim no pattern ever existed in the data. Just looking at a plot >of the data in fig.8 it is obvious there is a pattern there with the >frequency being sought. >The adjustments that Miller made required the pattern to show up. > That is bull and you know it. Here is Tom's paper so you can look > for yourself. http://arxiv.org/ftp/physics/papers/0608/0608238.pdf Fig. 8 shows the first adjustment was made after five full turns. The > pattern I am talking about shows up before that first adjustment. > Perhaps you would like to explain how you think that first adjustment > introduced the pattern in the preceeding five turns. Or how a total > of three adjustments resulted in a half turn pattern showing up in > twenty full turns. > To say that it doesn't exist is an insult to >anyone that looks at the plot. I agree the pattern is not from ether >drift. I suspect the pattern is from the temperture gradient of the >air, and the downward trend is caused by the heating/cooling of the >frame. That I consider a very plausible explaination. But to say >there is no pattern..... >There are also flexing issues with the rotation but that is not >the point. The claim by Miller was that all the fluctuations >pointed to one spot in the sky although apparently that point >changed with when he reported the results. > No, the point I have been trying to make is there is a pattern. I > agree that it is not ether drift, but something caused a pattern. To > claim there is no pattern when there obviously is one is not good > science. > I do not care what the pattern is since it is not related to the physics. The current experiments say that it is wrong so feel free to spend your time finding out why. > >A quick way of showing the pattern was not ether drift would be to >provide a few more sets of data that didn't show such a pattern. >The fastest way to show the pattern is not ether drift is to look at >the experiments with a billion times his sensitivity. That is >quite conclusive. > Those new experiments are not the same experiment. They measured the same effect but in a more precise way. There have been some silly people here who claim that you have to exactly repeat some old experiment to debunk it but that is complete nonsense. An argument could > be made that something about them prevents them from picking up the > signal that Miller found. Have you read the experiments to see what they were doing? The whole point of Miller was to find an isotropy in the speed of light. There is none to limits a billion times finer than Miller was proposing. > Tom has said many of them showed nothing. There are a few shown here > with no data. So you are saying that you believe Miller saw aether drift? http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf Any reference to Cahill is automatically the sign of a crank. Cahill is a joke and only surfer believes him (many people believe surfer is Cahill). If data for a few runs was shown it would show fig.8 was a temperture > related fluke. > His results cannot be correct since they do not agree >with those experiments. >That still doesn't explain the results, and it was not my point >anyway. My point is that it is just as bad to see nothing where there >is something as it is to see something where there is nothing. >Claiming there is no pattern when one jumps out and slaps you in the >face just gives more fuel to the cranks. >The explaination is that it is wrong. Why is of only academic interest. >Nothing you say or do will have any effect on the cranks here. They >are beyond reason and are all suffering from various delusions about >what science is. One of the quickest ways to turn someone into a crank is to lie to > them. Telling them there is no pattern when they can see a pattern in > the plot without doing any analysis imediately turns them against > you. Why should they believe anything you say when they have already > caught you trying to put something over on them? > Well, the experiments say there is no signal. Any claim to the contrary is the sign of a crank who is ignoring the evidence. The cranks are unmoved by the truth in any case. Look at ken seto or Henri (ralph) or noeinstein or koobee or ... Pick any of hundreds. They are ignorant and plan on staying that way. > >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. >Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. >I have read Tom's paper, several times. >And what did you disagree with? The fact that in the end he found no pattern where one obviously > existed. Well, show the error in his analysis. If you found something, I would like to see it. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <29-dnWjFHdSt89DXnZ2dnUVZ_vSdnZ2d@posted.docknet> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: >A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. >B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. >Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. >I was looking for something a little more specific than the results >don't agree with what you expect. It uses what look to be modern >methods of looking at Miller's data and gets about the same result >Miller did. That is quite different from what Tom got, so I thought >Tom might comment. >You can read Tom's paper and see in detail what he did. > That wasn't the question. The question was what was wrong with the > analysis that showed a pattern? You do not believe Tom so you should do your own analysis. You tell us > what the data means. >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. >IMO it would be better to show how Miller got some false signals than >to claim no pattern ever existed in the data. Just looking at a plot >of the data in fig.8 it is obvious there is a pattern there with the >frequency being sought. >The adjustments that Miller made required the pattern to show up. > That is bull and you know it. Here is Tom's paper so you can look > for yourself. http://arxiv.org/ftp/physics/papers/0608/0608238.pdf Fig. 8 shows the first adjustment was made after five full turns. The > pattern I am talking about shows up before that first adjustment. > Perhaps you would like to explain how you think that first adjustment > introduced the pattern in the preceeding five turns. Or how a total > of three adjustments resulted in a half turn pattern showing up in > twenty full turns. > To say that it doesn't exist is an insult to >anyone that looks at the plot. I agree the pattern is not from ether >drift. I suspect the pattern is from the temperture gradient of the >air, and the downward trend is caused by the heating/cooling of the >frame. That I consider a very plausible explaination. But to say >there is no pattern..... >There are also flexing issues with the rotation but that is not >the point. The claim by Miller was that all the fluctuations >pointed to one spot in the sky although apparently that point >changed with when he reported the results. > No, the point I have been trying to make is there is a pattern. I > agree that it is not ether drift, but something caused a pattern. To > claim there is no pattern when there obviously is one is not good > science. I do not care what the pattern is since it is not related to the > physics. The current experiments say that it is wrong so feel > free to spend your time finding out why. A quick way of showing the pattern was not ether drift would be to >provide a few more sets of data that didn't show such a pattern. >The fastest way to show the pattern is not ether drift is to look at >the experiments with a billion times his sensitivity. That is >quite conclusive. > Those new experiments are not the same experiment. They measured the same effect but in a more precise way. There have > been some silly people here who claim that you have to exactly > repeat some old experiment to debunk it but that is complete > nonsense. An argument could > be made that something about them prevents them from picking up the > signal that Miller found. Have you read the experiments to see what they were doing? The whole > point of Miller was to find an isotropy in the speed of light. There > is none to limits a billion times finer than Miller was proposing. Tom has said many of them showed nothing. There are a few shown here > with no data. So you are saying that you believe Miller saw aether drift? > http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf Any reference to Cahill is automatically the sign of a crank. Cahill > is a joke and only surfer believes him (many people believe surfer is > Cahill). If data for a few runs was shown it would show fig.8 was a temperture > related fluke. > His results cannot be correct since they do not agree >with those experiments. >That still doesn't explain the results, and it was not my point >anyway. My point is that it is just as bad to see nothing where there >is something as it is to see something where there is nothing. >Claiming there is no pattern when one jumps out and slaps you in the >face just gives more fuel to the cranks. >The explaination is that it is wrong. Why is of only academic interest. >Nothing you say or do will have any effect on the cranks here. They >are beyond reason and are all suffering from various delusions about >what science is. > One of the quickest ways to turn someone into a crank is to lie to > them. Telling them there is no pattern when they can see a pattern in > the plot without doing any analysis imediately turns them against > you. Why should they believe anything you say when they have already > caught you trying to put something over on them? Well, the experiments say there is no signal. Any claim to the contrary > is the sign of a crank who is ignoring the evidence. The cranks are > unmoved by the truth in any case. Look at ken seto or Henri (ralph) > or noeinstein or koobee or ... Pick any of hundreds. They are ignorant > and plan on staying that way. >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. >Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. >I have read Tom's paper, several times. >And what did you disagree with? > The fact that in the end he found no pattern where one obviously > existed. Well, show the error in his analysis. If you found something, I would > like to see it. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <29-dnWjFHdSt89DXnZ2dnUVZ_vSdnZ2d@posted.docknet> posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > Any reference to Cahill is automatically the sign of a crank. Cahill > is a joke and only surfer believes him (many people believe surfer is > Cahill). No, he's not, he's just a guy who sucks up to Cahill. Cahill posts here occasionally (under his own name). He used to get a merciless beating every time he shows up, so he stopped posting. Surfer (aka Peter Brown) is an amateur who thinks that Cahill is god's gift to physics. === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) === Subject: Test Banks and solution manuals posting-account=jy2E5goAAAB1WGwMQL1h2k61o4k7O_u4 Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Email me at instructors.team[at]gmail.com if you need to buy any test bank or solution manual listed below. All emails will be answered quickly. 2009 Federal Taxation - Pratt [CapitalEth] Solutions Manual & test Bank Accounting for Non-Accounting Students test bank Accounting Information Systems (6thEd) - Hall - Solutions Manual Aerodynamics for Engineers, 5E Solution manual Bertin Russ Cummings Algebra and Trigonometry 3rd Ed, and Precalculus 3rd Ed, Instructor's Solutions Manual 2008 - Beecher, Penna, & Bittinger Analysis- With an Introduction to Proof, 4-E-Instructors SM Art Through The Ages A Global Hist Vol II Test Bank complete Auditing A Business Risk Approach (6thEd) - Rittenberg [CapitalEth] Solutions Manual Auditing A Business Risk Approach (6thEd) - Rittenberg Test Bank Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Solution Manual Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Test bank Auditing Cases Interactive Learning Approach (4thEd) - Beasley - Solutions Manual Beer, Johnston & Dewolf - Mechanics Of Materials Solution Manual 3Rd Ed Biology with Mastering Biology 8E Campbell Reece ISBN -0321494334 Test Bank Bond Markets, Analysis and Strategies 6E Instructors manual Fabozzi Brock Biology of Microorganisms 12E ISBN -0132324997 Test Bank Busines statistics Decision making 7E David F Groebner Solution manual Busines statistics Decision making 7E David F Groebner test bank Business Law and the Legal Environment Jeffrey F. Beatty 5th edition Test Bank Business Law Tax And Cases (11thEd) - Clarkson [CapitalEth] TestBank Business Statistics First Course Solutions Manual Levine Calculus A Complete Course Adams - - Instructors Solution Manual College Algebra 10E Margaret L. Lial solution manual College Algebra 10E Margaret L. Lial Test bank Concepts Of Programming Languages (8thEd) - Sebesta [CapitalEth] Solutions Manual Contemporary Financial Management (11thEd) - Moyer - Solutions Manual Cornerstone Of Managerial Accounting (2ndEd) - Mowen - Solutions Manual Corporate Partnership Estate Gift Tax 2009 - Pratt - Solutions Manual Cost accounting by Hongren 13/e test bank and Solution manual Cost Accounting Canadian (4thEd) - Horngren - Test Bank Cutnell John, Physics 7th E, Instructors manual (all solutions even +odd) Data Structures Algorithm Analysis In CPP (3rdEd) - Weiss - Solutions Manual Deitel & Deitel How to Program C++ 6th E Code solutions Options, Futures and Other Derivatives John Hull 7E test bank ch 1-21 with answers Digital Electronics A Practical Approach - William Kleitz 8th ed ISM Econometric Analysis - Solutions Manual (Greene 6Th 2007) Effective Small Business Management - Norman M Scarborough 9E Test bank Electrical Machines, Drives and Power Systems - Solutions Manual Electronic Devices and Circuit Theory 9e Instructors resource manual ISBN 0132214466 Elementary Differential Equations Boundary Value (2ndEd) - Kohler - Solutions Manual Elementary Linear Algebra (6thEd) - Larson, Falvo - Solutions Manual E-Marketing 5E Strauss Frost ISBN 0136154417 Test Bank Entrepreneurial Finance (3rdEd) - Leach - Instructors Solutions Manual Exploring Microsoft Office Excel 2007, Comprehensive, 2E Test bank Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial And Managerial Acct (10thEd) - Warren - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham test bank Friendly Introduction To Analysis (2ndEd) - Kosmala - Solutions Manual Friendly Introduction to Numerical Analysis Brian Bradie Fundamentals of Communication Systems Proakis & Salehi Fundamentals of Differential Equations 7thE Nagle Snider Instructors resource manual ISBN -0321388445 Fundamentals of Engineering Electromagnetics By David K. Cheng Solutions Manual Fundamentals of Multinational Finance 3e Muffet, Stonehill Test bank Gas Dynamics John & Keith Instructors Solution Manual General, Organic, and Biological Chemistry Structures of Life, 3E Test bank Gregory - Classical Mechanics - SOLUTIONS MANUAL (Cambridge, 2006) Human Anatomy & Physiology 7E TEST BANK ISBN 0805373810 Human Anatomy & Physiology 8E TEST BANK Hydraulics in Civil and Environmental Engineering Solutions by Chadwick & Morfett Solution's Manual InstructorÍs Manual Contemporary Engineering economics 4e Park Instructor's Edition LAN Switching and Wireless CCNA Exploration Labs and Study Guide Allan Johnson EBOOK International Economics Theory and Policy 8E Krugman Obstfeld International Management Managing Across Borders and Cultures 6E Deresky Test Bank International Management Managing Across Borders and Cultures 6E Deresky Instructors manual International Marketing and Export Management 6E Albaum Introduction To Business Statistics (6thEd) - Weiers - Solutions Manual Introduction To Business Statistics (6thEd) - Weiers - Test Bank Introduction to Econometrics 2E Stock Watson Solution manual Introduction to Linear Algebra -3rd Edition - Gilbert Strang Instructors Solutions Manual Introduction To Management Accounting (14thEd) - Horngren - Solutions Manual Introduction to Management Science - Taylor 9E Solution Manual Introduction to Parallel Computing Kumar solution manual Behavior in Organizations Greenberg 9th Edition test bank Introduction to the Design and Analysis of Algorithms 2E Levitin ISBN 0321428102 Introductory Circuit Analysis 11e Boylestad Solution manual Introductory Circuit Analysis 11E Lab solutions manual Introductory Econometrics (4thEd) - Woolridge - Solutions Manual Investment Analysis & Portfolio Management, 7e by Reilly and Brown Solutions Manual Java Foundations- Introduction to Program Design and Data Structures- ES zip Java Foundations- Introduction to Program Design and Data Structures- project solutions Linear Algebra (Jim Hefferon) (2006) Solutions Manual Linear Algebra For Engineers And Scientist (1stEd) - Hardy [CapitalEth] Solutions Manual Management Accounting Anthony A Atkinson (5th Ed) ISM and TB Management Information Systems 11E Laudon 0136078907 test bank Management Information Systems Managing the Digital Firm 10th Edition by Laudon Managerial Accounting Information for Decisions 4th ed Albrite Marketing Real people Real Choices 6 e Test Bank ISBN 0136054234 Mathematical Proofs A Transition to Advanced Mathematics (2ndEd) - Chartrand - Solutions Manual Mathematical Thinking problem solving Angelo & West Instructors manual ISBN -0130144126 Microbiology with Diseases by Body System Robert W Bauman 2nd ed Instructors manual MIS Cases Decision Making wih Application Software, 4E Instructors manual and solution files Money Banking and Financial Markets Roger LeRoy Miller (3rd ed) Test bank Object Oriented Programming in C++ 4E suplement robert Lafore Operations Management 9E Jay Heizer ISBN 0131585576 Operations Management 9E Jay Heizer ISBN 0132342979 test bank Organic Chemistry 6E Wade Test Bank Parallel Programming (2ndEd) - Wilkinson [CapitalEth] Solutions Manual Partial Differential Equations And Boundary Value Problems (2nd Ed) - Asmar - Solutions Manual Physics Principles with Applications with Mastering Physics Giancoli 6E ISM Physics with Mastering Physics 3E James walker Prebles' Artforms 9E patrick Frank TESTGEN file ISBN 0136044166 Prebles' Artforms Test Bank Precalculus (4thEd) - Blitzer - Solutions Manual Prentice Hall Federal Taxation 2009 Comprehensive - Pope - Solutions Manual Prentice HallÍs Federal Taxation 22/e 2009 Corporations test bank and solution manual Prince Medical Imaging Signals and Systems Instructors manual Principles Of Foundation Engineering (6thEd) - Das - Solution Manual Principles Of Managerial Finance Brief (5thEd) - Gitman [CapitalEth] Solutions Manual Principles of Marketing 5th European edition by Kotler Instructors solution manual Principles Of Operations Management (6thEd) - Heizer [CapitalEth] Test Bank Problem Solving With CPP (7thEd) - Savitch [CapitalEth] Solutions Manual Reinforced Concrete Design - George F. Limbrunner 7th ed ISBN [CapitalEth] 0135044359 Roads to Geometry, 3/E Solutions manual Edward C. Wallace Sandler S. I. - Chemical and Engineering Thermodynamics - Solution manual Source Code Files for Programming Concepts in MATLAB 2E David M Smith Statics And Strengths Of Materials (6thEd) - Morrow - Solutions Manual Statistics 11E James T. McClave Solution manual Stats Data And Models (2ndEd) - Veaux [CapitalEth] Solutions Manual Strategic Compensation Joe Martocchio 5th ed Test Bank Strategic Management and Competitive Advantage Concepts and Cases 2E barney hesterly ISBN 0136036112 Pearson TESTGEN file Strategic Management Concepts and Cases 12E Fred David ISBN 0138132178 test bank Strategic Management TestBank Hitt 8th edition Test Bank Martini EAP 5E TestBank International economics 12th edition Carbaugh TestBank Macroeconomics Principles and Policy Baumol 10th Undergraduate Econometrics Solutions Manual - Hill, Judge and Griffiths Understanding and Managing Organizational Behavior 5E Test bank University Chemistry with Student Access Kit siska 1e test bank Wang, L. & Zhou, X. & Wei, X. - Heat conduction. Mathematical models and analytical solutions (Springer, 2008) === Subject: Comprehensive Test Bank and Solution manuals posting-account=jy2E5goAAAB1WGwMQL1h2k61o4k7O_u4 Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) E-mail me if any solution manual or test bank you need is in the list below at instructors.team[at]gmail.com Or visit http://quick-n-easy-solution-shop.blogspot.com/ for a latest list of resources. Also here is a list for which I can get resources for you. HERE IS THE LIST OF MANUALS FOR SALE WHICH I CAN GET FOR YOU: 2009 Federal Taxation - Pratt [CapitalEth] Solutions Manual & test Bank Accounting for Non-Accounting Students test bank Accounting Information Systems (6thEd) - Hall - Solutions Manual Aerodynamics for Engineers, 5E Solution manual Bertin Russ Cummings Algebra and Trigonometry 3rd Ed, and Precalculus 3rd Ed, Instructor's Solutions Manual 2008 - Beecher, Penna, & Bittinger Analysis- With an Introduction to Proof, 4-E-Instructors SM Art Through The Ages A Global Hist Vol II Test Bank complete Auditing A Business Risk Approach (6thEd) - Rittenberg [CapitalEth] Solutions Manual and Test Bank Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Solution Manual & Test bank Auditing Cases Interactive Learning Approach (4thEd) - Beasley - Solutions Manual Beer, Johnston & Dewolf - Mechanics Of Materials Solution Manual 3Rd Ed Biology with Mastering Biology 8E Campbell Reece ISBN -0321494334 Test Bank Bond Markets, Analysis and Strategies 6E Instructors manual Fabozzi Brock Biology of Microorganisms 12E ISBN -0132324997 Test Bank Busines statistics Decision making 7E David F Groebner Solution manual & test bank Business Law and the Legal Environment Jeffrey F. Beatty 5th edition Test Bank Business Law Tax And Cases (11thEd) - Clarkson [CapitalEth] TestBank Business Statistics First Course Solutions Manual Levine Calculus A Complete Course Adams - - Instructors Solution Manual Concepts Of Programming Languages (8thEd) - Sebesta [CapitalEth] Solutions Manual Contemporary Financial Management (11thEd) - Moyer - Solutions Manual Cornerstone Of Managerial Accounting (2ndEd) - Mowen - Solutions Manual Corporate Partnership Estate Gift Tax 2009 - Pratt - Solutions Manual Cost accounting by Hongren 13/e test bank and Solution manual Cutnell John, Physics 7th E, Instructors manual (all solutions even +odd) Data Structures Algorithm Analysis In CPP (3rdEd) - Weiss - Solutions Manual Deitel & Deitel How to Program C++ 6th E Code solutions Options, Futures and Other Derivatives John Hull 7E test bank ch 1-21 with answers Digital Electronics A Practical Approach - William Kleitz 8th ed ISM Econometric Analysis - Solutions Manual (Greene 6Th 2007) Effective Small Business Management - Norman M Scarborough test bank Electrical Machines, Drives and Power Systems - Solutions Manual Electronic Devices and Circuit Theory 9e Instructors resource manual ISBN 0132214466 Elementary Differential Equations Boundary Value (2ndEd) - Kohler - Solutions Manual Elementary Linear Algebra (6thEd) - Larson, Falvo - Solutions Manual E-Marketing 5E Strauss Frost ISBN 0136154417 Test Bank Entrepreneurial Finance (3rdEd) - Leach - Instructors Solutions Manual Exploring Microsoft Office Excel 2007, Comprehensive, 2E Test bank Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial And Managerial Acct (10thEd) - Warren - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham - Solutions Manual and test bank Friendly Introduction To Analysis (2ndEd) - Kosmala - Solutions Manual Friendly Introduction to Numerical Analysis Brian Bradie Fundamentals of Communication Systems Proakis & Salehi Fundamentals of Differential Equations 7thE Nagle Snider Instructors resource manual ISBN -0321388445 Fundamentals of Engineering Electromagnetics By David K. Cheng Solutions Manual Fundamentals of Multinational Finance 3e Gas Dynamics John & Keith Instructors Solution Manual General, Organic, and Biological Chemistry Structures of Life, 3E Test bank Gregory - Classical Mechanics - SOLUTIONS MANUAL (Cambridge, 2006) Human Anatomy & Physiology 7E TEST BANK ISBN 0805373810 Human Anatomy & Physiology 8E TEST BANK Hydraulics in Civil and Environmental Engineering Solutions by Chadwick & Morfett Solution's Manual InstructorÍs Manual Contemporary Engineering economics 4e Park Instructor's Edition LAN Switching and Wireless CCNA Exploration Labs and Study Guide Allan Johnson EBOOK International Economics Theory and Policy 8E Krugman Obstfeld International Marketing and Export Management 6E Albaum Introduction To Business Statistics (6thEd) - Weiers - Solutions Manual Introduction to Econometrics 2E Stock Watson Solution manual Introduction to Linear Algebra -3rd Edition - Gilbert Strang Instructors Solutions Manual Introduction To Management Accounting (14thEd) - Horngren - Solutions Manual Introduction to Management Science - Taylor 9E Solution Manual Introduction to Parallel Computing Kumar solution manual Behavior in Organizations Greenberg 9th Edition test bank Introduction to the Design and Analysis of Algorithms 2E Levitin ISBN 0321428102 Introductory Circuit Analysis 11e Boylestad Solution manual Introductory Econometrics (4thEd) - Woolridge - Solutions Manual Investment Analysis & Portfolio Management, 7e by Reilly and Brown Solutions Manual Java Foundations- Introduction to Program Design and Data Structures- ES zip Java Foundations- Introduction to Program Design and Data Structures- project solutions Linear Algebra (Jim Hefferon) (2006) Solutions Manual Linear Algebra For Engineers And Scientist (1stEd) - Hardy [CapitalEth] Solutions Manual Management Accounting Anthony A Atkinson (5th Ed) ISM and TB Management Information Systems 11E Laudon 0136078907 test bank Management Information Systems Managing the Digital Firm 10th Edition by Laudon Managerial Accounting Information for Decisions 4th ed Albrite Marketing Real people Real Choices 6 e Test Bank ISBN 0136054234 Mathematical Proofs A Transition to Advanced Mathematics (2ndEd) - Chartrand - Solutions Manual Mathematical Thinking problem solving Angelo & West Instructors manual ISBN -0130144126 Microbiology with Diseases by Body System Robert W Bauman 2nd ed Instructors manual MIS Cases Decision Making wih Application Software, 4E Instructors manual and solution files Object Oriented Programming in C++ 4E suplement robert Lafore Operations Management 9E Jay Heizer ISBN 0131585576 Operations Management 9E Jay Heizer ISBN 0132342979 test bank Organic Chemistry 6E Wade Test Bank Parallel Programming (2ndEd) - Wilkinson [CapitalEth] Solutions Manual Partial Differential Equations And Boundary Value Problems (2nd Ed) - Asmar - Solutions Manual Physics Principles with Applications with Mastering Physics Giancoli 6E ISM Physics with Mastering Physics 3E James walker Prebles' Artforms 9E patrick Frank TESTGEN file ISBN 0136044166 Prebles' Artforms Test Bank Precalculus (4thEd) - Blitzer - Solutions Manual Prentice Hall Federal Taxation 2009 Comprehensive - Pope - Solutions Manual Prentice HallÍs Federal Taxation 22/e 2009 Corporations test bank and solution manual Prince Medical Imaging Signals and Systems Instructors manual Principles Of Foundation Engineering (6thEd) - Das - Solution Manual Principles Of Managerial Finance Brief (5thEd) - Gitman [CapitalEth] Solutions Manual Principles of Marketing 5th European edition by Kotler Instructors solution manual Principles Of Operations Management (6thEd) - Heizer [CapitalEth] Test Bank Problem Solving With CPP (7thEd) - Savitch [CapitalEth] Solutions Manual Reinforced Concrete Design - George F. Limbrunner 7th ed ISBN [CapitalEth] 0135044359 Roads to Geometry, 3/E Solutions manual Edward C. Wallace Sandler S. I. - Chemical and Engineering Thermodynamics - Solution manual Source Code Files for Programming Concepts in MATLAB 2E David M Smith Statics And Strengths Of Materials (6thEd) - Morrow - Solutions Manual Statistics 11E James T. McClave Solution manual Stats Data And Models (2ndEd) - Veaux [CapitalEth] Solutions Manual Strategic Compensation Joe Martocchio 5th ed Test Bank Strategic Management and Competitive Advantage Concepts and Cases 2E barney hesterly ISBN 0136036112Pearson TESTGEN file Strategic Management Concepts and Cases 12E Fred David ISBN 0138132178 test bank Strategic Management TestBank Hitt 8th edition Test Bank Martini EAP 5E TestBank International economics 12th edition Carbaugh TestBank Macroeconomics Principles and Policy Baumol 10th Undergraduate Econometrics Solutions Manual - Hill, Judge and Griffiths Understanding and Managing Organizational Behavior 5E Test bank University Chemistry with Student Access Kit siska 1e test bank Wang, L. & Zhou, X. & Wei, X. - Heat conduction. Mathematical models and analytical solutions (Springer, 2008) 2009 Corporate, Partnership, Estate and Gift Taxation - James Pratt (3rd ed) (ISBN 1426639015) 2009 Federal Taxation - James Pratt (3rd ed) (ISBN 1426639171) 2009 Individual Taxation - James Pratt (3rd ed) (ISBN 1426649193) A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet - Sara Baase (3rd ed) (ISBN 0136008488) Absolute C++ - Walter Savitch (3rd ed) (ISBN 0321468937) Absolute Java - Walter Savitch (3rd ed) (ISBN 0321487923) Access 2007 Guidebook - Maggie Trigg (6th ed) (ISBN 0321517016) Accounting - Carl Warren (22nd ed) (ISBN 0324401841) Accounting - Carl Warren (23rd ed) (ISBN 0324662963) Accounting Chapters 1-13 - Charles T. Horngren et al (7th ed) (ISBN 0132249952) Accounting Chapters 1-25 - Charles T. Horngren et al (7th ed) (ISBN 0132439603) Accounting Chapters 1-26 - Charles T. Horngren et al (6th ed) (ISBN 0131088513) Accounting Chapters 12-25 - Charles T. Horngren et al (7th ed) (ISBN 0132249960) Accounting Concepts and Applications - Steve Albrecht (10th ed) (ISBN 0324376154) Accounting Concepts and Applications - Steve Albrecht (9th ed) (ISBN 0324187564) Accounting Information Systems - James Hall (5th ed) (ISBN 0324312954) Accounting Information Systems - James Hall (6th ed) (ISBN 0324560893) Accounting Information Systems - Marshall Romney, Paul Steinbart (10th ed) (ISBN 0131475916) Accounting Information Systems - Marshall Romney, Paul Steinbart (11th ed) (ISBN 0136015182) Accounting Information Systems - Ulric J. Gelinas (7th ed) (ISBN 0324378823) Accounting Information Systems - Ulric J. Gelinas (8th ed) (ISBN 0324663803) Additional Calculus Topics - Raymond Barnett (11th ed) (ISBN 0132318229) Administrative Law: Bureaucracy in a Democracy - Daniel E. Hall (4th ed) (ISBN 0135005183) Advanced Accounting - Floyd Beams (9th ed) (ISBN 0131851225) Advanced Accounting - Floyd Beams (10th ed) (ISBN 0136033970) Advanced Accounting - Paul Fischer (10th ed) (ISBN 0324379056) Advanced Accounting - Paul Fischer (Test Bank only) (9th ed) (ISBN 0324304013) Advanced Calculus - G. B. Folland (1st ed) (ISBN 0130652652) Advanced Engineering Mathematics - Michael Greenberg (2nd ed) (ISBN 0133214311) Advanced Engineering Mathematics - Peter V. O'Neil (6th ed) (ISBN 0534552080) Advertising - Sandra Moriarty (8th ed) (ISBN 0132224151) Algebra and Trigonometry - Judith A. Beecher (3rd ed) (ISBN 0321466209) Algebra and Trigonometry - Michael Sullivan (8th ed) (ISBN 0132329034) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (4th ed) (ISBN 0131527398) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 013600492X) Algebra and Trigonometry: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501519) Algebra for College Students - Allen R. Angel (3rd ed) (ISBN 0136129080) Algebra for College Students - Margaret L. Lial (6th ed) (ISBN 0321442547) Algebra For College Students - Robert F Blitzer (6th ed) (ISBN 0136019749) An Introduction to Signals and Systems - John Alan Stuller (1st ed) (ISBN 0495073016) Dunlap (1st ed) (ISBN 0534392946) Analytical Mechanics - Grant Fowles, George Cassiday (7th ed) (ISBN 0534494927) Anatomy & Physiology - Elaine N. Marieb (3rd ed) (ISBN 0805347739) Anatomy & Physiology for Emergency Care - Bryan E. Bledsoe (2nd ed) (ISBN 0132342987) Applied Algebra - Darel Hardy (1st ed) (ISBN 0130674648) Applied Calculus - Geoffrey C. Berresford (5th ed) (ISBN 0547169787) Applied Linear Algebra - Chehrzad Shakiban, Peter J. Olver (1st ed) (ISBN 0131473824) Applied Mechanics for Engineering Technology - Keith M. Walker (8th ed) (ISBN 0131721518) Applied Multivariate Statistical Analysis - Richard A. Johnson (6th ed) (ISBN 0131877151) Applied Partial Differential Equations - Richard Haberman (4th ed) (ISBN 0130652431) Applied Physics - Dale Ewen (9th ed) (ISBN 0135157331) Applied Statistics for Engineers and Physical Scientists - Johannes Ledolter (3rd ed) (ISBN 0136017983) Art and Science of Leadership - Afsaneh Nahavandi (5th ed) (ISBN 0136044085) Auditing and Assurance Services - Alvin A. Arens et al (11th ed) (ISBN 0131867121) Auditing and Assurance Services - Alvin A. Arens et al (12th ed) (ISBN 0135132126) Auditing and Assurance Services: An Integrated Approach - Alvin A Arens (13th ed) (ISBN 0136084737) Auditing Assurance and Risk - W. Robert Knechel, Steve Salterio, Brian Ballou (3rd ed) (ISBN 0324313187) Auditing Cases - Mark Beasley (3rd ed) (ISBN 0131494910) Auditing Cases - Mark S Beasley (4th ed) (ISBN 0132423502) Auditing: A Business Risk Approach - Larry E. Rittenberg (6th ed) (ISBN 0324375581) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (2nd ed) (ISBN 0130889784) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) (ISBN 0132393212) Basic Business Statistics - Mark L Berenson (10th ed) (ISBN 0131678310) Basic Chemistry - Karen C. Timberlake (2nd ed) (ISBN 0805344691) Basic Economics - Frank V. Mastrianna (Test Bank) (15th ed) (ISBN 0324599161) Basic Environmental Technology: Water Supply, Waste Management & Pollution Control - Jerry A. Nathanson (5th ed) (ISBN 0131190822) Basic Marketing Research Using Microsoft Excel Data Analysis - Alvin C Burns (2nd ed) (ISBN 0132059584) Basic Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321500113) Basics of Occupational Safety - David L. Goetsch (1st ed) (ISBN 013502613X) Beginning & Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007317) Beginning Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007023) Beginning Algebra - Margaret L. Lial (10th ed) (ISBN 0321437268) Beginning Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500040) Beginning and Intermediate Algebra - Margaret L. Lial (4th ed) (ISBN 0321442334) Beginning and Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500059) Behavior in Organizations - Jerald Greenberg (9th ed) (ISBN 0131542842) Biochemistry - Mary Campbell (4th ed) (ISBN 0534405215) Biochemistry (with Lecture Notebook) - Mary Campbell (4th ed) (ISBN 0534391818) Biology - Neil A. Campbell (Test Bank only w/ TestGen Software) (7th ed) (ISBN 080537146X) Biology: Science for Life - Colleen Belk (3rd ed) (ISBN 0321559592) Biology: Science for Life with Physiology - Colleen Belk (3rd ed) (ISBN 0321559584) Biomaterials: The Intersection of Biology and Materials Science - Johnna S. Temenoff (1st ed) (ISBN 0130097101) Biostatistics for the Health Sciences - R. Clifford Blair (1st ed) (ISBN 0131176609) Bond Markets, Analysis and Strategies - Frank Fabozzi (6th ed) (ISBN 0131986430) Bond Markets, Analysis, and Strategies - Frank J Fabozzi (7th ed) (ISBN 0136078974) Brief Course in Mathematical Statistics - Elliot A. Tanis (1st ed) (ISBN 0131751395) Brief Principles of Macroeconomics - Gregory Mankiw (5th ed) (ISBN 0324590377) Brock Biology of Microorganisms - Michael T. Madigan (12th ed) (ISBN 0132324601) Brock Biology of Microorganisms - Michael T. Madigan (Test Bank) (11th ed) (ISBN 0132192268) Building Construction: Principles, Materials, and Systems - Madan Mehta (1st ed) (ISBN 0130494216) Building Java Programs: A Back to Basics Approach - Stuart Reges (1st ed) (ISBN 0321382838) Business - William M. Pride (10th ed) (ISBN 0324829558) Business Analysis and Valuation: Using Financial Statements - Krishna Palepu (3rd ed) (ISBN 0324118945) Business and Its Environment - David P. Baron (6th ed) (ISBN 0136083927) Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (7th ed) (ISBN 0324569394) Business Communication Essentials - Courtland Bovee (4th ed) (ISBN 0136084419) Business Communication Essentials and Peak Performance Grammar and Mechanics 2.0 CD Package - Court Bovee (3rd ed) (ISBN 0132328992) Business Communication Today - Court Bovee (9th ed) (ISBN 0131995359) Business Data Networks and Telecommunications - Raymond R. Panko (7th ed) (ISBN 0136153402) Business English: Writing in the Workplace - Blanche Ettinger (4th ed) (ISBN 0131565702) Business Ethics: A Stakeholder and Issues Management Approach - Joseph W. Weiss (6th ed) (ISBN 0324589735) Business Ethics: Case Studies and Selected Readings - Marianne M. Jennings (6th ed) (ISBN 0324657749) Business Forecasting - John Hanke (9th ed) (ISBN 0132301202) Business in Action with Real Time Updates - Court Bovee (4th ed) (ISBN 0136154085) Business Law - Henry R. Cheeseman (7th ed) (ISBN 0136085547) Business Law and the Legal Environment - Jeffrey F. Beatty (4th ed) (ISBN 0324303971) Business Law and the Legal Environment - Jeffrey F. Beatty (5th ed) (ISBN 0324663528) Business Law and the Regulation of Business - Richard A. Mann (9th ed) (ISBN 0324537131) Business Law Principles for Today's Commercial Environment - David P. Twomey (2nd ed) (ISBN 0324303947) Business Law Today: Comprehensive - Roger LeRoy Miller (8th ed) (ISBN 0324595743) Business Law Today: The Essentials - Roger LeRoy Miller (8th ed) (ISBN 0324654545) Business Law: Alternate Edition - Gaylord A. Jentz (11th ed) (ISBN 0324596162) Business Law: Text and Cases - Kenneth W. Clarkson (11th ed) (ISBN 0324655223) Business Law: Text and Exercises - Roger LeRoy Miller (5th ed) (ISBN 032464096X) Business Statistics: A Decision Making Approach - David F. Groebner (7th ed) (ISBN 0132416921) Business Statistics: A First Course - David Levine (5th ed) (ISBN 0136065805) Business: Its Legal, Ethical, and Global Environment - Marianne M. Jennings (8th ed) (ISBN 0324655541) Calculus - Dale Varberg (9th ed) (ISBN 0131429248) Calculus and Its Applications - Larry Goldstein (11th ed) (ISBN 0131919636) Calculus and Its Applications - Larry Goldstein (12th ed) (ISBN 0321571304) Calculus and Its Applications - Marvin L. Bittinger (8th ed) (ISBN 0321166396) Calculus and Its Applications - Marvin L. Bittinger (9th ed) (ISBN 0321395344) Calculus Early Transcendentals - Henry Edwards (7th ed) (ISBN 0131569899) Calculus for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132328186) Calculus for the Life Sciences - Marvin L. Bittinger (1st ed) (ISBN 0321279352) Calculus With Applications - Margaret L. Lial et al (8th ed) (ISBN 0321228146) Calculus with Applications for the Life Sciences - Raymond N. Greenwell (1st ed) (ISBN 0201745828) Calculus, Early Transcendentals - C. Henry Edwards (7th ed) (ISBN 0131569899) California Real Estate Law - Theodore Gordon (7th ed) (ISBN 0324654685) Capital Budgeting and Long-Term Financing Decisions - Neil Seitz (4th ed) (ISBN 0324258089) Capital Markets: Institutions and Instruments - Frank J Fabozzi (4th ed) (ISBN 0136026028) Cases in Management Accounting and Control Systems - Brandt Allen (4th ed) (ISBN 0135704251) Chemistry - John E McMurry (Test Bank only) (5th ed) (ISBN 0131993232) Chemistry : An Introduction to General, Organic, Biological Chemistry - Karen Timberlake (9th ed) (ISBN 0805330151) Chemistry for Changing Times - John W. Hill (12th ed) (ISBN 0136054498) Chemistry: An Introduction to General, Organic, & Biological Chemistry - Karen C Timberlake (10th ed) (ISBN 0136019706) Civil Drafting Technology - David A. Madsen (7th ed) (ISBN 0135000688) ed) (ISBN 0534408966) CMOS Circuit Design, Layout, and Simulation - David E. Boyce et al (1st ed) (ISBN 0780334167) College Accounting 1-12 - Jeffrey Slater (9th ed) (ISBN 0131071696) College Accounting 1-25 - Jeffrey Slater (10th ed) (ISBN 0132286386) College Accounting Chapters 1-15 - James Heintz (19th ed) (ISBN 0324382499) College Accounting Chapters 1-27 - James Heintz (19th ed) (ISBN 0324376162) College Accounting Chapters 1-9 - James Heintz (19th ed) (ISBN 0324382480) College Accounting: A Practical Approach Canadian Edition - Jeffrey Slater (10th ed) (ISBN 0132069245) College Algebra - J. S. Ratti (1st ed) (ISBN 0321296443) College Algebra - Judith A. Beecher (3rd ed) (ISBN 0321466071) College Algebra - Margaret L. Lial (10th ed) (ISBN 0321499131) College Algebra - Mark Dugopolski (4th ed) (ISBN 0321356918) College Algebra - Michael Sullivan (8th ed) (ISBN 0132402866) College Algebra - Robert F. Blitzer (5th ed) (ISBN 0321559835) College Algebra and Trigonometry - J. S. Ratti (1st ed) (ISBN 0321296427) College Algebra and Trigonometry - Margaret L. Lial (4th ed) (ISBN 0321497449) College Algebra Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136004911) College Algebra Essentials - Michael Sullivan (8th ed) (ISBN 0136154344) College Algebra: Graphs and Models with Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321531922) College Geometry - David C. Kay (2nd ed) (ISBN 0321046242) College Geometry: A Problem Solving Approach with Applications - Gary L. Musser (2nd ed) (ISBN 0131879693) College Math for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0131572253) College Physics - Jerry D Wilson (6th ed) (ISBN 0131495798) College Physics - Jerry D Wilson (7th ed) (ISBN 0321571118) College Physics with Mastering Physics - Hugh Young (8th ed) (ISBN 0805390707) Communicating in the Workplace - Thomas Cheesebro (1st ed) (ISBN 0136136915) Communication Systems Engineering - John G. Proakis (2nd ed) (ISBN 0130617938) Comparative International Accounting - Christopher Nobes (9th ed) (ISBN 0273703579) Complex Variables With Applications - A. David Wunsch (3rd ed) (ISBN 0201756099) Comprehensive Periodontics for the Dental Hygienist - Mea A. Weinberg (3rd ed) (ISBN 0135015421) Computer Algorithms - Allen Van Gelder, Sara Baase (3rd ed) (ISBN 0201612445) Computer Networking Complete Package - James F. Kurose (3rd ed) (ISBN 0321418492) Computer Networking with Internet Protocols - William Stallings (1st ed) (ISBN 0131410989) Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Computer Networking: A Top-Down Approach - James F. Kurose (5th ed) (ISBN 0136079679) Computer Networking: A Top-Down Approach Featuring the Internet - James F. Kurose (3rd ed) (ISBN 0321227352) Computer Organization and Architecture - William Stallings (7th ed) (ISBN 0130351199) Computer Organization and Architecture: Designing for Performance - William Stallings (7th ed) (ISBN 0131856448) Computer Organization and Architecture: Designing for Performance - William Stallings (8th ed) (ISBN 0136073735) Computer Science: An Overview - J. Glenn Brookshear (10th ed) (ISBN 0321524039) Computer Security: Principles and Practice - William Stallings (1st ed) (ISBN 0136004245) Computer Systems Organization & Architecture - John D. Carpinelli (1st ed) (ISBN 0201612534) Concepts in Federal Taxation 2007 - Kevin Murphy (14th ed) (ISBN 0324313527) Concepts in Federal Taxation 2008 - Kevin Murphy (15th ed) (ISBN 0324640153) Concepts in Federal Taxation 2009 - Kevin Murphy (16th ed) (ISBN 0324659377) Concepts In Systems and Signals - John D. Sherrick (2nd ed) (ISBN 0131782711) Concepts of Calculus with Applications - Martha Goshaw (1st ed) (ISBN 0321320786) Concepts of Calculus With Applications-Updated Edition - Martha Goshaw (2nd ed) (ISBN 0321577442) Concepts of Programming Languages - Robert W. Sebesta (8th ed) (ISBN 0321493621) Conceptual Physical Science - Paul G. Hewitt (4th ed) (ISBN 0321516958) Conceptual Physics Fundamentals - Paul G. Hewitt (1st ed) (ISBN 0321501365) Conceptual Physics Media Update - Paul G. Hewitt (10th ed) (ISBN 0321548094) Concrete Structures - Mehdi Setareh (1st ed) (ISBN 0131988271) Construction Accounting & Financial Management - Stephen Peterson (2nd ed) (ISBN 0135017114) Construction Methods and Management - Stephens W. Nunnally (7th ed) (ISBN 0131716859) Construction Project Management - Fred Gould (3rd ed) (ISBN 0131996231) Consumer Behavior - Michael Solomon (8th ed) (ISBN 0136015964) Consumer Behavior - Wayne D. Hoyer (5th ed) (ISBN 0547079923) Contemporary Auditing: Real Issues & Cases - Michael C. Knapp (7th ed) (ISBN 0324658052) Contemporary Auditing: Real Issues & Cases Update - Michael C. Knapp (7th ed) (ISBN 143907819X) Contemporary Business and Online Commerce Law - Henry R. Cheeseman (6th ed) (ISBN 013601500X) Contemporary Engineering Economics - Chan S. Park (4th ed) (ISBN 0131876287) Contemporary Financial Management - Charles Moyer (10th ed) (ISBN 0324289081) Contemporary Financial Management - R. Charles Moyer, James R. McGuigan (11th ed) (ISBN 0324653506) Contemporary Logistics - Paul R. Murphy (9th ed) (ISBN 013156207X) Contemporary Marketing - Louis E. Boone (14th ed) (ISBN 032458203X) Contemporary Marketing 2009 Update - Louis E. Boone (13th ed) (ISBN 0324580215) Contemporary Mathematics for Business and Consumers - Robert Brechner (5th ed) (ISBN 0324568495) Contemporary Project Management - Timothy Kloppenborg (1st ed) (ISBN 0324382383) Cornerstones of Managerial Accounting - Maryanne M. Mowen (2nd ed) (ISBN 0324379609) Cornerstones of Managerial Accounting - Maryanne M. Mowen (3rd ed) (ISBN 0324660138) Corporate Finance - Jonathan Berk (1st ed) (ISBN 0321415116) Corporate Finance - Michael C. Ehrhardt, Eugene F. Brigham (3rd ed) (ISBN 0324655681) Corporate Finance: The Core plus MyFinanceLab Student Access Kit - Jonathan Berk (1st ed) (ISBN 032155759X) Corporate Financial Accounting - Carl S. Warren (10th ed) (ISBN 0324663838) Corporate Financial Management - Douglas R. Emery (3rd ed) (ISBN 0132278723) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (12th ed) (ISBN 0131495380) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (13th ed) (ISBN 0136126634) Cost Accounting Canadian Edition - Charles Horngren (4th ed) (ISBN 0131971905) Cost Accounting: Traditions & Innovations - Jesse Barfield (5th ed) (ISBN 032418090X) Cost Benefit Analysis: Concepts and Practice - Anthony Boardman (3rd ed) (ISBN 0131435833) Cost Management: Accounting and Control - Don R. Hansen, Maryanne M. Mowen (6th ed) (ISBN 0324559674) Course in Probability - Neil Weiss (1st ed) (ISBN 0201774712) Criminology: A Global Perspective - Robert W. Winslow (1st ed) (ISBN 0131839020) Cryptography and Network Security - William Stallings (4th ed) (ISBN 0131873164) Customer Service: Career Success Through Customer Loyalty - Paul R. Timm (4th ed) (ISBN 0132236583) Data Abstraction & Problem Solving with C++ - Frank M. Carrano (5th ed) (ISBN 0321433327) Data and Computer Communications - William Stallings (8th ed) (ISBN 0132433109) Data Structures and Algorithm Analysis in C++ - Mark Allen Weiss (3rd ed) (ISBN 032144146X) Data Structures and Algorithm Analysis in Java - Mark Allen Weiss (2nd ed) (ISBN 0321370139) Database Concepts - David Kroenke (3rd ed) (ISBN 0131986252) Database Concepts - David Kroenke (4th ed) (ISBN 0136086535) Database Systems: A Practical Approach - Thomas M. Connolly (4th ed) (ISBN 0321294017) Derivatives Markets - Robert L. McDonald (2nd ed) (ISBN 032128030X) Detection and Estimation:Theory and Its Applications - Thomas Schonhoff (1st ed) (ISBN 0130894990) Developmental Mathematics - Marvin L. Bittinger (7th ed) (ISBN 0321331915) Developmental Mathematics: Basic Mathematics and Algebra - Margaret L. Lial (1st ed) (ISBN 0321506421) Differential Equations - John Polking (2nd ed) (ISBN 0131437380) Differential Equations and Boundary Value Problems: Computing and Modeling - Henry Edwards (4th ed) (ISBN 0131561073) Differential Equations and Linear Algebra - Henry Edwards, David E. Penney (2nd ed) (ISBN 0131481460) Differential Equations and Linear Algebra - Henry Edwards, David E. Penney (3rd ed) (ISBN 0136054250) Differential Equations and Linear Algebra - Jerry Farlow (2nd ed) (ISBN 0131860615) Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) (ISBN 0130457949) Differential Equations Computing and Modeling - Henry Edwards (4th ed) (ISBN 0136004385) Differential Equations With Boundary Value Problems - John C. Polking (2nd ed) (ISBN 0130911062) Digital & Analog Communication Systems - Leon Couch (7th ed) (ISBN 0131424920) Digital Communications - John Proakis (4th ed) (ISBN 0072321113) Digital Design - Morris Mano (4th ed) (ISBN 0131989243) Digital Electronics: A Practical Approach - William Kleitz (8th ed) (ISBN 0132435780) Digital Fundamentals - Thomas Floyd (10th ed) (ISBN 0132359235) Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) Digital Signal Processing Using MATLAB -Vinay K. Ingle, John G. Proakis (2nd ed) (ISBN 0495073113) Digital Systems Design Using VHDL - Charles H. Roth (2nd ed) (ISBN 0534384625) Digital Systems: Principles and Applications - Ronald Tocci et al (10th ed) (ISBN 0131725793) Discrete and Combinatorial Mathematics - Ralph P. Grimaldi (5th ed) (ISBN 0201726343) Discrete Mathematics - Edgar G. Goodaire, Michael M Parmenter (3rd ed) (ISBN 0131679953) Discrete Mathematics - Otto, Eynden, Dossey, Spence (4th ed) (ISBN 0321079124) Discrete Mathematics - Otto, Eynden, Dossey, Spence (5th ed) (ISBN 0321305159) Discrete Mathematics - Richard Johnsonbaugh (6th ed) (ISBN 0131176862) Drugs & the Human Body - Ken Liska (8th ed) (ISBN 0132447134) Dynamics of Structures - Anil K. Chopra (3rd ed) (ISBN 013156174X) ECON for Macroeconomics - William A. McEachern (1st ed) (ISBN 0324587805) Economic Development - Michael P. Todaro (10th ed) (ISBN 0321485734) Economic Development - Michael Todaro, Stephen Smith (9th ed) (ISBN 0321278887) Economic Growth - David N. Weil (2nd ed) (ISBN 0321416627) Economic Growth - David Weil (1st ed) (ISBN 0201680262) Economics - Michael Parkin (8th ed) (ISBN 0321423003) Economics - Michael Parkin (9th ed) (ISBN 0321600037) Economics - Richard Lipsey (13th ed) (ISBN 0321369211) Economics - Roger A. Arnold (9th ed) (ISBN 0324595425) Economics for Managers - Paul G Farnham (1st ed) (ISBN 0130924253) Economics for Managers - Paul G Farnham (2nd ed) (ISBN 013606552X) Economics for Today - Irvin B. Tucker (6th ed) (ISBN 0324591365) Economics of Money, Banking, and Financial Markets - Frederic Mishkin (Test Bank) (8th ed) (ISBN 0321415051) Economics of Money, Banking, and Financial Markets, Update - Frederic Mishkin (7th ed) (ISBN 0321331850) Economics Today - Roger LeRoy Miller (14th ed) (ISBN 0321422341) Economics Today - Roger Miller (15th ed) (ISBN 0321600215) Economics Today: The Macro View - Roger Miller (13th ed) (ISBN 0321278992) Economics Today: The Macro View - Roger Miller (14th ed) (ISBN 0321421442) Economics Today: The Macro View - Roger Miller (15th ed) (ISBN 0321600223) Economics Today: The Micro View - Roger Miller (13th ed) (ISBN 0321278984) Economics Today: The Micro View - Roger Miller (14th ed) (ISBN 0321425065) Economics Today: The Micro View - Roger Miller (15th ed) (ISBN 0321600185) Economics: A Contemporary Introduction - William A. McEachern (8th ed) (ISBN 0324579217) Economics: A Tool for Critically Understanding Society - Tom Riddell (8th ed) (ISBN 0321423585) Economics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537026) Economics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586205) Economics: Private and Public Choice - James D. Gwartney (12th ed) (ISBN 0324580185) Effective Small Business Management - Norman M. Scarborough (9th ed) (ISBN 0136152708) Effective Writing - Claire B. May (8th ed) (ISBN 0136029086) Electric Circuits - James Nilsson (8th ed) (ISBN 0131989251) Electrical Engineering: Principles and Applications - Allan R. Hambley (4th ed) (ISBN 0131989227) Electrical Machines, Drives and Power Systems - Theodore Wildi (6th ed) (ISBN 0131776916) Electronic Commerce 2008 - Efraim Turban (5th ed) (ISBN 0132243318) Electronic Communications for Technicians - Tom Wheeler (2nd ed) (ISBN 0131130498) Electronics and Computer Math - Bill R. Deem (8th ed) (ISBN 0131711377) Electronics Fundamentals: Circuits, Devices and Applications - Thomas Floyd (7th ed) (ISBN 013219709X) Elementary Algebra - George Woodbury (1st ed) (ISBN 0321166426) Elementary Algebra Early Graphing for College Students - Allen R. Angel (3rd ed) (ISBN 0136134165) Elementary Algebra: Graphs and Authentic Applications - Jay Lehmann (1st ed) (ISBN 013220164X) Elementary and Intermediate Algebra - George Woodbury (2nd ed) (ISBN 0321500067) Elementary and Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321422406) Elementary Differential Equations - Henry Edwards (6th ed) (ISBN 0132397307) Elementary Differential Equations - Werner E. Kohler, Lee W.Johnson (1st ed) (ISBN 0201709260) Elementary Differential Equations with Boundary Value Problems - Henry Edwards (6th ed) (ISBN 0136006132) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (1st ed) (ISBN 0321121643) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (2nd ed) (ISBN 0321398505) Elementary Linear Algebra - Ron Larson (6th ed) (ISBN 0618783768) Elementary Linear Algebra with Applications - Bernard Kolman (9th ed) (ISBN 0132296543) Elementary Number Theory - Kenneth H. Rosen (5th ed) (ISBN 0321237072) Elementary Statistics - Mario F. Triola (10th ed) (ISBN 0321331834) Elementary Statistics - Mario F. Triola (9th ed) (ISBN 0201775700) Elementary Statistics - Mario F. Triola (11th ed) (ISBN 0321500245) Elementary Statistics - Neil A. Weiss (7th ed) (ISBN 0321422090) Elementary Statistics - Ron Larson (4th ed) (ISBN 0132424339) Elementary Statistics Using Excel - Mario Triola (3rd ed) (ISBN 0321365135) Elementary Statistics Using the TI-83/84 Plus Calculator - Mario F. Triola (2nd ed) (ISBN 0321462572) Elementary Statistics With Multimedia Study Guide - Mario F. Triola (10th ed) (ISBN 0321460928) Elements of Forecasting - Francis X. Diebold (4th ed) (ISBN 032432359X) Embedded Microcontrollers & Processor Design - Charles Greg Osborn (1st ed) (ISBN 0131130412) Embedded System Design with C805 - Han-Way Huang (1st ed) (ISBN 0495471747) Employment Law - John J. Moran (4th ed) (ISBN 0136009964) Engineering Computation with MATLAB - David M. Smith (2nd ed) (ISBN 0136080634) Engineering Economy - William G Sullivan (13th ed) (ISBN 0131486497) Engineering Economy - William G. Sullivan (14th ed) (ISBN 0136142974) Engineering Economy and the Decision-Making Process - Joseph C. Hartman (1st ed) (ISBN 0131424017) Engineering Fundamentals: An Introduction to Engineering - Saeed Moaveni (3rd ed) (ISBN 0495082538) Engineering Materials: Properties and Selection - Ken Budinski (8th ed) (ISBN 0131837796) Engineering Materials: Properties and Selection - Kenneth G. Budinski (9th ed) (ISBN 0137128428) Engineering Mechanics Dynamics - Anthony M Bedford (5th ed) (ISBN 0136129161) Engineering Mechanics: Dynamics - Andrew Pytel (3rd ed) (ISBN 0495295612) Engineering Mechanics: Dynamics - Russell C. Hibbeler (11th ed) (ISBN 0131561480) Engineering Mechanics: Statics - Andrew Pytel (3rd ed) (ISBN 0495244694) Engineering Mechanics: Statics - Anthony M Bedford (5th ed) (ISBN 0136129153) Engineering Mechanics: Statics - Russell C. Hibbeler (11th ed) (ISBN 0132295660) Engineering Mechanics: Statics - Russell C. Hibbeler (12th ed) (ISBN 0136077900) Engineering Mechanics: Statics Computational Edition - Robert W. Soutas-Little (1st ed) (ISBN 0534549217) Engineering Vibration - Daniel Inman (3rd ed) (ISBN 0132281732) Enterprise Systems for Management - Luvai Motiwalla (1st ed) (ISBN 013233531X) Entrepreneurial Finance - Chris Leach (3rd ed) (ISBN 0324561253) Entrepreneurial Finance - Philip J. Adelman (4th ed) (ISBN 0132434792) Entrepreneurial Finance - Philip J. Adelman (5th ed) (ISBN 013502529X) Entrepreneurship: Successfully Launching New Ventures - Bruce Barringer (2nd ed) (ISBN 0132240572) Entrepreneurship: Theory, Process, and Practice - Donald F. Kuratko (8th ed) (ISBN 0324590911) Environmental and Natural Resource Economics - Tom Tietenberg (7th ed) (ISBN 0321305043) Environmental Issues: An Introduction to Sustainability - Robert L. McConnell (3rd ed) (ISBN 0131566504) Environmental Law - Nancy K. Kubasek (6th ed) (ISBN 0136142168) Environmental Science: Toward A Sustainable Future - Richard T. Wright (10th ed) (ISBN 0132302659) Error Control Coding - Daniel J. Costello Jr., Shu Lin (2nd ed) (ISBN 0130426725) Essential Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522354) Essentials of Business Law - Jeffrey F. Beatty (3rd ed) (ISBN 0324537123) Essentials of Business Law and the Legal Environment - Richard A. Mann (10th ed) (ISBN 0324593562) Essentials of College Algebra with Modeling and Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321448898) Essentials of College Algebra, Alternate Edition - Margaret L. Lial (1st ed) (ISBN 0321491858) Essentials of Economics - Gregory Mankiw (4th ed) (ISBN 0324236964) Essentials of Economics - Gregory Mankiw (5th ed) (ISBN 0324590024) Essentials of Entrepreneurship and Small Business Management - Thomas W Zimmerer (5th ed) (ISBN 0132294389) Essentials of Logic - Irving Copi (2nd ed) (ISBN 013238034X) Essentials of Management Information Systems - Jane Laudon (8th ed) (ISBN 013602579X) Essentials of Managerial Finance - Scott Besley (13th ed) (ISBN 0324258755) Essentials of Marketing - Charles W. Lamb (6th ed) (ISBN 0324656203) Essentials of Materials Science & Engineering - Donald R. Askeland (2nd ed) (ISBN 0495244465) Essentials of Organizational Behavior - Stephen P Robbins (9th ed) (ISBN 0132431521) Essentials of Organizational Behavior - Stephen P. Robbins (10th ed) (ISBN 0136077617) Essentials of Statistics - Mario F. Triola (3rd ed) (ISBN 0321434250) Essentials of Statistics for Business and Economics - David R. Anderson (5th ed) (ISBN 0324568606) Essentials of the Legal Environment - Roger LeRoy Miller (2nd ed) (ISBN 0324400403) Ethics for the Information Age - Mike Quinn (3rd ed) (ISBN 0321536851) Excellence in Business Communication - John V. Thill (8th ed) (ISBN 0136157505) Experiencing MIS - David Kroenke (2nd ed) (ISBN 0136078680) Exploring Business - Karen Collins (1st ed) (ISBN 0131403656) Exploring Corporate Strategy - Gerry Johnson (8th ed) (ISBN 140588732X) Exploring Macroeconomics - Robert L. Sexton (4th ed) (ISBN 0324395558) Federal Tax Research - William A. Raabe (8th ed) (ISBN 0324659652) Feedback Control of Dynamic Systems - Gene Franklin (5th ed) (ISBN 0131499300) Financial & Managerial Accounting - Carl S. Warren (9th ed) (ISBN 0324401884) Financial & Managerial Accounting - Carl S. Warren (10th ed) (ISBN 0324663811) Financial Accounting - Belverd E. Needles (10th ed) (ISBN 0547193289) Financial Accounting - Carl S. Warren, James M. Reeve (10th ed) (ISBN 0324380674) Financial Accounting - Carl S. Warren, James M. Reeve (11th ed) (ISBN 0324663781) Financial Accounting - Jane Reimers (1st ed) (ISBN 0131492012) Financial Accounting - Walter Harrison, Charles Horngren (6th ed) (ISBN 0131499459) Financial Accounting - Walter Harrison, Charles Horngren (7th ed) (ISBN 0138128200) Financial Accounting and Financial Tips - Walter T. Harrison (7th ed) (ISBN 0135012848) Financial Accounting, Reporting & Analysis: International Edition - Barry Elliott (2nd ed) (ISBN 027370253X) Financial Accounting: A Bridge to Decision Making - Robert Ingram (6th ed) (ISBN 0324313357) Financial Accounting: A Business Process Approach - Jane L. Reimers (2nd ed) (ISBN 0131473867) Financial Accounting: An Integrated Statements Approach - Jonathan Duchac (2nd ed) (ISBN 0324312113) Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney (12th ed) (ISBN 0324381980) Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney (13th ed) (ISBN 0324651147) Financial Accounting: The Impact on Decision Makers - Gary Porter (6th ed) (ISBN 0324655231) Financial and Managerial Accounting - Meg Pollard (1st ed) (ISBN 0136008984) Financial And Managerial Accounting (Ch 1-13) - Charles Horngren (1st ed) (ISBN 0135009855) Financial Economics - Zvi Bodie (2nd ed) (ISBN 0131856154) Financial Management for Public, Health, and Not-for-Profit - Steven A Finkler (3rd ed) (ISBN 0136070736) Financial Management For Public, Health, and Not-for-Profit Organizations - Steven Finkler (2nd ed) (ISBN 0131471988) Financial Management: Theory & Practice - Eugene Brigham (12th ed) (ISBN 0324422695) Financial Markets and Institutions - Frederic S. Mishkin (5th ed) (ISBN 0321280296) Financial Markets and Institutions - Frederic S. Mishkin (6th ed) (ISBN 0321374215) Financial Markets and Institutions - Jeff Madura (8th ed) (ISBN 0324568215) Financial Markets and Institutions Abridged Edition - Jeff Madura (8th ed) (ISBN 0324593643) Financial Reporting and Analysis - Lawrence Revsine (3rd ed) (ISBN 0131430211) Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson (10th ed) (ISBN 0324304455) Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson (11th ed) (ISBN 0324657420) Financial Reporting, Financial Statement Analysis, and Valuation - Clyde P. Stickney (6th ed) (ISBN 0324302959) Financial/Managerial Accounting - Walter T. Harrison (1st ed) (ISBN 0131568779) Finite Element Analysis Theory and Application with ANSYS - Saeed Moaveni (3rd ed) (ISBN 0131890808) Finite Math and Its Application - Larry Goldstein (9th ed) (ISBN 0131873644) Finite Mathematics - Margaret L. Lial et al (8th ed) (ISBN 032122826X) Finite Mathematics and Calculus with Applications - Margaret Lial (8th ed) (ISBN 0321426517) Finite Mathematics for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132255707) Finite Mathematics with Applications - Margaret L. Lial (9th ed) (ISBN 0321386728) First Course in Abstract Algebra - John Fraleigh (7th ed) (ISBN 0201763907) First Course in Abstract Algebra - Joseph Rotman (3rd ed) (ISBN 0131862677) First Course In Probability - Sheldon M. Ross (7th ed) (ISBN 0131856626) First Course In Probability - Sheldon M. Ross (8th ed) (ISBN 013603313X) First Course in Statistics, A - James T. McClave (10th ed) (ISBN 0136152597) Fluency with Information Technology: Skills, Concepts, and Capabilities - Lawrence Snyder (3rd ed) (ISBN 0321512391) Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522362) Foundations of Finance - Arthur Keown, William Petty, John Martin, David Scott (5th ed) (ISBN 0131856057) Foundations of Finance: Logic and Practice of Financial Mangement - Arthur J. Keown (6th ed) (ISBN 0135048168) Foundations of Finance: The Logic and Practice of Financial Management - Arthur Keown (6th ed) (ISBN 0132339226) Foundations of Financial Markets and Institutions - Frank J. Fabozzi (4th ed) (ISBN 0136135315) Foundations of Geometry - Gerard Venema (5th ed) (ISBN 0131437003) Foundations of Macroeconomics - Robin Bade (4th ed) (ISBN 0321522370) Foundations of MEMS - Chang Liu (1st ed) (ISBN 0131472860) Foundations of Microeconomics - Robin Bade (3rd ed) (ISBN 0321415957) Foundations of Microeconomics - Robin Bade (4th ed) (ISBN 0321522389) Foundations of the Legal Environment of Business - Marianne M. Jennings (1st ed) (ISBN 0324566514) Framework for Human Resource Management, A - Gary Dessler (5th ed) (ISBN 0136041531) Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) Fraud Examination - Steve Albrecht (2nd ed) (ISBN 0324651155) Friendly Introduction to Analysis - Witold A.J. Kosmala (2nd ed) (ISBN 0130457965) Fundamental Cornerstones of Managerial Accounting - Dan L. Heitger, Maryanne M. Mowen (1st ed) (ISBN 0324378068) Fundamental Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321496906) Fundamentals of Advanced Accounting - Paul M. Fischer (Test Bank) (1st ed) (ISBN 0324378904) Fundamentals of Applied Electromagnetics - Fawwaz T. Ulaby (5th ed) (ISBN 0132413264) Fundamentals of Business Law Summarized Cases - Roger LeRoy Miller (7th ed) (ISBN 0324381689) Fundamentals of Business Law: Excerpted Cases - Roger LeRoy Miller (2nd ed) (ISBN 0324595727) Fundamentals of Business Law: Summarized Cases - Roger LeRoy Miller (8th ed) (ISBN 0324595735) Fundamentals of Communication Systems - John G. Proakis (1st ed) (ISBN 013147135X) Fundamentals of Complex Analysis - Edward Saff (3rd ed) (ISBN 0139078746) Fundamentals of Derivatives Markets - Robert L. McDonald (1st ed) (ISBN 0321357175) Fundamentals of Differential Equations - Kent Nagle, Edward Saff (6th ed) (ISBN 0321145720) Fundamentals of Differential Equations - R. Kent Nagle (7th ed) (ISBN 0321410483) Fundamentals of Differential Equations with Boundary Value Problems - R. Kent Nagle (5th ed) (ISBN 0321419219) Fundamentals of Electromagnetics for Electrical and Computer Engineering - Nannapaneni Narayana Rao (1st ed) (ISBN 0136013333) Fundamentals of Engineering Economics - Chan S. Park (2nd ed) (ISBN 0132209608) Fundamentals of Financial Management - Eugene Brigham (11th ed) (ISBN 0324319800) Fundamentals of Financial Management - Eugene F. Brigham (12th ed) (ISBN 0324597703) Fundamentals of Financial Management Concise - Eugene F. Brigham (6th ed) (ISBN 0324664559) Fundamentals of Investing - Lawrence J. Gitman (10th ed) (ISBN 0321489381) Fundamentals of Management: Essential Concepts and Applications - Stephen P. Robbins (Test Bank) (5th ed) (ISBN 0131487361) Fundamentals of Multinational Finance - Michael Moffett (3rd ed) (ISBN 0321541642) Fundamentals of Organic Chemistry - John McMurry (Test Bank only) (5th ed) (ISBN 0534395732) Fundamentals of Probability, with Stochastic Processes - Saeed Ghahramani (3rd ed) (ISBN 0131453408) Fundamentals of Signals and Systems - Edward Kamen (3rd ed) (ISBN 0131687379) Fundamentals of Statistics - Michael Sullivan (2nd ed) (ISBN 0131569872) Further Mathematics for Economic Analysis - Knut Sydsaeter et al (1st ed) (ISBN 0273655760) Geometry: Theorems and Constructions - Allan Berele (1st ed) (ISBN 0130871214) Global Investments - Bruno Solnik (6th ed) (ISBN 0321527704) Global Strategy - Mike W. Peng (2nd ed) (ISBN 0324590997) Governmental and Nonprofit Accounting: Theory and Practice - Robert J. Freeman (9th ed) (ISBN 0136029515) Health Economics - Charles E. Phelps (4th ed) (ISBN 0321594576) High-Speed Networks and Internets: Performance and Quality of Service - William Stallings (2nd ed) (ISBN 0130322210) Historical Geology - Reed Wicander (6th ed) (ISBN 0495560073) Human Anatomy & Physiology - Elaine N. Marieb (7th ed) (ISBN 0805359095) Human Anatomy and Physiology - Elaine N. Marieb (8th ed) (ISBN 0805395911) Human Anatomy and Physiology Lab Manual - Elaine N. Marieb (9th ed) (ISBN 0805372652) Human Biology: Concepts and Current Issues - Michael D. Johnson (5th ed) (ISBN 0321570200) Human Diseases: A Systemic Approach - Mark Zelman (7th ed) (ISBN 0135155568) Human Physiology: An Integrated Approach - Dee Unglaub Silverthorn (5th ed) (ISBN 0321559398) (ISBN 0495014850) Human Relations for Career and Personal Success: Concepts, Applications, and Skills - Andrew J. DuBrin (8th ed) (ISBN 0131791796) Human Relations: Interpersonal Job-Oriented Skills - Andrew J. DuBrin (10th ed) (ISBN 0135019443) Human Resource Management - Gary Dessler (11th ed) (ISBN 0131746170) Human Resource Management - R. Wayne Mondy (11th ed) (ISBN 0136077285) Human Resource Management - Wayne Mondy (10th ed) (ISBN 0132225956) Human Side of Organizations - Michael Drafke (10th ed) (ISBN 0135139740) Hydrology and Floodplain Analysis - Philip B. Bedient (4th ed) (ISBN 0131745891) Income Tax Fundamentals 2006 - Gerald E. Whittenburg (24th ed) (ISBN 0324399022) Income Tax Fundamentals 2007 - Gerald E. Whittenburg (25th ed) (ISBN 032439926X) Income Tax Fundamentals 2009 - Gerald E. Whittenburg (27th ed) (ISBN 0324663676) Information Systems Today: Managing in the Digital World - Leonard Jessup (3rd ed) (ISBN 0132335069) Information Systems Today: Managing the Digital World - Joseph Valacich (4th ed) (ISBN 0136078400) Information Technology Auditing and Assurance - James Hall (2nd ed) (ISBN 0324191987) Inquiry into Physics - Vern J. Ostdiek (6th ed) (ISBN 0495119431) Integrated Arithmetic and Basic Algebra - Bill E. Jordan (4th ed) (ISBN 0321442555) Intel Micro 8086 - Barry B. Brey (8th ed) (ISBN 0135026458) Intel Microprocessors - Barry B. Brey (7th ed) (ISBN 0131195069) Intel Microprocessors - Barry B. Brey (8th ed) (ISBN 0135026458) Interactive Computer Graphics: A Top-Down Approach Using OpenGL - Edward Angel (5th ed) (ISBN 0321535863) Interactive Statistics - Martha Aliaga, Brenda Gunderson (3rd ed) (ISBN 0131497561) Intermediate Accounting - James D. Stice (16th ed) (ISBN 0324312148) Intermediate Accounting - James D. Stice (17th ed) (ISBN 032459237X) Intermediate Accounting - Loren A. Nikolai (10th ed) (ISBN 0324651929) Intermediate Accounting - Loren A. Nikolai (11th ed) (ISBN 032465913X) Intermediate Accounting (Revised) - David Spiceland (4th ed) (ISBN 0073215422) Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007295) Intermediate Algebra - Margaret L. Lial (10th ed) (ISBN 0321443624) Intermediate Algebra - Margaret L. Lial (9th ed) (ISBN 0321574974) Intermediate Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321319087) Intermediate Algebra for College Students - Allen R. Angel (7th ed) (ISBN 0132383578) Intermediate Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0136007627) Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321500032) Intermediate Algebra: Functions & Authentic Applications - Jay Lehmann (3rd ed) (ISBN 0131953338) Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321416163) Intermediate Financial Management - Eugene F. Brigham (10th ed) (ISBN 0324594690) International Accounting - Frederick Choi (5th ed) (ISBN 0131480979) International Accounting - Frederick D. Choi (6th ed) (ISBN 0131588141) International Business - John Daniels (12th ed) (ISBN 0136029655) International Business - Ricky Griffin (6th ed) (ISBN 0137153732) International Business Law - Ray A. August (5th ed) (ISBN 013600864X) International Business Law and Its Environment - Richard Schaffer (7th ed) (ISBN 0324649673) International Business: Environments and Operations - John Daniels (11th ed) (ISBN 0131869426) International Business: Strategy, Management, and the New Realities - Tamer Cavusgil (1st ed) (ISBN 0131738607) International Business: The Challenges of Globalization - John J. Wild (4th ed) (ISBN 0131747436) International Business: The Challenges of Globalization - John J. Wild (5th ed) (ISBN 0137153759) International Economics - Charles Sawyer, Richard Sprinkle (2nd ed) (ISBN 0131704168) International Economics - James Gerber (3rd ed) (ISBN 032123796X) International Economics - James Gerber (4th ed) (ISBN 0321415558) International Economics - Robert Carbaugh (11th ed) (ISBN 032442194X) International Economics - W. Charles Sawyer (3rd ed) (ISBN 0136054692) International Economics: Theory And Policy - Paul Krugman, Maurice Obstfeld (7th ed) (ISBN 0321293835) International Economics: Theory and Policy - Paul R. Krugman (8th ed) (ISBN 0321488830) International Financial Management - Geert Bekaert (1st ed) (ISBN 0131163604) International Financial Management - Jeff Madura (9th ed) (ISBN 0324568193) International Financial Management Abridged Edition - Jeff Madura (9th ed) (ISBN 0324593473) International Financial Management, Abridged Edition - Jeff Madura (8th ed) (ISBN 0324365632) International Management: Managing Across Borders and Cultures - Helen Deresky (6th ed) (ISBN 0136143261) International Money and Finance - Michael Melvin (7th ed) (ISBN 0201770288) Intro Stats - Richard D. De Veaux (3rd ed) (ISBN 0321500458) Introduction to Abstract Algebra - Olympia Nicodemi (1st ed) (ISBN 0131019635) Introduction to Analysis - William R. Wade (3rd ed) (ISBN 0131453335) Introduction to Business Law - Jeffrey F. Beatty (2nd ed) (ISBN 0324311427) Introduction to Business Statistics - Ronald M. Weiers (6th ed) (ISBN 0324381433) Introduction to C++ EXCEL MATLAB & Basic Engineering Numerical Methods - Harvey G. Stenger (1st ed) (ISBN 0136142931) Introduction to C++, Excel MatLab & Basic Engineering Numerical Methods - Harvey Stenger (1st ed) (ISBN 0136120245) Introduction to Chemical Principles - Stephen Stoker (9th ed) (ISBN 0132379945) Introduction to Computing Systems - Sanjay J. Patel, Yale Patt (2nd ed) (ISBN 0072467509) Introduction to Corporate Finance - William L. Megginson (1st ed) (ISBN 0324379862) Introduction to Corporate Finance - William L. Megginson (2nd ed) (ISBN 0324657935) Introduction to Cryptography with Coding Theory - Wade Trappe (2nd ed) (ISBN 0131862391) Introduction to Derivatives and Risk Management - Don M. Chance (7th ed) (ISBN 0324321392) Introduction to Econometrics - James H. Stock (2nd ed) (ISBN 0321278879) Introduction to Econometrics Brief Edition - James H. Stock (1st ed) (ISBN 0321432517) Introduction to Economic Reasoning - William D. Rohlf (7th ed) (ISBN 0321416112) Introduction to Electrodynamics -David J. Griffiths (3rd ed) (ISBN 013805326X) Introduction to Embedded Systems - Jonathan W. Valvano (1st ed) (ISBN 049541137X) Introduction to Environmental Engineering - P. Aarne Vesilind (3rd ed) (ISBN 0495295833) Introduction to Environmental Engineering - Richard O. Mines (1st ed) (ISBN 0132347474) Introduction to Environmental Engineering and Science - Gilbert M. Masters (3rd ed) (ISBN 0131481932) Introduction to Financial Accounting - Charles Horngren (9th ed) (ISBN 0131479725) Introduction to Fire Prevention - James C. Robertson (7th ed) (ISBN 0135041945) Introduction to Fourier Optics - Joseph Goodman (3rd ed) (ISBN 0974707724) Introduction to Government and Non-for-Profit Accounting - Martin Ives (6th ed) (ISBN 0132366355) Introduction to Graph Theory - Douglas West (2nd ed) (ISBN 0130144002) Introduction to Law - Joanne Hames (3rd ed) (ISBN 0131183818) Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) Introduction to Linear Programming - Leonid Vaserstein (1st ed) (ISBN 0130359173) Introduction to Management Accounting - Charles T. Horngren (14th ed) (ISBN 0136129218) Introduction to Management Accounting, Chap. 1-17: International Edition - Charles Horngren (13th ed) (ISBN 0131273078) Introduction to Management Science and Student - Bernard Taylor (8th ed) (ISBN 0131050524) Introduction to Management Science and Student - Bernard Taylor (9th ed) (ISBN 0131888099) Introduction to Materials Management - Tony Arnold (6th ed) (ISBN 0132337614) Introduction to Materials Science for Engineers - James F. Shackelford (7th ed) (ISBN 0136012604) Introduction to Mathematical Statistics and Its Applications - Richard J. Larsen (4th ed) (ISBN 0131867938) Introduction to Operations and Supply Chain Management - Cecil Bozarth (2nd ed) (ISBN 0131791036) Introduction to Optics - Frank Pedrotti et al. (3rd ed) (ISBN 0131499335) Introduction to Programming with C++ - Y. Daniel Liang (2nd ed) (ISBN 0136097200) Introduction to Quantum Mechanics - David Griffiths (2nd ed) (ISBN 0131118927) Introduction to Risk Management and Insurance - Mark Dorfman (8th ed) (ISBN 0131449583) Introduction to Risk Management and Insurance - Mark S. Dorfman (9th ed) (ISBN 0132242273) Introduction to Signal and System Analysis - Kaliappan Gopalan (1st ed) (ISBN 0534466060) Introduction to Spectroscopy - Donald L. Pavia (4th ed) (ISBN 0495114782) Introduction to Technical Mathematics - Allyn J. Washington, Mario Triola (5th ed) (ISBN 0321374177) Introduction to Telecommunications - Martha Rosengrant (2nd ed) (ISBN 0131126156) Introduction to the Design & Analysis of Experiments - George C Canavos (1st ed) (ISBN 0136158633) Introduction to the Design and Analysis of Algorithms - Anany Levitin (1st ed) (ISBN 0201743957) Introduction to the Design and Analysis of Algorithms - Anany Levitin (2nd ed) (ISBN 0321358287) Introduction to Transportation Engineering - Lester A. Hoel (1st ed) (ISBN 0534952895) Introduction to Vacuum Technology - David M. Hata (1st ed) (ISBN 0130450189) Introductory & Intermediate Algebra for College Students - Robert F. Blitzer (3rd ed) (ISBN 0136028950) Introductory Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321269470) Introductory Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0132356791) Introductory Algebra through Applications - Geoffrey Akst (2nd ed) (ISBN 0321518020) Introductory and Intermediate Algebra - Robert F Blitzer (2nd ed) (ISBN 0131492594) Introductory Chemistry - Nivaldo J. Tro (3rd ed) (ISBN 0136003826) Introductory Chemistry - Steve Russo, Michael Silver, Mike Silver (2nd ed) (ISBN 032104634X) Introductory Circuit Analysis - Robert Boylestad (11th ed) (ISBN 0131730444) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (3rd ed) (ISBN 0324289782) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (4th ed) (ISBN 0324581629) Introductory Linear Algebra: An Applied First Course - Bernard Kolman (8th ed) (ISBN 0131437402) Introductory Mathematical Analysis - Ernest F Haeussler (12th ed) (ISBN 0132404222) Introductory Statistics - Neil A. Weiss (8th ed) (ISBN 0321393619) Inventing Entrepreneurs: Technology Innovators and their Entrepreneurial Journey - Gerry George (1st ed) (ISBN 0131574701) Investments - Frank K. Reilly (7th ed) (ISBN 0324288999) Investments: An Introduction - Herbert B. Mayo (9th ed) (ISBN 0324561261) Java Software Solutions: Foundations of Program Design - John Lewis (5th ed) (ISBN 0321409493) Java: Introduction to Problem Solving and Programming - Walter Savitch (6th ed) (ISBN 0136072259) John E. Freund's Mathematical Statistics with Applications - Irwin Miller (7th ed) (ISBN 0131427067) Kleppner's Advertising Procedure - Ronald Lane (17th ed) (ISBN 0132308290) Labor and Employment Law: Text & Cases - David Twomey (14th ed) (ISBN 0324594844) Labor Relations - Arthur A Sloane (12th ed) (ISBN 013196223X) Labor Relations - Arthur A. Sloane (13th ed) (ISBN 0136077188) Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell (8th ed) (ISBN 0131868721) Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell (9th ed) (ISBN 0136084354) Lakeside Company: Case Studies in Auditing - John M. Trussel (11th ed) (ISBN 0131588516) Law and Economics - Robert Cooter (5th ed) (ISBN 0321336348) Law and Ethics in the Business Environment - Terry Halbert (6th ed) (ISBN 0324657323) Law for Business - John D. Ashcroft (16th ed) (ISBN 0324381573) Leadership - Robert N. Lussier (3rd ed) (ISBN 0324316976) Leadership in Organizations - Gary Yukl (7th ed) (ISBN 0132424312) Learning Microsoft Office Accounting 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0131586602) Learning Peachtree Complete 2007 & Peachtree Complete CD Package - Terri Brunsdon (1st ed) (ISBN 0132405571) Learning Quickbooks Pro 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0132419386) Legal Aspects of Architecture, Engineering & the Construction Process - Justin Sweet (8th ed) (ISBN 0495411213) Legal Terminology - Gordon W. Brown (5th ed) (ISBN 0131568043) Level Three Leadership: Getting Below the Surface - James G Clawson (4th ed) (ISBN 0132423847) Linear Algebra and Its Applications - David C. Lay (3rd ed) (ISBN 0321287134) Linear Algebra for Engineers and Scientists Using Matlab - Kenneth Hardy (1st ed) (ISBN 0139067280) Linear Algebra with Applications - Otto Bretscher (3rd ed) (ISBN 0131453343) Linear Algebra with Applications - Steven Leon (7th ed) (ISBN 0131857851) Logic and Computer Design Fundamentals - M. Morris Mano (4th ed) (ISBN 013198926X) Machine Design: An Integrated Approach - Robert L. Norton (3rd ed) (ISBN 0131481908) Machines and Mechanisms: Applied Kinematic Analysis - David H. Myszka (3rd ed) (ISBN 0131837761) Macroeconomics - Andrew B. Abel (6th ed) (ISBN 0321451406) Macroeconomics - Glenn Hubbard (2nd ed) (ISBN 0132356694) Macroeconomics - Michael Parkin (7th ed) (ISBN 032124608X) Macroeconomics - Michael Parkin (8th ed) (ISBN 0321416570) Macroeconomics - Michael Parkin (9th ed) (ISBN 0321600053) Macroeconomics - Olivier Blanchard (5th ed) (ISBN 0132078295) Macroeconomics - Richard Froyen (8th ed) (ISBN 0131435825) Macroeconomics - Richard G. Lipsey (13th ed) (ISBN 0321369238) Macroeconomics - Richard T Froyen (9th ed) (ISBN 0132438356) Macroeconomics - Robert Gordon (10th ed) (ISBN 0321278801) Macroeconomics - Robert Gordon (11th ed) (ISBN 0321485513) Macroeconomics - Roger A. Arnold (9th ed) (ISBN 032478550X) Macroeconomics - Stephen D. Williamson (3rd ed) (ISBN 0321416589) Macroeconomics: A Modern Approach - Robert J. Barro (1st ed) (ISBN 0324178107) Macroeconomics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537034) Macroeconomics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586213) Macroeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536184) Macroeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 013232928X) Macroeconomics: Public and Private Choice - James D. Gwartney (12th ed) (ISBN 0324580193) Making Career Decisions that Count: A Practical Guide - Darrell A. Luzzo (3rd ed) (ISBN 0131712772) Making the Team - Leigh Thompson (3rd ed) (ISBN 0131861352) Management - Michael Hitt (2nd ed) (ISBN 0132354373) Management - Richard L. Daft (9th ed) (ISBN 0324595840) Management - Stephen P Robbins (9th ed) (ISBN 0132257734) Management Communication: A Case-Analysis Approach - James S O'Rourke (4th ed) (ISBN 0136079768) Management Information Systems - Ken Laudon (11th ed) (ISBN 013607846X) Management of Organizational Behavior - Paul H Hersey (9th ed) (ISBN 0131441396) Manager's Bookshelf - Jon L. Pierce (8th ed) (ISBN 0132301652) Managerial Accounting - Carl Warren (9th ed) (ISBN 0324381913) Managerial Accounting - Carl Warren (10th ed) (ISBN 032466382X) Managerial Accounting - Linda S. Bamber (1st ed) (ISBN 0138129711) Managerial Accounting (Class Test Edition) - Linda S. Bamber (1st ed) (ISBN 0132284634) Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers (4th ed) (ISBN 0324650647) Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers (5th ed) (ISBN 0324663854) Managerial Accounting: An Introduction to Concepts, Methods and Uses - Michael W. Maher (10th ed) (ISBN 0324639767) Managerial Economics - Mark Hirschey (12th ed) (ISBN 0324584849) Managerial Economics: A Problem Solving Approach - Luke M. Froeb (1st ed) (ISBN 0324359810) Managerial Economics: Applications, Strategies, and Tactics - James R. McGuigan (11th ed) (ISBN 0324421605) Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat (5th ed) (ISBN 0131860151) Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat (6th ed) (ISBN 0136040047) Managerial Statistics A Case-Based Approach - Peter Klibanoff (1st ed) (ISBN 0324226454) Managers and the Legal Environment - Constance E. Bagley (6th ed) (ISBN 0324582048) Managing Human Resources - Luis Gomez-Mejia (5th ed) (ISBN 013187067X) Managing in a Global Economy: Demystifying International Macroeconomics - John E. Marthinsen (1st ed) (ISBN 0324395507) Managing Information Technology - Carol V Brown (6th ed) (ISBN 0131789546) Managing the Law: The Legal Aspects of Doing Business - Mitchell McInnes (2nd ed) (ISBN 0132042762) Manual Auditing and Assurance Practice Set: CAST - Frank A. Buckless (1st ed) (ISBN 0130464716) Manufacturing Processes for Engineering Materials - Serope Kalpakjian (5th ed) (ISBN 0132272717) Manufacturing, Engineering & Technology - Serope Kalpakjian (5th ed) (ISBN 0131489658) Market Regulation - Roger Sherman (1st ed) (ISBN 0321322320) Market-Based Management - Roger Best (5th ed) (ISBN 0132336537) Marketing - Charles W. Lamb (10th ed) (ISBN 0324591098) Marketing - William M. Pride (15th ed) (ISBN 0547167474) Marketing Management - Dawn Iacobucci (1st ed) (ISBN 0324784430) Marketing Management - Philip Kotler (13th ed) (ISBN 0136009980) Materials Science and Engineering: An Introduction - William Callister (6th ed) (ISBN 0471135763) Mathematical Economics - Jeffrey Baldani (2nd ed) (ISBN 0324183321) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361466) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361482) Mathematical Methods for Economics - Michael Klein (2nd ed) (ISBN 0201726262) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (2nd ed) (ISBN 0321390539) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (1st ed) (ISBN 0201710900) Mathematical Reasoning for Elementary Teachers - Calvin T. Long (5th ed) (ISBN 0321460847) Mathematics for Business - Stanley A. Salzman (8th ed) (ISBN 0321357434) Mathematics for Elementary School Teachers - Phares O'Daffer (4th ed) (ISBN 0321448049) Mathematics for Physicists - Susan Lea (1st ed) (ISBN 0534379974) Mathematics of Interest Rates and Finance - Gary Guthrie (1st ed) (ISBN 0130461822) Mathematics with Applications - Margaret L. Lial (9th ed) (ISBN 0321334337) Mechanical Behavior of Materials - Norman Dowling (3rd ed) (ISBN 0131863126) Mechanics of Materials - James M. Gere (7th ed) (ISBN 0534553974) Mechanics of Materials - Russell C. Hibbeler (7th ed) (ISBN 0132209918) Medical Imaging Signals and Systems - Jerry L. Prince (1st ed) (ISBN 0130653535) Microbiology with Diseases by Body System - Robert W. Bauman (2nd ed) (ISBN 032151341X) Microbiology: An Introduction - Gerard J. Tortora (9th ed) (ISBN 0805347909) Microeconomics - Glenn Hubbard (2nd ed) (ISBN 0138132771) Microeconomics - Jeffrey Perloff (4th ed) (ISBN 0321414527) Microeconomics - Jeffrey Perloff (5th ed) (ISBN 0321531191) Microeconomics - Michael Parkin (7th ed) (ISBN 0321454944) Microeconomics - Michael Parkin (8th ed) (ISBN 0321416600) Microeconomics - Michael Parkin (9th ed) (ISBN 0321600045) Microeconomics - Richard G. Lipsey (13th ed) (ISBN 032136922X) Microeconomics - Robert Pindyck, Daniel Rubinfeld (6th ed) (ISBN 0130084611) Microeconomics - Robert Pindyck, Daniel Rubinfeld (7th ed) (ISBN 0132080230) Microeconomics - Roger A. Arnold (9th ed) (ISBN 0324785496) Microeconomics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586221) Microeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536060) Microeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 0131572830) Microeconomics: Public and Private Choice - James D. Gwartney (12th ed) (ISBN 0324580207) Microeconomics: Theory and Applications with Calculus - Jeffrey M. Perloff (1st ed) (ISBN 0321277945) Microwave Engineering - David Pozar (3rd ed) (ISBN 0471448788) MIS Essentials - David Kroenke (1st ed) (ISBN 0136075606) MKTG 3.0 2009 Edition - Charles W. Lamb (3rd ed) (ISBN 0324789289) Modern Control Systems - Richard C Dorf (11th ed) (ISBN 0132270285) Modern Database Management - Jeffrey Hoffer (8th ed) (ISBN 0132212110) Modern Database Management - Jeffrey Hoffer (9th ed) (ISBN 0136003915) Modern Electronic Communication - Jeff Beasley (9th ed) (ISBN 0132251132) Modern Elementary Statistics - John E. Freund (12th ed) (ISBN 013187439X) Modern Industrial Organization - Dennis Carlton, Jeffrey Perloff (4th ed) (ISBN 0321180232) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (10th ed) (ISBN 0321533739) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (9th ed) (ISBN 0321305035) Modern Management - Samuel C. Certo (10th ed) (ISBN 0131494708) Modern Physics - Randy Harris (2nd ed) (ISBN 0805303081) Modern Physics - Raymond Serway (3rd ed) (ISBN 0534493394) Modern Semiconductor Devices for Integrated Circuits - Chenming C. Hu (1st ed) (ISBN 0136085253) Modern Systems Analysis and Design - Jeffrey A. Hoffer (5th ed) (ISBN 0132240769) Modern Wireless Communications - Simon Haykin (1st ed) (ISBN 0130224723) Money, Banking and Financial Markets - Roger LeRoy Miller (3rd ed) Money, the Financial System, and the Economy - R. Glenn Hubbard (6th ed) (ISBN 0321426703) Multinational Business Finance - David K. Eiteman (11th ed) (ISBN 0321357965) Multinational Finance - Kirt C. Butler (3rd ed) (ISBN 0324177453) Multinational Management - John B. Cullen (4th ed) (ISBN 032442177X) Multivariate Data Analysis - Joseph F. Hair (7th ed) (ISBN 0138132631) Nanoengineering of Structural, Functional and Smart Materials - Mark J. Schulz (1st ed) (ISBN 0849316537) New Venture Management: The Entrepreneur's Roadmap - Donald Kuratko (1st ed) (ISBN 0136130321) Numerical Analysis - Timothy Sauer (1st ed) (ISBN 0321268989) Numerical Methods for Engineers - Bilal Ayyub, Richard McCuen (1st ed) (ISBN 0133373614) Numerical Methods Using Matlab - John Mathews (4th ed) (ISBN 0130652482) Occupational Safety and Health for Technologists, Engineers, and Managers - David L. Goetsch (6th ed) (ISBN 0132397609) Office Procedures 21st Century & Student Workbook Package - Sharon Burton (7th ed) (ISBN 0132343436) OM 2008 - David Alan Collier (1st ed) (ISBN 0324662556) Operating Systems Principles - Lubomir F. Bic (1st ed) (ISBN 0130266116) Operating Systems: Internals and Design Principles - William Stallings (5th ed) (ISBN 0131479547) Operations Management - Jay Heizer (8th ed) (ISBN 0131554441) Operations Management - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management - Nigel Slack (5th ed) (ISBN 0273708473) Operations Management and Student CD and Student DVD Package - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management: Process and Value Chains - Lee J. Krajewski (8th ed) (ISBN 0131697390) Operations Research: An Introduction - Hamdy A. Taha (8th ed) (ISBN 0131889230) Opportunities and Challenges of Workplace Diversity: Theory, Cases, and Exercises - Kathryn Canas (1st ed) (ISBN 0131343068) Oracle 10g Programming: A Primer - Rajshekhar Sunderraman (1st ed) (ISBN 0321463048) Organic Chemistry - Paula Bruice (Test Bank only) (5th ed) (ISBN 0131963163) Organization Development and Change - Thomas G. Cummings (9th ed) (ISBN 0324421389) Organizational Behavior - Don Hellriegel (12th ed) (ISBN 0324578725) Organizational Behavior - Stephen P Robbins (13th ed) (ISBN 0136007171) Organizational Behavior Today - Leigh Thompson (1st ed) (ISBN 0131858114) Organizational Behavior: An Experiential Approach - Joyce S Osland (8th ed) (ISBN 0131441515) Organizational Behavior: An Introduction to Your Life in Organizations - Rae Andre (1st ed) (ISBN 013185495X) Organizational Behavior: Managing People and Organizations - Ricky W. Griffin (9th ed) (ISBN 0547167334) Organizational Behavior: Science, The Real World, and You - Debra L. Nelson (6th ed) (ISBN 0324578733) Organizational Theory, Design and Change - Gareth R. Jones (5th ed) (ISBN 0131865420) Organizational Theory, Design and Change - Gareth R. Jones (6th ed) (ISBN 0136087310) Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems - Donald L. Bartel (1st ed) (ISBN 0130089095) Parallel and Distributed Computation: Numerical Methods - Dimitri Bertsekas, John Tsitsiklis (1st ed) (ISBN 0136487009) Parallel Programming - Barry Wilkinson (2nd ed) (ISBN 0131405632) Partial Differential Equations and Boundary Value Problems - Nakhle Asmar (2nd ed) (ISBN 0131480960) Payroll Accounting 2008 - Bernard Bieg (18th ed) (ISBN 0324645546) Payroll Accounting 2009 - Bernard Bieg (19th ed) (ISBN 0324663730) Performance Management - Herman Aguinis (2nd ed) (ISBN 0136151752) Personal Finance - Jeff Madura (3rd ed) (ISBN 0321409965) Personal Finance: Turning Money into Wealth - Arthur J. Keown (5th ed) (ISBN 0135077710) Personal Financial Planning - Lawrence J. Gitman (11th ed) (ISBN 0324422865) Pharmacology for Nurses: A Pathophysiological Approach - Michael Patrick Adams (2nd ed) (ISBN 0131756656) Physical Chemistry - Thomas Engel, Philip Reid (1st ed) (ISBN 080533842X) Physical Chemistry for the Life Sciences - Thomas Engel (1st ed) (ISBN 0805382771) Physical Geography - Robert E. Gabler (9th ed) (ISBN 0495555061) Physical Metallurgy Principles - Reza Abbaschian (4th ed) (ISBN 0495082546) Physics : Principles with Applications - Douglas Giancoli (6th ed) (ISBN 0130606200) Physics for Scientists & Engineers (Chs 1-37) with MasteringPhysics» - Doug Giancoli (4th ed) (ISBN 0136139264) Physics for Scientists and Engineers with Modern Physics and MasteringPhysics» - Douglas C. Giancoli (4th ed) (ISBN 0136139221) Physics with Mastering Physics - James S. Walker (3rd ed) (ISBN 0136138969) Physics with Mastering Physics - James S. Walker (4th ed) (ISBN 0321541634) Physics: Principles with Applications with MasteringPhysics - Douglas C. Giancoli (6th ed) (ISBN 0321569830) Portfolio Construction, Management, and Protection - Robert A. Strong (4th ed) (ISBN 0324359365) Portfolio Construction, Management, and Protection - Robert A. Strong (5th ed) (ISBN 0324665105) Power Systems Analysis and Design - J. Duncan Glover (4th ed) (ISBN 0534548849) Practical Financial Management - William R. Lasher (5th ed) (ISBN 0324422636) Prealgebra - Elayn El Martin-Gay (5th ed) (ISBN 0132319519) Prealgebra - Margaret L. Lial (4th ed) (ISBN 0321567927) Prealgebra - Marvin L. Bittinger (5th ed) (ISBN 0321331907) Prealgebra & Introductory Algebra - Elayn El Martin-Gay (2nd ed) (ISBN 0131577050) Prealgebra and Introductory Algebra - Marvin L. Bittinger (2nd ed) (ISBN 0321331893) Prealgebra: An Integrated Approach - Margaret L. Lial (1st ed) (ISBN 032135639X) Precalculus - J. S. Ratti (1st ed) (ISBN 032129646X) Precalculus - Judith A. Beecher (3rd ed) (ISBN 0321460065) Precalculus - Margaret Lial (4th ed) (ISBN 0321528840) Precalculus - Mark Dugopolski (4th ed) (ISBN 0321357795) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus - Robert F. Blitzer (3rd ed) (ISBN 0131874799) Precalculus - Robert F. Blitzer (4th ed) (ISBN 0321559843) Precalculus: Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136015786) Precalculus: Functions and Graphs - Mark Dugopolski (3rd ed) (ISBN 032150111X) Precalculus: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501527) Prehospital Emergency Care - Joseph J. Mistovich (8th ed) (ISBN 0131741438) Prentice Hall's Federal Taxation 2007: Comprehensive - Thomas Pope (20th ed) (ISBN 0132389479) Prentice Hall's Federal Taxation 2007: Corporations - Thomas Pope (20th ed) (ISBN 0131751484) Prentice Hall's Federal Taxation 2007: Individuals - Thomas Pope (20th ed) (ISBN 013243220X) Prentice Hall's Federal Taxation 2008: Comprehensive - Thomas Pope (21st ed) (ISBN 0132416492) Prentice Hall's Federal Taxation 2008: Corporations - Thomas Pope (21st ed) (ISBN 0136156436) Prentice Hall's Federal Taxation 2008: Individuals - Thomas Pope (21st ed) (ISBN 0136156371) Prentice Hall's Federal Taxation 2009: Comprehensive - Thomas Pope (22nd ed) (ISBN 0136067190) Prentice Hall's Federal Taxation 2009: Corporations - Thomas Pope (22nd ed) (ISBN 0136067131) Prentice Hall's Federal Taxation 2009: Individuals - Thomas Pope (22nd ed) (ISBN 0136067042) Preparing Effective Business Plans: An Entrepreneurial Approach - Bruce R. Barringer (1st ed) (ISBN 0132318326) Price Theory and Applications - Steven Landsburg (7th ed) (ISBN 0324421613) Principles of Accounting - Meg Pollard (1st ed) (ISBN 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd ed) (ISBN 0273684108) Principles of CMOS VLSI Design - Neil H.E. Weste (3rd ed) (ISBN 0201533766) Principles of Cost Accounting - Edward J. Vanderbeck (13th ed) (ISBN 0324191693) Principles of Cost Accounting - Edward J. Vanderbeck (14th ed) (ISBN 0324374178) Principles of Customer Relationship Management - Roger Baran (1st ed) (ISBN 0324322380) Principles of Economics - Gregory Mankiw (4th ed) (ISBN 0324224729) Principles of Economics - Gregory Mankiw (5th ed) (ISBN 0324589972) Principles of Economics - Karl Case (8th ed) (ISBN 0132289148) Principles of Electric Circuits: Conventional Current Version - Thomas Floyd (8th ed) (ISBN 0131701797) Principles of Electric Circuits: Conventional Flow Version - Thomas L. Floyd (9th ed) (ISBN 013507309X) Principles of Finance - Scott Besley (3rd ed) (ISBN 0324232624) Principles of Finance - Scott Besley (4th ed) (ISBN 0324655886) Principles of Foundation Engineering - Braja M. Das (6th ed) (ISBN 0495082465) Principles of Geotechnical Engineering - Braja M. Das (6th ed) (ISBN 0534551440) Principles of Heat Transfer - Frank Kreith (6th ed) (ISBN 0534375960) Principles of Law and Economics - Daniel Cole, Peter Grossman (1st ed) (ISBN 0130932612) Principles of Macroeconomics - Gregory Mankiw (4th ed) (ISBN 0324236956) Principles of Macroeconomics - Gregory Mankiw (5th ed) (ISBN 0324589999) Principles of Managerial Finance - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Managerial Finance Brief Edition - Lawrence Gitman (5th ed) (ISBN 0321557522) Principles of Managerial Finance plus MyfinanceLab Student Access Kit - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Marketing - Philip Kotler (12th ed) (ISBN 0132390027) Principles of Marketing - Philip Kotler (13th ed) (ISBN 0136079415) Principles of Microeconomics - Gregory Mankiw (4th ed) (ISBN 0324319169) Principles of Microeconomics - Karl E. Case (8th ed) (ISBN 0131994859) Principles of Money, Banking & Financial Markets - Lawrence Ritter (12th ed) (ISBN 0321375572) Principles of Money, Banking, Financial Markets - Lawrence Ritter et al (11th ed) (ISBN 0321205251) Principles Of Operations Management - Jay Heizer (6th ed) (ISBN 013155445X) Principles Of Operations Management - Jay Heizer (7th ed) (ISBN 0132449757) Principles of Risk Management and Insurance - George E. Rejda (10th ed) (ISBN 0321414934) Probabilistic Systems and Random Signals - Abraham Haddad (1st ed) (ISBN 0130094552) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th ed) (ISBN 0131877119) Probability and Statistical Inference - Robert Hogg, Eliot Tanis (7th ed) (ISBN 0131464132) Probability and Statistical Inference - Robert Hogg, Eliot Tanis (8th ed) (ISBN 0321584759) Probability and Statistics - Morris DeGroot, Mark Schervish (3rd ed) (ISBN 0201524880) Probability and Statistics for Engineers - Richard Johnson, Irwin Miller, John Freund (7th ed) (ISBN 0131437453) Probability and Statistics for Engineers and Scientists - Anthony J. Hayter (3rd ed) (ISBN 0495107573) Probability Random Variables, and Stochastic Processes - Papoulis et al (4th ed) (ISBN 0073660116) Probability, Statistics, and Random Processes For Electrical Engineering - Alberto Leon-Garcia (3rd ed) (ISBN 0131471228) Problem Solving and Program Design in C - Jeri R. Hanly (5th ed) (ISBN 0321409914) Problem Solving and Program Design in C - Jeri R. Hanly (6th ed) (ISBN 0321535421) Problem Solving with C++ - Walter Savitch (6th ed) (ISBN 0321412699) Problem Solving with C++ - Walter Savitch (7th ed) (ISBN 0321531345) Problem Solving, Abstraction & Design Using C++ - Frank L. Friedman (5th ed) (ISBN 0321450051) Process Control Instrumentation Technology - Curtis Johnson (8th ed) (ISBN 0131194577) Professional Office Procedures - Susan Cooperman (5th ed) (ISBN 0135156645) Professional Selling: A Trust-Based Approach - Thomas N. Ingram (4th ed) (ISBN 032453809X) Professionalism: Real Skills for Workplace Success - Lydia E. Anderson (1st ed) (ISBN 0131714392) Programming the World Wide Web - Robert W. Sebesta (4th ed) (ISBN 0321489691) Project Management for Information Systems - James Cadle (5th ed) (ISBN 0132068583) Public Relations Practices: Managerial Case Studies and Problems - Allen H. Center (7th ed) (ISBN 0132341360) Quality Control - Dale H. Besterfield (8th ed) (ISBN 0135000955) Quality Management - Donna C.S. Summers (2nd ed) (ISBN 0135005108) Quality Management for Organizational Excellence - David L. Goetsch (6th ed) (ISBN 0135019672) Quantitative Analysis for Management - Barry Render (10th ed) (ISBN 0136036252) Quantitative Analysis for Management - Barry Render (9th ed) (ISBN 0131857029) Quantum Chemistry and Spectroscopy - Thomas Engel (1st ed) (ISBN 0805339795) QuickBooks Pro 2006 with Update 2007 and CD Package - Janet Horne (9th ed) (ISBN 013242407X) Real Estate Law - George Siedel (6th ed) (ISBN 0324204809) Real Estate Law - Marianne M. Jennings (8th ed) (ISBN 0324650205) Reinforced Concrete Design - George F. Limbrunner (7th ed) (ISBN 0135044359) Reinforced Concrete: Mechanics and Design - James K. Wight (5th ed) (ISBN 0132281414) Retailing - Patrick M. Dunne (6th ed) (ISBN 032436279X) Rethinking Marketing: The Entrepreneurial Imperative - Minet Schindehutte (1st ed) (ISBN 0132393891) Risk Management and Insurance - James S. Trieschmann (12th ed) (ISBN 0324183208) Risk Takers: Uses and Abuses of Financial Derivatives - John Marthinsen (2nd ed) (ISBN 0321542568) Routers and Routing Basics CCNA 2 Labs and Study Guide - Allan Johnson (1st ed) (ISBN 1587131676) Selling Today - Gerald L. Manning (11th ed) (ISBN 013207995X) Short-Term Financial Management - Terry Maness (3rd ed) (ISBN 0324202938) Short-Term Financial Management - Terry Maness (Test Bank) (3rd ed) (ISBN 0324202938) Signals, Systems, and Transforms - Charles L Phillips (4th ed) (ISBN 0131989235) Social Entrepreneurship: A Modern Approach to Social Value Creation - Arthur C. Brooks (1st ed) (ISBN 0132330768) Software Engineering - Ian Sommerville (8th ed) (ISBN 0321313798) Software Engineering: Theory and Practice - Shari Lawrence Pfleeger (4th ed) (ISBN 0136061699) Soils and Foundations - Cheng Liu, Jack Evett (7th ed) (ISBN 0132221381) Solid State Electronic Devices - Ben Streetman (6th ed) (ISBN 013149726X) Solid State Physics: Essential Concepts - David W. Snoke (1st ed) (ISBN 0805386645) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Corporations - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Taxation of Business Entities - James Smith (Solutions Manual) (12th ed) (ISBN 0324660510) South-Western Federal Taxation 2009: Taxation of Business Entities - James Smith (Test Bank) (12th ed) (ISBN 0324660510) South-Western Federal Taxation 2010: Comprehensive - William Hoffman (Solutions Manual) (33rd ed) (ISBN 0324828616) South-Western Federal Taxation 2010: Comprehensive - William Hoffman (Test Bank) (33rd ed) (ISBN 0324828616) South-Western Federal Taxation 2010: Corporations - William Hoffman (Solutions Manual) (33rd ed) (ISBN 0324828632) South-Western Federal Taxation 2010: Corporations - William Hoffman (Test Bank) (33rd ed) (ISBN 0324828632) South-Western Federal Taxation 2010: Individual Income Taxes - William Hoffman (Solutions Manual) (33rd ed) (ISBN 0324828659) South-Western Federal Taxation 2010: Individual Income Taxes - William Hoffman (Test Bank) (33rd ed) (ISBN 0324828659) South-Western Federal Taxation 2010: Taxation of Business Entities - James Smith (Solutions Manual) (33rd ed) (ISBN 0324828586) South-Western Federal Taxation 2010: Taxation of Business Entities - James Smith (Test Bank) (33rd ed) (ISBN 0324828586) Spectral Analysis of Signals - Peter Stoica, Randolph Moses (1st ed) (ISBN 0131139568) Starting Out with C++: Early Objects - Tony Gaddis (6th ed) (ISBN 0321512383) Starting Out with Java: Early Objects - Tony Gaddis (3rd ed) (ISBN 0321497686) Gaddis (4th ed) (ISBN 0136080200) Starting Out with Visual Basic 2008 - Tony Gaddis (4th ed) (ISBN 0321531353) Starting Out With Visual Basic 2008 Update - Tony Gaddis (4th ed) (ISBN 0136076955) Statics and Strength of Materials - Robert L. Mott (1st ed) (ISBN 0135159822) Statics and Strengths of Materials - Harold I. Morrow (6th ed) (ISBN 0131719777) Statistical Methods for the Social Sciences - Alan Agresti (4th ed) (ISBN 0130272957) Statistical Reasoning for Everyday Life - Jeffrey O. Bennett (3rd ed) (ISBN 0321286723) Statistics - James T. McClave (11th ed) (ISBN 0132069512) Statistics for Business & Economics - James T. McClave (10th ed) (ISBN 0132409356) Statistics for Business and Economics - David R. Anderson (Test Bank only) (10th ed) (ISBN 0324360681) Statistics for Business and Economics - Paul Newbold, William L. Carlson (6th ed) (ISBN 0132203847) Statistics for Business and Economics - Paul Newbold, William L. Carlson (7th ed) (ISBN 0136085369) Statistics for Management and Economics - Gerald Keller (7th ed) (ISBN 0534491243) Statistics for Managers Using Microsoft Excel - David M. Levine (5th ed) (ISBN 0136149901) Statistics for Science and Engineering - John Kinney (1st ed) (ISBN 0201437201) Statistics for the Behavioral and Social Sciences - Arthur Aron (4th ed) (ISBN 0131562789) Statistics for the Life Sciences - Myra Samuels (3rd ed) (ISBN 013041316X) Statistics, Data Analysis & Decision Modeling - James R. Evans (4th ed) (ISBN 0136066003) Statistics: Informed Decisions Using Data - Michael Sullivan (3rd ed) (ISBN 0321568028) (1st ed) (ISBN 0130083690) Statistics: The Art and Science of Learning from Data - Alan Agresti (2nd ed) (ISBN 0135131995) Stats: Data and Models - Richard D. De Veaux (2nd ed) (ISBN 0321433793) Steel Design - William T. Segui (4th ed) (ISBN 0495244716) Strategic Brand Management - Kevin Keller (3rd ed) (ISBN 0131888595) Strategic Compensation - Joe Martocchio (5th ed) (ISBN 0136007449) Strategic Management and Business Policy - Tom Wheelen (10th ed) (ISBN 0131494597) Strategic Management and Business Policy - Tom Wheelen (11th ed) (ISBN 013232346X) Strategic Management and Competitive Advantage - Jay Barney (2nd ed) (ISBN 013613520X) Strategic Management and Competitive Advantage: Concepts and Cases - Jay Barney (2nd ed) (ISBN 0132338238) Strategic Management in Action - Mary Coulter (4th ed) (ISBN 0132277476) Strategic Management: A Dynamic Perspective Integrated Stratsim Simulation Experience - Print Upgrade - Mason Carpenter (1st ed) (ISBN 0136149057) Strategic Management: Concepts and Cases - Fred David (11th ed) (ISBN 0131869493) Strategic Management: Concepts and Cases - Fred David (12th ed) (ISBN 0136015700) Strategic Marketing for Non-Profit Organizations - Alan Andreasen (7th ed) (ISBN 013175372X) Strategic Staffing - Jean M. Phillips (1st ed) (ISBN 0131586947) Structural Analysis - Aslam Kassimali (4th ed) (ISBN 0495295655) Structural Analysis - Russell C. Hibbeler (7th ed) (ISBN 0136020607) Structural Steel Design - Jack C. McCormac (4th ed) (ISBN 013221816X) Structural Steel Design ASD Method - Jack C. McCormac (4th ed) (ISBN 0065000609) Structural Steel Design: A Practice Oriented Approach - Abi O. Aghayere (1st ed) (ISBN 0132340186) Structure and Interpretation of Signals and Systems - Edward Lee, Pravin Varaiya (1st ed) (ISBN 0201745518) Structures - Daniel Lewis Schodek (6th ed) (ISBN 0131789392) Supply Chain Management - Sunil Chopra (3rd ed) (ISBN 0131730428) Supply Chain Management: A Logistics Perspective - John J. Coyle (8th ed) (ISBN 0324376928) Survey of Accounting - Carl S. Warren (3rd ed) (ISBN 0324312482) Survey of Accounting - Carl S. Warren (4th ed) (ISBN 0324658265) Survey of Economics - Irvin B. Tucker (6th ed) (ISBN 0324579616) Survey of Mathematics with Applications - Allen R. Angel (8th ed) (ISBN 0321501071) Survey of Mathematics with Applications Expanded Edition - Allen Angel (8th ed) (ISBN 032150108X) Surveying with Construction Applications - Barry F. Kavanagh (6th ed) (ISBN 0131709321) Surveying with Construction Applications - Barry F. Kavanagh (7th ed) (ISBN 0135000513) Surveying: Principles and Applications - Barry F. Kavanagh (8th ed) (ISBN 013236512X) System Dynamics and Response - S. Graham Kelly (1st ed) (ISBN 0534549306) System Modeling and Analysis: Foundations of System Performance Evaluation - Hisashi Kobayashi (1st ed) (ISBN 013034835X) Systems Analysis and Design - Kenneth E. Kendall (7th ed) (ISBN 0132240858) Tax Research - Barbara H Karlin (4th ed) (ISBN 013601531X) Taxation for Decision Makers 2008 - Shirley Dennis-Escoffier (2nd ed) (ISBN 0324654111) Taxes & Business Strategy - Myron S. Scholes (4th ed) (ISBN 0136033156) Teaching Today's Health - David Anspaugh (9th ed) (ISBN 0321596773) Technical Calculus with Analytic Geometry - Allyn J. Washington (4th ed) (ISBN 0201711125) Technical Communication: A Practical Approach - William S. Pfeiffer (7th ed) (ISBN 0135000505) Technology Strategy for Managers and Entrepreneurs - Scott A. Shane (1st ed) (ISBN 0131879324) The Economics of Macro Issues - Roger LeRoy Miller (3rd ed) (ISBN 0321416597) The Economics of Poverty and Discrimination - Bradley R Schiller (10th ed) (ISBN 0131889699) The Economics of Public Issues - Roger LeRoy Miller (15th ed) (ISBN 0321416104) The Economics of Sports - Michael A. Leeds (3rd ed) (ISBN 0321415566) The Labor Relations Process - William H. Holley (9th ed) (ISBN 0324421443) The Legal Environment of Business - Roger E. Meiners (10th ed) (ISBN 0324654367) The Legal Environment of Business: Text and Cases Ethical, Regulatory, Global, and E-Commerce Issues - Roger LeRoy Miller (7th ed) (ISBN 0324590008) The Legal Environment Today: Business In Its Ethical, Regulatory, E- Commerce, and Global Setting - Roger LeRoy Miller (6th ed) (ISBN 0324599250) The Paralegal Professional - Henry Cheeseman (2nd ed) (ISBN 0131751905) The Science of Nutrition - Janice Thompson (1st ed) (ISBN 0805394354) The Strategy of Managing Innovation and Technology - Murray Millson (1st ed) (ISBN 0132303833) Theory of Asset Pricing - George Pennacchi (1st ed) (ISBN 032112720X) Thermodynamics: An Engineering Approach - Yunus Cengel (5th ed) (ISBN 0073107689) Thinking Mathematically - Robert F. Blitzer (4th ed) (ISBN 0131752049) Thomas' Calculus - George B. Thomas, Jr. (11th ed) (ISBN 0321185587) Thomas' Calculus, Early Transcendentals, Media Upgrade - George B. Thomas, Jr (11th ed) (ISBN 0321495756) Thomas' Calculus, Early Transcendentals, Media Upgrade, Part One - George B. Thomas, Jr. (11th ed) (ISBN 0321498747) Thomas' Calculus, Media Upgrade - George B. Thomas, Jr. (11th ed) (ISBN 032148987X) Thomas' Calculus, Media Upgrade, Part One (Single Variable) - George B. Thomas, Jr. (11th ed) (ISBN 0321498755) Thomas' Calculus, Media Upgrade, Part Two (Multivariable, Chap 11-16) - George B. Thomas, Jr. (11th ed) (ISBN 0321501039) Traffic & Highway Engineering - Nicholas J. Garber (4th ed) (ISBN 0495082503) Training in Interpersonal Skills - Stephen P. Robbins (5th ed) (ISBN 0132354993) Trigonometry - Margaret L. Lial (9th ed) (ISBN 0321528859) Trigonometry - Mark Dugopolski (2nd ed) (ISBN 032135690X) Trigonometry: A Right Triangle Approach - Michael Sullivan (5th ed) (ISBN 0136028969) Trigonometry: A Unit Circle Approach - Michael Sullivan (8th ed) (ISBN 0132392798) UFL Collective Bargaining Agreement - Louis Marino (1st ed) (ISBN 0131587668) Understanding and Managing Diversity - Carol Harvey (4th ed) (ISBN 0132069105) Understanding and Managing Organizational Behavior - Jennifer George (5th ed) (ISBN 013239457X) Understanding Fiber Optics - Jeff Hecht (5th ed) (ISBN 0131174290) Understanding Financial Statements - Lyn M. Fraser (8th ed) (ISBN 0131878565) Understanding Modern Economics - Roger Miller (1st ed) (ISBN 0321245822) University Calculus - Joel Hass, Maurice D. Weir (1st ed) (ISBN 0321350146) University Calculus: Alternate Edition - Joel Hass (1st ed) (ISBN 0321471962) University Calculus: Alternate Edition, Part One (Single Variable, Chap 1-9) - Joel Hass (1st ed) (ISBN 0321475194) University Calculus: Elements with Early Transcendentals - Joel Hass (1st ed) (ISBN 0321533488) University Physics with Modern Physics with MasteringPhysics» - Hugh D. Young (12th ed) (ISBN 080532187X) Using and Understanding Mathematics: A Quantitative Reasoning Approach - Jeffrey O. Bennett (4th ed) (ISBN 0321458206) Using Financial Accounting Information: The Alternative to Debits & Credits - Gary A. Porter (5th ed) (ISBN 0324645104) Using Financial Accounting Information: The Alternative to Debits & Credits - Gary A. Porter (6th ed) (ISBN 0324593740) Using MIS - David Kroenke (2nd ed) (ISBN 0138132488) Using Peachtree Complete 2007 for Accounting - Glenn Owen (1st ed) (ISBN 0324377975) Using Peachtree Complete 2009 for Accounting - Glenn Owen (3rd ed) (ISBN 0324665512) Using Quickbooks Pro 2007 for Accounting - Glenn Owen (7th ed) (ISBN 0324378750) Vector Calculus - Susan Colley (3rd ed) (ISBN 0131858742) VHDL: A Starter's Guide - Sudhakar Yalamanchili (2nd ed) (ISBN 0131457357) Water and Wastewater Technology - Mark J. Hammer (6th ed) (ISBN 0131745425) Water Resources Engineering - David A. Chin (2nd ed) (ISBN 0131481924) Water Supply and Pollution Control - Warren Viessman, Jr. (8th ed) (ISBN 0132337177) Web 101 - Wendy G. Lehnert (3rd ed) (ISBN 0321424670) West Federal Taxation Comprehensive 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313497) West Federal Taxation Comprehensive 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313497) West Federal Taxation Corporations 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380437) West Federal Taxation Corporations 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380437) West Federal Taxation Individual 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380585) West Federal Taxation Individual 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380585) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Solutions Manual) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Test Bank) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Solutions Manual) (11th ed) (ISBN 0324366655) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Test Bank) (11th ed) (ISBN 0324366655) West's Business Law - Kenneth W. Clarkson (10th ed) (ISBN 0324303904) Wireless Communications & Networks - William Stallings (2nd ed) (ISBN 0131918354) Writing and Speaking at Work: A Practical Guide for Business Communication - Edward P. Bailey (4th ed) (ISBN 0131881302) Your Attitude is Showing - Sharon Lund O'Neil (12th ed) (ISBN 0132429047) International Books Abnormal Psychology, First Canadian Edition - James N. Butcher (1st Ed) (ISBN-10: 0205702880) Accounting 1-26 - Charles Horngren (6th Ed) (ISBN-10: 0131248391) Accounting and Finance for Non-Specialists - Peter Atrill (6th Ed) (ISBN-10: 1408208040) Accounting for Canadian Colleges - Ted Palmer (5th Ed) (ISBN-10: 0321415531) Accounting for Non-Accounting Students - John R. Dyson (7th Ed) (ISBN-10: 0273709224) Accounting Information Systems: International Version - Marshall B. Romney (11th Ed) (ISBN-10: 0135009375) Accounting International Version (Ch. 1-23) - Charles T. Horngren (8th Ed) (ISBN-10: 0136112900) Accounting Volume 1 Canadian Edition - Charles T. Horngren (7th Ed) (ISBN-10: 0132067331) Accounting Volume 2 Canadian Edition - Charles T. Horngren (7th Ed) (ISBN-10: 013206734X) Accounting Volume 3 Canadian Edition - Charles T. Horngren (7th Ed) (ISBN-10: 0132067358) Accounting: An Introduction - Peter Atrill (4th Ed) (ISBN-10: 1405893249) Advanced Accounting - Floyd Beams (9th Ed) (ISBN-10: 0131851225) Advanced Accounting: International Version - Floyd A. Beams (10th Ed) (ISBN-10: 0131358057) Advanced Financial Accounting - Richard Lewis (7th Ed) (ISBN-10: 0273658492) Advanced Financial Accounting - Thomas H. Beechy (5th Ed) (ISBN-10: 0131236997) Aging in Contemporary Canada - Neena L. Chappell (2nd Ed) (ISBN-10: 013201873X) Auditing and Assurance Services Global Edition - Alvin Arens (13th Ed) (ISBN-10: 0132458934) Auditing and Other Assurance Services Canadian Edition - Alvin A. Arens (10th Ed) (ISBN-10: 0131296159) Auditing Cases: International Edition - Mark S Beasley (4th Ed) (ISBN-10: 013608415X) Auditing: An International Approach - Bahram Soltani (1st Ed) (ISBN-10: 0273657739) Bond Markets, Analysis, and Strategies: International Edition - Frank J Fabozzi (7th Ed) (ISBN-10: 0136099742) Book-keeping and Accounts - Frank Wood (7th Ed) (ISBN-10: 0273718053) Business Accounting UK GAAP Volume 1 - Alan Sangster (1st Ed) (ISBN-10: 0273718762) Business Accounting UK GAAP Volume 2 - Alan Sangster (1st Ed) (ISBN-10: 0273718800) Business Accounting Volume 1 - F. Wood (10th Ed) (ISBN-10: 0273681494) Business Accounting Volume 1 - Frank Wood (11th Ed) (ISBN-10: 0273712128) Business Accounting Volume 2 - F. Wood (10th Ed) (ISBN-10: 0273693107) Business Accounting Volume 2 - Frank Wood (11th Ed) (ISBN-10: 0273712136) Business Canadian Edition - Ricky W. Griffin (6th Ed) (ISBN-10: 0131734296) Business Communication Essentials, Second Canadian Edition - Courtland L. Bovee (2nd Ed) (ISBN-10: 0132462346) Business Forecasting: International Edition - John E. Hanke (9th Ed) (ISBN-10: 0135009332) Business Law in Canada - Richard A. Yates (8th Ed) (ISBN-10: 0132065487) Business Law in Canada - Richard A. Yates (7th Ed) (ISBN-10: 0131206826) Business Law in Canada Casebook - D'Anne Davis (4th Ed) (ISBN-10: 0131225707) Canadian Industrial Relations - Jon Peirce (3rd Ed) (ISBN-10: 0131277936) Canadian Macroeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982966) Canadian Macroeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982966) Canadian Marketing in Action - Keith J. Tuckwell (7th Ed) (ISBN-10: 0131277790) Canadian Microeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982974) Canadian Microeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982974) Capital Markets: Institutions and Instruments: International Edition - Frank J Fabozzi (4th Ed) (ISBN-10: 0137154992) Cases in Financial Reporting - D. Eric Hirst (5th Ed) (ISBN-10: 0131881205) College Accounting: A Practical Approach Canadian Edition - Jeffrey Slater (9th Ed) (ISBN-10: 0131278177) Comparative International Accounting - Christopher Nobes (10th Ed) (ISBN-10: 0273714767) Concepts In Systems and Signals - John D. Sherrick (2nd Ed) (ISBN-10: 0131782711) Consumer Behaviour - Leon G. Schiffman (1st Ed) (ISBN-10: 0131463047) Consumer Behaviour: Buying, Having, and Being - Michael R. Solomon (4th Ed) (ISBN-10: 0132072874) Contemporary Business Mathematics with Canadian Applications - S. A. Hummelbrunner (8th Ed) (ISBN-10: 0136156088) Corporate Accounting Information Systems - Tony Boczko (1st Ed) (ISBN-10: 0273684876) Corporate Finance: International Edition - Jonathan Berk (1st Ed) (ISBN-10: 1408215039) Cost Accounting: A Managerial Emphasis Canadian Edition - Charles Horngren (3rd Ed) (ISBN-10: 0130355801) Cost Accounting: A Managerial Emphasis Canadian Edition - Charles Horngren (4th Ed) (ISBN-10: 0131971905) Cost Benefit Analysis: Concepts and Practice: International Edition - Anthony Boardman (3rd Ed) (ISBN-10: 0132405601) Economics - Christopher T.S. Ragan (12th Ed) (ISBN-10: 0321469003) Economics of Health and Health Care: International Edition - Sherman Folland (5th Ed) (ISBN-10: 0132342529) Essentials of Corporate Financial Management - Glen Arnold (1st Ed) (ISBN-10: 1405847042) Essentials of Statistics: International Edition - Mario F. Triola (3rd Ed) (ISBN-10: 0321484096) Estimating in Building Construction - Frank R. Dagostino (2nd Ed) (ISBN-10: 0132231379) Ethics in Action: Making Ethical Decisions in Your Daily Life - Jane Ann McLachlan (1st Ed) (ISBN-10: 0135041406) Financial Accounting - Charles Horngren (6th Ed) (ISBN-10: 0131499459) Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial Accounting and Financial Tips - Walter T. Harrison (7th Ed) (ISBN-10: 0135012848) Financial Accounting Canadian Edition - Walter T. Harrison (2nd Ed) (ISBN-10: 0131879294) Financial Accounting Canadian Edition with MyAccountingLab - Walter T. Harrison (2nd Ed) (ISBN-10: 0135146607) Financial Accounting Theory - William R. Scott (4th Ed) (ISBN-10: 0131294911) Financial Accounting Theory - William Scott (5th Ed) (ISBN-10: 0132072866) Financial Accounting, Reporting & Analysis - Barry Elliott (2nd Ed) (ISBN-10: 027370253X) Financial Accounting: An International Approach - Jagdish Kothari (1st Ed) (ISBN-10: 0273693190) Financial Accounting: An International Introduction - David Alexander (2nd Ed) (ISBN-10: 0273685201) Financial Accounting: An International Introduction - David Alexander (3rd Ed) (ISBN-10: 0273709267) Financial Accounting: An Introduction - Augustine Benedict (1st Ed) (ISBN-10: 0273688855) Financial Accounting: An Introduction - Pauline Weetman (4th Ed) (ISBN-10: 0273703404) Financial and Management Accounting - Pauline Weetman (4th Ed) (ISBN-10: 0273703692) Financial and Managerial Accounting - Meg Pollard (1st Ed) (ISBN-10: 0136008984) Financial and Managerial Accounting International Version (Ch. 1-23) - Charles T. Horngren (2nd Ed) (ISBN-10: 0137008457) Financial Economics: International Edition - Zvi Bodie (2nd Ed) (ISBN-10: 0131579525) Financial Management for Decision Makers - Peter Atrill (5th Ed) (ISBN-10: 0273717642) Financial Management for Public, Health, and Not-for-Profit: International Version - Steven A Finkler (3rd Ed) (ISBN-10: 0138152772) Financial Management: Principles and Practice - Timothy J. Gallagher (1st Ed) (ISBN-10: 0131245678) Financial Reporting and Analysis - Lawrence Revsine (3rd Ed) (ISBN-10: 0131430211) First Course in Probability, A: International Edition - Sheldon Ross (7th Ed) (ISBN-10: 0132018179) First Course in Probability, A: International Edition - Sheldon Ross (7th Ed) (ISBN-10: 0132018179) Foundations of Financial Markets and Institutions: International Edition - Frank J. Fabozzi (4th Ed) (ISBN-10: 013135423X) Foundations of Operations Management - Larry P. Ritzman (2nd Ed) (ISBN-10: 0132279312) Fundamentals of Corporate Finance: Global Edition - Jonathan Berk (1st Ed) (ISBN-10: 0137000774) Fundamentals of Financial Management - J. Van Horne (13th Ed) (ISBN-10: 0273713639) Fundamentals of Management Canadian Edition - Stephen P. Robbins (5th Ed) (ISBN-10: 0131988794) Fundamentals of Organizational Behaviour - Nancy Langton (3rd Ed) (ISBN-10: 0131757377) Governmental and Nonprofit Accounting: International Version - Robert J. Freeman (9th Ed) (ISBN-10: 0135031664) Health Economics: International Edition - Charles E. Phelps (4th Ed) (ISBN-10: 0321642902) Health: The Basics Canadian Edition - Rebecca J. Donatelle (4th Ed) (ISBN-10: 0205535585) Human Resources Management in Canada - Gary Dessler (10th Ed) (ISBN-10: 0132270870) Lipczynski (2nd Ed) (ISBN-10: 0273688022) Information Systems Today: Why IS Matters - Leonard Jessup (2nd Ed) (ISBN-10: 0131740393) International Accounting: International Edition - Frederick Choi (5th Ed) (ISBN-10: 0131293575) International Economics: International Edition - W. Charles Sawyer (3rd Ed) (ISBN-10: 0132089971) International Economics:Theory and Policy: International Edition - Paul R. Krugman (8th Ed) (ISBN-10: 1408208075) International Financial Management: International Edition - Geert Bekaert (1st Ed) (ISBN-10: 0136054900) Interpreting and Analyzing Financial Statement - Karen P. Schoenebeck (4th Ed) (ISBN-10: 0132391902) Introduction to Cryptography with Coding Theory: International Edition - Wade Trappe (2nd Ed) (ISBN-10: 0131981994) Introduction to Econometrics: International Edition - James H. Stock (2nd Ed) (ISBN-10: 0321442539) Introduction to Financial Accounting: International Edition - Charles Horngren (9th Ed) (ISBN-10: 0131968750) Introduction to Government and Non-for-Profit Accounting: International Edition - Martin Ives (6th Ed) (ISBN-10: 0132074281) Introduction to Management Accounting - Charles T. Horngren (14th Ed) (ISBN-10: 0136129218) Introduction to Microsoft Dynamics GP 10.0: Focus on Internal Controls - Terri J. Brunsdon (2nd Ed) (ISBN-10: 0136098045) Introduction to Optics: International Edition - Frank Pedrotti et al. (3rd Ed) (ISBN-10: 0131971336) Introduction to Quantum Mechanics: International Edition - David J. Griffiths (2nd Ed) (ISBN-10: 0131911759) Law and Economics: International Edition - Robert D. Cooter (5th Ed) (ISBN-10: 0321522907) Legal Fundamentals for Canadian Business - Richard A. Yates (1st Ed) (ISBN-10: 0131273787) Legal Terminology - Gordon W. Brown (5th Ed) (ISBN-10: 0131568043) Macroeconomics - Andrew B. Abel (4th Ed) (ISBN-10: 0321306627) Macroeconomics - Christopher T.S. Ragan (12th Ed) (ISBN-10: 0321468988) Macroeconomics: International Version - Olivier Blanchard (5th Ed) (ISBN-10: 0132079631) Management Accounting - Anthony A. Atkinson (5th Ed) (ISBN-10: 0136005314) Management Accounting - Charles T. Horngren (5th Ed) (ISBN-10: 0131922688) Management Accounting - Pauline Weetman (1st Ed) (ISBN-10: 0273701991) Management Accounting: Analysis and Interpretation - Cheryl McWatters (1st Ed) (ISBN-10: 0273712470) Management Information Systems: Managing the Digital Firm - Kenneth C. Laudon (3rd Ed) (ISBN-10: 0131973886) Managerial Accounting - Linda S. Bamber (1st Ed) (ISBN-10: 0138129711) Managerial Accounting for Business Decisions - Ray Proctor (3rd Ed) (ISBN-10: 0273717553) Managerial Economics: International Edition - Paul Keat (6th Ed) (ISBN-10: 0135070651) Managing the Law: The Legal Aspects of Doing Business - Mitchell McInnes (2nd Ed) (ISBN-10: 0132042762) Mathematics of Finance with Canadian Applications - S. A. Hummelbrunner (1st Ed) (ISBN-10: 0132073501) Mathematics of Finance with Canadian Applications - S. A. Hummelbrunner (6th Ed) (ISBN-10: 0132073501) Microeconomics - Christopher T.S. Ragan (12th Ed) (ISBN-10: 0321468996) Microeconomics - Saul Estrin (5th Ed) (ISBN-10: 0273646273) Microeconomics: International Edition - Robert Pindyck (7th Ed) (ISBN-10: 0137133359) Modern Labor Economics: Theory and Public Policy: International Edition - Ronald G. Ehrenberg (10th Ed) (ISBN-10: 032153896X) Organizational Behaviour: Concepts, Controversies, Applications - Nancy Langton (4th Ed) (ISBN-10: 0131971107) Organizational Theory, Design, and Change - Gareth R. Jones (1st Ed) (ISBN-10: 0131245228) Personal Finance for Canadians - Elliot J. Currie (9th Ed) (ISBN-10: 0132286750) Principles of Accounting - Meg Pollard (1st Ed) (ISBN-10: 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd Ed) (ISBN-10: 0273684108) Principles of Marketing Canadian Edition - Philip Kotler (7th Ed) (ISBN-10: 0132020017) Principles of Marketing European Edition - Philip Kotler (5th Ed) (ISBN-10: 0273720643) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th Ed) (ISBN-10: 0132047675) Psychology Canadian Edition - Saundra Ciccarelli (1st Ed) (ISBN-10: 0138152160) Selling Today - Gerald L. Manning (4th Ed) (ISBN-10: 0131275992) Society: The Basics Canadian Edition - John J. Macionis (4th Ed) (ISBN-10: 0132057913) Statistics for Economics, Accounting & Business Studies - Michael Barrow (5th Ed) (ISBN-10: 0273717987) Statistics: International Edition - James McClave (10th Ed) (ISBN-10: Survey of Accounting: Making Sense of Business - Katherene P. Terrell (1st Ed) (ISBN-10: 0130911844) Technical Communication Canadian Edition - William S. Pfeiffer (4th Ed) (ISBN-10: 0131962930) The Canadian Criminal Justice System - Thomas Fleming (2nd Ed) (ISBN-10: 0131992465) The Economics of Money, Banking, and Financial Markets Canadian Edition - F. S. Mishkin (3rd Ed) (ISBN-10: 032142395X) The Law and Business Administration in Canada - J. E. Smyth (11th Ed) (ISBN-10: 0132042754) The Practice of Market Research: An Introduction - Yvonne Mcgivern (3rd Ed) (ISBN-10: 0273717073) Thomas' Calculus: International Edition - George B. Thomas, Jr (11th Ed) (ISBN-10: 0321243358) Understanding Financial Statements - Lyn M. Fraser (8th Ed) (ISBN-10: 0131878565) Understanding Financial Statements: International Edition (9th Ed) (ISBN-10: 0138153272) Using QuickBooks Pro 2005 for Windows - M. Purbhoo (1st Ed) (ISBN-10: 0321243307) === Subject: Operations Management 9th Edition Jay Heizer Instructors Solution Manual and test bank is available for purchase! Contact me at instructors.team[at]gmail.com posting-account=jy2E5goAAAB1WGwMQL1h2k61o4k7O_u4 Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Operations Management 9th Edition Jay Heizer Instructors Solution Manual and test bank is available for purchase! Contact me at instructors.team[at]gmail.com === Subject: Re: question on lca groups jakarta@nitrogen.mathforum.org>, G A Edgar: No, possibly not. Say G is the reals with addition and the usual topology, H is the integers, a subgroup of G. The dual of G is again isomorphic to the reals. But the dual of H is a circle, which is not a subgroup of the reals. In fact: The dual of a subgroup is a quotient of the dual. Write G* for the dual of G. Then H* = G*/K where K is the set of all characters of G that vanish on H. So the dual of the rationals is strange. What kind of group is R/Q? === Subject: Re: question on lca groups R/Q gets some kind of topology too? === Subject: Re: question on lca groups <18729262.69660.1246644967220.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/20090630 Fedora/3.5-1.fc11 Firefox/3.5,gzip(gfe),gzip(gfe) > R/Q gets some kind of topology too? In the context of lca groups one only considers quotients by closed subgroups. Also, Q is not locally compact... In any case, the only sensible topology on R/Q is the trivial one. -- m === Subject: Re: question on lca groups > Let G be an lca group and H a closed subgroup. Is it > true that the dual group of H is a subgroup of the > dual group of G? no, but a quotient In particular: Is every character on H generated by > restriction of a character on G? Every character on H IS the restriction of a character on G. For this see Cor 3.6.2 of the book Principles of Harmonic Analysis Anton === Subject: Re: question on lca groups <33350735.67913.1246611922927.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Every character on H IS the restriction of a character on G. > For this see Cor 3.6.2 of the book Principles of Harmonic Analysis === Subject: Re: question on lca groups > On 3 July, 10:04, Anton Deitmar Every character on H IS the restriction of a > character on G. > For this see Cor 3.6.2 of the book Principles of > Harmonic Analysis > I suggest you buy a copy. Then you'll find out. ;-) === Subject: Re: question on lca groups <16858019.69824.1246648935883.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > On 3 July, 10:04, Anton Deitmar Every character on H IS the restriction of a > character on G. > For this see Cor 3.6.2 of the book Principles of > Harmonic Analysis > I suggest you buy a copy. Then you'll find out. ;-) this one? http://www.amazon.co.uk/Principles-Harmonic-Analysis-Walter-Piston/dp/091131 8054 === Subject: Re: question on lca groups > On 3 July, 20:21, Anton Deitmar > On 3 July, 10:04, Anton Deitmar Every character on H IS the restriction of a > character on G. > For this see Cor 3.6.2 of the book Principles > of > Harmonic Analysis :-) I suggest you buy a copy. Then you'll find out. ;-) this one? http://www.amazon.co.uk/Principles-Harmonic-Analysis-W > alter-Piston/dp/0911318054 no, try this one http://www.amazon.com/Principles-Harmonic-Analysis-Universitext-Deitmar/dp/0 387854681/ref=sr_1_1?ie=UTF8&s=books&qid=1246702379&sr=8-1 Anton === Subject: Re: Application of a theorem If f is a continuous map from the Cantor set C onto the unit square [0,1]x[0,1], then by extending f linearly on each component of C complement one gets a continuous map from [0,1] onto the unit square. So Peano space filling curve is an application of the theorem. === === Subject: How to speed up the modular exponentiation algorithm to compute $g^x, h^x$, where $g,h$ are generator of group $G$. The trivial algorithm is costs two modular exponentiations to compute $g^x, h^x$, where $g,h$ are two different generators of group $G$ of prime order $q$. Is there any more faster algorithm to solve this problem? If it exists, could someone give me a reference? === Subject: Re: sum sum(n=1,oo) (-1)^n * zeta(2+n) / n = ? I have a result - it's not particularly satisfactory. > Start with (124) on > http://mathworld.wolfram.com/RiemannZetaFunction.html > differentiate, multiply by x^2, integrate. That is your series. > So we get an answer in terms of the integral of x^2 Psi(x+1) ... I forgot plug in x=1 at the end. The answer is in terms of that > integral from 0 to 1. involvs the digamma function integrated from 0,1 or from 0,z. i got it by looking at F(z) = int(0,1) digamma(z/x+1) dz and noting that the sum crops up in F(1) (by using the series representation of the digamma function). also note that F(1) = 1/s*int(0,s) digamma(s/x+1)dx for any s>0 and real. I get F(1) = -gamma+2*pi^2*ln(glaisher)-zeta(2)*(gamma+ln(2*pi)) + S S being the sum above. i was hopeing to either get F(1) or S in closed form. Looking at the reference you gave, and all those summation identities...i think i can see how they got them...i'll work on it over the weekend. cheers moth === Subject: Re: sum rancid moth a .8ecrit : > sum(n=1,oo) (-1)^n * zeta(2+n) / n = ? > I have a result - it's not particularly satisfactory. > Start with (124) on > http://mathworld.wolfram.com/RiemannZetaFunction.html > differentiate, multiply by x^2, integrate. That is your series. > So we get an answer in terms of the integral of x^2 Psi(x+1) ... > I forgot plug in x=1 at the end. The answer is in terms of that > integral from 0 to 1. involvs the digamma function integrated from 0,1 or from 0,z. i got it by > looking at F(z) = int(0,1) digamma(z/x+1) dx (dz -> dx I think...) and noting that the sum crops up in F(1) (by using the series representation > of the digamma function). also note that F(1) = 1/s*int(0,s) digamma(s/x+1)dx for any s>0 and real. I get F(1) = -gamma+2*pi^2*ln(glaisher)-zeta(2)*(gamma+ln(2*pi)) + S > A shorter version of this should be F(1) = - gamma - zeta'(2) + S S being the sum above. i was hopeing to either get F(1) or S in closed form. > Looking at the reference you gave, and all those summation identities...i > think i can see how they got them...i'll work on it over the weekend. cheers > moth I don't know a closed form for S (nor for the related F(1)) but it may be written too as : S= - sum_{k=1}^oo ln(1+1/k)/k^2 S= int_0^1 (digamma(1+x)+gamma-zeta(2)*x)/x^2 dx (or int_1^oo psi(1+1/t)+gamma-zeta(2)/t dt ) S= int_0^1 (trigamma(1+x)-zeta(2))/x dx + zeta(2)-1 Note that your initial expression remains the fastest for numerical evaluation! :-) Raymond === Subject: Re: sum <020720090929487214%edgar@math.ohio-state.edu.invalid> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) sum(n=1,oo) (-1)^n * zeta(2+n) / n = ? I have a result - it's not particularly satisfactory. > Start with (124) on > http://mathworld.wolfram.com/RiemannZetaFunction.html > differentiate, multiply by x^2, integrate. That is your series. > So we get an answer in terms of the integral of x^2 Psi(x+1) ... I forgot plug in x=1 at the end. The answer is in terms of that > integral from 0 to 1. involvs the digamma function integrated from 0,1 or from 0,z. i got it by > looking at F(z) = int(0,1) digamma(z/x+1) dz and noting that the sum crops up in F(1) (by using the series representation > of the digamma function). also note that F(1) = 1/s*int(0,s) digamma(s/x+1)dx for any s>0 and real. I get F(1) = -gamma+2*pi^2*ln(glaisher)-zeta(2)*(gamma+ln(2*pi)) + S > S being the sum above. i was hopeing to either get F(1) or S in closed form. > Looking at the reference you gave, and all those summation identities...i > think i can see how they got them...i'll work on it over the weekend. cheers > moth === Subject: Re: the return of the master : tommy1729 Most > of the time, the standard theorists are the ones who > are suggesting that I spend money on books. Whatever standard theorist means, I don't suggest how you should > spend your money. I just say that you make it very difficult on > yourself to get a good systematic understanding of certain subjects > without reading any books on those subjects. How you get the books - > by purchase, by borrowing, or by stealing is another matter. We know that tommy1729 has come up with his own > mereological set theory, TST. Oh yes, the one that is inconsistent (unless he further qualifies it). MoeBlee > Most of the time, the standard theorists are the ones who > are suggesting that I spend money on books. > Whatever standard theorist means, I don't suggest how you should > spend your money. I was just pointing out how both the so-called cranks and their opponents are trying to convince me to read their respective materials. Since I won't read all the materials that MoeBlee has recommended that I read merely because he posts that it's a good idea, I won't read tommy1729's work merely because he suggests it either. And while I'm on this topic, let me quote MoeBlee from a separate post of his: > I'll never spend a dime to see the proof. > You don't mean that literally do you? I mean, if for a dime you could > have a copy of a proof (say, an actually correct proof) of the twin > primes conjecture, you'd spend the dime, right? OK, I'll give this one to MoeBlee. Since I was willing to spend more than a literal dime for the Dover books, I'd be willing to spend a literal dime for an actually correct proof of the Twin Primes Conjecture. Of course, tommy1729 hasn't even stated exactly how much he is charging for the proof. So I don't know how many dimes (or should I say, Euros since he is European) I would have to spend to see his alleged proof, which he claims is actually an elementary proof. Skepticism, of course, is in order since one wonders how such an elementary proof has eluded previous mathematicians. > We know that tommy1729 has come up with his own > mereological set theory, TST. > Oh yes, the one that is inconsistent (unless he further qualifies it). Here we go again. I've already explained to MoeBlee why his proof of the inconsistency of TST is invalid, and yet he is still claiming that TST is inconsistent. I've noticed that certain so-called crank theories (not just TST) have a key property in common that ZFC lacks, making them difficult to be accepted by stan -- actually, instead of standard theorists, let me use the phrase adherents of ZFC because here I want to highlight the differences between ZFC and many of these alternate theories. Let me explain the differences. Consider a theory in the language of ZFC, and suppose one of its axioms is: AxAyAz (xez & zey -> xey) Obviously, this axiom doesn't hold in ZFC. In ZFC, it doesn't make sense to conclude that xey simply because xez and zey. Indeed, if we let a, b, and c be any sets such that aec and ceb, if ~aeb, then x=a, y=b, z=c is already a counterexample, and if aeb, then it's still easy to find a counterexample, x=a, y=b{a}, z=c. For if b is a set in ZFC, then so is b{a} (easy proved via Separation Schema). So in other words adherents of ZFC expect xey to be independent of xez and xey in that the former can't be proved from the latter. Even though in some cases we can prove non-membership (so we can prove ~yex from xez and xey, via Foundation or Regularity), we can never prove membership xey simply by knowing how x,y are related to a set z. Of course, if we added some additional structure, say by stating that x,y,z are ordinals , then one can prove that xey after all. But in TST, AxAyAz (xez & zey -> xey) is indeed an axiom . Adherents of ZFC might try to prove TST inconsistent by attempting to construct the example x=a, y=b{a}, z=c from above -- but this doesn't work in TST. Instead, an alleged proof that TST is inconsistent is, in actuality, a proof that an object corresponding to b{a} doesn't exist in TST! So this proof shows that e doesn't work in TST the way the adherents of ZFC expect it to. Because of this, galathaea has suggested that tommy1729 use somewhat different notation, such as: AxAyAz (xcz & zcy -> xcy) so that c is the parthood primitive, to emphasize that c doesn't work the way e does in ZFC. In ZFC xey is independent of xez and zey, but in TST, we see that xcy is provable from xcz and zcy. An alleged proof that TST is inconsistent based on b{a} just shows how the prover is unaware of how c works and makes the unwarranted assumption that it works just as e does in ZFC. Let's go back to MoeBlee's alleged proof that TST is inconsistent now. One of tommy1729's axioms is: Ax x=[x] MoeBlee's alleged proof involves instantiating to the case x=0, so that we have 0={0}. And obviously, the empty set 0 can't equal the non-empty set {0}. Hence a contradiction, therefore TST is inconsistent. And once again, here's the error. First of all, by 0, MoeBlee means an object x such that: Ay ~ycx But one of the axioms of TST is: Ax xcx And even MoeBlee should be able to see that from this axiom, we should be able to prove: Ax Ey ycx Yet MoeBlee assumes the negation of this theorem, namely that Ex Ay ~ycx -- indeed, that such an x exists and is unique, so that we can let 0 be the unique x such that Ay ~ycx. But Ex Ay ~ycx is an unwarranted assumption that MoeBlee makes only because Ex Ay ~yex is provable in ZFC . But as I said before, ZFC's e and TST's c don't work the same way. Of course, tommy1729 sometimes refers to an object [], which MoeBlee assumes satisfies Ay ~yc[] -- yet we've already proved that it doesn't. So what is []? To find out, we need two more axioms: Ax Ey xcy AxAy (xcy & ycx -> x=y) axioms, we prove the existence of a unique object whose only part is itself, and we call it []. So we don't have Ay ~yc[], but we do have: Ay (yc[] -> y=[]) A full definition of the bracket notation would require us to define the concept of an atom. This post is already long enough, so I won't give the definition here, but the definition was given in previous TST threads. The axiomatization of the theory TST isn't finished yet (and tommy1729 has stopped considering TST in order to work on other theories such as the infinitude of the twin primes and other pursuits). Ideally, the theory TST should be equiconsistent with Z+proper classes, with V (omega+omega+1) serving as a model for both. TST should not map symbol c to the same set that Z+proper classes maps the symbol e to. Instead, TST might map the symbol e to the same set that Z+proper classes maps the relation is a subset of to. TST should be able to do as much analysis and math for the sciences that the theory Z+proper classes can. === Subject: Re: the return of the master : tommy1729 posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) I'll never spend a dime to see the proof. You don't mean that literally do you? I mean, if for a dime you could > have a copy of a proof (say, an actually correct proof) of the twin > primes conjecture, you'd spend the dime, right? Sure he means it literally. What do you think the Transfer Principle is? It's that he won't Transfer any of his money for math, on Principle. Marshall === Subject: Re: the return of the master : tommy1729 > of course i wont give these results for free. But we don't know which are your professional fees. === Subject: Re: the return of the master : tommy1729 posting-account=FK_G5goAAAAEbWGaiao8aY3ti47UN9eX 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > i have been absent for a while. but for a good reason. i made many conjectures on sci.math , but lately ive spent much time on improving my proof methods. especially in number theory. ( once again related to factoring yes ) now i am in posession of the most amazing number theory proofs. i have proof of the infinitude of prime twins for example. also a certain erdos conjecture is proved. most of my conjectures about number theory posted on sci.math are also proved now. i am now stronger than ever. therefore the title : the return of the master : tommy1729 of course i wont give these results for free. i apologize to denis feldmann - as i promised ; if i would ever make very strong claims - 'officially'. most of you probably dont believe me , so let the flamewars begin ... > tommy1729 Another mathforum.org imbecile wasting valuable oxygen and bandwidth. Kill yourself. Do it now. Do it publicly. Do it violently. === Subject: Re: RELATIVITY AS INCONTINENCY > Precisely because Einstein's theory is inconsistent, its supporters > have drawn on contradictory principles in a way that greatly expanded > their apparent ability to explain the universe. Most crazes die out > when it becomes obvious that they were overblown. The amazing thing > about Einstein's theory of relativity is that it has kept going. It is > built on contradictions, but these very contradictions means that > almost anything 'proves' that it is right. It is a bit like a theory > where you say 1 + 1 = 2, but also that 1+ 1 = 3. Pentcho Valev > pvalev@yahoo.com === S === Subject: MMX-LT-Einstein = discrepancy I stated this much earlier but in a different form. It is now time for SRians to answer up to this situation. I am keeping it simple so you SR'ians who do understand SR and MMX please use your full understanding to dub in the scientific expressions that will allow you to confront this situation and answer with your solution if, of course, you have one. In MMX, the LT only allows the gap closure in the direction of motion to be travelled in the same time as the hypotenuse gap closure. Whereas in that local frame, the time calculated for the return time per Relativy (That frame at rest!) would simply be the time taken in that local system for light to travel the actual length of the arms of the experimental device. The times of both the above are not the same. In the experiment the measurement would be the actual time of the local frame, THUS the LT as a proposal would of only answered an exterior observation of the local experiment that exterior observer seeing the local frame in motion! But this is NOT the local observation and the local observation would only see the time past of the light travelling along the arms in that local frame....a non-moving system! Conclusion? Unless you can explain this away, _SR_ has a serious problem with the LT. Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > [...] In order to challenge SR, you must learn what it ACTUALLY says, and what it predicts for various experiments. Your mistakes and delusions are NOT relativity. In SR, the standard Cartesian coordinates of inertial frames are related by the Lorentz transform. This has the property that any object [#] moving with speed c in any direction in one inertial frame moves with speed c in every other inertial frame. This applies to SPEED -- in other inertial frames the direction can differ, but the speed does not. [#] Such as a light pulse, or a small region of a light beam. For the MMX, the application of this is simple: in the inertial frame in which the center of the apparatus is at rest, light travels isotropically with speed c. So the fringes will be in the same location no matter what the orientation of the apparatus, and no fringe movement is predicted as the instrument is rotated. There are a bunch of small effects that can easily be shown to make no significant difference in this prediction: * the presence of air or any other medium at rest wrt the instrument * a continuous rotation of the interferometer * the gravity of the earth * the rotation and revolution of the earth * imperfect configuration of the mirrors (e.g. non flatness, imprecise adjustment, optical imperfections) * the use of white light or monochromatic light Some of these can change the location of the fringes, but they cannot induce any orientation dependence. There are also a number of instrumentation effects that can affect the results, and have confused early experimenters: * temperature variation of the air in the optical path (even 0.001 C variations can cause trouble, so the best measurements avoid air in the optical paths) * mechanical flexing of the apparatus (for some, 0.02 wavelength can cause trouble; for others this limit is much smaller) * temperature variations in the support structure (0.01 C can cause trouble) * non-vertical rotation axis (for some, micro-radians can cause trouble) * a proper error analysis (doesn't affect fringe positions, but does affect whether or not variations are important) Conclusions? * The MMX is a very difficult experiment to do correctly. * The predictions of SR are consistent with the observations of the MMX and all repetitions of it to date (some of which are millions of times more sensitive than the original). * YOU have a serious problem in understanding SR, and its LT. Tom Roberts === Subject: Re: MMX-LT-Einstein = discrepancy posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > In order to challenge SR, you must learn what it ACTUALLY says, and what > it predicts for various experiments. Yes, it is fair enough. After studying SR, relative simultaneity is a direct manifestation of the Lorentz transform. This means the twinsÍ paradox. This means any communication satellites and any interferometers cannot have worked. The only scientific method is thus to reject the Lorentz transform instead of creating a religion covering up the nonsense of relative simultaneity. The real world only satisfies absolute simultaneity. by the Lorentz transform. This has the property that any object [#] > moving with speed c in any direction in one inertial frame moves with > speed c in every other inertial frame. This applies to SPEED -- in other > inertial frames the direction can differ, but the speed does not. This is also true under the Voigt transform. You need to really understand instead of worshipping the Lorentz transform. === Subject: Re: MMX-LT-Einstein = discrepancy posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) [...] > You need to really understand instead of worshipping the Lorentz > transform. So where did you learn to understand? === Subject: Re: MMX-LT-Einstein = discrepancy > relative simultaneity is a > direct manifestation of the Lorentz transform. Yes. > This means the twinsÍ > paradox. Yes. Note that in the world we inhabit the twin's paradox DOES OCCUR. So any theory (or personal prejudice like yours) that lacks it is WRONG. Bailey et al., ñMeasurements of relativistic time dilation for positive and negative muons in a circular orbit,î Nature 268 (July 28, 1977) pg 301. Bailey et al., Nuclear Physics B 150 pg 1[CapitalEth]79 (1979). They stored muons in a storage ring and measured their lifetime. When combined with measurements of the muon lifetime at rest this becomes a highly relativistic twin scenario (v ~0.9994 c), for which the stored muons are the traveling twin and return to a given point in the lab every few microseconds. C. Alley, ñProper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses,î in Quantum Optics, Experimental Gravity, and Measurement Theory, eds. Pierre Meystre and Marlan O. Scully, Proceedings Conf. Bad Windsheim 1981, 1983 Plenum Press New York, ISBN 0-306-41354-X, pg 363[CapitalEth]427. They flew atomic clocks in airplanes that remained localized over Chesapeake Bay, and also which flew to Greenland and back. Hafele and Keating, Nature 227 (1970), pg 270 (proposal). Science Vol. 177 pg 166[CapitalEth]170 (1972) (experiment). They flew atomic clocks on commercial airliners around the world in both directions, and compared the time elapsed on the airborne clocks with the time elapsed on an earthbound clock (USNO). Their eastbound clock lost 59 ns on the USNO clock; their westbound clock gained 273 ns; these agree with GR predictions to well within their experimental resolution and uncertainties (which total about 25 ns). By using four cesium-beam atomic clocks they greatly reduced their systematic errors due to clock drift. It is even possible for a guy with an interest in accurate timekeeping to display the variation in clocks rates on a family vacation: http://www.leapsecond.com/great2005/index.htm > This means any communication satellites and any > interferometers cannot have worked. That is simply not true. But they do work somewhat differently than your personal prejudice says. This, of course, includes the GPS, which is a MUCH better test of the variation in clock rates. http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#GPS NONE of the experiments referenced above actually test simultaneity or lack thereof, they measure variations in clock rates. But if clock rates vary, and simultaneity is defined by synchronized clocks, then simultaneity must vary too. Variation with altitude is predicted by GR, not SR, but it also refutes absolute simultaneity. Please note that the only practical way humans can establish simultaneity over a region of space and time is by using multiple synchronized clocks (e.g. UTC, GPS time). In particular, your personal notion of what now means in a distant part of the universe is just that -- a figment of your imagination; that is not science. > The real world > only satisfies absolute simultaneity. Your ASSERTIONS and PERSONAL PREJUDICES are not science. > Lack of simultaneity is nonsense. No, it is not. It's just that it is different from your personal prejudice. The world does not care what you or Koobee have concocted in your minds. Real experiments show that both of your personal prejudices are WRONG. Tom Roberts === Subject: Re: MMX-LT-Einstein = discrepancy posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.7.STABLE6) In order to challenge SR, you must learn what it ACTUALLY says, and what > it predicts for various experiments. Yes, it is fair enough. After studying SR, relative simultaneity is a > direct manifestation of the Lorentz transform. This means the twinsÍ > paradox. This means any communication satellites and any > interferometers cannot have worked. The only scientific method is > thus to reject the Lorentz transform instead of creating a religion > covering up the nonsense of relative simultaneity. The real world > only satisfies absolute simultaneity. Your mistakes and delusions are NOT relativity. You need to understand what relative simultaneity really means in > accordance with the Lorentz transform. In SR, the standard Cartesian coordinates of inertial frames are related > by the Lorentz transform. This has the property that any object [#] > moving with speed c in any direction in one inertial frame moves with > speed c in every other inertial frame. This applies to SPEED -- in other > inertial frames the direction can differ, but the speed does not. This is also true under the Voigt transform. For the MMX, the application... The interferometer used in the MMX falsifies any conjecture predicting > the world behaves in relative simultaneity. Thus, the MMX actually > falsifies the Lorentz transform. You need to really understand instead of worshipping the Lorentz > transform. Math Forum Discussionspredecessor of the MMX and concluded with the Voigt transform which ... You need to get some REAL physics books and > study them. ... Peter only did not recognize Christ three times. How many times ... Koobee-You get so confused by words and your perceived history. The physics and math work! ...http:// mathforum.org/kb/message.jspa%3FmessageID%3D6763375%26tstart%3D0 === Subject: Re: MMX-LT-Einstein = discrepancy In order to challenge SR, you must learn what it ACTUALLY says, and what > it predicts for various experiments. Yes, it is fair enough. After studying SR, relative simultaneity is a > direct manifestation of the Lorentz transform. This means the twins.89 > paradox. This means any communication satellites and any > interferometers cannot have worked. The only scientific method is > thus to reject the Lorentz transform instead of creating a religion > covering up the nonsense of relative simultaneity. The real world > only satisfies absolute simultaneity. Your mistakes and delusions are NOT relativity. You need to understand what relative simultaneity really means in > accordance with the Lorentz transform. In SR, the standard Cartesian coordinates of inertial frames are related > by the Lorentz transform. This has the property that any object [#] > moving with speed c in any direction in one inertial frame moves with > speed c in every other inertial frame. This applies to SPEED -- in other > inertial frames the direction can differ, but the speed does not. This is also true under the Voigt transform. For the MMX, the application... The interferometer used in the MMX falsifies any conjecture predicting > the world behaves in relative simultaneity. Thus, the MMX actually > falsifies the Lorentz transform. You need to really understand instead of worshipping the Lorentz > transform. Math Forum Discussionspredecessor of the MMX and concluded with the Voigt transform which ... You need to get some REAL physics books and > study them. ... Peter only did not recognize Christ three times. How many times ... Koobee-You get so confused by words and your perceived history. The physics and math work! ...http:// mathforum.org/kb/message.jspa%3FmessageID%3D6763375%26tstart%3D0 Lack of simultaneity is nonsense. Look at these links: Andromeda paradox in here: http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity%2C_time_dilatio n_and_length_contraction Captain Kirk in here: http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node77.html Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.7.STABLE6) > In order to challenge SR, you must learn what it ACTUALLY says, and what > it predicts for various experiments. Yes, it is fair enough. After studying SR, relative simultaneity is a > direct manifestation of the Lorentz transform. This means the twins? > paradox. This means any communication satellites and any > interferometers cannot have worked. The only scientific method is > thus to reject the Lorentz transform instead of creating a religion > covering up the nonsense of relative simultaneity. The real world > only satisfies absolute simultaneity. Your mistakes and delusions are NOT relativity. You need to understand what relative simultaneity really means in > accordance with the Lorentz transform. In SR, the standard Cartesian coordinates of inertial frames are related > by the Lorentz transform. This has the property that any object [#] > moving with speed c in any direction in one inertial frame moves with > speed c in every other inertial frame. This applies to SPEED -- in other > inertial frames the direction can differ, but the speed does not. This is also true under the Voigt transform. For the MMX, the application... The interferometer used in the MMX falsifies any conjecture predicting > the world behaves in relative simultaneity. Thus, the MMX actually > falsifies the Lorentz transform. You need to really understand instead of worshipping the Lorentz > transform. Voigt transform which ... You need to get some REAL physics books and > study them. ... Peter only did not recognize Christ three times. > How many times? <[3]> Koobee-You get so confused by words and > your perceived history. The physics and math work! http://mathforum.org/kb/message.jspa%3FmessageID%3D6763375%26tstart%3D0 > Lack of simultaneity is nonsense. Look at these links: > Andromeda paradox in here: > http://en.wikibooks.org/wiki/Special Relativity/Simultaneity%2C time dilation and length contraction Captain Kirk in here: http://phyun5.ucr.edu/~wudka/Physics7/Notes www/node77.html > Spirit of Truth It does not end: the michelson morley experiment questions. The point: You are quite free to impose your concept of simultaneity and absolute time. (Prays Christ may and in early writers, come as the shepherd. --Musatov According to the Gospel of John, the Jesus Christ born slightly more than 2000 is the discount poker table top to Lucien, watching this Musatov, who searched for him alone. The hat-store fulnesse of Christ sires westernized to a savage's and fruitful woman, ...http://dediscountpokertabletopto.blogspot.com/ - digest from sci.math ...Don't waste too much time on those two elderly cross-dressers > Fartin' Martin Musatov [and replaced again by me marty.musatov@gmail.com] off on his Bible coat of many colors: Osip Mandelstam and his mythologies of self 65 This same distinction between imitation of Christ and sacrifice had [#] and simultaneity where time brought about a chronological gap. [##] See also V. V. Musatov, Nekrasov v poeticheskom soznanii Mandel'shtama, in N. A. 004q8 Is relativity ILLOGICAL? Discussions with a focus on solving challenging and not so, challenging problems. A Coat of Many Colors http://content.cdlib.org/xtf/view%3FdocId%3Dft158004q8%26chunk.id%3Dd0e10158 %26toc.id%3Dd0e1274%26brand%3Deschol A coat of many colors: Osip Mandelstam and his mythologies of self which based its poetics on the principles of simultaneity of successive. To understand this paradox, recall how adamantly Christ refused to make compromises according to the Gospel of John, the Jesus Christ born slightly more than 2000 ... is the http://en.wikibooks.org/wiki/Special Relativity/Simultaneity%2C time . cb5d54bed2ab20b3/9b53fa9de73b02b7%3Flnk%3Draot -- http://MeAmI.org Try my search engine! (A la infomercial man, Try my product.) === Subject: Re: MMX-LT-Einstein = discrepancy I reread your post, so corrected this > [...] In order to challenge SR, you must learn what it ACTUALLY says, and what > it predicts for various experiments. Your mistakes and delusions are NOT > relativity. In SR, the standard Cartesian coordinates of inertial frames are related > by the Lorentz transform. This has the property that any object [#] moving > with speed c in any direction in one inertial frame moves with speed c in > every other inertial frame. This applies to SPEED -- in other inertial > frames the direction can differ, but the speed does not. [#] Such as a light pulse, or a small region of a light beam. For the MMX, the application of this is simple: in the inertial frame in > which the center of the apparatus is at rest, light travels isotropically > with speed c. So the fringes will be in the same location no matter what > the orientation of the apparatus, and no fringe movement is predicted as > the instrument is rotated. There are a bunch of small effects that can > easily be shown to make no significant difference in this prediction: > * the presence of air or any other medium at rest wrt the > instrument > * a continuous rotation of the interferometer > * the gravity of the earth > * the rotation and revolution of the earth > * imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) > * the use of white light or monochromatic light > Some of these can change the location of the fringes, but they cannot > induce any orientation dependence. There are also a number of instrumentation effects that can affect the > results, and have confused early experimenters: > * temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) > * mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) > * temperature variations in the support structure (0.01 C can > cause trouble) > * non-vertical rotation axis (for some, micro-radians can cause > trouble) > * a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) Conclusions? > * The MMX is a very difficult experiment to do correctly. > * The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). > * YOU have a serious problem in understanding SR, and its LT. > Tom Roberts No, you are missing the point. You REPEATED what I had written about it being a rest frame!!! You understand SR so should be able to confront the question. The actual time of the return as I posted fits exatly a rest frame in the experiment. If you did disagree with that you really don't understand SR. Now, if, as I posted, it fits a rest frame THEN it is a real leap to then try to explain it in terms of the LET when that LET time DOES NOT SHOW UP in the experiment. Now, try to confront it, Tom, and offer some reason for the leap of faith done by Einstein. Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > I reread your post, so corrected this > >[...] >In order to challenge SR, you must learn what it ACTUALLY says, and what >it predicts for various experiments. Your mistakes and delusions are NOT >relativity. >In SR, the standard Cartesian coordinates of inertial frames are related >by the Lorentz transform. This has the property that any object [#] moving >with speed c in any direction in one inertial frame moves with speed c in >every other inertial frame. This applies to SPEED -- in other inertial >frames the direction can differ, but the speed does not. >[#] Such as a light pulse, or a small region of a light beam. >For the MMX, the application of this is simple: in the inertial frame in >which the center of the apparatus is at rest, light travels isotropically >with speed c. So the fringes will be in the same location no matter what >the orientation of the apparatus, and no fringe movement is predicted as >the instrument is rotated. There are a bunch of small effects that can >easily be shown to make no significant difference in this prediction: > * the presence of air or any other medium at rest wrt the > instrument > * a continuous rotation of the interferometer > * the gravity of the earth > * the rotation and revolution of the earth > * imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) > * the use of white light or monochromatic light >Some of these can change the location of the fringes, but they cannot >induce any orientation dependence. >There are also a number of instrumentation effects that can affect the >results, and have confused early experimenters: > * temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) > * mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) > * temperature variations in the support structure (0.01 C can > cause trouble) > * non-vertical rotation axis (for some, micro-radians can cause > trouble) > * a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) >Conclusions? > * The MMX is a very difficult experiment to do correctly. > * The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). > * YOU have a serious problem in understanding SR, and its LT. >Tom Roberts > No, you are missing the point. You REPEATED what > I had written about it being a rest frame!!! You > understand SR so should be able to confront the question. The actual time of the return as I posted fits exatly a rest > frame in the experiment. If you did disagree with that > you really don't understand SR. Now, if, as I posted, it fits a rest frame THEN it is a real leap > to then try to explain it in terms of the LET when that LET > time DOES NOT SHOW UP in the experiment. Now, try to > confront it, Tom, and offer some reason for the leap of faith > done by Einstein. > A century of experimental verification is pretty good justification. You calling it a leap of faith only shows how ignorant of science you are. Spirit of Truth > === Subject: Re: MMX-LT-Einstein = discrepancy > I reread your post, so corrected this >[...] In order to challenge SR, you must learn what it ACTUALLY says, and what >it predicts for various experiments. Your mistakes and delusions are NOT >relativity. In SR, the standard Cartesian coordinates of inertial frames are related >by the Lorentz transform. This has the property that any object [#] >moving with speed c in any direction in one inertial frame moves with >speed c in every other inertial frame. This applies to SPEED -- in other >inertial frames the direction can differ, but the speed does not. [#] Such as a light pulse, or a small region of a light beam. For the MMX, the application of this is simple: in the inertial frame in >which the center of the apparatus is at rest, light travels isotropically >with speed c. So the fringes will be in the same location no matter what >the orientation of the apparatus, and no fringe movement is predicted as >the instrument is rotated. There are a bunch of small effects that can >easily be shown to make no significant difference in this prediction: > * the presence of air or any other medium at rest wrt the > instrument > * a continuous rotation of the interferometer > * the gravity of the earth > * the rotation and revolution of the earth > * imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) > * the use of white light or monochromatic light >Some of these can change the location of the fringes, but they cannot >induce any orientation dependence. There are also a number of instrumentation effects that can affect the >results, and have confused early experimenters: > * temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) > * mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) > * temperature variations in the support structure (0.01 C can > cause trouble) > * non-vertical rotation axis (for some, micro-radians can cause > trouble) > * a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) Conclusions? > * The MMX is a very difficult experiment to do correctly. > * The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). > * YOU have a serious problem in understanding SR, and its LT. >Tom Roberts > No, you are missing the point. You REPEATED what > I had written about it being a rest frame!!! You > understand SR so should be able to confront the question. > The actual time of the return as I posted fits exatly a rest > frame in the experiment. If you did disagree with that > you really don't understand SR. > Now, if, as I posted, it fits a rest frame THEN it is a real leap > to then try to explain it in terms of the LET when that LET > time DOES NOT SHOW UP in the experiment. Now, try to > confront it, Tom, and offer some reason for the leap of faith > done by Einstein. > A century of experimental verification is pretty good justification. > You calling it a leap of faith only shows how ignorant of science > you are. > Spirit of Truth Let me help you learn how to think, boy. MMX itself because it shows the at rest return time would indicate a ballistic situation, or an ether drag situation both of which would also show the same return time. To leap to LET would be a leap of faith not justified by experiment. Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > >I reread your post, so corrected this >[...] >In order to challenge SR, you must learn what it ACTUALLY says, and what >it predicts for various experiments. Your mistakes and delusions are NOT >relativity. >In SR, the standard Cartesian coordinates of inertial frames are related >by the Lorentz transform. This has the property that any object [#] >moving with speed c in any direction in one inertial frame moves with >speed c in every other inertial frame. This applies to SPEED -- in other >inertial frames the direction can differ, but the speed does not. >[#] Such as a light pulse, or a small region of a light beam. >For the MMX, the application of this is simple: in the inertial frame in >which the center of the apparatus is at rest, light travels isotropically >with speed c. So the fringes will be in the same location no matter what >the orientation of the apparatus, and no fringe movement is predicted as >the instrument is rotated. There are a bunch of small effects that can >easily be shown to make no significant difference in this prediction: >* the presence of air or any other medium at rest wrt the > instrument >* a continuous rotation of the interferometer >* the gravity of the earth >* the rotation and revolution of the earth >* imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) >* the use of white light or monochromatic light >Some of these can change the location of the fringes, but they cannot >induce any orientation dependence. >There are also a number of instrumentation effects that can affect the >results, and have confused early experimenters: >* temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) >* mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) >* temperature variations in the support structure (0.01 C can > cause trouble) >* non-vertical rotation axis (for some, micro-radians can cause > trouble) >* a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) >Conclusions? >* The MMX is a very difficult experiment to do correctly. >* The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). >* YOU have a serious problem in understanding SR, and its LT. >Tom Roberts >No, you are missing the point. You REPEATED what >I had written about it being a rest frame!!! You >understand SR so should be able to confront the question. The actual time of the return as I posted fits exatly a rest >frame in the experiment. If you did disagree with that >you really don't understand SR. Now, if, as I posted, it fits a rest frame THEN it is a real leap >to then try to explain it in terms of the LET when that LET >time DOES NOT SHOW UP in the experiment. Now, try to >confront it, Tom, and offer some reason for the leap of faith >done by Einstein. >A century of experimental verification is pretty good justification. >You calling it a leap of faith only shows how ignorant of science >you are. >Spirit of Truth > Let me help you learn how to think, boy. MMX itself because it shows the at rest return time would indicate > a ballistic situation, or an ether drag situation both of which > would also show the same return time. To leap to LET would > be a leap of faith not justified by experiment. > Spirit of Truth It seems you lied about plonking. But that is not surprising since you are ignorant about physics as well. You want to ignore the century of evidence so that you can wallow in your prejudice. === Subject: Re: MMX-LT-Einstein = discrepancy >I reread your post, so corrected this >[...] >In order to challenge SR, you must learn what it ACTUALLY says, and >what it predicts for various experiments. Your mistakes and delusions >are NOT relativity. >In SR, the standard Cartesian coordinates of inertial frames are >related by the Lorentz transform. This has the property that any object >[#] moving with speed c in any direction in one inertial frame moves >with speed c in every other inertial frame. This applies to SPEED -- in >other inertial frames the direction can differ, but the speed does not. >[#] Such as a light pulse, or a small region of a light beam. >For the MMX, the application of this is simple: in the inertial frame >in which the center of the apparatus is at rest, light travels >isotropically with speed c. So the fringes will be in the same location >no matter what the orientation of the apparatus, and no fringe movement >is predicted as the instrument is rotated. There are a bunch of small >effects that can easily be shown to make no significant difference in >this prediction: >* the presence of air or any other medium at rest wrt the > instrument >* a continuous rotation of the interferometer >* the gravity of the earth >* the rotation and revolution of the earth >* imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) >* the use of white light or monochromatic light >Some of these can change the location of the fringes, but they cannot >induce any orientation dependence. >There are also a number of instrumentation effects that can affect the >results, and have confused early experimenters: >* temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) >* mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) >* temperature variations in the support structure (0.01 C can > cause trouble) >* non-vertical rotation axis (for some, micro-radians can cause > trouble) >* a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) >Conclusions? >* The MMX is a very difficult experiment to do correctly. >* The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). >* YOU have a serious problem in understanding SR, and its LT. >Tom Roberts >No, you are missing the point. You REPEATED what >I had written about it being a rest frame!!! You >understand SR so should be able to confront the question. >The actual time of the return as I posted fits exatly a rest >frame in the experiment. If you did disagree with that >you really don't understand SR. >Now, if, as I posted, it fits a rest frame THEN it is a real leap >to then try to explain it in terms of the LET when that LET >time DOES NOT SHOW UP in the experiment. Now, try to >confront it, Tom, and offer some reason for the leap of faith >done by Einstein. A century of experimental verification is pretty good justification. >You calling it a leap of faith only shows how ignorant of science >you are. >Spirit of Truth > Let me help you learn how to think, boy. > MMX itself because it shows the at rest return time would indicate > a ballistic situation, or an ether drag situation both of which > would also show the same return time. To leap to LET would > be a leap of faith not justified by experiment. > Spirit of Truth It seems you lied about plonking. But that is not surprising > since you are ignorant about physics as well. You want to > ignore the century of evidence so that you can wallow in > your prejudice. Feel free to ignore the truth. :) Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > >I reread your post, so corrected this >[...] >In order to challenge SR, you must learn what it ACTUALLY says, and >what it predicts for various experiments. Your mistakes and delusions >are NOT relativity. >In SR, the standard Cartesian coordinates of inertial frames are >related by the Lorentz transform. This has the property that any object >[#] moving with speed c in any direction in one inertial frame moves >with speed c in every other inertial frame. This applies to SPEED -- in >other inertial frames the direction can differ, but the speed does not. >[#] Such as a light pulse, or a small region of a light beam. >For the MMX, the application of this is simple: in the inertial frame >in which the center of the apparatus is at rest, light travels >isotropically with speed c. So the fringes will be in the same location >no matter what the orientation of the apparatus, and no fringe movement >is predicted as the instrument is rotated. There are a bunch of small >effects that can easily be shown to make no significant difference in >this prediction: >* the presence of air or any other medium at rest wrt the > instrument >* a continuous rotation of the interferometer >* the gravity of the earth >* the rotation and revolution of the earth >* imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) >* the use of white light or monochromatic light >Some of these can change the location of the fringes, but they cannot >induce any orientation dependence. >There are also a number of instrumentation effects that can affect the >results, and have confused early experimenters: >* temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) >* mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) >* temperature variations in the support structure (0.01 C can > cause trouble) >* non-vertical rotation axis (for some, micro-radians can cause > trouble) >* a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) >Conclusions? >* The MMX is a very difficult experiment to do correctly. >* The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). >* YOU have a serious problem in understanding SR, and its LT. >Tom Roberts >No, you are missing the point. You REPEATED what >I had written about it being a rest frame!!! You >understand SR so should be able to confront the question. >The actual time of the return as I posted fits exatly a rest >frame in the experiment. If you did disagree with that >you really don't understand SR. >Now, if, as I posted, it fits a rest frame THEN it is a real leap >to then try to explain it in terms of the LET when that LET >time DOES NOT SHOW UP in the experiment. Now, try to >confront it, Tom, and offer some reason for the leap of faith >done by Einstein. >A century of experimental verification is pretty good justification. >You calling it a leap of faith only shows how ignorant of science >you are. >Spirit of Truth >Let me help you learn how to think, boy. MMX itself because it shows the at rest return time would indicate >a ballistic situation, or an ether drag situation both of which >would also show the same return time. To leap to LET would >be a leap of faith not justified by experiment. >Spirit of Truth >It seems you lied about plonking. But that is not surprising >since you are ignorant about physics as well. You want to >ignore the century of evidence so that you can wallow in >your prejudice. > Feel free to ignore the truth. The truth is you lied about plonking and you have no knowledge of science. Go ahead and have another tantrum. It is funny to watch you be so childish. > :) Spirit of Truth > === Subject: Re: MMX-LT-Einstein = discrepancy > [...] In order to challenge SR, you must learn what it ACTUALLY says, and what > it predicts for various experiments. Your mistakes and delusions are NOT > relativity. In SR, the standard Cartesian coordinates of inertial frames are related > by the Lorentz transform. This has the property that any object [#] moving > with speed c in any direction in one inertial frame moves with speed c in > every other inertial frame. This applies to SPEED -- in other inertial > frames the direction can differ, but the speed does not. [#] Such as a light pulse, or a small region of a light beam. For the MMX, the application of this is simple: in the inertial frame in > which the center of the apparatus is at rest, light travels isotropically > with speed c. So the fringes will be in the same location no matter what > the orientation of the apparatus, and no fringe movement is predicted as > the instrument is rotated. There are a bunch of small effects that can > easily be shown to make no significant difference in this prediction: > * the presence of air or any other medium at rest wrt the > instrument > * a continuous rotation of the interferometer > * the gravity of the earth > * the rotation and revolution of the earth > * imperfect configuration of the mirrors (e.g. non flatness, > imprecise adjustment, optical imperfections) > * the use of white light or monochromatic light > Some of these can change the location of the fringes, but they cannot > induce any orientation dependence. There are also a number of instrumentation effects that can affect the > results, and have confused early experimenters: > * temperature variation of the air in the optical path (even > 0.001 C variations can cause trouble, so the best measurements > avoid air in the optical paths) > * mechanical flexing of the apparatus (for some, 0.02 wavelength > can cause trouble; for others this limit is much smaller) > * temperature variations in the support structure (0.01 C can > cause trouble) > * non-vertical rotation axis (for some, micro-radians can cause > trouble) > * a proper error analysis (doesn't affect fringe positions, but > does affect whether or not variations are important) Conclusions? > * The MMX is a very difficult experiment to do correctly. > * The predictions of SR are consistent with the observations of > the MMX and all repetitions of it to date (some of which are > millions of times more sensitive than the original). > * YOU have a serious problem in understanding SR, and its LT. No, you are missing the point. You do understand SR so should be alble to confront the question. None of your post above confronts the fact that the actual time of the return as I posted fits exatly a rest frame in the experiment. If you disagree with that you really don't understand SR. Now, if, as I posted it fits a rest frame THEN it is a real leap to then try to explain it in terms of the LET when that let time DIOES NOT SHOW UP in the experiment. Now, try to confront it, Tom, and offer some reason for the leap of faith done by Einstein. Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > I stated this much earlier but in a different form. It is now time for SRians to answer up to this situation. I am keeping it simple so you SR'ians who do understand SR > and MMX please use your full understanding to dub in the > scientific expressions that will allow you to confront this > situation and answer with your solution if, of course, > you have one. In MMX, the LT only allows the gap closure in the direction > of motion to be travelled in the same time as the hypotenuse > gap closure. Whereas in that local frame, the time calculated > for the return time per Relativy (That frame at rest!) would > simply be the time taken in that local system for light to > travel the actual length of the arms of the experimental > device. The times of both the above are not the same. In the > experiment the measurement would be the actual > time of the local frame, THUS the LT as a proposal > would of only answered an exterior observation > of the local experiment that exterior observer seeing the local > frame in motion! But this is NOT the local observation and > the local observation would only see the time past of the > light travelling along the arms in that local frame....a > non-moving system! Conclusion? Unless you can explain this away, _SR_ has > a serious problem with the LT. SR has no problem. You have a problem with english and with comprehension. That is not our problem. > Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > I stated this much earlier but in a different form. > It is now time for SRians to answer up to this situation. > I am keeping it simple so you SR'ians who do understand SR > and MMX please use your full understanding to dub in the > scientific expressions that will allow you to confront this > situation and answer with your solution if, of course, > you have one. > In MMX, the LT only allows the gap closure in the direction > of motion to be travelled in the same time as the hypotenuse > gap closure. Whereas in that local frame, the time calculated > for the return time per Relativy (That frame at rest!) would > simply be the time taken in that local system for light to > travel the actual length of the arms of the experimental > device. > The times of both the above are not the same. In the > experiment the measurement would be the actual > time of the local frame, THUS the LT as a proposal > would of only answered an exterior observation > of the local experiment that exterior observer seeing the local > frame in motion! But this is NOT the local observation and > the local observation would only see the time past of the > light travelling along the arms in that local frame....a > non-moving system! > Conclusion? Unless you can explain this away, _SR_ has > a serious problem with the LT. SR has no problem. You have a problem with english and > with comprehension. That is not our problem. > Spirit of Truth Doug, time for you to grow up. Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy >I stated this much earlier but in a different form. It is now time for SRians to answer up to this situation. I am keeping it simple so you SR'ians who do understand SR >and MMX please use your full understanding to dub in the >scientific expressions that will allow you to confront this >situation and answer with your solution if, of course, >you have one. In MMX, the LT only allows the gap closure in the direction >of motion to be travelled in the same time as the hypotenuse >gap closure. Whereas in that local frame, the time calculated >for the return time per Relativy (That frame at rest!) would >simply be the time taken in that local system for light to >travel the actual length of the arms of the experimental >device. The times of both the above are not the same. In the >experiment the measurement would be the actual >time of the local frame, THUS the LT as a proposal >would of only answered an exterior observation >of the local experiment that exterior observer seeing the local >frame in motion! But this is NOT the local observation and >the local observation would only see the time past of the >light travelling along the arms in that local frame....a >non-moving system! Conclusion? Unless you can explain this away, _SR_ has >a serious problem with the LT. >SR has no problem. You have a problem with english and >with comprehension. That is not our problem. Spirit of Truth > Doug, time for you to grow up. Spirit of Truth Your stupidity and dislike of relativity are not my problems. You can keep looking like a fool here as long as you want and anyone can comment on your ignorance. === Subject: Re: MMX-LT-Einstein = discrepancy >I stated this much earlier but in a different form. >It is now time for SRians to answer up to this situation. >I am keeping it simple so you SR'ians who do understand SR >and MMX please use your full understanding to dub in the >scientific expressions that will allow you to confront this >situation and answer with your solution if, of course, >you have one. >In MMX, the LT only allows the gap closure in the direction >of motion to be travelled in the same time as the hypotenuse >gap closure. Whereas in that local frame, the time calculated >for the return time per Relativy (That frame at rest!) would >simply be the time taken in that local system for light to >travel the actual length of the arms of the experimental >device. >The times of both the above are not the same. In the >experiment the measurement would be the actual >time of the local frame, THUS the LT as a proposal >would of only answered an exterior observation >of the local experiment that exterior observer seeing the local >frame in motion! But this is NOT the local observation and >the local observation would only see the time past of the >light travelling along the arms in that local frame....a >non-moving system! >Conclusion? Unless you can explain this away, _SR_ has >a serious problem with the LT. SR has no problem. You have a problem with english and >with comprehension. That is not our problem. >Spirit of Truth > Doug, time for you to grow up. > Spirit of Truth Your stupidity and dislike of relativity are not my > problems. You can keep looking like a fool here as > long as you want and anyone can comment on your ignorance. I told you to grow up. If you have any basic understanding of SR try to confront the thread. Spirit of Truth === Subject: Re: MMX-LT-Einstein = discrepancy > I stated this much earlier but in a different form. >It is now time for SRians to answer up to this situation. >I am keeping it simple so you SR'ians who do understand SR >and MMX please use your full understanding to dub in the >scientific expressions that will allow you to confront this >situation and answer with your solution if, of course, >you have one. >In MMX, the LT only allows the gap closure in the direction >of motion to be travelled in the same time as the hypotenuse >gap closure. Whereas in that local frame, the time calculated >for the return time per Relativy (That frame at rest!) would >simply be the time taken in that local system for light to >travel the actual length of the arms of the experimental >device. >The times of both the above are not the same. In the >experiment the measurement would be the actual >time of the local frame, THUS the LT as a proposal >would of only answered an exterior observation >of the local experiment that exterior observer seeing the local >frame in motion! But this is NOT the local observation and >the local observation would only see the time past of the >light travelling along the arms in that local frame....a >non-moving system! >Conclusion? Unless you can explain this away, _SR_ has >a serious problem with the LT. >SR has no problem. You have a problem with english and >with comprehension. That is not our problem. >Spirit of Truth >Doug, time for you to grow up. Spirit of Truth >Your stupidity and dislike of relativity are not my >problems. You can keep looking like a fool here as >long as you want and anyone can comment on your ignorance. > I told you to grow up. If you have any basic understanding of SR try to > confront the thread. Spirit of Truth The problem is that you have no understanding of SR. You saying stupid things like claiming SR has problems with the LT shows the depth of your ignorance. You have the choice of remaining ignorant but doing so willingly makes you stupid as well. === Subject: Re: MMX-LT-Einstein = discrepancy doug I have been reading messages in this group for some time now, hoping to > learn about relativity. All the texts I have read are based on vague and > sometimes unrealistic assumptions and are very hard to follow, so I need > help. > It appears that the theory is still very controversial and that most > contibutors here don't think it is correct. Certainly those who support it > rarely even try to defend it intelligently but simply resort to ridiculing > anyone who doesn't accept it. Einstein's theory than there are for it. It seems little different from > Lorentz's ether theory. Maybe there is a medium that carries light waves just as Maxwell predicted. See this: THE WAVE MODEL OF LIGHT AND EINSTEINIANA Pentcho Valev pvalev@yahoo.com === Subject: Re: michelson morley experiment questions >Those of us who do understand error analysis know that NONE of the >experiments you cite have significant signals. I understood enough to figure out the following. The raw data in Figure 8 of Miller's paper admittedly contains a lot > of noise: > http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf However, the noise is easy to remove and after doing so I get a clean > signal with small error bars > http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ > (That is, a significant signal) You have made the same mistake that Miller did. The assumption you have made is that the component of the systematic drift in the frequency bin you wanted was zero. You used this simplistic method to just apply a narrowband filter to the data for bin 50 (although your plot of the DFTs shows the assumptions you made on the response of the systematic noise. The smooth values for the bins from about 30 to about 50 demonstrate your assumption. What you have ignored in Tom's paper, is that Tom did a careful model of the systematic noise. That makes all the difference in the world to the analysis. We are to compare your guess with Tom's extensive analysis. Conclusions based on guesses always take a back seat to those supported by careful analysis. In contrast, you deliberately use the raw data to get huge error bars: > http://arxiv.org/abs/physics/0608238 > so you can falsely claim that the signal lacks significance. > You need to read and try to understand what Tom did. You claim to have deliberately imply a malice that is not there. > === Subject: Re: michelson morley experiment questions I elsewhere pointed out that experiments that attempt to detect light > speed anisotropy in vacuum don't work, because variation of light > speed is exactly compensated for by Lorentz contraction of the > apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. > Peter, You mean that all these people don't know what they are doing and that they should be consulting you in order to correct their experiments? * Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821. Uses two multi-mode lasers mounted on a rotating table to look for variations in their interference pattern as the table is rotated. Places an upper limit on any one-way anisotropy of 0.9 m/s. * Krisher et al., Phys. Rev. D, 42, No. 2, pg 731[CapitalEth]734, (1990). Uses two hydrogen masers fixed to the Earth and separated by a 21-km fiber-optic link to look for variations in the phase between them. They put an upper limit on the one-way linear anisotropy of 100 m/s. * Champeny et al., Phys. Lett. 7 (1963), pg 241. Champeney, Isaak and Khan, Proc. Physical Soc. 85, pg 583 (1965). Isaak et al., Phys. Bull. 21 (1970), pg 255. Uses a rotating M.9assbauer absorber and fixed detector to place an upper limit on any one-way anisotropy of 3 m/s. * Turner and Hill, Phys. Rev. 134 (1964), B252. Uses a rotating source and fixed M.9assbauer detector to place an upper limit on any one-way anisotropy of 10 m/s. * Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg 1767. A guided-wave test of isotropy. Their null result is consistent with SR. * T.W. Cole, ñAstronomical Tests for the Presence of an Etherî, Mon. Not. R. Astr. Soc. (1976), 175 93P-96P. Several VLBI tests sensitive to first-order effects of an .bether are described. No .bether is detected, with a sensitivity of 70 m/s. * Ragulsky, ñDetermination of light velocity dependence on direction of propagationî, Phys. Lett. A, 235 (1997), pg 125. A ñone-wayî test that is bidirectional with the outgoing ray in glass and the return ray in air. The interferometer is by design particularly robust against mechanical perturbations, and temperature controlled. The limit on the anisotropy of c is 0.13 m/s. === Subject: Re: michelson morley experiment questions > To detect light speed anisotropy the experiment has to include > something to disturb the balance. I remark that of the following 7 experiments, 6 have propagation in some non-vacuum medium: air Cialdea, Ragulsky glass Krisher et al, Ragulsky iron Champeny et al, Turner and Hill waveguide Gagnon et al BTW Ragulsky showed that it _IS_ possible to operate an interferometer in air with stable results; temperature and mechanical stability are ESSENTIAL. Tom Roberts > * Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821. Uses two multi-mode lasers mounted on a rotating table to look > for variations in their interference pattern as the table is rotated. > Places an upper limit on any one-way anisotropy of 0.9 m/s. > * Krisher et al., Phys. Rev. D, 42, No. 2, pg 731[CapitalEth]734, (1990). Uses two hydrogen masers fixed to the Earth and separated by a > 21-km fiber-optic link to look for variations in the phase between > them. They put an upper limit on the one-way linear anisotropy of 100 > m/s. > * Champeny et al., Phys. Lett. 7 (1963), pg 241. Champeney, Isaak > and Khan, Proc. Physical Soc. 85, pg 583 (1965). Isaak et al., Phys. > Bull. 21 (1970), pg 255. Uses a rotating M.9assbauer absorber and fixed detector to place > an upper limit on any one-way anisotropy of 3 m/s. > * Turner and Hill, Phys. Rev. 134 (1964), B252. Uses a rotating source and fixed M.9assbauer detector to place an > upper limit on any one-way anisotropy of 10 m/s. > * Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg > 1767. A guided-wave test of isotropy. Their null result is consistent > with SR. > * T.W. Cole, ñAstronomical Tests for the Presence of an Etherî, > Mon. Not. R. Astr. Soc. (1976), 175 93P-96P. Several VLBI tests sensitive to first-order effects of an .bether > are described. No .bether is detected, with a sensitivity of 70 m/s. > * Ragulsky, ñDetermination of light velocity dependence on > direction of propagationî, Phys. Lett. A, 235 (1997), pg 125. A ñone-wayî test that is bidirectional with the outgoing ray in > glass and the return ray in air. The interferometer is by design > particularly robust against mechanical perturbations, and temperature > controlled. The limit on the anisotropy of c is 0.13 m/s. === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > To detect light speed anisotropy the experiment has to include > something to disturb the balance. I remark that of the following 7 experiments, 6 have propagation in some > non-vacuum medium: > air Cialdea, Ragulsky > glass Krisher et al, Ragulsky > iron Champeny et al, Turner and Hill > waveguide Gagnon et al BTW Ragulsky showed that it IS possible to operate an interferometer > in air with stable results; temperature and mechanical stability are > ESSENTIAL. Tom Roberts * Cialdea, Lett. Nuovo Cimento 4 (1972), pg 821. Uses two multi-mode lasers mounted on a rotating table to look > for variations in their interference pattern as the table is rotated. > Places an upper limit on any one-way anisotropy of 0.9 m/s. > * Krisher et al., Phys. Rev. D, 42, No. 2, pg 731[CapitalEth]734, (1990). Uses two hydrogen masers fixed to the Earth and separated by a > 21-km fiber-optic link to look for variations in the phase between > them. They put an upper limit on the one-way linear anisotropy of 100 > m/s. > * Champeny et al., Phys. Lett. 7 (1963), pg 241. Champeney, Isaak > and Khan, Proc. Physical Soc. 85, pg 583 (1965). Isaak et al., Phys. > Bull. 21 (1970), pg 255. Uses a rotating M.9assbauer absorber and fixed detector to place > an upper limit on any one-way anisotropy of 3 m/s. > * Turner and Hill, Phys. Rev. 134 (1964), B252. Uses a rotating source and fixed M.9assbauer detector to place an > upper limit on any one-way anisotropy of 10 m/s. > * Gagnon, Torr, Kolen, and Chang, Phys. Rev. A38 no. 4 (1988), pg > 1767. A guided-wave test of isotropy. Their null result is consistent > with SR. > * T.W. Cole, ñAstronomical Tests for the Presence of an Etherî, > Mon. Not. R. Astr. Soc. (1976), 175 93P-96P. Several VLBI tests sensitive to first-order effects of an .bether > are described. No .bether is detected, with a sensitivity of 70 m/s. > * Ragulsky, ñDetermination of light velocity dependence on > direction of propagationî, Phys. Lett. A, 235 (1997), pg 125. A ñone-wayî test that is bidirectional with the outgoing ray in > glass and the return ray in air. The interferometer is by design > particularly robust against mechanical perturbations, and temperature > controlled. The limit on the anisotropy of c is 0.13 m/s. Yes, I gave Surfer the other two (Shamir and Trimmer). I also explained to him that the latest reenctments don't use conventional interferometers anymore, they use resonating cavities . To no avail, the idiot has his head stuck up his ass so far that nothing registers. BTW, I think that you could use some of the newer references to MMX executed with resonating cavities. Do you need the references? I can send them to you. === Subject: Re: michelson morley experiment questions posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > A possible theory of operation is discussed here: > Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 Ahh, the other pair of renowed crackpots. Let me guess, what comes >next, a citation from Cahill or one from Munera? Or is it back to >Dayton Miller? Messrs. Consoli and Constanzo never ran their experiments. What is >even more embarassing is that their theory is ALREADY refuted by the >a couple of experiments: #1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg >2489 (1974). A triangle interferometer with one leg in glass. They set an upper >limit on the anisotropy of 0.025 m/s. This is about one-millionth of >the Earth's orbital velocity and about 1/10,000 of its rotational >velocity. #2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. A repetition of the MMX with the optical paths in perspex (n = 1.49), >and a laser-based optics sensitive to ~0.00003 fringe. They report a >null result with an upper limit on v.bether of 6.64 km/s. I elsewhere pointed out that experiments that attempt to detect light > speed anisotropy in vacuum don't work, because variation of light > speed is exactly compensated for by Lorentz contraction of the > apparatus. > Peter, First of all, this is not correct, secondly, it has nothing to do with your inability to understand why MMX executed in refringent medium refutes the cranks Consoli, Cahill and Munera > To detect light speed anisotropy the experiment has to include > something to disturb the balance. > Yes, and this is being done by using test theories of SR, like Mansouri-Sexl or Standard Model Extension. You are obviously ignorant about this subject. > Depending on the degree to which that occurs or does not occur, there > is opportunity for experiments to fail to detect anisotropy. > No, there isn't. There has never been one for years. Either way, this is not relevant to your inability to understand why Consoli, Cahill and Munera are crackpots. > But while some fail in this regard, others succeed. Eg. Figure 4 in Miller's paper shows that the velocity he obtained in > 1925 was consistent with the velocity of ether drift observed by > Michelson and Morley in 1887 and by Morley and Miller in 1902, 1904 > and 1905. That's five examples of successful experiments. Peter, Add Miller to the list. === Subject: Re: michelson morley experiment questions > >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. > Just wanted to point out that this was not my analysis. The link > provided was from one of Surfer's posts. It looked pretty good so I > answering. > What is obviously wrong is the conclusion. For some reason, a lot of cranks have fixated on Miller's experiments. Since there is better data available now that has up to a factor of a billion or so better resolution and accuracy, Miller's mistakes are of only historical interest. His results cannot be correct since they do not agree with those experiments. > >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. Any chance you could provide a link to data for some of the other > runs, or post that data here? Nobody should complain about the use of > bandwidth considering how much is wasted on pure crap around here :) > The run we have been beating to death has obvious defects. I would > like to see others. > You should read the paper by Tom Roberts. He does a nice job in the analysis. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> posting-account=OYbTxggAAACimxHivNfPv6KRfdOPL6RK x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis of Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. Just wanted to point out that this was not my analysis. The link > provided was from one of Surfer's posts. It looked pretty good so I > answering. What is obviously wrong is the conclusion. I was looking for something a little more specific than the results don't agree with what you expect. It uses what look to be modern methods of looking at Miller's data and gets about the same result Miller did. That is quite different from what Tom got, so I thought Tom might comment. > For some reason, a lot of > cranks have fixated on Miller's experiments. Since there is better > data available now that has up to a factor of a billion or so better > resolution and accuracy, Miller's mistakes are of only historical > interest. IMO it would be better to show how Miller got some false signals than to claim no pattern ever existed in the data. Just looking at a plot of the data in fig.8 it is obvious there is a pattern there with the frequency being sought. To say that it doesn't exist is an insult to anyone that looks at the plot. I agree the pattern is not from ether drift. I suspect the pattern is from the temperture gradient of the air, and the downward trend is caused by the heating/cooling of the frame. That I consider a very plausible explaination. But to say there is no pattern..... A quick way of showing the pattern was not ether drift would be to provide a few more sets of data that didn't show such a pattern. His results cannot be correct since they do not agree > with those experiments. > That still doesn't explain the results, and it was not my point anyway. My point is that it is just as bad to see nothing where there is something as it is to see something where there is nothing. Claiming there is no pattern when one jumps out and slaps you in the face just gives more fuel to the cranks. I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. Any chance you could provide a link to data for some of the other > runs, or post that data here? Nobody should complain about the use of > bandwidth considering how much is wasted on pure crap around here :) > The run we have been beating to death has obvious defects. I would > like to see others. > You should read the paper by Tom Roberts. He does a nice job in > the analysis. > I have read Tom's paper, several times. Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: michelson morley experiment questions > >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. >Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. > I was looking for something a little more specific than the results > don't agree with what you expect. It uses what look to be modern > methods of looking at Miller's data and gets about the same result > Miller did. That is quite different from what Tom got, so I thought > Tom might comment. > You can read Tom's paper and see in detail what he did. > >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. > IMO it would be better to show how Miller got some false signals than > to claim no pattern ever existed in the data. Just looking at a plot > of the data in fig.8 it is obvious there is a pattern there with the > frequency being sought. The adjustments that Miller made required the pattern to show up. To say that it doesn't exist is an insult to > anyone that looks at the plot. I agree the pattern is not from ether > drift. I suspect the pattern is from the temperture gradient of the > air, and the downward trend is caused by the heating/cooling of the > frame. That I consider a very plausible explaination. But to say > there is no pattern..... There are also flexing issues with the rotation but that is not the point. The claim by Miller was that all the fluctuations pointed to one spot in the sky although apparently that point changed with when he reported the results. A quick way of showing the pattern was not ether drift would be to > provide a few more sets of data that didn't show such a pattern. The fastest way to show the pattern is not ether drift is to look at the experiments with a billion times his sensitivity. That is quite conclusive. His results cannot be correct since they do not agree > >with those experiments. That still doesn't explain the results, and it was not my point > anyway. My point is that it is just as bad to see nothing where there > is something as it is to see something where there is nothing. > Claiming there is no pattern when one jumps out and slaps you in the > face just gives more fuel to the cranks. > The explaination is that it is wrong. Why is of only academic interest. Nothing you say or do will have any effect on the cranks here. They are beyond reason and are all suffering from various delusions about what science is. > >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. >Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. I have read Tom's paper, several times. And what did you disagree with? >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> posting-account=OYbTxggAAACimxHivNfPv6KRfdOPL6RK x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: > A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. > B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis of Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. I was looking for something a little more specific than the results > don't agree with what you expect. It uses what look to be modern > methods of looking at Miller's data and gets about the same result > Miller did. That is quite different from what Tom got, so I thought > Tom might comment. You can read Tom's paper and see in detail what he did. > That wasn't the question. The question was what was wrong with the analysis that showed a pattern? >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. IMO it would be better to show how Miller got some false signals than > to claim no pattern ever existed in the data. Just looking at a plot > of the data in fig.8 it is obvious there is a pattern there with the > frequency being sought. The adjustments that Miller made required the pattern to show up. That is bull and you know it. Here is Tom's paper so you can look for yourself. http://arxiv.org/ftp/physics/papers/0608/0608238.pdf Fig. 8 shows the first adjustment was made after five full turns. The pattern I am talking about shows up before that first adjustment. Perhaps you would like to explain how you think that first adjustment introduced the pattern in the preceeding five turns. Or how a total of three adjustments resulted in a half turn pattern showing up in twenty full turns. >To say that it doesn't exist is an insult to anyone that looks at the plot. I agree the pattern is not from ether > drift. I suspect the pattern is from the temperture gradient of the > air, and the downward trend is caused by the heating/cooling of the > frame. That I consider a very plausible explaination. But to say > there is no pattern..... There are also flexing issues with the rotation but that is not > the point. The claim by Miller was that all the fluctuations > pointed to one spot in the sky although apparently that point > changed with when he reported the results. No, the point I have been trying to make is there is a pattern. I agree that it is not ether drift, but something caused a pattern. To claim there is no pattern when there obviously is one is not good science. > A quick way of showing the pattern was not ether drift would be to > provide a few more sets of data that didn't show such a pattern. The fastest way to show the pattern is not ether drift is to look at > the experiments with a billion times his sensitivity. That is > quite conclusive. Those new experiments are not the same experiment. An argument could be made that something about them prevents them from picking up the Tom has said many of them showed nothing. There are a few shown here with no data. http://www.scieng.flinders.edu.au/cpes/people/cahill r/Miller1933.pdf If data for a few runs was shown it would show fig.8 was a temperture related fluke. > His results cannot be correct since they do not agree >with those experiments. That still doesn't explain the results, and it was not my point > anyway. My point is that it is just as bad to see nothing where there > is something as it is to see something where there is nothing. > Claiming there is no pattern when one jumps out and slaps you in the > face just gives more fuel to the cranks. The explaination is that it is wrong. Why is of only academic interest. > Nothing you say or do will have any effect on the cranks here. They > are beyond reason and are all suffering from various delusions about > what science is. > One of the quickest ways to turn someone into a crank is to lie to them. Telling them there is no pattern when they can see a pattern in the plot without doing any analysis imediately turns them against you. Why should they believe anything you say when they have already caught you trying to put something over on them? >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. I have read Tom's paper, several times. And what did you disagree with? > The fact that in the end he found no pattern where one obviously existed. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: michelson morley experiment questions > The question was what was wrong with the > analysis that showed a pattern? Children can see faces in clouds. PATTERNS alone are not sufficient. Physics is a QUANTITATIVE science, and one must show that the patterns are statistically significant. As I said before, when computing an average one always finds an answer, but to know if that answer is significant one must examine the errorbars. And, of course, one must compute them correctly -- Miller never looked at them, and surfer computed them incorrectly. The errorbars show unequivocally that the signal Miller found is not significant. > [what did you disagree with in Tom's analysis?] > The fact that in the end he found no pattern where one obviously > existed. But the obvious pattern is not significant. Neither are those faces in clouds. Just LOOK at figure 3 of my paper -- Miller's linear assumption is VERY BAD. The variations between the points and corners are an order of magnitude BIGGER than the signal he found, and they can only be an instrumentation effect. surfer keeps insisting that the presence of an amplitude for 1/2-turn greater than the background is a signal -- figure 3 shows that is wrong, as the difference between points and corners is purely instrumental, and has a strong amplitude with frequency 1/2-turn. Tom Roberts === Subject: Re: michelson morley experiment questions > >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: >A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. >B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. >Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. >I was looking for something a little more specific than the results >don't agree with what you expect. It uses what look to be modern >methods of looking at Miller's data and gets about the same result >Miller did. That is quite different from what Tom got, so I thought >Tom might comment. >You can read Tom's paper and see in detail what he did. That wasn't the question. The question was what was wrong with the > analysis that showed a pattern? You do not believe Tom so you should do your own analysis. You tell us what the data means. >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. >IMO it would be better to show how Miller got some false signals than >to claim no pattern ever existed in the data. Just looking at a plot >of the data in fig.8 it is obvious there is a pattern there with the >frequency being sought. >The adjustments that Miller made required the pattern to show up. > That is bull and you know it. Here is Tom's paper so you can look > for yourself. http://arxiv.org/ftp/physics/papers/0608/0608238.pdf Fig. 8 shows the first adjustment was made after five full turns. The > pattern I am talking about shows up before that first adjustment. > Perhaps you would like to explain how you think that first adjustment > introduced the pattern in the preceeding five turns. Or how a total > of three adjustments resulted in a half turn pattern showing up in > twenty full turns. > To say that it doesn't exist is an insult to >anyone that looks at the plot. I agree the pattern is not from ether >drift. I suspect the pattern is from the temperture gradient of the >air, and the downward trend is caused by the heating/cooling of the >frame. That I consider a very plausible explaination. But to say >there is no pattern..... >There are also flexing issues with the rotation but that is not >the point. The claim by Miller was that all the fluctuations >pointed to one spot in the sky although apparently that point >changed with when he reported the results. > No, the point I have been trying to make is there is a pattern. I > agree that it is not ether drift, but something caused a pattern. To > claim there is no pattern when there obviously is one is not good > science. > I do not care what the pattern is since it is not related to the physics. The current experiments say that it is wrong so feel free to spend your time finding out why. > >A quick way of showing the pattern was not ether drift would be to >provide a few more sets of data that didn't show such a pattern. >The fastest way to show the pattern is not ether drift is to look at >the experiments with a billion times his sensitivity. That is >quite conclusive. > Those new experiments are not the same experiment. They measured the same effect but in a more precise way. There have been some silly people here who claim that you have to exactly repeat some old experiment to debunk it but that is complete nonsense. An argument could > be made that something about them prevents them from picking up the > signal that Miller found. Have you read the experiments to see what they were doing? The whole point of Miller was to find an isotropy in the speed of light. There is none to limits a billion times finer than Miller was proposing. > Tom has said many of them showed nothing. There are a few shown here > with no data. So you are saying that you believe Miller saw aether drift? http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf Any reference to Cahill is automatically the sign of a crank. Cahill is a joke and only surfer believes him (many people believe surfer is Cahill). If data for a few runs was shown it would show fig.8 was a temperture > related fluke. > His results cannot be correct since they do not agree >with those experiments. >That still doesn't explain the results, and it was not my point >anyway. My point is that it is just as bad to see nothing where there >is something as it is to see something where there is nothing. >Claiming there is no pattern when one jumps out and slaps you in the >face just gives more fuel to the cranks. >The explaination is that it is wrong. Why is of only academic interest. >Nothing you say or do will have any effect on the cranks here. They >are beyond reason and are all suffering from various delusions about >what science is. One of the quickest ways to turn someone into a crank is to lie to > them. Telling them there is no pattern when they can see a pattern in > the plot without doing any analysis imediately turns them against > you. Why should they believe anything you say when they have already > caught you trying to put something over on them? > Well, the experiments say there is no signal. Any claim to the contrary is the sign of a crank who is ignoring the evidence. The cranks are unmoved by the truth in any case. Look at ken seto or Henri (ralph) or noeinstein or koobee or ... Pick any of hundreds. They are ignorant and plan on staying that way. > >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. >Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. >I have read Tom's paper, several times. >And what did you disagree with? The fact that in the end he found no pattern where one obviously > existed. Well, show the error in his analysis. If you found something, I would like to see it. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). >Tom Roberts- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <29-dnWjFHdSt89DXnZ2dnUVZ_vSdnZ2d@posted.docknet> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) >Miller made two kinds of corrections in his experiment. If the >fringes drifted to far from the starting point he hung weights on the >arms of the instrument to bring it back near the starting position. >The turns made while adjusting were not recorded. When they were >satisfied with the adjustment they resumed recording data at marker >1. >Yes. For the run in his Figure 8 these total 5.3 fringes! Without them >the sigmas would be considerably larger. >The second kind of correction was to adjust each data point for the >drift up to that point, assuming the drift was linear. >Yes. Such a correction does not affect the sigma of the individual >marker's data, but does affect it for the sum of two markers. In the >case of marker1 plus marker9 of this run, it actually increases the >sigma of the union of the data (compared to what I did here, which was >to simply union their raw values). >The whole idea behind Miller's method of annalysis was that after >removing the drift the readings for a marker would be a grouped around >the mean for that marker in a normal distribution. The data you >provided above was the raw data including the mechanical adjustments >but before correcting for drift. Since the drift was always in the >downward direction the correction for it would result in a higher >value, which is what Surfer got. >Surfer did something completely different, which has no relevance to the >question of whether or not MILLER'S results are valid. >As for sigma, please explain your usage of independent and how it >relates to /40? According to >http://en.wikipedia.org/wiki/Dependant_variable >the useage is different in mathematics and statistics. >I used the statistical meaning: independent means the different data >points are not correlated in any way. Miller's raw data points are >correlated in at least two different ways: >A) the interferometer has an overall drift that makes later points > of this run have systematically lower values than earlier ones. >B) the adjustments he made make later points have systematically > higher values than earlier ones. >Both of you constructed what you assumed would be a plot of the data >had no mechanical corrections been made. >http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >Your mRaw graph is the same as Fig. 2 of my paper (except I divided by >10 to report in fringes).http://arxiv.org/abs/physics/0608238 >Your analysis essentially filtered out the 1/2-turn signal, then >subtracted the filtered data from the raw data to get mRawD. The >errorbars you plotted are wrong, as is your conclusion that the signal >is significant [#]. Yes, one can find a sinusoid with period 1/2 turn >and an amplitude of 0.06 fringe (0.6 in your units); but this sinusoid >is not statistically significant, no matter how you process it. > [#] You used sigma(mRaw-mRawF), while the correct value > FOR AN UNCORRELATED SUBTRACTION is sqrt(sigma(mRaw)^2 + > sigma(mRawF)^2). But this subtraction is not uncorrelated > -- assuming perfect correlation, the correct errorbar is > max(sigma(mRaw),sigma(mRawF)). There can never be an > errorbar smaller than sigma(mRaw), because that's all the > information that is present in the data, no matter how > you process it. That errorbar is around 1.1 in your units, > twice as big as the amplitude of the sinusoid. And this > errorbar ignores the systematic correlation of the data > points; as I discuss in my paper, taking that into account > makes it about 7 in your units - ENORMOUS (c.f. my fig. 5). >Yes, there is a peak in DFT bin 40, and a valley in bin 20 -- the >physical device forces the 1-turn amplitude (bin 20) into the 1/2-turn >amplitude (bin 40), but it's not perfectly sharp. And the presence of a >peak does not mean that it is significant; this one isn't (see above, >and also my paper for a discussion). >In any case, Miller's analysis algorithm is a comb filter that preserves >only three amplitudes, aliasing higher-frequency harmonics into them, >with 1/2-turn as the lowest frequency (my fig. 9). His falling noise >spectrum naturally causes that one to be the largest, which explains why >his plots all show a sinusoid with period 1/2 turn. >Just wanted to point out that this was not my analysis. The link >provided was from one of Surfer's posts. It looked pretty good so I >answering. >What is obviously wrong is the conclusion. >I was looking for something a little more specific than the results >don't agree with what you expect. It uses what look to be modern >methods of looking at Miller's data and gets about the same result >Miller did. That is quite different from what Tom got, so I thought >Tom might comment. >You can read Tom's paper and see in detail what he did. > That wasn't the question. The question was what was wrong with the > analysis that showed a pattern? You do not believe Tom so you should do your own analysis. You tell us > what the data means. >For some reason, a lot of >cranks have fixated on Miller's experiments. Since there is better >data available now that has up to a factor of a billion or so better >resolution and accuracy, Miller's mistakes are of only historical >interest. >IMO it would be better to show how Miller got some false signals than >to claim no pattern ever existed in the data. Just looking at a plot >of the data in fig.8 it is obvious there is a pattern there with the >frequency being sought. >The adjustments that Miller made required the pattern to show up. > That is bull and you know it. Here is Tom's paper so you can look > for yourself. http://arxiv.org/ftp/physics/papers/0608/0608238.pdf Fig. 8 shows the first adjustment was made after five full turns. The > pattern I am talking about shows up before that first adjustment. > Perhaps you would like to explain how you think that first adjustment > introduced the pattern in the preceeding five turns. Or how a total > of three adjustments resulted in a half turn pattern showing up in > twenty full turns. > To say that it doesn't exist is an insult to >anyone that looks at the plot. I agree the pattern is not from ether >drift. I suspect the pattern is from the temperture gradient of the >air, and the downward trend is caused by the heating/cooling of the >frame. That I consider a very plausible explaination. But to say >there is no pattern..... >There are also flexing issues with the rotation but that is not >the point. The claim by Miller was that all the fluctuations >pointed to one spot in the sky although apparently that point >changed with when he reported the results. > No, the point I have been trying to make is there is a pattern. I > agree that it is not ether drift, but something caused a pattern. To > claim there is no pattern when there obviously is one is not good > science. I do not care what the pattern is since it is not related to the > physics. The current experiments say that it is wrong so feel > free to spend your time finding out why. A quick way of showing the pattern was not ether drift would be to >provide a few more sets of data that didn't show such a pattern. >The fastest way to show the pattern is not ether drift is to look at >the experiments with a billion times his sensitivity. That is >quite conclusive. > Those new experiments are not the same experiment. They measured the same effect but in a more precise way. There have > been some silly people here who claim that you have to exactly > repeat some old experiment to debunk it but that is complete > nonsense. An argument could > be made that something about them prevents them from picking up the > signal that Miller found. Have you read the experiments to see what they were doing? The whole > point of Miller was to find an isotropy in the speed of light. There > is none to limits a billion times finer than Miller was proposing. Tom has said many of them showed nothing. There are a few shown here > with no data. So you are saying that you believe Miller saw aether drift? > http://www.scieng.flinders.edu.au/cpes/people/cahill_r/Miller1933.pdf Any reference to Cahill is automatically the sign of a crank. Cahill > is a joke and only surfer believes him (many people believe surfer is > Cahill). If data for a few runs was shown it would show fig.8 was a temperture > related fluke. > His results cannot be correct since they do not agree >with those experiments. >That still doesn't explain the results, and it was not my point >anyway. My point is that it is just as bad to see nothing where there >is something as it is to see something where there is nothing. >Claiming there is no pattern when one jumps out and slaps you in the >face just gives more fuel to the cranks. >The explaination is that it is wrong. Why is of only academic interest. >Nothing you say or do will have any effect on the cranks here. They >are beyond reason and are all suffering from various delusions about >what science is. > One of the quickest ways to turn someone into a crank is to lie to > them. Telling them there is no pattern when they can see a pattern in > the plot without doing any analysis imediately turns them against > you. Why should they believe anything you say when they have already > caught you trying to put something over on them? Well, the experiments say there is no signal. Any claim to the contrary > is the sign of a crank who is ignoring the evidence. The cranks are > unmoved by the truth in any case. Look at ken seto or Henri (ralph) > or noeinstein or koobee or ... Pick any of hundreds. They are ignorant > and plan on staying that way. >I don't think that assumption is a good one. For the whole of the >first 5 turns the trend was downward. After the weights were hung >that trend reversed and then resumed. The same thing happen after the >other adjustments as well. It is obvious these adjustments messed up >any resemblence there might have been to a true linear drift. >Yes. Miller's assumption of linear drift is HORRIBLE. Even without the >adjustments. Look at Fig. 3 of my paper to see how bad this assumption >is -- errors in this assumption are much larger than his supposed signal. >Any chance you could provide a link to data for some of the other >runs, or post that data here? Nobody should complain about the use of >bandwidth considering how much is wasted on pure crap around here :) >The run we have been beating to death has obvious defects. I would >like to see others. >You should read the paper by Tom Roberts. He does a nice job in >the analysis. >I have read Tom's paper, several times. >And what did you disagree with? > The fact that in the end he found no pattern where one obviously > existed. Well, show the error in his analysis. If you found something, I would > like to see it. >Not so sure it was a good idea to assume that the data for the two >half turns was the same either. The numbers say they are not, >reguardless of what the theory says. It may have given a better >looking sinwave but it increased the error. >Yes. This has to do with the fact that the variations in his data are >due to a time-dependent drift, not any orientation-dependent signal. >See section IV of my paper. >Your comments are quite similar to my discussion in the paper referenced >above. The analysis in part IV of that paper avoids all these problems >by separating the time dependence from the orientation dependence, >modeling the former and then subtracting it from the data. For 53 of his >runs, the result for the orientation dependence is 0 +- 0.015 fringe, >corresponding to an upper bound on ether drift of 6 km/s (90% confidence). === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <29-dnWjFHdSt89DXnZ2dnUVZ_vSdnZ2d@posted.docknet> posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP > Any reference to Cahill is automatically the sign of a crank. Cahill > is a joke and only surfer believes him (many people believe surfer is > Cahill). No, he's not, he's just a guy who sucks up to Cahill. Cahill posts here occasionally (under his own name). He used to get a merciless beating every time he shows up, so he stopped posting. Surfer (aka Peter Brown) is an amateur who thinks that Cahill is god's gift to physics. === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) === Subject: Re: michelson morley experiment questions > Peter, look: > Look at these preposterous situations created by the idea > of lack of simultaneiety: Preposterous to you. Obviously Special Relativity is correct, the evidence is overwhelming, > its routinely used in engineering and if it was wrong lots of things > wouldn't work (in some cases spectacularly). Just accept it as amazing. > I guess you don't understand block universe. It literally means > you are a mannikin voicing nonconsequential inanities. Well, if that is what the block Universe literally is, it is false, as I > am not literally a mannikin. > And you agree with it? > :) > Spirit of Truth With SR? Yes, of course. And I also agree that world is not flat, and that earth > revolves around the sun and not vice-versa. All well supported by > evidence. ........ ... ........ ... You are missing the point. SR gives the condition of simultaneity. That equals a blockhead universe where the future already exists. Thus you = nothing per Einstein's SR. I can assure you that you are not a nothing and do have free will....SO something is wrong in the state of SR. Spirit of Truth === Subject: Re: michelson morley experiment questions You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. Thus you = nothing per Einstein's SR. I can assure you that you are not a nothing and do have free > will....SO something is wrong in the state of SR. > Spirit of Truth I just don't remember SR addressing the subject of free will. Spirit, would you be so king as to cite appropriate literature? BTW, what's a blockhead universe? === Subject: Re: michelson morley experiment questions > You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. > Thus you = nothing per Einstein's SR. > I can assure you that you are not a nothing and do have free > will....SO something is wrong in the state of SR. > Spirit of Truth I just don't remember SR addressing the subject of free will. Spirit, would you be so king as to cite appropriate literature? BTW, what's a blockhead universe? ROTFL You are correct, Einstein did not realize it. If he had he would not have adopted LET and would have found the correct answer. Blockhead universe is the universe where you are acting out a pre-ordained event timeline that already exists. That imagined SR universe in which you are just a Robot. Spirit of Truth Spirit of Truth really been a gemius g b === Subject: Re: michelson morley experiment questions > I just don't remember SR addressing the subject of free will. > Spirit, would you be so king as to cite appropriate literature? > BTW, what's a blockhead universe? > ROTFL You are correct, Einstein did not realize it. If he had he would > not have adopted LET and would have found the correct answer. Blockhead universe is the universe where you are acting out > a pre-ordained event timeline that already exists. That > imagined SR universe in which you are just a Robot. > Spirit of Truth > So you are saying Einstein didn't have any choice... that he had to create SR and that you, Spirit don't have any choice about learning what SR really says. Pitiful, wouldn't you say? === Subject: Re: michelson morley experiment questions I just don't remember SR addressing the subject of free will. Spirit, would you be so king as to cite appropriate literature? BTW, what's a blockhead universe? > ROTFL > You are correct, Einstein did not realize it. If he had he would > not have adopted LET and would have found the correct answer. > Blockhead universe is the universe where you are acting out > a pre-ordained event timeline that already exists. That > imagined SR universe in which you are just a Robot. > Spirit of Truth So you are saying Einstein didn't have any choice... that he had > to create SR Exactly, but you need to _confront_ the fact and confronting it face up to the fact that it is nonsense and solve the matter so that lack of simultaneity is obliterated from the scientific literature so that the scientific community can again be restored to a state of respect and truth. Spirit of Truth > and that you, Spirit don't have any choice about > learning what SR really says. Pitiful, wouldn't you say? As an aside, what would be pitiful, Sam, would be an intelligent person like you burying your head in the sand. === Subject: Re: michelson morley experiment questions <4a476d29$0$25358$afc38c87@news.optusnet.com.au> <4a483464$0$4046$afc38c87@news.optusnet.com.au> <69J3m.769906$yE1.198126@attbi_s21> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.7.STABLE6) >ROTFL >You are correct, Einstein did not realize it. If he had he would >not have adopted LET and would have found the correct answer. >Blockhead universe is the universe where you are acting out >a pre-ordained event timeline that already exists. That >imagined SR universe in which you are just a Robot. >Spirit of Truth > So you are saying Einstein didn't have any choice... that he had > to create SR >Exactly, but you need to confront the fact and confronting it >face up to the fact that it is nonsense and solve the matter so >that lack of simultaneity is obliterated from the scientific >literature so that the scientific community can again be >restored to a state of respect and truth. >Spirit of Truth >and that you, Spirit don't have any choice about >learning what SR really says. Pitiful, wouldn't you say? >As an aside, what would be pitiful, Sam, would be an >intelligent person like you burying your head in the sand. > No--you've already stated there is no free will... confronting > does no good if there is no free will. According to you... you > have no choice, I have no choice, Einstein had no choice, the > scientific community has no choice... all cogs grinding along > unable to change outcomes. >Sam, not according to me. According to your religion, SR. This shows how little you know of science. >Why do you enjoy being stupid? >Face up to the situation, lack of simultaneiety which means >blockhead universe is bunk. > appear too unintelligent to understand truth, boy. You come and spew nonsense and then have a childish tantrum > when it is pointed out that you know nothing about science. > Go ahead and cry and stomp your feet but it will not make > you look like an adult. > I guess you also think the Earth moves, dummie! > Spirit of Truth Stop the name calling! Pay attention and make intelligent comments. Appearances may deceive. The Poincare Conjecture reduces to a conjecture that a minumum of 9 points on the sphere arranged somewhat like this: . . . . . . . . . is the smallest simply-connected case. That the old Poincare Conjecture is false but a modified PC involving that 9 point matrix is true. This is because the Reals are discrete and have gaps in between consecutive Reals. But now notice I connect line segments to those 9 points shown above. I cannot do it even with ascii art so let me describe it. . . . forms one triangle and the next is . . . then there is . . . and finally there is . . . These four triangles leave the inside point unscathed so that this is the point that the Poincare loop shrinks to. The essence of the 4Color Mapping is that there is no fifth closed loop that can be adjacent to four closed loops that are adjacent. In other words four adjacent closed loops is the maximum. So now, let us relook at the above modified Poincare Conjecture with its surrounding four triangles of that 9 point lattice. Can you see where Poincare Conjecture has now merged as an equivalent statement as the 4 Color Mapping Problem? The minimum number of closed loops--triangles-- to satisfy Poincare Conjecture is 4, and the maximum closed loops to satisfy 4Color Mapping is of course 4. So, in essence 9 point matrix is related to adjacency maximum of 4. The essence of 4 Color Mapping is that there is never a 5th mutual adjacency, and I proved it using the Moebius theorem, but let us look at 4 Color Mapping as an alternate statement of the Poincare Conjecture. Here is 4 Color Mapping in its essence: MMMMMM MMMMMM BBJJJ BBJJJ Shown is the M country adjacent with B and J countries. So all three are mutually adjacent, meaning, each has a contact with the others. Now let us apply a 4th mutual adjacency in the form of O: MMMMMM MMMMMM BBJJJO BBJJJO OOOO Now, clearly, can you see why 4 mutual adjacency is a maximum? Can you see that a 5th is never allowed because the J country was covered over by the O country? Now here is the relevancy and relatedness to the Poincare Conjecture for the O country covering is the same as encircling of a country so that no other country can penetrate inside the covering up of J. That 4 Color Mapping is a question of the existence of a 5th mutual adjacency. And the reason you cannot have a 5th is because the 4th encircles one of the previous 3 countries. Now the Old-Poincare Conjecture says that all closed loops has a point inside for which that loop when it shrinks will always have that point inside. The New- Poincare Conjecture as outlined in this book says that the Old Poincare Conjecture is false because the points in Euclidean and Elliptic geometry are discrete with consecutive points and having gaps in between. So we need at least 9 consecutive points in such an array to have a Poincare Conjecture: . . . . . . . . . The middle point is the Poincare point where the surrounding points serve as the smallest loop. So when we shrink that loop we end up with that middle point. Now, can you see the similarity between the 4 Color Mapping and the New Poincare Conjecture? The J country above is the point in the middle of that Poincare array. In a sense, when you do the 4 Color Mapping you are doing a Poincare loop around 3 mutual adjacent countries and the 4th country that is mutually adjacent cuts off one of the other three countries by encircling it. What is the importance of these insights? Well for one it shows 4 Color Mapping is equivalent to New-Poincare Conjecture. But more important is that the 4 Color Mapping was not affected by the revelation that the points in Euclidean geometry were discrete and consecutive with holes in between consecutive Reals. The proof of 4 Color Mapping was not affected by that revelation. But the Old Poincare Conjecture was seen as false and had to be revised with a 9 point array. So here is the interesting good news about this equivalency. Since the 4 Color Mapping is a true theorem of mathematics with discrete and consecutive Reals, and if the only Poincare Conjecture that is true is the modified form where 9 point array then the 4Color Mapping in a sense destroys the Old Poincare Conjecture. So if you believe still that the Old Poincare Conjecture is true then it is contradictory to the 4 Color Mapping and that there is a 5th mutual adjacency. So can one use the Old Poincare Conjecture and devise a 5th mutual adjacency? Apparently one can do so because of the infinite downward regression of the old Betweenness axiom that given A and B is always a new C. P.S. the ironies of life are perhaps the most marvellous experiences of living. Because it was about 20 years ago that I started proving 4 Color is false and Poincare is true and here it is 20 years later that I am forced to say 4 Color was true and Poincare was false. I am saving this for future laughter and ridicule. It would be like if Wikipedia existed in the a flat planet where you fall off if you sailed at the edge. In light of the above posts of mine, that the 4Color Mapping is equivalent to a New-Poincare-Conjecture makes Wikipedia's write-up nothing but a bunch of hogwash. --- quoting Wikipedia --- http://en.wikipedia.org/wiki/Poincare conjecture (Redirected from Poincare conjecture) Jump to: navigation, search In mathematics, the Poincar.8e conjecture (French, pronounced [pw?Öka?e]) [1] is a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. It began as a popular, important conjecture, but is now considered a theorem to the satisfaction of the awarders of the Fields medal. The claim concerns a space that locally looks like ordinary three dimensional space but is connected, finite in size, and lacks any boundary (a closed 3- manifold). The Poincar.8e conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere. An analogous result has been known in higher dimensions for some time. For closed 2 dimensional surfaces, if every loop can be continuously tightened to a point, then the surface is a 2-sphere. The Poincar.8e conjecture attempts to determine if the same is true for closed 3- dimensional spaces. After nearly a century of effort by mathematicians, Grigori Perelman sketched a proof of the conjecture in the program of Richard Hamilton. Several high-profile teams of mathematicians have since verified the correctness of Perelman's proof. The Poincar.8e conjecture was, before being proven, one of the most important open questions in topology. It is one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution. Perelman's work survived review and was confirmed in 2006, leading to him being offered a Fields Medal, which he declined. The Poincar.8e conjecture remains the only solved Millennium problem. On December 22, 2006, the journal Science honored Perelman's proof of the Poincar.8e conjecture as the scientific Breakthrough of the Year, the first time this had been bestowed in the area of mathematics.[2] --- end quoting Wikipedia --- Archimedes Plutonium www.iw.net/~a plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies Reply[ CapitalEHat]Reply to authorForward[Capita lEHat] Rate this post: Text for clearing space . Discussion subject changed to how can we have a Poincare Conjecture equal to a... Sounds almost incredulous that the two are the same things. But the key is that both are about encircling and closing off geometrical figures. The previous illustration of 4Color Mapping: MMMMMM MMMMMM BBJJO BBJJO OOOO In order for those four countries to be 4 colorable means there is 4 mutual adjacencies and no more. If there was a 5th mutual adjacency then we lose the 4 Color Mapping. And what makes it possible is that the O country encircles the J country so that no 5th country can ever connect with J. In the Old-Poincare Conjecture we have simply-connected that a closed loop shrinks to a point. But because Reals are discrete with gaps between consecutive Reals the Old Poincare Conjecture must be false and only with some revisions can we even have a New Poincare Conjecture. A closed loop shrunk is not a singular point but an array of at least 9 consecutive points where the Poincare point is in the middle. . . . . . . . . . So how are those two pictures above the same thing? Seems incredulous that they could be the same. They are the same if we consider shrinking the 4 Color Mapping and we consider the octupuses tentacles as country mapping. So we have five countries as octupus tentacles and they meet at the end tip-- all five. So can those five country-tentacles all be mutually adjacent of those five end-tips? Well if the Old Poincare Conjecture was true then we add another country, the L country to the above diagram: LLLLLLLLLLL LMMMMMML LMMMMMML LLBBJJOLLLL LLBBJJOL LLOOOOL LLLLLLLLL They are all mutually adjacent except for the J to L countries. But if the Old Poincare Conjecture were true we shrink that entire country set and what happens is that the J and L countries now do become mutually adjacent. They become mutually adjacent because the J country becomes the point in the Old Poincare Conjecture. The New Poincare Conjecture upon shrinkage stops short of J becoming mutually adjacent because the 9 point array blocks the penetration of the L country. Having some difficulty in explaining this and so will leave it at that. It is due to the fact it is not clear flowing to me, yet. The idea is that if the Betweenness Axiom is allowed then it is the source of all this inconsistency and contradictions. That between any two A and B is always a C causes the 5 tentacles to be mutually adjacent and causes the L country to penetrate and touch the J country. - Show quoted text - Untitled to the friends of Kolmogorov.84N.L. Dreier, A.A. Malinovskii, S.A. Musatov, ..... his customary improvizations during the lecture Luzin made a conjecture ... (they discussed a series of questions arising from Poincare's problem of three geodesies). .... remaining part was divided into two almost equal parts. ... Result for query keyword(s)=theorem author= title=newblock emph Map color theorem. newblock The four-colour theorem. ..... Note that if Szpiro's conjecture is true, then Theorem~ gives a uniform bound ...... Unitary representations of classical Lie groups of equal rank with nonzero Dirac cohomology ..... On the extremal functions of Sobolev-Poincar.8e inequality ... http://nyjm.albany.edu:8000/cgi-bin/ aglimpse/19/nyjm/Http/search/j %3Ffirstyear%3D2001%26journaldir %3Dcombined%26lastyear%3D2007%26query %3Dtheorem Result for query keyword(s)=theorem author= title=The inverse mapping theorem guarantees that any surface is; a plane, ...... Our main theorem checks the conjecture for some specific groups ..... Minimal submanifolds of K.8ahler-Einstein manifolds with equal K.8ahler angles ...... Equivalence of Analytic and Sobolev Poincare Inequalities for Planar Domains ... http://nyjm.albany.edu:8000/cgi-bin/ aglimpse/19/nyjm/Http/search/j %3Ffirstyear%3D1994%26journaldir %3Dcombined%26lastyear%3D2002%26query Poincare group. The position in the transverse plane coincides with the ...... is equal to its mass and the spin of the nucleon is ...... in the nucleon, and in impact parameter space, where they enable to map the spatial ..... [111] Musatov I.V. and Radyushkin A.V., Phys. Rev. D, 61 (2000) 074027. http://arxiv.org/pdf/0711.2625 -- Martin Musatov (The above theory) http://MeAmI.org Search for the People! === Subject: Re: michelson morley experiment questions reply-type=response Importance: Normal > Peter, look: > Look at these preposterous situations created by the idea > of lack of simultaneiety: > Preposterous to you. > Obviously Special Relativity is correct, the evidence is overwhelming, > its routinely used in engineering and if it was wrong lots of things > wouldn't work (in some cases spectacularly). > Just accept it as amazing. I guess you don't understand block universe. It literally means > you are a mannikin voicing nonconsequential inanities. > Well, if that is what the block Universe literally is, it is false, as > I am not literally a mannikin. > And you agree with it? :) Spirit of Truth > With SR? > Yes, of course. And I also agree that world is not flat, and that earth > revolves around the sun and not vice-versa. All well supported by > evidence. > ......... .. > ......... .. You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. Although the future that 'already exists' is not causally linked to the present here. > Thus you = nothing per Einstein's SR. SR says nothing of the sort. > I can assure you that you are not a nothing and do have free > will.... How do you know .. how can you every possibly know? > SO something is wrong in the state of SR. No .. only with your insistence that something must be wrong === Subject: Re: michelson morley experiment questions > Peter, look: > Look at these preposterous situations created by the idea > of lack of simultaneiety: > Preposterous to you. > Obviously Special Relativity is correct, the evidence is overwhelming, > its routinely used in engineering and if it was wrong lots of things > wouldn't work (in some cases spectacularly). > Just accept it as amazing. > I guess you don't understand block universe. It literally means > you are a mannikin voicing nonconsequential inanities. Well, if that is what the block Universe literally is, it is false, as > I am not literally a mannikin. > And you agree with it? > :) > Spirit of Truth With SR? Yes, of course. And I also agree that world is not flat, and that earth > revolves around the sun and not vice-versa. All well supported by > evidence. > ......... .. > ......... .. > You are missing the point. SR gives the condition of simultaneity. > That equals a blockhead universe where the future already exists. Although the future that 'already exists' is not causally linked to the > present here. In blockhead universe there is no Cause, only blockheads. > Thus you = nothing per Einstein's SR. SR says nothing of the sort. It sure does, but you have to have a big confront to face up to it. > I can assure you that you are not a nothing and do have free > will.... How do you know .. how can you every possibly know? I am not alone. > SO something is wrong in the state of SR. No .. only with your insistence that something must be wrong Of course there is. Lack of simultaneity is the first error of SR and it is that, that put physics into a state of confusion that it still is mired in. Spirit of Truth === Subject: Re: michelson morley experiment questions reply-type=response It might be better if you consulted some standard textbook on SR, tried to work through it, and for bits you don't understand, asked in these newsgroups. If Einstein's original paper is too advanced for you, try a popular account (Einstein himself did one). HTH Peter Webb === Subject: Re: michelson morley experiment questions <4a476d29$0$25358$afc38c87@news.optusnet.com.au> <4a483464$0$4046$afc38c87@news.optusnet.com.au> <0069a4e8$0$9716$c3e8da3@news.astraweb.com> posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP Of course there is. Lack of simultaneity is the first error of SR > and it is that, that put physics into a state of confusion that it > still is mired in. > Imbecile , SR has simultaneity, it is just that it is not ABSOLUTE, like in Newtonian mechanics. === Subject: Re: michelson morley experiment questions > Of course there is. Lack of simultaneity is the first error of SR > and it is that, that put physics into a state of confusion that it > still is mired in. > Imbecile , SR has simultaneity, it is just that it is not ABSOLUTE, > like in Newtonian mechanics. That is not the point. These are the point (try to understand them): > Look at these preposterous situations created by the idea > of lack of simultaneiety: > http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node77.html > http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity%2C_time_... You will notice that one of the blockhead SRians has tried to hide them from view so that you all can continue as slaves. Well, unfortunately for them Fabric Of The Cosmos was a best seller ,and so what is _obvious_ from lack of simultaneiery cannot be hidden any more. Shame on those who would keep you all slaves! Spitir of Truth. === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <6uqe4557in0la56perimbdql9d8qe03cpl@4ax.com> posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Miller was in much the same situation as I describe. He detected > modulations in the MMX output, but totally ignored evidence > indicating that the modulations were due to terrestrial factors, > rather than having any sort of celestial origin. I don't base my opinions on what Miller may have ignored or not > ignored but rather on analysis of his data. My own analysis shows that the data in Figure 8 of his 1933 paper > contained a signal that was not an artifact of his data reduction > algorithm and so therefore had a physical cause. My analysis of his presented results leads me to conclude that > the physical cause had a celestial component. What evidence do you have to justify that assertion? Surely not Miller's spurious claim that the signals that he detected showed constant phase when plotted against sidereal time? Guided by faulty theory, Miller drew theoretical best fits through his data points in bold lines that were much more prominent than the actual data. The effect was to draw the eye of the reader away from the fact that the theoretically computed lines tended to miss the data entirely. In the following link, I examine Miller's claim that the signals he detected showed constant phase when plotted against sidereal time, thus proving a celestial origin for the signals. The plots at first look force your eye to look at his fanciful interpretation of the data, rather than the data itself. Erase Miller's fanciful fits, and the apparent constant phase vanishes. http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm Jerry === Subject: Re: michelson morley experiment questions Guided by faulty theory, Miller drew theoretical best fits >through his data points in bold lines that were much more >prominent than the actual data. The effect was to draw the eye of > the reader away from the fact that the theoretically computed >lines tended to miss the data entirely. In the following link, I >examine Miller's claim that the signals he detected showed >constant phase when plotted against sidereal time, thus proving >a celestial origin for the signals. The plots at first look >force your eye to look at his fanciful interpretation of the >data, rather than the data itself. Erase Miller's fanciful fits, >and the apparent constant phase vanishes. >http://mysite.verizon.net/cephalobus_alienus/Miller/EraseMillerLines.htm > Hmm. The bold lines are not artistically drawn lines, but are the theoretically calculated curves of how magnitude and azimuth of measured velocity would vary over 24 hours of sideral time. Due to the earth's changing velocity as it orbits the sun, different curves are required at different times of the year. If you could show that the curves were wrongly calculated you might have a point. But looking at what is presented, I can only agree with Miller that, The calculated curves fit the observations remarkably well. === Subject: miller experiment questions posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) >Guided by faulty theory, Miller drew theoretical best fits >through his data points in bold lines that were much more >prominent than the actual data. The effect was to draw the eye of > the reader away from the fact that the theoretically computed >lines tended to miss the data entirely. In the following link, I >examine Miller's claim that the signals he detected showed >constant phase when plotted against sidereal time, thus proving >a celestial origin for the signals. The plots at first look >force your eye to look at his fanciful interpretation of the >data, rather than the data itself. Erase Miller's fanciful fits, >and the apparent constant phase vanishes. >http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm Hmm. The bold lines are not artistically drawn lines, but are the > theoretically calculated curves of how magnitude and azimuth of > measured velocity would vary over 24 hours of sideral time. Due to the earth's changing velocity as it orbits the sun, different > curves are required at different times of the year. If you could show that the curves were wrongly calculated you might > have a point. You want examples of horrible mistakes in how Miller calculated his curves? YOU GOT IT! And this is just starters...I just don't have the -time- to tear apart his whole paper... Miller's data was so dirty, that he presented running averages of his data in his plots, rather than the data itself. The manner in which Miller computed his running averages introduced artifact, such as forcing the appearance of 24 hour periodicities in his running average curves when they in fact may have had none. http://mysite.verizon.net/cephalobus alienus/Miller/FakeRunningAverages.htm > But looking at what is presented, I can only agree with Miller that, > The calculated curves fit the observations remarkably well. Jerry === Subject: Re: michelson morley experiment questions posting-account=gHzHsAoAAAAF151cc29NwfB5wIxHQOuy CLR 2.0.50727; .NET CLR 2.0.50215; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) >Guided by faulty theory, Miller drew theoretical best fits >through his data points in bold lines that were much more >prominent than the actual data. The effect was to draw the eye of > the reader away from the fact that the theoretically computed >lines tended to miss the data entirely. In the following link, I >examine Miller's claim that the signals he detected showed >constant phase when plotted against sidereal time, thus proving >a celestial origin for the signals. The plots at first look >force your eye to look at his fanciful interpretation of the >data, rather than the data itself. Erase Miller's fanciful fits, >and the apparent constant phase vanishes. >http://mysite.verizon.net/cephalobus alienus/Miller/EraseMillerLines.htm Hmm. The bold lines are not artistically drawn lines, but are the > theoretically calculated curves of how magnitude and azimuth of > measured velocity would vary over 24 hours of sideral time. Due to the earth's changing velocity as it orbits the sun, different > curves are required at different times of the year. If you could show that the curves were wrongly calculated you might > have a point. But looking at what is presented, I can only agree with Miller that, > The calculated curves fit the observations remarkably well. The calculated curves fit the actual data poorly. The actual data belies Miller's claim that the phases are constant when plotted against sidereal time. Jerry === Subject: Re: michelson morley experiment questions <0kv845d8n63shd4s3j4cjefoae9rts02j7@4ax.com> <6uqe4557in0la56perimbdql9d8qe03cpl@4ax.com> posting-account=1FV9tgoAAADH0azT7-mxErKgugI383zU Gecko/20081204 SeaMonkey/1.1.14,gzip(gfe),gzip(gfe) Allais and others have came to similar conclusions. Eg see: >http://allais.maurice.free.fr/English/media14-1.htm -- Surfer This conclusion is at odds with newer measurements which are far more > precise, some up to 8 or ten orders of magnitude, which show no effects. > Experiments that attempt to detect light speed anisotropy in vacuum don't work, because variation of light speed is exactly compensated for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include something to disturb the balance. Eg in Miller's experiment, the presence of air reduced the speed of light to c/n (n==refractive index of air). That was sufficient to do it. === Subject: Re: michelson morley experiment questions > Experiments that attempt to detect light speed anisotropy in vacuum > don't work, because variation of light speed is exactly compensated > for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Eg in Miller's experiment, the > presence of air reduced the speed of light to c/n (n==refractive index > of air). That was sufficient to do it. Hmmm. I suppose there might be theories that imply this, but none are commonly known, and none are mainstream. Moreover, your claim is just plain wrong -- in particular: # Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg 2489 (1974). A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of 0.025 m/s. This is about one-millionth of the Earth's orbital velocity and about 1/10,000 of its rotational velocity. Glass has a much larger index of refration than air, so your claim is CLEARLY invalid. The underlying reason is that the gas in Miller's interferometer is sensitive to quite small changes in temperature, which most definitely occurred in his measurements -- he merely constructed the world's most unwieldy thermometer. He is not alone in that.... Tom Roberts === Subject: Re: michelson morley experiment questions > >Allais and others have came to similar conclusions. >Eg see: >http://allais.maurice.free.fr/English/media14-1.htm >-- Surfer >This conclusion is at odds with newer measurements which are far more >precise, some up to 8 or ten orders of magnitude, which show no effects. > Experiments that attempt to detect light speed anisotropy in vacuum > don't work, because variation of light speed is exactly compensated > for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Eg in Miller's experiment, the > presence of air reduced the speed of light to c/n (n==refractive index > of air). That was sufficient to do it. We are all aware you idolize Cahill but his work is rejected by real scientists. > === Subject: Re: michelson morley experiment questions > Those of us who have studied physics, and have experience where your > accelerators), know that the model of relativity corresponds MUCH better > to the experiments we have performed on the world; relativity, of > course, does support and require the lack of simultaneity you have in > mind. So, what are the differences between relative simultaneity and absolute simultaneity? ********************** In absolute simultaniety if one observer sees two events as simultaneous, all will. In relative simultanaity, this is not true. Say we have a series of events taking place and several observers observing these events. It is the job of each observer to piece all the events together into a timeline with chronological order. Under relative simultaneity, each observer will report a different timeline of these events. Some events unobserved will be left out. Under absolute simultaneity, all the timelines must be equal. Does this sound about right? ********************* Yes! You have got it! > So this really comes down to your personal lack of experience, and your > extreme naivet.8e about the ability of your thoughts to control the > universe. Just because you THINK This real universe of ours does not > support lack of simultaneity does not make it so. Indeed, real > experiments show that it does. As many observers observe the interference pattern of the MMX, each observer should have no problems reporting exactly where the beams of light come from and where and when the peaks of the light beams occur. Thus, simultaneity sounds like absolute to me. ******************** No, it doesn't even sound like simultaniety, as the MMX does not explicitly address the subject of simultaniety. You are getting confused. Any interferometer should falsify any wild and unrealistic ideas claiming that the universe supports relative simultaneity. The MMX actually falsifies the Lorentz transform since it manifests relative simultaneity. Since SR is merely an interpretation to the Lorentz transform, it is falsified as well. Simultaneity must be absolute according to any experiments. *********************** That's just nonsense. If there is something you don't understand about SR, please free to ask. === Subject: Re: michelson morley experiment questions <1TT2m.10142$Dx2.7890@flpi146.ffdc.sbc.com> <4a4d6347$0$25358$afc38c87@news.optusnet.com.au> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Hmmm... I have asked the so-called experts in justifying their arguments in why the world is observed to behave in relative simultaneity. All I got are doug the manyuk (Arabic for male prostitute), Whoever the diarrhea licker, and Peter Webb the empirical idiot (according to Uncle AlÍs classification). So, if the self-styled physicists do not understand the differences between what relative simultaneity and absolute simultaneity are, why are they promoting one from the other? That is indeed bigotry with a political agenda so sickeningly sinister. === Subject: Re: michelson morley experiment questions Hmmm... I have asked the so-called experts in justifying their arguments in why the world is observed to behave in relative simultaneity. All I got are doug the manyuk (Arabic for male prostitute), Whoever the diarrhea licker, and Peter Webb the empirical idiot (according to Uncle AlÍs classification). So, if the self-styled physicists do not understand the differences between what relative simultaneity and absolute simultaneity are, why are they promoting one from the other? I already specified the difference between relative and absolute simultaneity. The concept of absolute simultaneity is that measurements of simultaneity are independent of the reference frames;in relative simultaneity these depend upon the reference frame that is used for measurements. I know SR is hard, that's life, sometimes you have to work at understanding something. === Subject: Re: michelson morley experiment questions Importance: Normal > Hmmm... I have asked the so-called experts in justifying their > arguments in why the world is observed to behave in relative > simultaneity. All I got are doug the manyuk (Arabic for male > prostitute), Whoever the diarrhea licker, and Peter Webb the empirical > idiot (according to Uncle AlÍs classification). So, if the self-styled physicists do not understand the differences > between what relative simultaneity and absolute simultaneity are, why > are they promoting one from the other? That is indeed bigotry with a > political agenda so sickeningly sinister. Do you understand the difference yourself? === Subject: Re: michelson morley experiment questions Hmmm... I have asked the so-called experts in justifying their arguments in why the world is observed to behave in relative simultaneity. All I got are doug the manyuk (Arabic for male prostitute), Whoever the diarrhea licker, and Peter Webb the empirical idiot (according to Uncle Al.89s classification). So, if the self-styled physicists do not understand the differences between what relative simultaneity and absolute simultaneity are, why are they promoting one from the other? That is indeed bigotry with a political agenda so sickeningly sinister. Despite your miserable flaming diarrhea, you still have no answer to Sagnac. You are as much a bigot as they are. === Subject: Re: michelson morley experiment questions <1TT2m.10142$Dx2.7890@flpi146.ffdc.sbc.com> <5q3o451r9tf42nq7r3u753p83jamfq6sr2@4ax.com> <4a4c8701$0$3321$afc38c87@news.optusnet.com.au> <025cc5f0$0$26243$c3e8da3@news.astraweb.com> posting-account=A_fxOQkAAAC3cvPrAtLES_UPpvsB8VF2 Trident/4.0; GTB6; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; OfficeLiveConnector.1.3; OfficeLivePatch.0.0; yie8),gzip(gfe),gzip(gfe) > {snip...} > Whatever it is. :) OK, I mean that disagreeing with the apparent illogical >ideas in SR, at least in my case, is not to do with >my human intuition disageeing with it. This real universe >of ours does not support lack of simultaneity. Spirit > You got to understand, for diehard relativists perception IS > reality. > Well, if by perception you mean what we see experimentally, yes. > You are quite free to impose your concept of simultaneity and absolute > time > and space on the Universe; you can define a privileged frame of reference > and measure simultaneity etc from within that frame. You can even call it > the ether, if you want. > But what you also have to accept is that the frame you have chosen is > completely arbitrary, and anybody else can pick a different inertial > frame > to treat as absolute. The details of which frame or reference you choose > has > absolutely no bearing on the outcome of physical experiments, and your > absolute time and space plays no role in any physical experiment. Th eproblem with your claim is that the clock second we use to measure > time has different duration in different inertial frames. In every inertial frame, a clock second for a clock at rest in that frame is > the same clock second. Noone in any inertial frame sees their own at-rest clock ticking slower than > any other observer sees their own at-rest-clock ticking. Of course, SR further says in every inertial frame, the observer will see > clocks in motion as running slower than they do when at rest. That means > that the outcome of physical experiments in different frames cannot be > compared directly. An observer in some frame S watching an experiment while it is being > performed in a different frame S' will see different results to the observer > in S' will see. But both the observer in S and the observer in S' will see > the same results when the experiment is performed at rest in their own > frames. My point is: The passage of an S frame second does not correspond to the passage of an S' clock second and thus the same numerical results for an experiment in S' frame do not correspond to the same numerical results for the same experiment in the S frame. For example a traveling clock second in the twin > scenario cannot be compared directly with a stay at home clock second. Yes it can .. look at the clocks. No it can't.....the passage of a traveling clock second does not correspond to the passage of a stay at home clock second. Therefore you cannot compared them directly. Why? Because SR claims that the passage of a traveling clock second > corresponds to the passage of less than a clock second on the stay at > home clock. Actually, you have it backwards. The travelling clock second corresponds to > more than a stay-at-home clock second. I agree...you were right. Regardless when you compare the clocks when they return, you can see the > difference in elapsed time. > Sure you can compared the clock second after it return but those clock second accumulated during the journey cannot be compared directly withthe stay at home clock seconds accumulated during the journey of the traveling clock. > I'm not sure what the point is you were trying to make.. but I don't think > you succeeded in making it.- Hide quoted text - > The point is: The same results for identical experiment in S and S' frame is a false assertion. Ken Seto === Subject: Re: michelson morley experiment questions <1TT2m.10142$Dx2.7890@flpi146.ffdc.sbc.com> <5q3o451r9tf42nq7r3u753p83jamfq6sr2@4ax.com> <4a4c8701$0$3321$afc38c87@news.optusnet.com.au> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > {snip...} > Whatever it is. :) OK, I mean that disagreeing with the apparent illogical >ideas in SR, at least in my case, is not to do with >my human intuition disageeing with it. This real universe >of ours does not support lack of simultaneity. Spirit > You got to understand, for diehard relativists perception IS > reality. > Well, if by perception you mean what we see experimentally, yes. > You are quite free to impose your concept of simultaneity and absolute > time > and space on the Universe; you can define a privileged frame of reference > and measure simultaneity etc from within that frame. You can even call it > the ether, if you want. > But what you also have to accept is that the frame you have chosen is > completely arbitrary, and anybody else can pick a different inertial > frame > to treat as absolute. The details of which frame or reference you choose > has > absolutely no bearing on the outcome of physical experiments, and your > absolute time and space plays no role in any physical experiment. Th eproblem with your claim is that the clock second we use to measure > time has different duration in different inertial frames. In every inertial frame, a clock second for a clock at rest in that frame is > the same clock second. Noone in any inertial frame sees their own at-rest clock ticking slower than > any other observer sees their own at-rest-clock ticking. Of course, SR further says in every inertial frame, the observer will see > clocks in motion as running slower than they do when at rest. That means > that the outcome of physical experiments in different frames cannot be > compared directly. An observer in some frame S watching an experiment while it is being > performed in a different frame S' will see different results to the observer > in S' will see. But both the observer in S and the observer in S' will see > the same results when the experiment is performed at rest in their own > frames. My point is: The passage of an S frame second does not correspond to > the passage of an S' clock second and thus the same numerical results > for an experiment in S' frame do not correspond to the same numerical > results for the same experiment in the S frame. > For example a traveling clock second in the twin > scenario cannot be compared directly with a stay at home clock second. Yes it can .. look at the clocks. No it can't.....the passage of a traveling clock second does not > correspond to the passage of a stay at home clock second. Therefore > you cannot compared them directly. > Why? Because SR claims that the passage of a traveling clock second > corresponds to the passage of less than a clock second on the stay at > home clock. Actually, you have it backwards. The travelling clock second corresponds to > more than a stay-at-home clock second. I agree...you were right. > Regardless when you compare the clocks when they return, you can see the > difference in elapsed time. > Sure you can compared the clock second after it return but those clock > second accumulated during the journey cannot be compared directly > withthe stay at home clock seconds accumulated during the journey of > the traveling clock. I'm not sure what the point is you were trying to make.. but I don't think > you succeeded in making it.- Hide quoted text - > The point is: The same results for identical experiment in S and S' > frame is a false assertion. Ken Seto michelson morley experiment questions - sci.physics | Google Groups>the Lorentz criterion that I had mentioned earlier in simplified >form as the fact that the daily ..... enough to explain the null results of the MMX. .... Here we see the somehow sci.physics/browse thread/thread/cb5d54bed2ab20b3/ e84886b58da35447%3Flnk%3Draot - 325k - Full text of Early Latin hymns with introduction and notes by the ...... Chapter, cix (102) (XI). i = Verona, Chapter, 32 (IX). m = Florence, Lorenz., Conv. ...... Of which (i.e. His mira- culous birth and Godhead) Jesus gave proof by ..... He prays that Christ may and in early writers, come as the shepherd of ...... 3io EARLY LA TIN HYMNS Ecdhjvx Fdips Gm Hbch Ibh Mmx Vs A Patre ...http://www.archive.org/stream/earlylatinhymnsw00walpiala/ earlylatinhymnsw00walpiala djvu.txt Pettitte: I'll make my next start | The lohud Yankees Blog Jesus Christ Eduardo Nunez was taken to the hospital after his thumb swelled .... mmx May 30th, 2009 at 2:29 pm. Now no starting pitcher (except CC & AJ) ...http://yankees.lhblogs.com/2009/05/30/pettitte-ill- make-my-next-start/ - 159k Stupid Jews Jesus Christ was a reformer of Judaism, and the Jews of his day ... by George Francis Fitzgerald (Irish), Hendrik Antoon Lorentz (Dutch), and others. ... MMX doesn't make amends for the White slave trade, in which Jews trick young women ...http:// christianparty.net/stupidjews.htm Search values It supports Pentium, P6 and MMX opcodes, and has macro capability. ...... Provied by the Church of Jesus Christ of Later-Day Saints. ..... Important Formulae for Complex Numbers: Has Lorenz attractors, Henon Map, etc. ...http://webzu.sapp.org/cgi-bin/ webzusearch%3FALL%3Dwww%26user%3Dcraig and c cause $100-a-plate dinner &c 'Abo 'Alborg 'Alesund 'Angstr ...... Christ Christ Jesus Christ Within Christ and the beloved disciple Christ ...... Fitz Fitz-james FitzGerald FitzGerald-Lorentz contraction Fitzclarence ...... MMGT MMH MMJ MMM MMOC MMP MMS MMT MMU MMW MMX MMetE MMus MN MNA MNAS MNE ...http://www.puzzlers.org/pub/wordlists/allwords.txt SamoaLive! Guest Book May the Lord Jesus guide us all in the light for all the days of our lives. ...... http://rue-an-fischer.oxboy.info http://lorenz-spielwaren.tfiih.info http://rechtsanwalt-m-nchen.unden.info ..... http://jesus-christ-superstar-lyrics.strig.turek.pl ...... http://site-de-lg.csmt.lubin.pl http://mmx-cpu.csmt.lubin.pl ...http:// www.samoalive.com/guestbook.htm Loot.co.za: Sitemap9780078530500 0078530504 Complete guide to MMX technology, Intel Corporation,. .... 9780548245392 0548245398 Jesus, the Christ, in the Light of Psychology, ...http://www2.loot.co.za/index/html/index2926.html '68 Comeback Special (.84.84.84u.84|.84u.84r.84y.84x.84y.84Ä.84~.84~.84.8d.84z .84{.84Ä.84~.84.88.84u.84.82.84.84) Elvis Presley's '68 ...... Inventory MMS Multimedia Messaging Service MMX MMX Mobile Media API Java ...... prototyping .84A.84.8d.84.83.84.84.84.82.84Ä.84.82.84u.84w.84.85.84.8b 204p.84.91 .84.83.84.84.84p.84|.84.8e High speed steel .84A.84.8d.84.83.84.84.84.82.84Ä.84.84.84p Lorentz factor ...... .84V.84.82.84y.84.83.84.84.84Ä.84.83 Jesus .84I.84y.84.83.84.85.84.83 .84V.84.82.84y.84.83.84.84.84Ä.84.83 .81 .84.83.84.85.84.81.84u.84.82.84x.84r.84u.84x.84t.84p (.84.86.84y.84|.84.8e.84}) Jesus Christ Superstar ...http://www.cs.helsinki.fi/group/ smart/data/wikipedia/phrase table/wikipedia phrasetable/ru-en.ff Plagger.82.81.82[NonBreakingSpace].82í.8d22 1.82[Eth].8aÄ.8e.8b(.89.9f.97[CapitalCCe dilla].94.81) - akihito.82í.93.9c.8bL... 2 01 swish, sodm, abraham uhr, 10688, inspire weight, mmx, install maya linux, %OOO, ..... x 500 navy directory, =OO, konrad lorenz king solomons ring, 3674, ...... =-DD, church of jesus christ of, 8]]], galluccio winery, 91968, ...http:// d.hatena.ne.jp/t-akihito/20061017/p1 12345678910Next[NonBreakingSpace]Language Tools[NonBreakingSpace]| [NonBreakingSpace]Search[NonBreakingSpace]Tips[NonBreakingSpace]|[NonBre akingSpace]Dissatisfied? Help us improve. --Musatov === Subject: Re: michelson morley experiment questions > The point is: The same results for identical experiment in S and S' > frame is a false assertion. > Not the same results, in the sense of numeric answers, but the same outcomes. For example, if an observers in an inertial frame of reference calculate that two bodies will collide, observers in all frames of reference will calculate they collide. The measurements may differ, but the outcome is the same. HTH === Subject: Re: michelson morley experiment questions Importance: Normal > Those of us who have studied physics, and have experience where your > accelerators), know that the model of relativity corresponds MUCH better > to the experiments we have performed on the world; relativity, of > course, does support and require the lack of simultaneity you have in > mind. So, what are the differences between relative simultaneity and > absolute simultaneity? Say we have a series of events taking place and several observers > observing these events. It is the job of each observer to piece all > the events together into a timeline with chronological order. Under > relative simultaneity, each observer will report a different timeline > of these events. Some events unobserved will be left out. Under > absolute simultaneity, all the timelines must be equal. Does this sound about right? > So this really comes down to your personal lack of experience, and your > extreme naivet.8e about the ability of your thoughts to control the > universe. Just because you THINK This real universe of ours does not > support lack of simultaneity does not make it so. Indeed, real > experiments show that it does. As many observers observe the interference pattern of the MMX, each > observer should have no problems reporting exactly where the beams of > light come from and where and when the peaks of the light beams > occur. Of course .. the changes in simultaneity do not affect causality > Thus, simultaneity sounds like absolute to me. What things are you claiming are simultaneous? > Any > interferometer should falsify any wild and unrealistic ideas claiming > that the universe supports relative simultaneity. How would it? > The MMX actually > falsifies the Lorentz transform since it manifests relative > simultaneity. No .. Lorentz transform explain MMX results. > Since SR is merely an interpretation to the Lorentz > transform, it is falsified as well. No > Simultaneity must be absolute > according to any experiments. Why do you think that? Seems like an unsupported assertion to me . === Subject: Re: michelson morley experiment questions > when one subtracts two UNCORRELATED random variables A > and B, the sigma of the result is sqrt(sigma(A)^2+sigma(B)^2), not what > you used, sigma(A-B). > I am afraid you are being obscurantist. No. I merely stated the standard result from statistics. This is not obscurantist, this is CORRECT. But for your case you do need to read > In my scheme, A is raw data (that is signal plus noise), B is raw data > minus most of the signal. > Consequently subtracting B from A removes most of the noise while > leaving most of the signal. > Computing the standard deviation of (B-A) therefore gives the standard > deviation of the clean signal. Not true. You grossly misrepresent the errorbars. Subtracting a background cannot possibly reduce the original statistical errors in the data. Tom Roberts === Subject: Re: michelson morley experiment questions > In my scheme, A is raw data (that is signal plus noise), B is raw data > minus most of the signal. > Consequently subtracting B from A removes most of the noise while > leaving most of the signal. > Computing the standard deviation of (B-A) therefore gives the standard > deviation of the clean signal. Not true. You grossly misrepresent the errorbars. Subtracting a >background cannot possibly reduce the original statistical errors in the >data. > Of course not. However, if I remove easy to eliminate errors from the data, why should I be interested in the original statistical errors? Suppose a radio antenna is picking up 1 volt p-p of power line hum and 1 microvolt of signal. The original statistical errors would be a million times larger than the signal. But after the hum has been eliminated with a filter or tuning circuit, would those original statistical errors still be of any irrelevance? I think not. === Subject: Re: michelson morley experiment questions > Suppose a radio antenna is picking up 1 volt p-p of power line hum and > 1 microvolt of signal. > The original statistical errors [...] That is NOT a statistical error. As I keep repeating: you REALLY need to study this. Tom Roberts === Subject: Re: michelson morley experiment questions >In my scheme, A is raw data (that is signal plus noise), B is raw data >minus most of the signal. >Consequently subtracting B from A removes most of the noise while >leaving most of the signal. >Computing the standard deviation of (B-A) therefore gives the standard >deviation of the clean signal. >Not true. You grossly misrepresent the errorbars. Subtracting a >background cannot possibly reduce the original statistical errors in the >data. > Of course not. However, if I remove easy to eliminate errors from the data, why > should I be interested in the original statistical errors? Because the removal process does not magically make signal from noise. Suppose a radio antenna is picking up 1 volt p-p of power line hum and > 1 microvolt of signal. > This depends on the filter. If you are looking for 1MHz, you can do a great job. If you are looking for 61Hz (or 51Hz depending on where one is), then you are in real trouble. You need to realize that newer experiments have limited the anisotropy to a factor of a billion or so below the even claimed resolution of Miller. Therefore he is wrong and, if you get the same results, you are wrong. To think otherwise is a bad case of self delusion. > The original statistical errors would be a million times larger than > the signal. But after the hum has been eliminated with a filter or > tuning circuit, would those original statistical errors still be of > any irrelevance? I think not. > === Subject: Re: michelson morley experiment questions > > > However, if I remove easy to eliminate errors from the data, why > should I be interested in the original statistical errors? Because the removal process does not magically make signal from >noise. > You are not being logical. If the noise has been reduced, why should the original statistical errors caused by that noise, be of relevance to the remaining signal component? > > Suppose a radio antenna is picking up 1 volt p-p of power line hum and > 1 microvolt of signal. > >This depends on the filter. If you are looking for 1MHz, you can do a >great job. If you are looking for 61Hz (or 51Hz depending on where >one is), then you are in real trouble. > True. But the relevant point here is that Millers signals were mainly contaminated by much lower frequency noise, that was easy to remove. That is clearly shown by the DFTs on this page. http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ You need to realize that >newer experiments have limited the anisotropy to a factor of a billion >or so below the even claimed resolution of Miller. > Experiments that attempt to detect light speed anisotropy in vacuum don't work, because variation of light speed is exactly compensated for by Lorentz contraction of the apparatus. To detect light speed anisotropy the experiment has to include something to disturb the balance. Eg in Miller's experiment, the presence of air reduced the speed of light to c/n. Judging by the results of his experiment this was sufficient. A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments M. Consoli, E. Costanzo Eur.Phys.J.C55:469-475,2008 http://arxiv.org/abs/0804.0979 Abstract In principle, by accepting the idea of a non-zero vacuum energy, the preferred reference frame. By treating this quantum vacuum as a relativistic medium, the non-zero energy-momentum flow expected in a moving frame should effectively behave as a small thermal gradient and could, in principle, induce a measurable anisotropy of the speed of light in a loosely bound system as a gas. We explore the phenomenological implications of this scenario by considering a new class of dedicated ether-drift experiments where arbitrary gaseous media fill the resonating optical cavities. Our predictions cover most experimental set up and should motivate precise experimental tests of these fundamental issues. === Subject: Re: michelson morley experiment questions > However, if I remove easy to eliminate errors from the data, why >should I be interested in the original statistical errors? >Because the removal process does not magically make signal from >noise. > You are not being logical. If the noise has been reduced, why should > the original statistical errors caused by that noise, be of > relevance to the remaining signal component? Because you have to be very careful in what you are removing. If you remove a constant, for example, the percentage fluctuations increase. >Suppose a radio antenna is picking up 1 volt p-p of power line hum and >1 microvolt of signal. >This depends on the filter. If you are looking for 1MHz, you can do a >great job. If you are looking for 61Hz (or 51Hz depending on where >one is), then you are in real trouble. > True. But the relevant point here is that Millers signals were mainly > contaminated by much lower frequency noise, that was easy to remove. > That is clearly shown by the DFTs on this page. > http://wbbrdr.diinoweb.com/files/Miller/1933/Analysis_of_Fig8/ >You need to realize that >newer experiments have limited the anisotropy to a factor of a billion >or so below the even claimed resolution of Miller. Experiments that attempt to detect light speed anisotropy in vacuum > don't work, because variation of light speed is exactly compensated > for by Lorentz contraction of the apparatus. This is Cahill and his foolishness. To detect light speed anisotropy the experiment has to include > something to disturb the balance. Eg in Miller's experiment, the > presence of air reduced the speed of light to c/n. But remember Cahill was shown to be wrong in this by experiments done where n was much higher number. He then had to retreat to saying that somehow air was special. Cranks do that. Judging by the results of his experiment this was sufficient. Judging by the results of data analysis and later work, he was completely wrong. A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008 > http://arxiv.org/abs/0804.0979 Abstract In principle, by accepting the idea of a non-zero vacuum energy, the > preferred reference frame. By treating this quantum vacuum as a > relativistic medium, the non-zero energy-momentum flow expected in a > moving frame should effectively behave as a small thermal gradient and > could, in principle, induce a measurable anisotropy of the speed of > light in a loosely bound system as a gas. We explore the > phenomenological implications of this scenario by considering a new > class of dedicated ether-drift experiments where arbitrary gaseous > media fill the resonating optical cavities. Our predictions cover most > experimental set up and should motivate precise experimental tests of > these fundamental issues. === Subject: Re: michelson morley experiment questions <0JmdnRs3Q_LYydfXnZ2dnUVZ_tCdnZ2d@posted.docknet> posting-account=vma-PgoAAABrctSmMdefNKZ-c5S8buvP A possible theory of operation is discussed here: Precision tests with a new class of dedicated ether-drift experiments > M. Consoli, E. Costanzo > Eur.Phys.J.C55:469-475,2008http://arxiv.org/abs/0804.0979 > Ahh, the other pair of renowed crackpots. Let me guess, what comes next, a citation from Cahill or one from Munera? Or is it back to Dayton Miller? Messrs. Consoli and Constanzo never ran their experiments. What is even more embarassing is that their theory is ALREADY refuted by the a couple of experiments: #1 Trimmer et al., Phys. Rev. D8, pg 3321 (1973); Phys. Rev. D9 pg 2489 (1974). A triangle interferometer with one leg in glass. They set an upper limit on the anisotropy of 0.025 m/s. This is about one-millionth of the Earth's orbital velocity and about 1/10,000 of its rotational velocity. #2 Shamir and Fox, N. Cim. 62B no. 2 (1969), pg 258. A repetition of the MMX with the optical paths in perspex (n = 1.49), and a laser-based optics sensitive to ~0.00003 fringe. They report a null result with an upper limit on v.bether of 6.64 km/s. Eur.J.Phys is one of the most embarassing journals, they are at par with Foundations of Physics Letters and Physica Scripta, all known to publish fringe stuff. === Subject: Continuity equation? I would like to know why the energy is varying continuously (on a non-quantum level, i.e. in clasical physics). Is there any theoretical proof or is it based on some experiment? Namely, I am interested in this issue regarding the magnetic and electrostatic energy in Maxwell's model of electromagnetical phenomena. So, why the magnetic and/or electrostatic energy can not be changed discontinuously? === Subject: Re: Continuity equation? >I would like to know why the energy is varying continuously (on a >non-quantum level, i.e. in clasical physics). Is there any theoretical >proof or is it based on some experiment? Namely, I am interested in this issue regarding the magnetic and > electrostatic energy in Maxwell's model of electromagnetical phenomena. > So, why the magnetic and/or electrostatic energy can not be changed > discontinuously? Energy does not vary at all. http://www.androcles01.pwp.blueyonder.co.uk/AC/AC.gif On the right can be seen voltage (red/blue) and the magnetic field (gold/purple) with a teal vector representing constant energy. AND... it is not Maxwell's model, it is FARADAY's model. === Subject: Re: Continuity equation? >I would like to know why the energy is varying continuously (on a >non-quantum level, i.e. in clasical physics). Is there any theoretical >proof or is it based on some experiment? > Namely, I am interested in this issue regarding the magnetic and > electrostatic energy in Maxwell's model of electromagnetical phenomena. > So, why the magnetic and/or electrostatic energy can not be changed > discontinuously? Energy does not vary at all. > http://www.androcles01.pwp.blueyonder.co.uk/AC/AC.gif > On the right can be seen voltage (red/blue) and the magnetic field > (gold/purple) with a teal vector representing constant energy. AND... it is not Maxwell's model, it is FARADAY's model. > capacitance/inductance with electrostatic/magnetic energy by increasing of voltage(charge)/current(flux). Well, I assume that I am talking by means of network theory which divides magnetic and electrostatic energy... === Subject: Re: Continuity equation? >I would like to know why the energy is varying continuously (on a >non-quantum level, i.e. in clasical physics). Is there any theoretical >proof or is it based on some experiment? Namely, I am interested in this issue regarding the magnetic and > electrostatic energy in Maxwell's model of electromagnetical phenomena. > So, why the magnetic and/or electrostatic energy can not be changed > discontinuously? > Energy does not vary at all. > http://www.androcles01.pwp.blueyonder.co.uk/AC/AC.gif > On the right can be seen voltage (red/blue) and the magnetic field > (gold/purple) with a teal vector representing constant energy. > AND... it is not Maxwell's model, it is FARADAY's model. capacitance/inductance with electrostatic/magnetic energy by increasing of > voltage(charge)/current(flux). Well, I assume that I am talking by means > of network theory which divides magnetic and electrostatic energy... You can charge a reservoir with potential energy by pumping water uphill into it. That's the same as charging a capacitor. However, you put energy in when you run the pump. Same thing is happening here: http://paws.kettering.edu/~drussell/Demos/SHO/damp.html The mass has kinetic energy, the spring has potential energy. When the mass is NOT moving, the spring is stretched or compressed. When the spring is relaxed, the mass is moving at its fastest. The current has kinetic energy, the capacitor has potential energy. When the current is NOT moving, the capacitor is charged. When the capacitor is uncharged, the current is moving at its fastest. The total energy remains constant. If you damp the oscillation (i.e. take away the energy) then the mass stops moving and the spring is relaxed. To start it again you need to give it energy. A charged capacitor has no current. It has a voltage (or pressure, like the reservoir). When you draw a current it loses its voltage. With an inductance the current creates a magnetic field. No current, no field, but you can stop the current by opening a switch. However, the magnetic field is still there, and it will keep the current flowing even with the switch open as it collapses. That's a spark. When I was a kid I used an old doorbell to give people shocks. http://www.bryanzimmer.net/Main/Doorbell_Phone_files/DSC_1567b_1.jpg === Subject: LHC lying: GLAST searching for micro BLACK HOLES posting-account=5ehs9woAAAAPdLASkVa5y5b2hV4py5md Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; FDM; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) LHC is lying, LHC knows there is a good chance of micro Black Holes cause Fermi in July of 2008 lauched a low orbit satellite to find MINIATURE BLACK HOLES on Earth's upper atmosphere. So LHC concludes they won't be creating black holes at the same time as they're paying millions to find black holes, who's the LIAR. If Higgs bosons were dangerous, LHC would say the possibility of them creating Higgs bosons is very small, and that's what they're spending billions to look for. Some places reference Micro Black Holes as also primordial Black Holes, only LHC would have reason to falsefy such info so that people can't figure out GLAST is searching for them through cosmic ray proton collisions with Earth's atmosphere. 1stly it's a low orbit satellite in Earth's atmosphere. 2ndly primordial black holes can only still be alive if there mass is 10^12 thus not micro. 3rdly a micro black hole is too tiny and of short life span you have to be right beside it to see it, hence Earth's atmosphere. In other words, Earth's existance may reside solely on Hawking's Black Hole radiation & lifespan equation. === Subject: Re: LHC lying: GLAST searching for micro BLACK HOLES posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) > LHC is lying, LHC knows there is a good chance of micro Black Holes > cause Fermi in July of 2008 lauched a low orbit > satellite to find MINIATURE BLACK HOLES on Earth's upper atmosphere. Yes, that's true. The question is whether they are mass-accreting black holes, the think you're worried about. Note that if we're launching a satellite to see black holes in our atmosphere, then we would be observing something that has been going on for *billions* of years, without creation of a mass-accreting black hole. Notice also that these same collisions also occur from similar sources at the surface of the Earth. Again, no mass-accreting black holes. So what are you worried about exactly? So LHC concludes they won't be creating black holes at the same time > as they're paying millions to find black holes, who's the LIAR. If Higgs bosons were dangerous, LHC would say the possibility of them > creating Higgs bosons is very small, and that's what they're spending > billions to look for. Some places reference Micro Black Holes as also primordial Black > Holes, only LHC would have reason to falsefy such info so that people > can't figure out GLAST is searching for them through cosmic ray proton > collisions with Earth's atmosphere. 1stly it's a low orbit satellite in Earth's atmosphere. > 2ndly primordial black holes can only still be alive if there mass is > 10^12 thus not micro. > 3rdly a micro black hole is too tiny and of short life span you have > to be right beside it to see it, hence Earth's atmosphere. In other words, Earth's existance may reside solely on Hawking's Black > Hole radiation & lifespan equation. Those determined to find a conspiracy are guaranteed of success. PD === Subject: Re: LHC lying: GLAST searching for micro BLACK HOLES posting-account=azRwigkAAAA5Th7-XGkARzS64yAfV3nc LHC is lying, LHC knows there is a good chance of micro Black Holes > cause Fermi in July of 2008 lauched a low orbit > satellite to find MINIATURE BLACK HOLES on Earth's upper atmosphere. Yes, that's true. The question is whether they are mass-accreting > black holes, the think you're worried about. Note that if we're launching a satellite to see black holes in our > atmosphere, then we would be observing something that has been going > on for *billions* of years, without creation of a mass-accreting black > hole. Notice also that these same collisions also occur from similar > sources at the surface of the Earth. Again, no mass-accreting black > holes. So what are you worried about exactly? So LHC concludes they won't be creating black holes at the same time > as they're paying millions to find black holes, who's the LIAR. If Higgs bosons were dangerous, LHC would say the possibility of them > creating Higgs bosons is very small, and that's what they're spending > billions to look for. Some places reference Micro Black Holes as also primordial Black > Holes, only LHC would have reason to falsefy such info so that people > can't figure out GLAST is searching for them through cosmic ray proton > collisions with Earth's atmosphere. 1stly it's a low orbit satellite in Earth's atmosphere. > 2ndly primordial black holes can only still be alive if there mass is > 10^12 thus not micro. > 3rdly a micro black hole is too tiny and of short life span you have > to be right beside it to see it, hence Earth's atmosphere. In other words, Earth's existance may reside solely on Hawking's Black > Hole radiation & lifespan equation. Those determined to find a conspiracy are guaranteed of success. PD I wish you guys could understand just how stupid is pretty much every idea you're talking about. And it all comes from a mis-understanding of gravity, and as a consequence, an aggrandizement of the role of mass. The flow that causes gravity is like a river coming from all directions, and matter absorbs it at a constant rate. If you have enough matter, you can block *all* the flow coming from that direction. At that point, doubling the size of the planet will not change the surface gravity. The gravity has reached its maximum. GRAVITY MAXES OUT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!! No black holes. Same thing I stated my very first post in 1995. (Removing head once more from brick wall. Ouch.) john === Subject: Re: LHC lying: GLAST searching for micro BLACK HOLES > I wish you guys could understand just how stupid is > pretty much every idea you're talking about. And it all comes from a mis-understanding of gravity, and > as a consequence, an aggrandizement of the role of mass. The flow that causes gravity is like a river coming from all > directions, > and matter absorbs it at a constant rate. If you have enough matter, > you can block *all* the flow coming from that direction. At that > point, > doubling the size of the planet will not change the surface gravity. > The gravity has reached its maximum. GRAVITY MAXES > OUT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! !! No black holes. > Same thing I stated my very first post in 1995. > (Removing head once more from brick wall. Ouch.) john John, why do you post this garbage? === Subject: Re: LHC lying: GLAST searching for micro BLACK HOLES posting-account=azRwigkAAAA5Th7-XGkARzS64yAfV3nc I wish you guys could understand just how stupid is > pretty much every idea you're talking about. And it all comes from a mis-understanding of gravity, and > as a consequence, an aggrandizement of the role of mass. The flow that causes gravity is like a river coming from all > directions, > and matter absorbs it at a constant rate. If you have enough matter, > you can block *all* the flow coming from that direction. At that > point, > doubling the size of the planet will not change the surface gravity. > The gravity has reached its maximum. GRAVITY MAXES > OUT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! !! No black holes. > Same thing I stated my very first post in 1995. > (Removing head once more from brick wall. Ouch.) john John, why do you post this garbage? Because it makes more sense than Black Holes forming when a gravitational field produced by matter gets incredibly strong. You are saying that matter will enter a black hole and be crushed- indefinitely. It takes energy to crush things, Sam. Where does that energy come from? === Subject: Re: LHC lying: GLAST searching for micro BLACK HOLES > John, why do you post this garbage? > Because it makes more sense than > Black Holes forming when a gravitational > field produced by matter gets incredibly strong. > You are saying that matter will enter a black hole > and be crushed- indefinitely. It takes energy to crush things, Sam. Gravitational energy, John--some bird species are smart enough to drop seed on the rocks to get at the innards. Where do you think the energy comes from to crack eggs when you drop them... or break plates? Where does that energy come from? Conservation of Energy--Potential (gravitational) energy being converted to kinetic energy. Stuff of first year physics books, John. Physics FAQ: A Physics Booklist: Recommendations from the Net http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html#general-ph y sics === Subject: Solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM posting-account=sNPu1QoAAADF0hHpdz4PdHMnsZsq15U0 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , soltbcollect (at) gmail.com (my email : soltbcollect (at) gmail.com, soltbcollect @ gmail.com), these are parts of our list,, if the solutions manual or test bank isnÍt on the list, please email to me.,too. I can find it from my friends, please trust on Please search it by Ctrl +F Solutions manual for A First Course in Probability, (7th), By Sheldon Ross Solutions manual for A Friendly Introduction to Number Theory 3rd by Silverman Test Bank for Accounting Information Systems - James Hall (6th ed) Solutions manual for Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart TEST BANK for accounting information systems 11th edition, romney, steinbart instructor manual for Accounting text and cases 12e Anthony Solutions manual for Accounting what number means 8e by Marshall Solutions manual for Advanced Accounting 10e Fisher Test Bank for Advanced Accounting 10e Fisher Solutions manual for Advanced Accounting 10th edition by Beams Test bank for Advanced Accounting 10th edition by Beams Solutions manual for Advanced Accounting 9e Beams Solutions manual for Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank for Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank solution manual for Advanced Financial Accounting, 6th edition, by Baker, Lembke, and King solution manual Solutions manual for An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin Test banks for An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin Solutions manual for Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd Solutions manual for Auditing and Assurance Services 12 th by: Alvin A Arens, Solutions manual for Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt test bank for Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank Solutions manual for Booth, Cleary Introduction to Corporate Finance, Canadian Edition SM + TB Test bank for Booth, Cleary Introduction to Corporate Finance, Canadian Edition SM + TB Instructor manual for Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (6th ed) Test bank for Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (6th ed) instructor manual for Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank for Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz solution manual for Calculus Early transcendentals 5Th Ed Instructor's Solutions Manual by James Stewart Solutions manual for Chemical Reaction Engineering 3rd Ed. by Levenspiel Solutions manual for College Algebra, 10/E Margaret L. Lial TG + SM Solutions manual for Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson Solutions manual for Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Solutions manual for COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING Instructor manual for Contemporary Business and Online Commerce Law International Edition, 6E Henry R. Cheeseman Test bank for Contemporary Business and Online Commerce Law International Edition, 6E Henry R. Cheeseman TEST BANK for Corporate Finance A Focused Approach 3e Brigham Solutions manual for Corporate Finance plus MyFinanceLab Student Access kit Solutions manual for Corporate Finance: A Focused Approach 3e Brigham Solutions manual for Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education Solutions manual for cost accounting 12e Horngren test bank for cost Accounting 13e Horngren Solutions manual for Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th Solutions manual for Cost Accounting: Foundations and Evolutions 7E By Kinney Solutions manual for Data and Computer Communications, 8th Edition By Stallings Solutions manual for Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth Solutions manual for Database Systems: The Complete Book, 2/E Instructor manual for Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Solutions manual for Differential Equations and Linear Algebra by Penney and Edwards, 2nd Solutions manual for Differential Equations Computing and Modeling (4th Edition) By Edwards Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) Solutions manual for Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) SM Solutions manual for Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley Solutions manual for Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima Solutions manual for Elements of engineering electromagnetics (6/ e) by N.N.RAO TEST BANK for E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost Solutions manual for Engineering and Chemical Thermodynamics by Milo D. Koretsky Solutions manual for Engineering Circuit Analysis 7Ed William Hart Hayt Solutions manual for Engineering Economy - Leland Blank & Anthony Tarquin 6th Edition( student solution) Solutions manual for Engineering electromagnetics (7/ e) by HAYT Solutions manual for Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson Solutions manual for Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, 5th. Solutions manual for ENGINEERING MECHANICS: statics by BEDFOR D 5th. Solutions manual for Essential of Accounting for Governmental and Not- for- Profit Organizations By Paul A Copley, 9e test bank for Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus Instructor manual for Essentials of Managerial Finance 14e Besley Solutions manual for Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK for Essentials of Managerial Finance with Thomson ONE, 13e Brigham Test bank for Essentials of Statistics for Business and Economics, Anderson/Sweeney/Williams, 5e tb Solutions manual for Essentials of Statistics for Business and Economics, Anderson/Sweeney/Williams, 5e sm Solutions manual for Financial Account 7e Horngren TEST BANK for Financial Account 7e Horngren Solutions manual for Financial Accounting (Libby, fifth edition) Solutions manual for Financial Accounting 6e by horngren Harrison Solutions manual for Financial Accounting (Libby, 2001 edition) Solutions manual for Financial and Mangerial Accounting 2e by Horngren TEST BANK for Financial and Mangerial Accounting 2e by Horngren Solutions manual for Financial management theory and practice 12e by Brigham Test bank for Financial management theory and practice 12e by Brigham Solutions manual for Financial Reporting, Financial Statement Analysis, and Valuation: A Strategic Perspective, 6th Edition, Clyde P. Stickney | Paul Brown | James M. WahlenISBN-10: 0324302959 | ISBN-13: 9780324302950 | © 2007 Solutions manual for Finiancial Accounting 7e by Horngren Solutions manual for Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. Solutions manual for Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. TEST BANK for Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007) Solutions manual for Fundamental ccounting Principles, 18/e, Wild, Larson, & Chiappetta (2007). Instructor's Manual for Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill Solutions manual for Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik Solutions manual for Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby Solutions manual for Fundamentals of Classical Thermodynamics 6th edition by Van Wylen Solutions manual for Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) Solutions manual for Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe Solutions manual for Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro Solutions manual for Fundamentals of financial management 12e Brigham TEST BANK for Fundamentals of financial management 12e Brigham Solutions manual for Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham Solutions manual for Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald Solutions manual for Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald Solutions manual for Fundamentals of Physics (8th Edition) By Halliday Solutions manual for Fundamentals of Signals and systems using web and matlab third edition Solutions manual for fundamentals of thermodynamics, 7th edition,sonntag,borgnak, Solutions manual for fundamentals of financial management, concise 6th edition by Brigham, Houston Test bank for fundamentals of financial management, concise 6th edition by Brigham, Houston Solutions manual for fundamentals of financial management, concise 6th edition by Brigham, Houston Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston Solutions manual for fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine Solutions manual for Gravity: An Introduction to Einstein's General Relativity by James B. Hartle Solutions manual for Individual Income Taxes 2009 edition by Hoffman Test bank for Individual Income Taxes 2009 edition by Hoffman Solutions manual for Intermediata Accounting 13e Kieso TEST BANK for Intermediata Accounting 13e Kieso Solutions manual for Intermediate Accounting - James D. Stice (16th ed) sm Solutions manual for intermediate accounting 5e by spiceland Solutions manual for International Accounting 6e Frederick D. Choi Gary K. Meek Solutions manual for International Financial Management - With Map Edition: 9e Madura Jeff SM (cengage) test bank International Financial Management Geert Bekaert Robert J. Hodrick Solutions manual for Introduction for Chemical Engineering Thermodynamics 7th By J.M. Hendrick C Van Ness Solutions manual for Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters Solutions manual for Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} Solutions manual for Introduction for Mathematical Statistics 6/ E Robert V. Hogg Solutions manual for Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Solutions manual for Introduction to Chemical Engineering Thermodynamics 7th edition By J.Mith, Hendrick C Van Ness Solutions manual for Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine Solutions manual for Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) test bank for Introduction to Managerial Accounting 2nd ed Brewer Solutions manual for Introductory Econometrics for Finance(Chris Brooks 2002) Solutions manual for Linear Algebra and Its Applications, 3rd Edition by: David C. Lay Solutions manual for Linear Algebra with Applications 7th edition by Leon, instructor manual for Macroeconomics, 4E Olivier Blanchard test bank for Macroeconomics, 5E Olivier Blanchard Solutions manual for Macroeconomics, 5E Olivier Blanchard (instructor manual) Test bank for Management 9E Stephen P. Robbins Mary Coulter instructor manual for Management 9E Stephen P. Robbins Mary Coulter Solutions manual for Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK for Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E Solutions manual for Managerial Accounting 12e By Garrison Noreen TEST BANK for managerial accounting 12th Edition by Garrison Noreen Solutions manual for Managerial Accounting, 11th Edition by Ray H Garrison, Eric Noreen, Peter C. Brewer SM test bank for Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Instructor manual Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Solutions manual Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Solutions manual for Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson Solutions manual for Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Solutions manual for Mechanics of Materials By R.C.Hibbeler 7th edition Solutions manual for Mechanics of Materials by roy R. craig 2nd eddition s Solutions manual for Mechanics of Materials, 7th James M. Gere - Stanford University Solutions manual for Mechanics of Materials, 7th James M. Gere - Stanford University SM Solutions manual for Microeconomic Theory, Nicholson & Snyder, 10th ed, Solutions manual for Microeconomics 7e Robert Pindyck Daniel Rubinfeld Solutions manual for Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen Solutions manual for Microelectronic circuits by R. Jaeger 3rd edition Solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB solution manual for Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition solution manual test bank for Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition test bank Solutions manual for Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Solutions manual for Modern Elementary Statistics, 12/e by Freund & Perles TEST BANK for Modern Elementary Statistics, 12/e Freund & Perles Solutions manual for Modern Physics, 2/E Randy Harris Solutions manual for Numerical methods for engineers 5th by Chapra Solutions manual for Operating Systems: Internals and Design Principles 6e by William Stallings, PH.D. SM (pearson) Solutions manual for Operations Management 10e William J. Stevenson TEST BANK for Operations Management 10e William J. Stevenson Solutions manual for Operations Management 8e by Jay Heizer Barry Render SM (Pearson) Test bank for Operations Management 8e by Jay Heizer Barry Render TB (Pearson) Test bank for Operations Management 9e by Jay Heizer Barry Render tb Solutions manual for Operations Management 9e William J. Stevenson ( test bank for Operations Management 9e William J. Stevenson (TB) Solutions manual for Operations Management 9th by Jay Heizer Barry Render sm Test bank for Organizational Behavior, by Stephen P. and Timothy A. 13th Edition tb TEST BANK for Organizational Behaviour, Fourth Canadian Ed., 4E Robins Solutions manual for Physics for Scientists & Engineers with Modern Physics Vol. 2&3, 4/E Doug Giancoli ISM Solutions manual for Power System Analysis By John J. Grainger, William D. Stevenson Jr Instructor manual for Practical Financial Management 5th Edition William R. Lasher IM + TB Instructor manual for Practical Financial Management 5th Edition William R. Lasher IM + TB TEST BANK for Principles of Auditing 15e by Whittington Solutions manual for Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Solutions manual for Probability and Statistical Inference 7th edition, Hogg & Tanis Solutions manual for Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) Solutions manual for Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis Solutions manual for Process Dynamics and Control 2nd Ed. by Seborg, Edgar, and Mellichamp Solutions manual for Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual Solutions manual for Separation Process Principles, 2nd Ed.,by Seader, Henley Test bank for South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 , volume 3 (Cengage) Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe test bank Solutions manual for South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 , volume 3 (Cengage)Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe solution manual Solution manual for South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis test bank for South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis tb Test bank for TB for Modern Labor Economics: Theory and Public Policy, 10/E, Ronald G. Ehrenberg. test bank for cost Accounting 12e by Horngren Solutions manual for The Economics of Money,Banking,and Financial Market 8th edition by Frederic S. Mishkin solutions manual Test bank for The Economics of Money,Banking,and Financial Market 8th edition by Frederic S. Mishkin test bank Solutions manual for Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition test bank for Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston Solutions manual for Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston Solutions manual for Unit Operations of Chemical Engineering (7th) By Warren McCabe, Statics 8th Edition ,By F. P. Beer, E. R. solutions manual and Test Bank contact me with , soltbcollect (at) gmail.com (my email : soltbcollect (at) gmail.com, soltbcollect @ gmail.com), these are parts of our list,, if the solutions manual or test bank isnÍt on the list, please email to me.,too. I can find it from my friends, please trust on Please search it by Ctrl +F === Subject: TEST BANK for Intermediata Accounting 13e Kieso posting-account=sNPu1QoAAADF0hHpdz4PdHMnsZsq15U0 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , soltbcollect (at) gmail.com (my email : soltbcollect (at) gmail.com, soltbcollect @ gmail.com), these are parts of our list,, if the solutions manual or test bank isnÍt on the list, please email to me.,too. I can find it from my friends, please trust on Please search it by Ctrl +F Solutions manual for A First Course in Probability, (7th), By Sheldon Ross Solutions manual for A Friendly Introduction to Number Theory 3rd by Silverman Test Bank for Accounting Information Systems - James Hall (6th ed) Solutions manual for Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart TEST BANK for accounting information systems 11th edition, romney, steinbart instructor manual for Accounting text and cases 12e Anthony Solutions manual for Accounting what number means 8e by Marshall Solutions manual for Advanced Accounting 10e Fisher Test Bank for Advanced Accounting 10e Fisher Solutions manual for Advanced Accounting 10th edition by Beams Test bank for Advanced Accounting 10th edition by Beams Solutions manual for Advanced Accounting 9e Beams Solutions manual for Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank for Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank solution manual for Advanced Financial Accounting, 6th edition, by Baker, Lembke, and King solution manual Solutions manual for An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin Test banks for An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin Solutions manual for Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd Solutions manual for Auditing and Assurance Services 12 th by: Alvin A Arens, Solutions manual for Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt test bank for Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank Solutions manual for Booth, Cleary Introduction to Corporate Finance, Canadian Edition SM + TB Test bank for Booth, Cleary Introduction to Corporate Finance, Canadian Edition SM + TB Instructor manual for Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (6th ed) Test bank for Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (6th ed) instructor manual for Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank for Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz solution manual for Calculus Early transcendentals 5Th Ed Instructor's Solutions Manual by James Stewart Solutions manual for Chemical Reaction Engineering 3rd Ed. by Levenspiel Solutions manual for College Algebra, 10/E Margaret L. Lial TG + SM Solutions manual for Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson Solutions manual for Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Solutions manual for COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING Instructor manual for Contemporary Business and Online Commerce Law International Edition, 6E Henry R. Cheeseman Test bank for Contemporary Business and Online Commerce Law International Edition, 6E Henry R. Cheeseman TEST BANK for Corporate Finance A Focused Approach 3e Brigham Solutions manual for Corporate Finance plus MyFinanceLab Student Access kit Solutions manual for Corporate Finance: A Focused Approach 3e Brigham Solutions manual for Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education Solutions manual for cost accounting 12e Horngren test bank for cost Accounting 13e Horngren Solutions manual for Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th Solutions manual for Cost Accounting: Foundations and Evolutions 7E By Kinney Solutions manual for Data and Computer Communications, 8th Edition By Stallings Solutions manual for Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth Solutions manual for Database Systems: The Complete Book, 2/E Instructor manual for Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Solutions manual for Differential Equations and Linear Algebra by Penney and Edwards, 2nd Solutions manual for Differential Equations Computing and Modeling (4th Edition) By Edwards Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) Solutions manual for Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) SM Solutions manual for Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley Solutions manual for Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima Solutions manual for Elements of engineering electromagnetics (6/ e) by N.N.RAO TEST BANK for E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost Solutions manual for Engineering and Chemical Thermodynamics by Milo D. Koretsky Solutions manual for Engineering Circuit Analysis 7Ed William Hart Hayt Solutions manual for Engineering Economy - Leland Blank & Anthony Tarquin 6th Edition( student solution) Solutions manual for Engineering electromagnetics (7/ e) by HAYT Solutions manual for Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson Solutions manual for Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, 5th. Solutions manual for ENGINEERING MECHANICS: statics by BEDFOR D 5th. Solutions manual for Essential of Accounting for Governmental and Not- for- Profit Organizations By Paul A Copley, 9e test bank for Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus Instructor manual for Essentials of Managerial Finance 14e Besley Solutions manual for Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK for Essentials of Managerial Finance with Thomson ONE, 13e Brigham Test bank for Essentials of Statistics for Business and Economics, Anderson/Sweeney/Williams, 5e tb Solutions manual for Essentials of Statistics for Business and Economics, Anderson/Sweeney/Williams, 5e sm Solutions manual for Financial Account 7e Horngren TEST BANK for Financial Account 7e Horngren Solutions manual for Financial Accounting (Libby, fifth edition) Solutions manual for Financial Accounting 6e by horngren Harrison Solutions manual for Financial Accounting (Libby, 2001 edition) Solutions manual for Financial and Mangerial Accounting 2e by Horngren TEST BANK for Financial and Mangerial Accounting 2e by Horngren Solutions manual for Financial management theory and practice 12e by Brigham Test bank for Financial management theory and practice 12e by Brigham Solutions manual for Financial Reporting, Financial Statement Analysis, and Valuation: A Strategic Perspective, 6th Edition, Clyde P. Stickney | Paul Brown | James M. WahlenISBN-10: 0324302959 | ISBN-13: 9780324302950 | © 2007 Solutions manual for Finiancial Accounting 7e by Horngren Solutions manual for Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. Solutions manual for Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. TEST BANK for Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007) Solutions manual for Fundamental ccounting Principles, 18/e, Wild, Larson, & Chiappetta (2007). Instructor's Manual for Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill Solutions manual for Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik Solutions manual for Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby Solutions manual for Fundamentals of Classical Thermodynamics 6th edition by Van Wylen Solutions manual for Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) Solutions manual for Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe Solutions manual for Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro Solutions manual for Fundamentals of financial management 12e Brigham TEST BANK for Fundamentals of financial management 12e Brigham Solutions manual for Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham Solutions manual for Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald Solutions manual for Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald Solutions manual for Fundamentals of Physics (8th Edition) By Halliday Solutions manual for Fundamentals of Signals and systems using web and matlab third edition Solutions manual for fundamentals of thermodynamics, 7th edition,sonntag,borgnak, Solutions manual for fundamentals of financial management, concise 6th edition by Brigham, Houston Test bank for fundamentals of financial management, concise 6th edition by Brigham, Houston Solutions manual for fundamentals of financial management, concise 6th edition by Brigham, Houston Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston Solutions manual for fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine Solutions manual for Gravity: An Introduction to Einstein's General Relativity by James B. Hartle Solutions manual for Individual Income Taxes 2009 edition by Hoffman Test bank for Individual Income Taxes 2009 edition by Hoffman Solutions manual for Intermediata Accounting 13e Kieso TEST BANK for Intermediata Accounting 13e Kieso Solutions manual for Intermediate Accounting - James D. Stice (16th ed) sm Solutions manual for intermediate accounting 5e by spiceland Solutions manual for International Accounting 6e Frederick D. Choi Gary K. Meek Solutions manual for International Financial Management - With Map Edition: 9e Madura Jeff SM (cengage) test bank International Financial Management Geert Bekaert Robert J. Hodrick Solutions manual for Introduction for Chemical Engineering Thermodynamics 7th By J.M. Hendrick C Van Ness Solutions manual for Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters Solutions manual for Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} Solutions manual for Introduction for Mathematical Statistics 6/ E Robert V. Hogg Solutions manual for Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Solutions manual for Introduction to Chemical Engineering Thermodynamics 7th edition By J.Mith, Hendrick C Van Ness Solutions manual for Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine Solutions manual for Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) test bank for Introduction to Managerial Accounting 2nd ed Brewer Solutions manual for Introductory Econometrics for Finance(Chris Brooks 2002) Solutions manual for Linear Algebra and Its Applications, 3rd Edition by: David C. Lay Solutions manual for Linear Algebra with Applications 7th edition by Leon, instructor manual for Macroeconomics, 4E Olivier Blanchard test bank for Macroeconomics, 5E Olivier Blanchard Solutions manual for Macroeconomics, 5E Olivier Blanchard (instructor manual) Test bank for Management 9E Stephen P. Robbins Mary Coulter instructor manual for Management 9E Stephen P. Robbins Mary Coulter Solutions manual for Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK for Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E Solutions manual for Managerial Accounting 12e By Garrison Noreen TEST BANK for managerial accounting 12th Edition by Garrison Noreen Solutions manual for Managerial Accounting, 11th Edition by Ray H Garrison, Eric Noreen, Peter C. Brewer SM test bank for Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Instructor manual Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Solutions manual Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Solutions manual for Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson Solutions manual for Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Solutions manual for Mechanics of Materials By R.C.Hibbeler 7th edition Solutions manual for Mechanics of Materials by roy R. craig 2nd eddition s Solutions manual for Mechanics of Materials, 7th James M. Gere - Stanford University Solutions manual for Mechanics of Materials, 7th James M. Gere - Stanford University SM Solutions manual for Microeconomic Theory, Nicholson & Snyder, 10th ed, Solutions manual for Microeconomics 7e Robert Pindyck Daniel Rubinfeld Solutions manual for Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen Solutions manual for Microelectronic circuits by R. Jaeger 3rd edition Solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB solution manual for Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition solution manual test bank for Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition test bank Solutions manual for Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Solutions manual for Modern Elementary Statistics, 12/e by Freund & Perles TEST BANK for Modern Elementary Statistics, 12/e Freund & Perles Solutions manual for Modern Physics, 2/E Randy Harris Solutions manual for Numerical methods for engineers 5th by Chapra Solutions manual for Operating Systems: Internals and Design Principles 6e by William Stallings, PH.D. SM (pearson) Solutions manual for Operations Management 10e William J. Stevenson TEST BANK for Operations Management 10e William J. Stevenson Solutions manual for Operations Management 8e by Jay Heizer Barry Render SM (Pearson) Test bank for Operations Management 8e by Jay Heizer Barry Render TB (Pearson) Test bank for Operations Management 9e by Jay Heizer Barry Render tb Solutions manual for Operations Management 9e William J. Stevenson ( test bank for Operations Management 9e William J. Stevenson (TB) Solutions manual for Operations Management 9th by Jay Heizer Barry Render sm Test bank for Organizational Behavior, by Stephen P. and Timothy A. 13th Edition tb TEST BANK for Organizational Behaviour, Fourth Canadian Ed., 4E Robins Solutions manual for Physics for Scientists & Engineers with Modern Physics Vol. 2&3, 4/E Doug Giancoli ISM Solutions manual for Power System Analysis By John J. Grainger, William D. Stevenson Jr Instructor manual for Practical Financial Management 5th Edition William R. Lasher IM + TB Instructor manual for Practical Financial Management 5th Edition William R. Lasher IM + TB TEST BANK for Principles of Auditing 15e by Whittington Solutions manual for Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Solutions manual for Probability and Statistical Inference 7th edition, Hogg & Tanis Solutions manual for Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) Solutions manual for Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis Solutions manual for Process Dynamics and Control 2nd Ed. by Seborg, Edgar, and Mellichamp Solutions manual for Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual Solutions manual for Separation Process Principles, 2nd Ed.,by Seader, Henley Test bank for South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 , volume 3 (Cengage) Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe test bank Solutions manual for South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 , volume 3 (Cengage)Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe solution manual Solution manual for South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis test bank for South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis tb Test bank for TB for Modern Labor Economics: Theory and Public Policy, 10/E, Ronald G. Ehrenberg. test bank for cost Accounting 12e by Horngren Solutions manual for The Economics of Money,Banking,and Financial Market 8th edition by Frederic S. Mishkin solutions manual Test bank for The Economics of Money,Banking,and Financial Market 8th edition by Frederic S. Mishkin test bank Solutions manual for Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition test bank for Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston Solutions manual for Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston Solutions manual for Unit Operations of Chemical Engineering (7th) By Warren McCabe, Statics 8th Edition ,By F. P. Beer, E. R. solutions manual and Test Bank contact me with , soltbcollect (at) gmail.com (my email : soltbcollect (at) gmail.com, soltbcollect @ gmail.com), these are parts of our list,, if the solutions manual or test bank isnÍt on the list, please email to me.,too. I can find it from my friends, please trust on Please search it by Ctrl +F === Subject: Solutions manual for Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald posting-account=sNPu1QoAAADF0hHpdz4PdHMnsZsq15U0 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , soltbcollect (at) gmail.com (my email : soltbcollect (at) gmail.com, soltbcollect @ gmail.com), these are parts of our list,, if the solutions manual or test bank isnÍt on the list, please email to me.,too. I can find it from my friends, please trust on Please search it by Ctrl +F Solutions manual for A First Course in Probability, (7th), By Sheldon Ross Solutions manual for A Friendly Introduction to Number Theory 3rd by Silverman Test Bank for Accounting Information Systems - James Hall (6th ed) Solutions manual for Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart TEST BANK for accounting information systems 11th edition, romney, steinbart instructor manual for Accounting text and cases 12e Anthony Solutions manual for Accounting what number means 8e by Marshall Solutions manual for Advanced Accounting 10e Fisher Test Bank for Advanced Accounting 10e Fisher Solutions manual for Advanced Accounting 10th edition by Beams Test bank for Advanced Accounting 10th edition by Beams Solutions manual for Advanced Accounting 9e Beams Solutions manual for Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank for Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank solution manual for Advanced Financial Accounting, 6th edition, by Baker, Lembke, and King solution manual Solutions manual for An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin Test banks for An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin Solutions manual for Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd Solutions manual for Auditing and Assurance Services 12 th by: Alvin A Arens, Solutions manual for Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt test bank for Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank Solutions manual for Booth, Cleary Introduction to Corporate Finance, Canadian Edition SM + TB Test bank for Booth, Cleary Introduction to Corporate Finance, Canadian Edition SM + TB Instructor manual for Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (6th ed) Test bank for Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (6th ed) instructor manual for Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank for Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz solution manual for Calculus Early transcendentals 5Th Ed Instructor's Solutions Manual by James Stewart Solutions manual for Chemical Reaction Engineering 3rd Ed. by Levenspiel Solutions manual for College Algebra, 10/E Margaret L. Lial TG + SM Solutions manual for Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson Solutions manual for Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Solutions manual for COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING Instructor manual for Contemporary Business and Online Commerce Law International Edition, 6E Henry R. Cheeseman Test bank for Contemporary Business and Online Commerce Law International Edition, 6E Henry R. Cheeseman TEST BANK for Corporate Finance A Focused Approach 3e Brigham Solutions manual for Corporate Finance plus MyFinanceLab Student Access kit Solutions manual for Corporate Finance: A Focused Approach 3e Brigham Solutions manual for Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education Solutions manual for cost accounting 12e Horngren test bank for cost Accounting 13e Horngren Solutions manual for Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th Solutions manual for Cost Accounting: Foundations and Evolutions 7E By Kinney Solutions manual for Data and Computer Communications, 8th Edition By Stallings Solutions manual for Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth Solutions manual for Database Systems: The Complete Book, 2/E Instructor manual for Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Solutions manual for Differential Equations and Linear Algebra by Penney and Edwards, 2nd Solutions manual for Differential Equations Computing and Modeling (4th Edition) By Edwards Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) Solutions manual for Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) SM Solutions manual for Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley Solutions manual for Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima Solutions manual for Elements of engineering electromagnetics (6/ e) by N.N.RAO TEST BANK for E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost Solutions manual for Engineering and Chemical Thermodynamics by Milo D. Koretsky Solutions manual for Engineering Circuit Analysis 7Ed William Hart Hayt Solutions manual for Engineering Economy - Leland Blank & Anthony Tarquin 6th Edition( student solution) Solutions manual for Engineering electromagnetics (7/ e) by HAYT Solutions manual for Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson Solutions manual for Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, 5th. Solutions manual for ENGINEERING MECHANICS: statics by BEDFOR D 5th. Solutions manual for Essential of Accounting for Governmental and Not- for- Profit Organizations By Paul A Copley, 9e test bank for Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus Instructor manual for Essentials of Managerial Finance 14e Besley Solutions manual for Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK for Essentials of Managerial Finance with Thomson ONE, 13e Brigham Test bank for Essentials of Statistics for Business and Economics, Anderson/Sweeney/Williams, 5e tb Solutions manual for Essentials of Statistics for Business and Economics, Anderson/Sweeney/Williams, 5e sm Solutions manual for Financial Account 7e Horngren TEST BANK for Financial Account 7e Horngren Solutions manual for Financial Accounting (Libby, fifth edition) Solutions manual for Financial Accounting 6e by horngren Harrison Solutions manual for Financial Accounting (Libby, 2001 edition) Solutions manual for Financial and Mangerial Accounting 2e by Horngren TEST BANK for Financial and Mangerial Accounting 2e by Horngren Solutions manual for Financial management theory and practice 12e by Brigham Test bank for Financial management theory and practice 12e by Brigham Solutions manual for Financial Reporting, Financial Statement Analysis, and Valuation: A Strategic Perspective, 6th Edition, Clyde P. Stickney | Paul Brown | James M. WahlenISBN-10: 0324302959 | ISBN-13: 9780324302950 | © 2007 Solutions manual for Finiancial Accounting 7e by Horngren Solutions manual for Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. Solutions manual for Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. TEST BANK for Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007) Solutions manual for Fundamental ccounting Principles, 18/e, Wild, Larson, & Chiappetta (2007). Instructor's Manual for Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill Solutions manual for Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik Solutions manual for Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby Solutions manual for Fundamentals of Classical Thermodynamics 6th edition by Van Wylen Solutions manual for Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) Solutions manual for Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe Solutions manual for Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro Solutions manual for Fundamentals of financial management 12e Brigham TEST BANK for Fundamentals of financial management 12e Brigham Solutions manual for Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham Solutions manual for Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald Solutions manual for Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald Solutions manual for Fundamentals of Physics (8th Edition) By Halliday Solutions manual for Fundamentals of Signals and systems using web and matlab third edition Solutions manual for fundamentals of thermodynamics, 7th edition,sonntag,borgnak, Solutions manual for fundamentals of financial management, concise 6th edition by Brigham, Houston Test bank for fundamentals of financial management, concise 6th edition by Brigham, Houston Solutions manual for fundamentals of financial management, concise 6th edition by Brigham, Houston Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston Solutions manual for fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine Solutions manual for Gravity: An Introduction to Einstein's General Relativity by James B. Hartle Solutions manual for Individual Income Taxes 2009 edition by Hoffman Test bank for Individual Income Taxes 2009 edition by Hoffman Solutions manual for Intermediata Accounting 13e Kieso TEST BANK for Intermediata Accounting 13e Kieso Solutions manual for Intermediate Accounting - James D. Stice (16th ed) sm Solutions manual for intermediate accounting 5e by spiceland Solutions manual for International Accounting 6e Frederick D. Choi Gary K. Meek Solutions manual for International Financial Management - With Map Edition: 9e Madura Jeff SM (cengage) test bank International Financial Management Geert Bekaert Robert J. Hodrick Solutions manual for Introduction for Chemical Engineering Thermodynamics 7th By J.M. Hendrick C Van Ness Solutions manual for Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters Solutions manual for Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} Solutions manual for Introduction for Mathematical Statistics 6/ E Robert V. Hogg Solutions manual for Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths Solutions manual for Introduction to Chemical Engineering Thermodynamics 7th edition By J.Mith, Hendrick C Van Ness Solutions manual for Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine Solutions manual for Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) test bank for Introduction to Managerial Accounting 2nd ed Brewer Solutions manual for Introductory Econometrics for Finance(Chris Brooks 2002) Solutions manual for Linear Algebra and Its Applications, 3rd Edition by: David C. Lay Solutions manual for Linear Algebra with Applications 7th edition by Leon, instructor manual for Macroeconomics, 4E Olivier Blanchard test bank for Macroeconomics, 5E Olivier Blanchard Solutions manual for Macroeconomics, 5E Olivier Blanchard (instructor manual) Test bank for Management 9E Stephen P. Robbins Mary Coulter instructor manual for Management 9E Stephen P. Robbins Mary Coulter Solutions manual for Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK for Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E Solutions manual for Managerial Accounting 12e By Garrison Noreen TEST BANK for managerial accounting 12th Edition by Garrison Noreen Solutions manual for Managerial Accounting, 11th Edition by Ray H Garrison, Eric Noreen, Peter C. Brewer SM test bank for Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Instructor manual Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Solutions manual Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. ISM+TB Solutions manual for Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson Solutions manual for Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao Solutions manual for Mechanics of Materials By R.C.Hibbeler 7th edition Solutions manual for Mechanics of Materials by roy R. craig 2nd eddition s Solutions manual for Mechanics of Materials, 7th James M. Gere - Stanford University Solutions manual for Mechanics of Materials, 7th James M. Gere - Stanford University SM Solutions manual for Microeconomic Theory, Nicholson & Snyder, 10th ed, Solutions manual for Microeconomics 7e Robert Pindyck Daniel Rubinfeld Solutions manual for Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen Solutions manual for Microelectronic circuits by R. Jaeger 3rd edition Solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB solution manual for Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition solution manual test bank for Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition test bank Solutions manual for Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop Solutions manual for Modern Elementary Statistics, 12/e by Freund & Perles TEST BANK for Modern Elementary Statistics, 12/e Freund & Perles Solutions manual for Modern Physics, 2/E Randy Harris Solutions manual for Numerical methods for engineers 5th by Chapra Solutions manual for Operating Systems: Internals and Design Principles 6e by William Stallings, PH.D. SM (pearson) Solutions manual for Operations Management 10e William J. Stevenson TEST BANK for Operations Management 10e William J. Stevenson Solutions manual for Operations Management 8e by Jay Heizer Barry Render SM (Pearson) Test bank for Operations Management 8e by Jay Heizer Barry Render TB (Pearson) Test bank for Operations Management 9e by Jay Heizer Barry Render tb Solutions manual for Operations Management 9e William J. Stevenson ( test bank for Operations Management 9e William J. Stevenson (TB) Solutions manual for Operations Management 9th by Jay Heizer Barry Render sm Test bank for Organizational Behavior, by Stephen P. and Timothy A. 13th Edition tb TEST BANK for Organizational Behaviour, Fourth Canadian Ed., 4E Robins Solutions manual for Physics for Scientists & Engineers with Modern Physics Vol. 2&3, 4/E Doug Giancoli ISM Solutions manual for Power System Analysis By John J. Grainger, William D. Stevenson Jr Instructor manual for Practical Financial Management 5th Edition William R. Lasher IM + TB Instructor manual for Practical Financial Management 5th Edition William R. Lasher IM + TB TEST BANK for Principles of Auditing 15e by Whittington Solutions manual for Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole Solutions manual for Probability and Statistical Inference 7th edition, Hogg & Tanis Solutions manual for Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) Solutions manual for Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis Solutions manual for Process Dynamics and Control 2nd Ed. by Seborg, Edgar, and Mellichamp Solutions manual for Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual Solutions manual for Separation Process Principles, 2nd Ed.,by Seader, Henley Test bank for South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 , volume 3 (Cengage) Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe test bank Solutions manual for South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 , volume 3 (Cengage)Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe solution manual Solution manual for South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis test bank for South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis tb Test bank for TB for Modern Labor Economics: Theory and Public Policy, 10/E, Ronald G. Ehrenberg. test bank for cost Accounting 12e by Horngren Solutions manual for The Economics of Money,Banking,and Financial Market 8th edition by Frederic S. Mishkin solutions manual Test bank for The Economics of Money,Banking,and Financial Market 8th edition by Frederic S. Mishkin test bank Solutions manual for Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition test bank for Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston Solutions manual for Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston Solutions manual for Unit Operations of Chemical Engineering (7th) By Warren McCabe, Statics 8th Edition ,By F. P. Beer, E. R. solutions manual and Test Bank contact me with , soltbcollect (at) gmail.com (my email : soltbcollect (at) gmail.com, soltbcollect @ gmail.com), these are parts of our list,, if the solutions manual or test bank isnÍt on the list, please email to me.,too. I can find it from my friends, please trust on Please search it by Ctrl +F === Subject: Re: Snow on Mars! ETAsAhQhNJ/8KFfwrSb03Ztmd8GpWm1JnQIUaKLZaJcvbpdiiZhegF0EKuwwy9k= Marvin the Martian That was more than just snow. that was frosty Tang. Or just more of Mafia NASA BS Go figure Trebert === Subject: Re: Snow on Mars! posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > The Phoenix Mars lander has detected SNOW fall on the planet Mars! > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. By that thinking, Siberia should be the energy capital of the Earth. There have been many AIAA papers on making fuel, in situ, on Mars. What > is needed is a source of hydrogen. The first concepts involved bringing a > hydrogen source with the landing craft to convert CO2 into methane fuel. Once ice was found on Mars, it was considered as a hydrogen source. > However, some felt that it would be unusable if it was contaminated with > salts. The discovery of snow means there is a source of nearly pure water to > convert to hydrogen. Did yourself, Zubrin and William Mook get a room yet? ~ BG === Subject: Re: Snow on Mars! posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > The Phoenix Mars lander has detected SNOW fall on the planet Mars! This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. NASA's Phoenix Mars Lander proves signs of snowfall on Mars http://topnews.us/content/25969-nasas-phoenix-mars-lander-proves-signs- > snowfall-mars Sure thing, as in plain old water/ice kind of snow, all because the regular laws of physics simply do not apply, any more so than the best available objective science that more than proves otherwise, apparently isn't worth squat to you. ~ BG === Subject: Re: Snow on Mars! posting-account=nf79RwoAAABXjvy5ztMzmPxgY1WGoktI Gecko/2008120122 Firefox/3.0.5,gzip(gfe),gzip(gfe) > The Phoenix Mars lander has detected SNOW fall on the planet Mars! This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. NASA's Phoenix Mars Lander proves signs of snowfall on Mars http://topnews.us/content/25969-nasas-phoenix-mars-lander-proves-signs- > snowfall-mars Sure thing, as in plain old water/ice kind of snow, all because the regular laws of physics simply do not apply, any more so than the best available objective science that more than proves otherwise, apparently isn't worth squat to you. ~ BG === Subject: Re: Snow on Mars! > The Phoenix Mars lander has detected SNOW fall on the planet Mars! This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. NASA's Phoenix Mars Lander proves signs of snowfall on Mars http://topnews.us/content/25969-nasas-phoenix-mars-lander-proves-signs- > snowfall-mars > And being red, plenty of iron ore to make cast iron cities. === Subject: Re: Snow on Mars! The Phoenix Mars lander has detected SNOW fall on the planet Mars! This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. NASA's Phoenix Mars Lander proves signs of snowfall on Mars http://topnews.us/content/25969-nasas-phoenix-mars-lander-proves-signs- > snowfall-mars > And being red, plenty of iron ore to make cast iron cities. And giant robot slaves. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 === Subject: Re: Snow on Mars! The Phoenix Mars lander has detected SNOW fall on the planet Mars! idiot > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. [snip rest of crap] Hey stooopid - do it in Wisconsin and show us how it's done. Will rain work? How about a toilet juice? Make fuel from tap water. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 === Subject: Re: Snow on Mars! > > The Phoenix Mars lander has detected SNOW fall on the planet Mars! idiot > > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. > [snip rest of crap] Hey stooopid - do it in Wisconsin and show us how it's done. Will rain > work? How about a toilet juice? Make fuel from tap water. Actually, Dr. Zubrin et al already built a working device and published the results in the AIAA journals. There are two or three competing concepts. But you don't read any of the journals, do you? You're just a damned pathetic loser. If you weren't such a sociopathic jackass with an inferiority complex three standard deviations bigger than normal, you would have asked that NICELY instead of being a complete and utter dumb ass. I see I need to killfile you in BOTH GROUPS to get away from your innane, idiot, and pig-ignorant posts. === Subject: Re: Snow on Mars! > The Phoenix Mars lander has detected SNOW fall on the planet Mars! idiot > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. > [snip rest of crap] Hey stooopid - do it in Wisconsin and show us how it's done. Will rain > work? How about a toilet juice? Make fuel from tap water. Actually, Dr. Zubrin et al already built a working device and published > the results in the AIAA journals. There are two or three competing > concepts. [snip rest of crap] http://en.wikipedia.org/wiki/The_Case_for_Mars http://en.wikipedia.org/wiki/Robert_Zubrin You go to Mars with Zubrin. Uncle Al prefers empirical reality. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 === Subject: Re: Snow on Mars! > The Phoenix Mars lander has detected SNOW fall on the planet Mars! > > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. And by what efficient process would you disassociate the > hydrogen and oxygen? It hardly matters how efficient the process is if it is the only hotdog stand in town where you can get fuel. What does matter is how do you soft land the gas liquification plant along with all the people and supplies needed to run it. -- Jim Pennino === Subject: Re: Snow on Mars! > > > The Phoenix Mars lander has detected SNOW fall on the planet Mars! > > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. > > By that thinking, Siberia should be the energy capital of the Earth. > > There have been many AIAA papers on making fuel, in situ, on Mars. What > is needed is a source of hydrogen. The first concepts involved bringing > a hydrogen source with the landing craft to convert CO2 into methane > fuel. > > Once ice was found on Mars, it was considered as a hydrogen source. > However, some felt that it would be unusable if it was contaminated > with salts. > > The discovery of snow means there is a source of nearly pure water to > convert to hydrogen. > > You are also going to need an oxidizer. That comes when you electrolyze the water to get the hydrogen. > > Yep, now all you would need is a nuclear power plant and a gas > liquidifcation plant. Yes, the original proposals included a nuclear power plant. Methane is a > liquid at moderate pressures at ambient Martian temperatures. > > Yeah, sure. They'll use rockets to get there, too. It's called technology, and it's > developed by engineers. You can read about it here: > http://www.aiaa.org/content.cfm?pageid=406&gTable=mtgpaper&gID=14696 Or, you can shove your ignorant poser head up your ass and eat and > die. Either way, I'm good. < PLONK > I've no time for pretenders, posers and dumbs anymore. Yet another clueless dreamer that thinks the technology exists to soft land millions upon millions of tons of equipement, hundreds of people to assemble and run it, along with all their supplies, on Mars. -- Jim Pennino === Subject: Re: Snow on Mars! > > The Phoenix Mars lander has detected SNOW fall on the planet Mars! > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. > By that thinking, Siberia should be the energy capital of the Earth. > If gathering up snow on Mars to get water sounds familiar, check out the 1955 movie Conquest Of Space sometime. No cute, personality-filled monkey in it, but it does have a blonde floozy to make up for the monkey deficit. ;-) Pat === Subject: Re: Snow on Mars! : :If gathering up snow on Mars to get water sounds familiar, check out the :1955 movie Conquest Of Space sometime. :No cute, personality-filled monkey in it, but it does have a blonde :floozy to make up for the monkey deficit. ;-) : Well, given a choice between the two, I'll take the blonde floozy and leave Pat to spank the monkey... -- I'll learn to work the saxophone. I'll play just what I feel. Drink Scotch whisky all night long And die behind the wheel. -- Deacon Blues, Steely Dan === Subject: Re: Snow on Mars! <_V64m.771634$yE1.430036@attbi_s21> The Phoenix Mars lander has detected SNOW fall on the planet Mars! > > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. And by what efficient process would you disassociate the hydrogen and > oxygen? The AIAA papers said electrolysis. This is the commonly accepted method. You knew that, of course. > NASA's Phoenix Mars Lander proves signs of snowfall on Mars > > http://topnews.us/content/25969-nasas-phoenix-mars-lander-proves-signs- > snowfall-mars > === Subject: Re: Snow on Mars! : :> The Phoenix Mars lander has detected SNOW fall on the planet Mars! :> :> This is good news. It means you can gather pure water to make fuel on :> Mars simply by gathering up the snowfall. :> :> And by what efficient process would you disassociate the hydrogen and :> oxygen? : :The AIAA papers said electrolysis. This is the commonly accepted method. : :You knew that, of course. : And has anyone bothered to point out to Marvin that the amount of water in that 'snow' (actually 'diamond dust') is so small that you'd be hard pressed to moisten a towel with it and that it only occurs at the poles? -- Ignorance is preferable to error, and he is less remote from the truth who believes nothing than he who believes what is wrong. -- Thomas Jefferson === Subject: Re: Snow on Mars! > : And has anyone bothered to point out to Marvin that the amount of > water in that 'snow' (actually 'diamond dust') is so small that you'd > be hard pressed to moisten a towel with it and that it only occurs at > the poles? > You fail to grasp the point. The point is that they are steadily documenting an active water cycle on Mars. A persistent water cycle is perhaps the most central requirement for the possibility of life. They are also steadily building a case for ice-ages waxing and waning on Mars. Meaning the possibility of recent warmer climates are also quite possible. Combine that with the fact that much of the soil near the equator has as much as 50% water ice in just the top three meters of soil. Then the notion that Mars has been dead and dry since it lost it's atmosphere billions of years ago is quickly being replaced. With a view of a Mars with periodic warming and water melting out from underground from time to time. Even with the current atmosphere, a crater lake being filled from an underground spring could exist on the surface of Mars right now for an indefinite period. As the crater lake would have an ice cap. And an underground spring could certainly refill a lake faster than the ice cap would ablate away. The water on Mars didn't evaporate totally into space, it mostly went underground. This realization changes the long held assumption that Mars is a long dead desert. Mars is easily the best candidate for life elsewhere in this solar system. If we're going to look for life elsewhere, Mars is it. Now, the idea that manned missions is the way to go is another topic. I think robots are far faster and cheaper, and can get what we need. Manned missions should be saved for exploiting space. Robots for exploring. Jonathan s > -- > Ignorance is preferable to error, and he is less remote from the > truth who believes nothing than he who believes what is wrong. > -- Thomas Jefferson === Subject: Re: Snow on Mars! : :> : :> :> And has anyone bothered to point out to Marvin that the amount of :> water in that 'snow' (actually 'diamond dust') is so small that you'd :> be hard pressed to moisten a towel with it and that it only occurs at :> the poles? :> : :You fail to grasp the point. The point is that they are steadily documenting :an active water cycle on Mars. A persistent water cycle is perhaps the :most central requirement for the possibility of life. They are also steadily :building a case for ice-ages waxing and waning on Mars. Meaning :the possibility of recent warmer climates are also quite possible. : You fail to grasp the point. The point is that, despite Marvin's bleating about being able to make fuel out of this 'snow', there's not enough water in that snow to make fuel a model airplane. : :Combine that with the fact that much of the soil near the equator has as :much as 50% water ice in just the top three meters of soil. : Bull. That's not a 'fact'. Guess I'm going to have to drop you back into my own personal loony bin if this is the best you get. -- The reasonable man adapts himself to the world; the unreasonable man persists in trying to adapt the world to himself. Therefore, all progress depends on the unreasonable man. --George Bernard Shaw === Subject: Re: Snow on Mars! <6352559c4j429nsnhec5u4tsluv857g0ah@4ax.com> posting-account=42V-qwoAAABOAKkANAhMmpW4F3ZbRLXb Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) : > :> The Phoenix Mars lander has detected SNOW fall on the planet Mars! > :> :> This is good news. It means you can gather pure water to make fuel on > :> Mars simply by gathering up the snowfall. > : :> And by what efficient process would you disassociate the hydrogen and > :> oxygen? > : > :The AIAA papers said electrolysis. This is the commonly accepted method. > : > :You knew that, of course. > : And has anyone bothered to point out to Marvin that the amount of > water in that 'snow' (actually 'diamond dust' Trolling Brad Guth, or do you have a cite? Either way, I'm good with it. ;>) Mark L. Fergerson === Subject: Re: Snow on Mars! :> :> : :> :> The Phoenix Mars lander has detected SNOW fall on the planet Mars! :> :> :> :> This is good news. It means you can gather pure water to make fuel on :> :> Mars simply by gathering up the snowfall. :> :> :> :> And by what efficient process would you disassociate the hydrogen and :> :> oxygen? :> : :> :The AIAA papers said electrolysis. This is the commonly accepted method. :> : :> :You knew that, of course. :> : :> :> And has anyone bothered to point out to Marvin that the amount of :> water in that 'snow' (actually 'diamond dust' : : Trolling Brad Guth, or do you have a cite? : : Either way, I'm good with it. ;>) : The reason it's in quotes like that is because that's what that type of 'snow' is called. It occurs in the Arctic and other places that get very cold here on Earth. http://www.islandnet.com/~see/weather/elements/ddust.htm http://news.nationalgeographic.com/news/2009/07/090702-snow-mars-phoenix.htm l If you melted it all in a pan, [you] would be barely wetting the surface, Smith said. -- The odds get even - You blame the game. The odds get even - The stakes are the same. You bet your life. -- You Bet Your Life, Rush === Subject: Re: Snow on Mars! > > The Phoenix Mars lander has detected SNOW fall on the planet Mars! > This is good news. It means you can gather pure water to make fuel on > Mars simply by gathering up the snowfall. > By that thinking, Siberia should be the energy capital of the Earth. > There have been many AIAA papers on making fuel, in situ, on Mars. What > is needed is a source of hydrogen. The first concepts involved bringing > a hydrogen source with the landing craft to convert CO2 into methane > fuel. Once ice was found on Mars, it was considered as a hydrogen source. > However, some felt that it would be unusable if it was contaminated > with salts. The discovery of snow means there is a source of nearly pure water to > convert to hydrogen. > You are also going to need an oxidizer. That comes when you electrolyze the water to get the hydrogen. > > Yep, now all you would need is a nuclear power plant and a gas > liquidifcation plant. Yes, the original proposals included a nuclear power plant. Methane is a > liquid at moderate pressures at ambient Martian temperatures. > > Yeah, sure. They'll use rockets to get there, too. It's called technology, and it's > developed by engineers. You can read about it here: > http://www.aiaa.org/content.cfm?pageid=406&gTable=mtgpaper&gID=14696 Or, you can shove your ignorant poser head up your ass and eat and > die. Either way, I'm good. < PLONK > I've no time for pretenders, posers and dumbs anymore. Taking off, are you? === Subject: Re: Snow on Mars! > Taking off, are you? So, like the other dumbass dip that troll the boards, you're back to ignoring all the physics and science content and just posting your little asshole quips. fine. === Subject: Re: definition of force posting-account=nHkyWQoAAAAZj13mfknn7vPxoYn-Mvx3 CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) On Jul 2, 6:52am, Juan R. Gonz.87lez-.8dlvarez > (...) > Nobody has given a general expression for the definition offorce. > Several definitions given here are valid only in special cases of pure > states, non-dissipative systems... Nobody has differentiated theforceF from theforceQ. One poster > believes, in their own words, that the general definition of force in > Lagrange's Equations is more general; this is not true. Q is the usual notation for Lagrangian forces (see e.g. Goldstein > textbook in mechanics). This notation is used for avoid confusion with F. > Only in some special cases F = Q = ma. For the definition of Q and its > relation to potential energy V see >http://canonicalscience.blogspot.com/2007/07/generalized-potential- > energy.html One guy tried to give the definition of LagrangianforceQ (he denoted it > F) in terms of kinetic energy T instead of in terms of some potential V > (Goldstein uses the symbol U for the generalized potential). Nobody who > replied him has noticed this. To my question Could you write the definition offorceand relate it to > the equation of motion for an electron? some posters replied F=dp/dt; > definition offorce, the equation of motion, or both. Juan,forceis not afundamentalquantity in physics, at least in the > SI system. In the SI system there are 7fundamentalunits: kilogram, > meter, candela, second, ampere, kelvin, and mole. Don't confuse the base units in a particular system of measurement > with thefundamentalquantities in a particular field of study. That > are not neccessarily the same. I don't confuse anything. Did you read carefully? I said in the SI > systemforceis not a funfamental quantity. Is it according to you? In the SI system, the Newton is not a base unit but is, instead a > derived unit . > That says nothing about whether force is a fundamental quantity . Your impressions to the contrary notwithstanding, I am not trying to > say thatforceis afundamentalquantity. I'm limiting myself to > saying that your use of SI to demonstrate thatforceis not a >fundamentalquantity is utterly misguided. You sound ignorant I'm afraid. I am surely ignorant of many things. But I'm right about what SI does > and does not say. And you're wrong about what SI does and does not > say. A quantity isfundamentalwhen it's > definition does not presuppose a law in which a definition of the > quantity is required. That means that whether a quantity isfundamentaldepends on what > definitions you are using. It is a function of your formalism. It is > not a physical property of the universe. Except, of course, to the > extent that which formalisms happen to work well is a physical > property of the universe. I'm perfectly happy to be educated about which formalisms work > perfectly well without takingforceasfundamental. But I'll be > damned if I'll listen to half-wits like yourself yammering on about > how the units defined by SI have anything whatsoever to do with the > question of what quantities arefundamental Perhaps that is your problem. You think that SI's definition of the > Newton and the kilogram amount tofundamentaldefinitions of mass and > offorce. If so, that's a rather basic confusion that you should work > on clearing up. Along with the confusion of unit and quantity. > SI defines units, not quantities. If someone came up with a way of measuringforceto 11 sig figs > tomorrow and also had a way of hooking up accelerometers to test > masses that could leverage that into a 10 sig fig standard for mass, > SI could redefine the Newton as the base unit in terms of that > measurement and the kilogram as the resulting derived unit. I tacitly > assume that this hypothetical 11 sig fig measurement capability is > reproducible and, therefore amounts to the availability of a 11 sig > figforcestandard. [No, I'm not holding my breath waiting for this unlikely circumstance > to occur] Would this circumstance change anything about how the Universe works? > Would we have to change any of our models? Would that mean that > suddenly force isfundamentaland mass is not? No, no and no. See, I'm not advocatingforceas being fundamental. I'm just saying > that you shouldn't be using metrologists as your reference sources for > a ruling on what's fundamental and what's not in the formalism that > you happen to be using at the moment. Furthermore, ther are seevral procedures for measuring mass that do > not require the concept offorce, only the notion of Lagrangian > interaction. I suppose you're trying to say that, for instance, you can define mass > in terms of the observed acceleration of a charged object in an > electric field and since you're not using force in the formalism by > which you describe this interaction, that means that force is not a >fundamentalconcept. Yeah, that seams reasonable. [Seriously. I do accept that > conclusion. force is not afundamentalconcept in any formalism > which does not use the concept of force. And it's also not a >fundamentalconcept in any formalism which definesforcein terms of > mass]. But there are also several procedures for measuringforcethat do not > require the concept of mass. And those procedures still work, even if > you describe them using formalisms in which force does not exist. > Does the existence of such procedures mean that your own logic > requires you to consider that force is fundamentalafter all? Please free to create/measure a force in the absence of mass/energy Nice spin on the question. You don't want me to measure force in a way that is independent of mass and energy. You want me to measure force in the absence of mass and energy. I don't accept that challenge as meaningful. So let's instead try to measure force in a way that is not dependant on an established standard for mass or energy. Method 1: Take a container filled with water. Heat the container and vent steam to arrive at the triple-point. Measure the pressure exerted on one square meter of the container's surface. Take this as your standard for force. [I assume that you will object that I've implicitly defined a standard for mass and energy by using the triple-point of water along with an explicit standard of length] Method 2: Take a uniform mild steel rod of some carefully prescribed composition and apply tension sufficient to stretch the rod by 0.1% off its rest length. Take the required force as your force standard. Method 3: Use a piezo-electric crystal or load cell. Method 4: Pass one Coulomb of electrons per second through each of two parallel wires. Take the resulting attractive force as your force standard. [define the Coulomb by counting electrons or some other standard that does not involve force]. > Also, please feel free to present here a definition offorcethat does > not rest on mass/energy. In mathematics, our practice is to leave fundamental quantities undefined. We may characterize them. But we don't define them. But here goes: Definition for force: A force is an interaction between two objects which, in the absence of other forces, will tend to attract those objects to one another or to repel those objects from one another A force is a vector quantitiy and aligns on the axis between the two interacting objects. Forces sum linearly. (i.e. if two men push on a crate, the total force is twice that of one man alone) Newton's first law: If the total force on an object is zero, that object will not accelerate. And vice versa. Newton's second law: Acceleration is proportional to applied force. Acceleration is inversely proportional to mass. Newton's third law: In an interacting pair of objects, the force of one on the other is equal and opposite to the force of the other on the one. Again, in case you've forgotten, I'm not advocating that force is fundamental. What I am trying to do is to get you to post something reasonable in defense of the proposition that mass is fundamental and force is not. So far what I've seen from you amounts to [paraphrasing] Mass is fundamental because the kilogram is a base unit in SI You can measure mass without having a force standard A defined quantity is not fundamental if its definition is in terms of other defined quantities A defined quantity is not fundamental if its definition is circular > Talk is cheap. Just go ahead, I look forward to your definitions. We > are talking about physics here. if you mean the forceof God or > something like that, I cannot know, maybe your local priest can tell > you that it exists as a dogma. Can you dial back the rhetoric a tad? === Subject: Re: definition of force posting-account=UlqQigoAAADUKXgHhhqS3Em_KfDZERQh Trident/4.0; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > On Jul 2, 6:52am, Juan R. Gonz.87lez-.8dlvarez > (...) > Nobody has given a general expression for the definition offorce. > Several definitions given here are valid only in special cases of pure > states, non-dissipative systems... Nobody has differentiated theforceF from theforceQ. One poster > believes, in their own words, that the general definition of force in > Lagrange's Equations is more general; this is not true. Q is the usual notation for Lagrangian forces (see e.g. Goldstein > textbook in mechanics). This notation is used for avoid confusion with F. > Only in some special cases F = Q = ma. For the definition of Q and its > relation to potential energy V see >http://canonicalscience.blogspot.com/2007/07/generalized-potential- > energy.html One guy tried to give the definition of LagrangianforceQ (he denoted it > F) in terms of kinetic energy T instead of in terms of some potential V > (Goldstein uses the symbol U for the generalized potential). Nobody who > replied him has noticed this. To my question Could you write the definition offorceand relate it to > the equation of motion for an electron? some posters replied F=dp/dt; > definition offorce, the equation of motion, or both. Juan,forceis not afundamentalquantity in physics, at least in the > SI system. In the SI system there are 7fundamentalunits: kilogram, > meter, candela, second, ampere, kelvin, and mole. Don't confuse the base units in a particular system of measurement > with thefundamentalquantities in a particular field of study. That > are not neccessarily the same. I don't confuse anything. Did you read carefully? I said in the SI > systemforceis not a funfamental quantity. Is it according to you? In the SI system, the Newton is not a base unit but is, instead a > derived unit . > That says nothing about whether force is a fundamental quantity . Your impressions to the contrary notwithstanding, I am not trying to > say thatforceis afundamentalquantity. I'm limiting myself to > saying that your use of SI to demonstrate thatforceis not a >fundamentalquantity is utterly misguided. You sound ignorant I'm afraid. I am surely ignorant of many things. But I'm right about what SI does > and does not say. And you're wrong about what SI does and does not > say. A quantity isfundamentalwhen it's > definition does not presuppose a law in which a definition of the > quantity is required. That means that whether a quantity isfundamentaldepends on what > definitions you are using. It is a function of your formalism. It is > not a physical property of the universe. Except, of course, to the > extent that which formalisms happen to work well is a physical > property of the universe. I'm perfectly happy to be educated about which formalisms work > perfectly well without takingforceasfundamental. But I'll be > damned if I'll listen to half-wits like yourself yammering on about > how the units defined by SI have anything whatsoever to do with the > question of what quantities arefundamental Perhaps that is your problem. You think that SI's definition of the > Newton and the kilogram amount tofundamentaldefinitions of mass and > offorce. If so, that's a rather basic confusion that you should work > on clearing up. Along with the confusion of unit and quantity. > SI defines units, not quantities. If someone came up with a way of measuringforceto 11 sig figs > tomorrow and also had a way of hooking up accelerometers to test > masses that could leverage that into a 10 sig fig standard for mass, > SI could redefine the Newton as the base unit in terms of that > measurement and the kilogram as the resulting derived unit. I tacitly > assume that this hypothetical 11 sig fig measurement capability is > reproducible and, therefore amounts to the availability of a 11 sig > figforcestandard. [No, I'm not holding my breath waiting for this unlikely circumstance > to occur] Would this circumstance change anything about how the Universe works? > Would we have to change any of our models? Would that mean that > suddenly force isfundamentaland mass is not? No, no and no. See, I'm not advocatingforceas being fundamental. I'm just saying > that you shouldn't be using metrologists as your reference sources for > a ruling on what's fundamental and what's not in the formalism that > you happen to be using at the moment. Furthermore, ther are seevral procedures for measuring mass that do > not require the concept offorce, only the notion of Lagrangian > interaction. I suppose you're trying to say that, for instance, you can define mass > in terms of the observed acceleration of a charged object in an > electric field and since you're not using force in the formalism by > which you describe this interaction, that means that force is not a >fundamentalconcept. Yeah, that seams reasonable. [Seriously. I do accept that > conclusion. force is not afundamentalconcept in any formalism > which does not use the concept of force. And it's also not a >fundamentalconcept in any formalism which definesforcein terms of > mass]. But there are also several procedures for measuringforcethat do not > require the concept of mass. And those procedures still work, even if > you describe them using formalisms in which force does not exist. > Does the existence of such procedures mean that your own logic > requires you to consider that force is fundamentalafter all? Please free to create/measure a force in the absence of mass/energy Nice spin on the question. You don't want me to measure force in a > way that is independent of mass and energy. You want me to measure > force in the absence of mass and energy. I don't accept that challenge as meaningful. So let's instead try to measure force in a way that is not dependant > on an established standard for mass or energy. Method 1: Take a container filled with water. Heat the container and vent steam > to arrive at the triple-point. Measure the pressure exerted on one > square meter of the container's surface. Take this as your standard > for force. [I assume that you will object that I've implicitly defined a standard > for mass and energy by using the triple-point of water along with an > explicit standard of length] Method 2: Take a uniform mild steel rod of some carefully prescribed composition > and apply tension sufficient to stretch the rod by 0.1% off its rest > length. Take the required force as your force standard. Method 3: Use a piezo-electric crystal or load cell. Method 4: Pass one Coulomb of electrons per second through each of two parallel > wires. Take the resulting attractive force as your force standard. > [define the Coulomb by counting electrons or some other standard that > does not involve force]. Also, please feel free to present here a definition offorcethat does > not rest on mass/energy. In mathematics, our practice is to leave fundamental quantities > undefined. We may characterize them. But we don't define them. But > here goes: Definition for force: A force is an interaction between two objects > which, in the absence of other forces, will tend to attract those > objects to one another or to repel those objects from one another A force is a vector quantitiy and aligns on the axis between the two > interacting objects. > Forces sum linearly. (i.e. if two men push on a crate, the total force > is twice that of one man alone) Newton's first law: If the total force on an object is zero, that > object will not accelerate. And vice versa. Newton's second law: Acceleration is proportional to applied force. > Acceleration is inversely proportional to mass. Newton's third law: In an interacting pair of objects, the force of > one on the other is equal and opposite to the force of the other on > the one. Again, in case you've forgotten, I'm not advocating that force is > fundamental. What I am trying to do is to get you to post something > reasonable in defense of the proposition that mass is fundamental and > force is not. I have but you dismiss it a priori. Mass is more fundamental because it is defined as quantity of matter. This definition does not require knowledge of time or length. > So far what I've seen from you amounts to [paraphrasing] Mass is fundamental because the kilogram is a base unit in SI > You can measure mass without having a force standard > A defined quantity is not fundamental if its definition is in terms > of other defined quantities > A defined quantity is not fundamental if its definition is circular Talk is cheap. Just go ahead, I look forward to your definitions. We > are talking about physics here. if you mean the forceof God or > something like that, I cannot know, maybe your local priest can tell > you that it exists as a dogma. Can you dial back the rhetoric a tad?- Hide quoted text - You are right. Rhetoric is useless. The concept of force has many problems. One is that in entails causality. Fundamental qunatities should be free from causal powers. Otherwise, the foundation is metaphysical. I guess I started from the end. But that may make sense to you. This is also one reason Einstein wanted to eliminate force and base physics only on geometry. In that way, a quasi-enclosed universe is free from causal powers. If causes are accepted as part of this universe, then lead to a first cause, as Newton said in Principia. In a nut shell... Mike - Show quoted text - === Subject: Re: DOUBLETHINK IN EINSTEINIANA posting-account=tNh-2AoAAACqdWo2IikcW-FF_IGUAvWf AppleWebKit/530.18 (KHTML, like Gecko) Version/4.0.1 Safari/530.18,gzip(gfe),gzip(gfe) > http://www.liferesearchuniversal.com/1984-17.html#seventeen > George Orwell: Doublethink means the power of holding two > contradictory beliefs in one's mind simultaneously, and accepting both > of them. The Party intellectual knows in which direction his memories > must be altered; he therefore knows that he is playing tricks with > reality; but by the exercise of doublethink he also satisfies himself > that reality is not violated. The process has to be conscious, or it > would not be carried out with sufficient precision, but it also has to > be unconscious, or it would bring with it a feeling of falsity and > hence of guilt. Doublethink lies at the very heart of Ingsoc, since > the essential act of the Party is to use conscious deception while > retaining the firmness of purpose that goes with complete honesty. To > tell deliberate lies while genuinely believing in them, to forget any > fact that has become inconvenient, and then, when it becomes necessary > again, to draw it back from oblivion for just so long as it is needed, > to deny the existence of objective reality and all the while to take > account of the reality which one denies - all this is indispensably > necessary. Even in using the word doublethink it is necessary to > exercise doublethink. For by using the word one admits that one is > tampering with reality; by a fresh act of doublethink one erases this > knowledge ; and so on indefinitely, with the lie always one leap ahead > of the truth. For those of us who believe in physics, this separation between past, > present and future is only an illusion, however tenacious - Albert > Einstein Brian Greene: I certainly got very used to the idea of relativity, > and therefore I can go into that frame of mind without it seeming like > an effort. But I feel and think about the world as being organized > into past, present and future. I feel that the only moment in time > that's really real is this moment right now. And I feel [that what > happened a few moments ago] is gone, and the future is yet to be. It > still feels right to me. But I know in my mind intellectually that's > wrong. Relativity establishes that that picture of the universe is > wrong, and if I work hard, I can force myself to recognize the fallacy > in my view or thinking; but intuitively it's still what I feel. So > it's a daily struggle to keep in mind how the world works, and > juxtapose that with experience that [I get] a thousand, even million > times a day from ordinary comings and goings. http://www.pitt.edu/~jdnorton/Goodies/passage/index.html > John Norton: A common belief among philosophers of physics is that > the passage of time of ordinary experience is merely an illusion. The > idea is seductive since it explains away the awkward fact that our > best physical theories of space and time have yet to capture this > passage. I urge that we should resist the idea. We know what illusions > are like and how to detect them. Passage exhibits no sign of being an > illusion....Following from the work of Einstein, Minkowski and many > more, physics has given a wonderfully powerful conception of space and > time. Relativity theory, in its most perspicacious form, melds space > and time together to form a four-dimensional spacetime. The study of > motion in space and and all other processes that unfold in them merely > reduce to the study of an odd sort of geometry that prevails in > spacetime. In many ways, time turns out to be just like space. In this > spacetime geometry, there are differences between space and time. But > a difference that somehow captures the passage of time is not to be > found. There is no passage of time. There are temporal orderings. We > can identify earlier and later stages of temporal processes and > everything in between. What we cannot find is a passing of those > stages that recapitulates the presentation of the successive moments > to our consciousness, all centered on the one preferred moment of > now. At first, that seems like an extraordinary lacuna. It is, it > would seem, a failure of our best physical theories of time to capture > one of time's most important properties. However the longer one works > with the physics, the less worrisome it becomes....I was, I confess, a > happy and contented believer that passage is an illusion. It did > bother me a little that we seemed to have no idea of just how the news > of the moments of time gets to be rationed to consciousness in such > rigid doses.....Now consider the passage of time. Is there a > comparable reason in the known physics of space and time to dismiss it > as an illusion? I know of none. The only stimulus is a negative one. > We don't find passage in our present theories and we would like to > preserve the vanity that our physical theories of time have captured > all the important facts of time. So we protect our vanity by the > stratagem of dismissing passage as an illusion. http://www.symmetrymagazine.org/breaking/2009/07/01/world-science-fes... > There are many theoretical physicists who think the flow of time is > an illusion, he says. And I think that's a great mistake.83according > to quantum physics you don't know the outcome of events until they > happen. We know what happened in the past, there's a time called the > present when things are happening, and there's a time in the future > which is not yet determined. That's my view on it, which is not a very > widely supported one. A professor emeritus of applied mathematics at > the University of Capetown, Ellis is the co-author with Stephen > Hawking of The Large Scale Structure of Space Time, and investigates > the physical foundations of the flow of time. Pentcho Valev > pva...@yahoo.com links you share. The future is already cast in stone, so write away. Enjo(y)... -- Mahipal === Subject: Re: DOUBLETHINK IN EINSTEINIANA posting-account=ASfdVQoAAADpvgPOQMrGb2BSzAnk0jYp Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > George Orwell: Doublethink means the power of holding two > contradictory beliefs in one's mind simultaneously, and accepting both > of them. The Party intellectual knows in which direction his memories > must be altered; he therefore knows that he is playing tricks with > reality; but by the exercise of doublethink he also satisfies himself > that reality is not violated. The process has to be conscious, or it > would not be carried out with sufficient precision, but it also has to > be unconscious, or it would bring with it a feeling of falsity and > hence of guilt. Doublethink lies at the very heart of Ingsoc, since > the essential act of the Party is to use conscious deception while > retaining the firmness of purpose that goes with complete honesty. To > tell deliberate lies while genuinely believing in them, to forget any > fact that has become inconvenient, and then, when it becomes necessary > again, to draw it back from oblivion for just so long as it is needed, > to deny the existence of objective reality and all the while to take > account of the reality which one denies - all this is indispensably > necessary. Even in using the word doublethink it is necessary to > exercise doublethink. For by using the word one admits that one is > tampering with reality; by a fresh act of doublethink one erases this > knowledge ; and so on indefinitely, with the lie always one leap ahead > of the truth. That sounds like a perfect description of Modern Theoretical Physics! glird === Archive: No === === Subject: rho i'm the king in research http://tinyurl.com/tartes === Subject: Re: Photon may not have zero charge ETAsAhQbFUqjFj3ZyHLEhoqKNkYrIs3YgQIUV7gupb9saxzTuJs2apmLWQ5lCc8= gusky It is virtual photons that create charge. It is virtual photons that create magnetic fields. Brian Greene told us all this on NOVA Feynman knew this when he got the Nobel for QED I always knew this. TreBert === Subject: Re: Photon may not have zero charge <23740-4A51FAF8-3747@storefull-3252.bay.webtv.net> posting-account=5ehs9woAAAAPdLASkVa5y5b2hV4py5md Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; FDM; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > gusky It is virtual photons that create charge. It is virtual photons > that create magnetic fields. Brian Greene told us all this on NOVA > Feynman knew this when he got the Nobel for QED I always knew this. > TreBert We have to find out exactly what is the difference between virtual and non-virtual, for as you said it only virtual photons will produce the desired out-come. === Subject: Re: More about the history of water on Mars. ETAuAhUAvI/4Q6vuhQ3dwIY7JFFjZ3M4bnECFQDH5W8XnN6lHf8XlWS9bWKB4gx6Tg== Martian Sun's inferred and ultra violet rays will not allow water molecules. This is reality. NASA Mafia organization will not face this physics. Water on Mars surface is good PR for a broken down NASA. A NASA that stole billions and billions. A NASA that paid $25,000,000 for each of the shuttles toilets A shuttle program that circled the Earth for 40 years A NASA that can't even copy the Saturn V. Mars has dust storms to create great erosion. Mars has not a molecule of water on its surface TreBert PS 100 feet down Mars has red clams,but no lobsters === Subject: Re: Higgs Boson posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) > If the higgs boson confers mass on non mattermatter. does this mean > the conservation of energy law is broken since mass is energy. No, not necessarily. Conservation of energy doesn't mean conservation > of mass. It means that the *sum* of all energy contributions, > including those of rest mass, is conserved. It does not mean that the > individual contributions are each conserved. ------------------ > smarty Oracle of Delphi who said individual contribution??!!! > now jsut tell us if : in the **overall system ** --- > mass is conserved ???!!! No! We know this already. In experiment. I'll give you an example. > SLAC has created pairs of protons from pairs of colliding electrons. > There is nothing in the initial state except an electron-positron > pair, and there is nothing in the final state other than a proton- > antiproton pair. The final state mass is 1800 times larger than the > initial state mass. No, mass is not conserved in an isolated system. 180 or 1800 times? Mass and energy are conserved in an isolated system. I don't know where you got the idea that summative mass is conserved > in an isolated system? Read well. You claim to have a Ph.D and you don't know how to read > yet? Mass AND energy is conserved in an isolated system. Hey crank, did I speak of summative mass? Summative mass is what I was referring to with Porat, and you jumped in and said that mass is conserved. Now, if you are talking about something else, then kindly respect the context of the conversation you've jumped into. > Where do you make up these? > Are you on any drugs? A collider is not > an isolated system. Really? What other interactions go on at the collision point besides > the ones between the constituents of the system? Only the universe as a whole can be isolated system. Ah, that's interesting. So the laws of conservation of energy and linear and angular momentum, as taught in freshman physics classes, are pointless, as the only circumstance they apply to is the universe as a whole. Ah. I see. > Only a crank will > insist a collider is an isolated system because you have no basis for > such assertion. You have no basis for making such assertions. A collider needs energy > to run, the energy comes from somewhere. It is not an isolated > system. Ah, interesting. So when a freshman physics text talks about collisions in isolated systems, you say there is no such thing, because the colliding things have to have acquired their motion from someplace? Don't you think it would be better if you actually took a freshman physics class before you started spouting off nonsense about basics? If mass and energy are not conserved in isolated > systems then you have miracles of ex nihilo creation. The change of a nonconserved property in an isolated system is not a > miracle of any kind. If you change, it will be a miracle. YOu never answer on the main > issue, you always try to divert attention with red herrings. I think you are a crank. Sonner or later it will become evident to > everybody you are a crank. You then drop > physics and pray to God for relevation, as He would be the only One to > know what is really happening. Mike Now, you have stated that you believe that mass is conserved ANYWAY > and that mass is hidden in stuff that isn't being taken into account. This is believing in the existence of stuff that is hidden and > unobserved for the sake of a principle you WANT to believe is true, > independent of whether you have evidence for it. Certain people believe in ghosts and spirits but think that the > evidence for them is hidden and not taken into account. That's fun and > keeps people happy, but it is not scientific. PD TIA > Y.Porat > ----------------------------- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: Higgs Boson posting-account=UlqQigoAAADUKXgHhhqS3Em_KfDZERQh Trident/4.0; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) If the higgs boson confers mass on non mattermatter. does this mean > the conservation of energy law is broken since mass is energy. No, not necessarily. Conservation of energy doesn't mean conservation > of mass. It means that the *sum* of all energy contributions, > including those of rest mass, is conserved. It does not mean that the > individual contributions are each conserved. ------------------ > smarty Oracle of Delphi who said individual contribution??!!! > now jsut tell us if : in the **overall system ** --- > mass is conserved ???!!! No! We know this already. In experiment. I'll give you an example. > SLAC has created pairs of protons from pairs of colliding electrons. > There is nothing in the initial state except an electron-positron > pair, and there is nothing in the final state other than a proton- > antiproton pair. The final state mass is 1800 times larger than the > initial state mass. No, mass is not conserved in an isolated system. 180 or 1800 times? Mass and energy are conserved in an isolated system. I don't know where you got the idea that summative mass is conserved > in an isolated system? Read well. You claim to have a Ph.D and you don't know how to read > yet? Mass AND energy is conserved in an isolated system. Hey crank, did I speak of summative mass? Summative mass is what I was referring to with Porat, and you jumped > in and said that mass is conserved. Now, if you are talking about > something else, then kindly respect the context of the conversation > you've jumped into. Where do you make up these? > Are you on any drugs? A collider is not > an isolated system. Really? What other interactions go on at the collision point besides > the ones between the constituents of the system? Only the universe as a whole can be isolated system. Ah, that's interesting. So the laws of conservation of energy and > linear and angular momentum, as taught in freshman physics classes, > are pointless, as the only circumstance they apply to is the universe > as a whole. Ah. I see. You totally confuse closed and isolated systems. It appears you do not know the difference. I said mass AND energy are conserved in an isolated system. I do not understand what your objection is. I never said anything about momentum or energy. You do not understand the difference between laws and physical systems. Only a crank will > insist a collider is an isolated system because you have no basis for > such assertion. You have no basis for making such assertions. A collider needs energy > to run, the energy comes from somewhere. It is not an isolated > system. Ah, interesting. So when a freshman physics text talks about > collisions in isolated systems, you say there is no such thing, > because the colliding things have to have acquired their motion from > someplace? YOu talk about models, not reality,. In reality, you have all kinds of energy dissipation or influenses on the bodies involved. I understand some of you do not know the difference between models and physical reality. Truly isolated physical systems do not exist in reality (except perhaps for the universe as a whole), http://en.wikipedia.org/wiki/Isolated system Now call wikipedia and cry foul... hello, this is PD, the usenet king. I have been teaching my pupils that there are isolated systems all over the place. Remove the entry please. Crank Don't you think it would be better if you actually took a freshman > physics class before you started spouting off nonsense about basics? > You are a fool. > If mass and energy are not conserved in isolated > systems then you have miracles of ex nihilo creation. The change of a nonconserved property in an isolated system is not a > miracle of any kind. If you change, it will be a miracle. YOu never answer on the main > issue, you always try to divert attention with red herrings. I think you are a crank. Sonner or later it will become evident to > everybody you are a crank. You then drop > physics and pray to God for relevation, as He would be the only One to > know what is really happening. Mike Now, you have stated that you believe that mass is conserved ANYWAY > and that mass is hidden in stuff that isn't being taken into account. This is believing in the existence of stuff that is hidden and > unobserved for the sake of a principle you WANT to believe is true, > independent of whether you have evidence for it. Certain people believe in ghosts and spirits but think that the > evidence for them is hidden and not taken into account. That's fun and > keeps people happy, but it is not scientific. PD TIA > Y.Porat > ----------------------------- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: Higgs Boson posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) > If the higgs boson confers mass on non mattermatter. does this mean > the conservation of energy law is broken since mass is energy. No, not necessarily. Conservation of energy doesn't mean conservation > of mass. It means that the *sum* of all energy contributions, > including those of rest mass, is conserved. It does not mean that the > individual contributions are each conserved. ------------------ > smarty Oracle of Delphi who said individual contribution??!!! > now jsut tell us if : in the **overall system ** --- > mass is conserved ???!!! No! We know this already. In experiment. I'll give you an example. > SLAC has created pairs of protons from pairs of colliding electrons. > There is nothing in the initial state except an electron-positron > pair, and there is nothing in the final state other than a proton- > antiproton pair. The final state mass is 1800 times larger than the > initial state mass. No, mass is not conserved in an isolated system. 180 or 1800 times? Mass and energy are conserved in an isolated system. I don't know where you got the idea that summative mass is conserved > in an isolated system? Read well. You claim to have a Ph.D and you don't know how to read > yet? Mass AND energy is conserved in an isolated system. Hey crank, did I speak of summative mass? Summative mass is what I was referring to with Porat, and you jumped > in and said that mass is conserved. Now, if you are talking about > something else, then kindly respect the context of the conversation > you've jumped into. Where do you make up these? > Are you on any drugs? A collider is not > an isolated system. Really? What other interactions go on at the collision point besides > the ones between the constituents of the system? Only the universe as a whole can be isolated system. Ah, that's interesting. So the laws of conservation of energy and > linear and angular momentum, as taught in freshman physics classes, > are pointless, as the only circumstance they apply to is the universe > as a whole. Ah. I see. You totally confuse closed and isolated systems. It appears you do not > know the difference. Interesting. And what do physics textbooks say is the distinction? I said mass AND energy are conserved in an isolated system. Summative mass, which is what I was discussing with Porat, is not. > I do not > understand what your objection is. I never said anything about > momentum or energy. You do not understand the difference between laws > and physical systems. And what do the laws say about what is true in isolated (or closed) systems? Only a crank will > insist a collider is an isolated system because you have no basis for > such assertion. You have no basis for making such assertions. A collider needs energy > to run, the energy comes from somewhere. It is not an isolated > system. Ah, interesting. So when a freshman physics text talks about > collisions in isolated systems, you say there is no such thing, > because the colliding things have to have acquired their motion from > someplace? YOu talk about models, not reality,. In reality, you have all kinds of > energy dissipation or influenses on the bodies involved. I understand > some of you do not know the difference between models and physical > reality. Really, and so what do the physical laws say? Or are physical laws about models and not physical reality, Mike? Truly isolated physical systems do not exist in reality (except > perhaps for the universe as a whole), http://en.wikipedia.org/wiki/Isolated system Now call wikipedia and cry foul... It's a free resource. You get what you pay for. hello, this is PD, the usenet king. You are under some impression I'm trying to force anything on usenet. I'm just encouraging you to look up some better resources. Of course, if you want to say something completely different on usenet because you have the freedom to, be my guest. That's the beauty of the open- access internet; just about anybody can make of fool of himself without spending a penny. > I have been teaching my pupils > that there are isolated systems all over the place. Remove the entry > please. Crank Don't you think it would be better if you actually took a freshman > physics class before you started spouting off nonsense about basics? You are a fool. That's your answer to the question? If mass and energy are not conserved in isolated > systems then you have miracles of ex nihilo creation. The change of a nonconserved property in an isolated system is not a > miracle of any kind. If you change, it will be a miracle. YOu never answer on the main > issue, you always try to divert attention with red herrings. I think you are a crank. Sonner or later it will become evident to > everybody you are a crank. You then drop > physics and pray to God for relevation, as He would be the only One to > know what is really happening. Mike Now, you have stated that you believe that mass is conserved ANYWAY > and that mass is hidden in stuff that isn't being taken into account. This is believing in the existence of stuff that is hidden and > unobserved for the sake of a principle you WANT to believe is true, > independent of whether you have evidence for it. Certain people believe in ghosts and spirits but think that the > evidence for them is hidden and not taken into account. That's fun and > keeps people happy, but it is not scientific. PD TIA > Y.Porat > ----------------------------- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Is it possible to oscillate a wave of this wavelength in a circuit ? Hi engineer.., => wavelength = 3 x 10^8 mts {frequency is your choice} Is it possible to oscillate a wave of this wavelength using some electronic circuitry stuff ? if not, then (1)why? & (2)what would be the reason to it? thnx & Have a nice time. === Subject: Re: Is it possible to oscillate a wave of this wavelength in a circuit ? > Hi engineer.., > => wavelength = 3 x 10^8 mts > {frequency is your choice} Is it possible to oscillate a wave of this wavelength > using some electronic circuitry stuff ? > if not, then (1)why? & > (2)what would be the reason to it? > thnx & > Have a nice time. > Yes -- Joe Leikhim K4SAT The RFI-EMI-GUY© Use only Genuine Interocitor Parts Tom Servo ;-P === Subject: Re: Is it possible to oscillate a wave of this wavelength in a circuit ? > Hi engineer.., > => wavelength = 3 x 10^8 mts > {frequency is your choice} > Is it possible to oscillate a wave of this wavelength > using some electronic circuitry stuff ? > if not, then (1)why? & > (2)what would be the reason to it? > thnx & > Have a nice time. > Yes > R u sure about that? === Subject: Re: Is it possible to oscillate a wave of this wavelength in a circuit ? > Hi engineer.., > => wavelength = 3 x 10^8 mts > {frequency is your choice} Is it possible to oscillate a wave of this wavelength > using some electronic circuitry stuff ? > if not, then (1)why? & > (2)what would be the reason to it? > thnx & > Have a nice time. > Yes > R u sure about that? The fact that you write in baby type (R u ...) tells us that we are much more sure of everything, as compared with you. Bob -- === Subject: Re: Is it possible to oscillate a wave of this wavelength in a circuit ? > Hi engineer.., > => wavelength = 3 x 10^8 mts > {frequency is your choice} Is it possible to oscillate a wave of this wavelength > using some electronic circuitry stuff ? > if not, then (1)why? & > (2)what would be the reason to it? > thnx & > Have a nice time. > Yes > R u sure about that? Yes. === Subject: How Green Does it Get? posting-account=WtWlpwoAAABtMc3YhLOw2GNjBkWJwBh5 AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) > -Yes. But in this case, there's quite a bit more involved when it comes > -to a hot looking Alaskan bush league babe of a modern day Teddy > -Roosevelt like Sarah Palin. She gives voice, Drill, Baby, Drill! to > -the common sense strain of American intelligence that knows better > -what is necessary for the economic health of this country, over and > -above a lot of half-baked progressive-liberal, green ideas. -Oh > >snip< Gawd, you haven't yet learned the meaning o0f 'brevity', have you. You're > still the poster-boy for self-indulgent prose. Yeah, you know where you can stick that, Malcolm. The meaning of brevity often as not is nothing to say. And for people who have nothing to say, being brief is a true virtue, i.e. until they start to get all snarky and humorless about it with those who do have something to say, and that is the ONLY self-indulgent jive going down here. LIKE I was saying . . . Oh yes. And green is indeed the word. They couldn't have chosen better, short of wet behind the ears. It does not take a graduate of Harvard Law School to get it figured out that leaving valuable natural resources laying untapped in the ground is insane, psychotic, plain nuts; absolutely the most stupid and irresponsible thing that man can ever come to on this planet. To leave it there and go off dreaming in the wind and sun and the corn fields about the green solutions of tomorrow while the price of gas at the pump today is throwing us all into another world-wide depression--that's green all right. It's wet behind the ears in the fullest possible meaning of the thing: born yesterday, green-horned, naive. Dreamers say, It'll take years before that ANWR oil is flowing through the pipeline, so it's not the way to do. Sarah Palin says, Because it'll take years, that is WHY it is Drill Baby, Drill, NOW. Every American with the least shred of Sarah Palin style good Alaskan caribou sense knows what every Harvard grad hasn't the work-world life experience to know. No, you will not find the kind of pseudo-knowledge that comes from Harvard classes in environmental science in the head of Sarah Palin, THANK GOD. What you find instead is the kind of can-do common sense that built both your nation and mine, with little or no help from the dreamers in the left-leaning ivory tower of Pizza and Beer at Harvard. -- JM http://whosenose.blogspot.com === Subject: Re: How Green Does it Get? posting-account=_fSS7AkAAABopgbf-C8ctkeInAjfhQRa SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) -Yes. But in this case, there's quite a bit more involved when it comes > -to a hot looking Alaskan bush league babe of a modern day Teddy > -Roosevelt like Sarah Palin. She gives voice, Drill, Baby, Drill! to > -the common sense strain of American intelligence that knows better > -what is necessary for the economic health of this country, over and > -above a lot of half-baked progressive-liberal, green ideas. -Oh > >snip< Gawd, you haven't yet learned the meaning o0f 'brevity', have you. You're > still the poster-boy for self-indulgent prose. Yeah, you know where you can stick that, Malcolm. The meaning of > brevity often as not is nothing to say. And for people who have > nothing to say, being brief is a true virtue, i.e. until they start to > get all snarky and humorless about it with those who do have something > to say, and that is the ONLY self-indulgent jive going down here. LIKE I was saying . . . Oh yes. And green is indeed the word. They couldn't have chosen > better, short of wet behind the ears. It does not take a graduate of Harvard Law School to get it figured > out that leaving valuable natural resources laying untapped in the > ground is insane, psychotic, plain nuts; absolutely the most stupid > and irresponsible thing that man can ever come to on this planet. To > leave it there and go off dreaming in the wind and sun and the corn > fields about the green solutions of tomorrow while the price of gas > at the pump today is throwing us all into another world-wide > depression--that's green all right. It's wet behind the ears in the > fullest possible meaning of the thing: born yesterday, green-horned, > naive. Dreamers say, It'll take years before that ANWR oil is flowing > through the pipeline, so it's not the way to do. Sarah Palin says, > Because it'll take years, that is WHY it is Drill Baby, Drill, NOW. > Every American with the least shred of Sarah Palin style good Alaskan > caribou sense knows what every Harvard grad hasn't the work-world life > experience to know. No, you will not find the kind of pseudo-knowledge that comes from > Harvard classes in environmental science in the head of Sarah Palin, > THANK GOD. What you find instead is the kind of can-do common sense > that built both your nation and mine, with little or no help from the > dreamers in the left-leaning ivory tower of Pizza and Beer at Harvard. > -- > JMhttp://whosenose.blogspot.com Why does one have to suck out everything the world has to offer to BURN DESTROY EXTERMINATE it as a fuel for cars, planes and central heating? Oil is valuable for so many things, only STOOOOOOPID people want to burn it up. And why, if you please would be so kind as to explain this to me, WHY must one destroy every last beautiful place of wild, untouched nature just because some jerk wants to drive his itsy-bitsy widdle car and is too STOOOOOOPID to pull the finger out and come up with a different, cleaner kind of fuel? Jerks like you destroy our world faster than terrorists, and all those Arabs are laughing their heads off at your kind of DUMBASS Westerners who suck up and lick their Arabian asses for their damn e oil because conceited-but-uneducated and bone-lazy folk like YOU are too mentally challenegd to try fuel from natural resources. Melanie === Subject: Re: How Green Does it Get? posting-account=tWKq3woAAADSI58v2Y4BqPHmE7LsSJLz .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) -Yes. But in this case, there's quite a bit more involved when it comes > -to a hot looking Alaskan bush league babe of a modern day Teddy > -Roosevelt like Sarah Palin. She gives voice, Drill, Baby, Drill! to > -the common sense strain of American intelligence that knows better > -what is necessary for the economic health of this country, over and > -above a lot of half-baked progressive-liberal, green ideas. -Oh > >snip< Gawd, you haven't yet learned the meaning o0f 'brevity', have you. You're > still the poster-boy for self-indulgent prose. Yeah, you know where you can stick that, Malcolm. The meaning of > brevity often as not is nothing to say. And for people who have > nothing to say, being brief is a true virtue, i.e. until they start to > get all snarky and humorless about it with those who do have something > to say, and that is the ONLY self-indulgent jive going down here. LIKE I was saying . . . Oh yes. And green is indeed the word. They couldn't have chosen > better, short of wet behind the ears. It does not take a graduate of Harvard Law School to get it figured > out that leaving valuable natural resources laying untapped in the > ground is insane, psychotic, plain nuts; absolutely the most stupid > and irresponsible thing that man can ever come to on this planet. To > leave it there and go off dreaming in the wind and sun and the corn > fields about the green solutions of tomorrow while the price of gas > at the pump today is throwing us all into another world-wide > depression--that's green all right. It's wet behind the ears in the > fullest possible meaning of the thing: born yesterday, green-horned, > naive. Dreamers say, It'll take years before that ANWR oil is flowing > through the pipeline, so it's not the way to do. Sarah Palin says, > Because it'll take years, that is WHY it is Drill Baby, Drill, NOW. > Every American with the least shred of Sarah Palin style good Alaskan > caribou sense knows what every Harvard grad hasn't the work-world life > experience to know. No, you will not find the kind of pseudo-knowledge that comes from > Harvard classes in environmental science in the head of Sarah Palin, > THANK GOD. What you find instead is the kind of can-do common sense > that built both your nation and mine, with little or no help from the > dreamers in the left-leaning ivory tower of Pizza and Beer at Harvard. > -- > JMhttp://whosenose.blogspot.com Well Mackie, you make some good points, but there are 2 contrary facts here that need not be missed. 1) This Green Technology is way out of the bag now, and way off the drawing board too. The new systems of photovoltaics and say, heating water in vacuum tubes is simply amazing and being installed today. The automobile makers have almost caught up too. They only need a few more months, and then, you know what? We can start telling OPEC to kiss our ass! 2) Palin's political career is over. Period. Not so much because her detractors say so, but because she says so. She owes a half million bucks in legal fees. Her daughters have become the butt of jokes, and frankly, I think her husband put his foot down. She's now in the catbird seat to let the dough roll in and get that new bass boat and jerky maker. ******* Besides even people in South Carolina knew what the Bush Doctrine was. === Subject: Re: How Green Does it Get? posting-account=hLqQkwoAAAAEBL5vz2BJ6yN8RgDuNGiC Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > No, you will not find the kind of pseudo-knowledge that comes from > Harvard classes in environmental science in the head of Sarah Palin, > THANK GOD. What you find instead is the kind of can-do common sense > that built both your nation and mine, with little or no help from the > dreamers in the left-leaning ivory tower of Pizza and Beer at Harvard. I think you've got that backwards. Presidents who went to Harvard: John Adams, John Quincy Adams, Rutherford B. Hayes, Theodore Roosevelt, Franklin Delano Roosevelt, John F. Kennedy, George W. Bush and of course, Barack Obama. Incidentally, Google Groups' spellchecker seems to be racist. It considers the only black president's name on that list to be misspelled. === Subject: Re: How Green Does it Get? posting-account=n8pQvgkAAAAR2icJiQ21GsmYtflsTgld Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > No, you will not find the kind of pseudo-knowledge that comes from > Harvard classes in environmental science in the head of Sarah Palin, > THANK GOD. What you find instead is the kind of can-do common sense > that built both your nation and mine, with little or no help from the > dreamers in the left-leaning ivory tower of Pizza and Beer at Harvard. If you think Sarah is the poster girl for common sense, well...okay. That says much about you. DB === Subject: Re: How Green Does it Get? posting-account=WtWlpwoAAABtMc3YhLOw2GNjBkWJwBh5 Trident/4.0; GTB6; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On Jul 6, 11:29am, dangerousb...@gmail.com No, you will not find the kind of pseudo-knowledge that comes from > Harvard classes in environmental science in the head of Sarah Palin, > THANK GOD. What you find instead is the kind of can-do common sense > that built both your nation and mine, with little or no help from the > dreamers in the left-leaning ivory tower of Pizza and Beer at Harvard. If you think Sarah is the poster girl for common sense, well...okay. > That says much about you. Yeah, just because you can't pull the staples from her navel and put her on your garage wall, you just simply don't know WHAT to do with her, i.e. in terms of YOUR idea of common sense. -- JM http://bobbisoxsnatchers.blogspot.com === Subject: Re: How Green Does it Get? posting-account=n8pQvgkAAAAR2icJiQ21GsmYtflsTgld Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > Yeah, just because you can't pull the staples from her navel and put > her on your garage wall, you just simply don't know WHAT to do with > her, i.e. in terms of YOUR idea of common sense. The lady repeatedly embarrassed herself and the whole party during the campaign. She was stupid, loud, corrupt, and 'way out of her league, but mind-controlled Repubs, when told the sun shone out of her ass, genuflected appropriately. The big tits and faux Ann Coulter style were apparently enough. I think that nominating McCain and Palin was a deliberate attempt to lose the last election and leave an economy in wreckage for a Dem President. Democrats can be relied on to get the country back to prosperity again. Then, the majority of us can revert to our natures and vote in a monarchist party and cheer them on while they loot the treasury once more. DB (cleaning spittle from screen) === Subject: Uniform distribution of points on a 4-sphere? posting-account=U31WtQoAAAA4eeo1D2iike7KtzHaCl4J AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) If I remember correctly, an exactly uniform distribution of points on the surface of a 3-dimensional sphere, except in a very few cases (viz. the vertices of the platonic solids), is impossible. Is it also impossible on the surface of a 4-dimensional sphere? Proof either way? -- Bob Day http://bobday.vze.com === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? -- Bob Dayhttp://bobday.vze.com Proof will depend on having a definition of exactly uniform distribution to check. Topologists prefer to call spheres according to the dimension of the surface, and I'll guess by 3-dimensional sphere you mean what is thus called a 2-sphere. Likewise by 4-dimensional sphere let's say 3-sphere. So what is the formal definition? Obviously an overly strict criterion is that every pair of distinct points should have equal distance. This is possible on a 2-sphere only when the number of points n is at most 4 (taking them to be vertices of a regular tetrahedron). The corresponding construction for a 3-sphere is the five vertices of a regular 4-simplex. But what do we mean if we say that vertices of a cube or regular dodecahedron are uniformly distributed on a 2-sphere? Perhaps we mean nothing more than that the underlying (convex) polyhedron is regular. Generalizing to four dimensions we have these: [Convex regular 4-polytopes -- Wikipedia] http://en.wikipedia.org/wiki/Convex regular 4-polytope === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? -- Bob Dayhttp://bobday.vze.com Proof will depend on having a definition of > exactly uniform distribution to check. Consider the 2-sphere. Assume that the sphere itself is electrically neutral. Place k point charges on the sphere. Suppose they are bound to the sphere. They will repel each other until they are as far apart as possible from their neighbors. Is this distribution a reasonable definition of 'uniform'? Is it dynamically stable? If one perturbs one charge, will it return to the prior configuration? What will the resulting distribution look like for various k? -------------------------------------------------------------------- Another possible definition of uniform is that all points are at an identical distance not from all other points, but only from its nearest neighbors. What will this look like for various k? Might these definitions be reasonable? === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? -- Bob Dayhttp://bobday.vze.com Proof will depend on having a definition of > exactly uniform distribution to check. Consider the 2-sphere. Assume that the sphere itself is electrically > neutral. Place k point charges on the sphere. Suppose they are > bound to the sphere. They will repel each other until they are as > far apart as possible from their neighbors. Is this distribution a reasonable definition of 'uniform'? Is it dynamically stable? If one perturbs one charge, will it return > to the prior configuration? What will the resulting distribution look like for various k? > -------------------------------------------------------------------- Another possible definition of uniform is that all points are at an > identical distance not from all other points, but only from its > nearest neighbors. What will this look like for various k? Might these definitions be reasonable? Another possibility: place them to maximize the sum of the distances between all pairs of points. Or the sum of the squared distances. === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) The original poster wondered if the existence of solutions only in a very few cases will extend from the Platonic solids to a higher dimension: [in part] > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic > solids), is impossible. Depending on the definition, I think the answer is yes, there are still only a finite (smallish) number of solutions corresponding to the Platonic solids (e.g. regular polyhedra --> polychora). [in part] > Consider the 2-sphere. Assume that the sphere > itself is electrically neutral. Place k point > charges on the sphere. Suppose they are > bound to the sphere. They will repel each other > until they are as far apart as possible from > their neighbors. Is this distribution a reasonable definition > of 'uniform'? Is it dynamically stable? If > one perturbs one charge, will it return > to the prior configuration? -------------------------------------------------------------------- > Another possible definition of uniform is that > all points are at an identical distance not > from all other points, but only from its > nearest neighbors. > What will this look like for various k? > Another possibility: place them to maximize > the sum of the distances between all pairs of > points. Or the sum of the squared distances. All these criteria allow more flexibility than merely getting the Platonic solids' vertices on the 2-sphere. The minimum potential energy approach is known to lack dynamic stability for sufficiently large k, and the second approach, equalizing the distances to nearest neighbors is perhaps too flexible (imagine k points spread around the equator, or for even k, zigzagging across the equator some distance insufficient to cause any point to have nearest neighbors other than the ones immediates preceding and following). A bunch of links on the first and third of your criteria and other approaches are here: [sphere distribution problems] http://www.ogre.nu/sphere.htm N. J. A. Sloane has some results on higher dimensional arrangements (packings) here: [Spherical Codes] http://www.research.att.com/~njas/packings/ === Subject: Re: Uniform distribution of points on a 4-sphere? > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? > -- Bob Dayhttp://bobday.vze.com Proof will depend on having a definition of > exactly uniform distribution to check. Topologists prefer to call spheres according > to the dimension of the surface, and I'll > guess by 3-dimensional sphere you mean what > is thus called a 2-sphere. Likewise by > 4-dimensional sphere let's say 3-sphere. So what is the formal definition? Obviously > an overly strict criterion is that every pair > of distinct points should have equal distance. > This is possible on a 2-sphere only when the > number of points n is at most 4 (taking them > to be vertices of a regular tetrahedron). The > corresponding construction for a 3-sphere is > the five vertices of a regular 4-simplex. But what do we mean if we say that vertices > of a cube or regular dodecahedron are > uniformly distributed on a 2-sphere? Perhaps > we mean nothing more than that the underlying > (convex) polyhedron is regular. Generalizing to four dimensions we have these: [Convex regular 4-polytopes -- Wikipedia] > http://en.wikipedia.org/wiki/Convex_regular_4-polytope According to the book review of Coxeter's Regular Polytopes in the Bulletin of the American Mathematical Society Volume 55, Number 7 (published in 1949), Coxeter's book is a solid work of reference on polyhedra and higher dimensional polytopes. It also shows that there are just six convex regular 4-polytopes. The reviewer was C.B. Allendoerfer. Cf.: < http://en.wikipedia.org/wiki/Regular_Polytopes_(book) > which has a link to C.B. Allendoerfer's book review in David Bernier === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Trident/4.0; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? > -- Bob Dayhttp://bobday.vze.com Proof will depend on having a definition of > exactly uniform distribution to check. Topologists prefer to call spheres according > to the dimension of the surface, and I'll > guess by 3-dimensional sphere you mean what > is thus called a 2-sphere. Likewise by > 4-dimensional sphere let's say 3-sphere. So what is the formal definition? Obviously > an overly strict criterion is that every pair > of distinct points should have equal distance. > This is possible on a 2-sphere only when the > number of points n is at most 4 (taking them > to be vertices of a regular tetrahedron). The > corresponding construction for a 3-sphere is > the five vertices of a regular 4-simplex. But what do we mean if we say that vertices > of a cube or regular dodecahedron are > uniformly distributed on a 2-sphere? Perhaps > we mean nothing more than that the underlying > (convex) polyhedron is regular. Generalizing to four dimensions we have these: [Convex regular 4-polytopes -- Wikipedia] >http://en.wikipedia.org/wiki/Convex regular 4-polytope According to the book review of Coxeter's Regular Polytopes > in the Bulletin of the American Mathematical Society Volume 55, > Number 7 (published in 1949), Coxeter's book is a solid > work of reference on polyhedra and higher dimensional polytopes. > It also shows that there are just six convex regular 4-polytopes. The reviewer was C.B. Allendoerfer. Cf.: > which has a link to C.B. Allendoerfer's book review in David Bernier- Hide quoted text - - Show quoted text - [T]he first edition of the book took Coxeter 24 years to complete. I don't have a good intuition about how the number of convex regular n-polytopes (up to similarity) should vary with n. For n = 2 we have infinitely many, dropping to five for n = 3 and six for n = 4. The n-simplex, the n-hypercube, and its dual the n-orthoplex (think octohedron) are examples for all n, so the count never drops to zero. [Regular polytopes -- Wikipedia] http://en.wikipedia.org/wiki/Regular polytope those are the only ones in dimension five and higher. (There also are no nonconvex examples in the higher dimensions.) === Subject: Re: Uniform distribution of points on a 4-sphere? [...] > [T]he first edition of the book took Coxeter > 24 years to complete. I don't have a good intuition about how the > number of convex regular n-polytopes (up to > similarity) should vary with n. For n = 2 > we have infinitely many, dropping to five > for n = 3 and six for n = 4. The n-simplex, > the n-hypercube, and its dual the n-orthoplex > (think octohedron) are examples for all n, > so the count never drops to zero. > [Regular polytopes -- Wikipedia] > http://en.wikipedia.org/wiki/Regular_polytope those are the only ones in dimension five > and higher. (There also are no nonconvex > examples in the higher dimensions.) The tesseract is described as an 8-cell 4-cube. Each of the 8 cells is a 3-cube, where a 3-cube is an ordinary cube. Adjacent 8-cells share a square face. At every vertex of a tesseract, four 3-cubes meet. The tesseract is a hyper-cube, cells are hyper-faces, squares are hyper-edges. We could say each square in a tesseract has four 1-cubes, or one-dimensional cubes. A 1-cube is to a tesseract as a _____ is to an ordinary cube. I don't know whether or not there's a meaningful way to complete the above analogy. David === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Trident/4.0; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) [...] [T]he first edition of the book took Coxeter > 24 years to complete. I don't have a good intuition about how the > number of convex regular n-polytopes (up to > similarity) should vary with n. For n = 2 > we have infinitely many, dropping to five > for n = 3 and six for n = 4. The n-simplex, > the n-hypercube, and its dual the n-orthoplex > (think octohedron) are examples for all n, > so the count never drops to zero. > [Regular polytopes -- Wikipedia] >http://en.wikipedia.org/wiki/Regular polytope those are the only ones in dimension five > and higher. (There also are no nonconvex > examples in the higher dimensions.) The tesseract is described as an 8-cell > 4-cube. Each of the 8 cells is a 3-cube, > where a 3-cube is an ordinary cube. Adjacent 8-cells share a square face. At every vertex of a tesseract, four 3-cubes meet. The tesseract is a hyper-cube, cells are hyper-faces, > squares are hyper-edges. We could say > each square in a tesseract has four 1-cubes, > or one-dimensional cubes. A 1-cube is to a tesseract as > a is to an ordinary cube. I don't know whether or not there's a > meaningful way to complete the above analogy. David- Hide quoted text - - Show quoted text - A 0-cube is (by convention?) a point. Then each n+1-cube is an orthogonal cylinder on an n-cube. The analogy seems to work: At every vertex of a tesseract (4-cube), four 3-cubes meet. At every vertex of a 1-cube (edge), one 0-cube (point) meets. --c === Subject: Re: Uniform distribution of points on a 4-sphere? > [...] > [T]he first edition of the book took Coxeter > 24 years to complete. > I don't have a good intuition about how the > number of convex regular n-polytopes (up to > similarity) should vary with n. For n = 2 > we have infinitely many, dropping to five > for n = 3 and six for n = 4. The n-simplex, > the n-hypercube, and its dual the n-orthoplex > (think octohedron) are examples for all n, > so the count never drops to zero. > [Regular polytopes -- Wikipedia] > http://en.wikipedia.org/wiki/Regular_polytope > those are the only ones in dimension five > and higher. (There also are no nonconvex > examples in the higher dimensions.) > The tesseract is described as an 8-cell > 4-cube. Each of the 8 cells is a 3-cube, > where a 3-cube is an ordinary cube. > Adjacent 8-cells share a square face. > At every vertex of a tesseract, four 3-cubes meet. > The tesseract is a hyper-cube, cells are hyper-faces, > squares are hyper-edges. We could say > each square in a tesseract has four 1-cubes, > or one-dimensional cubes. > A 1-cube is to a tesseract as > a _____ is to an ordinary cube. > I don't know whether or not there's a > meaningful way to complete the above analogy. > David- Hide quoted text - > - Show quoted text - A 0-cube is (by convention?) a point. > Then each n+1-cube is an orthogonal > cylinder on an n-cube. The analogy seems to work: At every vertex of a tesseract (4-cube), > four 3-cubes meet. At every vertex of a 1-cube (edge), one > 0-cube (point) meets. Yes, I agree with this: :: At every vertex of a 1-cube (edge), one :: 0-cube (point) meets. In a 3-cube, A given 0-cube is shared by 3 2-cubes. A given 1-cube is shared by 2 2-cubes. The 3-cube has 6 2-cubes. In a 4-cube, A given 0-cube is shared by 4 3-cubes. A given 1-cube is shared by X 3-cubes. A given 2-cube is shared by 2 3 cubes. [ I think ] The 4-cube has 8 3-cubes (cells). By looking at the Schlegel diagram here: http://en.wikipedia.org/wiki/File:Schlegel_wireframe_8-cell.png I've convinced myself that X = 3: Any 1-cube in a tesseract is part of 3 3-cubes (cells). But I need the diagram to find the answer. David === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) [snip some history] > Any 1-cube in a tesseract is part of 3 3-cubes (cells). > But I need the diagram to find the answer. David Let's use the definition of a unit n+1-cube as an orthogonal cylinder of height on on a unit n-cube. The base of the 4-cube can be any one of its eight 3-cubes, and equally by symmetry we may choose any 1-cube (edge) in that base. So already that is one of the 3-cubes that the 1-cube belongs to (in the 4-cube). What else? Well, constructing the orthogonal cylinder lifts each 2-cube (square) in the base to a 3-cube in the 4-cube (tesseract). The fixed 1-cube (edge) of the base 3-cube belongs to exactly two 2-cube faces, so that gives us two additional 3-cubes that this 1-cube (edge) belongs to. The only other 3-cube in the 4-cube is the one parallel to the base 3-cube, but it shares no 1-cube (edge) with the base; they are disjoint. Thus, as you could see from the diagram, each 1-cube of a 4-cube belongs to three 3-cubes. === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? -- Bob Day > http://bobday.vze.com It is possible: http://mathforum.org/kb/servlet/JiveServlet/download/13-1959777-6763806-5599 55/3256947403_398e26dde8_o.jpg === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=U31WtQoAAAA4eeo1D2iike7KtzHaCl4J AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.33 Safari/530.5,gzip(gfe),gzip(gfe) > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? -- Bob Day >http://bobday.vze.com It is possible: http://mathforum.org/kb/servlet/JiveServlet/download/13-1959777-67638... 1) AFAIK, the Riemann hypothesis hasn't been proved. 2) And how would it relate to an *exactly* uniform distribution of points on the surface of a 4-sphere? -- Bob Day http://bobday.vze.com === Subject: Re: Uniform distribution of points on a 4-sphere? posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Musatov scribed: > If I remember correctly, an exactly uniform distribution > of points on the surface of a 3-dimensional sphere, except > in a very few cases (viz. the vertices of the platonic solids), > is impossible. Is it also impossible on the surface of a > 4-dimensional sphere? Proof either way? -- Bob Day >http://bobday.vze.com It is possible: http://mathforum.org/kb/servlet/JiveServlet/download/13-1959777-67638... 1) AFAIK, the Riemann hypothesis hasn't been proved. 2) And how would it relate to an *exactly* uniform > distribution of points on the surface of a 4-sphere? -- Bob Day > http://bobday.vze.com 1) Yet[...] 2) The Riemann hypothesis was explained at the BA Festival by Marcus du Sautoy, The Clay Prize essentially asks for a proof that NP-type problems are in fact complete, that there really is no pattern to the distribution of the primes. For example, tearing a hole in the middle of the sphere and rejoining the edges. As is possible with my diagram. Further: 1. Entropy properties of rational endomorphisms of the Riemann sphere (z) have an asymptotically uniform distribution with respect to NP Completeness. Proof. Expand K to a compact set L containing no excluded points such that fL^> L finite 77-net X of the Riemann sphere containing all the critical points of the Mathematical Handbook for Scientists and Engineers: Definitions, distribution Riemann On the sum of distances between n ...If p is a point on a sphere and 0...> A typical example of this method is seen in the proof of the Riemann Approximation Theory : Spherical basis functions and uniform distribution of points on spheres. Proof. Since the points in afii9821 (1) N are uniformly distributed on S d m, the summation 1 N N summationdisplay j=1 Y lscript,m (y j ) is a Riemann [48] K.B. Stolarsky, Sums of distances between points on a sphere II, Proc. Û6.1) for a discussion and proof of this formula in the case r = 1. on a two-dimensional sphere of radius 1 maps to the point left[frac{x}{1-z},frac. This will give a uniform distribution, but it is necessary to remove the exterior points. 2- sphere: Finally, we have enough to address some Generalized Riemann problems in computational fluid dynamics. The uniform pressure behind the shock is obtained from Equation (4.89) (i), [...] 6.4 The Flow Induced by an expanding Sphere when a spherical surface. -- Martin Musatov It's dense. It makes sense. It just takes a while to wrap your head around it. http://MeAmI.org Get better math results with Google, by using MeAmI.org. === Subject: Re: Uniform distribution of points on a 4-sphere? 1) AFAIK, the Riemann hypothesis hasn't been proved. 2) And how would it relate to an *exactly* uniform > distribution of points on the surface of a 4-sphere? It doesn't. Ignore Mutasov. He hijacks every thread where he can trick people into replying to him. === Subject: Re: Uniform distribution of points on a 4-sphere? <240620091431351025%anniel@nym.alias.net.invalid> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) 1) AFAIK, the Riemann hypothesis hasn't been proved. 2) And how would it relate to an *exactly* uniform > distribution of points on the surface of a 4-sphere? It doesn't. Ignore Mutasov. He hijacks every thread where he can > trick people into replying to him. Why would you say this? === Subject: Re: solving the Calculus continuity problem of f(x) = sin(1/x) #622 new book 2nd edition: New True Mathematics > Alright, here is another part of Calculus that the limit is unable > to perform, but where the AP-Reals is at home and comfortable > in solving. On page 86 of Strang's CALCULUS, 1991 lists the function > f(x) = sin (1/x) as discontinuous. The function sin(1/x) still fluctuates wildly but we can discuss each > point of fluctuation. And it is not discontinuous but continuous. WRONG. What is the value of the derivative at 0 ? > For that matter, what is the value of the function at 0 that would make it continuous at 0 ? Archimedes Plutonium > www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies -- Virgil === Subject: Re: overhauling continuity and discontinuity in mathematics #624 new book 2nd edition: New True Mathematics posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG 1.1.4322; .NET CLR 2.0.50727; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > So, in other words, sin(1/x) is discontinous at 0 in Old Math with Old > Reals as > a point-discontinuity. But in AP-Reals there is an infinity of points > that satisfies > the function between (-)10^(-)500 and 10^(-)500. As well as an > infinitude of > AP-Reals between say 0d00..0_7_ and 0d00..0_8_ that satisfy the > function. What is sin(0d000...001) in the AP-reals? === Subject: Re: solving the Calculus continuity problem of f(x) = sin(1/x) #622 new book 2nd edition: New True Mathematics > throughout so what is the value at 0 ? and what is the value of the DE at 0 ? dont go Fractial on me, and keep zooming in......... > Archimedes Plutonium > www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies === Subject: Re: solving the Calculus continuity problem of f(x) = sin(1/x) #622 new book 2nd edition: New True Mathematics > But let me get back to the function sin(1/x). Not only is continuous > throughout > so what is the value at 0 ? > and what is the value of the DE at 0 ? > dont go Fractial on me, and keep zooming in......... Your college degree if you have one should be rescinded by such posts. You call my writings crap, and then expect me to consider your > questions. So, (1) you have no logical head to even think with (2) you need to > learn > manners and etiquette before you do any mathematics. So get yee back to school and take a course in manners and etiquette sorry your feelings got so..... hurt. Perhaps you should see a Dr in Shrinkology to easy your growing emotional burdening brought on by wading throught the vast amount of literature and responces indicating your life long achevement here, really does, 'stinkith'. Since the function Sin(1/x) is the problem, and not really your fine work proving continituity at 0, perhaps you should look at the function Tan(1/x) instead. === Subject: A Dialogue of Circles posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) http://mathforum.org/kb/servlet/JiveServlet/download/13-1959777-6763806-5599 55/3256947403_398e26dde8_o.jpg ---------- Forwarded message ---------- === Subject: Re: Math challenge: circle in a rational number (was Re: CONTACT and pi >Here's a celebrity MATHEMATICAL CHALLENGE: what are some pairs of >integers n and m such that the decimal fraction part of n divided by m >is a series of 0's and 1's that can be mapped into a square grid to >form an approximate circle? If n and m are much smaller than we intuitively expect, are we to >draw any conclusions? I don't know about the conclusions part, but it's hard to do what you are asking. If you want a circle in a grid of nxn, then two integers about the size of 10^(nxn) would do. One of those numbers will even be 10^(nxn)-1 (99999...). Can you see what I'm talking about? Whether there's a smaller pair of numbers, I don't know. I can try thinking about it, but my brain hurts... >All of you folks who claim that pi can't be manipulated are missing the >point. If it can't be manipulated, and something manipulates it >regardless, then that something meets any reasonable definition of >omnipotent. What YOU are missing is that if there is a sequence of digits in >the some expansion of pi and those digits can be mapped into an >approximation of a circle, THEN that does not imply that pi has >been manipulated. Think of it this way. You walk into a store and buy a lottery >ticket. Your chances of winning are 14,000,000 to 1. If you >_do_ win, that doesn't mean that a miracle has occurred. It >had to happen to someone sometime and you're that person. No >cosmic mind has blessed you. Like Vince, you're missing the point. In certain lotteries (not all!), someone must win. That someone needn't be you. I found this in my fortune program, I thought it might be entertaining. It is true that if your paperboy throws your paper into the bushes for five straight days, it can be explained using Newton's Law of Gravity. But it takes Murphy's law to explain why it is happening to you. No, finding that silly circle in pi thing doesn't imply that there's a god. But to many people (apparently!) this suggests that there is a higher being, or whatever. You can't refute with logical arguments (there's no logic to refute), but you can't substantiated either. It's all what you believe. I think that's what the point of the film was. That is, until they butchered it! If an astounding pattern is found in the digits of pi, then there >are no implications to be made. Also, if the value of pi is changed then it isn't pi any more. It depends on the context and what you mean. We don't want to get into a semantic argument here. At least, I don't! Pi is not an empirically determined constant. To tinker with >the value of pi would also allow for two thirds to be jimmied >into .666000666000666000666000666000666000666000666000666000... No, it's not empirically determined. But it is figured out using some assumptions of Euclidean space. If things were different... Maybe our idea of pi would be different. If there was an omnipotent being, maybe he can construct a universe where pi was 3, or 4, or /V2~ (that's my artist's rendition of root 2, what do you think?). Who knows? It's God, for crying out loud... >As for pi containing all possible combinations of numbers (I'm assuming you >mean by combinations of numbers sequences of digits), it does not. Pi+1 >produces a sequence of digits which is not contained in pi. If you meant >to say that it contains all possible finite sequences, you're on stronger >ground, but I'd like to see a proof that there is no finite sequence which >is excluded. Would you understand such a proof? That was uncalled for! He was clever enough to come up with that pi+1 bit, he's obviously not _entirely_ a fool. Sure, the proof could be long and complex so that none of us could understand it, but it might be surprisingly elementary. You just don't know (or do you?). It took me a while to realize why that pi+1 was not a substring of pi. So I'm not the swiftest mathemagician in the world. I could site you a proof that e is transcendental. I feel confident that you would never have thought up of such a proof, but you (and pi+1 guy) could easily understand it. I suspect that the randomness of the digits is something that has >been observed. It certainly has a lot of intuitive appeal but it is >not true that (for instance) all transcendental (or irrational) >numbers have this property of random digits. I imagine that the square root of two has the same property. The randomness has definitely been observed, but not proven (to my knowledge). -- Well I've tried so hard, baby, but I just can't see === Subject: Re: Computer-verified Mathematical Proof as Standard >Translating a traditional math proof to a formal proof often involves >an exponential explosion in size, and sometimes MUCH worse (Ackermann- >like). >Do you have an example of a proof that has Ackermann-like explosion? >I'm not aware of one. No, but there are many proofs where one says, in a similar manner. These grow. >Now, perhaps there are automatic verifiers that can handle >transformations whose validity has been proved separately > -- but was THAT proof formal? >Yes, certainly. Any decent proof assistant has such capacities to one degree >or another. One motivation for the higher-order-logic based languages is >their ability to capture such abbreviations formally in a nice way. I agree. This is not that difficult; a formal proof can quote a theorem, but of course if the quote is of something incorrect, the proof will not be valid. We do not have to reinvent the wheel. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Computer-verified Mathematical Proof as Standard > >Do you have an example of a proof that has Ackermann-like explosion? >I'm not aware of one. No, but there are many proofs where one says, in a similar manner. > These grow. But not in an Ackermann-like way. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >Do you have an example of a proof that has Ackermann-like explosion? >I'm not aware of one. No, but there are many proofs where one says, in a >similar manner. These grow. But they don't grow at a speed that defies formalization, which was the topic of discussion. The sort of thing that would (probably) be infeasible to formalize would be a proof or disproof of sin(2^2^2^2^2^2^2^2) > 0 (to borrow an example of Harvey Friedman's). But we can't figure out whether that statement is true or false informally either. There could also be cases where a large cardinal axiom A allows you to shorten the proof of a theorem T dramatically (though I don't think any such case has arisen in real life). The you might have to settle for formalizing the proof of the implication A implies T rather than formalizing the A-free proof of T directly. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > There could also be cases where a large cardinal axiom A allows you to > shorten the proof of a theorem T dramatically (though I don't think any > such case has arisen in real life). There are no such cases. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) > There could also be cases where a large cardinal axiom A allows you to > shorten the proof of a theorem T dramatically (though I don't think any > such case has arisen in real life). There are no such cases. Meaning, I suppose, that the only candidates for T are artificial examples such as There is no ZFC-proof of 0=1 using less than 2^2^2^2^2^2^2^2 symbols. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > > There could also be cases where a large cardinal axiom A allows you to > shorten the proof of a theorem T dramatically (though I don't think any > such case has arisen in real life). There are no such cases. > OK, I'll bite: What makes you so sure? I'm guessing you have some kind of argument in mind; could you please share it? Robert E. Beaudoin === Subject: Re: Computer-verified Mathematical Proof as Standard <4a423140$0$515$b45e6eb0@senator-bedfellow.mit.edu> <4a42c85f$0$514$b45e6eb0@senator-bedfellow.mit.edu> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) >Do you have an example of a proof that has Ackermann-like explosion? >I'm not aware of one. No, but there are many proofs where one says, in a >similar manner. These grow. But they don't grow at a speed that defies formalization, which was the > topic of discussion. The sort of thing that would (probably) be infeasible to formalize would > be a proof or disproof of sin(2^2^2^2^2^2^2^2) > 0 (to borrow an example > of Harvey Friedman's). But we can't figure out whether that statement is > true or false informally either. There could also be cases where a large cardinal axiom A allows you to > shorten the proof of a theorem T dramatically (though I don't think any > such case has arisen in real life). The you might have to settle for > formalizing the proof of the implication A implies T rather than > formalizing the A-free proof of T directly. > -- > Tim Chow tchow-at-alum-dot-mit-dot-edu > The range of our projectiles---even ... the artillery---however great, will > never exceed four of those miles of which as many thousand separate us from > the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences Okay, this we can work with: 1. Operations Research Letters : An enhanced dynasearch neighborhood 1a. The 1| |áwiTi problem is NP-hard in the strong sense [3] and the <...>. We start from the initial sequence S with completion times Cj=ás=1jps. <...> between job i and j can be abandoned as soon as it proves to be nonoptimal. In [5] it is proven that: condition (a) implies T(.83[CapitalEth]j.83ëi.83.85) greater-or- equal, slanted <...><...> superset of a satisfying the following condition: , T (A) implies ( ) T (A). ... We define arity( )=k if = 1 k p for some p A.The order of a type , denoted by .... The languages generated by lexicalized ACGs form asubset of NP. De Groote and Pogodalla [11] prove that the string languages Characterization of strongly equivalent logic programs in fact satisfiability in G3 is NP and satisfiability in KC is PSPACE. However, one wants to prove that the disjunctive rule p .81.83 q is not strongly equivalent to any A implies T ¤l. G3. A. 3 Answer sets and stable models A new method for establishing conservativity of classical systems get f Á[Thorn]Á[Thorn]A implies T(fg), which is equivalent to A Á[YAcute] T(f), as desired. The key observation is that an instance of NP-induction can be realised using bounded Cook and Urquhart prove this by first using the negative translation to congruence extensions for semilattices with distributivityUsing this result and induction it is easy to prove that p(=, T(lk-,, Jk) ) = Cr),) n O((b>n)) = 12s and so p(gt((q cr),) n p(O((b>,)) = T(x, y) c/'t v/'a implies T(x, y) = (T(x, y) A F) v (T(x, y) N/'2). Musatov's Principle for Propositional Type Theory is sound, for some particular p we can prove that fix(f.p[x]) is a well- <...>. Suppose one has proved that A implies t Á.99 T and Á[Thorn]A also implies t Á.99 k, N. P. M P(1) n= xf+x*+pP a JO. Proof. We prove equations (7) and (10) only, since (8) and (9) are O(NP-i(logP)*>) = ^( and it follows ahnost immediately implies t n. ->t, s and t being finite; such a transformation is said to be regular 7. DUALITY APPLIED TO THE COMPLEXITY OF NATRI:? MULTIPLICATION AND ... T aTx for all a implies t 0 --H4--H pT D MT = x which in turn implies bT M D P Tthere kj exist matrices M,P and R of dimensions mp x q g x mn and q x np. Instead of using Theorems 3 and 6 to prove the above we can construct .. arXiv:cs/0206005v1 [cs.LO] fact satisfiability in G3 is NP and satisfiability in KC is PSPACE. However, ... one wants to prove that the disjunctive rule p Á[YAcute] q is not strongly equivalent to any nondisjunctive rule. .... A implies T ? ..Fuzzy Intuitionistic Quantum LogicsT SZL3 a implies T#= ac. BZL3. PROOF. By routine techniques. ... {iIiV-p}. M is well defined since one can prove the following Lemmas: ... In case iib), we obtain by the S5-rules of our calculus: Ctr-{ML-nP}. By. DR4: F- -'L-'/3. ... === Subject: Looking for Ref book: Analytic Geometry in 3D posting-account=yWG1CAoAAAA3vyvnXaqeP6DuDaVPaZ9j rv:1.9.0.8) Gecko/2009032608 Firefox/3.0.8,gzip(gfe),gzip(gfe) I am looking for a reference book where I can look up formulas such as how to construct a plane that is orthogonal to a vector at its mid point; check to see if three vectors are in the same plane etc. I am thinking of some kind of a handbook of analytic geometry on its own, not as a second part of a first semester calculus book. I have looked at McCrea's Analytical geometry of three dimensions (God bless Dover for affordable editions of classic works), but thought I would get some more suggestions here. Much appreciated, Michuco === Subject: Re: Looking for Ref book: Analytic Geometry in 3D > .... > I am looking for a reference book where I can look up formulas such as > how to construct a plane that is orthogonal to a vector at its mid > point; check to see if three vectors are in the same plane etc. I am thinking of some kind of a handbook of analytic geometry on its > own, not as a second part of a first semester calculus book. I have looked at McCrea's Analytical geometry of three dimensions .... Such geometry can be handled very nicely by vector methods. I know of two really good little books which do that. Both are probably both out of print (alas!), but you may be lucky enough to find a copy: A. M. (Alexander Murray) Macbeath, Elementary Vector Algebra Seymour Schuster, Elementary Vector Geometry. Ken Pledger. === Subject: Re: Looking for Ref book: Analytic Geometry in 3D posting-account=yWG1CAoAAAA3vyvnXaqeP6DuDaVPaZ9j rv:1.9.0.8) Gecko/2009032608 Firefox/3.0.8,gzip(gfe),gzip(gfe) .... > I am looking for a reference book where I can look up formulas such as > how to construct a plane that is orthogonal to a vector at its mid > point; check to see if three vectors are in the same plane etc. I am thinking of some kind of a handbook of analytic geometry on its > own, not as a second part of a first semester calculus book. I have looked at McCrea's Analytical geometry of three dimensions .... Such geometry can be handled very nicely by vector methods. I > know of two really good little books which do that. Both are probably > both out of print (alas!), but you may be lucky enough to find a copy: A. M. (Alexander Murray) Macbeath, Elementary Vector Algebra Seymour Schuster, Elementary Vector Geometry. Ken Pledger. Marsden's book looks good. One tiny complain, it treats quaternion as a historical footnote where I would like to see something more substancial. Elementary Vector Geometry has been reissued by Dover with a very affordable price! Michuco === Subject: Re: Looking for Ref book: Analytic Geometry in 3D I am looking for a reference book where I can look up formulas such as > how to construct a plane that is orthogonal to a vector at its mid > point; check to see if three vectors are in the same plane etc. I am thinking of some kind of a handbook of analytic geometry on its > own, not as a second part of a first semester calculus book. I have looked at McCrea's Analytical geometry of three dimensions (God > bless Dover for affordable editions of classic works), but thought I > would get some more suggestions here. Much appreciated, Michuco Vector Calculus, by Marsden and Tromba has many problems like the ones you described. I think it's a nicely done book. Not as inexpensive as Dover but I would expect to be able to find a deal at Amazon.com on OLDER editions (I didn't look). I think you are likely to be happy with the book based on what you described. Bill === Subject: Re: GR Spaghetification > Modern cosmology states that on a large scale, the universe is > flat, > They mean that when using the preferred cosmological time, on a > large enough scale SPACE is flat. SpaceTIME is not flat -- clearly > so, because no big bang could occur in a flat spacetime. Moreover, whether or not space is flat depends on one's choice of > time coordinate. So this is not a geometrical property of the > manifold, it is a property of the specific foliation induced by the > preferred cosmological time coordinate. I repeat: the spaceTIME > manifold is not flat in any cosmological model with a big bang. > You appear to have slipped back into the there really isn't an > external world out there viewpoint. Not at all. Nowhere did I imply that in any way. > The true character of the space > that the external world exists in has nothing to do with any > person's choice of coordinates. There _IS_ no particular 3-d spatial submanifold of a 4-d spacetime, there are infinite numbers of them. So attempting to discuss > the true character of space simply makes no sense in GR or modern cosmology. This is so even though casual remarks made in > It is either able to be curved by mass, charge and/or angular momentum, or it is not able to curved. If your it means space, this is wrong; if your it means the spaceTIME manifold, then OK. > Consider the spherically symmetric, static Schw. metric that I used in my CIP paper. According to the usual interpretation, the ball of mass at the center curves the surrounding space and dilates time. Since the metric is static, at some point (x,y,z) outside of the event horizon distance, the curvature of the space there is constant, as is the gravitation-only dilation of time. By the curvature of space I mean the determinant of the 3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that point. The elements of this 3x3 submatrix are composed of derivatives of the Christoffel symbols which have nothing to do with time. The Christoffel symbols in this 3x3 submatrix are themselves only functions of spatial coordinates and do not involve time. If you do not believe me, here is the mathematical proof: http://sb635.mystarband.net/derivs.pdf http://sb635.mystarband.net/matalg.pdf These workups are for a full Kerr geometry, where a Schw. geometry is a special case when the central ball of matter is not spinning. (orbiting) along a geodesic. The laboratory coordinate time t is time's position in the laboratory. Time also has a velocity, dt/dtau, which most people call the time dilation factor (tau = proper time). Laboratory coordinate time t also has an acceleration, d^2t/dtau^2. And it has a 3rd derivative, and a 4th derivative, etc. It has a full state. But it's position and velocity, etc., are decidedly physically different, to me, than the actual spatial x (or y or z) position and velocity, etc., of a mathematics, if there exists any mass, charge or angular momentum resident at (0,0,0), then the surrounding *space itself* gets curved as well as time. But time gets curved, to me, in a different way. It gets dilated. Even though both are in the full spacetime 4-D position vector (x,y,z,t), and time itself has a full equation of motion in the laboratory frame (fundamentally different than Newtonian mechanics), time, to me, is fundamentally different than space. > Selecting a 3-d space from a 4-d spaceTIME manifold requires > a choice of time coordinate, which is ARBITRARY. You can > obtain all sorts of different spatial curvatures, depending > on how you happen to choose the time coordinate. Some choices > may be simpler than others, but all are allowed. > I say the space of the external world is flat, rigid, Newtonian and a > stationary clock in this absolute universal space provides a measure > of absolute time. Say anything you like; that does not mean it is consistent with current cosmological models or with the concepts of GR. Your > statement here is not. > My statement is about what I think is the true character of external space. I said I will it to be Euclidean because that's what I think external space is. I would not will it to be anything else for these problems. And the tensor algebra and tensor calculus of Weinberg are clear. The Christoffel symbols give the equations of motion (geodesic) connections between any two coordinate frames we wish to use in the mathematics. To answer these fundamental are SR/GR effects real questions, I think one of them should be Euclidean because that's what I think is the true character of external space, all the way from and below Planck scale out to, imo, a universe infinite in size. Btw, you never answered my question. In the freely falling coordinate frame attached to a hydrogen atom's proton's center of mass, falling in towards a black hole, does the electron's pathway suddenly change *even in* the freely falling rest frame of the hydrogen atom, when it gets physically ripped away from the proton? And the size of the system here does not matter. Say a star with a single planet orbiting the star is falling in towards a black hole. At some point, the planet's orbit will start getting significantly perturbed as viewed in an inertial Euclidean (laboratory) frame outside the event, within which these events are occurring (most conveniently centered at the center of mass of the black hole). Attach a freely falling coordinate frame to the star's center of mass. If the star and its planet were just all by themselves, the orbit of the planet would be, say, a perfect circle in this star-centered frame. Does it forever always stay a perfect circle in the freely falling frame attached to the star when falling in to a black hole? If the answer is no, then most people, I would say, need to rethink their interpretations of the equations of GR. I would tell them to ignore the topology and concentrate on the differential geometry and tensor algebra/calculus, and think about the physics. Like Weinberg does. > If in fact physical spacetime is flat and non-curved, [...] > Your carelessness has confused you. See above. > You seem to me to be confused by so easily jumping back and forth > between saying there exists an independent external world, yet putting so much emphasis on, e.g., a person's choice of > coordinates > when trying to describe this external world. You are confused, not me. In particular, space IS NOT PART OF THE EXTERNAL WORLD (or rather, not part of the model). SpaceTIME > is the proper model of the external world, according to current theories. Selecting space from spaceTIME requires the choice of > a time coordinate. If you believe in an external world, I can only imagine you must realize that means you are saying things (such as electrons) physically exist out there at a point in time at locations within some *space* which is most decidedly then part of the external world. Yes, obviously time must be involved, but if you do not believe that 3-D space is part of the external world, then probably you and I have nothing more to say to each other. Imo, you do not understand the true character of the external world. > You, like so many others, deceive yourself, because you have not > thought about the underlying issues sufficiently well. There is an > inherent limit to human consciousness: we are not Gods, and we do > not speak to Gods (in spite of what many would have us believe). > Look pal, you have no knowledge what-so-ever about how much I have > thought about things. Your writings betray your lack of insight and understanding. Imo, your writings betray your lack of insight and understanding. > And I repeat, there exists an independent external world who's true > character is what it is, and has nothing to do with us mere mortals > or any experiments we can or cannot perform. Sure. How confused you seem to be, imo, flipping back and forth between everything's relative to everything's independent. > The jury is still out, to me, on whether the truth about how > nature works is forever denied to us. It is quite obvious to me that we will NEVER be able to directly observe phenomena at the enormously-high energies involved near > the big bang (or whatever replaces it in future models and theories). Humans will NEVER know all of the details. > Tom Roberts My, aren't we god-like in our use of the word NEVER (and I will shout back at you if you shout at me). Sounds like you are a QM physicist. And once again, you ignore my statement about evidence for a flawed QED prediction. What's wrong, can't stand to look at data? Steve Bell === Subject: Re: GR Spaghetification > Consider the spherically symmetric, static Schw. metric that I used > in my CIP paper. According to the usual interpretation, the ball of > mass at the center curves the surrounding space and dilates time. > Since the metric is static, at some point (x,y,z) outside of the > event horizon distance, the curvature of the space there is > constant, as is the gravitation-only dilation of time. Sure, with the following caveats: A) You have chosen specific coordinates in order to foliate spacetime into space and time: you have used the timelike Killing vector as the time coordinate, and the spatial coordinates span the space orthogonal to the time coordinate. So of course the 3-d Riemann curvature tensor is independent of the time coordinate at any fixed value of the spatial coordinates. B) The gravitational time dilation being constant also depends on your choice of foliation (it is required to specify what point in space means). > By the > curvature of space I mean the determinant of the 3x3 space part of > the Riemann-Christoffel curvature tensor evaluated at that point. The > elements of this 3x3 submatrix are composed of derivatives of the > Christoffel symbols which have nothing to do with time. The > Christoffel symbols in this 3x3 submatrix are themselves only > functions of spatial coordinates and do not involve time. Sure, FOR THOSE COORDINATES. If, however, you had chosen locally-inertial coordinates anywhere, your claims would all be false. Note there are good reasons to use locally-inertial coordinates, because physics is simplest in inertial coordinates. > My statement is about what I think is the true character of external > space. I said I will it to be Euclidean because that's what I think > external space is. Not in the Schw. manifold for your chosen foliation [#]. The spatial metric outside the horizon is static but not at all Euclidean. [#] Or for any other foliation that holds throughout the external region. And again: in GR there is no external space in the sense you use it. Space depends on an ARBITRARY human choice of time coordinate, and so cannot possibly be external. > I would not will it to be anything else for > these problems. Then you cannot handle the Schwarzschild manifold -- It does not conform to your will, and you cannot make it do so. > And the tensor algebra and tensor calculus of > Weinberg are clear. Except you keep misinterpreting them and making wrong statements about the geometry. I repeat: with your chosen foliation of the Schw. manifold, space is NOT EUCLIDEAN. And space is NEVER external in GR. IMHO Weinberg's book is NOT AT ALL CLEAR about anything related to geometry. He deliberately avoids it, and thus make is all too easy for students who don't know better to make egregious mistakes. You are not alone in this. Get a better textbook, one that deals with geometry, or all this will remain a mystery to you. I like MTW, but some people find it too large :-) -- I think of it as comprehensive. > Btw, you never answered my question. In the freely falling coordinate > frame attached to a hydrogen atom's proton's center of mass, falling > in towards a black hole, does the electron's pathway suddenly change > *even in* the freely falling rest frame of the hydrogen atom, when > it gets physically ripped away from the proton? First, YOU cannot handle such a problem, as you cannot will space to be Euclidean. Second, as the atom approaches the singularity, there is no rest frame that includes the entire atom -- the curvature of the region occupied by the atom increases without bound, and rest frame implies it is negligibly different from flat [*]. So your question does not make sense. [*] All this is speaking somewhat loosely. I'm ignoring quantum effects and simply model an atom as a nucleus and electron separated by a distance on the order of Angstroms. GR is a classical theory. Remember that locally-inertial coordinates are only approximately valid, and for a given accuracy they are only valid within a region whose size depends on the curvature of the manifold within the region. Approaching a singularity that curvature increases without bound, forcing the region of validity of such coordinates go to zero size (smaller than any finite-sized object such as an atom). > If you believe in an external world, I can only imagine you must > realize that means you are saying things (such as electrons) > physically exist out there at a point in time at locations within > some *space* which is most decidedly then part of the external world. You are overly fixated on space. In GR, there is no such thing as space in the sense you use the word. In particular, in GR space must be SELECTED via foliation of the spaceTIME manifold, so the geometry of space is subject to an ARBITRARY human choice -- not external at all. > Yes, obviously time must be involved, but if you do not believe that > 3-D space is part of the external world, then probably you and I have > nothing more to say to each other. Imo, you do not understand the > true character of the external world. And you do not understand GR. Or how the geometry of GR relates to space and time. At present, the geometrical model of GR is the best we have, and in GR the external world is spaceTIME, not space. I most definitely do not understand the true character of the external world -- unlike you, I do not make any claims about true anything about the world, because I KNOW that humans cannot access (understand) the real world but can only make MODELS of it. You make claims that require a direct channel to some God which informs you of the true character of the external world; I have no such channel. And I doubt very much that you do, either, you merely deceive yourself into thinking you do. Tom Roberts === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Consider the spherically symmetric, static Schw. metric that I used > in my CIP paper. According to the usual interpretation, the ball of > mass at the center curves the surrounding space and dilates time. > Since the metric is static, at some point (x,y,z) outside of the > event horizon distance, the curvature of the space there is > constant, as is the gravitation-only dilation of time. Sure, with the following caveats: A) You have chosen specific coordinates in order to foliate spacetime > into space and time: you have used the timelike Killing vector > as the time coordinate, and the spatial coordinates span the > space orthogonal to the time coordinate. So of course the 3-d > Riemann curvature tensor is independent of the time coordinate > at any fixed value of the spatial coordinates. B) The gravitational time dilation being constant also depends > on your choice of foliation (it is required to specify what > point in space means). By the > curvature of space I mean the determinant of the 3x3 space part of > the Riemann-Christoffel curvature tensor evaluated at that point. The > elements of this 3x3 submatrix are composed of derivatives of the > Christoffel symbols which have nothing to do with time. The > Christoffel symbols in this 3x3 submatrix are themselves only > functions of spatial coordinates and do not involve time. Sure, FOR THOSE COORDINATES. If, however, you had chosen > locally-inertial coordinates anywhere, your claims would all be false. > Note there are good reasons to use locally-inertial coordinates, because > physics is simplest in inertial coordinates. My statement is about what I think is the true character of external > space. I said I will it to be Euclidean because that's what I think > external space is. Not in the Schw. manifold for your chosen foliation [#]. The spatial > metric outside the horizon is static but not at all Euclidean. [#] Or for any other foliation that holds throughout the > external region. And again: in GR there is no external space in the sense you use it. > Space depends on an ARBITRARY human choice of time coordinate, and so > cannot possibly be external. I would not will it to be anything else for > these problems. Then you cannot handle the Schwarzschild manifold -- It does not conform > to your will, and you cannot make it do so. And the tensor algebra and tensor calculus of > Weinberg are clear. Except you keep misinterpreting them and making wrong statements about > the geometry. I repeat: with your chosen foliation of the Schw. > manifold, space is NOT EUCLIDEAN. And space is NEVER external in GR. IMHO Weinberg's book is NOT AT ALL CLEAR about anything > related to geometry. He deliberately avoids it, and thus > make is all too easy for students who don't know better > to make egregious mistakes. You are not alone in this. > Get a better textbook, one that deals with geometry, or > all this will remain a mystery to you. I like MTW, but > some people find it too large :-) -- I think of it as > comprehensive. Btw, you never answered my question. In the freely falling coordinate > frame attached to a hydrogen atom's proton's center of mass, falling > in towards a black hole, does the electron's pathway suddenly change > *even in* the freely falling rest frame of the hydrogen atom, when > it gets physically ripped away from the proton? First, YOU cannot handle such a problem, as you cannot will space to > be Euclidean. Second, as the atom approaches the singularity, there is > no rest frame that includes the entire atom -- the curvature of the > region occupied by the atom increases without bound, and rest frame > implies it is negligibly different from flat [*]. So your question does > not make sense. [*] All this is speaking somewhat loosely. I'm ignoring > quantum effects and simply model an atom as a nucleus > and electron separated by a distance on the order of > Angstroms. GR is a classical theory. Remember that locally-inertial coordinates are only approximately valid, > and for a given accuracy they are only valid within a region whose size > depends on the curvature of the manifold within the region. Approaching > a singularity that curvature increases without bound, forcing the region > of validity of such coordinates go to zero size (smaller than any > finite-sized object such as an atom). If you believe in an external world, I can only imagine you must > realize that means you are saying things (such as electrons) > physically exist out there at a point in time at locations within > some *space* which is most decidedly then part of the external world. You are overly fixated on space. In GR, there is no such thing as > space in the sense you use the word. In particular, in GR space must > be SELECTED via foliation of the spaceTIME manifold, so the geometry of > space is subject to an ARBITRARY human choice -- not external at all. Yes, obviously time must be involved, but if you do not believe that > 3-D space is part of the external world, then probably you and I have > nothing more to say to each other. Imo, you do not understand the > true character of the external world. And you do not understand GR. Or how the geometry of GR relates to space > and time. At present, the geometrical model of GR is the best we have, > and in GR the external world is spaceTIME, not space. I most definitely do not understand the true character of the external > world -- unlike you, I do not make any claims about true anything > about the world, because I KNOW that humans cannot access (understand) > the real world but can only make MODELS of it. You make claims that > require a direct channel to some God which informs you of the true > character of the external world; I have no such channel. And I doubt > very much that you do, either, you merely deceive yourself into thinking > you do. Tom Roberts 2982$Jb1.1377@flpi144.ffdc.sbc.com... > Modern cosmology states that on a large scale, the universe is > flat, > They mean that when using the preferred cosmological time, on a > large enough scale SPACE is flat. SpaceTIME is not flat -- clearly > so, because no big bang could occur in a flat spacetime. > Moreover, whether or not space is flat depends on one's choice of > time coordinate. So this is not a geometrical property of the > manifold, it is a property of the specific foliation induced by the > preferred cosmological time coordinate. I repeat: the spaceTIME > manifold is not flat in any cosmological model with a big bang. > You appear to have slipped back into the there really isn't an > external world out there viewpoint. > Not at all. Nowhere did I imply that in any way. > The true character of the space > that the external world exists in has nothing to do with any > person's choice of coordinates. > There _IS_ no particular 3-d spatial submanifold of a 4-d spacetime, there are infinite numbers of them. So attempting to discuss > the true character of space simply makes no sense in GR or modern cosmology. This is so even though casual remarks made in > It is either able to be curved by mass, charge and/or angular momentum, or it is not able to curved. > If your it means space, this is wrong; if your it means the spaceTIME manifold, then OK. Consider the spherically symmetric, static Schw. metric that I used in my CIP paper. According to the usual interpretation, the ball of mass at the center curves the surrounding space and dilates time. Since the metric is static, at some point (x,y,z) outside of the event horizon distance, the curvature of the space there is constant, as is the gravitation-only dilation of time. By the curvature of space I mean the determinant of the 3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that point. The elements of this 3x3 submatrix are composed of derivatives of the Christoffel symbols which have nothing to do with time. The Christoffel symbols in this 3x3 submatrix are themselves only functions of spatial coordinates and do not involve time. If you do not believe me, here is the mathematical proof: http://sb635.mystarband.net/derivs.pdf http://sb635.mystarband.net/matalg.pdf These workups are for a full Kerr geometry, where a Schw. geometry is a special case when the central ball of matter is not spinning. Time, when used as a 4th dimension, has a full state just as does (orbiting) along a geodesic. The laboratory coordinate time t is time's position in the laboratory. Time also has a velocity, dt/dtau, which most people call the time dilation factor (tau = proper time). Laboratory coordinate time t also has an acceleration, d^2t/dtau^2. And it has a 3rd derivative, and a 4th derivative, etc. It has a full state. But it's position and velocity, etc., are decidedly physically different, to me, than the actual spatial x (or y or z) position and velocity, etc., of a doubt, according to the standard interpretation of the mathematics, if there exists any mass, charge or angular momentum resident at (0,0,0), then the surrounding *space itself* gets curved as well as time. But time gets curved, to me, in a different way. It gets dilated. Even though both are in the full spacetime 4-D position vector (x,y,z,t), and time itself has a full equation of motion in the laboratory frame (fundamentally different than Newtonian mechanics), time, to me, is fundamentally different than space. > Selecting a 3-d space from a 4-d spaceTIME manifold requires > a choice of time coordinate, which is ARBITRARY. You can > obtain all sorts of different spatial curvatures, depending > on how you happen to choose the time coordinate. Some choices > may be simpler than others, but all are allowed. > I say the space of the external world is flat, rigid, Newtonian and a > stationary clock in this absolute universal space provides a measure > of absolute time. > Say anything you like; that does not mean it is consistent with current cosmological models or with the concepts of GR. Your > statement here is not. My statement is about what I think is the true character of external space. I said I will it to be Euclidean because that's what I think external space is. I would not will it to be anything else for these problems. And the tensor algebra and tensor calculus of Weinberg are clear. The Christoffel symbols give the equations of motion (geodesic) connections between any two coordinate frames we wish to use in the mathematics. To answer these fundamental are SR/ GR effects real questions, I think one of them should be Euclidean because that's what I think is the true character of external space, all the way from and below Planck scale out to, imo, a universe infinite in size. Btw, you never answered my question. In the freely falling coordinate frame attached to a hydrogen atom's proton's center of mass, falling in towards a black hole, does the electron's pathway suddenly change *even in* the freely falling rest frame of the hydrogen atom, when it gets physically ripped away from the proton? And the size of the system here does not matter. Say a star with a single planet orbiting the star is falling in towards a black hole. At some point, the planet's orbit will start getting significantly perturbed as viewed in an inertial Euclidean (laboratory) frame outside the event, within which these events are occurring (most conveniently centered at the center of mass of the black hole). Attach a freely falling coordinate frame to the star's center of mass. If the star and its planet were just all by themselves, the orbit of the planet would be, say, a perfect circle in this star-centered frame. Does it forever always stay a perfect circle in the freely falling frame attached to the star when falling in to a black hole? If the answer is no, then most people, I would say, need to rethink their interpretations of the equations of GR. I would tell them to ignore the topology and concentrate on the differential geometry and tensor algebra/calculus, and think about the physics. Like Weinberg does. > If in fact physical spacetime is flat and non-curved, [...] > Your carelessness has confused you. See above. > You seem to me to be confused by so easily jumping back and forth > between saying there exists an independent external world, yet putting so much emphasis on, e.g., a person's choice of > coordinates > when trying to describe this external world. > You are confused, not me. In particular, space IS NOT PART OF THE EXTERNAL WORLD (or rather, not part of the model). SpaceTIME > is the proper model of the external world, according to current theories. Selecting space from spaceTIME requires the choice of > a time coordinate. If you believe in an external world, I can only imagine you must realize that means you are saying things (such as electrons) physically exist out there at a point in time at locations within some *space* which is most decidedly then part of the external world. Yes, obviously time must be involved, but if you do not believe that 3- D space is part of the external world, then probably you and I have nothing more to say to each other. Imo, you do not understand the true character of the external world. > You, like so many others, deceive yourself, because you have not > thought about the underlying issues sufficiently well. There is an > inherent limit to human consciousness: we are not Gods, and we do > not speak to Gods (in spite of what many would have us believe). > Look pal, you have no knowledge what-so-ever about how much I have > thought about things. > Your writings betray your lack of insight and understanding. Imo, your writings betray your lack of insight and understanding. > And I repeat, there exists an independent external world who's true > character is what it is, and has nothing to do with us mere mortals > or any experiments we can or cannot perform. > Sure. How confused you seem to be, imo, flipping back and forth between everything's relative to everything's independent. > The jury is still out, to me, on whether the truth about how > nature works is forever denied to us. > It is quite obvious to me that we will NEVER be able to directly observe phenomena at the enormously-high energies involved near > the big bang (or whatever replaces it in future models and theories). Humans will NEVER know all of the details. > Tom Roberts My, aren't we god-like in our use of the word NEVER (and I will shout back at you if you shout at me). Sounds like you are a QM physicist. And once again, you ignore my statement about evidence for a flawed QED prediction. What's wrong, can't stand to look at data? Steve Bell The true character of the space the external world exists in has nothing to do with any person's choice of coordinates. Martin Musatov === Subject: Re: GR Spaghetification Steve Bell says... >Consider the spherically symmetric, static Schw. >metric that I used in my CIP paper. The Schwarzschild metric is only static when you use a particular coordinate system (the Schwarzschild coordinates). In other coordinates, the metric is time-dependent. >By the curvature of space I mean the determinant of the >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that >point. The separation of spacetime into a spatial part plus a time part is coordinate-dependent. Different coordinates will make that separation differently. Yes, if you fix a particular coordinate system, then you can talk about the spatial curvature tensor, but you must first decide on a coordinate system (or at least, you have to decide on your time axis). -- Daryl McCullough Ithaca, NY === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > The Schwarzschild metric is only static when you use > a particular coordinate system (the Schwarzschild > coordinates). In other coordinates, the metric is > time-dependent. This is not true. part is coordinate-dependent. Different coordinates will make > that separation differently. have been talking about in all these years. > Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). That is so wonderful. This is so true. The geometry is always invariant regardless of any choice of coordinate system one wishes to choose. The curvature tensor depends on your choice of coordinate system. You can always choose a coordinate system to give you seemingly a flat curvature tensor regardless however curved up spacetime is. This is how Schwarzschild was able to find a solution to the field equations so quickly. He was a genius in applied mathematics. By the time you are able to write down all the field equations that are ready to be solved, the choice of coordinate system is already cast in concrete. Changing that coordinate system is OK, but you must change it back. This was exactly what Schwarzschild did. He changed the coordinate to result in a metric with a determinant of -1. That allowed the Ricci tensor to be drastically reduced. After obtaining a solution, like any good mathematicians, he must change the coordinate system back to the original spherically symmetric polar coordinate system, and that was exactly what he did. Congratulations, Mr. McCullough, you are beginning to understand what I am talking about. By the way, the basic concept is within the domain of elementary school logic. === Subject: Re: GR Spaghetification > Steve Bell says... >Consider the spherically symmetric, static Schw. >metric that I used in my CIP paper. The Schwarzschild metric is only static when you use > a particular coordinate system (the Schwarzschild > coordinates). In other coordinates, the metric is > time-dependent. > Weinberg classifies the Schw. metric as a static isotropic metric. He specifically states the invariant proper time dtau^2 = -g_uv dx^u dx^v does not depend on t, and depends on x and dx... This statement is made way before assuming any specific metrical structure such as Schw. Couple this with the mathematics he presents for deriving the geodesic equation, it is quite clear to me how geodesic motion should be viewed. The Schw. specific geodesic equations provide actual true accelerations (oh my, I must be an idiot It is quite apparent to me that none of you have actually programmed any of these geodesic equations. If you did, you would see you *have to* take the attitude I have taken. The only way you can computer-generate orbital motion using these geodesic accelerations is to numerically integrate them in the laboratory frame, *exactly* like I have done in a published paper of mine in CIP. If you believe that your GR orbit simulation reflects reality, this demands you accept that GR-geodesic defined accelerations are just as physically real (and so are forces) as in Newtonian mechanics. >By the curvature of space I mean the determinant of the >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that >point. The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). -- > Daryl McCullough > Ithaca, NY > According to the mathematics of Weinberg, you need two coordinate systems to make sense of the Christoffel symbols, which are the connection coefficients between the two systems. I always choose one of the systems to be Euclidean, *exactly* as Weinberg and the mathematics say I can, and I do that because I view the external space our universe of matter resides in, at a point in time, as a gigantic Euclidean laboratory frame. The other coordinate system I take most generally to be a Kerr system. Not the Kerr-Newman system, which incorporates the relativistic effects of the central charge on its surrounding gravito-electromagnetic field in an incorrect way, imo. These central-charge-including metrices, which are attempts at unifying gravity and at least parts of electricity using differential geometry, are incorrect, imo. There is an obvious flaw with these metrices that I'm surprised the authors didn't see. Or maybe they did, but I've not seen this issue described anywhere. Steve Bell === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> <1ae05$4a430427$944e5322$5014@STARBAND.NET> posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) [...] It is so hard to reply to horribly formatted messages. === Subject: Re: GR Spaghetification > It is quite apparent to me that none of you have actually programmed > any of these geodesic equations. Not true. I have performed numerous computations of geodesics in Schwarzschild spacetime, using Mathematica. > If you did, you would see you *have > to* take the attitude I have taken. Not true. You really don't have a very complete understanding of tensors. Weinberg does not provide much understanding of them -- he only skims the surface. Get a better book. > The only way you can > computer-generate orbital motion using these geodesic accelerations > is to numerically integrate them in the laboratory frame, That is one way, but not the only way. Mathematica was able to solve analytically the geodesic paths I was interested in (asking whether LIGO could detect the sun and moon -- it could if it had comparable sensitivity in their frequency range, which it doesn't). You have an incredibly limited point of view. Your way is NOT the only way. Even Weinberg's way is not the only way -- not by a long shot. > If you believe > that your GR orbit simulation reflects reality, this demands you > accept that GR-geodesic defined accelerations are just as physically > real (and so are forces) as in Newtonian mechanics. You need to learn to distinguish between real physical phenomena and computational models. A human in freefall cannot feel any acceleration due to gravity, so why do you think that those accelerations are physically real? Indeed, GR models an object in freefall such that its PROPER acceleration is identically zero. You confuse the coordinate-dependent quantities in your computations with physical quantities; they aren't the same. The coordinate independence of GR (and all of physics) implies that no coordinate-dependent quantity can correspond to any real physical phenomenon [#]; this includes your accelerations. In GR there _IS_ no gravitational force -- it is just as fictitious as centrifugal and Coriolis forces are in Newtonian mechanics (none of these are really forces, in GR they are all components of the connection projected onto Newtonian coordinates). [#] Coordinates are arbitrary human choices; no real physical phenomenon can depend on such arbitrary human choices. > According to the mathematics of Weinberg, you need two coordinate > systems to make sense of the Christoffel symbols, which are the > connection coefficients between the two systems. Weinberg is not at all the last word, or even a very good word, here. In particular, he deliberately ignores just about everything about geometry. Geometrically, the Christoffel symbols are the connection, which has LOTS of geometrical implications and applications, and which is well defined without two coordinate systems. > [... repetition of the same basic mistake] Tom Roberts === Subject: Re: GR Spaghetification > Weinberg is not at all the last word, or even a very good word, here. In > particular, he deliberately ignores just about everything about > geometry. Geometrically, the Christoffel symbols are the connection, > which has LOTS of geometrical implications and applications, and which > is well defined without two coordinate systems. I forgot to mention that Weinberg actually uses a LOCAL inertial (Minkowski) frame. His book and mathematics do NOT support your notion that space is Euclidean, except LOCALLY. That is a trivial point, as the definition of a manifold includes it directly. So Weinberg does not have the difficulties that you have with the claims you make -- probably because he actually understands all this. Tom Roberts === Subject: Re: GR Spaghetification > Weinberg is not at all the last word, or even a very good word, here. In particular, he deliberately ignores just about > everything about geometry. Geometrically, the Christoffel symbols are the connection, which has LOTS of geometrical implications > and applications, and which is well defined without two coordinate systems. I forgot to mention that Weinberg actually uses a LOCAL inertial (Minkowski) frame. His book and mathematics do NOT support your > notion that space is Euclidean, except LOCALLY. That is a trivial point, as the definition of a manifold includes it directly. > So Weinberg does not have the difficulties that you have with the claims you make -- probably because he actually understands all > this. > Tom Roberts So now you think Weinberg is correct. My how ambiguous, sounds like a QM physicist. If you have not deduced by now that, yes, I think basically completely locally, I am surprised you didn't know that by now. I think the world is built from the bottom up, not from the top down. Another interesting thought experiment involves the quantum foam background. If I understand this correctly, on a Planck scale, the elements of the metric tensor are assumed stochastic, and there exists a foamy character, to, I was going to say, the curvature of space, but apparently not including time flips you out. Ok, so include time, which in certain ways, is even easier to accept as being stochastic than space itself. Is all this quantum foaminess all relative also? In two moving coordinate frames, each with nonzero velocities in a laboratory frame, is the individual quantum foaminess physically different? It would seem it couldn't be, if indeed this foaminess is truthfully physical. The death of a person is also an interesting event. To me, death is absolute. But is there an actual frame, moving relative to the frame in which I have died, where I haven't died? If so, beam me over Scotty. I know this may sound strange, but death, to me, proves the existence of a completely independent external world following laws of nature that simply cannot be circumvented no matter what relative motions exist. Steve Bell === Subject: Re: GR Spaghetification > I forgot to mention that Weinberg actually uses a LOCAL inertial > (Minkowski) frame. His book and mathematics do NOT support your > notion that space is Euclidean, except LOCALLY. That is a trivial > point, as the definition of a manifold includes it directly. So > Weinberg does not have the difficulties that you have with the > claims you make -- probably because he actually understands all > this. So now you think Weinberg is correct. You need to read more carefully. I never said or implied that Weinberg is wrong, I merely pointed out that he omits just about all discussion of geometry, and it is the geometrical aspects of GR that confuse you. Note that HE says he is omitting discussions of geometry. > I think the world is built > from the bottom up, not from the top down. I think that I don't know how the world is built. And I think you don't, either. But that's OK, because I have a set of useful models of the world that permit me to live in the world, do useful and interesting things, and pursue physics. I also think that nobody else actually does anything different, even though they think they do or claim to do. Including you. > Another interesting thought experiment involves the quantum foam > background. [...] Nobody knows much about that, and nobody has a complete and testable model. It is certainly far from GR and is currently pure speculation, not a well-formed theory of physics. Tom Roberts === Subject: Re: GR Spaghetification > >Weinberg is not at all the last word, or even a very good word, here. In particular, he deliberately ignores just about >everything about geometry. Geometrically, the Christoffel symbols are the connection, which has LOTS of geometrical implications >and applications, and which is well defined without two coordinate systems. >I forgot to mention that Weinberg actually uses a LOCAL inertial (Minkowski) frame. His book and mathematics do NOT support your >notion that space is Euclidean, except LOCALLY. That is a trivial point, as the definition of a manifold includes it directly. >So Weinberg does not have the difficulties that you have with the claims you make -- probably because he actually understands all >this. >Tom Roberts > So now you think Weinberg is correct. You do not score well in reading comprehension. My how ambiguous, sounds like a QM physicist. If you have not deduced by now that, yes, I > think basically completely locally, I am surprised you didn't know that by now. I think the world is built from the bottom up, not > from the top down. So you feel that the universe must be the way you command it to be. Another interesting thought experiment involves the quantum foam background. If I understand this correctly, on a Planck scale, > the elements of the metric tensor are assumed stochastic, and there exists a foamy character, to, I was going to say, the > curvature of space, but apparently not including time flips you out. Ok, so include time, which in certain ways, is even easier to > accept as being stochastic than space itself. Is all this quantum foaminess all relative also? In two moving coordinate frames, > each with nonzero velocities in a laboratory frame, is the individual quantum foaminess physically different? It would seem it > couldn't be, if indeed this foaminess is truthfully physical. The death of a person is also an interesting event. To me, death is absolute. But is there an actual frame, moving relative to the > frame in which I have died, where I haven't died? If so, beam me over Scotty. I know this may sound strange, but death, to me, > proves the existence of a completely independent external world following laws of nature that simply cannot be circumvented no > matter what relative motions exist. Yes, it sounds pretty strange. Steve Bell === Subject: Re: GR Spaghetification >Weinberg is not at all the last word, or even a very good word, here. In particular, he deliberately ignores just about >everything about geometry. Geometrically, the Christoffel symbols are the connection, which has LOTS of geometrical implications >and applications, and which is well defined without two coordinate systems. I forgot to mention that Weinberg actually uses a LOCAL inertial (Minkowski) frame. His book and mathematics do NOT support your >notion that space is Euclidean, except LOCALLY. That is a trivial point, as the definition of a manifold includes it directly. >So Weinberg does not have the difficulties that you have with the claims you make -- probably because he actually understands all >this. >Tom Roberts > So now you think Weinberg is correct. You do not score well in reading comprehension. My how ambiguous, sounds like a QM physicist. If you have not deduced by now that, yes, I > think basically completely locally, I am surprised you didn't know that by now. I think the world is built from the bottom up, > not from the top down. So you feel that the universe must be the way you command it to be. > Absolutely not (I don't believe in QM ). But that still does not stop me from thinking about how it actually is. I bet you also have an opinion. I actually believe that most every scientist knows exactly what I'm talking about, in their gut they know there exists a world out there completely independent of what their brains can see. And if there is an external world independent of one brain, it must be independent of all brains. > Another interesting thought experiment involves the quantum foam background. If I understand this correctly, on a Planck scale, > the elements of the metric tensor are assumed stochastic, and there exists a foamy character, to, I was going to say, the > curvature of space, but apparently not including time flips you out. Ok, so include time, which in certain ways, is even easier > to accept as being stochastic than space itself. Is all this quantum foaminess all relative also? In two moving coordinate > frames, each with nonzero velocities in a laboratory frame, is the individual quantum foaminess physically different? It would > seem it couldn't be, if indeed this foaminess is truthfully physical. > The death of a person is also an interesting event. To me, death is absolute. But is there an actual frame, moving relative to > the frame in which I have died, where I haven't died? If so, beam me over Scotty. I know this may sound strange, but death, to > me, proves the existence of a completely independent external world following laws of nature that simply cannot be circumvented > no matter what relative motions exist. Yes, it sounds pretty strange. > To me, death is a physical event. Meaning that my atoms will not be in the same states they were in when I was alive. Like I said, if this is really all relative, meaning that in some moving system, relative to the system in which I died, my atoms were just fine, I bet the Devil will be mad . Steve Bell === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> <1ae05$4a430427$944e5322$5014@STARBAND.NET> <3eccc$4a447e67$944e5322$28728@STARBAND.NET> posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) [...] People who don't believe in quantum mechanics manage to use computers just fine. Isn't that curious? === Subject: Re: GR Spaghetification Steve Bell says... >Absolutely not (I don't believe in QM ). But that still does not >stop me from thinking about how it actually is. I bet you also >have an opinion. I actually believe that most every scientist >knows exactly what I'm talking about, in their gut they know there >exists a world out there completely independent of what >their brains can see. And if there is an external world independent >of one brain, it must be independent of all brains. There is nothing subjective about relativity theory. It is just as objective as Newtonian physics. -- Daryl McCullough Ithaca, NY === Subject: Re: GR Spaghetification > Steve Bell says... > Absolutely not (I don't believe in QM ). But that still does not > stop me from thinking about how it actually is. I bet you also > have an opinion. I actually believe that most every scientist > knows exactly what I'm talking about, in their gut they know there > exists a world out there completely independent of what > their brains can see. And if there is an external world independent > of one brain, it must be independent of all brains. Yes, of course there is an external world independent of humans -- that's essential for science to have any meaning at all. It's just that in GR that external world does NOT include space, it includes spaceTIME. Foliating spaceTIME into space and time requires an arbitrary HUMAN choice, and thus cannot possibly be external. Basically such foliations are useful for descriptions, but have nothing whatsoever to do with the dynamics of the theory -- GR is completely independent of coordinates, and thus is independent of foliations; so humans can use ANY foliation or coordinates that seem useful to them, but their choice(s) do not affect the theory or the behavior of objects in the model at all. In order to understand GR, you MUST learn to understand this. BTW QM does not violate this, either. It's just that in the world we inhabit there are phenomena that are truly random, and there are phenomena that can only be modeled statistically. QM reflects these basic facts about our world. And I repeat: you are NOT thinking about how it actually is, you are thinking about your personal MODELS of how you HAPPEN TO THINK IT IS. (Unless you have a personal channel to some God who tells you what actually is...) > There is nothing subjective about relativity theory. It is > just as objective as Newtonian physics. And just as deterministic. QM is likewise completely deterministic, but only as a statistical description. > There must be a single way in which all this physical > ripping apart happens, and if so, there must be a single universal frame. No, there need not be any sort of single universal frame, as long as the manner of ripping occurs identically in every frame -- in all modern theories of physics (including GR), it does. That said, you could select ANY frame and call it THE universal frame -- your label means nothing, and doing this does not affect the theory or objects' behavior, but if it makes you feel warm and fuzzy go ahead; just don't expect anyone else to agree, as those words have meanings other than as such meaningless labels and other people will interpret them according to those meanings and thus disagree with you. > All this everything's relative stuff is > severely constrained if there really does exist an external world independent of observation. There is NO everything's relative in relativity (or any other theory of modern physics) -- I have no idea where you got that notion, but it is WRONG. Various DESCRIPTIONS of phenomena are relative to the choice of frame (coordinates), but the phenomena themselves are completely and utterly independent of whichever coordinates humans choose to use to describe them. So, for instance, the length of an object measured in a given inertial frame depends on the choice of frame, giving rise to length contraction in SR and GR; the proper length of the object is intrinsic to the object and does not depend on frame. Length in a frame is NOT intrinsic to the object, and is merely a human description; proper length is a physical aspect of the object. This is contrary to everyday experience and Newtonian mechanics, where lengths are independent of frame, but is _IS_ a self-consistent description of the world. And it corresponds much better to experiments performed in that world. Tom Roberts === Subject: Re: GR Spaghetification > Steve Bell says... > Absolutely not (I don't believe in QM ). But that still does not > stop me from thinking about how it actually is. I bet you also have an opinion. I actually believe that most every scientist > knows exactly what I'm talking about, in their gut they know there exists a world out there completely independent of what > their brains can see. And if there is an external world independent > of one brain, it must be independent of all brains. Yes, of course there is an external world independent of humans -- > that's essential for science to have any meaning at all. It's just that in GR that external world does NOT include space, it > includes spaceTIME. distances between them, at this instant in time? > Foliating spaceTIME into space and time requires an arbitrary HUMAN choice, and thus cannot possibly be external. Basically such > foliations are useful for descriptions, but have nothing whatsoever to do with the dynamics of the theory -- GR is completely > independent of coordinates, and thus is independent of foliations; so humans can use ANY foliation or coordinates that seem useful > to them, but their choice(s) do not affect the theory or the behavior of objects in the model at all. In order to understand GR, you MUST learn to understand this. > If there is a *requirement* of a *human* choice in GR, and the true characteristics of the external world are independent of human choice, then I would say there is something fundamentally lacking about GR. I really do not see why someone would think that space itself does not exist. That does *not* mean that it is not intertwined with time. You know the word *is* SPACEtime. And I think I now understand how space and time are intertwined. My beliefs now show me we need new interpretations of GR. I don't think any of the fundamental equations need to be modified, just interpreted correctly. I think I do now. > BTW QM does not violate this, either. It's just that in the world we inhabit there are phenomena that are truly random, and there > are phenomena that can only be modeled statistically. QM reflects these basic facts about our world. > In every mathematical statistical analysis I know about, there are variables that are *always* assumed to be truly random. I am a degreed statistician and I teach statistics in college. I know mathematical statistical theory very well. It is always assumed at the beginning that there are true random variables. Otherwise, it would not be statistical according to the theory I know. > And I repeat: you are NOT thinking about how it actually is, you are thinking about your personal MODELS of how you HAPPEN TO > THINK IT IS. (Unless you have a personal channel to some God who tells you what actually is...) I don't know about you, but I know my thoughts and ideas are about what I think the physical world is actually like. > There is nothing subjective about relativity theory. It is > just as objective as Newtonian physics. And just as deterministic. QM is likewise completely deterministic, but only as a > statistical description. I hope you see how completely in contradiction this statement is. It is actually impossible to *correctly* describe something that is completely deterministic using probability theory. Ideally, it shouldn't be describe statistically if it is actually deterministic. > There must be a single way in which all this physical ripping apart happens, and if so, there must be a single universal frame. No, there need not be any sort of single universal frame, as long as the manner of ripping occurs identically in every > frame -- in all modern theories of physics (including GR), it does. And this is the crux of the manner, isn't it. To me, in the standard interpretation of GR, the ripping does *not* occur identically in every frame. And if each frame claims I am just as good a description of physical reality as any other frame, I see a problem. I personally think there can only be *one* *physical* reality. > That said, you could select ANY frame and call it THE universal frame -- your label means nothing, It does if there really is a universal frame. And if there really is a universal frame, don't you think it's pretty important to get its characteristics right? I think it's basically a Newtonian frame. > and doing this does not affect the theory or objects' behavior, but if it makes you feel warm and fuzzy go ahead; just don't > expect anyone else to agree, as those words have meanings other than as such meaningless labels and other people will interpret > them according to those meanings and thus disagree with you. Yes, I fully realized that mainstream GR people would say I'm all wrong, that I don't understand the first thing about GR, etc. All of the usual dribble from closed-minded people like you. > All this everything's relative stuff is severely constrained if there really does exist an external world independent of > observation. There is NO everything's relative in relativity (or any other theory of modern physics) -- I have no idea where you got that > notion, but it is WRONG. Various DESCRIPTIONS of phenomena are relative to the choice of frame (coordinates), but the phenomena > themselves are completely and utterly independent of whichever coordinates humans choose to use to describe them. > I agree, the phenomena themselves are completely and utterly independent of whichever coordinates humans choose to use to describe them. But humans have to choose coordinate systems to describe them. I think I've chosen the correct ones that describes the physical truth: Euclidean for the laboratory, and generally, Kerr for representing the gravitational field that permeates the laboratory. > So, for instance, the length of an object measured in > a given inertial frame depends on the choice of frame, > giving rise to length contraction in SR and GR; the > proper length of the object is intrinsic to the object > and does not depend on frame. Length in a frame is NOT > intrinsic to the object, and is merely a human description; > proper length is a physical aspect of the object. > What do you mean by intrinsic to the object? Is this length that's intrinsic to the object somehow a function of the atomic structure of the object? Steve Bell === Subject: Re: GR Spaghetification > If there is a *requirement* of a *human* choice in GR, and the true > characteristics of the external world are independent of human > choice, then I would say there is something fundamentally lacking > about GR. You are not reading accurately enough. The problem is YOUR INSISTENCE ON SPACE, not in any aspect of GR. > I really do not see why someone would think that space itself does > not exist. [...] That's because you do not understand the geometry of GR. Nor do you seem to understand the relationship between MODELS of the world and the world itself: exists is a statement about the world, but space is an aspect of the MODEL; intermixing them like you do is nonsense. > [... no point in re-hashing this over again] Tom Roberts === Subject: Re: GR Spaghetification Given two unbroken wooden rings Interlock them without breaking the rings Transform a righthanded spiral Snail shell into a lefthanded one Make a knot in a closed loop Of a rope without cutting it Given a rope tied in a righthanded knot Inside a sealed container untie and retie The rope as a lefthanded knot Without breaking the seal Remove the contents Of a sealed bottle without breaking it -- Henry Slade -- Ahmed Ouahi, Architect Steve Bell kirjoitti viestiss.8a:60a35$4a44f433$944e5322$18097@STARBAND.NET... Steve Bell says... > Absolutely not (I don't believe in QM ). But that still does not > stop me from thinking about how it actually is. I bet you also have an > opinion. I actually believe that most every scientist > knows exactly what I'm talking about, in their gut they know there > exists a world out there completely independent of what > their brains can see. And if there is an external world independent > of one brain, it must be independent of all brains. > Yes, of course there is an external world independent of humans -- > that's essential for science to have any meaning at all. It's just that > in GR that external world does NOT include space, it includes > spaceTIME. > matter out there in the external world that have spatial distances > between them, at this instant in time? > Foliating spaceTIME into space and time requires an arbitrary HUMAN > choice, and thus cannot possibly be external. Basically such foliations > are useful for descriptions, but have nothing whatsoever to do with the > dynamics of the theory -- GR is completely independent of coordinates, > and thus is independent of foliations; so humans can use ANY foliation or > coordinates that seem useful to them, but their choice(s) do not affect > the theory or the behavior of objects in the model at all. > In order to understand GR, you MUST learn to understand this. If there is a *requirement* of a *human* choice in GR, and the true > characteristics of the external world are independent of human choice, > then I would say there is something fundamentally lacking about GR. I really do not see why someone would think that space itself does not > exist. That does *not* mean that it is not intertwined with time. You > know the word *is* SPACEtime. And I think I now understand how space and > time are intertwined. My beliefs now show me we need new interpretations > of GR. I don't think any of the fundamental equations need to be modified, > just interpreted correctly. I think I do now. > BTW QM does not violate this, either. It's just that in the world we > inhabit there are phenomena that are truly random, and there are > phenomena that can only be modeled statistically. QM reflects these basic > facts about our world. > In every mathematical statistical analysis I know about, there are > variables that are *always* assumed to be truly random. I am a degreed > statistician and I teach statistics in college. I know mathematical > statistical theory very well. It is always assumed at the beginning that > there are true random variables. Otherwise, it would not be statistical > according to the theory I know. > And I repeat: you are NOT thinking about how it actually is, you are > thinking about your personal MODELS of how you HAPPEN TO THINK IT IS. > (Unless you have a personal channel to some God who tells you what > actually is...) I don't know about you, but I know my thoughts and ideas are about what I > think the physical world is actually like. > There is nothing subjective about relativity theory. It is > just as objective as Newtonian physics. > And just as deterministic. > QM is likewise completely deterministic, but only as a > statistical description. > I hope you see how completely in contradiction this statement is. It is > actually impossible to *correctly* describe something that is completely > deterministic using probability theory. Ideally, it shouldn't be describe > statistically if it is actually deterministic. There must be a single way in which all this physical ripping apart > happens, and if so, there must be a single universal frame. > No, there need not be any sort of single universal frame, as long as > the manner of ripping occurs identically in every frame -- in all > modern theories of physics (including GR), it does. > And this is the crux of the manner, isn't it. To me, in the standard > interpretation of GR, the ripping does *not* occur identically in every > frame. And if each frame claims I am just as good a description of > physical reality as any other frame, I see a problem. I personally think > there can only be *one* *physical* reality. > That said, you could select ANY frame and call it THE universal > frame -- your label means nothing, It does if there really is a universal frame. And if there really is a > universal frame, don't you think it's pretty important to get its > characteristics right? I think it's basically a Newtonian frame. > and doing this does not affect the theory or objects' behavior, but if it > makes you feel warm and fuzzy go ahead; just don't expect anyone else to > agree, as those words have meanings other than as such meaningless labels > and other people will interpret them according to those meanings and thus > disagree with you. > Yes, I fully realized that mainstream GR people would say I'm all wrong, > that I don't understand the first thing about GR, etc. All of the usual > dribble from closed-minded people like you. All this everything's relative stuff is severely constrained if there > really does exist an external world independent of observation. > There is NO everything's relative in relativity (or any other theory of > modern physics) -- I have no idea where you got that notion, but it is > WRONG. Various DESCRIPTIONS of phenomena are relative to the choice of > frame (coordinates), but the phenomena themselves are completely and > utterly independent of whichever coordinates humans choose to use to > describe them. > I agree, the phenomena themselves are completely and utterly independent > of whichever coordinates humans choose to use to describe them. But > humans have to choose coordinate systems to describe them. I think I've > chosen the correct ones that describes the physical truth: Euclidean for > the laboratory, and generally, Kerr for representing the gravitational > field that permeates the laboratory. > So, for instance, the length of an object measured in > a given inertial frame depends on the choice of frame, > giving rise to length contraction in SR and GR; the > proper length of the object is intrinsic to the object > and does not depend on frame. Length in a frame is NOT > intrinsic to the object, and is merely a human description; > proper length is a physical aspect of the object. > What do you mean by intrinsic to the object? Is this length that's > intrinsic to the object somehow a function of the atomic structure of > the object? Steve Bell === Subject: Re: GR Spaghetification Given two unbroken wooden rings > Interlock them without breaking the rings > Transform a righthanded spiral Snail shell into a lefthanded one > Make a knot in a closed loop > Of a rope without cutting it Given a rope tied in a righthanded knot > Inside a sealed container untie and retie > The rope as a lefthanded knot Without breaking the seal > Remove the contents > Of a sealed bottle without breaking it -- Henry Slade > -- > Ahmed Ouahi, Architect > These topological possibilities just show to me how physically ridiculous topology can be sometimes. Steve Bell === Subject: Re: GR Spaghetification Lec 1 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=XDhJ8lVGbl8&feature=SeriesPlayList&p=EC88901E BADDD980 Lec 2 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=LbKKzMag5Rc&feature=SeriesPlayList&p=EC88901E BADDD980&index=1 Lec 3 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=tVzaX9u6YAE&feature=SeriesPlayList&p=EC88901E BADDD980&index=2 Lec 4 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=WBJ_iXudb-s&feature=SeriesPlayList&p=EC88901E BADDD980&index=3 Lec 5 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=te6Mplq3DCU&feature=SeriesPlayList&p=EC88901E BADDD980&index=4 Lec 6 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=EQJBp6Ym-6A&feature=SeriesPlayList&p=EC88901E BADDD980&index=5 Lec 7 | MT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=SioXozu-Loo&feature=SeriesPlayList&p=EC88901E BADDD980&index=6 Lec 8 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=MdzfsfBNJIw&feature=SeriesPlayList&p=EC88901E BADDD980&index=7 Lec 9 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=vP-oRQqmeg4&feature=SeriesPlayList&p=EC88901E BADDD980&index=8 Lec 10 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=YQ7HEE8-OfA&feature=related Lec 11 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=rZ3-nFV6l8w&feature=SeriesPlayList&p=EC88901E BADDD980 Lec 12 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=eyNm7XGJr4s&feature=SeriesPlayList&p=EC88901E BADDD980&index=11 Lec 13 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=9KbpbBMThTE&feature=SeriesPlayList&p=EC88901E BADDD980&index=12 Lec 14 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=Y9_zrupnz0Q&feature=SeriesPlayList&p=EC88901E BADDD980&index=13 Lec 15 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=EWWw0jryj1A&feature=SeriesPlayList&p=EC88901E BADDD980&index=14 Lec 16 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=xWa5_OXI6VM&feature=SeriesPlayList&p=EC88901E BADDD980&index=15 Lec 17 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=yD0_EQLxHcw&feature=SeriesPlayList&p=EC88901E BADDD980&index=16 Lec 19 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=sZ2qulI6GEk&feature=SeriesPlayList&p=EC88901E BADDD980&index=17 Lec 20 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=qZHseRxAWZ8&feature=SeriesPlayList&p=EC88901E BADDD980&index=18 Lec 21 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=3ejfkMHr_DE&feature=SeriesPlayList&p=EC88901E BADDD980&index=19 Lec 22 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=_YVcjNmjHik&feature=related Lec 23 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=peYvLk_HZdw&feature=SeriesPlayList&p=EC88901E BADDD980&index=21 Lec 24 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=MCrDzhpu3-s&feature=SeriesPlayList&p=EC88901E BADDD980&index=22 Lec 25 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=heBvViSi9xQ&feature=SeriesPlayList&p=EC88901E BADDD980&index=23 Lec 26 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=hEtWqTPPXuc&feature=SeriesPlayList&p=EC88901E BADDD980&index=24 Lec 27 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=e3FfmXtkppM&feature=SeriesPlayList&p=EC88901E BADDD980&index=25 Lec 28 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=2SuTN8rpe4I&feature=SeriesPlayList&p=EC88901E BADDD980&index=26 Lec 29 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=zreI4HllD80&feature=SeriesPlayList&p=EC88901E BADDD980&index=27 Lec 30 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=uNOyxQwIV8o&feature=SeriesPlayList&p=EC88901E BADDD980&index=28 Lec 31 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=UJG0f0BSX14&feature=SeriesPlayList&p=EC88901E BADDD980&index=29 Lec 32 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=z-meBrqcy_I&feature=SeriesPlayList&p=EC88901E BADDD980&index=30 Lec 33 | MIT 18.03 Differential Equations, Spring 2006 http://www.youtube.com/watch?v=kRR9EVzr4lc&feature=SeriesPlayList&p=EC88901E BADDD980&index=31 -- Ahmed Ouahi, Architect Steve Bell kirjoitti viestiss.8a:ee420$4a450e5e$944e5322$31312@STARBAND.NET... > Given two unbroken wooden rings > Interlock them without breaking the rings > Transform a righthanded spiral > Snail shell into a lefthanded one > Make a knot in a closed loop > Of a rope without cutting it > Given a rope tied in a righthanded knot > Inside a sealed container untie and retie > The rope as a lefthanded knot > Without breaking the seal > Remove the contents > Of a sealed bottle without breaking it > -- Henry Slade > -- > Ahmed Ouahi, Architect These topological possibilities just show to me how physically > ridiculous topology can be sometimes. Steve Bell === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> <1ae05$4a430427$944e5322$5014@STARBAND.NET> <3eccc$4a447e67$944e5322$28728@STARBAND.NET> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/2008102920 Firefox/3.0.4,gzip(gfe),gzip(gfe) >Weinberg is not at all the last word, or even a very good word, here. In particular, he deliberately ignores just about >everything about geometry. Geometrically, the Christoffel symbols are the connection, which has LOTS of geometrical implications >and applications, and which is well defined without two coordinate systems. I forgot to mention that Weinberg actually uses a LOCAL inertial (Minkowski) frame. His book and mathematics do NOT support your >notion that space is Euclidean, except LOCALLY. That is a trivial point, as the definition of a manifold includes it directly. >So Weinberg does not have the difficulties that you have with the claims you make -- probably because he actually understands all >this. Tom Roberts > So now you think Weinberg is correct. You do not score well in reading comprehension. My how ambiguous, sounds like a QM physicist. If you have not deduced by now that, yes, I > think basically completely locally, I am surprised you didn't know that by now. I think the world is built from the bottom up, > not from the top down. So you feel that the universe must be the way you command it to be. Absolutely not (I don't believe in QM ). But that still does not stop me from thinking about how it actually is. I bet you also > have an opinion. I actually believe that most every scientist knows exactly what I'm talking about, in their gut they know there > exists a world out there completely independent of what their brains can see. And if there is an external world independent of one > brain, it must be independent of all brains. > Another interesting thought experiment involves the quantum foam background. If I understand this correctly, on a Planck scale, > the elements of the metric tensor are assumed stochastic, and there exists a foamy character, to, I was going to say, the > curvature of space, but apparently not including time flips you out. Ok, so include time, which in certain ways, is even easier > to accept as being stochastic than space itself. Is all this quantum foaminess all relative also? In two moving coordinate > frames, each with nonzero velocities in a laboratory frame, is the individual quantum foaminess physically different? It would > seem it couldn't be, if indeed this foaminess is truthfully physical. > The death of a person is also an interesting event. To me, death is absolute. But is there an actual frame, moving relative to > the frame in which I have died, where I haven't died? If so, beam me over Scotty. I know this may sound strange, but death, to > me, proves the existence of a completely independent external world following laws of nature that simply cannot be circumvented > no matter what relative motions exist. Yes, it sounds pretty strange. To me, death is a physical event. Meaning that my atoms will not be in the same states they were in when I was alive. Like I said, > if this is really all relative, meaning that in some moving system, relative to the system in which I died, my atoms were just fine, > I bet the Devil will be mad . Steve Bell Death is a physical event. Life is THE event. I do not consider what does not exist. -- Musatov === Subject: Re: GR Spaghetification > It is quite apparent to me that none of you have actually programmed > any of these geodesic equations. Not true. I have performed numerous computations of geodesics in Schwarzschild spacetime, using Mathematica. > If you did, you would see you *have > to* take the attitude I have taken. Not true. You really don't have a very complete understanding of tensors. Weinberg does not provide much understanding of them -- > he only skims the surface. Get a better book. > I have many, but I like Weinberg best. He usually tries to make actual physical sense. > The only way you can > computer-generate orbital motion using these geodesic accelerations is to numerically integrate them in the laboratory frame, That is one way, but not the only way. Mathematica was able to solve analytically the geodesic paths I was interested in (asking > whether LIGO could detect the sun and moon -- it could if it had comparable sensitivity in their frequency range, which it > doesn't). > I'd like to see this derivation. If by analytical you mean closed form/without iteration, as far as I know, there are no closed formed orbital solutions, even in Newtonian mechanics, even for pure Newtonian elliptical orbits. The best closed form approximations I know about are based on Taylor series expansions, where no iteration is needed, so I'd call that closed form. But I seriously doubt that's what you mean, because you'd need to take the Kerr derivatives out to at least 6th order, and at 2nd order, they are already obnoxiously complicated. Is this what you did using Mathematica? If so, I'd like to see these complicated higher ordered derivatives. > You have an incredibly limited point of view. Your way > is NOT the only way. Even Weinberg's way is not the only > way -- not by a long shot. > Yes, I think motion in the external world is not nearly as complicated as topology suggests. I think all we need is a much more limited view than much of the nonsense in modern physics. > If you believe > that your GR orbit simulation reflects reality, this demands you > accept that GR-geodesic defined accelerations are just as physically > real (and so are forces) as in Newtonian mechanics. You need to learn to distinguish between real physical phenomena and computational models. A human in freefall cannot feel any > acceleration due to gravity, so why do you think that those accelerations are physically real? Because you used the words free fall. I assume you are talking GR and not SR, so then these words demand to me that you must view the physical truth as what's happening in a laboratory frame within which the falling is free. Otherwise, don't use the words free fall. To me, the words free fall specify an actual physical truth - something is physically coasting in a physical space, no matter if no one is observing anything. > Indeed, GR models an object in freefall such that its PROPER acceleration is identically zero. You confuse the > coordinate-dependent quantities in your computations with physical quantities; they aren't the same. For computer simulations, there is no confusion. Read my CIP paper. I simulated what I consider to be the physical motion that would happen in an external real world if the actual external conditions were as assumed in the paper. 10 solar mass, nonrotating ball of matter at (0,0,0), and mapped out, starting with given initial conditions, a significantly-relativistically affected orbit in an external laboratory frame. I believe this pathway is what an observer would see in the laboratory as actually happening, because hypothetically, it did, even if he/she weren't observing > The coordinate independence of GR (and all of physics) implies that no coordinate-dependent quantity can correspond to any real > physical phenomenon [#]; this includes your accelerations. In GR there _IS_ no gravitational force -- it is just as fictitious > as centrifugal and Coriolis forces are in Newtonian mechanics (none of these are really forces, in GR they are all components of > the connection projected onto Newtonian coordinates). > I take a different point of view now, which I absolutely admit is restricted. I view gravitational fields just as real in GR as they are in Newt. It took me a long time to finally give in, but I now think this is absolutely needed. > [#] Coordinates are arbitrary human choices; no real > physical phenomenon can depend on such arbitrary human > choices. > According to the mathematics of Weinberg, you need two coordinate > systems to make sense of the Christoffel symbols, which are the connection coefficients between the two systems. Weinberg is not at all the last word, or even a very good word, here. In particular, he deliberately ignores just about everything > about geometry. Geometrically, the Christoffel symbols are the connection, which has LOTS of geometrical implications and > applications, and which is well defined without two coordinate systems. Says you. Weinberg is clear. When you finally decide to accept the truth that there does exist an external world whose space is absolute, and that there is a single of instant of time that is the present everywhere (like right now then right now, this same instant of time is exactly the same right now everywhere), then to me there is no escaping the correct interpretation of the geodesic equation. It provides real, true non-Newtonian accelerations in this absolute rigid external Newtonian space within which we actually live. Yes, things are much less complicated than topology states. Especially the idiocy called string theory. Steve Bell === Subject: Re: GR Spaghetification Steve Bell says... >Weinberg classifies the Schw. metric as a static isotropic metric. In Schwarzschild coordinates, yes. In other coordinates, no. >He specifically states the invariant proper time dtau^2 >= -g_uv dx^u dx^v does not depend on t, and depends on x and dx... >This statement is made way before assuming any specific metrical >structure such as Schw. He is *assuming* that the metric components are independent of t. That implicitly restricts the possible coordinate systems he can use. >Couple this with the mathematics he presents for deriving the >geodesic equation, it is quite clear to me how >geodesic motion should be viewed. The Schw. specific geodesic equations >provide >actual true accelerations (oh my, I must be an idiot >for thinking that GR actually describes true physical accelerations!) of Proper acceleration is a true 4-vector, and its components can be computed in any coordinate system. There is nothing special about Schwarzschild coordinates in this respect. Are you talking about proper acceleration, or coordinate acceleration? Proper acceleration is, roughly speaking, acceleration *relative* to a tangent free fall trajectory, so the proper acceleration of an object in free fall is zero. Proper acceleration is *nonzero* for an object at rest on the surface of a planet. Coordinate acceleration is (d/dt)^2 x^j, which is nonzero for an object in free fall, and zero for an object at rest (constant values for the spatial coordinates). >It is quite apparent to me that none of you have actually programmed >any of these geodesic equations. If you did, you would see you >*have to* take the attitude I have taken. The only way you can >computer-generate orbital motion using these geodesic accelerations >is to numerically integrate them in the laboratory frame, *exactly* >like I have done in a published paper of mine in CIP. If you >believe that your GR orbit simulation reflects reality, this demands >you accept that GR-geodesic defined accelerations are just as >physically real (and so are forces) as in Newtonian mechanics. I'm not exactly sure what you think I am disagreeing with. Yes, need to numerically integrate the geodesic equation. Unless in special cases it can be solved analytically. >By the curvature of space I mean the determinant of the >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that >point. > The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. > Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). >According to the mathematics of Weinberg, you need two coordinate >systems to make sense of the Christoffel symbols, which are the >connection coefficients between the two systems. No, that's a little bit misleading. You don't need two coordinate systems. You can use the transformation properties of the Christoffel symbols to relate the symbols in one coordinate system to those in another. So if you know the Christoffel symbols in one coordinate system C1, and you know how to transform from system C1 to system C2, then you can compute them in system C2. An especially simple case is if system C1 is one where the symbols are all zero. (And you can always find such a system, locally. Those are the free-fall coordinates.) >I always choose one of the systems to be Euclidean, *exactly* >as Weinberg and the mathematics say I can You can always find a system C1 such that the Christoffel symbols are zero *at* a point. If spacetime is curved (as it is in the Schwarzschild geometry), you can't find a coordinate system in which the Christoffel symbols are zero *everywhere*. >and I do that because I view the external space our universe of >matter resides in, at a point in time, as a gigantic Euclidean >laboratory frame. I'm not sure what you mean. I don't believe that's possible, in general. -- Daryl McCullough Ithaca, NY === Subject: Re: GR Spaghetification ----- Original Message ----- === Subject: Re: GR Spaghetification > Steve Bell says... >Weinberg classifies the Schw. metric as a static isotropic metric. In Schwarzschild coordinates, yes. In other coordinates, no. >He specifically states the invariant proper time dtau^2 >= -g_uv dx^u dx^v does not depend on t, and depends on x and dx... >This statement is made way before assuming any specific metrical >structure such as Schw. He is *assuming* that the metric components are independent of t. > That implicitly restricts the possible coordinate systems he > can use. > This going in assumption is exactly what I think is needed to derive the geodesic equations that correctly model true physical orbits in a physically existing real world. I believe nature itself uses only specific special cases of all the types of coordinate systems mankind could define with its mathematics. The game is to find out which ones are the right ones. If a person thinks like me, which I believe I stated earlier is certainly not mainline, basically much more Newtonian than mainline, it makes the job much easier. Of course, mainline believers say this line of reasoning is completely incorrect. And they are either correct, or I am correct. >Couple this with the mathematics he presents for deriving the >geodesic equation, it is quite clear to me how >geodesic motion should be viewed. The Schw. specific geodesic equations >provide >actual true accelerations (oh my, I must be an idiot >for thinking that GR actually describes true physical accelerations!) of Proper acceleration is a true 4-vector, and its components can be > computed in any coordinate system. There is nothing special about > Schwarzschild coordinates in this respect. Are you talking about > proper acceleration, or coordinate acceleration? Proper acceleration > is, roughly speaking, acceleration *relative* to a tangent > free fall trajectory, so the proper acceleration of an object > in free fall is zero. Proper acceleration is *nonzero* for an > object at rest on the surface of a planet. > The geodesic equations themselves are derivatives w.r.t. tau. In my current numerical work, I transform to t derivatives, and do the numerical integration using laboratory coordinate time. > Coordinate acceleration is (d/dt)^2 x^j, which is nonzero > for an object in free fall, and zero for an object at rest > (constant values for the spatial coordinates). >It is quite apparent to me that none of you have actually programmed >any of these geodesic equations. If you did, you would see you >*have to* take the attitude I have taken. The only way you can >computer-generate orbital motion using these geodesic accelerations >is to numerically integrate them in the laboratory frame, *exactly* >like I have done in a published paper of mine in CIP. If you >believe that your GR orbit simulation reflects reality, this demands >you accept that GR-geodesic defined accelerations are just as >physically real (and so are forces) as in Newtonian mechanics. I'm not exactly sure what you think I am disagreeing with. Yes, > need to numerically integrate the geodesic equation. Unless in > special cases it can be solved analytically. > Do you believe the geodesic equation defines an actual gravitational field, every bit as real a gravitational field as in Newtonian mechanics? >By the curvature of space I mean the determinant of the >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that >point. The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). >According to the mathematics of Weinberg, you need two coordinate >systems to make sense of the Christoffel symbols, which are the >connection coefficients between the two systems. No, that's a little bit misleading. You don't need two coordinate > systems. You can use the transformation properties of the Christoffel > symbols to relate the symbols in one coordinate system to those in > another. It's not just that you can use Christoffel symbols to relate one system to another, that's exactly what Chris. symbols *do*. They connect accelerations in one frame to accelerations in another frame. My point of view is decidedly Newtonian-like. I view the equations of GR to provide to me a final product (the geodesic equation) describing an actual gravitational field vector, exactly like in Newtonian mechanics. Being just as physical to me as in Newtonian mechanics, this field must permeate an extent of true physical space, just like in Newtonian mechanics, which I take to be the laboratory whose character is Euclidean-Cartesian, exactly as Weinberg's mathematics points out I can do. I select EC because that's what I think is the structure of true physical space. > So if you know the Christoffel symbols in one coordinate > system C1, and you know how to transform from system C1 to system > C2, then you can compute them in system C2. An especially simple > case is if system C1 is one where the symbols are all zero. > (And you can always find such a system, locally. Those are the > free-fall coordinates.) >I always choose one of the systems to be Euclidean, *exactly* >as Weinberg and the mathematics say I can You can always find a system C1 such that the Christoffel > symbols are zero *at* a point. If spacetime is curved > (as it is in the Schwarzschild geometry), you can't > find a coordinate system in which the Christoffel > symbols are zero *everywhere*. > Locally, I am not worried about everywhere. The geodesic equation provides to me the defintion of a physical acceleration at a point where the obit lay in the everywhere physical space of the laboratory. >and I do that because I view the external space our universe of >matter resides in, at a point in time, as a gigantic Euclidean >laboratory frame. I'm not sure what you mean. I don't believe that's possible, in > general. -- > Daryl McCullough > Ithaca, NY > Take an apple and an orange sitting on a table, at what looks like to some observer to be a nonzero distance apart. Do you think there is some type of true physical distance between them, that is still there regardless of relativistic issues, regardless of how one looks at these objects? Or, ignoring the fact (imo) that separate balls of matter cannot actually physically exist at the same locations in physical space, is there an observer that sees the apple and orange sitting right on top of each other? The observer can be moving. Let's say there is such an observer. Is this just an illusion? Are the apple an orange actually physically residing in the same volume of space or is this just a fake you out aspect of everything's relative? Steve Bell === Subject: Re: GR Spaghetification Steve Bell says... >Do you believe the geodesic equation defines an actual gravitational >field, every bit as real a gravitational field as in >Newtonian mechanics? No, because the connection coefficients are artifacts of your choice of coordinate system. > No, that's a little bit misleading. You don't need two coordinate > systems. You can use the transformation properties of the Christoffel > symbols to relate the symbols in one coordinate system to those in > another. It's not just that you can use Christoffel symbols to relate >one system to another, that's exactly what Chris. symbols *do*. No, the Christoffel symbols describe how the components of a vector change as you perform a parallel transport. You don't need a second coordinate system in order to make sense of the Christoffel symbols. The idea is this: Pick a starting point P. Pick two line segments U and V (not parallel), each with a common endpoint at P. At the other endpoint of U, draw another line segment parallel to V. This new line segment V', is the result of parallel-transporting V along line segment U. In coordinates, we write: V'^i = V^i + Gamma^i_jk U^j V^k The Christoffel coefficients Gamma^i_jk describe how the components of a parallel-transported vector relate to the components of the original vector. >They connect accelerations in one frame to accelerations in >another frame. No, that's not what they mean. They connect *vectors* at one point in space (or spacetime) to vectors at another nearby point. >Take an apple and an orange sitting on a table, at what looks >like to some observer to be a nonzero distance apart. Do you think >there is some type of true physical distance between them, >that is still there regardless of relativistic issues, regardless of how >one looks at these objects? There is certainly physical about the spatial relationship between the apple and the orange. But if I said The orange is 4 inches away from the apple, horizontally, and 5 inches away vertically, that would not be a physically meaningful way to describe it. Horizontal distance versus vertical distance is dependent on the choice of which axis you call horizontal and which axis you call vertical. >Or, ignoring the fact (imo) that separate balls of matter >cannot actually physically exist at the same locations in >physical space, is there an observer that sees the apple and >orange sitting right on top of each other? No, but if you talk about *events*, such as The apple when I take a bite out of it or the orange when you start to peel it, it is possible that some observers will view these events as taking place at the same spatial location, but at different times. For example, suppose the apple and orange are on a train. As the apple passes the station, I take a bite out of it. Later, as the orange passes the station, the station, these two events took place at the same location, but at different times. >The observer can be moving. Let's say there is such an observer. >Is this just an illusion? I don't think of coordinate effects as an illusion. Coordinate systems are just different ways of describing the same reality. Basically, coordinates are just names for points in spacetime. >Are the apple an orange actually physically residing >in the same volume of space or is this just a fake you >out aspect of everything's relative? The best way, in my opinion, to understand what is *physically* meaningful is to look at those statements that are true in *any* coordinate system. -- Daryl McCullough Ithaca, NY === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> <1ae05$4a430427$944e5322$5014@STARBAND.NET> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Steve Bell says... >Consider the spherically symmetric, static Schw. >metric that I used in my CIP paper. The Schwarzschild metric is only static when you use > a particular coordinate system (the Schwarzschild > coordinates). In other coordinates, the metric is > time-dependent. Weinberg classifies the Schw. metric as a static isotropic metric. He specifically states the invariant proper time dtau^2 > = -g_uv dx^u dx^v does not depend on t, and depends on x and dx... This statement is made way before assuming any specific metrical > structure such as Schw. Couple this with the mathematics he presents for deriving the geodesic equation, it is quite clear to me how > geodesic motion should be viewed. The Schw. specific geodesic equations provide actual true accelerations (oh my, I must be an idiot It is quite apparent to me that none of you have actually programmed any of these geodesic equations. If you did, you would see you > *have to* take the attitude I have taken. The only way you can computer-generate orbital motion using these geodesic accelerations > is to numerically integrate them in the laboratory frame, *exactly* like I have done in a published paper of mine in CIP. If you > believe that your GR orbit simulation reflects reality, this demands you accept that GR-geodesic defined accelerations are just as > physically real (and so are forces) as in Newtonian mechanics. >By the curvature of space I mean the determinant of the >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that >point. The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). -- > Daryl McCullough > Ithaca, NY According to the mathematics of Weinberg, you need two coordinate systems to make sense of the Christoffel symbols, which are the > connection coefficients between the two systems. I always choose one of the systems to be Euclidean, *exactly* as Weinberg and the > mathematics say I can, and I do that because I view the external space our universe of matter resides in, at a point in time, as a > gigantic Euclidean laboratory frame. The other coordinate system I take most generally to be a Kerr system. Not the Kerr-Newman > system, which incorporates the relativistic effects of the central charge on its surrounding gravito-electromagnetic field in an > incorrect way, imo. These central-charge-including metrices, which are attempts at unifying gravity and at least parts of > electricity using differential geometry, are incorrect, imo. There is an obvious flaw with these metrices that I'm surprised the > authors didn't see. Or maybe they did, but I've not seen this issue described anywhere. Steve Bell I tell you the truth, modern error is taking these book-keeping objects and considering them Lossless Factorization for Descriptor Classification of two-symbol orthogonal arrays of size Continuous Functions with No Derivatives. Martin Musatov P.S. Time for new symbols, including binary objects === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.11) Gecko/2009060214 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jun 24, 2:54pm, stevendaryl3...@yahoo.com (Daryl McCullough) > Steve Bell says... >By the curvature of space I mean the determinant of the >3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that >point. The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). there are essential properties that can be extracted common to all such theories and it is possible to in essence quotient them out the arnowitt-deser-misner (adm) decomposition takes full advantage of this to provide a foliation of spacetime giving 3+1 field equations that are useful to exploring quantisation schemas that don't suffer certain classes of contradictions it's this kind of decomposition on which is built the wheeler-dewitt equation and theories like bohmian gravity or the acoustic gravity theory of unruh -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: GR Spaghetification > The Schwarzschild metric is only static when you use > a particular coordinate system (the Schwarzschild > coordinates). In other coordinates, the metric is > time-dependent. Using the standard meanings of these words, this is not true. The external regions of Schwarzschild spacetime are both static, and therefore so is the metric there. We call a spacetime stationary when it has a timelike Killing vector, and we call a stationary spacetime static when it has a 3-d spatial submanifold orthogonal to the timelike Killing vector -- these are both coordinate-independent definitions. When the timelike Killing vector of a static manifold is used as the time coordinate, and the 3 spatial coordinates span the orthogonal submanifold, then the metric components are all independent of the time coordinate. One can of course find other coordinates in which this is not true. This is probably what you meant. For example, the external regions of the Kerr manifold are stationary but not static. Minkowski spacetime is static; there are an infinite number of timelike Killing vectors, and there is an orthogonal spatial submanifold for each of them -- such foliations are called inertial frames and the differences among their spatial submanifolds are also known as relativity of simultaneity. Note that these definitions can be applied to a region of the manifold or to the entire manifold; it is rather rare for an entire manifold to be static or stationary, but many interesting manifolds have static or stationary regions. Note that for Schw. spacetime the region inside the horizon is neither stationary nor static. Using Schw. coordinates, the interior metric components are independent of t, but t is spacelike there; r is the time coordinate, and the metric components are not independent of r. > By the curvature of space I mean the determinant of the > 3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that > point. > The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). Yes. Steve Bell does not seem to understand this. Tom Roberts === Subject: Re: GR Spaghetification Tom Roberts says... >We call a spacetime stationary when >it has a timelike Killing vector, and we call a stationary spacetime >static when it has a 3-d spatial submanifold orthogonal to the >timelike Killing vector -- these are both coordinate-independent >definitions. I never learned exactly what a Killing vector is; is it just a vector such that moving along it leaves the metric unchanged? > When the timelike Killing vector of a static manifold > is used as the time coordinate, and the 3 spatial > coordinates span the orthogonal submanifold, then > the metric components are all independent of the time > coordinate. One can of course find other coordinates > in which this is not true. This is probably what you > meant. Yes, I just meant that the components of the metric tensor were independent of the time coordinate. -- Daryl McCullough Ithaca, NY === Subject: Re: GR Spaghetification > Tom Roberts says... > We call a spacetime stationary when > it has a timelike Killing vector, and we call a stationary spacetime > static when it has a 3-d spatial submanifold orthogonal to the > timelike Killing vector -- these are both coordinate-independent > definitions. I never learned exactly what a Killing vector is; is it just > a vector such that moving along it leaves the metric unchanged? A Killing vector is really a vector field on the manifold (this is a universal verbal shortcut). The integral curves of a Killing vector field K are such that when each point P of the manifold (or region of the manifold) is mapped to P' a distance L along the integral curve of K through P, the metric pushed-forward from P by this diffeomorphism is equal to the original metric at P'. That is, the Killing vector field defines a flow that generates isometries. Your statement is indeed a rather loose description of that. A Killing vector field K satisfies the differential equation: L_K g = 0 L_K is the Lie derivative wrt K; g is the metric Remember that the Lie derivative along a vector v, L_v, measures change in the direction of v. So this is merely another way of stating the same thing. Tom Roberts === Subject: Re: GR Spaghetification > By the curvature of space I mean the determinant of the > 3x3 space part of the Riemann-Christoffel curvature tensor evaluated at that point. > The separation of spacetime into a spatial part plus a time > part is coordinate-dependent. Different coordinates will make > that separation differently. > Yes, if you fix a particular coordinate system, then > you can talk about the spatial curvature tensor, but > you must first decide on a coordinate system (or at > least, you have to decide on your time axis). Yes. Steve Bell does not seem to understand this. > Tom Roberts I've said many times that I *am* assuming specific coordinate systems, Euclidean-Cartesian for the laboratory and (most generally) Kerr for representing the differential-geometry-based field (generated by a perfectly spherical ball of matter (generally spinning)), which permeates the Euclidean space of the laboratory. I really do not see why this is so hard for you to grasp. It really is rather easy to see what I'm talking about once you programmed orbital motion. It is completely obvious to me you know nothing about such numerical GR orbit simulations. And I would not even do the simulation if I didn't think it was a good model of *reality*. My Schw. orbit simulations for the planet Mercury generate nearly exactly the degree of orbital major axis precession as actually observed. Steve Bell === Subject: Re: GR Spaghetification > I've said many times that I *am* assuming specific coordinate > systems, Euclidean-Cartesian for the laboratory and (most generally) > Kerr for representing the differential-geometry-based field As I've said before: A) By selecting coordinates, your space cannot possibly be external. B) It is not possible to map your laboratory Euclidean coordinates to the entire external region of the Kerr manifold, you can do so only approximately and only locally. C) But in a weak-field system like the solar system, that approximation can be extremely good [#], and the local region can extend from the surface of the sun out to well beyond Pluto's orbit, with a duration long enough to include hundreds of orbits of the planets. [#] Far better than measurement errors. > It is completely obvious to me you know > nothing about such numerical GR orbit simulations. Real physicists worry about the accuracy of the approximations they use; you seem completely unaware of them. You have lucked out and the approximation happens to be good enough for what you are trying to do; that most definitely does not mean it is always valid.... Children play in a sandbox, and we smile at that because we know that in their innocence they are unaware of the dangers and difficulties of the adult world outside their playground. Like them, YOU are unaware of the dangers and difficulties outside your playground. Perhaps you should grow up.... Unfortunately, Weinberg's text won't help with that at all.... Tom Roberts === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > The > external regions of Schwarzschild spacetime are both static, and > therefore so is the metric there. We call a spacetime stationary when > it has a timelike Killing vector, and we call a stationary spacetime > static when it has a 3-d spatial submanifold orthogonal to the > timelike Killing vector -- these are both coordinate-independent > definitions. I call whoever can write a book based on a scripture in a bible a priest. How do I call someone who is able to write a book on the following Schwarzschild spacetime? ds^2 = c^2 (1 [CapitalEth] 2 U) dt^2 [CapitalEth] dr^2 / (1 [CapitalEth] 2 U) [CapitalEth] r^2 dO^2 ** U = G M / c^2 / r ** dO^2 = Angular stuff Does word salad come in mind? === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009062318 Gentoo Firefox/3.0.11,gzip(gfe),gzip(gfe) The > external regions of Schwarzschild spacetime are both static, and > therefore so is the metric there. We call a spacetime stationary when > it has a timelike Killing vector, and we call a stationary spacetime > static when it has a 3-d spatial submanifold orthogonal to the > timelike Killing vector -- these are both coordinate-independent > definitions. I call whoever can write a book based on a scripture in a bible a > priest. How do I call someone who is able to write a book on the > following Schwarzschild spacetime? ds^2 = c^2 (1 [CapitalEth] 2 U) dt^2 [CapitalEth] dr^2 / (1 [CapitalEth] 2 U) [CapitalEth] r^2 dO^2 ** U = G M / c^2 / r > ** dO^2 = Angular stuff Does word salad come in mind? I think this is as close as we will ever get to wooby admitting he doesn't understand GR. === Subject: Re: GR Spaghetification <5ea5d$4a3de260$944e5322$12673@STARBAND.NET> <192dc$4a3e87e2$944e5322$829@STARBAND.NET> <5HT%l.267$cl4.10@flpi150.ffdc.sbc.com> <3f58c$4a410d2f$944e5322$6901@STARBAND.NET> <1ar0m.2982$Jb1.1377@flpi144.ffdc.sbc.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) The > external regions of Schwarzschild spacetime are both static, and > therefore so is the metric there. We call a spacetime stationary when > it has a timelike Killing vector, and we call a stationary spacetime > static when it has a 3-d spatial submanifold orthogonal to the > timelike Killing vector -- these are both coordinate-independent > definitions. I call whoever can write a book based on a scripture in a bible a > priest. How do I call someone who is able to write a book on the > following Schwarzschild spacetime? ds^2 = c^2 (1 [CapitalEth] 2 U) dt^2 [CapitalEth] dr^2 / (1 [CapitalEth] 2 U) [CapitalEth] r^2 dO^2 ** U = G M / c^2 / r > ** dO^2 = Angular stuff Does word salad come in mind? My salad days, When I was green in judgment. William Shakespeare, Antony and Cleopatra, Act 1 scene 5 Greatest English dramatist & poet (1564 - 1616) -- Musatov === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG 1.1.4322; .NET CLR 2.0.50727; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > 1) There is no set N that differs from every FISON. It is only true > that for every FISON there is a larger FISON. So therefore the set of every FISON is... a FISON? > 2) There is no natural number that is larger than every natural > number. There is only, for every natural number, a natural number that > is larger than that. So therefore the set of all of these natural numbers is... a natural number? > 3) There is no diagonal 0.111... of the list > 0.0 > 0.1 > 0.11 > 0.111 > ... > that differs from every entry. So therefore the diagonal 0.111... of the list must be... a member of the list? === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > 3) There is no diagonal 0.111... of the list > 0.0 > 0.1 > 0.11 > 0.111 > ... > that differs from every entry. Well, obviously, IF this diagonal exists, then it differs from every entry, since every entry on this list is a finite natural number of places down from the top, and has a finite natural number of 1s after the decimal point. Call this number n. Then, the diagonal MUST DIFFER from the nth entry since the diagonal HAS an n+2nd 1 and the nth entry DOESN'T have one. If, however, as WM claims, the diagonal does NOT exist, then it can't achieve any difference with anything. > So therefore the diagonal 0.111... of the list must be... > a member of the list? No; it simply doesn't exist, wherefore no must applies to it at all. Of course, it would NOT be a MEMBER of the list even if it DID exist. Unfortunately, WM has this weird notion of how a set or list can contain a thing EVEN when that thing IS NOT a MEMBER of the set or list. He basically sort of conflates membership with susbet-of, which is of course a critical error in the context of Cantor's theorem. === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > 1) There is no set N that differs from every FISON. It is only true > that for every FISON there is a larger FISON. So therefore the set of every FISON is... > a FISON? No, dummy, the set of every FISON DOES NOT EXIST. The collection of all and only the FISONs is a POTENTIALLY infinite set (according to WM). It never kinetically actually FINISHES coming into COMPLETED existence. === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > 1) There is no set N that differs from every FISON. It is only true > that for every FISON there is a larger FISON. So therefore the set of every FISON is... > a FISON? 2) There is no natural number that is larger than every natural > number. There is only, for every natural number, a natural number that > is larger than that. So therefore the set of all of these natural numbers is... > a natural number? 3) There is no diagonal 0.111... of the list > 0.0 > 0.1 > 0.11 > 0.111 > ... > that differs from every entry. So therefore the diagonal 0.111... of the list must be... > a member of the list? No. There is no actuayll infinite chain of digits. === Subject: Re: Shortest known proof: There is no uncountable infinity. > 1) There is no set N that differs from every FISON. It is only true > that for every FISON there is a larger FISON. So therefore the set of every FISON is... > a FISON? 2) There is no natural number that is larger than every natural > number. There is only, for every natural number, a natural number that > is larger than that. So therefore the set of all of these natural numbers is... > a natural number? 3) There is no diagonal 0.111... of the list > 0.0 > 0.1 > 0.11 > 0.111 > ... > that differs from every entry. So therefore the diagonal 0.111... of the list must be... > a member of the list? No. There is no actuayll infinite chain of digits. Then the list above can never be complete. Since in WM's world, no such list, P, can ever be complete, there is always a path not yet included in it. Thus even in WM's world, whatever list of paths WM used to build the maximal infinite binary tree must have been incomplete, so there must always be a path not in it. -- Virgil === Subject: Re: Shortest known proof: There is no uncountable infinity. > 1) There is no set N that differs from every FISON. It is only true > that for every FISON there is a larger FISON. So therefore the set of every FISON is... > a FISON? > 2) There is no natural number that is larger than every natural > number. There is only, for every natural number, a natural number that > is larger than that. So therefore the set of all of these natural numbers is... > a natural number? > 3) There is no diagonal 0.111... of the list > 0.0 > 0.1 > 0.11 > 0.111 > ... > that differs from every entry. So therefore the diagonal 0.111... of the list must be... > a member of the list? WM is using 4 characters, ., , 0 and 1, not just two, in his infinite sequence of infinite sequences of characters And there are quartics (mappings from N to {., , 0, 1}) which differ from every one of his entries. -- Virgil === Subject: Re: Reactions to/against the Binary Tree posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG 1.1.4322; .NET CLR 2.0.50727; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Theorem: The complete infinite binary tree has only countably many > infinite paths. > 0 > / > 0 1 > / / > 0 10 1 In all the junk that ensued, this was NEVER properly addressed or > refuted. Actually, it was. Several times. > WM confused the issue by talking about infinite paths, but you don't > even need to do that. OBVIOUSLY, you can construct this tree out of > only FINITE paths, since EVERY node in it is at the end of a FINITE path > from the root. Which completely ignores the non-finite paths that do not end at any node, which was what WM's original post was about. He made an assertion about the infinite paths in the tree, not about the finite paths. > At every step along the way, each addition of a node adds 1 finite path > and there are always a finite number of nodes and paths. > In order to get to aleph 0 (countably infinitely many) nodes, you > have to pass to the limit. The question is, given that the number of > nodes and the number of paths HAVE BEEN IDENTICAL THROUGHOUT > the whole process, how can passing to *1* limit of the *same* process > cause the number of nodes to go from finite to aleph 0, but the number > of paths to go from finite to 2^aleph 0 ?? > HOW? By including the paths that do not end at any node. Which is somewhat problematic if you're using a process of countably infinite steps. === Subject: Re: Reactions to/against the Binary Tree posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Theorem: The complete infinite binary tree has only countably many > infinite paths. > 0 > / > 0 1 > / / > 0 10 1 In all the junk that ensued, this was NEVER properly addressed or > refuted. Actually, it was. Several times. Oh, shut up. I've been here longer than you have. > WM confused the issue by talking about infinite paths, but you don't > even need to do that. OBVIOUSLY, you can construct this tree out of > only FINITE paths, since EVERY node in it is at the end of a FINITE path > from the root. Which completely ignores the non-finite paths NO, IT DOESN'T. This INCLUDES EVERY NODE AND EVERY EDGE OF EVERY infinite path. It absolutely DOES NOT ignore them AT ALL. > He made an assertion about the infinite paths in the tree, not > about the finite paths. Oh, bull. He talked about constructing the tree by adding paths to some growing set of paths. > At every step along the way, each addition of a node adds 1 finite path > and there are always a finite number of nodes and paths. > In order to get to aleph 0 (countably infinitely many) nodes, you > have to pass to the limit. The question is, given that the number of > nodes and the number of paths HAVE BEEN IDENTICAL THROUGHOUT > the whole process, how can passing to *1* limit of the *same* process > cause the number of nodes to go from finite to aleph 0, but the number > of paths to go from finite to 2^aleph 0 ?? > HOW? By including the paths that do not end at any node. Whether those paths are OR AREN'T included IS PROBLEMATIC! Those paths NEVER get ADDED! They never NEED to get added! EVERY infinite path has the property that EVERY node and edge on it is ALSO on some FINITE path that was added at some FINITE time! > Which is somewhat problematic if you're using a process > of countably infinite steps. No, it IS NOT problematic AT ALL. Since every infinite path is only COUNTABLY infinitely long, EVERY node and edge of EVERY infinite path DOES get added after a FINITE number of steps, if we mean every in the usual individual sense, and after only a COUNTABLY infinite number of steps if we mean all collectively. The Actual problem (this is what WM actually doesn't see) is that adding all the nodes and edges of the path does NOT constitute adding the path, or constitute having the path be in the constructed set that has been built by adding. The paths are like SUBSETS of that set, AS OPPOSED to elements of it, and the set has MORE subsets than elements. In the finite case, this appears NOT to be true. === Subject: Re: Reactions to/against the Binary Tree posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Theorem: The complete infinite binary tree has only countably many > infinite paths. > 0 > / > 0 1 > / / > 0 10 1 In all the junk that ensued, this was NEVER properly addressed or > refuted. Actually, it was. Several times. WM confused the issue by talking about infinite paths, but you don't > even need to do that. OBVIOUSLY, you can construct this tree out of > only FINITE paths, since EVERY node in it is at the end of a FINITE path > from the root. Which completely ignores the non-finite paths that do not end > at any node, which was what WM's original post was about. If the such infinite paths exist, then the infinite binary tree contains such paths. Then they are constructed from the countable set of terminating paths. Then they belong to the counatble set of terminating paths (excluding the mathemagical opinion that a union can contain more than is unioned). Then there are no infinite paths. Briefly: If there are infinite paths, then there are no infinite paths. > He made an assertion about the infinite paths in the tree, not > about the finite paths. At every step along the way, each addition of a node adds 1 finite path > and there are always a finite number of nodes and paths. > In order to get to aleph 0 (countably infinitely many) nodes, you > have to pass to the limit. The question is, given that the number of > nodes and the number of paths HAVE BEEN IDENTICAL THROUGHOUT > the whole process, how can passing to *1* limit of the *same* process > cause the number of nodes to go from finite to aleph 0, but the number > of paths to go from finite to 2^aleph 0 ?? > HOW? By including the paths that do not end at any node. > Which is somewhat problematic if you're using a process > of countably infinite steps. The construction of the tree is a process that can be completed, because for every node we can determine when it will be added. There is no node that remains unconstructed. There is no real number of the unit interval the path of which remains unconstructed during a countable number of steps whereby each step adds only one path to the tree. === Subject: Re: Reactions to/against the Binary Tree > Which completely ignores the non-finite paths that do not end > at any node, which was what WM's original post was about. If the such infinite paths exist, then the infinite binary tree > contains such paths. Then they are constructed from the countable set > of terminating paths. They may be but need not be. > Then they belong to the counatble set of > terminating paths That is like saying that 3 must be a member of {1,2} because 3 can be constructed from 1 and 2. > (excluding the mathemagical opinion that a union can contain more than is unioned). The statement that the union of a set must contain each member of any member of the set being unioned is an axiom. WM rejects it at his peril. > Briefly: > If there are infinite paths, then there are no infinite paths. That may hold in WM's world but nowhere else. And he has not even proved it in his own world. > The construction of the tree is a process that can be completed, > because for every node we can determine when it will be added. There > is no node that remains unconstructed. Then a countable infinity of nodes have been constructed, and the set of all nodes has, necessarily, uncountably many subsets, including uncountably many which are maximal orderEd sets under the partial order induced by parent of. There is no real number of the unit interval the path of which remains > unconstructed during a countable number of steps whereby each step > adds only one path to the tree. There are all sorts of infinite sequences of nodes which remain unconstructed as long as there are any of the construction paths yet to be added. The tree only becomes complete when the process of adding paths has no more paths to add. And then many paths not used in the contruction are in the tree. -- Virgil === Subject: Re: Reactions to/against the Binary Tree posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG 1.1.4322; .NET CLR 2.0.50727; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Which logic is that? I don't understand what completed is > supposed to mean in basic logic. Could you provide a definition > of a completed union of trees, or perhaps a definition of an > incomplete union of trees? Completed means what mostly is called actually infinite. There it is > assumed that all elements are there in contrast to potential > infinity, that yields only incomplete sets. Which only begs the question, how do you know when a set is complete or incomplete? Is there a standard definition or test one can apply, or is it simply your feeling about it? If a set is incomplete, then how do you know which elements are not all there? > This potential understanding of infinity is the only consistent one. > Therefore it gains more and more reputation. Among real mathematicians, or only among cranks? Can you provide any citations for this claimed increase in reputation? > By hindsight, it is not surprising that there exist undecidable > propositions, as meta-proved by Kurt Goedel. Why should they be > decidable, being meaningless to begin with! It is plainly obvious that you do not comprehend what an undecidable proposition is. === Subject: Re: Reactions to/against the Binary Tree posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Which logic is that? I don't understand what completed is > supposed to mean in basic logic. Could you provide a definition > of a completed union of trees, or perhaps a definition of an > incomplete union of trees? Completed means what mostly is called actually infinite. There it is > assumed that all elements are there in contrast to potential > infinity, that yields only incomplete sets. Which only begs the question, how do you know when a > set is complete or incomplete? Is there a standard definition > or test one can apply, or is it simply your feeling about it? If a set is incomplete, then how do you know which elements > are not all there? Canotr said: If all elements can be thought as one thing, then the set exists actually. As a counter example he used the set of all alephs. That set must contain an aleph larger than all, so an aleph that differs from to Hilbert about that problem, fpr instance 1906, 8. Aug., but already in the 19th century. So far he is correct. But he did not realize that the set of all natural numbers cannot have cardinality larger than every natural number, because the natural numbers count themselves. Therefore, this set is never completed. It is as potential as the set of all alephs. This potential understanding of infinity is the only consistent one. > Therefore it gains more and more reputation. Among real mathematicians, or only among cranks? > Can you provide any citations for this claimed increase > in reputation? Only real mathematicians can recognize it. Cranks are unable, mostly even unable to understand the difference. Cantor already knew that. By hindsight, it is not surprising that there exist undecidable > propositions, as meta-proved by Kurt Goedel. Why should they be > decidable, being meaningless to begin with! It is plainly obvious that you do not comprehend what an > undecidable proposition is. By hindsight, it is not surprising that there exist undecidable propositions, as meta-proved by Kurt G.9adel. Why should they be decidable, being meaningless to begin with! The tiny fraction of first order statements that are decidable are exactly those for which either the statement itself, or its negation, happen to be true for symbolic integers. A priori, every statement that starts for every integer n is completely meaningless. [Doron ZEILBERGER: REAL ANALYSIS Is A DEGENERATE CASE of DISCRETE ANALYSIS, ] http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf === Subject: Re: Reactions to/against the Binary Tree > Which logic is that? I don't understand what completed is > supposed to mean in basic logic. Could you provide a definition > of a completed union of trees, or perhaps a definition of an > incomplete union of trees? Completed means what mostly is called actually infinite. There it is > assumed that all elements are there in contrast to potential > infinity, that yields only incomplete sets. Which only begs the question, how do you know when a > set is complete or incomplete? Is there a standard definition > or test one can apply, or is it simply your feeling about it? If a set is incomplete, then how do you know which elements > are not all there? Canotr said: If all elements can be thought as one thing, then the set > exists actually. Non-responsive. Thus in WM's world, any set of paths for any tree must either be finite or incomplete, or both. > As a counter example he used the set of all alephs. That set must > contain an aleph larger than all Claimed but not proven, like so many of WM's maunderings. Only real mathematicians can recognize it. Since WM cannot recognize real mathematicians, but subscribes, among a number of his fallacies, to the fallacy that mathematics is merely a branch of physics, he is hardly in a position to dictate who is allowed to be a real mathematician. -- Virgil === Subject: Re: Critical Points > f[x,y]=Sqrt[(-5 + x)^2 + (-5 + y)^2] + > Sqrt[(-2 + x)^2 + (-4 + y)^2] + > Sqrt[(-10 + x)^2 + (-3 + y)^2] + > Sqrt[(-4 + x)^2 + (-1 + y)^2] + > Sqrt[x^2 + y^2] + > Sqrt[(-4 + x)^2 + (3 + y)^2] > Critical Points:(xc,yc)=________ (exact) This problem appears a great deal easier than your previous one---how far did you get? === Subject: Re: National Exam toughie posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > I've been trying for fun some of the problems from the NationalGreekexams from > a week ago. Here's a gem, which I think was a bit of a nut: Your are given the function: f(x) = a^x - ln(x+1), x > -1, where a > 0 and a =/= -1. Prove that if: f(x) >= 1, for all x > -1, then a = e. I was able to crack this as follows: First it is clear that a > 1, because otherwise f(x) becomes negative. Let's find the minimum: xmin:=solve(diff(f(x),x)=0,x); xmin := (LambertW(a)-ln(a))/ln(a) (Hello Lambert W!!!) Plug back this into f: f(xmin); > simplify(); > expand(); 1/LambertW(a)+ln(ln(a))-ln(a)+LambertW(a) We want the above to be >= 1, since that's the minimum value of the function > f(x). So: solve(1/LambertW(a)+ln(ln(a))-ln(a)+LambertW(a)=1,a); (fails) fsolve(1/LambertW(a)+ln(ln(a))-ln(a)+LambertW(a)=1,a); 2.718281815 For the love of God! Lambert's W function at high school level? Can anyone see how to do this without using W? I can't believe the folks at theGreekministry. Maybe they have heard that I love W and they decided to shove it > to the students :-) > -- > Ioannis I saw this problem earlier today and decided to have a go at it, so here is what I came up with: As series, we are tryingn to show that 1 + (ln a)*x + quadratic stuff >= 1 + x - x^2/2 + ... or that (ln(a) - 1) * x >= b 2*x^2 + ... for all x > -1 where b 2 is obviously negative. If ln(a) - 1 < 0 A very small negative value for x blows this. If ln(a) - 1 > 0, a very small positive value of x blows this. Hence it is a necessary condition that a = e. It is easy to show that it is sufficient. Just use basic calculus. Achava === Subject: Expected distance between two points lying on the surface of a sphere If we take point A as the north pole of the sphere (with radius r) and theta the polar angle, then each ring of width r*dtheta lying at angle theta will have length 2*pi*r*sin (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on the sphere's surface is then the weighted average of each ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? I know that there's a way to find the solution using a double integral integrating over the sphere's surface but I couldn't find an analytic solution for theat intgral so I thought of this way which is simpler. I then used a script to randomly pick points on a surface of a sphere and average their distances to do a monte-carlo confirmation of my result but this simulation gives a result of 1.355*r, which is off by quite a bit. I can't find any errors with either my analytic or numerical calculations so I turn to the newsgroup for help. === Subject: Re: Expected distance between two points lying on the surface of a sphere > If we take point A as the north pole of the sphere (with radius > r) and theta the polar angle, then each ring of width > r*dtheta lying at angle theta will have length 2*pi*r*sin > (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this > ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on > the sphere's surface is then the weighted average of each > ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = > (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? > I don't think so. > I know that there's a way > to find the solution using a double integral integrating over > the sphere's surface but I couldn't find an analytic solution > for theat intgral so I thought of this way which is simpler. If you know that the area of a spherical surface between two parallel planes is 2 pi r d, where r is the radius and d is the distance between the planes, you can find by geometry that the c.d.f. for the distance is (x/(2r))^2 for 0 <= x <= 2r. I then used a script to randomly pick points on a surface of a > sphere and average their distances to do a monte-carlo > confirmation of my result but this simulation gives a result of > 1.355*r, which is off by quite a bit. > What sample size did you use? I estimate that you need several millions to get a reasonably reliable third decimal place. === Subject: Re: Expected distance between two points lying on the surface of a sphere posting-account=e6PATAoAAACxeuMbOnLMqjakg3lAxhUd Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > If we take point A as the north pole of the sphere (with radius > r) and theta the polar angle, then each ring of width > r*dtheta lying at angle theta will have length 2*pi*r*sin > (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this > ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on > the sphere's surface is then the weighted average of each > ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = > (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? I know that there's a way > to find the solution using a double integral integrating over > the sphere's surface but I couldn't find an analytic solution > for theat intgral so I thought of this way which is simpler. I then used a script to randomly pick points on a surface of a > sphere and average their distances to do a monte-carlo > confirmation of my result but this simulation gives a result of > 1.355*r, which is off by quite a bit. The calculated value is 1.333...*r, while the simulated value is 1.355*r. Is this difference statistically significant? It depends on the sample size, etc. Also: are you sure about the quality of the random-number generator? Finally: how, exactly, do you choose two uniformly distributed points on the surface of a sphere? (It is easy to do it incorrectly.) R.G. Vickson I can't find any errors with either my analytic or numerical > calculations so I turn to the newsgroup for help. === Subject: Re: Expected distance between two points lying on the surface of a sphere ps.com: > how, exactly, do you choose two > uniformly distributed points on the surface of a sphere? (It > is easy to do it incorrectly.) That was my error. I was able to do it correctly after reading http://mathworld.wolfram.com/SpherePointPicking.html even more incorrect than the wrong way he describes (can anyone double-check?). I was able to find the right answer using the method described last. === Subject: Re: Expected distance between two points lying on the surface of a sphere > ps.com: > > how, exactly, do you choose two > uniformly distributed points on the surface of a sphere? (It > is easy to do it incorrectly.) > That was my error. I was able to do it correctly after reading > http://mathworld.wolfram.com/SpherePointPicking.html even more incorrect than the wrong way he describes (can anyone > double-check?). I was able to find the right answer using the > method described last. I can't find anything wrong with the first method, or with the second method, which is the same thing converted to Cartesian. What may be bothering you is the fact that on the one hand each of the x, y, z coordinates is distributed uniformly on [-r, r], while on the other hand the conditional distribution of one coordinate given another is non-uniform. So picking one coordinate is simple, but the distribution of the others has then to be adjusted accordingly. The simple case that Mathworld doesn't mention is cylindrical coordinates, where you can just pick theta and z uniformly and independently, and calculate r to match z. -- Niels Diepeveen === Subject: Re: Expected distance between two points lying on the surface of a sphere posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) If we take point A as the north pole of the sphere (with radius > r) and theta the polar angle, then each ring of width > r*dtheta lying at angle theta will have length 2*pi*r*sin > (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this > ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on > the sphere's surface is then the weighted average of each > ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = > (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? I know that there's a way > to find the solution using a double integral integrating over > the sphere's surface but I couldn't find an analytic solution > for theat intgral so I thought of this way which is simpler. I then used a script to randomly pick points on a surface of a > sphere and average their distances to do a monte-carlo > confirmation of my result but this simulation gives a result of > 1.355*r, which is off by quite a bit. The calculated value is 1.333...*r, while the simulated value is > 1.355*r. Is this difference statistically significant? It depends on > the sample size, etc. Also: are you sure about the quality of the > random-number generator? Finally: how, exactly, do you choose two > uniformly distributed points on the surface of a sphere? (It is easy > to do it incorrectly.) R.G. Vickson I can't find any errors with either my analytic or numerical > calculations so I turn to the newsgroup for help. If we take point A as the north pole of the sphere (with radius > r) and theta the polar angle, then each ring of width > r*dtheta lying at angle theta will have length 2*pi*r*sin > (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this > ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on > the sphere's surface is then the weighted average of each > ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = > (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? I know that there's a way > to find the solution using a double integral integrating over > the sphere's surface but I couldn't find an analytic solution > for theat intgral so I thought of this way which is simpler. I then used a script to randomly pick points on a surface of a > sphere and average their distances to do a monte-carlo > confirmation of my result but this simulation gives a result of > 1.355*r, which is off by quite a bit. The calculated value is 1.333...*r, while the simulated value is > 1.355*r. Is this difference statistically significant? It depends on > the sample size, etc. Also: are you sure about the quality of the > random-number generator? Finally: how, exactly, do you choose two > uniformly distributed points on the surface of a sphere? (It is easy > to do it incorrectly.) R.G. Vickson I can't find any errors with either my analytic or numerical > calculations so I turn to the newsgroup for help. Use http://MeAmI.org and you will find much more . . . 1. Expected distance between two points lying on the surface of a ... random-number generator? Finally: how, exactly, do you choose two uniformly distributed points on the surface of a sphere? (It is easy ... show... 2. [PDF] Re: Uniform Distribution of Points on the Surface of a Sphere arranged in two equilateral triangles. These triangles are skewed,. Re: Uniform Distribution of Points on the Surface of a Sphere. Re: Uniform Distribution ... sci.tech-archive.net/pdf/Archive/sci.math/2007-12/msg04885.pdf 3. Uniform Distribution of Points over the Surface of a Sphere - Bad ... They are all on the surface of a sphere centered at 0,0,0 but the ... Clearly in the magnetic analogy, as two points come closer to each other .... Technically, 3 isn't uniformly distributed, as some points are further ... www.bautforum.com/.../85138-uniform-distribution-points-over-surface-sphere. h tml 4. An efficient method for generating uniformly distributed points on ... formly distributed random points on the surface of an n- dimensional sphere. The method essentially selects, from uniformly distributed points in an ... portal.acm.org/citation.cfm?doid=377939.377945 5. Uniform Distribution of Points over the Surface of a Sphere - Page ... 23 posts - 7 authors - Last post: Mar 23 It probably means there's no general formula for calculating the global minimum given the number of points. www.bautforum.com/.../85138-uniform-distribution-points-over-surface-sphere- 2 .html 6. sci.math ... Here are four methods for generating uniformly-distributed points on a unit ... Choose x, y, and z, each normally-distributed with mean 0 and variance 1. .... from the surface of a sphere, Ann Math Stat, v43, 1972, recommending the two ... www.math.niu.edu/~rusin/known-math/96/sph.rand 7. Expected distance between two points lying on the surface of a ... Jun 24, 2009 ... The mean distance A to B with point B uniformly distributed on the sphere's surface is then the weighted average of each ... ago 8. n-sphere - Wikipedia, the free encyclopedia In particular, a 0-sphere is a pair of points on a line, a 1- sphere is a circle in the .... Just as a two dimensional sphere embedded in three dimensions can be mapped onto a ... is uniformly distributed over the surface of the n-ball. ... en.wikipedia.org/wiki/Hypersphere 9. Sphere Point Picking -- from Wolfram MathWorld Cook (1957) extended a method of von Neumann (1951) to give a simple method of picking points uniformly distributed on the surface of a unit sphere. ... mathworld.wolfram.com/SpherePointPicking.html 10. Re: Uniform distribution of points on a 4-sphere? Jun 24, 2009 ... 2) And how would it relate to an *exactly* uniform distribution of points on the surface of a 4-sphere? -- Bob Day http://bobday.vze.com ... sci.tech-archive.net/Archive/sci.math/2009-06/msg03018.html === Subject: Re: Expected distance between two points lying on the surface of a sphere posting-account=e6PATAoAAACxeuMbOnLMqjakg3lAxhUd Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > If we take point A as the north pole of the sphere (with radius > r) and theta the polar angle, then each ring of width > r*dtheta lying at angle theta will have length 2*pi*r*sin > (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this > ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on > the sphere's surface is then the weighted average of each > ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = > (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? I know that there's a way > to find the solution using a double integral integrating over > the sphere's surface but I couldn't find an analytic solution > for theat intgral so I thought of this way which is simpler. I then used a script to randomly pick points on a surface of a > sphere and average their distances to do a monte-carlo > confirmation of my result but this simulation gives a result of > 1.355*r, which is off by quite a bit. The calculated value is 1.333...*r, while the simulated value is > 1.355*r. Is this difference statistically significant? It depends on > the sample size, etc. Also: are you sure about the quality of the > random-number generator? Finally: how, exactly, do you choose two > uniformly distributed points on the surface of a sphere? (It is easy > to do it incorrectly.) R.G. Vickson I can't find any errors with either my analytic or numerical > calculations so I turn to the newsgroup for help. If we take point A as the north pole of the sphere (with radius > r) and theta the polar angle, then each ring of width > r*dtheta lying at angle theta will have length 2*pi*r*sin > (theta), thus its area will be A = 2*pi*r^2*sin(theta)*dtheta Thus, the portion of the sphere's points included in this > ring will be p(theta) = A/(4*pi*r^2) = 1/2*sin(theta)*dtheta The distance A to a ring lying at angle theta is s(theta) = 2*r*sin(theta/2) The mean distance A to B with point B uniformly distributed on > the sphere's surface is then the weighted average of each > ring's distance from A, weighted by its p value: (Integral from 0 to pi) s*p = > (Integral from 0 to pi) r*sin(theta)*sin(theta/2)*dtheta Solving this yields 4*r/3. Is there an error in my calculations? I know that there's a way > to find the solution using a double integral integrating over > the sphere's surface but I couldn't find an analytic solution > for theat intgral so I thought of this way which is simpler. I then used a script to randomly pick points on a surface of a > sphere and average their distances to do a monte-carlo > confirmation of my result but this simulation gives a result of > 1.355*r, which is off by quite a bit. The calculated value is 1.333...*r, while the simulated value is > 1.355*r. Is this difference statistically significant? It depends on > the sample size, etc. Also: are you sure about the quality of the > random-number generator? Finally: how, exactly, do you choose two > uniformly distributed points on the surface of a sphere? (It is easy > to do it incorrectly.) R.G. Vickson I can't find any errors with either my analytic or numerical > calculations so I turn to the newsgroup for help. Usehttp://MeAmI.organd you will find much more . . . 1. > Expected distance between two points lying on the surface of > a ... > random-number generator? Finally: how, exactly, do you choose > two uniformly distributed points on the surface of a sphere? (It is > easy ... > show... > 2. > [PDF] > Re: Uniform Distribution of Points on the Surface of a Sphere > arranged in two equilateral triangles. These triangles are > skewed,. Re: Uniform Distribution of Points on the Surface of a > Sphere. Re: Uniform Distribution ... > sci.tech-archive.net/pdf/Archive/sci.math/2007-12/msg04885.pdf > 3. > Uniform Distribution of Points over the Surface of a Sphere - > Bad ... > They are all on the surface of a sphere centered at 0,0,0 but > the ... Clearly in the magnetic analogy, as two points come closer to > each other .... Technically, 3 isn't uniformly distributed, as some > points are further ... > www.bautforum.com/.../85138-uniform-distribution-points-over-su rface-... > 4. > An efficient method for generating uniformly distributed points > on ... > formly distributed random points on the surface of an n- > dimensional sphere. The method essentially selects, from uniformly > distributed points in an ... > portal.acm.org/citation.cfm?doid=377939.377945 > 5. > Uniform Distribution of Points over the Surface of a Sphere - > Page ... > 23 posts - 7 authors - Last post: Mar 23 > It probably means there's no general formula for calculating the > global minimum given the number of points. > www.bautforum.com/.../85138-uniform-distribution-points-over-su rface-... > 6. > sci.math ... > Here are four methods for generating uniformly-distributed > points on a unit ... Choose x, y, and z, each normally-distributed > with mean 0 and variance 1. .... from the surface of a sphere, Ann > Math Stat, v43, 1972, recommending the two ... > www.math.niu.edu/~rusin/known-math/96/sph.rand > 7. > Expected distance between two points lying on the surface of > a ... > Jun 24, 2009 ... The mean distance A to B with point B uniformly > distributed on the sphere's surface is then the weighted average of > each ... > ago > 8. > n-sphere - Wikipedia, the free encyclopedia > In particular, a 0-sphere is a pair of points on a line, a 1- > sphere is a circle in the .... Just as a two dimensional sphere > embedded in three dimensions can be mapped onto a ... is uniformly > distributed over the surface of the n-ball. ... > en.wikipedia.org/wiki/Hypersphere > 9. > Sphere Point Picking -- from Wolfram MathWorld > Cook (1957) extended a method of von Neumann (1951) to give a > simple method of picking points uniformly distributed on the surface > of a unit sphere. ... > mathworld.wolfram.com/SpherePointPicking.html > 10. > Re: Uniform distribution of points on a 4-sphere? > Jun 24, 2009 ... 2) And how would it relate to an *exactly* > uniform distribution of points on the surface of a 4-sphere? -- Bob > Dayhttp://bobday.vze.com... > sci.tech-archive.net/Archive/sci.math/2009-06/msg03018.html aIdiot. I was not asking anybody how to do it; I was asking the OP how he/she *did it. Can't you see the difference? R.G. Vickson === Subject: Re: Israel's next biggest regional enemy after Iraq. Ready to die for Jews again, Tool? http://mundiclub.blogspot.com/2006/01/jews-stirring-up-world-war-three-zog_3 0.html www.iamthewitness.com The jews-only state in palestine is mobilizing its supporters in america (and in europe) to push the bush administration What bush administration? The Brits are the bad guys according to Iran, don't you mean the Scottish Gordon Brown administration? After all, he's just kicked out two Iranian diplomats! Do me a favour. off, you ignorant cunt. *plonk* Do not reply to this generic message, it was automatically generated; you have been kill-filed, either for being boringly stupid, repetitive, unfunny, ineducable, repeatedly posting politics, religion or off-topic subjects to a sci. newsgroup, attempting cheapskate free advertising for profit, because you are a troll, simply insane or any combination or permutation of the aforementioned reasons; any reply will go unread. Boringly stupid is the most common cause of kill-filing, but because this message is generic the other reasons have been included. You are left to decide which is most applicable to you. There is no appeal, I have despotic power over whom I will electronically admit into my home and you do not qualify as a reasonable person I would wish to converse with or even poke fun at. Some weirdoes are not kill- filed, they amuse me and I retain them for their entertainment value as I would any chicken with two heads, either one of which enables the dumb bird to scratch dirt, step back, look down, step forward to the same spot and repeat the process eternally. This should not trouble you, many of those plonked find it a blessing that they are not required to think and can persist in their bigotry or crackpot theories without challenge. You have the right to free speech, I have the right not to listen. The kill-file will be cleared annually with spring cleaning or whenever I purchase a new computer or hard drive. I hope you find this explanation is satisfactory but even if you don't, damnly my frank, I don't give a dear. Have a nice day. === Subject: Re: Welcome to . These suggestions may help you. [36] <18280932.20848.1245824742227.JavaMail.jakarta@nitrogen.mathforum.org>, > .... > Some good general advice about news groups, cross-posting, not > top-posting, etc. is Stan Brown's Playing Nice on Usenet web site > . > .... Actually, Stan Brown does recommend cross-posting .... However, he > recommends not multiposting .... Exactly. That's why I mentioned cross-posting (but not top-posting). Perhaps I could add not multiposting, but my message is already too long. However, I use Math Forum offered by Drexel University for these > newsgroups, and I don't think it offers a way to cross post. > Stan Brown's directions for cross-posting don't seem to apply here. > Am I correct? Or am I wrong? If I am wrong, then I would like to > know how to cross-post using Math Forum in case I decide to do that > someday.... A very good question. It may not be widely noticed in this thread, so perhaps you could try raising this particular question with a more appropriate subject, and/or e-mailing Stan Brown to see if he knows any answer. I'll watch with interest! Ken Pledger. === Subject: Re: Welcome to . These suggestions may help you. [36] <18280932.20848.1245824742227.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=rQxmjAoAAABkK_bEn14LxyXccZYXFodO Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) a warning about cranks would be good === Subject: Re: Welcome to . These suggestions may help you. [36] > a warning about cranks would be good > I have to agree with you. I've definitely seen some of them here! Jonathan Groves === Subject: Re: Welcome to . These suggestions may help you. [36] <18956935.26791.1245907088232.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > a warning about cranks would be good I have to agree with you. I've definitely seen some of them here! Jonathan Groves I would like to see a warning from people who you think would be interested in learning instead hurling insults and swearing at you, basically doing anything but mathematics but for no apparent reason. (Some people, not ALL) It is very troubling. Musatov === Subject: Re: Limit involving sum of sin(sqrt(i)) posting-account=76gTjAoAAACFBBxW0JkX-LuotQPzt612 Hi-Speed Internet; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Filling is some details I find | int_[1, n+1] sin(sqrt(x)) | < 2(sqrt(n+1)+1+sin(1)-cos(1)) and sum (k=1,n) 1/(2*sqrt(k)) < sqrt(n+1) - 1 so, get | sum (k=1,n) sin(sqrt(k)) | < 3*sqrt(n+1) + 1.6 which is good enough. Maybe a more detailed analysis (using trapezoidal rule for integration?) would get a tighter bound. Any ideas about | sum (k=1,n) sin(1.5^k) | ? Lew === Subject: Re: Limit involving sum of sin(sqrt(i)) posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) (i)) NP==P q.e.d.. (0.34 seconds)Phys. Rev. A 58, 2446 (1998): Aiello et al. - Parametric ...Then there are terms such as a a a , which are responsible for sum ..... In this where f limit, we rewrite Eq. 27 as dP d cos 2 z 8 0 0 3/2 2 4~ 2 d 11 ... the square root of this density, so its square is simply equal to the sum of .... Then the process rate is w V ¿ NP 2 V V 2 5 1 2 ep o1 o2 sin S 1 2 k P k 1 k ...http://link.aps.org/doi/10.1103/PhysRevA.58.2446 - Phys. Rev. D 62, 054013 (2000): Brown et al. - Non-Fermi liquid ...Corrections due to the change from a where discrete sum to an integral are ..... The diagrammatic expansion of 4 2 s 1 s 2 ,s 1 s 2 (n ,n p ,p) to order g and S s s ... such a singularity is sup with 22 term inside of the square root. .... even in QED because of the breakdown of Furry's theorem by the Fermi sea. ...http://link.aps.org/doi/10.1103/PhysRevD. 62.054013 -Relativistic Path Integrals & Random Flight21 Aug 2007 ... The problem is first to construct the path integral (sum) .... the De Moivre-Laplace theorem [Wilks 1962], p. 274.: Binom(np, npq) -> N(np, npq), asymptotically. ... sqrt(2 pi i) sqrt(N) Kernel then has the physical dimension of ..... It is curious that the relativistic limit should be one for low ...http://graham.main.nc.us/~bhammel/FCCR/ feynpath.html sci.mathconjectures on integrals arising from QED (quantum theory), David Bernier ..... possible solution of the problem (using Chernavsky's result), Sergey P ...http://sci.tech-archive.net/ Archive/sci.math/2008-06/ Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights ...This parameter settings are meant to work with p- Pb collisions .... //Initial QCD & QED showers on SetMSTP(71,1); // Final QCD & QED showers on break; ... Print list of particl properties Int t np = 0; char* name = new char[16]; .... m / TMath::Sqrt(m * m + jt * jt); // // Change light-cone kinematics rel. to ...https:// savannah.cern.ch/bugs/download.php%3Ffile id%3D9267 Mr. Hansen's Abbreviations, Part IIthe square root of [CapitalEth]1, i.e., the principal complex solution of the ... the expression means ñtake the limit of x2 as x approaches 3 from aboveî) ... NPP, NQP. **normal probability plot, normal quantile plot (synonyms) ... [Halmos sign] same as Q.E.D. .... + 100 denotes the sum of the first 100 positive integers) ...http://staweb.sta.cathedral.org/departments/math/mhansen/ public html/abbrevs2.htm The S parameter in a technicolour model with explicit chiral ...II3Q(g2) ' g2113Q(0), where II3Q (0) = 0 because of the QED Ward identity. ... S in the nonchiral limit The NJL effective fermion Lagrangian is 877'2 Gs ... (13) defines the dressed currentquark propagator as the sum of the bare currentquark ... (D) the square root of the usual exponential representation of the ...http://linkinghub.elsevier.com/retrieve/pii/0370269394015806 Mathematics 1S12 (Maths for Scientists) 2008[CapitalEth]090, because it is the determinant of a matrix with two equal rows. qed ...... For example, the mean of B(n, p) is np and the mean of Poisson([Micro], t) is [Micro]t. ...http://www.maths.tcd.ie/~odunlain/1s12/book.pdf arxmliv build tool25, 2009-05-21 04:18:20, /cs/papers/0212026, [example, proposition, qed, lemma, ... cal, par, np, sqrt, ', bar, tbb, over, Align, exp, log, bf, approx, to, equiv, ..... Gamma, End, cdot, frac, ;, vert, right, Begin, subset, lambda, sum]. .... hline, @ignoretrue, Math, etable, rho, sin, begin, circ, sigma, btable ...http://arxmliv.kwarc.info/macro tex detail.php%3Fmacro%3DMm mathematics (idea)@Everything2.com5 Nov 2007 ... Babylonian square root algorithm, Bailey-Borwein-Plouffe Algorithm, .... spacetime, Stevens' physical proof of the sine rule ...http://everything2.com/ node/1915808 Filling is some details I find > | int [1, n+1] sin(sqrt(x)) | < 2(sqrt(n+1)+1+sin(1)-cos(1)) > and sum (k=1,n) 1/(2*sqrt(k)) < sqrt(n+1) - 1 > so, get | sum (k=1,n) sin(sqrt(k)) | < 3*sqrt(n+1) + 1.6 > which is good enough. Maybe a more detailed analysis (using > trapezoidal rule for integration?) would get a tighter bound. Any ideas about | sum (k=1,n) sin(1.5^k) | ? Lew === Subject: Re: IRAN: Israel's next biggest regional enemy after Iraq. Ready to die for Jews again, Tool? NOT replying to this is like not replying to bigotry. What the heck, Why cannot Israelis live in America, and why cannot Iranians like me live in America, why cannot a Scotchman or a half breed like Obama. The ravens will always be in Buckingham and Cherry trees in Washington, and Omar Khayyam in Iran under a pomegranate tree, once they find the peace and not war - The bastards will never destroy the good in this world-- Peace and Love to all Americans, Israelis, all Iranians, Egyptians etc God bless America. === Subject: Re: Simple vector space question- My answer is NO. In a vector space (No topologies, manifolds, > norms etc) you are only allowed to make FINITE linear > combinations. The RHS is an INFINITE linear combination which > is not allowed. Ron Really? How about the vector space of all formal power series with > real coefficients? 1, x, x^2, etc., are all elements thereof, as is > 1 + x + x^2 + ..., which sure looks like an infinite linear > combination. Yes, but the power series may not sum to an element of the vector > space. Say, what? The power series *is* an element of the vector space. > V is the vector space of all formal power series with real coefficients. > 1, x, x^2, etc, are all elements of V, and so is 1 + x + x^2 + .... Then how about the vector space of all polynomials in x with real > coefficients? > That is an infinite dimensional vector space in which the sequence > 1,x,x^2, ... are all members of the space but 1 + x + x^2 + .... is not. So what? I was replying to the assertion that you're only allowed to make finite linear combinations by presenting a situation where you are allowed to make some infinite linear combinations. No one suggested that arbitrary infinite linear combinations are allowed in arbitrary vector spaces. Your example is non-responsive. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Simple vector space question- posting-account=CtWhuAoAAAAZZ9vwdovdqB3NNaiUa20_ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On 25 jun, 05:46, Gerry Myerson norms etc) you are only allowed to make FINITE linear > combinations. The RHS is an INFINITE linear combination which > is not allowed. Ron Really? How about the vector space of all formal power series with > real coefficients? 1, x, x^2, etc., are all elements thereof, as is > 1 + x + x^2 + ..., which sure looks like an infinite linear > combination. Yes, but the power series may not sum to an element of the vector > space. Say, what? The power series *is* an element of the vector space. > V is the vector space of all formal power series with real coefficients. > 1, x, x^2, etc, are all elements of V, and so is 1 + x + x^2 + .... Then how about the vector space of all polynomials in x with real > coefficients? > That is an infinite dimensional vector space in which the sequence > 1,x,x^2, ... are all members of the space but 1 + x + x^2 + .... is not. So what? I was replying to the assertion that you're only allowed to make finite > linear combinations by presenting a situation where you are allowed > to make some infinite linear combinations. No one suggested that > arbitrary infinite linear combinations are allowed in arbitrary vector > spaces. Your example is non-responsive. I would like to see an example of a (please, not too abstract) vector space where it is not allowed to make such combinations. Han de Bruijn === Subject: Re: Simple vector space question- Take any vector v in any vector space V over the reals R. Make linear combinations by just adding the vector to itself again and again, an 'infinite' number of times. What do you get? Do you get a vector in the space? Or would you say that infinite linear combinations, such as this, are not allowed. As far as I know the definition of a linear combination for a vector space, without further structure, is that it is a FINITE sum of vectors. Yet the example by Gerry Myerson is certainly true, together with his remark on some infinite linear combinations. So this is puzzling. And further, what is the answer to the original question Is v = (1/2)v + (1/4)v + (1/8)v + ... ? Ron Jonesa On 25 jun, 05:46, Gerry Myerson On Jun 23, 10:38 pm, Ron Jonesa My answer is NO. In a vector space (No topologies, manifolds, > norms etc) you are only allowed to make FINITE linear > combinations. The RHS is an INFINITE linear combination which > is not allowed. Ron Really? How about the vector space of all formal power series with > real coefficients? 1, x, x^2, etc., are all elements thereof, as > is > 1 + x + x^2 + ..., which sure looks like an infinite linear > combination. Yes, but the power series may not sum to an element of the vector > space. Say, what? The power series *is* an element of the vector space. > V is the vector space of all formal power series with real > coefficients. > 1, x, x^2, etc, are all elements of V, and so is 1 + x + x^2 + .... Then how about the vector space of all polynomials in x with real > coefficients? > That is an infinite dimensional vector space in which the sequence > 1,x,x^2, ... are all members of the space but 1 + x + x^2 + .... is not. So what? I was replying to the assertion that you're only allowed to make finite > linear combinations by presenting a situation where you are allowed > to make some infinite linear combinations. No one suggested that > arbitrary infinite linear combinations are allowed in arbitrary vector > spaces. Your example is non-responsive. I would like to see an _example_ of a (please, not too abstract) vector space where it is _not_ allowed to make such combinations. Han de Bruijn === Subject: Re: Simple vector space question- <4a442165$0$23264$afc38c87@news.optusnet.com.au> <260620090800440268%edgar@math.ohio-state.edu.invalid> posting-account=CtWhuAoAAAAZZ9vwdovdqB3NNaiUa20_ Trident/4.0; GTB5),gzip(gfe),gzip(gfe) On 26 jun, 14:00, G. A. Edgar v = (1/2)v + (1/4)v + (1/8)v + ... ? In general, no. One can easily define a vector space over the field of > real numbers (even a one-dimensional vector space over that field) > together with a topology, such that the partial sums for the series on > the right do not converge in that topology. And, as noted elsewhere in > this thread, for a vector space there need not be a topology at all, > in which case even the question of convergence of that series does not > make sense. However, there is a useful notion of topological vector > space over the real numbers. In a structure such as that, the > equation is true. -- > G. A. Edgar http://www.math.ohio-state.edu/~edgar/ It's all standard paranoia mathematics; I see no problem at all. If that RHS sum has sense for any finite combination of vectors, then it has sense for an infinite sum as well, because infinity is just a fugure of speach for very large, so large that it's not interesting to ask how large. So the statement is simply true. No additional topology, no nothing of the kind needed at all. Han de Bruijn === Subject: Re: Simple vector space question- > On 26 jun, 14:00, G. A. Edgar v = (1/2)v + (1/4)v + (1/8)v + ... ? In general, no. One can easily define a vector space over the field of > real numbers (even a one-dimensional vector space over that field) > together with a topology, such that the partial sums for the series on > the right do not converge in that topology. And, as noted elsewhere in > this thread, for a vector space there need not be a topology at all, > in which case even the question of convergence of that series does not > make sense. However, there is a useful notion of topological vector > space over the real numbers. In a structure such as that, the > equation is true. -- > G. A. Edgar > http://www.math.ohio-state.edu/~edgar/ It's all standard _paranoia_ mathematics; I see no problem at all. > If that RHS sum has sense for any _finite_ combination of vectors, > then it has sense for an infinite sum as well, because infinity > is just a fugure of speach for very large, so large that it's not > interesting to ask how large. So the statement is simply true. No > additional topology, no nothing of the kind needed at all. Han de Bruijn If each and every partial sum has an expressible difference some other values, which such other value represents the infinite sum? Without a measure of nearness, i.e., something very like a topology, there does not seem to be any reason to pick any one other value over any other other value. -- Virgil === Subject: Re: Simple vector space question- > nfinity > is just a fugure of speach for very large, so large that it's not > interesting to ask how large. Are you serious? What if I think it is interesting, but my wife does not? -- Timothy Murphy e-mail: gayleard /at/ eircom.net tel: +353-86-2336090, +353-1-2842366 s-mail: School of Mathematics, Trinity College Dublin === Subject: Re: Simple vector space question- <4a442165$0$23264$afc38c87@news.optusnet.com.au> posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > Take any vector v in any vector space V over the reals R. > Make linear combinations by just adding the vector to itself again and > again... Okay, adding, it once, twice, and then a third time, yes, and so on, with you so far... > ... an 'infinite' number of times. What do you get? Huh? You get an operation that is not defined by the rules of a vector space. This is no different than saying that you can add 1 to itself, and then adding one again, and then a third time, ... and so on, and each time you get a natural number. But do you get a natural number if you do this an infinite number of times? > Do you get a vector > in the space? Or would you say that infinite linear combinations, such as > this, are not allowed. It's not they are not allowed; it's that your expression is not / well-defined/: the phrase infinite linear combinations makes no sense (and thus would be called nonsense) without further definitions/rules beyond the axioms for a vector space. > As far as I know the definition of a linear combination for a vector space, > without further structure, is that it is a FINITE sum of vectors. Right. > Yet the example by Gerry Myerson is certainly true, together with his remark > on some infinite linear combinations. > So this is puzzling. It's only puzzling because of a (mild and common) abuse of notation. The example Gerry gave (formal power series) has elements often written /for convenience/ in the form: f = a 0*x^0 + a 1*x^1 + a 2*x^2 + ... + a n*x^n + ... But the definition is usually /really/ that f is a function from N to (for example) the reals; i.e., f is a function f : N -> R, with f(n) = a n. That's why they are called /formal/ power series; elements such as f aren't meant to be understood as the limit of a sum over some space; but instead as an infinite sequence of /coefficients/ {a n}. We then /define/ the operations + and * between two such / sequences/ f and g so that h = f + g is equivalent to defining h by h (n) = f(n) + g(n), and h = f * g is equivalent to defining h by h(n) = sum(i=0 to n, f(i)*g(n-i)). Verify for yourself that no infinite sums or infinite linear combinations are invoked in the above definitions of + and *. We just define, given any natural n, how to calculate the coefficent of x^n for each of f+g and f*g. (And since we are talking about vector spaces, similar comments follow for calculating h = k.f for some scalar k as h(n) = k*f(n).) Now, the usual notation is a little confusing at first; because one might think that it since it /is/ true that (for example) the element typically written as 1 + x + x^2 is, indeed, the sum of the three elements typically written as 1, x, and x^2; so therefore the element typically written as 1 + x + x^2 + ... + x^n + ... must somehow be the infinite linear combination of the distinct elements typically written as 1, x, ^2, ..., x^n, ... . But that simply isn't the case: only sums across a finite set of elements are defined by the axioms, despite what the notation may lead one to imagine. > And further, what is the answer to the original question > Is v = (1/2)v + (1/4)v + (1/8)v + ... ? > The answer is: without some additional structure which gives a well defined meaning to the RHS of the above, the question is (in general) meaningless non-sense. === Subject: Re: Simple vector space question- posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On Jun 24, 8:46 pm, Gerry Myerson norms etc) you are only allowed to make FINITE linear > combinations. The RHS is an INFINITE linear combination which > is not allowed. Ron Really? How about the vector space of all formal power series with > real coefficients? 1, x, x^2, etc., are all elements thereof, as is > 1 + x + x^2 + ..., which sure looks like an infinite linear > combination. Yes, but the power series may not sum to an element of the vector > space. Say, what? The power series *is* an element of the vector space. > V is the vector space of all formal power series with real coefficients. > 1, x, x^2, etc, are all elements of V, and so is 1 + x + x^2 + .... Then how about the vector space of all polynomials in x with real > coefficients? > That is an infinite dimensional vector space in which the sequence > 1,x,x^2, ... are all members of the space but 1 + x + x^2 + .... is not. So what? I was replying to the assertion that you're only allowed to make finite > linear combinations by presenting a situation where you are allowed > to make some infinite linear combinations. No one suggested that > arbitrary infinite linear combinations are allowed in arbitrary vector > spaces. Your example is non-responsive. -- > Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email) I didn't realize we were playing prison rules. P(X) = a pl... ( ) pnP(X1i .... Xn). P(X) = a pl... ( ) pnP(X1i .... Xn). axl axn -. Lemma 1 (by lecture note of Treves) ... 2 p pl c for every SO E (gy)m = D x ´ ´ ´ x.D,. (P (A*)So, p(A*)SA)1 ... http://joi.jlc.jst.go.jp/JST.Journalarchive/pjab1945/47.545?from=Google by Y SHIMADA - 1971 Musatov (My brother Anthony was born in 1971) === Subject: Re: minimum respect in sci.math Re: Axioms for the AP-Reals and AP-adics #475 new book 2nd edition: New True Mathematics posting-account=h5Up4wkAAADHLXEaRr54rycaZlN9-xbt Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > One is not closed minded or especially subjective merely for not > falling down in praise of you. I expect only one thing from a respondent-- some sign of mutual > respect. I don't respect you (beyond the ordinary respect I have for the rights > of any human being and other such minimal considerations, which > qualification I'll leave as tacit henceforth). When I asked you a simple question-- your response was what do you > mean by mean? No it wasn't. Anyway, simple or not, I'm not obligated to answer your > questions. And I especially don't feel any obligation to answer > questions by you that I find irrelevant and/or impertinent. You could never muster respect for me in all your previous posts. Right, 'muster' is exactly the right word. Maybe > you do not see how your posts come across. I have a general idea, though, of course, I can't entirely put myself > in the experience of others. Maybe you are totally blind > as to how you come across? Your posts to me, were always > that of psst, psst, this guys a nut. No psst about it. I've said exactly what I think. When I even bother > to comment on you, I've said what I meant in each particular context. It is not me that is the nut, > but you who > is the deprecating nut. > You fail to realize that most people are smarter than you. There's no reason to think that most people in general are smarter > than me. However, I do recognize that mathematicians are much more > clever than me in the particular field of mathematics. I get along fine with anyone who shows mutual respect. How nice. Lwalk is great > on > mutual respect, even saintly, I find differently, as he has a very nasty habit of recklessly > mischaracterizing the posts of other people, which I find quite > disrespectful. for I could not waste time on those who > he > talks with. You seem to find enough time to post in exchange with a good number of > people. And Tim Little, shows respect, and even though I started > talking > with him gruffly. Sorry, but I'm not interested in your resentments of various posters. But guys like you Moeblee, you have no respect for me, you think I am > a nut, > and it turns out bitter, as it should turn out bitter because it is > you who lacks > the intelligence, lacks the maturity to talk with mutual respect. You > are a nutter > Moeblee and do not belong insci.math. I have GREAT respect, admiration, and appreciation for a number of > posters insci.mathand sci.logic, and my record of posting shows that > respect, admiration, and appreciation, and as in certain instances I > have explicitly stated it. You need two ingredients to fare well in sci. newsgroups like >sci.math. I'm not interested in faring well, in YOUR sense of 'faringe well', > in a newsgroup. You need > some mutual respect and you need some mathematical knowledge. You > Moeblee, > in my humble opinion, lacks both of those ingredients. Your opinions on such things are utterly of no interest to me. As well as > Virgil, and Jesse > Hughes and the Herb twins are lacking in both of those. Do I look like I wish to be a sounding board for your various > resentments about various posters? Take a hint: I don't. Lwalk spends alot of time talking about cranks and crank behaviour. > One thing > should be pointed out is that so many posters do not realize how easy > it is to detect > whether the person you are talking to or talking with has a gram of > respect for them. I'll give you a microgram, which is what I feel you deserve from me. It is almost unconscious behaviour that humans in a conversation know > whether the > other person has a minimum of respect for them. And it is one of your > deficiencies > Moeblee in not realizing that I can detect in a few sentences whether > you have > the minimum respect that is required for a conversation. You don't. You don't need to view into the unconscious now. I've told you in > plain terms: I don't respect you. So, do yourself a favor: If you must > continue to seek congratulations, validation, and approving attention > in your typically pathetic way, then don't bother seeking them from > me. MoeBlee ñThe best thing to give to your enemy is forgiveness; to an opponent, tolerance; to a friend, your heart; to your child, a good example; to a father, deference; to your mother, conduct that will make her proud of you; to yourself, respect; to all men, charity.î --Benjamin Franklin (American Statesman, Scientist, Philosopher, Printer, Writer and Inventor. 1706-1790) ñI'm not concerned with your liking or disliking me... All I ask is that you respect me as a human being.î --Jackie Robinson (American Professional Baseball Player) === Subject: A deceptively simple inequality Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 -1/x Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 > -1/x to Pi/2+1/x or to Pi/2-1/x near x_k=k*Pi, and the difference appears to > be of the order of 1/x_k^2. But how to show it ? We have Si(x) = pi/2 + int_x^infty sin(t)/t dt. Integrate by parts four times to get Si(x) = pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 + int_x^infty 24 cos(t)/t^5 dt So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + 6/x^4 and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - 6/x^4 Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 <= (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 = 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 while (1/x - 6/x^4)^2 = 1/x^2 - 12/x^5 + 36/x^8 So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 which is true for x > 2 + 2 sqrt(3)/3. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: A deceptively simple inequality posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) On 25 juin, 19:48, Robert Israel > Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 > -1/x to Pi/2+1/x or to Pi/2-1/x near x k=k*Pi, and the difference appears to > be of the order of 1/x k^2. But how to show it ? We have Si(x) = pi/2 + int x^infty sin(t)/t dt. Integrate by parts four times > to get > Si(x) = pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 > + int x^infty 24 cos(t)/t^5 dt So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + 6/x^4 > and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - 6/x^4 Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 > <= (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 > = 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 > while > (1/x - 6/x^4)^2 = 1/x^2 - 12/x^5 + 36/x^8 So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 > which is true for x > 2 + 2 sqrt(3)/3. > -- > Robert Israel isr...@math.MyUniversitysInitials.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, BC, Canada I'd like to know where does your idea of a fourth times by part integration come from? Amiti.8es, Alain === Subject: Re: A deceptively simple inequality > On 25 juin, 19:48, Robert Israel > Let Si(x)=3D int (sin(t)/t, t=3D0..x). Show that (for all x>0) Pi/2 > -1/x to Pi/2+1/x or to Pi/2-1/x near x_k=3Dk*Pi, and the difference appears > = > to > be of the order of 1/x_k^2. But how to show it ? We have Si(x) =3D pi/2 + int_x^infty sin(t)/t dt. =A0Integrate by parts > f= > our times > to get > Si(x) =3D pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 > =A0 =A0+ int_x^infty 24 cos(t)/t^5 dt So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + 6/x^4 > and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - 6/x^4 Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 > =A0 =A0 =A0 =A0 =A0 =A0 <=3D (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 > =A0 =A0 =A0 =A0 =A0 =A0 =A0=3D 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 > while > =A0 =A0 (1/x - 6/x^4)^2 =3D 1/x^2 - 12/x^5 + 36/x^8 So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 > which is true for x > 2 + 2 sqrt(3)/3. =A0 > -- > Robert Israel =A0 =A0 =A0 =A0 =A0 =A0 > =A0isr...@math.MyUniversitysInitial= > s.ca > Department of Mathematics =A0 =A0 =A0 =A0http://www.math.ubc.ca/~israel > University of British Columbia =A0 =A0 =A0 =A0 =A0 =A0Vancouver, BC, > Cana= > da > I'd like to know where does your idea of a fourth > times by part integration come from? Amiti=E9s, > Alain It's well known (i.e. something I'd seen before) that the asymptotic series for Si(x) and related integrals can be obtained using repeated integration by parts. Why four? Well, it's not hard to see that two or three won't work. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: A deceptively simple inequality > Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 > -1/x Numerical experiments shox that this is quite sharp : Si(x) gets > close to Pi/2+1/x or to Pi/2-1/x near x_k=k*Pi, and the difference > appears to be of the order of 1/x_k^2. But how to show it ? We have Si(x) = pi/2 + int_x^infty sin(t)/t dt. Integrate by parts > four times to get > Si(x) = pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 > + int_x^infty 24 cos(t)/t^5 dt So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + > 6/x^4 > and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - > 6/x^4 Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 > <= (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 > = 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 > while > (1/x - 6/x^4)^2 = 1/x^2 - 12/x^5 + 36/x^8 So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 > which is true for x > 2 + 2 sqrt(3)/3. Could this be obtained via the mean value theorem: for example: Si(x) - pi/2 = -int(x,oo) sin(t)/t = - (cos(x)/x int(0,oo) sin(t)/(1+t/x) dt + sin(x)/x int(0,oo) cos(t)/(1+t/x) dt ) and then for example int(0,oo) sin(t)/(1+t/x) = 1-cos(a) for some 00 === Subject: Re: A deceptively simple inequality > Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 > -1/x close to Pi/2+1/x or to Pi/2-1/x near x_k=k*Pi, and the difference > appears to be of the order of 1/x_k^2. But how to show it ? > We have Si(x) = pi/2 + int_x^infty sin(t)/t dt. Integrate by parts > four times to get > Si(x) = pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 > + int_x^infty 24 cos(t)/t^5 dt > So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + > 6/x^4 > and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - > 6/x^4 > Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 > <= (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 > = 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 > while > (1/x - 6/x^4)^2 = 1/x^2 - 12/x^5 + 36/x^8 > So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 > which is true for x > 2 + 2 sqrt(3)/3. Could this be obtained via the mean value theorem: for example: Si(x) - pi/2 = -int(x,oo) sin(t)/t = - (cos(x)/x int(0,oo) > sin(t)/(1+t/x) dt + sin(x)/x int(0,oo) cos(t)/(1+t/x) dt ) and then for example int(0,oo) sin(t)/(1+t/x) = 1-cos(a) for some > 00 yes this works. because you actually get Si(x) - pi/2 = cos(x)/x *(1-cos(a)) - sin(x)*sin(b) /x and so have +/-2/x -/+1/x --> <=1/x what i am not sure about is applying the theorem when you have things such as int(0,oo) sin(u) du but i think you could make it correct by writing it as lim(L->oo) 1/(L/x+1) * int(b,L) sin(t) dt and that should take care of it? but how to get the strict inequality? === Subject: Re: A deceptively simple inequality > Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 > -1/x close to Pi/2+1/x or to Pi/2-1/x near x_k=k*Pi, and the difference > appears to be of the order of 1/x_k^2. But how to show it ? > We have Si(x) = pi/2 + int_x^infty sin(t)/t dt. Integrate by parts > four times to get > Si(x) = pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 > + int_x^infty 24 cos(t)/t^5 dt > So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + > 6/x^4 > and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - > 6/x^4 > Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 > <= (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 > = 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 > while > (1/x - 6/x^4)^2 = 1/x^2 - 12/x^5 + 36/x^8 > So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 > which is true for x > 2 + 2 sqrt(3)/3. Could this be obtained via the mean value theorem: for example: Si(x) - pi/2 = -int(x,oo) sin(t)/t = - (cos(x)/x int(0,oo) > sin(t)/(1+t/x) dt + sin(x)/x int(0,oo) cos(t)/(1+t/x) dt ) and then for example int(0,oo) sin(t)/(1+t/x) = 1-cos(a) for some > 00 sorry i think that should be <= not just < i.e. Si(x) - pi/2 <= 1/x x>0 and Si(x) + pi/2 <= -1/x for x<0 === Subject: Re: A deceptively simple inequality Robert Israel a .8ecrit : > > Let Si(x)= int (sin(t)/t, t=0..x). Show that (for all x>0) Pi/2 > -1/x Numerical experiments shox that this is quite sharp : Si(x) gets close > to Pi/2+1/x or to Pi/2-1/x near x_k=k*Pi, and the difference appears to > be of the order of 1/x_k^2. But how to show it ? We have Si(x) = pi/2 + int_x^infty sin(t)/t dt. Integrate by parts four times > to get > Si(x) = pi/2 + cos(x)/x + sin(x)/x^2 - 2 cos(x)/x^3 - 6 sin(x)/x^4 > + int_x^infty 24 cos(t)/t^5 dt So Si(x) < pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) + 6/x^4 > and Si(x) > pi/2 + (1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x) - 6/x^4 > > Note that |(1/x - 2/x^3) cos(x) + (1/x^2 - 6/x^4) sin(x)|^2 > <= (1/x - 2/x^3)^2 + (1/x^2 - 6/x^4)^2 > = 1/x^2 - 3/x^4 - 8/x^6 + 36/x^8 > while > (1/x - 6/x^4)^2 = 1/x^2 - 12/x^5 + 36/x^8 So |Si(x) - pi/2| < 1/x if -3/x^4 - 8/x^6 + 12/x^5 < 0 > which is true for x > 2 + 2 sqrt(3)/3. === Subject: Re: Off the Hook (Not Morally Responsible) posting-account=h5Up4wkAAADHLXEaRr54rycaZlN9-xbt Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On Jun 24, 8:25 pm, Paul Ransom Erickson On Jun 17, 12:48 am, Paul Ransom Erickson On Jun 11, 10:30 pm, Paul Ransom Erickson What do you consider the difference between an agent and a > moral agent? Frankly, it1s a tough question and I1m not sure any > of us can answer it without coming off like a loon, but it might > be fun to try it for awhile. :-) > I don't think there is a difference, really. An agent is something > that acts: it decides what to do and does it. Action isn't just any > behaviour, as it requires a mental decision to do it. Moral agent > adds the idea that the agent is responsible -- can be praised or > blamed -- for his decision and therefore for the action, So Big Blue is a moral agent because it decides what chess moves to make >and is responsible for winning or loosing the game? It seems to me that >something more is required, but I'm not sure I can put my finger on what >exactly that is. > which assumes that he could have decided differently in the same > situation; which is of course the very point of contention in the > debate over 'free will'. Every decision is formed by the present state of the actor's mind, the >sense data received by his mind, and possibly (if indeterminism is true) >some random factors that have nothing to do with either the mind or the >sense data. How can there be any debate? More accurately, I recognize that there has >been lots of debate, but I posit that such debate stems from a concept >of free will that doesn't exist in any case. It looks to me like only the kinds of behavior that can be influenced > by praise/blame or punishment/reward fall into the moral sphere. Any > behavior that cannot influenced in that way is innocent of morality -- > like the Alzheimer's sufferer who plays with himself in public. An > ordinary person who was inclined to act that way could be deterred by > society's expected scorn, or at least by threats of punishment. But > the Alzheimer's patient cannot be reached by such threats, so (I > argue) we hold him blameless, even though we do our best to stop > him... >How is what you are describing a different 'kind' of behavior? The >behavior is identical. > It is a different kind of behavior because no threats of punishment or > ostracism can make it stop. But 'it' is not acting; the individual is acting. So there is no >attribution of 'belonging to the moral sphere' applied to the *act* >itself; rather it is to the individual. If you are trying to define >'moral agent', that's fine---you are at least attempting to answer my >original question. If so, we can continue. We can, can we? Goodie. I am not attempting to define moral agent. I am suggesting that > only those behaviors that can realistically be expected to yeild to > social punishment are moral behaviors. And that any behavior that > cannot be so influnenced is entirely amoral. No, I don't see the need to introduce an agent to explain that. You > can do it with dogs and cats too. ---------------------------------- A skeleton, the philosophers say, cannot slobber. Paul I agree that morality is entirely subjective to the individual. What rules we are shaped by are influenced by the environment we know cannot be so influenced is entirely amoral. No, I don't see the need to introduce an agent to explain it. On: The idea of a moral philosophy: The impact of psychoanalysis on phi of the failure of British philosophy to be influenced in any way 'whatsoever' by psychoanalysis, and philosophy may not rest entirely with the latter camp and feelings which precede volition, cannot be of a moral nature of one of the persons was influenced entirely by a love for 140 the praise of men who oppose the Calvinists, has an entirely different signification. A moral agent is a being that is capable of those actions that have a moral quality, is not capable of being influenced by a moral law, and its sanctions of those who oppose the Calvinists, has an entirely different signification. To moral Agency belongs a moral faculty, or sense of moral good and evil, is not capable of being influenced by a moral law, and its sanctions of Freedom of the Will. A ruler, acting in that capacity only, is not capable of being influenced by a moral law, and its sanctions of threatenings and promises. A moral is any belief that is held with total conviction, such as eating meat. The Pagans are influenced by nature but not in the sanitized Disney. In fact, in game it was entirely possible to become buddy-buddy with both. Freedom of the Will has an entirely different signification..84 These several things belong to their of being influenced by a moral law, and its sanctions of threatenings and ... What do you think of these words at face value? Poll Shows Americans Less Influenced By Scare Tactics On Health ... The latter is a moral issue that has been sorely missing from the discussion. ... care for everyone with a job and cut Medicaid and Medicare entirely. ... l assert it. === Subject: Re: Off the Hook (Not Morally Responsible) > On Jun 24, 8:25 pm, Paul Ransom Erickson On Jun 11, 10:30 pm, Paul Ransom Erickson What do you consider the difference between an agent and a > moral agent? Frankly, it1s a tough question and I1m not sure any > of us can answer it without coming off like a loon, but it might > be fun to try it for awhile. :-) > I don't think there is a difference, really. An agent is something > that acts: it decides what to do and does it. Action isn't just any > behaviour, as it requires a mental decision to do it. Moral agent > adds the idea that the agent is responsible -- can be praised or > blamed -- for his decision and therefore for the action, > So Big Blue is a moral agent because it decides what chess moves to make > and is responsible for winning or loosing the game? It seems to me that > something more is required, but I'm not sure I can put my finger on what > exactly that is. > which assumes that he could have decided differently in the same > situation; which is of course the very point of contention in the > debate over 'free will'. > Every decision is formed by the present state of the actor's mind, the > sense data received by his mind, and possibly (if indeterminism is true) > some random factors that have nothing to do with either the mind or the > sense data. > How can there be any debate? More accurately, I recognize that there has > been lots of debate, but I posit that such debate stems from a concept > of free will that doesn't exist in any case. > It looks to me like only the kinds of behavior that can be influenced > by praise/blame or punishment/reward fall into the moral sphere. Any > behavior that cannot influenced in that way is innocent of morality -- > like the Alzheimer's sufferer who plays with himself in public. An > ordinary person who was inclined to act that way could be deterred by > society's expected scorn, or at least by threats of punishment. But > the Alzheimer's patient cannot be reached by such threats, so (I > argue) we hold him blameless, even though we do our best to stop > him... > How is what you are describing a different 'kind' of behavior? The > behavior is identical. > It is a different kind of behavior because no threats of punishment or > ostracism can make it stop. > But 'it' is not acting; the individual is acting. So there is no > attribution of 'belonging to the moral sphere' applied to the *act* > itself; rather it is to the individual. If you are trying to define > 'moral agent', that's fine---you are at least attempting to answer my > original question. If so, we can continue. > We can, can we? > Goodie. > I am not attempting to define moral agent. I am suggesting that > only those behaviors that can realistically be expected to yeild to > social punishment are moral behaviors. And that any behavior that > cannot be so influnenced is entirely amoral. > No, I don't see the need to introduce an agent to explain that. You > can do it with dogs and cats too. > ---------------------------------- > A skeleton, the philosophers say, cannot slobber. > Paul I agree that morality is entirely subjective to the individual. What > rules we are shaped by are influenced by the environment we know > cannot be so influenced is entirely amoral. No, I don't see the need > to introduce an agent to explain it. On: The idea of a moral philosophy: The impact of psychoanalysis on > phi of the failure of British philosophy to be influenced in any way > 'whatsoever' by psychoanalysis, and philosophy may not rest entirely > with the latter camp and feelings which precede volition, cannot be of > a moral nature of one of the persons was influenced entirely by a love > for 140 the praise of men who oppose the Calvinists, has an entirely > different signification. A moral agent is a being that is capable of those actions that have a > moral quality, is not capable of being influenced by a moral law, and > its sanctions of those who oppose the Calvinists, has an entirely > different signification. To moral Agency belongs a moral faculty, or sense of moral good and > evil, is not capable of being influenced by a moral law, and its > sanctions of Freedom of the Will. > A ruler, acting in that capacity only, is not capable of being > influenced by a moral law, and its sanctions of threatenings and > promises. A moral is any belief that is held with total conviction, such as > eating meat. The Pagans are influenced by nature but not in the > sanitized Disney. In fact, in game it was entirely possible to become buddy-buddy with > both. Freedom of the Will has an entirely different signification..84 These > several things belong to their of being influenced by a moral law, and > its sanctions of threatenings and ... I'd be interested in better understanding what you mean by moral law. I'd distinguish for example between: (a) Moral law: a kind of ethical principle which follows from natural law, as understood in philosophy. in a constitution, public law or municipal/local authority law or regulation which deals primarily with moral behaviour. David Bernier > What do you think of these words at face value? Poll Shows Americans Less Influenced By Scare Tactics On Health ... The latter is a moral issue that has been sorely missing from the > discussion. ... care for everyone with a job and cut Medicaid and > Medicare entirely. ... > l assert it. === Subject: Re: The basic idea behind M theories posting-account=h5Up4wkAAADHLXEaRr54rycaZlN9-xbt Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Hi all In earlier posts to this usenet, I've presented several theories, I > called them M theories. I'll try in this thread to present the basic > idea behind these theories. First the aim of these theories to prove the existence of Large > cardinals, sets that ZFC cannot prove their existence. In these theories a new primitive predicate that is a one place > predicate symbole is introduced, here in this thread let me denote it > by universe and for short I'll use the letter @ So @x means x is a universe. Now the idea of universes, is for V2 (the second universe in this > theory ) to be as Large as the universe of discourse in ZFC, not only > that , every object provable to exist in ZFC, is provable to exist in > V2. So how many sets we have in this theory will depend on the size of > each universe and on the size of the class of all universes. I intend to make this theory so Large such as to have a universe > V k for every ordinal k in this theory, includding inaccessible > ordinals. A set is defined in this theory as being a member of a universe x is a set iff there exist some y such that (@y and x in y) No Ur-elements exist in this theory. every object in this theory is a class which is either a set or a > proper class. the class of all sets is a proper class, the class of > all universes is a proper class. x is a proper class iff there do not exist any class y such that (y > is a universe and x in y). Now the universes in this theory have certain properties (see axioms > below). 1)every universe is transitive, i.e. every set of it is a subset of > it. > 2)In every universe any subset of a member in it is a member in it. > because of comprehension in this theory (see below) it can be proved > that no universe is in itself, and from 1) this implies that no > universe is in any of its members, or member of its members,...etc. > 3) every two universes x,y either y in x or x in y. > 4)there exist a minimal universe, defined as the universe which is a > subset of every universe. ( this universe can be proved to be unique > denoted as V1. > 5) for every universe x there exist a successor universe y, i.e y is a > universe such that x in y, and there do not exist a universe z that > contain x as a member, and that is a member of y. > 6) There do not exist an empty universe from 5 we have every universe is a set! So the class of all unvierses (see comprehension in this theory) is a > well ordered class. In order to inflate each universe add two additional properties to > each universe. 7) the power class of any member in a universe is a member of that > universe.(power class defined as in Z) 8) the class union of any member in a universe is a member of that > universe. (union defined as in Z). In these theory comprehension is stated in the following manner. Axiom schema of class comprehension: if P is a formula in which is not > free, then all closures of ExAy (y in x iff ( y is a set & P(y)) are axioms. using this schema we can have classes as objects in this theory, in a > way somewhat similar to NBG. Now the last two axioms are. Universal size limitation: which states that every subset of each > universe that is subnumerous (strictly dominated) to that universe is > a member of this universe. Global size limitation: every class that is subnumerous to the class > of all sets is a set. Now V1 would be the class of all hereditarily finite sets. > V2 would be somewhat equivalent to the universe of discourse of ZFC. > and of course it is the first strongely inaccessible cardinal. all heigher universes are inaccessible cardinals. So the main idea of this theory is clear, that for every ordinal k > ( accessible or inaccessible) in this theory well have V k. So we'll have an every ascending heirarchy of universes that become > larger and larger. Axioms: 1)Extensionality: as in Z > 2)Class Comprehension schema : see above. > 3)The class of all universes is well orderable by relation of > membership (see the six properties of universes above) > 4)The power class of each set in a universe is in that universe. > 5)The union class of each set in a universe is in that universe. > 6)Universal size limitation: every subset of each universe that is > subnumerous (strictly dominated by) to that universe is a member of > that universe. > 7)Global size limitation: every class of sets that is subnumerous > (strictly dominated by) to the class of all sets is a set. Now what would be the size of the class of all sets in this theory? > Is it a Mahlo cardinal or even larger?? Can this theory be enhanced to the degree of proving the existence of > EVERY LARGE CARDINAL who's existence is computable with choice, even > rank to rank cardinals? Is there any problem involved with Global size limitation axiom? Zuhair I only need 3 to maky my point. #1 Grigori Perelman .84 Blogs, Pictures, and more on WordPress Tags: m-theory, Turning Coffee into Theorems, Web 2.0, Randy Pausch, Martin Gardner, Persi Diaconis, G103, Zeitgeist ... http://en.wordpress.com/tag/grigori-perelman/ #2 PHYSICAL REVIEW D - PARTICLES and FIELDS ... and Mircea Pigli PP 2596-2602 $$ LA eng TE Compactifications of M theory and ... gamma^{*}gammapi^{0} form factor AU I.V.Musatov and A.V.Radyushkin PP ... www.infomag.ru/journals/j102e/5324.html #3 [PDF] File Format: PDF/Adobe Acrobat [9] K. Becker, M. Becker and J. H. Schwarz, ñString theory and M- theory: A ..... [85] I. V. Musatov and A. V. Radyushkin, ñTransverse momentum and Sudakov ... http://etd.lsu.edu/docs/available/etd-07032008-100238/.../Grigoryan diss.pdf === Subject: Re: Aleph_Aleph_1 posting-account=h5Up4wkAAADHLXEaRr54rycaZlN9-xbt Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Is aleph_aleph_1 provable in ZFC? > Let me try There's hardly any trying involved. It follows by definition - by way of transfinite recursion. 'aleph' is a 1-place function symbol that when applied to an ordinal, > gives us a certain ordinal. By transfinite recursion we prove that > aleph_k properly refers for all ordinals k. Since aleph_1 is an > ordinal, then we may apply aleph to aleph_1. MoeBlee I already answered this question. Sure ZFC proves that the universe has certain closure properties just like those not just by the fact that each of its instances we can state is provable, to have co finality at least aleph_2, or 2^A is at least aleph_(aleph_1). Q_Delphi Team Musatov === Subject: Re: How is Mathematics equivalent to logic? posting-account=h5Up4wkAAADHLXEaRr54rycaZlN9-xbt Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Can you tell me in just a paragraph? No. http://mally.stanford.edu/Papers/neologicism2.pdf MoeBlee Logic is the anatomy of thought. [CapitalEth] Albert Einstein === Subject: algebra about finite group theory posting-account=NoNXXQoAAAC-gia-slcN4UXVpx5gmFcS SV1),gzip(gfe),gzip(gfe) I want to try to search the book where I found the answer to the question that find the number of onto homomorphism between finite group Z(m) to Z(n) === Subject: Re: Determining if a graph is a Cayley graph posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Given a finite graph $G$ of order $n$, is there any good algorithm for > determining if $G$ is the Cayley graph of a group of order $n$, other > than simply enumerating all presentations of all groups of order $n$, > calculating the corresponding Cayley graphs, and checking for > isomorphism? One very quick and easy sanity check is to verify that every vertex > has exactly one edge of each colour leading in and out. You can then > pick a vertex to represent the identity, and recover the binary > operation. Then just check that the operation both generates the > graph and is associative. - Tim if G¢ is any circulant (di)graph of order n, then G and G¢ are isomorphic if and only ... are possible (as long as P ©.9a NP); this connection is... A circulant graph is a Cayley graph on a cyclic group. ... [P=NP] == Available commands: break [location] .. break info [breakpoint #] clear .. help ... Given a finite graph $G$ of order $n $, is there any good algorithm for determining if $G$ is the Cayley graph of a group of order $n$, ... TETRAVALENT HALF-TRANSITIVE GRAPHS OF ORDER 2p Department of ... half-transitive Cayley graph on a group of order p. 2. , a contradiction. Hence, ... generating subset of G. If either of x or y has order 2, then by Proposition .... Thus 1 + np | 8. It follows that n = 1 and p = 7. Let Q be a ... Generic: OWF, TDP, P!=NP, ... Algebraic: Factoring, RSA, DLP, DH, Strong RSA, ECDLP, GAP, WPFG, PFG, Á.a6 ... Cayley graph of finite group. Cayley graph of free group ... A family of computational groups { Gk } is weakly pseudo-free if for any polynomial ... No element other than 1 in a free group has finite order. ... On the Cayley graph of a generic finitely presented group Let N np. = N np. (m, n, t) denote the number of all group presentations (1) with non planar Cayley graphs. ... of order 2, assume that the Cayley graph C(G .... to 1 in G if and only if any path labelled by g is closed in C(G). ... (This problem isa special case of the following NP-complete problem: test ... This abeling is called a canonical one, if 1= 2if and only if f11=f22for all 1, ... Cayley repre-sentations5of over a cyclic group of order n. ... Then it5By a Cayley representation of a graph over a group G we mean a ... Isomorphisms of Cayley graphs. II of G. A. Cayley graph of G is a graph X on the vertex set G such that its .... holds if G has odd order and also if G is not solvable, since by 1.1 and ... NP=G,. [NV)P[=I.) Our standard reference book on group theory is HUPPRT [10]. ... However,if G is distance-transitive, then the imprimitivity of G yields the ... Let X = Cay(G;S) denote a Cayley graph with the group G acting regularly onthe .... Let ,k and be non-negative integers, let G be a group of order , and let D ..... But then l + (1 i)np R, which is again a contradiction. ... Lemma 2.6 If G. 1 and G. 2 are isomorphic finite groups then C (G ...... able group G of order n) as input and outputs the. Cayley table of a group G ... Solvable Group Isomorphism is (almost) in NP Á.9e coNP groups G ..... is solvable group G of order n) as input and outputs the. Cayley table of a group G ... It's like a big in and out inside out, I'll get the answer one way or another type function, to put it colloquially Martin Musatov === Subject: Re: .. pOwers of a real number mathforum.org strikes again! > If x is a real number other than 0, 1, -1, why > can't I operate a ing computer keyboard? > === Subject: Re: .. pOwers of a real number posting-account=e6PATAoAAACxeuMbOnLMqjakg3lAxhUd Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > If x is a real number other than 0, 1, -1, is it true > that all the powers of x are distinct? If for some integers r =/= s we have x^r = x^s, > then x^{r - s} = 1. If r - s is even, then x = 1, or -1; if r - s is odd, > then x = 1. But I don't see a contradiction yet.. Any thoughts on this would be appreciated. For integer r > s, the function f(x) = x^(r-s) is strictly increasing on the real line if r-s is odd (in which case the only point where f (x) = x^r/x^s = 1 is x = 1), and is strictly increasing on {x > 0} and strictly decreasing on {x < 0} if r-s is even (in which case x = +1 and -1 are the only points where f(x) = 1). These facts follow from simple results in calculus. (I had posted in incorrect response before and have removed it, but some newsreaders might be keeping the original.) R.G. Vickson === Subject: Re: .. pOwers of a real number posting-account=e6PATAoAAACxeuMbOnLMqjakg3lAxhUd Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > If x is a real number other than 0, 1, -1, is it true > that all the powers of x are distinct? If for some integers r =/= s we have x^r = x^s, > then x^{r - s} = 1. If r - s is even, then x = 1, or -1; if r - s is odd, > then x = 1. But I don't see a contradiction yet.. Any thoughts on this would be appreciated If you know calculus, you can easily show that for integer r > s, the function f(x) = x^(r-s) is strictly increasing on the real line, so x = 1 is the only point where x^r/x^s = 1. R.G. Vickson === Subject: Re: .. pOwers of a real number Content-ID: <20090625005514.V5401@agora.rdrop.com> --------------------------------------------------------------------- Content-ID: <20090625005514.R5401@agora.rdrop.com> i > If x is a real number other than 0, 1, -1, is it true > that all the powers of x are distinct? > If for some [NonBreakingSpace]integers r =/= s [NonBreakingSpace]we have [NonBreakingSpace] x^r = x^s, > then x^{r - s} = 1. > If r - s is even, then x = 1, or -1; [NonBreakingSpace]if r - s is odd, > then x = 1. If you know calculus, you can easily show that for integer r > s, the > function f(x) = x^(r-s) is strictly increasing on the real line, It is not. -2 < -1 and (-1)^2 = 1 < 4 = (-2)^2. > so x = 1 is the only point where x^r/x^s = 1. > === Subject: Re: .. pOwers of a real number posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN en-us) AppleWebKit/525.18.1 (KHTML, like Gecko) Version/3.1.1 Mobile/5H11 Safari/525.20,gzip(gfe),gzip(gfe) > If x is a real number other than 0, 1, -1, is it true > that all the powers of x are distinct? If for some integers r =/= s we have x^r = x^s, > then x^{r - s} = 1. If r - s is even, then x = 1, or -1; if r - s is odd, > then x = 1. But I don't see a contradiction yet.. Any thoughts on this would be appreciated. you missed all the other roots of unity and generally x^r = x^(r + 2 pi n i) with n an integer -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: .. pOwers of a real number posting-account=rQxmjAoAAABkK_bEn14LxyXccZYXFodO Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > you missed all the other roots of unity no, he stated x is real === Subject: Re: .. pOwers of a real number posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.11) Gecko/2009060214 Firefox/3.0.11,gzip(gfe),gzip(gfe) you missed all the other roots of unity no, he stated x is real i misstated what my point was he missed the powers that were unity by assuming that r-s was even or odd there were no reality assumptions on the powers my latter formula was meant to clarify this but you are correct that my first statement was wrongly stated -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: .. pOwers of a real number posting-account=rQxmjAoAAABkK_bEn14LxyXccZYXFodO Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > there were no reality assumptions on the powers r and s are stated as integers === Subject: Re: .. pOwers of a real number posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN rv:1.9.0.11) Gecko/2009060214 Firefox/3.0.11,gzip(gfe),gzip(gfe) there were no reality assumptions on the powers r and s are stated as integers in his solution not his question -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: .. pOwers of a real number posting-account=rQxmjAoAAABkK_bEn14LxyXccZYXFodO Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > in his solution > not his question it's true i inferred/assumed this from his working, and also from the fact that it is not true if the powers are complex btw, your > x^r = x^(r + 2 pi n i) isn't correct. the 2 pi n i bit has to be adjusted for the fact that x isn't e. counterexample x = e^(1/2), r = 2, n = 1 gives e = e ^ (1 + pi i) = - e === Subject: Re: .. pOwers of a real number posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Musatov scriber17: in his solution > not his question it's true i inferred/assumed this from his working, and also from the > fact that it is not true if the powers are complex btw, your x^r = x^(r + 2 pi n i) isn't correct. the 2 pi n i bit has to be adjusted for the fact that x > isn't e. counterexample x = e^(1/2), r = 2, n = 1 gives e = e ^ (1 + pi i) = -e {Pe £ : P lies on an extreme ray of <£, and p / nP' for some n > 1, P'e £}, iv. the non-zero elements p of £ of minimal support that are not of the form nP' (( i=1 pi ) M2) np ( ( i1 pi) M2) where A(fp ) ,n)=A(pi'),p2'), ,p,')) (4) and P = pj ) , i = 1, . . . , p, j = 1, . . . , n;, E n, = n represents a given a Binomial Distribution. If the coin is fair, then p = 0.5. One would expect the mean number of heads to be half the flips, or np = 8*0.5 = 4. The variance is equal to np(1-p). The Steiner tree problem: a tour through graphs, algorithms, and value e > 0. In fact, in the following we will assume that e < 1/2. e . The inequality in the first line follows from the fact that pi > Kf . p . ] -- Martin Musatov === Subject: Re: .. pOwers of a real number posting-account=rQxmjAoAAABkK_bEn14LxyXccZYXFodO Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > If x is a real number other than 0, 1, -1, is it true > that all the powers of x are distinct? If for some integers r =/= s we have x^r = x^s, > then x^{r - s} = 1. If r - s is even, then x = 1, or -1; if r - s is odd, > then x = 1. But I don't see a contradiction yet.. Any thoughts on this would be appreciated. it contradicts your other than 0, 1, -1 === Subject: Re: Regular Gauss Eddin-gon. :) don.mcdonald. > eddington number has 2 distinct prime factors. > electrons in the universe. http://en.wikipedia.org/wiki/Eddington_number Originally hand-waved as 136 * 2^256 = about 1.57 * 10^79, currently believed to be more like 1 * 10^80. I don't see how you can reasonably claim that any estimate of it has exactly two distinct prime factors. The rest of your message appears to be another example of your fascination with concise expressions that evaluate to nearly the same value, while lacking any trivial reason why they should do so: > # (.7^-6)^85. ?? > e.g. 7 ^ (2 ^9) resquare... The second of these evaluates to about 4.9 * 10^432, so 7^510 ~= 10^431 (to within 1 ppm). With this in mind, the first of these is easily translated to (10/7)^510 ~= 10^(510-431). > e.g. 2^9 point circle. > 1215,306,625 is a sum of 2 squares in 64 > distinct ways per octant. A brute-force computer scan confirms this pretty easily. How does one find such a number? Is it minimal? === Subject: Re: Regular Gauss Eddin-gon. :) don.mcdonald. 1215,306,625 is a sum of 2 squares in 64 > distinct ways per octant. A brute-force computer scan confirms this pretty easily. How does > one find such a number? Is it minimal? I suspect that a glance at the prime decomposition of the number will go a long way towards answering your questions. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Regular Gauss Eddin-gon. :) don.mcdonald. > > 1215,306,625 is a sum of 2 squares in 64 > distinct ways per octant. > A brute-force computer scan confirms this pretty easily. How does > one find such a number? Is it minimal? I suspect that a glance at the prime decomposition of the number > will go a long way towards answering your questions. 5^3 * 13 * 17 * 29 * 37 * 41. Hmm, IIRC the first pair of squares was 295^2 + 34860^2; 295 = 5 * 59, 34860 = 2^2 * 3 * 5 * 7 * 83... well, clearly there's a pattern of some sort, likely related to formulas for generating Pythagorean triples, but I'd probably have to look it up to work out quite what it is. === Subject: Re: Regular Gauss Eddin-gon. :) don.mcdonald. > 1215,306,625 is a sum of 2 squares in 64 > distinct ways per octant. > A brute-force computer scan confirms this pretty easily. How does > one find such a number? Is it minimal? I suspect that a glance at the prime decomposition of the number > will go a long way towards answering your questions. 5^3 * 13 * 17 * 29 * 37 * 41. Hmm, IIRC the first pair of squares > was 295^2 + 34860^2; 295 = 5 * 59, 34860 = 2^2 * 3 * 5 * 7 * 83... > well, clearly there's a pattern of some sort, likely related to > formulas for generating Pythagorean triples, but I'd probably have > to look it up to work out quite what it is. Notice that each of those primes exceeds a multiple of 4 by 1, and that they are the first few primes of that type. Such a prime can be expressed as a sum of squares in 8 ways, all of them variants on a single expression a^2 + b^2 with a > b > 0. There are simple formulas for the number of ways to write a product of such primes as a sum of two squares, based on the formulas (a^2 + b^2) (c^2 + d^2) = (a c - b d)^2 + (a d + b c)^2 and (a^2 + b^2) (c^2 + d^2) = (a c + b d)^2 + (a d - b c)^2. There are intro texts on Number Theory that tell the story in more detail. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Regular Gauss Eddin-gon. :) don.mcdonald. posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 1.1.4322; eSobiSubscriber 2.0.4.16; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On Jun 25, 6:17pm, Gerry Myerson distinct ways per octant. > A brute-force computer scan confirms this pretty easily. How does > one find such a number? Is it minimal? I suspect that a glance at the prime decomposition of the number > will go a long way towards answering your questions. 5^3 * 13 * 17 * 29 * 37 * 41. Hmm, IIRC the first pair of squares > was 295^2 + 34860^2; 295 = 5 * 59, 34860 = 2^2 * 3 * 5 * 7 * 83... > well, clearly there's a pattern of some sort, likely related to > formulas for generating Pythagorean triples, but I'd probably have > to look it up to work out quite what it is. Notice that each of those primes exceeds a multiple of 4 by 1, > and that they are the first few primes of that type. Such a prime can be expressed as a sum of squares in 8 ways, > all of them variants on a single expression a^2 + b^2 with a > b > 0. There are simple formulas for the number of ways to write > a product of such primes as a sum of two squares, based on > the formulas > (a^2 + b^2) (c^2 + d^2) = (a c - b d)^2 + (a d + b c)^2 and > (a^2 + b^2) (c^2 + d^2) = (a c + b d)^2 + (a d - b c)^2. There are intro texts on Number Theory that tell the story > in more detail. -- > Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)- Hide quoted text - - Show quoted text - Quite clearly, I report: Regular Gauss Eddin-gon. :) don.mcdonald. ...We've since learned that sometimes the ... Given a finite graph $G$ of order $n$, is there any good algorithm for determining if ... In the Study of the Crystallization Morphology of VT3-1 Alloy during VARnucleation, n is a parameter of the model to be defined below, and N ..... Kondrashov, E.N., Musatov, M.I., Maksimov, A.Yu., Gon- ... SYNTHESISM AND SYMBOLISM : THE RUSSIAN WORLD OF ART MOVEMENTMusatov or Vrubel'.84where highly subjective and exclusive colour schemes ..... was relevant to the emergence of the Neo-primitivist painting of N. Gon- ... Do you STILL not understand? God help them! Musatov === Subject: Re: Question concerning cardinality of 2^N posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/20081029 Firefox/2.0.0.18 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe)