mm-2159 === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation >x(i) = not F(i,i) >therefore F is incomplete .. is used in most every proof of >incompleteness in all theory. >>Yes, this is what is used. So let's go with the computable function >>example (which I presume that you are hinting at with A.I.) One way to >>see the Turing halting theorem is this. If you give me a computer >>program which you claim can check if programs halt or not, I can create >>a program for which your program will fail. It is a highly constructive >>proof. That doesn't prove F is incomplete. I have to admit that your thoughts are too fast for me to follow completely. When you use the word incomplete I presume that you are refering to the notion that there are statements that can be neither proven or disproven in certain theories. >You extend the proof of nonexistence from A FUNCTION to THE COMPLETE > MATHEMATICAL SET. >What function, if any, did the halting proof disprove? > What real, if any, did Cantors proof disprove? >Sure you can disprove certain specific defined functions don't exist. > the function that calculates halt values for every program, the > function that sums infinite objects in a microsecond, the function that > tells me the weather 10 days from now, the function that tells me the > maximum output of a program of size n, the function that does this... > NO PROBLEM. you have accepted that the diagonal style argument works. > But when you make a proof about reals, AND YOU SAY ITS VALID BECAUSE IT > WORKED WITH THE FUNCTIONS. >THEN YOU BETTER ALSO HAVE A SPECIFIC, DEFINABLE REAL THAT YOU ARE > MAKING PROOFS ABOUT. > YOU DON'T. >What you've done is pegged a lease on a bit of beach front property, > everybody agreed, then you claimed ownership on all the sand in the > world. WORKED FOR THE SPECIFIC CASE! typical americans. I am having a hard time understanding you completely here, but I think I can see what you are getting at. There is something profoundly counterintuitive about the proof that the real numbers are uncountable. It starts with a puported list of real numbers, and then creates just ONE more. How is creating just ONE more real number showing that it is uncountable. The problem is, you are thinking about it in the wrong way. Rather, think of it as similar to the proof that the halting problem is uncomputable. The proof is really stated as a challenge - you give me a list of reals that you claim contains all of them, and I in turn will respond with a real number that is not in your list. It is kind of like a couple of nineteenth century people arguing - is it possible to send a man to the moon? Person A keeps coming up with different schemes for how to do it, and person B keeps telling him how this particular scheme just isn't going to work. Now maybe it is possible that person A will come up with a scheme for which person B simply cannot give him a good reason why it will fail. And of course, we know that person A could do this because it has actually been done. In our twenty first century we have similar problems. Can we predict the weather in 10 days time? You tell me any prediction method you like, and I'm sure I could come up with an example with which your method just won't work. But of course, we know these do not consitute proofs. But the situation with the lack of existence of a list of reals is fundamentally different. In this case, I am not simply coming up with counterexamples to any list you show me - no, it is more than that - I have shown you a systematic process by which if you give me any list, I can give you the example of the real number that is not on your list. Now you respond that I have given you a number that is not on you list. So, you'll simply add it to your list, and now my number is on your list. No, I reply, you are not following the rules. Because now you have given me a different list. You have to give me a chance to come up with another real number. You could then add this new number to your list, but then you have to allow me to say that this is another new list, and come up with yet another number. It is like playing chess. You play your move, and then I play mine. Oh, you realise, you would like to change your mind and play a different move instead. Fine, I say, but if you change your move, you have to allow me to change my move also. Stephen === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation > >> x(i) = not F(i,i) >> therefore F is incomplete .. is used in most every proof of >> incompleteness in all theory. Yes, this is what is used. So let's go with the computable function > example (which I presume that you are hinting at with A.I.) One way to > see the Turing halting theorem is this. If you give me a computer > program which you claim can check if programs halt or not, I can create > a program for which your program will fail. It is a highly constructive > proof. >> That doesn't prove F is incomplete. I have to admit that your thoughts are too fast for me to follow > completely. When you use the word incomplete I presume that you are > refering to the notion that there are statements that can be neither > proven or disproven in certain theories. > You extend the proof of nonexistence from A FUNCTION to THE COMPLETE >> MATHEMATICAL SET. >> What function, if any, did the halting proof disprove? >> What real, if any, did Cantors proof disprove? >> Sure you can disprove certain specific defined functions don't exist. >> the function that calculates halt values for every program, the >> function that sums infinite objects in a microsecond, the function that >> tells me the weather 10 days from now, the function that tells me the >> maximum output of a program of size n, the function that does this... >> NO PROBLEM. you have accepted that the diagonal style argument works. > But when you make a proof about reals, AND YOU SAY ITS VALID BECAUSE IT >> WORKED WITH THE FUNCTIONS. >> THEN YOU BETTER ALSO HAVE A SPECIFIC, DEFINABLE REAL THAT YOU ARE >> MAKING PROOFS ABOUT. >> YOU DON'T. >> What you've done is pegged a lease on a bit of beach front property, >> everybody agreed, then you claimed ownership on all the sand in the >> world. WORKED FOR THE SPECIFIC CASE! typical americans. I am having a hard time understanding you completely here, but I think I > can see what you are getting at. >There is something profoundly counterintuitive about the proof that the > real numbers are uncountable. It starts with a puported list of real > numbers, and then creates just ONE more. How is creating just ONE more > real number showing that it is uncountable. >The problem is, you are thinking about it in the wrong way. Rather, > think of it as similar to the proof that the halting problem is > uncomputable. The proof is really stated as a challenge - you give me a > list of reals that you claim contains all of them, and I in turn will > respond with a real number that is not in your list. He doesn't accept that proof either. -- Will Twentyman email: wtwentyman at copper dot net === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation > Their work implies that given any machine designed to solve math > problems, I can find a problem that it cannot do. And you can't do either, in general. === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation >Their work implies that given any machine designed to solve math >>problems, I can find a problem that it cannot do. And you can't do either, in general. Yes. Isn't this what I said in the sentence that followed (which you snipped)? === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation > Imagine infinite people are all flipping coins infinite times. Can you come up with a new sequence every time? The anti-diagonal of the list you have is always new, so yes, if you admit the legitimacy of taking an infinite anti-diagonal. The TM paradigm and first-order logic BOTH DO admit it, and there is nothing you can do about that. Person Flips > 1 HHTTHTHTH.. > 2 THTTTHTHT.. > 3 HHTHTHTHH.. > 4 TTTTHTHTH.. > 5 HTTHTHTHT.. > 6 THTHTHTHH.. > 7 HHHHHHTHT.. > 8 HHHTHTHTH.. > .. > AHA! take the diagonal you say. OK thats 12345678 > HHTTTHTT... you could have chosen another diagonal by rearranging the elements of > the list. Of course. There are uncountably many different ways of rearranging the list (if every element on it is different). There are many more ways of rearranging tht list than THERE ARE ELEMENTS on the list. Lets swap rows (person) 1 and 2 Person Flips > 1 THTTHTHTH.. > 2 HHTTTHTHT.. > 3 HHTHTHTHH.. > Now the diagonal is 1234 > THTTHTT... > The 1st diagonal started > HH... the second diagonal is > TH.. all the flips after these are the same. So it appears the 1st digit of the diagonal can > be H or T, and it > doesn't affect the rest of the number at all! This is not true JUST for the FIRST digit. This is true for ANY FINITE number of digits, IF both H and T occur INFINITELY often in EVERY *column* of the list. If they do, then for any n, you can rearrange the list such that the first n digits of the diagonal are ANYTHING YOU LIKE. That is because n is *finite*. You canNOT, however, rearrange the list so that some anti-diagonal of ANY arrangement appears ON the list! NOT ONLY the anti- diagonal of the original list, BUT ALSO the anti-diagonals of EVERY (finitary) permutation of the list, ALL FAIL to occur ANYwhere on the list! And swapping things DOESN'T CHANGE that! Same for digit/flip 2, 3, 4, 5... This clearly demonstrates, > IT DOESNT MATTER WHAT ANY DIGIT OF THE > DIAGONAL IS. That's right, it doesn't. What DOES matter is what happens with all the INFINITELY MANY digits AFTER that digit! You can get AS LONG A FINITE match as you like! But you will NEVER get an INFINITE match! You can match ALL finite prefixes and STILL NEVER get an infinite match! > Whether the diagonal is HTHTHT.. or THTHTH.., No, your ..'s are WRONG. What you MEANT to say is, Whether the diagonal is HTHTHT..H or THTHTH..T, i.e., you have to STOP somewhere. > they both came from the > same list, who cares what the diagonal is. We care what the ANTI-diagonal is, DUMBASS! Whether the DIAGONAL is or isn't on the list VARIES. SOMETIMES IT IS, sometimes it isn't. That is HARD to prove. It depends on what OTHER assumptions you make about the structure of the list. But whether the ANTI-diagonal is or isn't on the list does NOT vary. That is ALWAYS not on the list. And, I repeat, NOT ONLY is the anti-diagonal of the ORIGINAL list not on the list, the anti-diagonals of all these infinitely many finite permutations of the original list ARE NOT ON THE LIST, EITHER. By adding in swaps, you DON'T show the IRrelevance of the anti-diagonal: rather, you give us uncountably MANY MORE anti-diagonals that are ALSO GUARANTEED NOT to be on the list! There are WAY WAY MORE sequences NOT on the list THAN ON it! SUMMARY : > HHTTHTT.. is the original diagonal > THTTHTT.. is the diagonal of the same > list of flips in a different order. Right, and you don't know about whether either of these diagonals is or isn't on the list. But you DO know that the COMPLEMENTS of BOTH of them are NOT on the list! > It doesn't matter what the 1st digit of the diagonal is! Or the 2nd, or the 69th, or the googolplexth. fOR ANY FINITE number, it doesn't matter what any of the numbers UP to that point are, because THAT IS ONLY A FINITE number of numbers! AFTER that number are INFINITELY many numbers, and you CAN'T MATCH ALL of THEIR complements! > Using the diagonal to prove > properties of a list can be hazardous. Well, if YOU are using it, certainly, because YOU'RE STUPID. But that doesn't mean anybody else is mis-proving with it. === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation Watch closely this time. HT.... TT... xxT.... xxxH... diag = HTTH... swap rows 1 and 2 TT... HT... xxT... xxxH... diag = TTTH... We can flip any digits we want. Herc === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation you're a bore and a waste of other people's time. === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation > Imagine infinite people are all flipping coins infinite times. >Can you come up with a new sequence every time? >Person Flips > 1 HHTTHTHTH.. > 2 THTTTHTHT.. > 3 HHTHTHTHH.. > 4 TTTTHTHTH.. > 5 HTTHTHTHT.. > 6 THTHTHTHH.. > 7 HHHHHHTHT.. > 8 HHHTHTHTH.. > .. AHA! take the diagonal you say. OK thats >12345678 > HHTTTHTT... And that means its anti-: TTHHHTHH... is not on the list. > you could have chosen another diagonal by rearranging the elements of > the list. >Lets swap rows (person) 1 and 2 >Person Flips > 1 THTTHTHTH.. > 2 HHTTTHTHT.. > 3 HHTHTHTHH.. Now the diagonal is >1234 > THTTHTT... Which means its anti-: HTHHTHH... is not on the list either. The 1st diagonal started > HH... >the second diagonal is > TH.. >all the flips after these are the same. Which means there are two different flip sequences that are not listed. And? >So it appears the 1st digit of the diagonal can be H or T, and it > doesn't affect the rest of the number at all! And? >Same for digit/flip 2, 3, 4, 5... >This clearly demonstrates, IT DOESNT MATTER WHAT ANY DIGIT OF THE > DIAGONAL IS. Of course not, as long as the ENTIRE anti-diagonal is not on the list, which it isn't. >Whether the diagonal is HTHTHT.. or THTHTH.., they both came from the > same list, who cares what the diagonal is. >SUMMARY : > HHTTHTT.. is the original diagonal > THTTHTT.. is the diagonal of the same list of flips in a different > order. >It doesn't matter what the 1st digit of the diagonal is! > Using the diagonal to prove properties of a list can be hazardous. What this suggests is that when you go for the anti-diagonal, you can show that there are MANY possible sequences that were missed. -- Will Twentyman email: wtwentyman at copper dot net === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation Keep up the Red Herring arguments Herc, it's great to show my children what faulty reasoning looks like and you provide so many abundant examples. Why not try and refute what Cantor actually said rather then some analogy of your own devising? === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation If you want to set a good example you could always point out the 1st step you disagree with. Proof by induction. Given a set of random coin flips. The 1st digit can be H or T (demonstrated # ) similary the 2nd digit can be H or T. similary the next digit can be H or T. for any digit, the next digit can be H or T. by induction, all digits of the diagonal are arbitrary. therefore , the diagonal is independant of the list. # without effecting the rest of the sequence. Herc === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation In sci.logic, HERC777 on 7 Jun 2005 05:00:33 -0700 > If you want to set a good example you could always point out the 1st > step you disagree with. Proof by induction. Given a set of random coin flips. The 1st digit can be H or T (demonstrated # ) similary the 2nd digit can be H or T. > similary the next digit can be H or T. > for any digit, the next digit can be H or T. by induction, all digits of the diagonal are arbitrary. > therefore , the diagonal is independant of the list. # without effecting the rest of the sequence. Herc > There are at least two forms of induction. 1. Weak induction. Given P(1) and P(n) => P(n+1), deduce (An)(P(n)). 2. Strong induction. Given P(1) and (An)( (Ak < n) P(k) => P(n)), deduce (An)(P(n)). Neither one quite fits. Now, given a set of *normal* [*] coin flips, any of the columns can in fact be H or T infinitely many times. However, that doesn't say much about the inclusion of the infinite sequence A defined by X[n] = !L[n][n] in list L -- or a set containing L -- mostly because X is an infinite sequence, and induction only works over the set of all finite numbers (N). In short, you've proven that all *finite* subsequences of X are in L. But it's like 1/3 in T_10 = {b/10^k : 0 <= b < 10^k}, Herc. Every finite subsequence of 1/3 is in T_10, but 1/3 is not in T_10. If one rigorously defines S = T <=> (Ai)(S[i] = T[i]) S in L <=> (Ex)(Ai)(S[i] = L[x][i]) then one can conclusively show the following set of equivalences, by De Morgan's: (Ai)(~(X = L[i])) <=> (Ai)~(Aj)(X[j] = L[i][j]) <=> (Ai)(Ej)(X[j] != L[i][j]) Since j = x is one such j, it's true. :-) [*] the concept is an extension of a normal binary expansion, only in this case it applies to all list entries. -- #191, ewill3@earthlink.net It's still legal to go .sigless. === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation I already did, using an analogy rather then the original argument that Cantor used. After all, he did prove this fact himself and you have still not adressed the correctness of his proof. After all if *you* wanted to set a good example you'd point out which line of the original proof you diagreeded with. === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation > If you want to set a good example you could always point out the 1st > step you disagree with. Proof by induction. Given a set of random coin flips. The 1st digit can be H or T (demonstrated # ) There are orderings where the first digit is H, and the second digit is T. > similary the 2nd digit can be H or T. Not independently. You showed an ordering in which the diagonal starts HH... and another in which it starts TH... Note that the 2nd element was H in both choices. You haven't proved that there exists a diagonal HT or TT. More importantly, you haven't proved that there exists some arrangement such that any possible binary can be a diagonal (or its complement, the anti-diagonal). However, I can prove that your first sequence will NEVER be the anti-diagonal, no matter what order you put your list. How do I do that? Suppose you rearrange the list so that what was the first sequence is now in position n. The anti-diagonal I generate for that list is different from this sequence in bit n. Thus, no matter where this sequence appears, the anti-diagonal differs in at least one bit, and is never equal to the whole sequence. Proof complete: your sequence #1 is not the anti diagonal for any reordering of your list. Of course, this proof applies to any sequence in your first list. - Randy === Subject: Re: The WHO CARES proof of anti-anti-diagonalisation > Imagine infinite people are all flipping coins infinite times. Can you come up with a new sequence every time? Person Flips > 1 HHTTHTHTH.. > 2 THTTTHTHT.. > 3 HHTHTHTHH.. > 4 TTTTHTHTH.. > 5 HTTHTHTHT.. > 6 THTHTHTHH.. > 7 HHHHHHTHT.. > 8 HHHTHTHTH.. > .. > AHA! take the diagonal you say. OK thats 12345678 > HHTTTHTT... you could have chosen another diagonal by rearranging the elements of > the list. Lets swap rows (person) 1 and 2 Person Flips > 1 THTTHTHTH.. > 2 HHTTTHTHT.. > 3 HHTHTHTHH.. > Now the diagonal is 1234 > THTTHTT... > The 1st diagonal started > HH... the second diagonal is > TH.. all the flips after these are the same. So it appears the 1st digit of the diagonal can be H or T, and it > doesn't affect the rest of the number at all! Same for digit/flip 2, 3, 4, 5... This clearly demonstrates, IT DOESNT MATTER WHAT ANY DIGIT OF THE > DIAGONAL IS. Whether the diagonal is HTHTHT.. or THTHTH.., they both came from the > same list, who cares what the diagonal is. SUMMARY : > HHTTHTT.. is the original diagonal > THTTHTT.. is the diagonal of the same list of flips in a different > order. It doesn't matter what the 1st digit of the diagonal is! > Using the diagonal to prove properties of a list can be hazardous. > But if you take a diagonal for one arrangement of the list, and change all its digits, you are guaranteed to get something which isn't in the list. > Herc === Subject: This Week's Finds in Mathematical Physics (Week 218) Also available as http://math.ucr.edu/home/baez/week218.html June 5, 2005 This Week's Finds in Mathematical Physics - Week 218 John Baez Classes are over! Summer is here! Now I can finally get some work done! I'll be travelling to Sydney, Canberra, Beijing, Chengdu and Calgary, but mainly I want to finish writing some papers. First, though, I need to recover from a hard quarter. I need to goof off a bit! I spent most of yesterday lying in bed reading. Now I want to talk some more about number theory. Let's see, where were we? I had just begun to introduce the theme of L-functions and their corresponding automorphic forms. My ultimate goal is to understand the Langlands Conjectures well enough to give a decent explanation of what they say. Instead of simply stating them, I'd like to really make them plausible, and this will take quite an elaborate warmup. So, this Week I want to talk about some background. problem, he needed the feeling he had some inside track - some insight or trick up his sleeve that nobody else had. Most of us will never be as good as Feynman at choosing an inside track. But I think we all need one to convert what would otherwise be a dutiful and doomed struggle to catch up with the experts into something more hopeful and exciting: a personal quest! For anyone with a physics background, a good inside track on almost any math problem is to convert it into some kind of crazy physics problem. It doesn't need to be realistic physics, just anything you can apply physics intuition to! This is part of why string theorists have been so successful in cracking math problems. It also underlies Alain Connes' attempt to prove the Riemann Hypothesis: 1) Alain Connes, Noncommutative Geometry, Trace Formulas, and the Zeros of the Riemann Zeta Function. Ohio State course notes and videos at http://www.math.ohio-state.edu/lectures/connes/Connes.html Alain Connes, Trace Formula in Noncommutative Geometry and the Zeros of the Riemann Zeta function, available as math.NT/9811068. 2) Mathilde Marcolli, Noncommutative Geometry and Number Theory, available at http://www.math.fsu.edu/~marcolli/ncgntE.pdf Of course, Connes also has another inside track, namely his theory of noncommutative geometry. By the way: a number theorist I know says he thinks Connes has essentially proved the Riemann Hypothesis, in the same way that Riemann essentially proved the Prime Number Theorem. Namely, he has reduced it to some facts that seem obviously true! Of course, it took about 40 years, from 1859 to 1896, for Riemann's plan to be fulfilled by Hadamard and De La Vallee Poussin. So, even if Connes' insights are correct, it may be a while before the Riemann Hypothesis is actually proved. For anyone with a background in geometry, a good inside track on almost any math problem is to convert it into a geometry problem. In the case of number theory this trick is old news, but still very much worth knowing. It's based on an analogy which I began discussing in week198. The analogy starts out like this: NUMBER THEORY COMPLEX GEOMETRY Integers, Z Polynomial functions on the complex plane, C[z] Rational numbers, Q Rational functions on the complex plane, C(z) Prime numbers, P Points in the complex plane, C Why is this analogy good? Well, for starters: Every rational number is a ratio of integers. Every rational function is a ratio of polynomials. Better yet: Every integer can be uniquely factored into primes (modulo invertible integers, namely +1 and -1). Every complex polynomial can be uniquely factored into linear polynomials (modulo invertible polynomials, namely nonzero constants). There's one linear polynomial z-a for each point a in the complex plane, so PRIMES are like POINTS in the complex plane. We can make this precise using the concept of spectrum, which I defined in week199. Ignoring a certain little sublety which is discussed there: The spectrum of Z is the set of prime numbers. The spectrum of C[z] is the complex plane. This way of thinking lets us treat the spectrum of any algebraic extension of the integers, like the Gaussian integers, as a covering space of the set of prime numbers. I've already drawn this picture: 2+i 3+2i --- 1+i --- 3 --- --- 7 --- 11 --- --- GAUSSIAN INTEGERS 2-i 3-2i -----2------3------5------7-----11------13----- INTEGERS But, now I'm saying that the line down below really acts like the complex *plane*. Taking this strange idea seriously leads to all sorts of amazing insights. For example, if you poke a hole in this plane at some prime, there's something like a little *loop* that goes around this hole! In other words, there's a sense in which the spectrum of Z has a nontrivial fundamental group, which contains an element for each prime. Technically this group is called the Galois group Gal(Qbar/Q), and we get an element in it for each prime, called the Frobenius automorphism for that prime. Another cool thing is that we can study integers locally, one prime at a time, just like we study complex functions locally. We can analyze functions at a point using Taylor series and Laurent series. And, we can stretch our analogy to include these concepts: NUMBER THEORY COMPLEX GEOMETRY Integers, Z Polynomial functions on the complex plane, C[z] Rational numbers, Q Rational functions on the complex plane, C(z) Prime numbers, P Points a in the complex plane, C Integers mod p^n, Z/p^n (n-1)st-order Taylor series, C[z]/(z-a)^n p-adic integers, Z_p Taylor series, C[[z-a]] p-adic numbers, Q_p Laurent series, C((z-a)) All the weird symbols are just the standard notations for these gadgets. The analogy goes as follows: To study a polynomial at a point a in the complex plane, we can look at its value modulo (z-a), or more generally mod (z-a)^n. To study an integer at a prime p, we can look at its value modulo p, or more generally mod p^n. This is nice because the value of a polynomial modulo (z-a)^n is just its Taylor series at the point a, where we keep terms up to order n-1. We can also also take the limit as n -> infinity. If we do this to the integers mod p^n we get a ring called the p-adic integers. For example, a typical 3-adic integer, written in base 3, looks like this: ......21001102020110102012102201 They're just like natural numbers in base 3, except they go on forever to the left! We add and multiply them in the obvious way, for example: ......21001102020110102012102201 + ......10201101012201201122010012 ----------------------------------- ......01202210110012010211112220 If we take the same sort of limit for Taylor series, we get Taylor series that go on forever - in other words, formal power series. We can also ratios of p-adic integers, which are called p-adic numbers, and ratios of Taylor series, which are called Laurent series. A typical 3-adic number, written in base 3, looks like this: .......121010010012121201201201011.2102122020101022102011022........ Laurent series can be used to describe functions that have a pole at some point, like rational functions. Similarly, p-adic numbers can be used to describe rational numbers. Using more math jargon: For any point a in C, there's a homomorphism from the field of rational functions to the field of Laurent series, which sends polynomials to Taylor series. For any prime p, there's a homomorphism from the field of rational numbers to the field of p-adic numbers, which sends integers to p-adic integers. This lets us study rational numbers locally at the prime p using p-adic numbers, just as we can study a rational function locally at a point using its Laurent series. This technique can be quite useful. For example, a polynomial equation can have rational solutions only if it has p-adic solution for all primes p. We might hope for the converse, but then we would be ignoring a funny extra prime besides the usual ones... something called the real prime! The point is, besides being able to embed the rational numbers in the p-adics for any prime p, we can also embed them in the real numbers! This embedding is a bit different than the rest: it's based on a weird thing called an Archimedean valuation, while the usual primes correspond to non-Archimedean valuations. I'm sort of joking here, since if you're more used to real numbers than p-adics, you'll probably find Archimedean valuations to be *less* weird than non-Archimedean ones. The Archimedean valuation on the rational numbers is just the usual absolute value, while the non-Archimedean ones are other concepts of absolute value, one for each prime p. If we take limits of rational numbers that converge using the usual distance function |x-y|, we get real numbers; if we take limits that converge using one of the non-Archimedean versions of this distance function, we get p-adic numbers. But from the viewpoint of number theory, it's the Archimedean valuation that's the odd man out! It indeed does act very weird and different than 3) M. J. Shai Haran, The Mysteries of the Real Prime, Oxford U. Press, Oxford, 2001. .. which you will see is deeply connected to mathematical physics. If we take this weird real prime into account, things work better. We sometimes get results saying that some kind of polynomial equations have a rational solution if they have p-adic solutions for all primes p and also a real solution. For example, Hasse proved this was true for systems of quadratic equations in many variables. Results like this are called local-to-global results, since they're analogous to constructing a function from local information, like its Laurent series at all different points. In 1950, in his famous PhD thesis, John Tate came up with a clever way to formalize this Laurent series at all different points idea in the context of number theory. To do this, he formed a ring called the adeles. Indeed, this is what my whole discussion so far has been leading up to! Adeles are a really nice formalism, and you pretty much need to understand them to follow what people are doing in work on the Langlands Conjectures, or even simpler things, like class field theory. But, adeles seem like an arbitrary construction until you see them as an inevitable outgrowth of our desire to study integers locally at all different primes, including the real prime. The definition is simple. An adele consists of a p-adic number for each prime p, together with a real number... but where all but finitely many of the p-adic numbers are p-adic integers! This is the number-theoretic analogue of a Laurent series for each point in the complex plane, including the point at infinity... but with poles at only finitely many points! We could call such a thing an adele for the rational functions. Any rational function gives such a thing, just as any rational number gives an adele. And, we don't lose any information this way: There's a one-to-one (but not onto) homomorphism from the rational functions to the adeles for the rational functions. There's a one-to-one (but not onto) homomorphism from the rational numbers to the adeles for the rational numbers. So, our table now looks like this. For good measure, I'll combine it with the related table in week205: NUMBER THEORY COMPLEX GEOMETRY Integers Polynomial functions on the complex plane Rational numbers Rational functions on the complex plane Prime numbers Points in the complex plane Integers mod p^n (n-1)st-order Taylor series p-adic integers Taylor series p-adic numbers Laurent series Adeles for the rationals Adeles for the rational functions Fields One-point spaces Homomorphisms to fields Maps from one-point spaces Algebraic number fields Branched covering spaces of the complex plane There's a *lot* more to say about this analogy, but I think this is enough for now. Again, one of my secret goals was to start getting you comfy with adeles and the idea of studying number theory locally. For more on the geometrical side of number theory, I again recommend these: 4) Juergen Neukirch, Algebraic Number Theory, trans. Norbert Schappacher, Springer, Berlin, 1986. 5) Dino Lorenzini, An Invitation to Arithmetic Geometry, American Mathematical Society, Providence, Rhode Island, 1996. But now, back to the subject of inside tracks - sneaky ways to get the beneficial feeling that you have secret insights into some problem. For anyone with a background in categories, a good inside track on almost any math problem is to categorify it: to see that people are using sets where they could, and therefore *should*, be using categories or n-categories. I've already hinted that zeta functions are an example of decategorification. Now I'd like to make this more precise. Let's think about the zeta function of a set X equipped with a one-to-one and onto function f: X -> X If you're a physicist, you might call this a discrete dynamical system, with f describing one step of time evolution. If you're a mathematician, you might call this a Z-set. After all, for any group G, a G-set is a set equipped with an action of G. If G = Z (the additive group of integers), this amounts to a one-to-one and onto function from some set to itself. No matter what you call them, these are fundamental things. So, let's look at the *category* of Z-sets! Here the objects are Z-sets and the morphisms are functions that commute with time evolution. As explained near the end of week216, we can define a kind of zeta function for a Z-set as follows: Z(x) = exp(sum_{n>0} |fix(f^x)| x^n / n) where |fix(f^n)| is the number of fixed points of f^n. Of course, this only makes sense if all these numbers are finite; henceforth I'll assume my Z-sets are finite in this special sense. It turns out that you know a finite Z-set up to isomorphism if you know its zeta function. So, a zeta function is just a sneaky way of talking about an ISOMORPHISM CLASS of finite Z-sets. This is a fancy example of something we all learn as kids: counting! When we count a finite set, assigning a natural number to it, we are really determining its isomorphism class. Two finite sets are isomorphic if and only if they have the same number of elements. Operations on finite sets, like disjoint union and Cartesian product, are what give rise to operations on natural numbers, like addition and multiplication. Summarizing this, we have the following motto, suitable for making into a bumper sticker: THE SET OF NATURAL NUMBERS IS THE DECATEGORIFICATION OF THE CATEGORY OF FINITE SETS Similarly, this is what we're seeing now: THE SET OF ZETA FUNCTIONS IS THE DECATEGORIFICATION OF THE CATEGORY OF FINITE Z-SETS Beware: here I'm only talking about zeta functions of the above form. There are lots of other things people call zeta functions. So, don't read too much into this statement. But don't read too little into it, either! With an extra twist we can get most of the zeta functions showing up in number theory. In number theory, we typically get a Z-set for each prime p, coming from the Frobenius for that prime. We thus get a bunch of local zeta functions Z_p(x), one for each prime. We then multiply these to get one big fat global zeta function: zeta(s) = product_p Z(p^{-s)) Each local zeta function is a formal power series, while this global zeta function is a Dirichlet series. As I mentioned in week217, formal power series live in the monoid algebra of (N,+,0), while Dirichlet series live in the monoid algebra of (N,x,1). (N,+,0) is the free commutative monoid on one generator, while (N,x,1) is the free commutative monoid on countably many generators - the primes! Everything fits together sweetly. So, it's a good first step to think about the zeta function of a single Z-set. Now, there's another motto along the lines of the above two, which I've talked about before: THE SET OF GENERATING FUNCTIONS IS A DECATEGORIFICATION OF THE CATEGORY OF STRUCTURE TYPES I explained this in week185, week190, and week202. I've even taught a whole course on structure types (also known as species) and the combinatorics of Feynman diagrams. The course notes by Derek Wise are available online: 6) John Baez and Derek Wise, Quantization and Categorification, available at: So, I think this third example of decategorification is great. But, I'm not going to explain it in much detail here - just enough to say how it's related to zeta functions! A stucture type F is a gadget that gives a set F_n for each n = 0,1,2,.... We think of the elements of F_n as structures of type F on an n-element set - for example, orderings, or cyclic orderings, or n-colorings, or whatever type of structure you like. We only require that permutations of the n-element set act on this set of structures. But for what we're doing now, let's also assume this set F_n is finite. Any structure type has a generating function, which is a formal power series |F| given by |F_n| |F|(x) = sum ------- x^n n! Isomorphic structure types have the same generating function. However, structure types with the same generating function can fail to be isomorphic. This is why I said generating functions are a decategorification of structure types, instead of the decategorification. Despite this defect, generating functions are still very useful in combinatorics. So, when we see a zeta function like Z(x) = exp(sum_{n>0} |fix(f^n)| x^n / n) as a trick for decategorifying Z-sets, we should instantly wonder if it's a generating function in disguise. And of course, it is! Actually it's easiest to leave out the exponential at first. This power series: sum_{n>0} |fix(f^n)| x^n / n is the generating function for the structure type being cyclically ordered and equipped with a morphism to the Z-set X. Huh? We cyclically order a finite set by drawing it as a little circle of dots with arrows pointing clockwise from each dot to the next. A cyclically ordered set is automatically a Z-set in an obvious way. So, here's a type of structure you can put on a finite set: cyclically ordering it and equipping the resulting Z-set with a morphism to the Z-set X. And, if you work out the generating function of this structure type, you get sum_{n>0} |fix(f^n)| x^n / n Check it and see! What about the exponential? Luckily, there's a standard way to take the exponential of a structure type: to put an exp(F)-structure on a finite set S, we chop S into disjoint parts and put an F-structure on each part. So, the zeta function Z(x) = exp(sum_{n>0} |fix(f^n)| x^n / n) is the generating function for being chopped up into cyclically ordered parts, each equipped with a morphism to the Z-set X. But this is just a long way of saying: being made into a Z-set and equipped with a morphism to the Z-set X. Or, in category theory jargon, being a Z-set over X. So: THE ZETA FUNCTION OF THE Z-SET X IS THE GENERATING FUNCTION OF BEING A Z-SET OVER X By the way, this is the kind of thing you could do with *any* structure type F. Given an F-structured set X, we get a new structure type being an F-structured set equipped with a morphism to X. Or, in category theory jargon, being an F-structured set over X. The generating function of this could be called the zeta function of our F-structured set X. I have no idea how important this is... .. but I want to keep gnawing away on the connection between zeta functions and the generating functions of combinatorics, because to understand number theory, I need all the inside tracks I can get! Quote of the week, brought to me by David Corfield: The scientific life of mathematicians can be pictured as a trip inside the geography of the mathematical reality which they unveil gradually in their own private mental frame. It often begins by an act of rebellion with respect to the existing dogmatic description of that reality that one will find in existing books. The young to be mathematician realize in their own mind that their perception of the mathematical world captures some features which do not fit with the existing dogma. This first act is often due in most cases to ignorance but it allows one to free oneself from the reverence to authority by relying on one's intuition provided it is backed by actual proofs. Once mathematicians get to really know, in an original and personal manner, a small part of the mathematical world, as esoteric as it can look at first, their trip can really start. It is of course vital not to break the fil d'arianne which allows one to constantly keep a fresh eye on whatever one will encounter along the way, and also to go back to the source if one feels lost at times... It is also vital to always keep moving. The risk otherwise is to confine oneself in a relatively small area of extreme technical specialization, thus shrinking one's perception of the mathematical world and its bewildering diversity. The really fundamental point in that respect is that while so many mathematicians have been spending their entire life exploring that world they all agree on its contours and on its connexity: whatever the origin of one's itinerary, one day or another if one walks long enough, one is bound to reach a well known town i.e. for instance to meet elliptic functions, modular forms, zeta functions. All roads lead to Rome and the mathematical world is connected. In other words there is just one mathematical world, whose exploration is the task of all mathematicians, and they are all in the same boat somehow. - Alain Connes ----------------------------------------------------------------------- mathematics and physics, as well as some of my research papers, can be obtained at http://math.ucr.edu/home/baez/ For a table of contents of all the issues of This Week's Finds, try http://math.ucr.edu/home/baez/twf.html A simple jumping-off point to the old issues is available at http://math.ucr.edu/home/baez/twfshort.html If you just want the latest issue, go to http://math.ucr.edu/home/baez/this.week.html === Subject: Symmetry-adapted functions (I take a 4 variable example) Symmetrizing is easy, a+b+c+d, ab+ac+ad+bc+bd+cd,... Antisymmetrizing already needs degree six (does it??), (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) These are functions corresponding to the irreps A1 and A2 of the permutation group S4. But how on earth does a pair of E symmetric functions look, not to mention T1 and T2? like f(x,y,z)+f(y,z,x)+f(z,x,y)=0 was the E representation of S3, but how does this generalize?) -- Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de His-Ala-Sec-Lys-Glu Arg-Glu-Asp-Asp-Met-Ala-Asn-Asn === Subject: dense set Take the interval [0,1].Then exclude all points of the form a/2^m (with a and m positive integers and a<2^m) and the intervals around them [(a/2^m) - k/4^m ,(a/2^m)+k/4^m] for some real k with 0<=k<=2 For 0 Take the interval [0,1].Then exclude all points of the form > a/2^m (with a and m positive integers and a<2^m) and the intervals > around them [(a/2^m) - k/4^m ,(a/2^m)+k/4^m] for some real k with > 0<=k<=2 For 0 Has anybody a proof of that? The closure of the set can't contain any point of the form a/2^m (since neighbourhoods of these points have been excluded) so can't contain any interval. Hence the set is nowhere dense. It's pretty easy to obtain an upper bound on the measure of the set removed and thereby prove that what's left has positive measure. === Subject: Re: Help in answering news story on refutation of fermat's last theorem Nntp-Posting-Host: hera.cwi.nl > How about he was more than one person - Nicholas Bourbaki? > it's bogus. General Bourbaki can only be one person > *at a time*. But General Bourbaki was Charles Bourbaki. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Help in answering news story on refutation of fermat's last theorem *at a time*. But General Bourbaki was Charles Bourbaki. That doesn't sound very general to me. === Subject: Re: Help in answering news story on refutation of fermat's last theorem <4u6dnYlczLK_1R_fRVn-uA@comcast.com> <3aadnaWDAaygVR_fRVn-uQ@comcast.com> <429cb26e$24$fuzhry+tra$mr2ice@news.patriot.net> <429f3d43$9$fuzhry+tra$mr2ice@news.patriot.net> 06/03/2005 at 12:13 PM, anzaurres1@hotmail.com said: >He did? For some reason I seem to recall the name Riemann and not >Bolyai when hearing the term Elliptic Geometry. Is my >recollection wrong? Incomplete rather than wrong. Similarly, Hyperbolic Geometry was also invented by Gauss. >Wasn't Bolyai's purpose to show that it's possible for there to be >MORE than one parallel line (through the given point, of course)? No; he was trying to prove by contradiction that the Fifth Postulate All Defect. >I am not an expert on geometry, but wouldn't the name elliptic >indicate that there would be NO parallel lines whatsoever? Yes. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Help in answering news story on refutation of fermat's last theorem >>Wasn't Bolyai's purpose to show that it's possible for there to be >>MORE than one parallel line (through the given point, of course)? No; he was trying to prove by contradiction that the Fifth Postulate > All Defect. I think you're at least in part confusing Bolyai with Saccheri. Saccheri's work Euclid Freed from every Flaw was published in 1733; Janos Bolyai published his Appendix exhibiting the absolute science of space: independent of the truth or falsity of Euclid's Axiom XI (by no means previously decided) in 1832 as an appendix to a school geometry text by W. Bolyai. I seem to recall that the by no means previously decided was in reference to Saccheri's work. === Subject: Re: Help in answering news story on refutation of fermat's last theorem <3aadnaWDAaygVR_fRVn-uQ@comcast.com> <429cb26e$24$fuzhry+tra$mr2ice@news.patriot.net> <429f3d43$9$fuzhry+tra$mr2ice@news.patriot.net> <42a3716f$1$fuzhry+tra$mr2ice@news.patriot.net> <3gkhlkFcu9qhU1@individual.net> the half-plane with hemispheres as geodesics can be used as a model, I think; half-planar slices are 2-dimensional. I suppose this holds with the disk model, as well. thus: it's bogus. General Bourbaki can only be one person *at a time*. but he may be busy writing stuff. > How about he was more than one person - Nicholas Bourbaki? --ils ducs d'Enron! http://members.tripod.com/~american_almanac === Subject: Re: Help in answering news story on refutation of fermat's last theorem <3aadnaWDAaygVR_fRVn-uQ@comcast.com> <429cb26e$24$fuzhry+tra$mr2ice@news.patriot.net> <429f3d43$9$fuzhry+tra$mr2ice@news.patriot.net> <42a3716f$1$fuzhry+tra$mr2ice@news.patriot.net> <3gkhlkFcu9qhU1@individual.net How about he was more than one person - Nicholas Bourbaki? > Is there any particluar reason why you now quote me in each and every post of yours, making my search for replies to my posts almost impossible? What's so surprising about 'Nicholas Bourbaki' being more than one person? Moreover, the quote you attribute to me, isn't mine. === Subject: Re: Help in answering news story on refutation of fermat's last theorem <429cb26e$24$fuzhry+tra$mr2ice@news.patriot.net> <429f3d43$9$fuzhry+tra$mr2ice@news.patriot.net> <42a3716f$1$fuzhry+tra$mr2ice@news.patriot.net> <3gkhlkFcu9qhU1@individual.net> oh yeah; it was begun at Nanci Universite, or some thing. thus: I'm not suggesting that Republicans Are Them were not organized using P2P freeware from MIT. remember, they supposedly got the idea from H.Dean the 3rd, although I read that they prototyped it in the 2002 elections. he overcame his 3rd-generation Episcopalianess, lawyering and ... what was that other club? oh, yes; investmentbankering ... software development ... ATMs, using asynchronous transfer mechanism, which is, like, level two of the net. thus: that's why it's a wordproblemma, and not a 2x4xX. here's a neat problem: cut six approximately tetragonal slabs from a 2x4, so that yhey'll be nominally 2x4x4, and find the most compact hexahedron that can be made from them. thus quoth:: > I'm just grizzling that it isn't a very good puzzle, relying > as heavily as it does on 'youngest' implying 'more than two', > which is not a distinction much observed these days, > and also on not allowing one twin to be older than the other. > Agreed. And even in this small collection, it isn't alone in that. Refering > to Bourbaki as 'a mathematician' , and making the solution to the > puzzle be that he's actually several mathematicians is not very > satisfying either. --ils ducs d'Ebron! http://tarpley.net/bush12.htm === Subject: Re: Help in answering news story on refutation of fermat's last theorem <429cb26e$24$fuzhry+tra$mr2ice@news.patriot.net> <429f3d43$9$fuzhry+tra$mr2ice@news.patriot.net> <42a3716f$1$fuzhry+tra$mr2ice@news.patriot.net> <3gkhlkFcu9qhU1@individual.net> oops; 3rd generation Republican; invesment banking was his own thing. > oh, yes; investmentbankering ... software development ... > ATMs, using asynchronous transfer mechanism, > which is, like, level two of the net. thus: > that's why it's a wordproblemma, and > not a 2x4xX. here's a neat problem: > cut six approximately tetragonal slabs from a 2x4, so that > yhey'll be nominally 2x4x4, and find the most compact hexahedron > that can be made from them. --ils ducs d'Ebron! http://tarpley.net/bush12.htm === Subject: Re: Help in answering news story on refutation of fermat's last theorem <429cb26e$24$fuzhry+tra$mr2ice@news.patriot.net> <429f3d43$9$fuzhry+tra$mr2ice@news.patriot.net> <42a3716f$1$fuzhry+tra$mr2ice@news.patriot.net> <3gkhlkFcu9qhU1@individual.net How about he was more than one person - Nicholas Bourbaki? > Is there any particluar reason why you now quote me in each and every > post of yours, making my search for replies to my posts almost > impossible? What's so surprising about 'Nicholas Bourbaki' being more than one > person? Moreover, the quote you attribute to me, isn't mine. > Of course it isn't. I know the right French spelling: Nicolas Bourbaki. Just noticed... === Subject: Mass With the following revelation, I find myself back at squarw one; time to reconoiter: Jim Spriggs Jun 5, 12:12 pm show options messages by this author Local: Sun,Jun 5 2005 12:12 pm === Subject: Re: The magic that turns mass into weight Reply |Reply to Author| Forward| Print| Individual Message| Show original| Report Abuse > The imaginary difference between mass and weight depends on the > acceleration due to gravity Weight = acceleration due to gravity times mass It's really that simple. It's not magic, it's certainly not imaginary. It's a particular case of something Newton knew well and that is taught to school children: Force = acceleration times mass. --------------------------------------------------- Well that ain't right: So here's an oportunity for you sci.math guys to start earning your salaries: Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the mustard. Maybe it needs to be combined into one marvelous, magnificient whole: Like (m)=wa/fg? way. Then we'll just have a number. This is something I've got to think some more about... Don === Subject: Re: Mass Don has found a new way to chase his own tail, but is wronger than ever: > With the following revelation, I find myself back at squarw one; time > to reconoiter: Don, you've never left square one, to begin with. Now try again, but this time think, Think, THINK! > Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the > mustard. Once more: Stating 1=1 is hardly worth a nobel prize. > Maybe it needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg? Whoa! Don's famous mathematic (or should I say mathemagic?) at work again. So by multiplying m=w/g by a/F you get (m)=wa/Fg? Let's see if I can do this, too: m = w/g = F/a | multiply ALL parts by a/F m * a/F = w/g * a/F = 1 | m=F/a, therefore a/F=1/m m * a/F = w/g * 1/m = 1 | m=w/g m * a/F = 1 = 1 | decrease redundancy m * a/F = 1 So, I get m * a/F=1 or a=F/m or m=F/a or F=m*a, which most of us prefer. Nevertheless, all formulas are equivalent. Yes, you're really back to square one, I guess. > way. Then we'll just have a number. > This is something I've got to think some more about... Well, maybe you should start thinking about mathematics before you delve into such a complicated issue as seventh-grade physics. Your turn, A. Friend === Subject: Re: Mass Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the mustard. It just needs to be combined into one marvelous, magnificient whole: Like (m)=wa/fg, which has the same units as water. but an unknown quantity; to which other quantities with those units can be compared. we'll just have a number; not too unlike specific gravity: Where the the same units but a different quantity. Just thinking out loud Now to see what sort of definituin can be made: === Subject: Re: Mass > Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the > mustard. It just needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg, which has the same units as water. but an > unknown quantity; to which other quantities with those units can be > compared. > we'll just have a number; not too unlike specific gravity: Where the > the same units but a different quantity. Just thinking out loud Now to see what sort of definituin can be made: Didn't you ask this exact question and get a load of replies? === Subject: Re: Mass mustard. It just needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg, which has the same units as water. but an > unknown quantity; to which other quantities with those units can be > compared. > we'll just have a number; not too unlike specific gravity: Where the > the same units but a different quantity. Just thinking out loud Now to see what sort of definituin can be made: Didn't you ask this exact question and get a load of replies? All worthless. None address, or even recognize the problem. Don === Subject: Re: Mass Ok, I must admit I don't see a problem to address. As mentioned, there is no point having a unitless number for mass. What is it, you have a problem with? === Subject: Re: Mass > Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the > mustard. It just needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg, which has the same units as water. but an > unknown quantity; to which other quantities with those units can be > compared. > we'll just have a number; not too unlike specific gravity: Where the > the same units but a different quantity. Just thinking out loud Now to see what sort of definituin can be made: > Try 0 = 0 sr === Subject: Re: Mass Don's proving again that he doesn't understand neither physics nor math: > Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the > mustard. I answered that already. Do you actually read answers to your posts or is usenet just write-only to you? > It just needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg, which is complete and utter bull, as proven in my last post. Dan, you couldn't find a mathematical error in your calculations even if it stuck out his ugly head right in front of you and shoved a pencil up your nostril. No, they won't. At least not for someone with at least minimal mathematical knowledge. Obviously that's something you're completely lacking. Your turn, A. Friend === Subject: Re: Mass > Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the > mustard. No Sherlock... > It just needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg, which has the same units as water. Water has units? So water is a dimension now? Be out of our way? Wish that could work with you somehow. > Just thinking out loud Go ahead and think... just shut your pie hole while you do it. === Subject: Re: Mass > to school children: >Force = acceleration times mass. momentum. Bob Kolker === Subject: Re: Mass Weight = acceleration due to gravity times mass It's really that simple. It's not magic, it's certainly not > imaginary. It's a particular case of something Newton knew well and that is taught > to school children: Force = acceleration times mass. > === Subject: Re: Mass > With the following revelation, I find myself back at squarw one; time > to reconoiter: While you're 'reconoiter'ing you might reconsider your continued, off-topic, posting to sci.math. The argument that the physics contains math doesn't fly -- so does retail sales or music. Your posts are not about math. -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com === Subject: Re: Mass > Apparently my infamous equation [(m)=w/g=f/a] just isn't cutting the > mustard. Maybe it needs to be combined into one marvelous, magnificient > whole: Like (m)=wa/fg? > way. Then we'll just have a number. This is something I've got to think some more about... Don Inertial mass is the quantity m in F = m a; Gravitational mass is the quantity m in F = m g. If there is, in fact, a discrepancy between the two, then wa/Fg would give the magnitude of the discrepancy, which wouldn't necessarily be related to the mass itself. No matter what the object, wa/Fg would equal 1 out to several decimal places, if not strictly equal 1. === Subject: Re: Mass Since weight IS a force, and gravity IS an acceleration, If you are using a single object, then a=g, and w=f, so you would be finding that m=1 for all masses. This is not very useful. Mass has a unit- you may choose to use grams, ounces, slugs, or bindlewortles, but you cannot make a dimensionless mass. If you have a standard unit of mass, then you can divide through by that- but then you have simply created a new unit, and the mass will still have a dimension. It is like angle measurement in radians- you may not WRITE a unit, but it is there. === Subject: Re: Mass > This is something I've got to think some more about... It would seem adventurous of you, at your advanced age, to be trying something so novel, sHead. Tom Davidson Richmond, VA === Subject: Re: Mass Inertia http://scienceworld.wolfram.com/physics/Inertia.html The resistance to change in state of motion which all matter exhibits. It's a concept, Shead, not a number with units, not a ratio. Newton's First Law http://scienceworld.wolfram.com/physics/NewtonsFirstLaw.html Also called the law of inertia, Newton's first law states that a body at rest remains at rest and a body in motion continues to move at a constant velocity unless acted upon by an external force. Newton's Second Law is about inertial mass http://scienceworld.wolfram.com/physics/NewtonsSecondLaw.html A force F acting on a body gives it an acceleration a which is in the direction of the force and has magnitude inversely proportional to the mass m of the body: F = ma Inertia is an intrinsic property of mass. Most of what follows is quoted from http://www.physlink.com/ae305.cfm Gravitational Mass F = GmM/r^2 Inertial Mass F = ma Acceleration a = dv/dt 1) Inertial mass. This is mainly defined by Newton's law, the all-too-famous F = ma, which states that when a force F is applied to an object, it will accelerate proportionally, and that constant of proportion is the mass of that object. In very concrete terms, to determine the inertial mass, you apply a force of F Newtons to an object, measure the acceleration in m/s^2, and F/a will give you the inertial mass m in kilograms. 2) Gravitational mass. This is defined by the force of gravitation, which states that there is a gravitational force between any pair of objects, which is given by F = G m1 m2/r^2 where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. This, in effect defines the gravitational mass of an object. As it turns out, these two masses are equal to each other as far as we can measure. Also, the equivalence of these two masses is why all objects fall at the same rate on earth. The only difference that we can find between inertial and gravitational mass that we can find is the method. Gravitational mass is measured by comparing the force of gravity of an unknown mass to the force of gravity of a known mass. This is typically done with some sort of balance scale. The beauty of this method is that no matter where, or what planet, you are, the masses will always balance out because the gravitational acceleration on each object will be the same. This does break down near supermassive objects such as black holes and neutron stars due to the high gradient of the gravitational field around such objects. Inertial mass is found by applying a known force to an unknown mass, measuring the acceleration, and applying Newton's Second Law, m = F/a. This gives as accurate a value for mass as the accuracy of your measurements. When the astronauts need to be weighed in outer space, they actually find their inertial mass in a special chair. The interesting thing is that, physically, no difference has been found between gravitational and inertial mass. Many experiments have been performed to check the values and the experiments always agree to within the margin of error for the experiment. Einstein used the fact that gravitational and inertial mass were equal to begin his Theory of General Relativity in which he postulated that gravitational mass was the same as inertial mass and that the acceleration of gravity is a result of a valley or slope in the space-time continuum that masses fell down much as pennies spiral around a hole in the common donation toy at your favorite chain store. Useful references for Shead http://scienceworld.wolfram.com/physics/Inertia.html http://scienceworld.wolfram.com/physics/MomentofInertia.html http://scienceworld.wolfram.com/physics/Mass.html http://scienceworld.wolfram.com/physics/Momentum.html http://scienceworld.wolfram.com/physics/NewtonsLaws.html http://scienceworld.wolfram.com/physics/Weight.html === Subject: Re: Mass fruitcake. what is with your obsession on this. if you want to try and see if the formula works, try the bloody things. m=w/g this would give you a pretty weird number unless you use SI units. for example: m=w/g with an objects weighing 100 newtons and undergoing 10m s^-2 gravitational acceleration. m= 100 newtons / 10 m s^-2 m = 10 kg so to all intents and purposes, using SI units m=w/g can be solved. Note. this does not mean it is the correct formula to use. Now try it with non-SI units. m= 100lbs / 10 f s^-2 m= ouch - I give up. m=f/a must be valid as f=ma is, and its a simple re-arrangement. m=wa/fg is a bit odd. Again, lets try with values. w = 100 newtons, a = 20m s^-2, f = 100 newtons, g = 10 m s^-2 m=(100 newtons x 20m s^-2) / (100newtons x 10 m s^-2) m=2 is that the goal you were looking for? its pretty obvious the end result will have no units, as w and f will units. you cant say something has a mass of two. its madness. IMPORTANT BIT. why is F=ma not right? when you rearrange things, you need to make sure you are getting it all correct. === Subject: Re: Mass > fruitcake. what is with your obsession on this. if you want to try and see if the formula works, try the bloody things. m=w/g this would give you a pretty weird number unless you use SI units. for example: m=w/g with an objects weighing 100 newtons and undergoing 10m s^-2 > gravitational acceleration. m= 100 newtons / 10 m s^-2 > m = 10 kg so to all intents and purposes, using SI units m=w/g can be solved. Note. this does not mean it is the correct formula to use. Now try it with non-SI units. m= 100lbs / 10 f s^-2 > m= ouch - I give up. m=f/a must be valid as f=ma is, and its a simple re-arrangement. m=wa/fg is a bit odd. Again, lets try with values. w = 100 newtons, a = > 20m s^-2, f = 100 newtons, g = 10 m s^-2 m=(100 newtons x 20m s^-2) / (100newtons x 10 m s^-2) > m=2 is that the goal you were looking for? its pretty obvious the end result will have no units, as w and f will > units. you cant say something has a mass of two. >its madness. In Dons case it is massness sr IMPORTANT BIT. why is F=ma not right? when you rearrange things, you need to make sure you are getting it all > correct. === Subject: Conglomerates For references: http://katmat.math.uni-bremen.de/acc Pege 16 tells somenthing about codable and uncodable conglomerates. Could yo describe a mapping from a certain class to Uv{U} ? I think it is something similar to the function F(x): x in U if x=U y in U if x in U. === Subject: Re: Conglomerates > Could yo describe a mapping from a certain class to Uv{U} ? > for all x in domain f, f(x) in U or f(x) = U > U = nulset; f(x) = nulset for all x in domain f U = R; f(x) = x if x in R0, f(0) = R U = P(N) f(A) = A if A in P(N)N, f(N) = P(N) g(A) = A if A in P(N)nulset, g(nulset) = P(N) U = {0} f(x) = 0 for all x in R g(x) = {0} for all x in R h(x) = 0 for all x in R0, h(0) = {0} === Subject: Re: Conglomerates William Elliot ha scritto nel messaggio >> Could yo describe a mapping from a certain class to Uv{U} ? > for all x in domain f, f(x) in U or f(x) = U U = nulset; f(x) = nulset for all x in domain f > U = R; f(x) = x if x in R0, f(0) = R Here which is the counterpart of 0? I mean that you have found a surjective map from R to R0 v {R}, not R v {R}. U = P(N) > f(A) = A if A in P(N)N, f(N) = P(N) The same as above: this is a surjection between P(N) and P(N)N v {P(N)}, not between P(N) and P(N) v {P(N)}. However, I'm interested in the case in which is U = the class which members are all sets (universe). === Subject: Re: Conglomerates William Elliot ha scritto nel messaggio >> Could yo describe a mapping from a certain class to Uv{U} ? > for all x in domain f, f(x) in U or f(x) = U U = nulset; f(x) = nulset for all x in domain f > U = R; f(x) = x if x in R0, f(0) = R Here which is the counterpart of 0? I mean that you have found a surjective map from R to R0 v {R}, not R v {R}. U = P(N) > f(A) = A if A in P(N)N, f(N) = P(N) The same as above: this is a surjection between P(N) and P(N)N v {P(N)}, not between P(N) and P(N) v {P(N)}. However, I'm interested in the case in which is U = the class which members are all sets (universe). === Subject: Re: Conglomerates William Elliot ha scritto nel messaggio >> Could yo describe a mapping from a certain class to Uv{U} ? > for all x in domain f, f(x) in U or f(x) = U U = nulset; f(x) = nulset for all x in domain f > U = R; f(x) = x if x in R0, f(0) = R Here which is the counterpart of 0? I mean that you have found a surjective map from R to R0 v {R}, not R v {R}. U = P(N) > f(A) = A if A in P(N)N, f(N) = P(N) The same as above: this is a surjection between P(N) and P(N)N v {P(N)}, not between P(N) and P(N) v {P(N)}. However, I'm interested in the case in which is U = the class which members are all sets (universe). === Subject: Re: Conglomerates William Elliot ha scritto nel messaggio >> Could yo describe a mapping from a certain class to Uv{U} ? > for all x in domain f, f(x) in U or f(x) = U U = nulset; f(x) = nulset for all x in domain f > U = R; f(x) = x if x in R0, f(0) = R Here which is the counterpart of 0? I mean that you have found a surjective map from R to R0 v {R}, not R v {R}. U = P(N) > f(A) = A if A in P(N)N, f(N) = P(N) The same as above: this is a surjection between P(N) and P(N)N v {P(N)}, not between P(N) and P(N) v {P(N)}. However, I'm interested in the case in which is U = the class which members are all sets (universe). === Subject: Re: Conglomerates === Subject: Re: Conglomerates Kiss Your farted > William Elliot ha scritto nel messaggio >> Could yo describe a mapping from a certain class to Uv{U} ? > for all x in domain f, f(x) in U or f(x) = U U = nulset; f(x) = nulset for all x in domain f > U = R; f(x) = x if x in R0, f(0) = R > Here which is the counterpart of 0? I mean that you have found a > surjective map from R to R0 v {R}, not R v {R}. So what, you didn't ask for a surjection. > U = P(N) > f(A) = A if A in P(N)N, f(N) = P(N) > The same as above: this is a surjection between P(N) and P(N)N v > {P(N)}, not between P(N) and P(N) v {P(N)}. U = P(N)N f(A) = A if A in P(N)N, f(N) = P(N)N > However, I'm interested in the case in which is U > = the class which members are all sets (universe). Depending upon choice of set theory, U is an absurdity or {U} is an absurdity or the question mute as U / {U} = U. ---- === Subject: Re: Conglomerates William Elliot ha scritto nel messaggio > So what, you didn't ask for a surjection. > Depending upon choice of set theory, U is an absurdity or > {U} is an absurdity or the question mute as U / {U} = U. Here is the point. I think you have misunderstood what I was asking. I was talking about codable conglomerates. === Subject: Re: Conglomerates <6wApe.997032$b5.43203388@news3.tin.it William Elliot ha scritto nel messaggio So what, you didn't ask for a surjection. Depending upon choice of set theory, U is an absurdity or > {U} is an absurdity or the question mute as U / {U} = U. Here is the point. I think you have misunderstood what I was asking. I was > talking about codable conglomerates. > The point is, Big Ass, that your question isn't clearly stated. === Subject: Re: Conglomerates William Elliot ha scritto nel messaggio >> William Elliot ha scritto nel messaggio >> So what, you didn't ask for a surjection. >> Depending upon choice of set theory, U is an absurdity or >> {U} is an absurdity or the question mute as U / {U} = U. >> Here is the point. I think you have misunderstood what I was asking. I >> was >> talking about codable conglomerates. > The point is, Big Ass, that your question isn't clearly stated. 1)I started a thread which name was Conglomerates; 2)I gave a specific url; 3)I was talking abuot *codable* congloms. === Subject: Conglomerates <6wApe.997032$b5.43203388@news3.tin.it> <3_Upe.1002417$b5.43355569@news3.tin.it> big.fat.ass farted > William Elliot ha scritto nel messaggio >> William Elliot ha scritto nel messaggio >> So what, you didn't ask for a surjection. >> Depending upon choice of set theory, U is an absurdity or >> {U} is an absurdity or the question mute as U / {U} = U. >> Here is the point. I think you have misunderstood what I was asking. >> I was talking about codable conglomerates. > The point is, Big Ass, that your question isn't clearly stated. 1)I started a thread which name was Conglomerates; > 2)I gave a specific url; Oh sure, you expect us to read a lengthy track? > 3)I was talking about *codable* congloms. > You didn't succinctly explain what codable congloms are. Nor did you focus upon what the actual math problem is, expecting us to instead to study up on golums and clarify for you what the math question is and then answer it. > No, nor is your nom de plume. === Subject: null space, please help hello ! I am brain storming to find a solution to the following problem, please help ... find G_i and F_i matrices s.t. G_i*H_i*F_j = (0) with for all i,j in [1,3] and i neq j G, H and F are matrices and there two special cases : case 1 : G_i is 3x3, H_i : 3x5 and F_i : 5x3 for all i case 2 : G_i is 2x3, H_i : 3x5 and F_i : 5x4 for all i Jonathan jonagold at gmail dot com === Subject: Re: null space, please help > hello ! I am brain storming to find a solution to the following problem, > please help ... find G_i and F_i matrices s.t. G_i*H_i*F_j = (0) with for all i,j in [1,3] and i neq j > G, H and F are matrices and there two special cases : case 1 : G_i is 3x3, H_i : 3x5 and F_i : 5x3 for all i > case 2 : G_i is 2x3, H_i : 3x5 and F_i : 5x4 for all i > Jonathan jonagold at gmail dot com **************************************** Hi: What's Hi? What does i neq j mean? Does it mean i not equal to j? take: (1 0 0) (0 0 0)=G (0 0 0) (0 0 0 0 0) (0 1 0 0 0)=H (0 0 0 0 0) (0 0 1) (0 0 0) (0 0 0)=F (0 0 0) (0 0 0) Tonio === Subject: closed form? I know that sum {n choose i} x^(i) on {i = 0....n} = (1+x)^{n} But is there a similar simple closed form for sum {n choose i} x^{i^2} on {i = 0....n} (Here n and x are integers, if that makes the problem any easier) stu === Subject: Re: closed form? > I know that >sum {n choose i} x^(i) on {i = 0....n} = (1+x)^{n} >But is there a similar simple closed form for >sum {n choose i} x^{i^2} on {i = 0....n} >(Here n and x are integers, if that makes the problem any easier) I doubt it. Anyway, I've never seen one. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Comparing two numerical algorithms, other way than big-O? For iterative algorithms, which are prevalent in OR, many researchers use computational experiments on well-known, representative, or randomly generated problem sets to compare techniques. This approach can provide practical insight on algorithm performance when implemented and applied to specific problem instances, and is often used to demonstrate the effectiveness of heuristics on NP-hard models. For more info, see: (1) Coffin, Marie, and Saltzman, Matthew J., 2000, Statistical analysis of computational tests of algorithms and heuristics, INFORMS Journal on Computing, 12:1, pp 24-44 (2) Barr, R., B. Golden, J. Kelly, M. Rescende, and W. Stewart, Designing and Reporting on Computational Experiments with Heuristic Methods, Journal of Heuristics 1:1 (1995) 9-32 (Please excuse the self-reference.) Dick Barr If I have two numerical algorithms and I want to compare the time > complexity, what should I do? For example, to solve an eigenvalue > problem, there might be method A and method B. If both methods are > O(n^2), where n is the size of the matrix, and the constant depends on > the required precision, then should I give up and say they are equally > good? > === Subject: Re: Comparing two numerical algorithms, other way than big-O? If I have two numerical algorithms and I want to compare the time > complexity, what should I do? For example, to solve an eigenvalue > problem, there might be method A and method B. If both methods are > O(n^2), where n is the size of the matrix, and the constant depends on > the required precision, then should I give up and say they are equally > good? O is just an upper bound. An O(n^2) algorithm is also an O(n^4) > algorithm. The terminology is often abused, however, so that > an algorithm known to be Theta(f(n)) is referred to as O(f(n)). If you know two algorithms to be Theta(n^2), you can say nothing > about which is preferable on the basis of complexity considerations. > It all depends on the size and form of the input, and on the details > of the algorithm and its implementation. In a particular application, > a Theta(n^2) algorithm can be just as good as or better than a > Theta(n*log(n)) algorithm. Is there an example where Theta(n^2) is faster than Theta(n*log(n)) ? === Subject: Re: Comparing two numerical algorithms, other way than big-O? ... > Is there an example where Theta(n^2) is faster than > For any pair of methods, A and B, where A is Theta(n^2) and B is Theta(n*log(n)), there is a size N such that, for all n>N, A is slower than B. However, that problem size may be far bigger than anyone actually runs. You seem to be on the edge between two types of algorithm performance: 1. Asymptotic complexity analysis. 2. Practical algorithm comparison. Asymptotic analysis can tell you a lot about trends, and give warnings of algorithms that appear practical for small problem sizes but do not scale. On the other hand, if you want to know which method to use for some bounded size set of problems on real computers, you need to deal with issues that it abstracts away. For example, on modern computers and with practical problem sizes, you will often get a more realistic estimate of performance by counting transfers between layers of the memory hierarchy than by counting flops. Patricia === Subject: Re: Comparing two numerical algorithms, other way than big-O? If I have two numerical algorithms and I want to compare the time > complexity, what should I do? For example, to solve an eigenvalue > problem, there might be method A and method B. If both methods are > O(n^2), where n is the size of the matrix, and the constant depends on > the required precision, then should I give up and say they are equally > good? O is just an upper bound. An O(n^2) algorithm is also an O(n^4) > algorithm. The terminology is often abused, however, so that > an algorithm known to be Theta(f(n)) is referred to as O(f(n)). If you know two algorithms to be Theta(n^2), you can say nothing > about which is preferable on the basis of complexity considerations. > It all depends on the size and form of the input, and on the details > of the algorithm and its implementation. In a particular application, > a Theta(n^2) algorithm can be just as good as or better than a > Theta(n*log(n)) algorithm. >Is there an example where Theta(n^2) is faster than Theta(n*log(n)) ? Obviously. _For some inputs_. Alg1(n) let s=size of n repeat s times repeat s times twiddle thumbs output n Alg2(n) let s=size of n repeat s times repeat log(s) times repeat 1000000 times twiddle thumbs output n Phil -- If a religion is defined to be a system of ideas that contains unprovable statements, then Godel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one. -- John Barrow === Subject: LEGACY of ITS's Langjahr STOLEN! Pls STAND UP for Eric To Everyone Involved in Horse-Racing or Handicapping: Eric Langjahr, the pioneer of computerized handicapping, was my brother. Eric, a founder of International Thoroughbred Superhighway, Inc. (a/k/a ITS), was the sole developer of, among other things, all ITS software. Last week I discovered that my brother's company, ITS, was shut down. Even though my parents and I inherited NO LESS THAN a fifty (50%) percent interest in ITS, I found out about the closing FROM THE ITS WEBSITE. [It may be easier on your eyes to read this post at http://dirtythief.bravehost.com/ ] PIZZOLLA RAPES AND ROBS ITS Needless to say, Michael Pizzolla didn't shut down ITS in the proper, legal way. You see, Nevada law requires distribution of the corporate assets TO THE SHAREHOLDER(S), not SQUATTERS. PIZZOLLA STEALS ITS INTELLECTUAL PROPERTY WHILE DENYING VALUE So, instead, Michael Pizzolla, apparently, just walked away once his plot was ready for execution. Then, WITHOUT PERMISSION OR VALID LEGAL RIGHT, Pizzolla STOLE all of ITS'S intangible, intellectual property (including the intellectual property contributed to ITS SOLELY by Eric)... Property which, since Eric's death, both Pizzolla and his hired mouthpiece, Michael H. Singer, have represented to my family has NO VALUE. That's right, Pizzolla and Singer have represented that ITS has no value but for its few TANGIBLE assets, namely DESKS AND CHAIRS AND ... EQUIPMENT according to Pizzolla [upper case added to quote] . (I still have those FALSEHOODS, WRITTEN on their respective LETTERHEADS under their own respective SIGNATURES. Of course, I do not suggest that counsel lied; perhaps he was DUPED.) PIZZOLLA STEALS ITS CUSTOMERS WHILE DENYING PROFITABILITY Adding insult to the injury of the THEFTS of the intellectual property, Pizzolla also has the gall to use Eric's own company's website to DEFRAUD the customers of ITS products, that is, users of my brother's software, to DISLOYALLY DIVERT them away from the ITS website to the website of Pizzolla's own PERSONAL company... At which website Pizzolla's own directly COMPETING company conducts passwords... After Pizzolla and Singer represented that ITS has turned NO PROFIT since Eric's death - and WILL NOT for the foreseeable future. PIZZOLLA STEALS ERIC LANGJAHR'S LEGACY But there is one glaring difference at PIZZOLLA'S COMPETING website: it is AS THOUGH ERIC LANGJAHR NEVER EXISTED, let alone conceived and developed all of the ITS products and materials that Pizzolla STOLE to sell on his own website. After FALSELY holding himself out to the handicapping community as my DISGUSTINGLY, STOLEN all the CREDIT for MY BROTHER'S LIFE'S WORK, HIS LEGACY. AND FOR WHAT - PIZZOLLA WAS STEALING ALL ITS'S MONEY ANYWAY Since Eric's death, Pizzolla / ITS have NOT PAID ONE PENNY to Eric's estate or to my family anyway. In fact, there has been no contact between my family and Pizzolla for many, many months. (We've really tried to blot this sorry excuse for a human being out of our minds.) Bottom line: since Eric's death, Pizzolla has been having his cake and eating it too - PLUS ERIC'S! But even that wasn't enough for Pizzolla... MEMORY OF ERIC AND ALL ERIC DID What with Pizzolla's high-priced (the hired gun boasted of it IN WRITING), well-connected (according to colleagues), LOCAL attorney, it will take YEARS and tens, if not HUNDREDS OF THOUSANDS OF DOLLARS to get justice in the DISTANT Nevada courts. BUT YOU CAN HELP GET JUSTICE FOR ERIC RIGHT NOW!! PLEASE...please...please...if you knew and liked my brother - or respected him from afar - even one tiny little bit (or even if you didn't, but simply believe in fairness and justice) ... PLEASE DON'T HELP PIZZOLLA FEAST ON ERIC'S GRAVE .87 don't reward this THIEF by buying STOLEN PROPERTY from him .87 don't reward this THIEF by buying data delivered via STOLEN PROPERTY .87 tell EQUIBASE COMPANY (pohara@equibase.com; hzeitlin@equibase.com) to STOP PARTNERING with and endorsing the likes of THIEVES (there are plenty of good companies and products left in handicapping) (Equibase has already removed the stolen ITS logo hyperlinked on its partners page but that is not nearly enough) .87 tell VIAWEST INTERNET SERVICES (sales@viawest.net; netsupport@viawest.net) to TAKE DOWN the stolen intellectual property they are hosting on at least three Pizzolla websites PLEASE DON'T LET PIZZOLLA ERASE ERIC'S LEGACY Eric was a good person who never hurt a soul or took anything that wasn't his. Unlike some people, Eric never lacked for his own clever, original ideas. Eric was a programming genius, always generously mentoring others in the programming community. Eric's intellectual property was a great LEGACY. Eric DESERVES to be remembered for his LIFE'S WORK. Not oh-so-casually whited-out by a LIAR, THIEF AND CHEAT like Pizzolla. PLEASE FORWARD THIS MESSAGE TO HONEST HANDICAPPERS EVERYWHERE Do it FOR ERIC. Do it because it's the RIGHT THING TO DO. THANK YOU from the bottom of Eric's family's hearts. Janet Langjahr Janlan212@mail.com === Subject: Galois Theory Problem Let E be a finite degree normal extension of F and let K and L be fields between E and F. Suppose that E is separable over both K and L. Prove that E is separable over (K intersect L). === Subject: Re: Galois Theory Problem days. My association with the Department is that of an alumnus. >Let E be a finite degree normal extension of F and let K and L be >fields between E and F. Suppose that E is separable over both K and L. >Prove that E is separable over (K intersect L). No need to post it twice. Have some patience. What have you done so far, and what are you having trouble with? -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Galois Theory Problem fields between E and F. Suppose that E is separable over both K and L. >Prove that E is separable over (K intersect L). No need to post it twice. Have some patience. What have you done so far, and what are you having trouble with? Sorry about posting it twice. I'm just not sure whether or not it's right and even if correct how prove this without using the next chapter. Here is what I have: First 2 theorems: 1. Let F be a subfield of K and f belong to F[x]. Then f has distinct roots as a member of F[x] if and only if it has distinct roots as a member of K[x]. *2. Let F be a subfield of L and L be a subfield of E where E is separable over L and L is separable over F. THen E is separable over F. (* this is from the next chapter). Proof: By assumption for all f in E, f is separable over K. Also f is separable over L. By Theorem 1, for any f in (K intersect L)[x] f has distinct roots as a member of K[x] implies that f has distint roots as a member of (K intersect L)[x]. Also by Theorem 1, f has distinct roots as a member of L[x] implies that f has distinct roots as a member of (K intersect L)[x]. So K is separable over (K intersect L) and L is separable over (K intersect L). So now we have (K intersect L) is a subfield of K and K is a subfield of E as well as (K intersect L) is a subfield of L and L is a subfield of E where E is separalbe over K and E is separable over L. Also L is separable over (K intersect L) and K is separable over (K intersect L). Now by THeorem 2, E is separable over (K intersect L). James === Subject: Re: Galois Theory Problem days. My association with the Department is that of an alumnus. >>Let E be a finite degree normal extension of F and let K and L be >>fields between E and F. Suppose that E is separable over both K and L. >>Prove that E is separable over (K intersect L). >> No need to post it twice. Have some patience. >> What have you done so far, and what are you having trouble with? Sorry about posting it twice. I'm just not sure whether or not it's >right and even if correct how prove this without using the next >chapter. Here is what I have: First 2 theorems: 1. Let F be a subfield of K and f belong to F[x]. Then f has distinct >roots as a member of F[x] if and only if it has distinct roots as a >member of K[x]. I'm not sure what this means. Certainly f has distinct roots as a member of F[x] does ->not<- mean distinct roots in F, because we can take a purely inseparable polynomial with no roots in F and let K be its splitting field. So what does it mean? Does it mean distinct roots in some algebraic closure of F? >*2. Let F be a subfield of L and L be a subfield of E where E is >separable over L and L is separable over F. THen E is separable over >F. (* this is from the next chapter). Proof: By assumption for all f in E, f is separable over K. Also f is >separable over L. By Theorem 1, for any f in (K intersect L)[x] f has >distinct roots as a member of K[x] This makes no sense. f was an element of E, now you are talking about f as if it were a polynomial. Perhaps you should not use f to denote elements. >implies that f has distint roots as >a member of (K intersect L)[x]. This is nonsense. > Also by Theorem 1, f has distinct >roots as a member of L[x] implies that f has distinct roots as a >member of (K intersect L)[x]. This is also nonsense. In general, the minimal polynomial for your element over K will DIVIDE the minimal polynomial over (K intersect L), but only in K[x]. The minimal over K need not lie in M[x], where M=(K intersect L). You need to start over. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Galois Theory Problem days. My association with the Department is that of an alumnus. >>Let E be a finite degree normal extension of F and let K and L be >>fields between E and F. Suppose that E is separable over both K and L. >>Prove that E is separable over (K intersect L). >> No need to post it twice. Have some patience. >> What have you done so far, and what are you having trouble with? Sorry about posting it twice. I'm just not sure whether or not it's >right and even if correct how prove this without using the next >chapter. Here is what I have: First 2 theorems: 1. Let F be a subfield of K and f belong to F[x]. Then f has distinct >roots as a member of F[x] if and only if it has distinct roots as a >member of K[x]. What does this mean? What does distinct roots as a member of F[x] mean? Where are you taking the roots? Surely you do not mean roots in F, because you can take a purely inseparable irreducible polynomial over F, and let K be its splitting field, and the theorem would be false. Anyway. Presumably, judging from what you quote in 2, E/F is a separable extension if and only if for every x in E, x is separable over F, which in turn means that the irreducible polynomial of x over F is separable, which means it has no repeated roots. So, let E/F be an extension, K,L intermediate extensions, E/F is normal, E/K and E/L are separable, and you want to show that E/(K intersect L) is separable. So we let a in E, and f(x) be the irreducible of a over M=(K intersect L). Let g(x) be the irreducible of a over K. Then g(x)|f(x) in K[x], say f(x) = g(x)u(x), with u(x) in K[x]. Since g(x) is irreducible, we must either have gcd(g(x),u(x))=1, or else g(x)|u(x). -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: mathematician salaries ... stuff deleted ... > If you make tenure, it's a SINE CARE position for life. Did you mean sinecure? Just curious. Dale. === Subject: Re: mathematician salaries ... stuff deleted ... If you make tenure, it's a SINE CARE position for life. Did you mean sinecure? Just curious. ...or perhaps cynosure? Tom Davidson Richmond, VA === Subject: Re: mathematician salaries >> ... stuff deleted ... >> If you make tenure, it's a SINE CARE position for life. >> Did you mean sinecure? >> Just curious. ...or perhaps cynosure? Duh. He meant SINE CURVE, of course. Lee Rudolph === Subject: Re: mathematician salaries OK, go ahead and make fun of Mark. Mark has a full wallet, a full head of hair, and a full blown PhD from the best uni in the world. You are just jealous because you can not do as much with your degree as Mark has done with his. MD === Subject: Re: mathematician salaries >Mark is pleased he has accumulated such a faithful following. You What's Mark's latest? Will Mark disclose his dissertation title? Who >will fail? Who will succeed? Who will become the next Harvard PhD? >MD > daily just to read The Mark's next... -- Coincidences, in general, are great stumbling blocks in the way of that class of thinkers who have been educated to know nothing of the theory of probabilities. -- Edgar Allen Poe === Subject: Re: mathematician salaries > OK, go ahead and make fun of Mark. Mark has a full wallet, a full head > of hair, and a full blown PhD from the best uni in the world. You are > just jealous because you can not do as much with your degree as Mark > has done with his. Ah, so it's filled with hair? That explains a great deal. There's no wallet in the world fat enough to make any sensible person jealous of you. As for your PhD -- if it really exists -- it's probably just in Marketing or some other non-subject. And the best uni in the world? I'd prefer MIT or Princeton or Oxford or Cambridge over Harvard any time. -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock === Subject: Re: mathematician salaries As for your PhD -- if it really exists -- it's probably just in Marketing or some other non-subject. Wayne Brown, O why do you despise marketing scholars so? Isn't it a tad narrowminded to believe your own field is superior to another just because you know nothing about the other? What gives you the right to dismiss the marketing professors at Harvard and Wharton just because you took some math courses at Podunk State U and can trace your math geneaology back to some obscure 19th century German who proved a couple of obscure theorems about partial fractions? Ain't that high and mighty of you! Is this superior attitude the product of your keen intellect and mathematics education? === Subject: Re: mathematician salaries > >> OK, go ahead and make fun of Mark. Mark has a full wallet, a full >> head of hair, and a full blown PhD from the best uni in the world. >> You are just jealous because you can not do as much with your degree >> as Mark has done with his. Ah, so it's filled with hair? That explains a great deal. >There's no wallet in the world fat enough to make any sensible person > jealous of you. As for your PhD -- if it really exists -- it's > probably just in Marketing or some other non-subject. And the best > uni in the world? I'd prefer MIT or Princeton or Oxford or Cambridge > over Harvard any time. > Please...leave me some pride. I'm starting grad school there in the fall. Fortunately they situated themselves right next to MIT so I can go get an education if the inclination strikes me. And if all else fails I can take advantage of a subtlety of the English language and claim that I got a PhD in Cambridge. -- Ryan Reich ryanr@uchicago.edu === Subject: Re: mathematician salaries Welcome to the Harvard Club Ryan Reich! I strongly recommend the Gato Rojo. Mark has fond memories of dunking some donuts at the Rojo after his dry as dirt group theory class at the science center before walking along Mass Ave to his cross-reg classes in the MIT mathematics department, which is situated behind the infamous infinite corridor. If you keep your math grades up, perhaps you will get to meet Mark when he interviews job applicants on campus. And those of you who know your Cambridge geography will know that Clinton street lies half-way between H and MIT. Mark has fond memories of Clinton street and the little grocery store nearby because Mark resided there for 3 years while winning top scores in The PhD program. Unfortunately, that little grocery store has since been torn down. Progress... sigh! MD === Subject: Re: mathematician salaries Welcome to the Harvard Club Ryan Reich! I strongly recommend the Gato Rojo in the new science center at H. And do cross-reg at MIT. Mark has fond memories of dunking some donuts at the Rojo after his group theory class at the science center before walking along Mass Ave to his cross-reg classes in the MIT mathematics department, which is situated behind the infamous infinite corridor. If you keep your grades up, perhaps you will get to meet Mark when he interviews job applicants on campus. And those of you who know your Cambridge geography will know that Clinton street lies half-way between H and MIT. Mark has fond memories of Clinton street and the little grocery store nearby because Mark resided there for 3 years while winning top scores in The PhD program. Unfortunately, that little grocery store has since been torn down. Progress... sigh! MD === Subject: Re: mathematician salaries > Welcome to the Harvard Club Ryan Reich! Gosh, I get club membership too? > I strongly recommend the Gato Rojo in the new science center at H. And > do cross-reg at MIT. Mark has fond memories of dunking some donuts at > the Rojo after his group theory class at the science center before > walking along Mass Ave to his cross-reg classes in the MIT mathematics > department, which is situated behind the infamous infinite corridor. Who taught the group theory class back then? > If you keep your grades up, perhaps you will get to meet Mark when he > interviews job applicants on campus. If you come I'll be sure to hear about it from the English department. -- Ryan Reich ryanr@uchicago.edu === Subject: Re: mathematician salaries Who taught the group theory class back then? Mark took group theory from the one and only David Kazhdan. Here's some insider details: Professor Kazhdan coughed about once every 10 minutes back when Mark took his class, which was a real snoozer. The highlight of the course was the dark-haired undergrad, who always sat in the front row. (If you are reading this, darling, do send Marky a personal email! Mark loves brainy math chicks.) Professor Kazhdan speaks in a somewhat thick accent but had wonderfully succinct notes that penetrated the essence of rings and homeomorphism, and so on and so forth. Despite his A in the course (of course, of course), Mark found those notes COMPLETELY WORTHLESS in his subsequent journey through the wealthy halls of finance, and he can't really remember what a ring is nowadays. But who cares, really? English? That sounds like a very lucrative career --- if you combine it with marketing that is. Mark has a friend who, after her PhD in English, went on to write commercial tv jingles and makes a decent enough living to live in Mark's neighborhood. === Subject: Re: mathematician salaries > OK, go ahead and make fun of Mark. Mark has a full wallet, a full head > of hair, and a full blown PhD from the best uni in the world. I have my doubts about the Harvard Ph.D. The fat wallet claims could be true, but unremarkable. > You are > just jealous because you can not do as much with your degree as Mark > has done with his. Anyone can telephone the Harvard Office of Alumni Records at (617) 495-2371 and ask them to verify a degree of anyone who claims to be a grad. The school does this to help deal with the problem of imposter resumes. I think that they will not give any details other than yes or no to the grad question. Mark Demers claims a Ph.D. from there, and I doubt that based on his moronic posts (or did he perhaps have a stoke after graduating?). I have my doubts, but I have not bothered to make the call. If anyone else here is motivated to check that and report back here, please feel free! I figure that you will need to sound like you have his resume in front of you if you want to make it work, so some research into who Mark actually is might be required to get the info that you would need. Perhaps just his name and his claimed graduation year might do it. === Subject: Re: mathematician salaries >> OK, go ahead and make fun of Mark. Mark has a full wallet, a full head >> of hair, and a full blown PhD from the best uni in the world. I have my doubts about the Harvard Ph.D. The fat wallet claims could be >true, but unremarkable. > You are >> just jealous because you can not do as much with your degree as Mark >> has done with his. Anyone can telephone the Harvard Office of Alumni Records at (617) 495-2371 >and ask them to verify a degree of anyone who claims to be a grad. The >school does this to help deal with the problem of imposter resumes. I think >that they will not give any details other than yes or no to the grad >question. Mark Demers claims a Ph.D. from there, and I doubt that based on >his moronic posts (or did he perhaps have a stoke after graduating?). Dave wonders whether stoke was a typo for stroke or toke... >I have >my doubts, but I have not bothered to make the call. If anyone else here is >motivated to check that and report back here, please feel free! I figure >that you will need to sound like you have his resume in front of you if you >want to make it work, so some research into who Mark actually is might be >required to get the info that you would need. Perhaps just his name and his >claimed graduation year might do it. > ************************ David C. Ullrich === Subject: Re: mathematician salaries Discussion, linux) > Anyone can telephone the Harvard Office of Alumni Records at > (617) 495-2371 and ask them to verify a degree of anyone who claims > to be a grad. The school does this to help deal with the problem of > imposter resumes. I think that they will not give any details other > than yes or no to the grad question. Mark Demers claims a Ph.D. from > there, and I doubt that based on his moronic posts (or did he > perhaps have a stoke after graduating?). I have my doubts, but I > have not bothered to make the call. If anyone else here is motivated > to check that and report back here, please feel free! I figure that > you will need to sound like you have his resume in front of you if > you want to make it work, so some research into who Mark actually is > might be required to get the info that you would need. Perhaps just > his name and his claimed graduation year might do it. You could try the archives dept., too, for information about a dissertation. There should be no need for any ruse. After all, dissertations are publicly accessible information that the school should be happy to share. Just ask for the title of his dissertation. -- It has been shown that no man can sit down to write without a very profound design. Thus to authors in general trouble is spared. A novelist, for example, need have no care of his moral. It is there -- that is to say, it is somewhere -- and the moral and the critics can take care of themselves. --E.A. Poe === Subject: Re: mathematician salaries <87oeah4ebr.fsf@phiwumbda.org> Discussion, linux) > You could try the archives dept., too, for information about a > dissertation. Harvard's archives have no works by any Mark Demers. My faith in mankind (and particularly in Mark Demers) is badly shaken. I need a good lie-down. -- Jesse F. Hughes Well, if I can get [my proof of FLT accepted], then I hopefully get a book deal down the road, and maybe I get to go on 'Oprah'. James Harris, on the rewards of mathematical endeavours. === Subject: Re: mathematician salaries <87oeah4ebr.fsf@phiwumbda.org> <87vf4o95p1.fsf@phiwumbda.org> Jesse F. Hughes announces: > Harvard's archives have no works by any Mark Jesse, Are you the same guy who investigated the identity of Deep Throat for 30 years and, then, identified the wrong dude? Jesse, do you think Mark would make his identity so easily stolen as to plaster his full official name on the internet? Think about it. You know Mark's name. You look in Mark's Harvard dissertation. You discover the names of all of Mark's family members in the acknowledgement section. You see Mark's birthday, which is listed on his dissertation vitae. You know Mark's scholastic history. You know where Mark works. You know Mark has a full wallet. Next thing you know, you are opening bank and credit card accounts in Mark's name! Mark prays that Jesse is not such an easy mark. If you are as financially sophisticated as Mark, you would run over to your alma mater and put a lid on dissertation quickly! === Subject: Re: mathematician salaries <87oeah4ebr.fsf@phiwumbda.org> <87vf4o95p1.fsf@phiwumbda.org> Discussion, linux) > Jesse, do you think Mark would make his identity so easily stolen as to > plaster his full official name on the internet? Think about it. You > know Mark's name. You look in Mark's Harvard dissertation. You > discover the names of all of Mark's family members in the > acknowledgement section. You see Mark's birthday, which is listed on > his dissertation vitae. You know Mark's scholastic history. You know > where Mark works. You know Mark has a full wallet. Next thing you > know, you are opening bank and credit card accounts in Mark's name! Just the other day, you said that we could learn about Mark Demers by looking up alumni that contributed millions to Harvard. Now you claim that Mark Demers is an alias. Of course, anyone interested in kidnapping Mark Demers or whoever he is could look at Harvard dissertations involving Brownian motion and Ito's theorems over the past couple of decades. Oh. Mark Demers is so clever that nothing Mark Demers says about Mark Demers is true. Except the bits about having a Harvard PhD in some math-related topic and being a millionaire due to financial skills involving quaternions. That bit's okay. Clever that you use the Mark Demers alias to communicate with employees in your publicly accessible Google group. > Mark prays that Jesse is not such an easy mark. If you are as financially sophisticated as Mark, you would run over > to your alma mater and put a lid on dissertation quickly! Oh, sure, I still believe that you're a millionaire mathematician looking for like-minded millionaire mathematicians. Why, who wouldn't believe that? After all, everything in your story checks out, except for the checkable parts. -- I have to break the code of how [mere humans] work, and I have made a lot of progress over years of effort, and I feel like I am close to figuring out all the inner details of human wiring. -- James S. Harris on the extra problems of conveying his research === Subject: Re: mathematician salaries <87oeah4ebr.fsf@phiwumbda.org> <87vf4o95p1.fsf@phiwumbda.org> <87psuw905z.fsf@phiwumbda.org> kidnapping Mark Demers or whoever he is could look at Harvard dissertations involving Brownian motion and Ito's theorems over the past couple of decades. Such a criminal mind would be too cunning to waste time gathering dozens of dusty Ito's Theorem dissertations in the Harvard stacks. (How does he get inside in the first place if he has no Harvard ID card?) He would prefer look for easy prey elsewhere, like googling all the wonderful poster on this group. Why spend 1 week to track down Mark and his completely anonymous accounts when the thief can spend 1 day to identify 20 of you unsophisticated PhDs? === Subject: Re: mathematician salaries <87oeah4ebr.fsf@phiwumbda.org> <87vf4o95p1.fsf@phiwumbda.org> <87psuw905z.fsf@phiwumbda.org> Discussion, linux) > Such a criminal mind would be too cunning to waste time gathering > dozens of dusty Ito's Theorem dissertations in the Harvard stacks. Dozens? Just at Harvard? Golly, what a popular topic. > (How does he get inside in the first place if he has no Harvard ID > card?) One doesn't have to go to Harvard to find abstracts of dissertations and then to get a single dissertation. -- Jesse F. Hughes A gorgeous display of homoerotic lust. -- Review blurb found on the back of a Chinese black market Dawn of the Dead DVD === Subject: Re: mathematician salaries <87oeah4ebr.fsf@phiwumbda.org> <87vf4o95p1.fsf@phiwumbda.org> <87psuw905z.fsf@phiwumbda.org kidnapping Mark Demers or whoever he is could look at Harvard > dissertations involving Brownian motion and Ito's theorems over the > past couple of decades. Such a criminal mind would be too cunning to waste time gathering > dozens of dusty Ito's Theorem dissertations in the Harvard stacks. (How > does he get inside in the first place if he has no Harvard ID card?) You underestimate the criminal mind. Think about that next time you're poking around the Harvard stacks (if you do indeed have any connection with Harvard) -- half the people around you are actually criminals who finessed their way past security without ID. The horror. Seriously, do you really think it's impossible to get past a college security officer? You have such a charmingly naive faith in the boys and girls in blue. - Randy === Subject: Re: mathematician salaries > OK, go ahead and make fun of Mark. Mark has a full wallet, a full head > of hair, and a full blown PhD from the best uni in the world. You are > just jealous because you can not do as much with your degree as Mark > has done with his. > MD > Like what Mark is doing on these newsgroups right now? -- Ryan Reich ryanr@uchicago.edu === Subject: Re: mathematician salaries 1) Mark has new playable laptop, top of the line. 2) Mark is in charge of internet recruiting of mathematics PhDs for his equity firm; see his previous posts and do spread the word. 3) Mark enjoys the intellectual discourse of consumating with other math affectionadoes. MD === Subject: Re: mathematician salaries ^OX9W/.#XpUmm`>TD2zNE-t}emfPkFR.Z5`flY:3QYT$>dUwN^sm;MBV:F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/'>}Pc?@rl8cz]d9RXOt 1) Mark has new playable laptop, top of the line. Maybe when I figure out the final details of that quaternion model of finance (which is my idea BTW not yours), I'll get my Ph.D. in Theoretical Physics and my Ph.D. in Finance so I could be just like you (I'll even get them under a different name). But it'll all be for nought unless I get that laptop. > 2) Mark is in charge of internet recruiting of mathematics PhDs for his > equity firm; see his previous posts and do spread the word. You're doing a great job. I've been spreading the word among my friends. They thank me profusely for letting them know of your Usenet posts, MD. But my friends and I are more interested in using my quaternion model and starting our own equity firm. We've gotten some wealthy families to back us. I don't want to drop names, but maybe you've heard of Miller, Anheiser, Guinness, Heineken. We've even picked a pretty cool name, but it's secret so I can't tell you. I'm sure you understand. Look for our Google group, coming soon. > 3) Mark enjoys the intellectual discourse of consumating with other > math affectionadoes. > Oooh yeah, baby. How do I get in line to bear your children? === Subject: Re: mathematician salaries I'll get my Ph.D. in Theoretical Physics and my Ph.D. in Finance so I could be just like you You are already headed down the wrong path. We never hire PhD's in finance. All they do is write squiggly equations about pricing options; that is so 1980s. It's 2005. Options pricing and stock investing are dogs and cats, apples and oranges. Warren Buffett and Charlie Munger never studied black scholes. What a waste of time! They were too smart to waste their time on nonsense. Mark studies companies, not their stock prices. Mark would like more people like Chan Ho to invest in the market. With more players like that, Mark will win even bigger. C'mon in... we need more hands at the poker table. === Subject: Re: mathematician salaries Discussion, linux) > I'll get my Ph.D. in Theoretical Physics and my Ph.D. in Finance so I > could be just like you You are already headed down the wrong path. We never hire PhD's in > finance. All they do is write squiggly equations about pricing > options; that is so 1980s. It's 2005. Golly, Mark Demers needs to fix his fraudulent job posting. Though the abstract mentions math and hard science, we find this entry: PhD fields sought: Finance > Options pricing and stock investing are dogs and cats, apples and > oranges. Warren Buffett and Charlie Munger never studied black > scholes. What a waste of time! They were too smart to waste their > time on nonsense. Mark studies companies, not their stock prices. Man, Mark is brilliant. Too many people think that successful investing depends on the price when you buy and sell. It is to laugh. > Mark would like more people like Chan Ho to invest in the market. With > more players like that, Mark will win even bigger. C'mon in... we need > more hands at the poker table. You shark, you! -- Jesse F. Hughes I already have major discoveries, which mathematicians have simply avoided bothering to inform the public about, so I'll solve the factoring problem, and that will end. JSH: A Man with a Plan! === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> Jesse F. Hughes: about the job posting. Though the abstract mentions math and hard science, we find this entry: PhD fields sought: Finance What is Jesse's point? Mark is in the finance industry. Jesse obviously does not know what finance is about. Jesse obviously believes finance is just about pricing options using esoteric mathematics. Jesse, dude, finance is a vast field, and options pricing is just 7% of it. Most of finance is about companies and how they obtain financing in its various forms. That's why it's called finance. Get it? Why doesn't Jesse learn about the other 93% of a field before criticizing? Warren Buffett doesn't price options. Is Jesse going to tell Mr. Buffett he is not in finance? Saying that stochastic mathematics defines finance is equivalent to saying that knot theory defines math. Knot theory is just a tiny subfield of math. === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> Discussion, linux) > Jesse F. Hughes: about the job posting. Though > the abstract mentions math and hard science, we find this entry: > PhD fields sought: Finance What is Jesse's point? You said: We never hire PhD's in finance. Your advertisement says PhD fields sought: Finance. If you see no contradiction, I can't help you. -- After years of arguing I realize that your intellects are too limited to fully grasp my work. [...] Still, no matter how child-like your minds are, [...] since you have language, [...] there's a chance that I'll be able to find something that your minds can handle. --JSH === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> <873brr7prs.fsf@phiwumbda.org You said: We never hire PhD's in finance. Your advertisement says PhD fields sought: Finance. > You claim 2 PhDs. You guys think too literally. Your mind is seared from proving too many theorems with pedagogical logic. Assumptions, implications, proof. 0+1=1 implies 0+2=2. Yeah. Righto. You should wish the real world is so simplistic, so sensible, so organized. Not! Mark thinks in terms of the real world. Yes, we do not typically hire PhDs in Finance. But there are many PhDs in the math and hard or financial sciences who have a keen interest in finance. For instance, Mark does not have a phd in finance. But Mark was very interested in finance when writing his Ito's Theorem dissertation, and took it upon himself to take business, marketing, and accounting courses. Thus, Mark has a phd AND it is a phd in a finance-related area. This is why Mark can say he has a PhD in Science and a PhD in finance in a figurative sense. Mark prefers to talk to people like that. Get it? Mark does not like PhDs who has a PhD strictly within finance because such people's mindset is very narrow. Mark prefers interdisciplinary minded individuals who, while majoring in something else, has actively also pursued knowledge in finance out of passion. In summary, Mark does not like careerists who solely focus on the finance course and knows little about science and math and literature and marketing. Such people are not educated. They are not entrepreneurs. Mark is a risk taker, an entreprenueur, a leader in his field, a new thinker. His friends call Mark a renaisance man. As for the job ad -- it is not a pedagogical theorem. === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> <873brr7prs.fsf@phiwumbda.org You said: We never hire PhD's in finance. > Your advertisement says PhD fields sought: Finance. > You claim 2 PhDs. You guys think too literally. >> Mark Demers (PhD in Theoretical Physics, PhD in Finance) >> Co-CEO, EquityValue Investments wants us to believe he is a PhD in Theoretical Physics and a PhD in Finance? Yes, I must admit that if I saw that on a resume, I would believe that the claim is indeed to have a PhD in Finance. > Mark thinks in terms of the real world. Even in the real world, when you put PhD in X on a resume, it is a claim that you have completed doctoral requirements for X at some accredited university, and left a paper trail which can be validated. Now in the real world it is certainly the case that many people put credentials on their resume that are not verifiable and are patently false. But nevertheless, it is certainly true in the real world that writing PhD in X amounts to a claim of having a PhD in X. > For instance, > Mark does not have a phd in finance. That seems to have been established. Nevertheless, Mark *claimed* to have a PhD in finance. - Randy === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> <873brr7prs.fsf@phiwumbda.org> Randy Poe, did you ever see Mark's resume? You are getting your information from Usenet newsgroups (and second hand from another poster, who might have made it up). Is second-hand information on usenet newsgroups equivalent to what is on a formal resume? Is Mark applying for a job here? In a courtroom, they disallow hearsay evidence for that reason. Marky === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> <873brr7prs.fsf@phiwumbda.org Randy Poe, > did you ever see Mark's resume? You are getting your information from > Usenet newsgroups (and > second hand from another poster, who might have made it up). Um, not quite. http://www.mathforum.org/kb/message.jspa?messageID=3785511&tstart=0 I'm getting it from a usenet posting by someone who used the return address markdemers15@hotmail.com, the same as yours. This is also the same e-mail return address that appears at this site: http://jobs.phds.org/jobs/markdemers15/listing_2005_05_12 What is your position, that the above message is a forgery? It certainly isn't second hand from another poster. > Is second-hand information on usenet newsgroups equivalent to what is > on a formal resume? > Is Mark applying for a job here? I don't know whether you are or aren't claiming to be Mark Demers. I do know that you are posting from an address markdemers15@hotmail.com , or forging that as a return address on your postings. I also know that in one such message, the text PhD in Theoretical Physics, PhD in Finance appeared after the name Mark Demers. No, this isn't a formal resume. It is nevertheless a claim to having those credentials. Is your position that you did not intend the parenthetical PhD in Theoretical Physics, PhD in Finance to be interpreted as your having a PhD in Theoretical Physics or Finance? It's not as serious an ethical lapse as putting that on the resume for a job application. On Usenet it just amounts to petty lying. Is that your position? That you inflated your credentials for Usenet purposes, and merely engaged in a petty lie in this forum? - Randy === Subject: Re: mathematician salaries <877jh484ol.fsf@phiwumbda.org> <873brr7prs.fsf@phiwumbda.org> Mark knows nothing about a mathforum. Mark has never visited such a site. Anybody could have forged that mathforums message. Mark suspects that Randy Poe did, or Chan Ho Suh did. Tsk, tsk... you shouldn't resort to such things. Now you know why mark has to be careful about not completely revealing Mark's secret identity. Too many identity theives on usenet. Mark Demers is a common name. Why is Mark's address markdemers15 on hotmail? It's because 15 other Mark Demers had already claimed the id numbers #0 - #14. don't you go causing trouble for them either. === Subject: Re: mathematician salaries ^OX9W/.#XpUmm`>TD2zNE-t}emfPkFR.Z5`flY:3QYT$>dUwN^sm;MBV:F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/'>}Pc?@rl8cz]d9RXOt You are already headed down the wrong path. We never hire PhD's in > finance. Then you admit your (alleged) Ph.D. in finance was a waste of time? === Subject: Re: mathematician salaries TD2zNE-t}emfPkFR.Z5`flY:3QYT$>dUwN^sm;MBV:F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/'>}Pc?@rl8cz]d9RXOt Then you admit your (alleged) Ph.D. in finance was a waste of time? >Wad chew talking 'bout, Willis? Mark never said he had a phd in > finance. Mark never says he has 2 phds. Oh yeah, and what is this next excerpt? > There is no distinction between physics and fiance or accounting. >Mark Demers (PhD in Theoretical Physics, PhD in Finance) > Co-CEO, EquityValue Investments Hey Mark, why do you deny having claimed a Ph.D. in finance, when you clearly claim it here? Why do you deny claiming two Ph.D.s when you clearly claim it here? Here's a question for onlookers: why is this post by Double D not on Google Groups anymore, even though it was some time ago and is still floating around on Usenet? Could it be that Double D removed his post from Google Groups using their remove option? Could it be that Double D is not aware that his Google column as he calls it, does not require people logging in is being distributed through Usenet? === Subject: Re: mathematician salaries >Then you admit your (alleged) Ph.D. in finance was a waste of time? >Wad chew talking 'bout, Willis? Mark never said he had a phd in > finance. Mark never says he has 2 phds. >Oh yeah, and what is this next excerpt? There is no distinction between physics and fiance or accounting. >Mark Demers (PhD in Theoretical Physics, PhD in Finance) > Co-CEO, EquityValue Investments >Hey Mark, why do you deny having claimed a Ph.D. in finance, when you > clearly claim it here? Why do you deny claiming two Ph.D.s when you > clearly claim it here? Cut the guy some slack---he's having enough trouble trying to remember his advisor's name. -- A. === Subject: Re: mathematician salaries Then you admit your (alleged) Ph.D. in finance was a waste of time? >>Wad chew talking 'bout, Willis? Mark never said he had a phd in >>finance. Mark never says he has 2 phds. Oh yeah, and what is this next excerpt? >>There is no distinction between physics and fiance or accounting. >>Mark Demers (PhD in Theoretical Physics, PhD in Finance) >>Co-CEO, EquityValue Investments Hey Mark, why do you deny having claimed a Ph.D. in finance, when you > clearly claim it here? Why do you deny claiming two Ph.D.s when you > clearly claim it here? >Here's a question for onlookers: why is this post by Double D not on > Google Groups anymore, even though it was some time ago and is still > floating around on Usenet? Could it be that Double D removed his post > from Google Groups using their remove option? Could it be that Double > D is not aware that his Google column as he calls it, does not > require people logging in is being distributed through Usenet? It's still archived on mathforum: http://www.mathforum.org/kb/message.jspa?messageID=3785511&tstart=0 And http://www.groupsrv.com/science/about99562-15.html Anyway... it's obvious that this guy is a phony. === Subject: Re: mathematician salaries ^OX9W/.#XpUmm`>TD2zNE-t}emfPkFR.Z5`flY:3QYT$>dUwN^sm;MBV:F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/'>}Pc?@rl8cz]d9RXOt Anyway... it's obvious that this guy is a phony. Yup. So I don't really understand why I even bother reading his posts, except to say that I must find it terribly entertaining somehow. I guess it's the sheer ridiculousness of what he says and how he continually attempts to defend his statements. There's also the mystery of why he would bother with such an elaborate is he actually an idiot that thinks he can make a killing on Wall Street if only he got expert mathematical advice on quaternions? === Subject: Re: mathematician salaries On 7 Jun 2005 17:11:18 -0700, double d 2) Mark is in charge of internet recruiting of mathematics PhDs for his >equity firm; see his previous posts and do spread the word. >3) Mark enjoys the intellectual discourse of consumating with other >math affectionadoes. Mark needs to be aware that when he says things like enjoys the intellectual discourse of consumating with other math affectionadoes he sounds like a blithering idiot (whatever you meant, consumating with isn't it - also note the spelling, and that there's no such word as affectionadoes.) Someone should also explain to Mark that when he speaks of himself in the third person the way he does he comes off as exremely wacky. >MD ************************ David C. Ullrich === Subject: Re: mathematician salaries >On 7 Jun 2005 17:11:18 -0700, double d >1) Mark has new playable laptop, top of the line. >>2) Mark is in charge of internet recruiting of mathematics PhDs for his >>equity firm; see his previous posts and do spread the word. >>3) Mark enjoys the intellectual discourse of consumating with other >>math affectionadoes. Mark needs to be aware that when he says things like enjoys the >intellectual discourse of consumating with other math affectionadoes >he sounds like a blithering idiot (whatever you meant, >consumating with isn't it - also note the spelling, and that >there's no such word as affectionadoes.) Mathturbation? -- Things should be made as simple as possible -- but no simpler. -- Albert Einstein === Subject: Re: mathematician salaries >>On 7 Jun 2005 17:11:18 -0700, double d 2) Mark is in charge of internet recruiting of mathematics PhDs for his >equity firm; see his previous posts and do spread the word. >3) Mark enjoys the intellectual discourse of consumating with other >math affectionadoes. >>Mark needs to be aware that when he says things like enjoys the >>intellectual discourse of consumating with other math affectionadoes >>he sounds like a blithering idiot (whatever you meant, >>consumating with isn't it - also note the spelling, and that >>there's no such word as affectionadoes.) Mathturbation? > ROTFLMAO. /BAH Subtract a hundred and four for e-mail. === Subject: Re: mathematician salaries > 1) Mark has new playable laptop, top of the line. > 2) Mark is in charge of internet recruiting of mathematics PhDs for his > equity firm; see his previous posts and do spread the word. > 3) Mark enjoys the intellectual discourse of consumating with other > math affectionadoes. Good heavens! First, referring to yourself in the third person like Bob Dole over and over again. Then the intellectual discourse of consumating with other math affectionadoes?! It almost makes one long for James Harris. Michael affectionadoes?! === Subject: Re: mathematician salaries > Good heavens! First, referring to yourself in the third person like Bob > Dole over and over again. Then the intellectual discourse of consumating > with other math affectionadoes?! It almost makes one long for James > Harris. Yes... much better than Mark... I wish James would come back. I promise to be nicer to him this time. === Subject: Re: mathematician salaries Mark is pleased he has accumulated such a faithful following. You What's Mark's latest? Will Mark disclose his dissertation title? Who will fail? Who will succeed? Who will become the next Harvard PhD? MD === Subject: Re: mathematician salaries ^OX9W/.#XpUmm`>TD2zNE-t}emfPkFR.Z5`flY:3QYT$>dUwN^sm;MBV:F7aL9x*q!` ln!l}>Y6_45$%R|P7DSrBkEph@1-;P*s~F_28vO@e4p/'>}Pc?@rl8cz]d9RXOt Mark is pleased he has accumulated such a faithful following. You > Log in? Google column? It won't be long before *everyone* just killfiles you. Enjoy this while it lasts. > What's Mark's latest? Will Mark disclose his dissertation title? Who > will fail? Who will succeed? Who will become the next Harvard PhD? > MD > I feel uncomfortable, like I caught someone masturbating. === Subject: Re: mathematician salaries > Mark is pleased he has accumulated such a faithful following. You Starting to smell a bit like James Harris. === Subject: Re: mathematician salaries Discussion, linux) > 1) Mark has new playable laptop, top of the line. > 2) Mark is in charge of internet recruiting of mathematics PhDs for his > equity firm; see his previous posts and do spread the word. > 3) Mark enjoys the intellectual discourse of consumating with other > math affectionadoes. 4) Mark desperately needs a spell-checker if he wants to pull off this intellectual superiority nonsense. Anyway, no consumating with me. I'm a married man. But if you want to make plausible you really went to Harvard, why drop all the in-knowledge about local geography? Just give us the title of your dissertation. Maybe an abstract, too. After all, you said one should be judged on his merits and not that of the school he attended or the advisor he had. -- Jesse F. Hughes All information is subject to change without notice. -- California Alternative High School === Subject: Re: mathematician salaries > 1) Mark has new playable laptop, top of the line. What is a playable laptop? > 2) Mark is in charge of internet recruiting of mathematics PhDs for his > equity firm; see his previous posts and do spread the word. Yes... spread the word about Mark D that he is a liar and a looser. > 3) Mark enjoys the intellectual discourse of consumating with other > math affectionadoes. What are you consummating? You are here fulfilling some kind of personal goal or sexual desire somehow? === Subject: Re: mathematician salaries >Mark used to think PhD's in math were smart. Mark needed to have a > public site to provide information to job applicants in an unfettered, > unencrypted fashion at the lowest cost possible. Duh! Mark sounds like a pompous idiot when he refers to himself in the third person. -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock === Subject: supply parameterization of domain for integration? The author is trying to calculate the fractional area of the sphere S(x;r) contained in the ball B(0;a) in dimension 3. Here's how he starts out (I understand this much): f = 1/(4pi) Int[ d(w) over the domain {w: |x+rw|<=a} ] = 1/2 Int[ sin(th) d(th) over the domain {|x|^2 + 2r|x| cos(th) + r^2 <= a^2} ] I'm trying to understand how the author changed from integration over a domain specified by an inequality to a numerical answer: 1/2 Int[ sin[th] d(th) over the domain {|x|^2 + 2r|x| cos(th) + r^2 <= a^2} ] = 1/2 ((a^2-r^2-|x|^2)/(2r|x|) + 1) How did he parameterize the domain? Alex === Subject: Re: supply parameterization of domain for integration? >The author is trying to calculate the fractional area of the sphere >S(x;r) contained in the ball B(0;a) in dimension 3. Here's how he >starts out (I understand this much): f = 1/(4pi) Int[ d(w) over the domain {w: |x+rw|<=a} ] > = 1/2 Int[ sin(th) d(th) over the domain {|x|^2 + 2r|x| cos(th) + r^2 ><= a^2} ] I'm trying to understand how the author changed from integration over a >domain specified by an inequality to a numerical answer: 1/2 Int[ sin[th] d(th) over the domain {|x|^2 + 2r|x| cos(th) + r^2 <= >a^2} ] >= >1/2 ((a^2-r^2-|x|^2)/(2r|x|) + 1) How did he parameterize the domain? Alex I'll take a shot at it, using t for th: 1/2 Int[ sin[t] d(t) = - 1/2 cos(t) where my guess is that t varies from 0 to the value of t that satisfies the equality in your inequality: |x|^2 + 2r|x| cos(t) + r^2 = a^2 so cos(t) = (a^2 - |x|^2 - r^2) / (2 r |x| ) at the upper limit and 1 at the lower limit giving an answer of: -(1/2)((a^2 - |x|^2 - r^2) / (2 r |x| ) - 1) Getting pretty close.... --Lynn === Subject: ??? Quaternions ??? Hi all, I am trying to apply PID control on the yaw, pitch and roll angles of my aircraft to keep it in a desired orientation. However, this orientation is for a pitch angle of theta=90 degrees -> GIMBAL LOCK!! To avoid this, I obviously have to use quaternions. However, my problem is once I have the aircraft attitude information in quaternion form, how can I apply PID control to that quaternion in order to keep the aircraft at a specific attitude (e.g. yaw=0, pitch=90, roll=0 degrees)? Can I apply the Derivation of Quaternion Error Angles and still avoid gimbal lock (see page 120 of: www.ae.gatech.edu/~ejohnson/Thesis-repro.pdf for more information)? -Bill === Subject: Re: ??? Quaternions ??? I'm not sure how well it translates from spacecraft to aircraft, but try Space Vehicle Dynamics and Control by Bong Wie. Chapter 7, Rotational Maneuvers and Control, includes lots of good stuff concerning the use of quaternion feedback with PID like controllers. See, especially, some of Wie's references to this chapter. I used some of this stuff and got a very simple and robust controller for spacecraft attitude control that was much better than using Euler angles. MzF > Hi all, I am trying to apply PID control on the yaw, pitch and roll angles of > my aircraft to keep it in a desired orientation. However, this > orientation is for a pitch angle of theta=90 degrees -> GIMBAL LOCK!! > To avoid this, I obviously have to use quaternions. However, my > problem is once I have the aircraft attitude information in quaternion > form, how can I apply PID control to that quaternion in order to keep > the aircraft at a specific attitude (e.g. yaw=0, pitch=90, roll=0 > degrees)? Can I apply the Derivation of Quaternion Error Angles and still avoid > gimbal lock (see page 120 of: > www.ae.gatech.edu/~ejohnson/Thesis-repro.pdf for more information)? >-Bill === Subject: Re: ??? Quaternions ???- I am not familiar with PID control, but I guess that there is a way to PID-control =constrained= variables. In this case the four quaternion components (a, b, c, d), which have to satisfy the constraint aa + bb + cc + dd = 1. If I had to find out from scratch I would apply a kind of Lagrange Multiplier technique. An alternative to the quaternion technique that avoids the gimbal-lock-like singularities of nose-up and nose-down attitudes and at the same time makes use of three independent variables was published in 1996. Students of me established the usability of this new technique in a dynamical simulation setting. Two sets of independent variables are used: one for nose-down, the other for nose-up attitudes. For nose-down and nose-up the Euler angles phi and psi are indeterminate. However, phi+psi is well-determinedfor nose-down. Likewise, for nose-up, phi-psi is well-determined. In both cases the other two variables are the plane Cartesian coordinates of a certain point related to the AC's attitude by a below. http://www.xs4all.nl/~jemebius/Joa1996.htm - http://www.xs4all.nl/~jemebius/Jemkk.htm Good luck: Johan E. Mebius >Hi all, I am trying to apply PID control on the yaw, pitch and roll angles of >my aircraft to keep it in a desired orientation. However, this >orientation is for a pitch angle of theta=90 degrees -> GIMBAL LOCK!! >To avoid this, I obviously have to use quaternions. However, my >problem is once I have the aircraft attitude information in quaternion >form, how can I apply PID control to that quaternion in order to keep >the aircraft at a specific attitude (e.g. yaw=0, pitch=90, roll=0 >degrees)? Can I apply the Derivation of Quaternion Error Angles and still avoid >gimbal lock (see page 120 of: >www.ae.gatech.edu/~ejohnson/Thesis-repro.pdf for more information)? -Bill > === Subject: Re: ??? Quaternions ???- <42A6CD2B.4020602@xs4all.nl> I know that Euler angles are widely used, but they are computationally quite clumsy and have discontinuities starting at 90Á. Do you know about the Gibbs-Rodrigues representation, which is described in: http://www.arxiv.org/ftp/cs/papers/0104/0104016.pdf Even if you eventually want Euler angles, the GR representation has a number of quick algorithms e.g. for combining two rotations in sequence. When generating a rotation from its Euler angles, the resulting sequence of GR vectors goes as follows: the origin -> a coordinate axis -> a coordinate plane (xy, yz or xz) -> all of space. Extracting the Euler angles just involves retracing your steps. Zigoteau. === Subject: Re: ??? Quaternions ???-- Hello Bill and Zigoteau, There exists a vast literature on PID control of quaternion variables; just look for quaternion PID control on your favorite search engine. Many of the papers in question appeared in journals of the AIAA. One can obtain paid subscriptions to AIAA journals or otherwise buy separate Google Scholar search: of 3D rotations. that Gibbs also studied 3D rotations along this path. Whatever savings in numbers of arithmetical operations one may achieve by a representation different from the unit quaternion representation, one will be set back by the effort needed to test if the rotation at hand is a half-turn, and subsequently handling half-turns separately. Half-turns are kind of troublemakers in the 3D rotation business; they often need special treatment. I prefer the quaternion representation because of its robustness and freedom from exceptional cases. In practice one even need not normalize at each time step; deviations from unit norm build up about half a unit in the least significant decimal place per time step. So with the 18D precision of Intel floating point arithmetic one will not incur a single-pixel error on the usual 800x600 resolution until after many weeks of running a dynamical simulation. Finally I would like to draw your attention to a paper of mine at arXiv at URL http://www.arxiv.org/PS_cache/math/pdf/0501/0501249.pdf where conversions of 4D rotation matrices into quaternions and vice versa are treated. This stuff ie easily specialized to 3D by putting a00 = 1 in the 4D rotation matrix. Conversion from quaternions to 3D matrices is of course Euler-Rodrigues; conversion of 3D rotation matrix to quaternion shows up the trickiness associated with half-turns. Good luck and happy flying: Johan E. Mebius >I know that Euler angles are widely used, but they are computationally >quite clumsy and have discontinuities starting at 90Á. Do you know >about the Gibbs-Rodrigues representation, which is described in: http://www.arxiv.org/ftp/cs/papers/0104/0104016.pdf Even if you eventually want Euler angles, the GR representation has a >number of quick algorithms e.g. for combining two rotations in >sequence. When generating a rotation from its Euler angles, the >resulting sequence of GR vectors goes as follows: the origin -> a >coordinate axis -> a coordinate plane (xy, yz or xz) -> all of space. >Extracting the Euler angles just involves retracing your steps. >Zigoteau. > === Subject: Re: ??? Quaternions ???-- <42A6CD2B.4020602@xs4all.nl> <42A72306.4040101@xs4all.nl of 3D rotations. > that Gibbs also studied 3D rotations along this path. Whatever savings in numbers of arithmetical operations one may achieve > by a representation different from the unit quaternion representation, > one will be set back by the effort needed to test if the rotation at > hand is a half-turn, and subsequently handling half-turns separately. > Half-turns are kind of troublemakers in the 3D rotation business; they > often need special treatment. I prefer the quaternion representation because of its robustness and > freedom from exceptional cases. In practice one even need not normalize > at each time step; deviations from unit norm build up about half a unit > in the least significant decimal place per time step. So with the 18D > precision of Intel floating point arithmetic one will not incur a > single-pixel error on the usual 800x600 resolution until after many > weeks of running a dynamical simulation. You are of course right, and of course the connection between the Gibbs-Rodrigues vector and the quaternion is so close that they are not really distinct entities. > Finally I would like to draw your attention to a paper of mine at arXiv > at URL http://www.arxiv.org/PS_cache/math/pdf/0501/0501249.pdf where conversions of 4D rotation matrices into quaternions and vice > versa are treated. afraid I do not understand what you mean by a 4D rotation matrix. It does not seem to mean a linear transform in 4D preserving lengths and angles. > This stuff ie easily specialized to 3D by putting a00 = 1 in the 4D > rotation matrix. > Conversion from quaternions to 3D matrices is of course Euler-Rodrigues; > conversion of 3D rotation matrix to quaternion shows up the trickiness > associated with half-turns. AFAICS the main advantage of the Gibbs-Rodrigues vector over the corresponding quaternion is that it is much easier to visualize. It may be that I have not read widely enough. Is the quaternion algorithm well-known that allows you to find the rotation which transforms two unit vectors v1 and v2 into two others v3 and v4? Zigoteau. === Subject: Re: ??? Quaternions ???-- <42A6CD2B.4020602@xs4all.nl> <42A72306.4040101@xs4all.nl of 3D rotations. > that Gibbs also studied 3D rotations along this path. Whatever savings in numbers of arithmetical operations one may achieve > by a representation different from the unit quaternion representation, > one will be set back by the effort needed to test if the rotation at > hand is a half-turn, and subsequently handling half-turns separately. > Half-turns are kind of troublemakers in the 3D rotation business; they > often need special treatment. I prefer the quaternion representation because of its robustness and > freedom from exceptional cases. In practice one even need not normalize > at each time step; deviations from unit norm build up about half a unit > in the least significant decimal place per time step. So with the 18D > precision of Intel floating point arithmetic one will not incur a > single-pixel error on the usual 800x600 resolution until after many > weeks of running a dynamical simulation. You are of course right, and of course the connection between the Gibbs-Rodrigues vector and the quaternion is so close that they are not really distinct entities. > Finally I would like to draw your attention to a paper of mine at arXiv > at URL http://www.arxiv.org/PS_cache/math/pdf/0501/0501249.pdf where conversions of 4D rotation matrices into quaternions and vice > versa are treated. afraid I do not understand what you mean by a 4D rotation matrix. It does not seem to mean a linear transform in 4D preserving lengths and angles. > This stuff ie easily specialized to 3D by putting a00 = 1 in the 4D > rotation matrix. > Conversion from quaternions to 3D matrices is of course Euler-Rodrigues; > conversion of 3D rotation matrix to quaternion shows up the trickiness > associated with half-turns. AFAICS the main advantage of the Gibbs-Rodrigues vector over the corresponding quaternion is that it is much easier to visualize. It may be that I have not read widely enough. Is the quaternion algorithm well-known that allows you to find the rotation which transforms two unit vectors v1 and v2 into two others v3 and v4? Zigoteau. === Subject: Re: ??? Quaternions ???--- Hello Zigoteau - and other interested fellow mathematicians, Let me start with the 4D rotation matrices. In essence they are no different from 2D and 3D rotation matrices. Of course they refer to a four-dimensional space. Let me explain: distances in ordinary 3D space with Cartesian coordinates are readily visualized as body diagonals of rectangular blocks. In formula: D = sqrt (xx + yy + zz), where x, y, z are the lengths of the edges of the block. Well-known stuff, of course. Euler (1707-1783) did a research into the kind of transformations of variables under which the quadratic form (xx + yy + zz) is invariant. Euler's orientation and terminology were algebraic, not geometric, so he did not speak of blocks and diagonals, but of independent variables and quadratic forms. Euler generalized his studies to quadratic forms in four and more variables. In particular, he obtained striking results in studying the four-variable quadratic form (uu + xx + yy + zz). Nowadays his results in four variables are denoted as 4D isometric transformations or as orthogonal transformations. Euler did not use the transformations as tables that are essentially matrices. Reference: [EULE 1770] L. Euler: Problema algebraicum ob affectiones prorsus singulares memorabile. Euleri Opera Omnia, 1st series, 6, p. 287-315 It is not too difficult to imagine the possibility of a 4D Euclidean geometry with Cartesian coordinates (u, x, y, z) and distance function D = sqrt (uu + xx + yy + zz). Euler's results in four variables are easily re-interpreted as transformations of 4D coordinates that leave the quadratic form, and so the distance of any two points in 4D space, invariant. leaves (uu + xx + yy + zz) unchanged, as long as (aa + bb + cc + dd)(pp + qq + rr + ss) = 1. To make a long story short: this 4D rotation matrix represents a rotation in 4D Euclidean space in exactly the same manner as 3D and 2D rotation matrices represent 3D and 2D rotations. About the Gibbs vector: indeed it is far more easily visualized than the corresponding quaternion. There is, at least to my taste, one catch in the visualization: its length tan(phi/2) is far more than proportional than the rotation angle phi. In my previous posting I forgot to mention what actually happens when one specializes the 4D formulas to 3D. The complete recipe to specialize the 4D stuff to 3D: a00=1, p=a, q=-b, r=-c, s=-d, so quaternions a+bi+cj+dk and p+qi+rj+sk are each other's conjugates. Actually all this follows from setting a00=1, but the proof is somewhat tricky. Finally the problem of how to find the rotation from given vectors v1 and v2 to given vectors v3 and v4: assume that the triangle defined by v3 and v4 is congruent to that defined by v1 and v2 (necessary condition): strangely enough, I never came across this problem in my software practice, so I have no clear-cut quaternion algorithm. I will try and find out some time. Ciao: Johan E. Mebius >of 3D rotations. >>that Gibbs also studied 3D rotations along this path. >>Whatever savings in numbers of arithmetical operations one may achieve >>by a representation different from the unit quaternion representation, >>one will be set back by the effort needed to test if the rotation at >>hand is a half-turn, and subsequently handling half-turns separately. >>Half-turns are kind of troublemakers in the 3D rotation business; they >>often need special treatment. >>I prefer the quaternion representation because of its robustness and >>freedom from exceptional cases. In practice one even need not normalize >>at each time step; deviations from unit norm build up about half a unit >>in the least significant decimal place per time step. So with the 18D >>precision of Intel floating point arithmetic one will not incur a >>single-pixel error on the usual 800x600 resolution until after many >>weeks of running a dynamical simulation. >> You are of course right, and of course the connection between the >Gibbs-Rodrigues vector and the quaternion is so close that they are not >really distinct entities. >Finally I would like to draw your attention to a paper of mine at arXiv >>at URL >>http://www.arxiv.org/PS_cache/math/pdf/0501/0501249.pdf >>where conversions of 4D rotation matrices into quaternions and vice >>versa are treated. >> afraid I do not understand what you mean by a 4D rotation matrix. It >does not seem to mean a linear transform in 4D preserving lengths and >angles. >This stuff ie easily specialized to 3D by putting a00 = 1 in the 4D >>rotation matrix. >>Conversion from quaternions to 3D matrices is of course Euler-Rodrigues; >>conversion of 3D rotation matrix to quaternion shows up the trickiness >>associated with half-turns. >> AFAICS the main advantage of the Gibbs-Rodrigues vector over the >corresponding quaternion is that it is much easier to visualize. It may >be that I have not read widely enough. Is the quaternion algorithm >well-known that allows you to find the rotation which transforms two >unit vectors v1 and v2 into two others v3 and v4? > Zigoteau. > === Subject: Re: ??? Quaternions ???--- <42A6CD2B.4020602@xs4all.nl> <42A72306.4040101@xs4all.nl> <42A774F7.7060808@xs4all.nl Let me start with the 4D rotation matrices. In essence they are no > different from 2D and 3D rotation matrices. Of course they refer to a > four-dimensional space. in 4D have 6 degrees of freedom, and you represent each one by an ordered pair of unit quaternions, with a quick algorithm for generating the 4x4 unitary matrix. > Finally the problem of how to find the rotation from given vectors v1 > and v2 to given vectors v3 and v4: > assume that the triangle defined by v3 and v4 is congruent to that > defined by v1 and v2 (necessary condition): strangely enough, I never > came across this problem in my software practice, so I have no clear-cut > quaternion algorithm. I will try and find out some time. It seems to me that this is an important algorithm for computer graphics, when you want to align an object e.g. to the curvature and torsion vectors of a trajectory. You don't need to find out. Since it's quite easy in Gibbs-Rodrigues representation, it's also easy in quaternion representation. It's just that I've never seen it in the quaternion literature, and it seems to me that this is because it's hard to get a mental image of a 4D vector. Zigoteau. === Subject: factoring algorithm I've been working on a factoring algorithm using quadratic residues and would appreciate any comments. It's a variation on Fermat. For any N not prime, let N=ab. Then (a-b)^2 + 4ab ------------------ (a+b)^2 There are only certain allowable quadratic residues for any number squares. For example , the only quadratic residues mod 10 are 0,1,4,5,6,9 (all square numbers end in 0,1,4,5,6,9 ); the only quadratic residues mod 9 are 0,1,4,7; the only quadratic mod 144 are 0,1,4,9,16,25,36,49,52,64,73,81,97,100,112,121;etc., As an example, let N = 101*13=1313. Then 4ab =5252 and 5252 mod 10 =2.Plugging in the allowable residues we get 0+2=2 which is not an allowable quadratic residue mod 10, 1+2 =3 not allowable, 4+2 = 6 allowable, 5+2=7 not allowable, 6+2 = 8 not allowable, 9+2 =1 allowable. Therefore (a-b)^2 mod = 4 or 9. Since N is not even (or else N would have a trivial factor of 2) a and b must be odd and a-b must be even. Therefore 9 cannot be a possibility and (a-b)^2 mod = 4 . Similarly, 5252 mod 144 =68 and the only allowable residue is 112 so (a-b)^2 mod 144 =112.The first number = 4 mod 10 and =112 mod 144 is 544.Using the Chinese Remainder Theorem we find our number (a-b)^2= 544 + 720 k where k=0,1,2,...We could continue to try this by modding with different numbers. For example using mod 10,mod144,mod 784 we get (a-b)^2 = 2704 + 5040K and using mod 10,mod144,mod 784,mod 1296 we get (a-b)^2 = 7744 + 15,120k or = 42,768+45,360k. I found this metod works best by modding by numbers of the form 16*m^2 where m = an odd prime. Like Fermat, this algorithm works best for a almost equal to b. However its efficiency can be extended for a almost equal to 2b using the fact (a-2b)^2 + 8ab ------------- (a+2b)^2 for a almost equal to 3b (a-3b)^2 + 12ab ------------- (a+3b)^2 for a almost equal to kb (a-kb)^2 + 12ab ------------- (a+kb)^2 === Subject: Re: factoring algorithm Difference of squares using exclusion moduli has been known for a long time. In fact, D.H. Lehmer built machines just for this purpose (e.g. DLS-127) The choice of any fixed set of moduli does give a decent speedup, but it is a CONSTANT FACTOR speedup. It does not affect the underlying complexity. Weighted difference of squares has also been known. S. Lehman showed how using a Farey sequence of fractions one could find factors p,q if p/q were close to an element of the Farey sequence. It changes difference of squares from O(sqrt(n)) to O(n^1/3), but still exponential. One could apply exclusion moduli to Lehman's method, but it will still only give a constant factor speed improvement. These methods simply are not competitive with modern techniques. === Subject: Re: factoring algorithm > I've been working on a factoring algorithm using quadratic residues > and would appreciate any comments. My comment is that it's always nice to see someone take an interest in these questions, and I hope you have a lot of fun along the way. You won't find anything that hasn't been known for 300 years, but don't let that stop you from enjoying the ride. If your motivations are more serious than recreational then I'd recommend you do a little analysis of algorithms to see how your methods stack up against those commonly in use. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Integer equations problem number two Given positive integers n,l,k, choose a positive integer b such that all i+j*b for i=0,...,k and j=0,...,l are pairwise distinct. Proof or disproof: for any two k times l matrices (n_ij) and (m_ij) with ---- ---- > n_ij = > m_ij = n ---- ---- i,j i,j and ---- ---- > n_ij * (i+j*b) = > m_ij * (i+j*b) ---- ---- i,j i,j it follows that ---- ---- > n_ij * i = > m_ij * i ---- ---- i,j i,j where ---- > ---- i,j denotes the sum over i=0,...,k and j=0,...,l leaving out (i,j) = (0,0). Have fun! Oswald Kluge === Subject: A Magnificent Sum Here is my latest result. It needs to be verified, I would guess, since I may have made an error somewhere. This result is a generalization of the earlier result of mine: H(x) = Euler's constant + (Gamma(x+1))'/Gamma(x+1) = sum{k=1 to x}1/k if x = positive integer, the xth harmonic number; and zeta(j,x) = sum{k>=0} 1/(k+x)^j, the Hurwitz zeta function; For x >= 0, S(j,x) = --- H(k) / -------- = --- (k+x)^j k>=1 j-1 --- j 1 --- zeta(j+1,x) + H(x-1) zeta(j,x) - --- / zeta(k,x) zeta(j+1-k,x) 2 2 --- k=2 (View above with fixed-width font.) In linear mode: S(j,x) = sum{k>=1} H(k) /(k+x)^j = (j/2) zeta(j+1,x) + H(x-1) zeta(j,x) -(1/2) sum{k=2 to j-1} zeta(k,x) zeta(j+1-k,x). And now the main (more general) result: For x and y >=0, x not= y, for m and n >= 1, --- H(k) / ----------------- = --- (k+x)^m (k+y)^n k>=1 2 2 m / m+n-2 (H(x-1) - H(y-1) - zeta(2,x) + zeta(2,y)) (-1) ( | | --------------------------------------------- m-1 / 2 (y-x)^(m+n-1) m --- j (-1) S(j,x) / m+n-j-1 + / -------------- | | --- (y-x)^(m+n-j) n-1 / j=2 n --- S(j,y) / m+n-j-1 + / -------------- | | ) --- (y-x)^(m+n-j) m-1 / j=2 (S(j,x) is as defined above.) In linear mode: sum{k>=1} H(k) /((k+x)^m (k+y)^n) = (-1)^m * (binomial(m+n-2,m-1) (H(x-1)^2 - H(y-1)^2 - zeta(2,x) + zeta(2,y))/(2((y-x)^(m+n-1)) + sum{j=2 to m} (-1)^j S(j,x) binomial(m+n-j-1,n-1)/(y-x)^(m+n-j) + sum{j=2 to n} S(j,y) binomial(m+n-j-1,m-1)/(y-x)^(m+n-j) ) So, if I am right, the above sum approaches S(m+n,y) as x approaches y. Leroy Quet === Subject: Re: A Magnificent Sum >Here is my latest result. It needs to be verified, I would guess, since I >may have made an error somewhere. This result is a generalization of the earlier result of mine: >H(x) = Euler's constant + (Gamma(x+1))'/Gamma(x+1) >= sum{k=1 to x}1/k >if x = positive integer, the xth harmonic number; and zeta(j,x) = sum{k>=0} 1/(k+x)^j, >the Hurwitz zeta function; For x >= 0, >S(j,x) = --- > H(k) >/ -------- = >--- (k+x)^j >k>=1 j-1 > --- > j 1 >--- zeta(j+1,x) + H(x-1) zeta(j,x) - --- / zeta(k,x) zeta(j+1-k,x) > 2 2 --- > k=2 (View above with fixed-width font.) In linear mode: S(j,x) = sum{k>=1} H(k) /(k+x)^j = (j/2) zeta(j+1,x) >+ H(x-1) zeta(j,x) >-(1/2) sum{k=2 to j-1} zeta(k,x) zeta(j+1-k,x). >And now the main (more general) result: For x and y >=0, x not= y, for m and n >= 1, --- > H(k) >/ ----------------- = >--- (k+x)^m (k+y)^n >k>=1 2 2 > m / m+n-2 (H(x-1) - H(y-1) - zeta(2,x) + zeta(2,y)) >(-1) ( | | --------------------------------------------- > m-1 / 2 (y-x)^(m+n-1) m > --- j > (-1) S(j,x) / m+n-j-1 > + / -------------- | | > --- (y-x)^(m+n-j) n-1 / > j=2 n > --- > S(j,y) / m+n-j-1 > + / -------------- | | ) > --- (y-x)^(m+n-j) m-1 / > j=2 (S(j,x) is as defined above.) In linear mode: sum{k>=1} H(k) /((k+x)^m (k+y)^n) = (-1)^m * (binomial(m+n-2,m-1) (H(x-1)^2 - H(y-1)^2 - zeta(2,x) + >zeta(2,y))/(2((y-x)^(m+n-1)) + sum{j=2 to m} (-1)^j S(j,x) binomial(m+n-j-1,n-1)/(y-x)^(m+n-j) + sum{j=2 to n} S(j,y) binomial(m+n-j-1,m-1)/(y-x)^(m+n-j) ) So, if I am right, the above sum approaches >S(m+n,y) >as x approaches y. >Leroy Quet Here are some references: http://mathworld.wolfram.com/EulerSum.html http://mathworld.wolfram.com/HurwitzZetaFunction.html http://mathworld.wolfram.com/DigammaFunction.html http://mathworld.wolfram.com/HarmonicNumber.html Leroy Quet === Subject: Basic Questions on Z-tables and Sampling Suppose that it is found that in the USA, the average height of an adult male is exactly 70 inches with a standard deviation of exactly 3 inches. Moreover, this distribution is very normal. This is data compiled from exactly 100,000,000 men. Suppose that I wanted to calculate the height that 95% of the population. Of course, I'd calculate the range by looking at the z-tables for 95% (2-sided tail), and the Z-value is 1.96. Therefore, it can be stated that 95% of American males' height is 70 +/- (1.96)(3.0) = 64.12 - 75.88. However, I'm quite confused and baffled why we must include the Standard Error of the Sample: Sxbar = Xbar/(n)^0.5 Where Xbar is the mean of a random sample of n samples. According to my book, the 95% of the population is actually this (for a sample of 10,000 and Xbar calculated to be 70): 70 +/- (0.7)*1.96 = 68.63 - 71.37. I can't understand (a) why there is such a big change in the range from the first example and the second example. (b) Whether or not I am correct in the first example. (c) How should one interpret my data from example 1 and example 2? === Subject: Re: Basic Questions on Z-tables and Sampling On 2005-06-07 18:33:39 -0500, Brablo said: > Suppose that it is found that in the USA, the average height of an > adult male is exactly 70 inches with a standard deviation of exactly 3 > inches. Moreover, this distribution is very normal. This is data > compiled from exactly 100,000,000 men. Suppose that I wanted to > calculate the height that 95% of the population. Of course, I'd > calculate the range by looking at the z-tables for 95% (2-sided tail), > and the Z-value is 1.96. Therefore, it can be stated that 95% of > American males' height is 70 +/- (1.96)(3.0) = 64.12 - 75.88. However, I'm quite confused and baffled why we must include the > Standard Error of the Sample: Sxbar = Xbar/(n)^0.5 Where Xbar is > the mean of a random sample of n samples. According to my book, the > 95% of the population is actually this (for a sample of 10,000 and Xbar >calculated to be 70): 70 +/- (0.7)*1.96 = 68.63 - 71.37. What you are doing is attempting to not derive the 95% CI for all males, but the 95% CI for the mean of all males; e.g., xbar +/- z(alpha/2) (sigma/ sqrt(n)) This is an entirely different thing than calculating the 5th-95th percentile. (If you know the mean and variance, it is just mu +- z(a/2) sigma) -Stu === Subject: Re: Basic Questions on Z-tables and Sampling <2005060719401716807%student@studentstu> want to come up with the confidence interval for the *MEAN* of a sample? > On 2005-06-07 18:33:39 -0500, Brablo said: Suppose that it is found that in the USA, the average height of an > adult male is exactly 70 inches with a standard deviation of exactly 3 > inches. Moreover, this distribution is very normal. This is data > compiled from exactly 100,000,000 men. Suppose that I wanted to > calculate the height that 95% of the population. Of course, I'd > calculate the range by looking at the z-tables for 95% (2-sided tail), > and the Z-value is 1.96. Therefore, it can be stated that 95% of > American males' height is 70 +/- (1.96)(3.0) = 64.12 - 75.88. > However, I'm quite confused and baffled why we must include the > Standard Error of the Sample: Sxbar = Xbar/(n)^0.5 Where Xbar is > the mean of a random sample of n samples. According to my book, the > 95% of the population is actually this (for a sample of 10,000 and Xbar calculated to be 70): > 70 +/- (0.7)*1.96 = 68.63 - 71.37. > What you are doing is attempting to not derive the 95% CI for all > males, but the 95% CI for the mean of all males; e.g., xbar +/- z(alpha/2) (sigma/ sqrt(n)) This is an entirely different thing than calculating the 5th-95th > percentile. (If you know the mean and variance, it is just mu +- > z(a/2) sigma) >-Stu === Subject: Pension crisis Isn't this scandal worse than Enron? === Subject: Re: exponential equation with constant > I had a problem in an electrical circuits class, which was to find the >point at which the voltage on two exponential curves is equal. These >were the decaying voltage on an inductor and the rising voltage on a >capacitor, the curves starting from a fixed voltage and from zero >(respectively) at the same instant. The equated formulas were >VL = 2* exp(-2000t) = 1 - exp(-1000t) = VC >By luck, I found I could solve it for t by turning it into a quadratic- >let y = exp(-1000t) >2y^2 + y - 1 = 0 = (2y-1)(y+1) >Then, using (2y-1), >2 exp(-1000t) = 1, >ln(2) = 1000t >t = 693.2 us. This solution depends on the coincidence that one exponent is exactly >twice the other. >This brings me to the question -- is there a way, other than computer >simulation, to solve a*exp(-ct) = 1 - b*exp(-dt) for t? Similar to your solution: let x = exp(-ct). Then you want to solve > a*x + b*x^e = 1 where e = d/c. I'll assume e > 1 (if e < 1 you can > interchange the terms a*exp(-ct) and b*exp(-dt)). In only a few cases > you have a polynomial equation that can be solved using radicals. > However, at least if b/(a^e) is small there is a series solution x = This sort of problem arises fairly frequently. Having given a series solution earlier myself, I am interested in your different series solution. Attempting to use your series to solve the problem original posed here, we seem to arrive at x + 2*x^2 = 1, so that a = 1, b = 2 and e = 2, and then b/(a^e) = 2. But b/(a^e) was required to be small (and I presume that 2 is not adequately small) and so we cannot proceed. Is there perhaps some reasonably simple way to transform the equation so that your series solution can then be used? David Cantrell === Subject: Bilinear Paaring and groups I have some understanding problems with elliptic curves. Let G_1 and G_2 be 2 groups of order q. Let e: G_1 x G_1 -> G_2 be a bilinear pairing. Can I then for example say, that G_2 = Z_q? Or how do I have to understand the group G_2? Zsuzsanna === Subject: Re: Bilinear Paaring and groups days. My association with the Department is that of an alumnus. I have some understanding problems with elliptic curves. Let G_1 and G_2 >be 2 groups of order q. Let e: G_1 x G_1 -> G_2 be a bilinear pairing. >Can I then for example say, that G_2 = Z_q? Not generally. For example, if G_1 and G_2 are two elementary abelian groups of order p^2, then you can define a non-degenerate pairing which is onto an elementary abelian group of order p^4 by taking the 2-nilpotent product of G1 and G2, and using the commutator bracket to define the pairing. What properties are you requiring your bilinear pairing to have? What properties do you require of G_1 and G_2? Is there anything special about q (prime? power of a prime? anything?) -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Bilinear Paaring and groups > Not generally. For example, if G_1 and G_2 are two elementary abelian > groups of order p^2, then you can define a non-degenerate pairing > which is onto an elementary abelian group of order p^4 by taking the > 2-nilpotent product of G1 and G2, and using the commutator bracket to > define the pairing. >What properties are you requiring your bilinear pairing to have? What > properties do you require of G_1 and G_2? Is there anything special > about q (prime? power of a prime? anything?) G_1 and G_2 are of prime order q. Is there any big difference, whether I choose G_1 to be additive or multiplicative? Zsuzsi === Subject: effective Method to calculate n-th power is there any efficient way to calculate for a given g^x and given n in a group G with order q, the value: g^{x^n}? Zsuzsanne === Subject: Re: effective Method to calculate n-th power is there any efficient way to calculate for a given g^x and given n in a >group G with order q, the value: g^{x^n}? Although other posters have been trying to answer you question, I find it so unclear that I don't know where to start. Presumably g is in G and n is a postive integer (although, reading what you write exactly, you seem to be saying that n is in G). But what about x? Is that supposed to be an element of G, or is it an integer too? And what has order q? Is it G, or g^x ? Derek Holt. === Subject: Re: effective Method to calculate n-th power Hi > Presumably g is in G and n is a postive integer (although, reading what > you write exactly, you seem to be saying that n is in G). Yes g is in G and n is only just a positive integer, which usually never exceeds the value 200 or so. > But what about x? Is that supposed to be an element of G, > or is it an integer too? It is an integer too, but cause g is in G, the value g^x is in G either. > And what has order q? Is it G, or g^x ? G has order q. I hope I could clear up some things. -Zsuzsi === Subject: Re: effective Method to calculate n-th power > is there any efficient way to calculate for a given g^x and given n in a > group G with order q, the value: g^{x^n}? > Use o(a^k) = o(a)/gcf(k,o(a)) === Subject: Re: effective Method to calculate n-th power >>is there any efficient way to calculate for a given g^x and given n in a >>group G with order q, the value: g^{x^n}? >Use > o(a^k) = o(a)/gcf(k,o(a)) What do you meant with this? === Subject: Re: effective Method to calculate n-th power is there any efficient way to calculate for a given g^x and given n in a >>group G with order q, the value: g^{x^n}? Use > o(a^k) = o(a)/gcf(k,o(a)) > What do you meant with this? > o(a) is the order of a. gcf(n,m) is the greatest common factor of the integers n and m. === Subject: Re: effective Method to calculate n-th power is there any efficient way to calculate for a given g^x and given n in a > group G with order q, the value: g^{x^n}? Zsuzsanne Are you sure that you stated this correctly?? === Subject: Re: effective Method to calculate n-th power > >>is there any efficient way to calculate for a given g^x and given n in a >>group G with order q, the value: g^{x^n}? >>Zsuzsanne >Are you sure that you stated this correctly?? I hope so. Can you tell me what am I missing? Zsuzsanna === Subject: Re: effective Method to calculate n-th power is there any efficient way to calculate for a given g^x and given n in a >>group G with order q, the value: g^{x^n}? Are you sure that you stated this correctly?? > I hope so. Can you tell me what am I missing? > If q is the order of the G, then the value of g^x^n is g^r where r = remainder of x^n upon division by q. You need to clarify that x is an integer and n a positive integer. You can't compute g^x^n, at best you can only 'simplify' it and be careful when x is negative. If q is the order of g^x, then the order of g^x^n can be calculated as I hinted in other post. That is different than the value of g^x^n which, knowing the order, can be 'simplified'. Have I clarified how your question is hard to interpret and ambiguous of intent? === Subject: Re: effective Method to calculate n-th power > If q is the order of g^x, then the order of g^x^n can be calculated > as I hinted in other post. That is different than the value of g^x^n > which, knowing the order, can be 'simplified'. How can you compute the order of g^x^n starting from the order of g^x alone?? E.g. consider the multiplicative group Z_{17}^* of order 16. Assume that the other given data is g^x=4 and n=3. Now we could have A) g=2,x=2, so the answer would be g^x^n=2^8=1 (mod 17), an element of order 1, or B) g=4,x=1, so the answer would be g^x^n=4^1=4 (mod 17), an element of order 4. Do you now see that we are given insufficient information? Jyrki === Subject: Re: effective Method to calculate n-th power as I hinted in other post. That is different than the value of g^x^n > which, knowing the order, can be 'simplified'. How can you compute the order of g^x^n starting from the > order of g^x alone?? > g^x^n = (g^x)^x^(n-1) o(a^k) = o(a)/(k,o(a)) > E.g. consider the multiplicative group Z_{17}^* of order 16. > Assume that the other given data is g^x=4 and n=3. > Now we could have > A) g=2,x=2, so the answer would be g^x^n=2^8=1 (mod 17), > an element of order 1, or > B) g=4,x=1, so the answer would be g^x^n=4^1=4 (mod 17), > an element of order 4. Do you now see that we are given insufficient information? No,Iofternavoideyestrain,bynotreadingequationswithoutspaces. === Subject: Re: effective Method to calculate n-th power >>How can you compute the order of g^x^n starting from the >>order of g^x alone?? >g^x^n = (g^x)^x^(n-1) > o(a^k) = o(a)/(k,o(a)) > So the smallest monetary unit didn't drop, yet. How do you compute (x^(n-1),o(a)), when you don't know what x is? Jyrki === Subject: Re: effective Method to calculate n-th power >How can you compute the order of g^x^n starting from the >>order of g^x alone?? g^x^n = (g^x)^x^(n-1) > o(a^k) = o(a)/(k,o(a)) So the smallest monetary unit didn't drop, yet. How do you > compute (x^(n-1),o(a)), when you don't know what x is? > How do you compute (-b +- sqr(b^2 - 4ac))/2a when you don't know what a,b and c are? === Subject: Re: effective Method to calculate n-th power > is there any efficient way to calculate for a given g^x and given n in a > group G with order q, the value: g^{x^n}? I don't think the question is well-defined. If you are truly given only g^x (but not g and not x) and n then there could be other items h and y such that g^x = h^y but g^{x^n} doesn't equal h^{y^n}. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: determine the irreducible polynomial Determine the irreducible polynomial for x = sqrt(3) + sqrt(5) over each of the following fields. (1) Q (rationals); (2) Q(sqrt(10)); I think the answers are both x^4-16x^2+4. But I don't know how to prove it === Subject: Re: determine the irreducible polynomial > Determine the irreducible polynomial for x = sqrt(3) + sqrt(5) > over each of the following fields. > (1) Q (rationals); > (2) Q(sqrt(10)); I think the answers are both x^4-16x^2+4. > But I don't know how to prove it > I'll show you the 1st one, even though it requires only high school algebra. x = sqrt(3) + sqrt(5) =>x - sqrt(3) = sqrt(5) =>(x - sqrt(3))^2 = (sqrt(5))^2 =>x^2 - 2sqrt(3)x +3 =5 => x^2 - 2sqrt(3)x = 2 =>x^2 - 2 = 2sqrt(3)x => (x^2 - 2)^2= (2sqrt(3)x)^2 => x^4 - 4x^2 + 4 = 12x^2 => x^4 - 16x^2 +4 =0. Now try the next part. === Subject: Re: determine the irreducible polynomial > Determine the irreducible polynomial for x = sqrt(3) + sqrt(5) >> over each of the following fields. >> (1) Q (rationals); >> (2) Q(sqrt(10)); >> I think the answers are both x^4-16x^2+4. >> But I don't know how to prove it > I'll show you the 1st one, even though it requires only high school > algebra. x = sqrt(3) + sqrt(5) =>x - sqrt(3) = sqrt(5) =>(x - sqrt(3))^2 = > (sqrt(5))^2 =>x^2 - 2sqrt(3)x +3 =5 => x^2 - 2sqrt(3)x = 2 =>x^2 - 2 = > 2sqrt(3)x => (x^2 - 2)^2= (2sqrt(3)x)^2 => x^4 - 4x^2 + 4 = 12x^2 => x^4 - > 16x^2 +4 =0. > Now try the next part. > that does not prove that the polynomial is irreducible. perhaps a proof that Q(sqrt(3),sqrt(5)) = Q(sqrt(3) + sqrt(5)) will help. === Subject: Re: determine the irreducible polynomial > over each of the following fields. >> (1) Q (rationals); >> (2) Q(sqrt(10)); >> I think the answers are both x^4-16x^2+4. >> But I don't know how to prove it > I'll show you the 1st one, even though it requires > only high school algebra. x = sqrt(3) + sqrt(5) =>x - sqrt(3) = sqrt(5) =>(x - sqrt(3))^2 = > (sqrt(5))^2 =>x^2 - 2sqrt(3)x +3 =5 => x^2 - 2sqrt(3)x = 2 =>x^2 - 2 = > 2sqrt(3)x => (x^2 - 2)^2= (2sqrt(3)x)^2 => x^4 - 4x^2 + 4 = 12x^2 => x^4 - > 16x^2 +4 =0. > Now try the next part. > that does not prove that the polynomial is irreducible. A little Galois theory should help here. If sqrt(3) + sqrt(5) is a root of a polynomial p(x) with integer coefficients, then p(x) will also have -sqrt(3) + sqrt(5), sqrt(3) - sqrt(5), and -sqrt(3) - sqrt(5) as roots. (Use the conjugate operation.) > perhaps a proof that Q(sqrt(3),sqrt(5)) = Q(sqrt(3) + sqrt(5)) > will help. Let Q be the set of rational numbers, Q1 = Q(sqrt(3)), Q2 = Q1(sqrt(5), and Q3 = Q(sqrt(3) + sqrt(5)). Clearly Q3 is a subset of Q2. The degree of the extension of Q1 over Q is 2 (since there is a polynomial with integral coefficients with sqrt(3) as a root), the degree of Q2 over Q1 is 2 (the previous argument shows that the degree is either 2 or 1, and it's easy to show it isn't 1, since sqrt(5) is not in Q1). The degree of Q2 over Q is thus 4. The degree of Q3 over Q is a factor of 4 (I think this follows ...), and since it isn't 1 or 2, it must be 4. Thus Q2 has degree 4 as well. The degree of extension fields behaves like the dimension of a vector space. (It actually is, when you get down to it ...) Thus Q3 = Q2, as claimed. --- Christopher Heckman === Subject: Re: determine the irreducible polynomial > over each of the following fields. >> (1) Q (rationals); >> (2) Q(sqrt(10)); >> I think the answers are both x^4-16x^2+4. >> But I don't know how to prove it > I'll show you the 1st one, even though it requires > only high school algebra. x = sqrt(3) + sqrt(5) =>x - sqrt(3) = sqrt(5) =>(x - sqrt(3))^2 = > (sqrt(5))^2 =>x^2 - 2sqrt(3)x +3 =5 => x^2 - 2sqrt(3)x = 2 =>x^2 - 2 = > 2sqrt(3)x => (x^2 - 2)^2= (2sqrt(3)x)^2 => x^4 - 4x^2 + 4 = 12x^2 => x^4 - > 16x^2 +4 =0. > Now try the next part. > that does not prove that the polynomial is irreducible. A little Galois theory should help here. If sqrt(3) + sqrt(5) is a root > of a polynomial p(x) with integer coefficients, then p(x) will also > have > -sqrt(3) + sqrt(5), > sqrt(3) - sqrt(5), and > -sqrt(3) - sqrt(5) as roots. > (Use the conjugate operation.) Right but I think you need to know that Q(sqrt(3) + sqrt(5)) = Q(sqrt(3), sqrt(5)) in order to easily conclude this. The conjugates of an algebraic integer are the other roots of its minimal polynomial and if Q(sqrt(3) + sqrt(5)) = Q(sqrt(2), sqrt(5)) then the conjugates are those listed since conjugates of quadratic fields are classified by the quadratic formula (square roots being the simplest case). > perhaps a proof that Q(sqrt(3),sqrt(5)) = Q(sqrt(3) + sqrt(5)) > will help. Let Q be the set of rational numbers, > Q1 = Q(sqrt(3)), Q2 = Q1(sqrt(5), and > Q3 = Q(sqrt(3) + sqrt(5)). Clearly Q3 is a subset of Q2. The degree of the extension of Q1 over Q is 2 (since there is a > polynomial with integral coefficients with sqrt(3) as a root), the > degree of Q2 over Q1 is 2 (the previous argument shows that the degree > is either 2 or 1, and it's easy to show it isn't 1, since sqrt(5) is > not in Q1). The degree of Q2 over Q is thus 4. Agreed. So you just have to show that sqrt(5) is not contained in Q1. We know that elements of Q1 can be written in the form a sqrt(3) + b where a and b are rational. Clearly a sqrt(3) + b = sqrt(5) implies 3a^2 + b^2 + 2ab sqrt(3) = 5. We cannot have both a and b nonzero since then the equation would imply that sqrt(3) is rational. We cannot have a = 0 since that would imply that sqrt(5) is rational. The remaining possibility is that a sqrt(3) = sqrt(5) and thus a^2 3 = 5. Suppose a = m/n is in lowest terms. Then m^2 3 = 5 n^2, which implies that m^2 is divisible by 5^2 (since 5 is prime), and also that n^2 is divisible by 3^2 (since 3 is prime). Thus the prime factorization of m^2 3 has at least 2 factors of 5 and thus 5 n^2 must likewise have at least two factors of 5. The 5 in 5 n^2 contributes just one of the factors, so n^2 must contain another. Since n^2 is a square, it must in fact contain 2 factors of 5 and thus n is divisible by 5. Hence m and n are both divisible by 5, which contradicts a = m/n being in lowest terms. In conclusion, sqrt(5) is not contained in Q(sqrt(3)). This argument seems to work in general: if p and q are distinct positive primes then sqrt(p) is not contained in Q(sqrt(q)). Per === Subject: Re: determine the irreducible polynomial > over each of the following fields. >> (1) Q (rationals); >> (2) Q(sqrt(10)); >> I think the answers are both x^4-16x^2+4. >> But I don't know how to prove it > I'll show you the 1st one, even though it requires only high school > algebra. x = sqrt(3) + sqrt(5) =>x - sqrt(3) = sqrt(5) =>(x - sqrt(3))^2 = > (sqrt(5))^2 =>x^2 - 2sqrt(3)x +3 =5 => x^2 - 2sqrt(3)x = 2 =>x^2 - 2 = > 2sqrt(3)x => (x^2 - 2)^2= (2sqrt(3)x)^2 => x^4 - 4x^2 + 4 = 12x^2 => x^4 - > 16x^2 +4 =0. > Now try the next part. > that does not prove that the polynomial is irreducible. Indeed. Here is my very low-tech attempt at a proof of its irreducibility. If f = x^4 - 16x^2 + 4 were to factor then there would just be two possible factorizations signatures, namely (1,3) and (2,2). In the former case it has a rational root, so use the rational roots theorem to rule this case out. In the (2,2) case we have a factorization of the form (x^2 + ax + b)(x^2 + cx + d) = x^4 + (a+c)x^3 + (b+d+ac)x^2 + (ad+bc)x + bd. If we equate coefficients of f and its factorization into quadratics, we get the equations a+c = 0, b+d+ac = -16, ad+bc = 0, bd = 4. Since the constant term of f is 4 we must either have (b,d) = (2,2), (b,d) = (1,4) or (b,d) = (4,1). (The two latter cases are symmetrical.) We have the coefficient equations a+c = 0 and b+d+ac = -16 and together they imply -a^2 = -16-b-d. In the first case b+d = 4 and so the equation is -a^2 = -12. In the second case b+d = 5, so the equation is -a^2 = -11. Neither 11 nor 12 have integer square roots so this is not possible. I hope I didn't make any algebra errors. Per === Subject: Re: determine the irreducible polynomial 0 and b+d+ac = -16 and together they imply -a^2 = -16-b-d. In the first > case b+d = 4 and so the equation is -a^2 = -12. In the second case b+d > = 5, so the equation is -a^2 = -11. Neither 11 nor 12 have integer > square roots so this is not possible. I hope I didn't make any algebra errors. Doh, I most certainly did. The two equations at the end should have been a^2 = 20 and a^2 = 21. In any case the same reasoning still applies since 20 and 21 don't have integer square roots. Per === Subject: Re: determine the irreducible polynomial > >Determine the irreducible polynomial for x = sqrt(3) + sqrt(5) >over each of the following fields. >(1) Q (rationals); >(2) Q(sqrt(10)); I think the answers are both x^4-16x^2+4. >But I don't know how to prove it >I'll show you the 1st one, even though it requires only high school >>algebra. >>x = sqrt(3) + sqrt(5) =>x - sqrt(3) = sqrt(5) =>(x - sqrt(3))^2 = >>(sqrt(5))^2 =>x^2 - 2sqrt(3)x +3 =5 => x^2 - 2sqrt(3)x = 2 =>x^2 - 2 = >>2sqrt(3)x => (x^2 - 2)^2= (2sqrt(3)x)^2 => x^4 - 4x^2 + 4 = 12x^2 => x^4 - >>16x^2 +4 =0. >>Now try the next part. > I think Li had already proved that his answer x^4 - 16x^2 + 4 has zero sqtr(3) + sqrt(5). >that does not prove that the polynomial is irreducible. > perhaps a proof that Q(sqrt(3),sqrt(5)) = Q(sqrt(3) + sqrt(5)) will help. > Yes, good idea, use sqrt(15) somewhere, but then we still need Q(sqrt(3)) < Q(sqrt(3), sqrt(5)). For the next part, we even need Q(sqrt(10)) < Q(sqrt(2), sqrt(5)) < Q(sqrt(2), sqrt(3), sqrt(5)) or something. === Subject: Simulating biased coin having only a fair coin How could you simulate a biased coin landing heads with probability p=1/3 if you only had a fair coin? How could you simulate fair coin tossing if you only had available a coin with unknown bias p stricly between 0 and 1? Hint: use the conditional probability. Truly Yours, Simon Dexter === Subject: Re: Simulating biased coin having only a fair coin >How could you simulate fair coin >tossing if you only had available a coin with unknown bias p stricly >between 0 and 1? Hint: use the conditional probability. Is it a question or a challenge? In any case there is a handwritten paper on this by E W Dijkstra somewhere on www.cs.utexas.edu/users/EWD/welcome.html Soeren (abc3@nameplanet.com) === Subject: Re: Simulating biased coin having only a fair coin AS for the first... Write the bias to be simulated as a binary decimal fraction. Let Heads represent 1 and Tails represent 0. Flip the unbiased coin multiple times to create a binary string. Stop when the binary string so created is greater than or less than the bias. === Subject: Re: Simulating biased coin having only a fair coin >How could you simulate a biased coin landing heads with probability >p=1/3 if you only had a fair coin? How could you simulate fair coin >tossing if you only had available a coin with unknown bias p stricly >between 0 and 1? Hint: use the conditional probability. There is essentially one most efficient way of simulating a discrete distribution with a fair coin. This does not mean that there are not other ways of doing it. This method is well known. As for simulating the results of fair coins by using results of independent tosses of a coin with the same p, there are again many methods, and the more one tries to simulate at a time, the easier it is. There is a method which will maintain full asymptotic efficieny, but it is clumsy. -- 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: Simulating biased coin having only a fair coin How could you simulate a biased coin landing heads with probability > p=1/3 if you only had a fair coin? How could you simulate fair coin > tossing if you only had available a coin with unknown bias p stricly > between 0 and 1? Hint: use the conditional probability. > Truly Yours, Simon Dexter > For the 1st part how about tossing the fair coin twice. If you get HH then call it H. If it comes up TT then call it T. If HT comes up then call it T. If TH comes up ignore this toss. Then prob (H)= 1/3. ????? Supersedes: === Subject: Invariant Galilean Transformations (FAQ) On All Laws Summary: All laws/equations are Galilean invariant when expressed in the generalized cartesian coordinates demanded by basic analytic geometry, vector algebra, and measurement theory. Originator: faqserv@penguin-lust.mit.edu Disclaimer: approval for *.answers is based on form, not content. Opponents of the content should first actually find out what it is, then think, then request/submit-to arbitration by the appropriate neutral mathematics authorities. Flaming the hard- working, selfless, *.answers moderators evidences ignorance and despicable netiquette. Archive-Name: physics-faq/criticism/galilean-invariance Version: 0.04.03 Posting-frequency: 15 days Invariant Galilean Transformations (FAQ) On All Laws (c) Eleaticus/Oren C. Webster Thnktank@concentric.net An obvious typo or two corrected. The Brittanica section revised to less 'pussy-footing' and to more directly anticipate the elementary measurement theory and basic analytic geometry that is applied to the transformation concept. ------------------------------ === Subject: 1. Purpose The purpose of this document is to provide the student of Physics, especially Relativity and Electromagnetism, the most basic princ- iples and logic with which to evaluate the historic justification of Relativity Theory as a necessary alternative to the classical physics of Newton and Galileo. We will prove that all laws are invariant under the Galilean transformation, rather than some being non-invariant, after we show you what that means. We shall also show that another primal requirement that SR exist is nonsense: Michelson-Morley and Kennedy-Thorndike do indeed fit Galilean (c+v) physics. ------------------------------ === Subject: 2. Table of Contents 1. Foreword and Intent 2. Table of Contents 3. The Principle of Relativity 4. The Encyclopedia Brittanica Incompetency. 5. Transformations on Generalized Coordinate Laws 6. The data scale degradation absurdity. 7. The Crackpots' Version of the Transforms. 8. What does sci.math have to say about x0'=x0-vt? 9. But Doesn't x.c'=x.c? 10. But Isn't (x'-x.c')=(x-x.c) Actually Two Transformations? 11. But Doesn't (x'-x.c+vt) Prove The Transformation Time Dependent? 12. But Isn't (x'-x.c')=(x-x.c) a Tautology? 13. But Isn't (x'-x.c')=(x-x.c) Almost the Definition of a Linear Transform? 14. But The Transform Won't Work On Time Dependent Equations? 15. But The Transform Won't Work On Wave Equations? 16. But Maxwell's Equations Aren't Galilean Invariant? 17. First and Second Derivative differential equations. ------------------------------ === Subject: 3. The Principle of Relativity and Transformation If a law is different over there than it is here, it is not one law, but at least two, and leaves us in doubt about any third location. This is the Principle of Relativity: a natural law must be the same relative to any location at which a given event may be perceived or measured, and whether or not the observer is moving. The idea of location translates to a coordinate system, largely because any object in motion could be considered as having a coordinate system origin moving with it. If you perceive me moving relative to you - who have your own coordinate system - will your measurements of my position and velocity fit the same laws my own, different measurements fit? If a law has the same form in both cases it is called covariant. If it is identical in form, var- ables, and output values, it is called invariant. What we're asking is that if the x-coordinate, x, on one coordinate axis works in an equation, does the coordinate, x', on some other, parallel axis work? Speaking in terms of the axis on which x is the coordinate, x' is the 'transformed' coordinate. The situation is complicated because we're talking about coordinates - locations - but in most mean- ingful laws/equations, it is lengths/distances (and time intervals) the equations are about, and x coord- inates that represent good, ratio scale measures of distances are only interval scale measures on the x' axis. [See Table of Contents for discussion of scales.] So, if we have an x-coordinate in one system, then we can call the x' value that corresponds to the same point/location the transform of x. In particular, the Principle of Relativity is embodied in the form of the Galilean transformation, which relates the original x, y, z, t to x', y', z', t' by the transform equations x'=x-vt, y'=y, z'=z, t'=t in the simplified case where attention is focused only on transforming the x-axis, and not y and z. In the case of Special Relativity, the x' transform is the same except that x' is then divided by sqrt(1-(v/c)^2), and t'=(t-xv/cc)/sqrt(1-(v/c)^2). In either case, v is the relative velocity of the coordinate systems; if there is already a v in the equations being trans- formed use u or some other variable name. ------------------------------ === Subject: 4. The Encyclopedia Brittanica Incompetency. One example of the traditional fallacious idea that an equation is not invariant under the galilean transformation comes from the Encyclopedia Brittanica: Before Einstein's special theory of relativity was published in 1905, it was usually assumed that the time coordinates measured in all inertial frames were identical and equal to an 'absolute time'. Thus, t = t'. (97) The position coordinates x and x' were then assumed to be related by x' = x - vt. (98) The two formulas (97) and (98) are called a Galilean transformation. The laws of nonrelativ- istic mechanics take the same form in all frames related by Galilean transformations. This is the restricted, or Galilean, principle of relativity. The position of a light wave front speeding from the origin at time zero should satisfy x^2 - (ct)^2 = 0 (99) in the frame (t,x) and (x')^2 - (ct')^2 = 0 (100) in the frame (t',x'). Formula (100) does not transform into formula (99) using the transform- ations (97) and (98), however. ................................................. Besides the trivially correct statement of what the Galilean 'transform' equations are, there is exactly one thing they got right. I. Eq-100 is indeed the correct basis for discussing the question of invariance, given that eq-99 is the correct 'stationary' (observer S) equation. [Let observer M be the 'moving'system observer.] In particular, eq-100 is of exactly the same form [the square of argument one minus the square of argument two equals zero (argument three).] II. It is nonsense to say eq-99 should be derivable from eq-100; for one thing, the transforms are TO x' and t' from x and t, not the other way around, and the idea that either observer's equation should contain within itself the terms to simplify or rearrange to get to the other is ridiculous. As the transform equations say, the relationship of t', x' to t, x is based on the relative velocity between the two systems, but neither the original (eq-99) equation nor the M observer equation is about a relationship between coordinate systems or observers. One might as well expect the two equations to contain banana export/import data; there is no relevancy. The 'transform' equations are the relationships between x' and x, t' and t and have nothing to do with what one equation or the other ought to 'say'. The equations' content is the rate at which light emitted along the x-axes moves. III. Most remarkable, the True Believer SR crackpots who most despise the consequences of measurement theory (demonstrable fact) contained in this document are those who want to argue against our saying the Britt- anica got eq-100 right; They insist that the correct equation is derived directly from x'=x-vt and t'=t. Solve for x=x'+vt and replace t with t', then substitute the result in eq-99: (x'+vt')^2 - (ct')^2 = 0. Besides the fact that this results in an equation with arguments exactly equal to eq-99, they will insist the transform is not invariant. IV. A major justification they have for their idea of the correct M system equation on which to base the the discussion of invariance, is that the variables are M system variables, never mind the fact that the arguments are S system values. That argument of theirs is arrant nonsense. The velocity v that S sees for the M system relative to herself is the negative of what the M system sees for the S system relative to himself. In other words, x'+vt' is a mixed frame expression and it is x'+(-v)t' that would be strictly M frame notation, and that equation is far off base. [Work it out for yourself, but make sure you try out an S frame negative v so as not to mislead yourself.] V. In I. we said: given that eq-99 is the correct 'stationary' equation. Let's look at it closely: x^2 - (ct)^2 = 0 (99) This whole matter is supposed to be about coordinate transforms. Is that what t is, just a coordinate? No. It isn't, in general. Suppose you and I are both modelling the same light event and you are using EST and I'm using PST. 'Just a time coordinate' is just a clock reading amd your t clock reading says the light has been moving three hours longer than my clock reading says. Well, that's what the idea that t is a coordinate means. Eq-99 works if and only if t is a time interval, and in particular the elapsed time since the light was emitted. Thus, that equation works only if we understand just what t is, an elapsed time, with emissioon at t=0. However, we don't have to 'understand' anything if we use a more intelligent and insightful form of the equation: (x)^2 - [ c(t-t.e) ]^2 = 0, where t.e is anyone's clock reading at the time of light emission, and t is any subsequent time on the same clock. Similarly, x is not just a coordinate, but a distance since emission. (x-x.e)^2 - [ c(t-t.e) ]^2 = 0 (99a) VI. In the spirit of 'there is exactly one thing they got right', the correct M system version of eq-99a is eq-100a: (x'-x.e')^2 - [ c(t'-t.e') ]^2 = 0 (100a) Every observer in the universe can derive their eq-100a from eq-99a and vice versa, not to mention to and from every other observer's eq-99a. Now, THAT's invariance. [You do realize that every eq-100a reduces to eq-99a, when you back substitute from the transforms, right? t.e'=t.e, x.e'=x.e-vt.] ------------------------------ === Subject: 5. Transformations on Generalized Coordinate Laws The traditional Gallilean transform is correct: t' = t x' = x - vt. But remember this: a transform of x doesn't effect just some values of x, but all of them, whether they are in the formula or not. This is important if you want to do things right. The crackpot position is strongly against this sci.math verified position, and the apparently standard coordinate pseudo-transformation they suggest is perhaps the result. {See Table of Contents.] Let's use a simple equation: x^2 + y^2 = r^2, which is the formula for a circle with radius r, centered at a location where x=0. But what if the circle center isn't at x=0? Well, we'd want to use the form analytic geometry, vector algebra, and elementary measurement theory tells us to use, a form where we make explicit just where the circle center is, even if it is at x=x0=0: (x-x0)^2 + (y-y0)^2 = r^2. The circle center coordinate, x0, is an x-axis coordinate, just like all the x-values of points on the circle. So, in proper generalized cartesian coordinate forms of laws/equations we want to transform every occurence of x and x0 - by whatever name we call it: x.c, x_e, whatever. So, what is the transformed version of (x-x0)? Why, (x'-x0'); both x and x0 are x-coordinates, and every So, what is the value of (x'-x0') in terms of the original x data? is also true for x0'=x0-vt: (x'-x0')=[ (x-vt)-(x0-vt) ]=(x-x0). In other words, when we use the generalized coordinate form specified by analytic geometry, we find that the value of (x'-x0') does not depend on either time or velocity in any way, shape, form, or fashion. Similarly for (y-y0). We can treat time the same way if necessary: (t-t0). The above is a proof that any equation in x,y,z,t is invariant under the galilean transforms. Just use the generalized coordinate form, with (x-x0)/etc, in the transformation process, not the incompetently selected privileged form, with just x/etc. [The form is privileged because it assumes the circle center, point of emission, whatever, is at the origin of the axes instead at some less convenient point. After transform the coordinate(s) of the circle center/origin are also changed but the privileged form doesn't make this explicit and screws up the calculations, which should be based on (x'-x0') but are calculated as (x'-0).] The value of (x'-x0') is the same as (x-x0). That makes sense. Draw a circle on a piece of paper, maybe to the right side of the paper. On a transparent sheet, draw x and y coordinate axes, plus x to the right, plus y at the top. Place this axis sheet so the y-axis is at the left side of the circle sheet. Now answer two questions after noting the x-coordinate of the circle center and then moving the axis sheet to the right: (a) did the circle change in any way because you moved the axis sheet (ie because you transformed the coordin- nate axis)? (b) did the coordinate of the circle center change? The circle didn't change [although SR will say it did]; that means that (x'-x0') does indeed equal (x-x0). The coordinate of the circle center did change, and it changed at the same rate (-vt) as did every point on the circle. That means that x0'<>x0, and the fact the circle center didn't change wrt the circle, means that the relationship of x0' with x0 is the same as that of any x' on the circle with the corresponding x: x'=x-vt; x0'=x0-vt. This is to prepare you for the True Believer crackpots that say 'constant' coordinates can't be transformed; some even say they aren't coordinates. These crackpots include some that brag about how they were childhood geniuses, btw. QED: The galilean transformation for any law on generalized Cartesian coordinates is invariant under the Galilean transform. The use of the privileged form explains HOW the transformed equation can be messed up, the next Subject explains what the screwed up effect of the transform is, and how use of the generalized form corrects the screwup. ------------------------------ === Subject: 6. The data scale degradation absurdity. The SR transforms and the Galilean transforms both convert good, ratio scale data to inferior interval scale data. The effect is corrected, allowed for, when the transforms are conducted on the generalized coordinate forms specified by analytic geometry and vector algebra. Both sets of transforms are 'translations' - lateral movements of an axis, increasing over time in these cases - but with the SR transform also involving a rescaling. It is the translation term, -vt in the x transform to x', and -xv/cc in the t transform to t', that degrades the ratio scale data to interval scale data. In general, rescaling does not effect scale quality in the size-of-units sense we have here. SR likes to consider its transforms just rotations, however - in spite of the fact Einstein correctly said they were 'translations' (movements) - and in the case of 'good' rotations, ratio scale data quality is indeed preserved, but SR violates the conditions of good ro- tations; they are not rigid rotations and they don't appropriately rescale all the axes that must be rescaled to preserve compatibility. The proof is in the pudding, and the pudding is the combination of simple tests of the transformations. We can tell if the transformed data are ratio scale or interval. Ratio scale data are like absolute Kelvin. A measure- ment of zero means there is zero quantity of the stuff being measured. Ratio scale data support add- ition, subtraction, multiplication, and division. The test of a ratio scale is that if one measure looks like twice as much as another, the stuff being measured is actually twice as much. With absolute Kelvin, 100 degrees really is twice the heat as 50 degrees. 200 degrees really is twice as much as 100. Interval scale data are like relative Celsius, which is why your science teacher wouldn't let you use it in gas law problems. There is only one mathematical operation interval scales support, and that has to be between two measures on the same scale: subtraction. 100 degrees relative (household) Celsius is not twice as much as 50; we have to convert the data to absolute Kelvin to tell us what the real ratio of temperatures is. However, whether we use absolute Kelvin or relative Celsius, the difference in the two temperature readings is the same: 50 degrees. Thus, if we know the real quantities of the 'stuff' being measured, we can tell if two measures are on a ratio scale by seeing if the ratio of the two measures is the same as the ratio of the known quant- ities. If a scale passes the ratio test, the interval scale test is automatically a pass. If the scale fails the ratio test, the interval scale test becomes the next in line. It isn't just the bare differences on an interval scale that provides the test, however. Differences in two interval scale measures are ratio scale, so it is ratios of two differences that tell the tale. Let's do some testing, and remember as we do that our concern is for whether or not the data are messed up, not with 'reasons', excuses, or avoidance. ------------------------------------------------------ Are we going to take a transformed length (difference) and see whether that length fits ratio or interval scale definitions? Of course, not. Interval scale data are ratio after one measure is subtracted from another. That is the major reason the SR transforms can be used in science. Let there be three rods, A, B, C, of length 10, 20, 40, respectively. These lengths are on a known ratio scale, our original x-axis, with one end of each rod at the origin, where x=0, and the other end at the coordinate that tells us the correct lengths. Note that these x-values are ratio scale only because one end of each rod is at x=0. That may remind you of the correct way to use a ruler or yard/meter-stick: put the zero end at one end of the thing you are measuring. Put the 1.00 mark there instead of the zero, and you have interval scale measures. Let A,B,C, be 10, 20, 40. Let a,b,c be x' at v=.5, t=10. x'=x-vt. A B C a b c ---------------- -------------------- 10 20 40 5 15 35 ---------------- -------------------- B/A = 2 b/a = 3 C/A = 4 c/a = 7 C/B = 2 c/b = 2.333 Obviously, the transformed values are no longer ratio scale. The effect is less on the greater values. C-A = 10 b-a = 10 C-A = 30 c-a = 30 C-B = 20 c-b = 20 Obviously, the transformed values are now interval scale. This will hold true for any value of time or velocity. (C-A)/(B-A) = 3 (c-a)/(b-a) = 3 (C-B)/(B-A) = 2 (c-b)/(b-a) = 2 Obviously, the ratios of the differences are ratio scale, being identical to the ratios of the corresponding original - ratio scale - differences. The main difference between these results and the SR results is that the differences do not correspond so neatly to the original, ratio scale, differences. This is due only to the rescaling by 1/sqrt(1-(v/c)^2). The ratios of the differences on the transformed values do correspond neatly and exactly to the ratio scale results. Using the generalized coordinate form, such as (x-x0), the transform produces an interval scale x' and an interval scale x0'. That gives us a ratio scale (x'-x0'), just like - and equal to - (x-x0). ------------------------------ === Subject: 7. The Crackpots' Version of the Transforms. It has become apparent - whether misleading or not - that the crackpot responses to the obvious derive from a common source, whether it be bandwagoning or their SR instructors. Below, in the sci.math subject, we see that all sci.math respondents agree with the basic controversial position of this faq: every coordinate is transformed, whether a supposed constant or not. Think about it, the generalized coordinate of a circle center, x0, applies to infinities upon infinities of circle locations (given y and z, too); it is a constant only for a given circle, and even then only on a given coordinate axis. And even variables are often held 'constant' during either integration or differentiation. The utility of a variable is that you can discuss all possible particular values without having to single out just one. That utility does not make particular - singled out - values on the variable's axis not values of the variable just because they have become named values. In any case, all that is preamble to the incompetent idea they have proposed for a transform of coordinates. It is based on the idea that the circle center, point of emission, whatever, has coordinates that cannot be transformed. Let there be an equation, say (x)^2 - (ict)^2 = 0. What is the transformed version of that equation? Answer: (x')^2 - (ict')^2 = 0. That's the one thing the Brittanica got right. Note that the leading crackpot just criticized this faq for presuming to correct the Britt- anica, but it then and before poses the incompetent pseudo- transform we analyze here in this section. x to x' and t to t' are obviously coordinate transforms; the x and t coordinates have been replaced by the coord- inates in the primed system. A tranform of an equation from one coordinate system to another is NOT a substitution of the/a definition of x for itself; that is not a coordinate transformation. The most that can said for such a substitution is that it is a change of variable. But the crackpots are calling this a coordinate trans- form of the original equation: (x'+vt)^2 - (ict')^2 = 0. It is not a coordinate transform, of course, except accidentally. (x'+vt) is not the primed system coordinate, it is another form/expression of x. They get that substitution by solving x'=x-vt for x; x=x'+vt. So, by incompetent misnomer, they accomplish what they have been railing against all along. It has been the generalized coordinate form in question all this time: (x-x0)^2 - (ict)^2 = 0. Here they substitute for x instead of transforming to the primed frame: (x'+vt-x0)^2 - (ict')^2. ----- ^ | ^ | It is still x ^ but see what they have accomplished by their mis/malfeasance: [x'+vt-x0]=[x'+(vt-x0)]=[x'-(x0-vt)]. =[x'-x0'] The crackpots have been bragging about how you don't have to transform the circle center's coordinate to transform the circle center's coordinate. Bragging that what they were doing was not what they said they were doing. This does give us insight as to some of the crackpot variations on their x0'<>x0-vt theme, which in all the variations will be discussed in later sections.. They are used to seeing the mixed coordinate form, (x'+vt-x0) without realizing what it respresented, so - accompanied with a lack of understanding of the term 'dependent' - they are used to seeing just the one vt term, and not the one hidden in the defi- nition of x' and are used to imagining it makes the whole expression time dependent and thus not invariant. About which, let x=10, let, x0=20, v=10, and t variously 10 and 23: (x-x0)=-10. Using their (x'+vt-x0): For t=10, we have (x'+vt-x0) = [ (10-10*10) + (10*10) - (20) ] = -90 + 100 - 20 = -10 = (x-x0) For t=23, we have (x'+vt-x0) = [ (10-10*23) + (10*23) - (20) ] = -220 + 230 - 20 = -10 = (x-x0) The result depends in no way on the value of time; we showed the obvious for a couple of instances of t just so you can see that the crackpots not only do not understand the obvious logic of the algebra { (x'-x0')=[ (-vt)-(x0-vt) ]=(x-x0) } - which shows that the transform has no possible time term effect - but they don't understand even a simple arithmetic demonstration of the facts. Oh. Their (x'+vt-x0) or (x'+vt'-x0) reduces the same way since t'=t: (x-vt+vt-x0)=(x-x0). Their process, which says (x'+vt') is the transform of x, says that (x'+vt') is the moving system location of x, but it can't be because x is moving further in the negative direction from the moving viewpoint. That formula will only work out with v<0 which is indeed the velocity the primed system sees the other moving at. However, that formula cannot be derived from x'=x-vt, the formula for transformation of the coordinates from the unprimed to the primed, ------------------------------ === Subject: 8. What does sci.math have to say about x0'=x0-vt? The crackpots' positions/arguments were put to sci.math in such a way that at least two or three who posted re- sponses thought it was your faq-er who was on the idiot's side of the questions. Their responses: ---------------------------------------------------------- I. x0' = x0. In other words: x0' <> x0-vt, or constant values on the x-axis are not subject to the transform. No. x0' = x0 - vt. Well, if you want, you could define constant values on the x-axis, but in the context of the question that is not relevant. The relevant fact is that if the unprimed observer holds an object at point x0, then the primed observer assigns to that object a coordinate x0' which is numerically related to x0 by x0'= x0 -vt. What does this mean? The line x=x0 will give x'=x-v*t=x0-vt', so if x0' is to give the coordinate in the (x',t',)-system, it will be given by x0'=x0-v*t': ie., it is not given by a constant. Thus, being at rest (constant x-coordinate) is a coordinate-dependent concept. Sounds very false. We can say that the representation of the point X0 is the number x0 in the unprimed system, and x0' in the primed system. Clearly x0 and x0' are different, if vt is not zero. However one may say that (though it sounds/is stupid) the point X0 itself is the same throughout the transformation. However that expression sounds meaningless, since a transform (ok, maybe we should call it a change of basis) is only a function that takes the point's representation in one system into the same point's representation in another system. It is preferrable to use three notations: X0 for the point itself and x0 and x0' for the points' representations in some coordinate systems. ------------------------------ === Subject: 9. But Doesn't x.c'=x.c? That idea is one of the most idiotic to come up, and it does so frequently. And in a number of guises. The idea being that x.c' <> x.c-vt, with x.c being what we have called x0 above; the notation makes no difference. Some crackpots have managed to maintain that position even after graphs have illustrated that such an idea means that after a while a circle center represented by x.c' could be outside the circle. The leading crackpot just make that explicit, as far as one can tell from his befuddled post in response to a line about active transforms, which are actually moving body situations, not coordinate transformations: -------------------------------------------------------------------- e>An active transform is not a coordinate transform, ... Right, it is a transform of the center (in the opposite direction) done to effect the change of coordinates without a coordinate transform. ... E: Transform of the center? Center of a circle? He really is saying a circle center moves in the opposite direction of the circle! Right? -------------------------------------------------------------------- If r=10 and x.c was at x.c=0, then the points on the circle (10,0), (-10,0), (0,10) and (0,-10) could at some time become (-10,0), (-30,0), (-20,10), and (-20,-10), but with x.c'=x.c, the circle center would be at (0,0) still! The circle is here but its center is way, way over there! Indeed, although a change of coordinate systems is not movement of any object described in the coordinates, the x.c'=x.c crackpottery is tantamount to the circle staying put but the center moving away. Or vice versa. ------------------------------ === Subject: 10. But Isn't (x'-x.c')=(x-x.c) Actually Two Transformations? One crackpot puts the (x'-x.c')=(x-vt - x.c+vt) relationship like this: (x-vt+vt - x.c). See, he says, that is transforming x (with x-vt - x.c) and then reversing the transform (x-vt+vt - x.c). That's just another crackpot form of the idiocy that x.c' <> x.c-vt. You'll have noticed the implication is that there is no transform vt term relating to x.c. ------------------------------ === Subject: 11. But Doesn't (x'-x.c+vt) Prove The Transformation Time Dependent? That particular crackpottery is perhaps more corrupt than moronic, since it includes deliberately hiding a vt term from view, and pretending it isn't there. [However, we have seen above that it is a familiar incompetency, and not likely an original.] Look, the crackpots say, there is a time term in the transformed (x' - x.c+vt). The transform isn't invariant! It's time dependent! Just put x' in its original axis form, also, which reveals the other time term, the one they hide: (x'-x.c+vt) = (x-vt - x.c+vt) = (x-x.c). So, at any and all times, the transform reduces to the original expression, with no time term on which to be dependent. Then there is the fact that if you leave the equation in any of the various notation forms - with or without reducing them algebraicly - the arithmetic always comes down to the same as (x-x.c). That means nothing to crack- pots, but may mean something to you. ------------------------------ === Subject: 12. But Isn't (x'-x.c')=(x-x.c) a Tautology? My dictionary relates 'tautology' to needless repetition. That's another form of the x.c' <> x.c-vt idiocy. The repetition involved is the vt transformation term. Apply the -vt term to the x term, and it is needless repetition to apply it anywhere again? The 'again' is to the x.c term. The x.c' = x.c crackpot idiocy. The repetition of the vt terms is required by the presence of two x values to be transformed. Be sure to note the next section. ------------------------------ === Subject: 13. But Isn't (x'-x.c')=(x-x.c) Almost the Definition of a Linear Transform? Now, how on earth can we relate a tautology to a basic definition in math? we get this definition: -------------------------------------------------------------- A linear transformation, A, on the space is a method of corr- esponding to each vector of the space another vector of the space such that for any vectors U and V, and any scalars a and b, A(aU+bV) = aAU + bAV. ------------------------------------------------------------- Let points on the sphere satisfy the vector X={x,y,z,1}, and the circle center satisfy C={x.c,y.c,z.c,1}. Let a=1, and b=-1. Let A= ( 1 0 0 -ut ) ( 0 1 0 -vt ) ( 0 0 1 -wt ) ( 0 0 0 1 ) A(aX+bC) = aAX + bAC. aX+bC = (x-x.c, y-y.c, z-z.c, 0 ). The left hand side: A( x - x.c , y - y.c, z - z.c, 0 ) = ( x-x.c , y-y.c, z-z.c, 0 ). The right hand side: aAX= ( x-ut, y-vt, z-wt, 1 ). bAC= (-x.c+ut, -y.c+vt, -z.c+wt, -1 ). and aAX+bAC = ( x-x.c, y-y.c, z-z.c, 0 ). Need it be said? Sure: QED. On the galilean transform the definition of a linear transform, A(aU+bV)=aAU + bAV, is completely satisfied. The generalized form transforms exactly and non-redundantly - with ONE TRANSFORM, not a transform and reverse transform - and non- tautologically, just as the very definition of a linear transform says it should. And does so with absolute invariance, with this galilean transformation. ------------------------------ === Subject: 14. But The Transform Won't Work On Time Dependent Equations? The main crackpot that has asserted such a thing was referring to equations such as in Subject 4, above. The Light Sphere equation; for which we have shown repeatedly elsewhere that the numerical calculations are identical for any primed values as for the unprimed values. The presence - before transformation - of a velocity term seems to confuse the crackpots. It turns out there is ex- treme historical reason for this, as you will see in the subject on Maxwell's equations. ------------------------------ === Subject: 15. But The Transform Won't Work On Wave Equations? See Subject 17, below, for a discussion of Second Derivative forms and the galilean transforms. ------------------------------ === Subject: 16. But Maxwell's Equations Aren't Galilean Invariant? Oh? Just what is the magical term in them that prevents (x'-x.c')=(x-vt - x.c+vt)=(x-x.c) from holding true? It turns out not to be magic, but reality, that interferes with the application of the galilean transforms to the gen- eralized coordinate form(s) of Maxwell: there are no coordi- nates to transform! When True Believer crackpots are shown the simple demonstration that the galilean transform on generalized cartesian coordinates is invariant, their first defense is usually an incredibly stupid x0'=x0, because the coordinate of a circle center, or point of emission, etc, is a constant and can't be transformed. The last defense is but Maxwell's equations are not invariant under that coordinate transform. When asked just what magic occurs in Maxwell that would prevent the simple algebra (x'-x0')=[ (x-vt)-(x0-vt) ]=(x-x0) from working, and when asked them for a demonstration, they will never do so, however many hundreds of times their defense is asserted. The reason may help you understand part of Einstein's 1905 paper in which he gave us his absurd Special Relativity derivation: THERE ARE NO COORDINATES IN THE EQUATIONS TO BE TRANSFORMED. Einstein gave the electric force vector as E=(X,Y,Z) and the magnetic force vector as B=(L,M,N), where the force components in the direction of the x axis are X and L, Y and M are in the y direction, Z and N in the z direction. Those values are not, however, coordinates, but values very much like acceleration values. BTW, the current fad is that E and B are 'fields', having been 'force fields' for a while, after being 'forces'. So, when Einstein says he is applying his coordinate transforms to the Maxwell form he presented, he is either delusive or lying. (a) there are no coordinates in the transform equations he gives us for the Maxwell transforms, where B=beta=1/sqrt(1-(v/c)^2): X'=X. L'=L. Y'=B(Y-(v/c)N). M'=B(M+(v/c)Z). Z'=B(Z+(v/c)M). N'=B(N-(v/c)Y). X is in the same direction as x, but is not a coordinate. Ditto for L. They are not locations, coordinates on the x-axis, but force magnitudes in that direction. Similarly for Y and M and y, Z and N and z. (b) the v of the coordinate transforms is in Maxwell before any transform is imposed; Einstein's transform v is the velocity of a coordinate axis, not the velocity he touched it. (c) if they were honest Einsteinian transforms, they'd be x, which means it is X and L that are supposed to be transformed, not Y and M, and Z and N. And when SR does transform more than one axis, each axis has its own velocity term; using the v along the x-axis as the v for a y-axis and z-axis transform is thus trebly absurd: the axes perpendicular to the motion are not changed according to SR, the v used is not their v, and the v is not a transform velocity anyway. (d) as everyone knows, the effect of E and B are on the direction. Both the speed and direction are changed by E and B, but v - the speed - is a constant in SR. As absurd as are the previously demonstrated Einsteinian blunders, this one transcends error and is an incredible example of True Believer delusion propagating over decades. The components of E and B do differ from point to point, and in the variations that are not coordinate free, they are subject to the usual invariant galilean trans- formation when put in the generalized coordinate form. ------------------------------------------------------------- The SR crackpots don't know what coordinates are. The various things they call coordinates include coordin- nates, but also include a variety of other quantities. ------------------------------------------------------ 1. One may express coordinates in a one-axis-at-a-time manner [like x^2+y^2=r^2] but it is the use of vector notation that shows us what is going on. In vector notation the triplet x,y,z [or x1,x2,x3, whatever] represents the three spatial coordinates, but there are so-called basis vectors that underlie them. Those may be called i,j,k. Thus, what we normally treat as x,y,z is a set of three numbers TIMES a basis vector each. 2. These e*i, f*j, g*k products can have a lot of meanings. If e, f, j are distances from the origin of i,j,k then e*i, f*j, g*k are coordinates: distances in the directions of i,j,k respectively, from their origin. That makes the triplet a coordinate vector that we describe as being an x,y,z triplet; perhaps X=(x,y,z). The e*i, f*j, g*k products could be directions; take any of the other vectors described above or below and divide the e,f,g numbers by the length of the vector [sqrt(e^2+f^2+g^2)]. That gives us a vector of length=1.0, the e,f,g values of which show us the direction of the original vector. That makes the triplet a direction vector that we describe as being an x,y,z triplet; perhaps D=(x,y,z). The e*i, f*j, g*k products could be velocities; take any of the unit direction vectors described above and multiply by a given speed, perhaps v. That gives a vector of length v in the direction specified. That makes the triplet a velocity vector that we describe as being an x,y,z triplet; perhaps V=(x,y,z). Each of the three values, e,f,g, is the velocity in the direction of i,j,k respectively. The e*i, f*j, g*k products could be accelerations; take any of the unit direction vectors described above and multiply by a given acceleration, perhaps a. That gives a vector of length a in the direction specified. That makes the triplet an acceleration vector that we describe as being an x,y,z triplet; perhaps A=(x,y,z). Each of the three values, e,f,g, is the acceleration in the direction of i,j,k respectively. The e*i, f*j, g*k products could be forces (much like accel- erations); take any of the unit direction vectors described above and multiply by a given force, perhaps E or B. That gives a vector of length E or B in the direction specified. That makes the triplet a force vector that we describe as being an x,y,z triplet; perhaps E=(x,y,z) or B=(x,y,z). Each of the three values, e,f,g, is the force in the direction of i,j,k respectively. Einstein's - and Maxwell's - E and B are not coordinate vectors. There is another variety of intellectual befuddlement that misinforms the idea that Maxwell isn't invariant under the galilean transform: confusions about velocities. Velocities With Respect to Coordinate Systems. ----------------------------------------------- Aaron Bergman supplied the background in a post to a sci.physics.* newsgroup: Imagine two wires next to each other with a current I in each. Now, according to simple E&M, each current generates a magnetic field and this causes either a repulsion or attraction between the wires due to the interaction of the magnetic field and the current. Let's just use the case where the currents are parallel. Now, suppose you are running at the speed of the current between the wires. If you simply use a galilean transform, each wire, having an equal number of protons and electrons is neutral. So, in this frame, there is no force between the wires. But this is a contradiction. First of all, the invariance of the galilean transform (x'-x.c') =(x-x.c), insures that it is an error to imagine there is any difference between the data and law in one frame and in another; the usual, convenient rest frame is the best frame and only frame required for universal analysis. [Well, (x'<>x, x,c'<>x.c, but (x'-x.c')=(x-x.c).] Second, given that you decide unnecessarily to adapt a law to a moving frame, don't confuse coordinate systems with meaningful physical objects, like the velocity relative to a coordinate system instead of relative to a physical body or field. In other words, what does current velocity with respect to a coordinate system have to do with physics? Nothing. Certainly not anything in the example Bergman gave. What is relevant is not current velocity with respect to a coordinate system, but current velocity with respect to wires and/or a medium. The velocity of an imaginary coordinate sys- tem has absolutely nothing to do with meaningful physical vel- ocity. You can - if you are insightful enough and don't violate item (e) - identify a coordinate system and a relevant physical object, but where some v term in the pre-transformed law is in use, don't confuse it with the velocity of the coordinate transform. Velocities With Respect to ... What? ----------------------------------------------- Albert Einstein opened his 1905 paper on Special Relativity with this ancient incompetency: The equations of the day had a velocity term that was taken as meaning that moving a magnet near a conductor would create a current in the conductor, but moving a conductor near a wire would not. This was belied by fact, of course. The important velocity quantity is the velocity of the magnet and conductor with respect to each other, not to some absolute coordinate frame (as far as we know) and not to an arbitrary coordinate system. One possible cause was the idea: but the equation says the magnet must be moving wrt the coordinate system or ... the absolute rest frame. There not being anything in the equation(s) to say either of those, it is amazing that folk will still insist the velocity term has nothing to do with velocity of the two bodies wrt each other. ----------------------------------------------------------- ------------------------------ === Subject: 17. First and Second Derivative differential equations. One of the intellectually corrupt ways of denying the very simple demonstration of galilean invariance of all laws expressed in the generalized coordinate form demanded by analytic geometry, vector analysis, and measurement theory [ (x'-x.c')=[ (x-vt)-(x.c-vt) ]=(x-x.c) ] is the assertion that those equations 'over there' (usually Maxwell or wave) are somehow immune to the elementary laws of algebra used to demon- strate the invariance. [Unfortunately, the assertions are never accompanied by reference to the magical math that makes elementary al- gebra invalid. Wonder why that is?] Part of the time it is based on the old lore based on the incompetent transformation of the privileged form of an equation instead of the correct form. [Evidence of this is any reference to an effect due to the velocity of the transform; it falls out algebraicly metically - as you can see above.] But usually it is just whistling in the dark, waving the cross (zwastika, I'd say) at the mean old vampire. The most general equation that could be conjured up is a differential with either First or Second Derivatives. Let's examine the plausibility of such magical magical, non-invariance assertions. (a) to get a Second Derivative you must have a First Derivative. (b) to get a First Derivative you must have a function to differentiate. (c) to get a Second Derivative you must have a function in the second degree. So, let us examine the question as to whether any such common Maxwell/wave equation will differ for (a) the common, privileged form, represented as ax^2, with a being an unknown constant function. (b) the generalized cartesian form, represented as a(x-x.c)^2 = ax^2 -2ax(x.c) + ax.c^2, with a being an unknown constant function. (c) the transformed generalized cartesian form, represented as a(x-vt -x.c+vt)^2, same as for (b), = ax^2 -2ax(x.c) + ax.c^2, of course, with a being an unknown constant function. I. for (a), remembering that x.c is a constant, and that this version is only correct because x.c=0, otherwise (b) is the correct form: d/dx ax^2 = 2ax (d/dx)^2 ax^2 = 2a II. for (b), remembering that x.c is a constant. d/dx (ax^2 -2ax(x.c) + ax.c^2) = 2ax - 2ax.c (d/dx)^2 (ax^2 -2ax(x.c) + ax.c^2) = 2a III. for (c); same as for (b). So, what we have seen so far is (1) differential equations in the second degree - the wave equations - must clearly be the same for all forms: the privileged form in x, the generalized cartesian form in x and the centroid, x.c, or the transformed generalized cartesian form. That is, anyone who imagines that correct usage gives different results for galilean transformed frames is at first showing his ignorance, and in the end showing his intellectual corruption. (2) As far as the First Derivatives are concerned, the only cases in which there really is a difference between the two forms is where x.c <> 0, and in that case, the use of the privileged form is obviously incompetent. So, how do you correctly use the differential equations? If you are using rest frame data with the centroid at x=0, etc, you can't go wrong without trying to go wrong. If you are using rest frame data with the centroid not at x=0, you must use (x-x.c) anyplace x appears in the equation. If you are using moving frame data, you must use the moving frame centroid as well as the light front (or whatever) moving frame data itself, perhaps first calculating (x'-x.c'), which equals (x-x.c) which is obviously correct, and which is obviously the plain old correct x of the privileged form. Unless, of course, there really is some magical term or expression that invalidates the obvious and elemen- tary algebra of the invariance demonstration. Or maybe you just whistle when you don't want basic algebra to hold true. Eleaticus !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ! Eleaticus Oren C. Webster ThnkTank@concentric.net ? ! Anything and everything that requires or encourages systematic ? ! examination of premises, logic, and conclusions ? !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? === Subject: Re: Invariant Galilean Transformations (FAQ) On All Laws [snip lies] > Invariant Galilean Transformations (FAQ) On All Laws > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net [snip 1300 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) that would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t' = t, x' = x - vt, y' = y, z' = z. His refusal to accept that t' must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to fields over space and time (electric and magnetic fields for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt' = d/dt + v d/dx, d/dx' = d/dx, d/dy' = d/dy, d/dz' = d/dz. This shows the necessity of introducing a new variable t', since partial differentiation with respect to t' (constant x', y', z') is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt' = dt/dt' d/dt + dx/dt' d/dx + dy/dt' d/dy + dz/dt' d/dz, d/dx' = dt/dx' d/dt + dx/dx' d/dx + dy/dx' d/dy + dz/dx' d/dz, d/dy' = dt/dy' d/dt + dx/dy' d/dx + dy/dy' d/dy + dz/dy' d/dz, d/dz' = dt/dz' d/dt + dx/dz' d/dx + dy/dz' d/dy + dz/dz' d/dz. The presence of the term involving d/dx in the expression for d/dt' is indicative of the fact that x depends on t' (x', y', z', being held constant), as can be seen from the fact that the coefficient of d/dx in the expression for d/dt' is dx/dt'. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt' is indicative of t' depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell's Equations under the Galilean Transformation. The first advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell's Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x' = E_x, E_y' = E_y - v B_z, E_z' = E_z + v B_y, B_x' = B_x, B_y' = B_y, B_z' = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x' = E_x, E_y' = E_y, E_z' = E_z, B_x' = B_x, B_y' = B_y + v/c^2 E_z, B_z' = B_z - v/c^2 E_y, rho' = rho, J_x' = J_x - v rho, J_y' = J_y, J_z' = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell's Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM field for the two cases are inconsistent with each other. The transformation law for the EM field which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM field which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell's equations are invariant under the Lorentz Transformation, with transformation laws: E_x' = E_x, E_y' = gamma (E_y - v B_z), E_z' = gamma (E_z + v B_y), B_x' = B_x, B_y' = gamma (B_y + v/c^2 E_z), B_z' = gamma (B_z - v/c^2 E_y), rho' = gamma (rho - v/c^2 J_x), J_x' = gamma (J_x - v rho), J_y' = J_y, J_z' = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arxiv.org/abs/gr-qc/0103044 http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light http://metrologyforum.tm.agilent.com/cesium.shtml http://arxiv.org/abs/physics/0008012 Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://physicstoday.org/vol-57/iss-7/p40.shtml No aether http://fsweb.berry.edu/academic/mans/clane/ No Lorentz violation http://arXiv.org/abs/gr-qc/0409089 Spin-2 gravitons have problems (so does the proposal) http://arXiv.org/abs/gr-qc/0411113 http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect http://map.gsfc.nasa.gov/ http://arxiv.org/abs/astro-ph/0403292 http://arXiv.org/abs/astro-ph/0310723 WMAP + Sloane Digital Sky Survey http://arxiv.org/abs/hep-ph/0404175 Dark matter candidates Carroll on what it all means. Special Relativity is physics on a topologically trivial Lorentzian manifold with a metric whose curvature tensor is zero. This is a perfectly diffeomorphism-invariant condition and does not require any particular coordinate choice. It is invariant under the full group of diffeomorphisms. The Poincare group is the group of *isometries* of the metric in special relativity. The Special Relativity metric is *non-dynamical* (unlike GR). It defines the coupling *constants* of your theory. If you change the metric in any nontrivial way you are changing your theory. An operation can only be called a symmetry of a special-relativistic (non-gravitational) theory if it preserves the metric, and therefore the symmetry of special-relativistic theories is the Poincare group only. General Relativity (gravitation) has a dynamic metric. NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf Longitudinal and transverse mass Physics Today 58(3) 34 (2005) Time passage, equator vs. poles http://arxiv.org/abs/gr-qc/0306076.pdf http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf Supersedes: === Subject: (SR) Lorentz t', x' = Intervals Summary: The Lorentz transforms themselves are proof t' and x' cannot possibly be just coordinates. Examination of their derivation verifies their identity as intervals. Originator: faqserv@penguin-lust.mit.edu Disclaimer: approval for *.answers is based on form, not content. Opponents should first actually find out what the content is, then think, then request/submit-to arbitration by the appropriate neutral mathematics authorities. Flaming the hard- working, selfless, *.answers moderators evidences ignorance and atrocious netiquette. Version: 0.02.1 Archive-name: physics-faq/criticism/lorentz-intervals Posting-frequency: 15 days (SR) Lorentz t', x' = Intervals (c) Eleaticus/Oren C. Webster Thnktank@concentric.net ------------------------------ === Subject: 1. Introduction with the obvious debunking of the use of 'just coordinates' in any scientific formula. Defenders of the Special Relativity faith are especially fond of telling opponents of their space-time fairy tales that they do not know the difference between coordinates and magnitudes. That may often be so, but the fault lies ultimately with SR dogma. The Lorentz-Einstein transformations cannot possibly be 'just coordinates', which is the interpre- tation required to support the many sideshow carnival acts with which the SR faithful bedazzle the public, and establish their moral and intellectual superiority. If I get in my car and drive steadily for a few hours at 50 kilometers per hour, is 50t the distance I travel? Of course not. The last time my hours-counting 'just coord- inates' clock was set to zero was when Zeno first reported one of his paradoxes to Parmenides. That was a long time ago, so my t is not useful for such purposes unless you also use my clock to established the starting time, perhaps t0, and use the formula 50(t-t0) to calculate the distance. In any case, my t is even then not 'just a coordinate' because it always represents particular elapsed times that can be used in the (t-t0) form to calculate perfectly good time intervals (elapsed times). Alternatively, I could (re)set my clock to zero at the start of some meaningful time interval, in which case my t shows a scientifically perfect current and/or end time. In which case, the Lorentz-Einstein t'=(t-vx/cc)/g is a function of an elapsed time interval (not 'just a coordinate') and a time interval (-vx/cc; the interval amount the t' clock is being screwed up at time t) and thus cannot be 'just a coordinate' since neither of the independent variables is such a 'just' thing. {Their meaning is shown below, step-by-step.] If it takes me 50 minutes to cross the Interstate highway, was x/50 my velocity crossing it? Of course not. The origin of all my axes is at the very spot where Zeno first presented his first paradox to Parmenides. That makes my x equal a couple of thousands of miles, plus, and is not useful for such purposes unless you establish the starting x value, perhaps x0, and use the formula (x-x0)/50 to calculate my velocity. In any case, even then my x is not 'just a coordinate' because it always repesents particular distance intervals that can always be used in the (x-x0) form for any and every scientific purose. Alternatively, I could move my x-axis origin to the starting (zero) point of some meaningful distance, in which case my x shows a scientifically perfect current and/or end distance. In which case, the Lorentz-Einstein x'=(x-vt)/g is a function of a current/ending distance interval (not 'just a coordinate') and a distance interval (-vt; the interval amount the x' axis is being screwed up at time t) and thus cannot be 'just a coordinate' since neither of the independent variables is such a 'just' thing. {Their meaning is shown below, step-by-step.] ------------------------------ === Subject: 2. Table of Contents 1. Introduction with the obvious debunking of the use of 'just coordinates' in any scientific formula. 2. Table of Contents. 3. The Lorentz-Einstein transforms. 4. The 'just coordinates' argument. 5. Single-system, little-purpose ambiguity. 6. Relating two coordinate measures/systems. 7. Distances and moving coordinate axes. 8. Time intervals. 9. Einstein's (1905) derivations. 10. A word about intervals. 11. Intervals versus the Twins Paradox. 12. Summary ------------------------------ === Subject: 3. The Lorentz-Einstein transforms Special Relativity's space-time circus is based on the 'transformation' equations by which it is believed one can relate a nominally 'stationary' system's space and time coordinates to those of an inertially (not accelerating) moving other observer. That moving observer's own physical body and coordinate system might have been identical in size to those of the stationary observer before the traveller began moving, but are 'seen' as very different by the stationary observer when the relative velocity of the two is great enough, a high percentage of the velocity of light. Concerning ourselves - as is customary - with just the spatial coordinate axis that lies parallel to the direction of motion, and with time, Einstein arrived at these formulas that relate the moving system measures or coordinates (x' and t') to the stationary system coordinates (x and t): x' = (x - vt)/sqrt(1-vv/cc) (Eq 1x) t' = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) The v is for the two systems' relative velocity as seen by the stationary observer, and is positive if the dir- ection is toward higher values of x. By concensus, the moving system x'-axis higher values also lie in that direction, and all axes parallel the other system's corresponding axis. We used vv to mean the square of v but might use v^2 for that purpose below. Similarly for c. Because it is believed that no physical object can reach or exceed c, the square-root term in both denominators is presumed always less than one, which means that the formulas say both x' and t' will tend to be greater than x and t, respectively. However, SRians call the x' result 'contraction' - which means shortening - and the t' result 'dilation' - which means increasing. ------------------------------ === Subject: 4. The 'just coordinates' argument The 'just coordinates' argument is so patently ridiculous that even opponents have a hard time accepting just how simple and obvious its debunking can be, as shown in this section. However, further sections take a more arithmet- ical approach that you'll maybe find more professorial. The 'just coordinates' argument is that t is mot a duration, not a time interval; it's just an arbitrary clock reading. But what if the moving system observer comes speeding by while you make your annual 'spring forward' or 'fall back' change? The formula says that the moving system clock's 'just coordinate' reading can be calculated from yours: t' = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) Imagine the moving system oberver's confusion if his clock changes its reading while he's looking at it! If his clock doesn't change when yours does, the formula is wrong; if it is truly a 'just coordinates' formula. And then what happens if you realize you were a day early and put your clock back to what it had said previously? And suppose you are in NYC and your twin in LA and both are watching the moving observer. You'll both be using the same v because you are at rest wrt (with respect to) each other. You're on Eastern Standard Time and your twin is on Pacific Standard Time maybe. You have three hours more on your clock than does your twin. On which 'just coordinate' clock will the Lorentz transforms base the 'just coordinate' time the moving system clock says? The formula applies to both of your t-times: t' = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) Sure, the idea that you can change someone else's clock with no connection of any kind is really ridiculous, but Eqs 1x and 1t aren't MY equations. Are they yours? And we aren't the ones to say x, t, x', and t' are just coordinates. If the t' formula is actually either an elapsed time formula, or the basis of a t'/t ratio, then there is no implication that one clock's reading has anything to do with the other's. It can only be rates of clock ticking, or how one time INTERVAL compares to the other that the formula is about. ------------------------------ === Subject: 5. Single-system, little-purpose ambiguity. Since we're going to be comparing measurements on two coordinate systems in the next section, let's go to our supply cabinet and get our yard-stick (which we use to measure things in inches) and our meter-stick (which we use to measure things in centimeters). Here, I'm getting mine. Oh! Oh! There's an ant on mine, and he ... she ... sure is hanging on, right at the 3.5 inch mark of the yard- stick. Let's see if I can wave the stick around enough that she'll let go. Nope. However, before I gave up I waved the stick and the ant 'all over the place. Always, however, the ant was at the 3.5 mark on the yard-stick, and always 3.5 away from the end of the stick, however far and wide I have transported her. Neither of those 3.5 facts means very much. Of the two, the distance aspect meant almost nothing. So the distance was 3.5 from the end. So what? That length, distance, was not in use. And only maybe the ant might have been concerned with just what location, 'just coordinate', on the stick she was at. Just so with x and t. So, is the 3.5 reading just a coordinate? Or a distance/length? It's ambiguous in and of itself, and really makes no difference what you say until you try to make use of the number. Hey, my address is 5047 Newton Street. If you are looking for me and you're at 4120 Newton, it is helpful information, because it tells you which direction to go. Is that 'just coordinate'? Where it really becomes useful, perhaps, is in telling you how far away I am. That's not just a coordinate value, that's a distance, length, interval. However, it is subtracting 4120 from 5047 that tells you which direction and how far. It is only because both 5047 and 4120 are distances from the same point - ANY same point - that the result means anything. My x - my yardstick reading - is always a distance or length; it is impossible to be otherwise with an honest, competently designed yardstick. Whether or not its reading is of good use in some particular scientific formula depends on whether I put the zero end of the yardstick at some useful place. As in the introduction, we should either put it at the starting location/end, or use two readings from it: (x-x0). ------------------------------ === Subject: 6. Relating two coordinate measures/systems. Taking care to not damage our brave little ant, I place my yard-stick onto the table, zero end to the left, 36 end to the right. Now I place the 'just coordinate' meter-stick on the table in the same orientation, in a random location, and find that the ant's coordinate on the meter-stick is 51. The formula relating centimeters to inches is cm=i*2.54 but we want a formula similar to x'=(x-vt)/sqrt(1-vv/cc). That would be c=i/.03937 approximately, but let's use x' for the meter-stick reading, and x for the inch reading: x'=x/.3937. 3.5/.3937 = 8.89 Wait a minute. It's not just science but definition that says c=i/.3937=8.89, so something is wrong. 8.89 is not 51. We already knew that 51 cm was just an arbitrary coordinate. Arbitrary not because that point isn't 51 cm from the zero end of the meter-stick, but because the zero point was in an arbitrary position. Let's put the meter-stick in a position where it's zero point is at the yard-stick zero point. What is the centimeter coordinate now? Hey. 8.89, just like the formula says. The only way for a 'transform' like x'=x/g to work, whatever g might be, is for both coordinate systems to have their zero points aligned, in which case saying the two measures are not intervals is pure idiocy. Noe that with both zero points at the same position both x' and x are great measures for scientific purposes, in any and every case where we were smart enough to put those zero points at a useful location. There is one extension of x'=x/g that will let us use the meter-stick in arbitrary position. When the cm reading was 51, the zero point of the yard-stick read (51-8.89=) 42.11 cm. If we call that point x.z' we get x' = x.z' + x/.3937. = 42.11 + 3.5/.3937 = 42.11 + 8.89 = 51. Obviously, in this formula x/.3937 is the distance from the x' coordinate of the location where x=0. An interval. Just as obviously, the fact that we now have the correct formula for relating an x interval to an arbitrary x' coordinate, does not mean that x' is anything more than nonsense for use in any scientific formula. Unless we were smart enough to put the x zero point in a useful location, and use (x'-x.z') in the scientific formula. (x'-x.z') equals the useful, Ratio Scale value x/.3937. So, we have discovered a basic fact: a transformation formula like x'=x/g works only if the two zero points of the coordinate systems coincide. That makes it non- sense to say the two coodinates are only coordinates and not intervals. Both must be values that represent distances from their respective zero points unless you take the proper steps to adjust for the discrepancy. Make sure you understand that although the inclusion of x.z' made it possible to correctly calculate x', the result is nonsense when it comes to use of x' for general length/distance purposes; it is x'-x.z' that is a useful number in such cases. It could be that we're measuring a sheet of paper with one end at x=0 and the other at x=3.5; x'=51 is nonsense as a centimeter measure of the paper. But, you say, the Lorentz transform contain a -vt term. ------------------------------ === Subject: 7. Distances and moving coordinate axes. We discovered x'=x.z' + x/g as the correct formula for relating one coordinate to another system's. But the Lorentz transform contains another term, -vt/sqrt(1-vv/cc). What is it? Let's start with our x'=51 cm, x=3.5, x.z'=42.11 example. Every minute, let's move the meter-stick one inch to our right. At minute 0, the cm reading was 51 cm. At minute 1, the cm reading is now 50 cm. At minute 2, the cm reading is now 49 cm. In this instance, v=1 inch/minute. And t was 0, 1, 2. What has happened is that we have made our x.z' a lie, and increasingly so. -vt/.3937 is the change in x.z'. x' = (x.z - vt/.3937) + x/.3937. Obviously, vt/.3937 is not a coordinate; even most SRians wouldn't imagine it was. It is an interval, the distance over which the moving system has moved since t=0. And, of course, x/.3937 is the distance of our brave little ant from the point where x=0 and the centimeter reading is x.z'-vt/.3937. Yes, every minute the meter- stick moves to the right and the meter-stick coordinate of the spot where x=0 gets less and less - and eventually negative. Make sure you understand that every minute the x' coordinate, because of -vt/g, becomes a better measure of, say, the 3.5 paper we might be measuring with the yard-stick, given that 51 was too big a number and -vt is negative. That is, until the two origins coincide at x'=x=0, and then it gets worse and worse. With -vt positive (because v<0) the situation is different. With 51 and -vt positive, x' just gets worse and worse over time. Quite obviously, the fact that we now have the correct formula for relating an x interval to an arbitrary x' coordinate even when the x' axis is moving, does not mean that x'is anything more than nonsense for use in any scientific formula. Unless we were smart enough to put the x zero point in a useful location, and use (x'-x.z'+vt/.3937) in the scientific formula. (x'-x.z'+vt/.3937) equals the useful, Ratio Scale value x/.3937. ------------------------------ === Subject: 8. Time intervals. Instead of using our sticks, let's get out two clocks. Mind you, we're not going to deal with different clock rates here, just establish the same basics as for distance. Your clock says 9:00 Eastern Standard Time (EST) and we note that t=540 minutes when we put down the clock. Blindly, let's turn the setting knob of your twin's Pacific Standard Time clock and put it down before us. According to what we see, EST's 540 minutes (9:00) corre- sponds to PST's 14:30; t'=870. We know the formula relating PST to EST is t' (pacific) = t (eastern) - 180 (minutes). Thus, it is not correct that the second clock can have an arbitrary setting, because 870 <> 540-180. We know that the two clocks are related by t' = t/1 since both are using the same second, hour, etc units. But 870 (14:30 in minutes) is not 540/1-180, so once again we know something is wrong. However, t'=t.z' + t/1 works. EST midnight equals PST 0.0 (midnite) - 180, so t.z' = -180, and t' = -180 + 540/1 = 360. Since EST-180=PST, 9:00 EST is 6:00 PST = 360 minutes. We see thus that like distance measures/coordinates, time axis origins (zero points) must either be 'lined up' or adjusted for. So, the Lorentz/Einstein t'=t/sqrt(1-vv/cc) must be the moving system elapsed time interval since the time axes were both at a common zero. There is no t.z' adjustment: t' = (t - vx/cc)/sqrt(1-vv/cc) (Eq 1t) Make sure you understand that in the clock case, if the EST is showing a good number for elapsed time since the travelling observer passed NYC, then the PST clock is silliness. t.z' must be zero or must be taken out of time lapse calculations for the PST clock to be used intelligently, just as was true for x.z'. What is lacking as yet for Lorentz t' is the -vx/cc term that corresponds to the x' formula -vt term. Break it up into two parts: v/c and x/c. v/c is a scaling factor that changes velocity from whatever kind of unit you are using over to fractions of c. x/c is distance divided by velocity, which is time. x/c is thus the time interval since the two time axes had a common zero point - which they have to have in the Lorentz transforms which do not have the t.z' term we learned to use above. Thus, (-vx/cc)/sqrt(1-vv/cc) is the interval amount the moving system clock has been changed - since the common/ adjusted time - over and beyond the elapsed time interval represented by x/sqrt(1-vv/cc). We have discovered that the only way for t' to be t/g is for t' and t to have a common zero point, just as for x' and x. It would be otherwise if the t' formula contained an adjustment t.z' under some name or other, but the necessity to include such a term correlates 100% with t' numbers that aren't directly usable. As for x and x', our knowledge of how to setup a proper formula relating t and t' is of no use unless we use the knowledge in scientific formulas; (t'-t.z'+xv/gcc) gives us the only directly useful value: t/g. ------------------------------ === Subject: 9. Einstein's (1905) derivations. When we return to Einstein's derivations of the transform formulas with a well-focused eye, we find he was a wee bit confused - or at least self-contradictory. When he set up his (at first unknown) tau=moving system time formulas, he created three particular instances of tau. Tau.0 is the time at which light is emitted at the moving origin toward a mirror to the right that is moving at rest wrt that moving origin and at a constant distance from that origin. He lets the stationary time slot have the value t, a constant, the stationary system starting time. Tau.1 is the time at which the light is reflected. He lets the stationary time be t+x'/(c-v); t is still a constant and x'/(c-v) is the time interval since t. Tau.2 is the time at which the light gets (back) to the moving origin. The stationary time value is put as t + x'/(c-v) + x'/(c+v); t is still a constant and x'/(c-v) + x'/(c+v) is the time interval since t. On the thesis that the moving observer sees the time to the mirror as the same as the time back to the origin, he sets .5[ tau.0 + tau.2 ] = tau.1. Tau.0 completely drops out of the analysis and leaves no trace, and has no effect. Further, the t you see in tau.0, tau.1, and tau.2 also completely drops out with no trace and no effect, leaving us with exactly what you'd get if you had explicilty said t' is an interval and so is t. What doesn't drop out in the stationary time values is x'/(c-v) and x'/(c+v), the time interval it takes for light to get to the fleeing mirror, and the time interval it takes for light to get back to the approaching origin. Thus, his resultant t' formula is strictly based on time intervals in the stationary system. Time intervals since some starting time, yes, but time intervals. There is absolutely nothing in the derived formulas that depends on arbitrary coordinates like the constant t in the stationary time arguments. Let's look at the x dimension; it is x'=x-vt [as x increases by vt, the effect over time is x'=(x+vt)-vt)], which Einstein explicitly sets up as a constant stationary distance. He uses that x' not just in the time interval parts of the stationary time arguments, but also in the x (distance) stationary system argument for the tau at the time light is reflected. x' can't be the stationary system coordinate of the mirror at that time. That value is x'+vt. x' is explicitly an interval, distance. Thus, the whole tau derivation of the t' formula is fully and explicitly based on x' - a spatial length/distance/interval - and the two time interals x'/(c-v) and x'/(c+v). While we're at it, if the starting t is not zero, his x'=x-vt formula is complete nonsense also. Given that there was some L that was the mirror x-location and length when the light is emitted, if t was already, say, 500, then x'=L-vt could have been a very negative length. ------------------------------ === Subject: 10. A word about intervals. There are intervals, and there are intervals. If we put our yard stick zero point at one end of a piece of paper and read off the coordinate at the other end of the paper, we have a good measure of the paper's length, a Ratio Scale measure. [Absolute temperature scales are ratio scale.] If instead we put the one end of the paper at the one inch mark (or the zero end of the stick one inch 'into' the length of the paper) we get measures that are one inch off the true, ratio scale length. The two messed up measures are still intervals, but they are Interval Scale measures. [Household temperature scales are interval scale, which is why your physics and chemistry professors won't let you use them without first converting to the ratio scale absolute temperatures.) t'=t/g and x'=x/g represent ratio scale measures, given that t and x were ratio scalae to start with. t'=t.z'+t/g and t'=t/g-vx/gcc are both interval scale measures, even given a good ratio scale t and a good ratio scale x. x'=x.z'+x/g and x'=x/g-vt/g are both interval scale measures, even given a good ratio scale x and a good ratio scale t. Look for the (SR) Lorentz t', x' = degraded measures document soon at a newsgroup near you. ------------------------------ === Subject: 11. Intervals versus the Twins Paradox. t'=(t-vx/cc)/g shows t' being greater than t. The reason Special Relativity will not allow the use of its basic time equation in determining what SR has to say about the twins' ages, is that t' and x' are supposedly just coordinates, and they say you have to take the coordinate pairs (t',x') and (x,t) into consideration in both the time and place the twins' separation started and the time and place the twins reunited. Since t' and x' are actually both intervals, not just coordinates, the 'excuse' is spurious, and is so even without use of the obvious (x_b-x_a) and (t_b-t_a) usages. However, SR is right to be embarrassed by their transformation formulas. Look for the (SR) Lorentz t', x' = degraded measures document at a newsgroup near you. ------------------------------ === Subject: 12. Summary A. t'=t/g and x'=x/g can be almost 'just coordinates' in the sense that the values obtained may not be of much use except in the most primal and useless way: how long and how far since/from the time/ place they were zero. Even here, however, the zero points within each of the two scale pairs (t',t) and (x'.x) must have been lined up. If the zero points have been intelligently selected (such as at the starting point and time of a trip) they can be rationally used 'as is' in any valid sci- entific equation. B. Even the interval scale t'=t.z' - xv/gcc + t/g and x'=x.z' - vt/g + x/g are not 'just coordinates'. They can be used to good effect by establishing the relevant starting times/points and using (t'-t.z'+xv/gcc) and (x'-x.z'+vt/g), as the situation may require. C. When you see vx/gcc or vt/g in use in any guise with non-zero values, you know the resultant t' or x' is a degraded, interval scale value. E-X: Anytime you do not see what amounts to t.z' and xv/gcc in the time case, or x.z' and vt/g in the distance case, you know that the t' and/or x' in use are intervals. Period. Y: Either set your clock to zero at the start of the relevant time interval, or use (t-t0), with both being readings on the same clock. Either move your x-axis origin to the starting end or point, or use (x-x0), with both being readings on the same axis. Z: In _(SR) Lorentz t', x' = Degraded (Interval) Scales_ we see that t' and x' satisfy the mathematical tests for/of interval scales when -vt and -vx/cc are not zero; thus, they must be intervals. When -vt and -vx/cc are zero, t' and x' satisfy the much better mathematical definition of ratio scales, and are thus not just mere intervals, but (rescaled) good ones. Eleaticus !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? ! Eleaticus Oren C. Webster ThnkTank@concentric.net ? ! Anything and everything that requires or encourages systematic ? ! examination of premises, logic, and conclusions ? !---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---? === Subject: Re: (SR) Lorentz t', x' = Intervals > [snip lies (SR) Lorentz t', x' = Intervals > (c) Eleaticus/Oren C. Webster > Thnktank@concentric.net [snip 700 lines of trolled garbage] eleaticus, Oren Webster, is a despised and stooopid troll, http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/Crimes.html Several crimes against logic and science Ha ha ha! Originally trolled across sci.physics sci.physics.relativity alt.physics sci.math sci.answers alt.answers news.answers Psychotic ineducable boring troll Eleaticus, Were there to be internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) that would automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Eleaticus explicitly demonstrates that he is completely ignorant of multivariable calculus. He has no concept of the Chain Rule in multivariable calculus. Consider his Galilean Transformation goo and dribble: t' = t, x' = x - vt, y' = y, z' = z. His refusal to accept that t' must be introduced as a separate variable springs from a massive emprical stupidity re space and time are described as a four-dimensional manifold, with four coordinates instead of a time evolution of a three-dimensional manifold, and that the change of coordinate system should be a change of four coordinates, and not a time-dependent change of three coordinates. This is particularly vital when it comes to fields over space and time (electric and magnetic fields for example). The transformation law for the differential operators under the Galilean transformation is given by: d/dt' = d/dt + v d/dx, d/dx' = d/dx, d/dy' = d/dy, d/dz' = d/dz. This shows the necessity of introducing a new variable t', since partial differentiation with respect to t' (constant x', y', z') is a different operation to partial differentiation with respect to t (constant x, y, z). The above transformation law is determined by the Chain Rule: d/dt' = dt/dt' d/dt + dx/dt' d/dx + dy/dt' d/dy + dz/dt' d/dz, d/dx' = dt/dx' d/dt + dx/dx' d/dx + dy/dx' d/dy + dz/dx' d/dz, d/dy' = dt/dy' d/dt + dx/dy' d/dx + dy/dy' d/dy + dz/dy' d/dz, d/dz' = dt/dz' d/dt + dx/dz' d/dx + dy/dz' d/dy + dz/dz' d/dz. The presence of the term involving d/dx in the expression for d/dt' is indicative of the fact that x depends on t' (x', y', z', being held constant), as can be seen from the fact that the coefficient of d/dx in the expression for d/dt' is dx/dt'. Because of the now demonstrated fact that Eleaticus has no formal education in multivariable calculus, he has managed, somehow, to get it into his head that the presence of the term involving d/dx in the expression for d/dt' is indicative of t' depending on x (t, y, z, being held constant). Because of his stupidty Eleaticus cannot get the correct transformation law for the differential operators under the Galilean Transformation, and he cannot determine the invariance or otherwise of Maxwell's Equations under the Galilean Transformation. The first advice to Eleaticus is to learn multivariable calculus. Eleaticus should not pretend that he can understand how to determine invariance or otherwise of Maxwell's Equations under the Galilean Transformation, or under the Lorentz Transformation, until he understands the multivariable calculus which underlies such considerations. Eleaticus is a loud idiot. The homogeneous Maxwell equations are invariant under the Galilean Transformation, with transformation laws: E_x' = E_x, E_y' = E_y - v B_z, E_z' = E_z + v B_y, B_x' = B_x, B_y' = B_y, B_z' = B_z. The derivation of these transformation laws was determined using the transformation laws for the differential operators given above. These transformation laws have the additional advantage that they determine the correct transformation for the force law, thus providing further evidence in favour of the transformation law for the differential operators, as above. The inhomogeneous Maxwell equations are also invariant under the Galilean transformation, with transformation laws: E_x' = E_x, E_y' = E_y, E_z' = E_z, B_x' = B_x, B_y' = B_y + v/c^2 E_z, B_z' = B_z - v/c^2 E_y, rho' = rho, J_x' = J_x - v rho, J_y' = J_y, J_z' = J_z. Note the the transformation laws for the charge density and current density are as they should be under the Galilean transformation. Homogeneous equations are invariant under the Galilean Transformation, and inhomogeneous equations are invariant under the Galilean Transformation, but Maxwell's Equations as a whole are NOT invariant under the Galilean Transformation, since the transformation laws required for the EM field for the two cases are inconsistent with each other. The transformation law for the EM field which makes the homogeneous equations invariant will not also make the inhomogeneous equations invariant. The transformation law for the EM field which makes the inhomogeneous equations invariant will not also make the homogeneous equations invariant. On the other hand, all of Maxwell's equations are invariant under the Lorentz Transformation, with transformation laws: E_x' = E_x, E_y' = gamma (E_y - v B_z), E_z' = gamma (E_z + v B_y), B_x' = B_x, B_y' = gamma (B_y + v/c^2 E_z), B_z' = gamma (B_z - v/c^2 E_y), rho' = gamma (rho - v/c^2 J_x), J_x' = gamma (J_x - v rho), J_y' = J_y, J_z' = J_z, where gamma = 1/sqrt(1 - v^2/c^2). Idiot Oren Webster sees himself this way, http://www.mazepath.com/uncleal/effete6.jpg The entire remainder of the planet sees him this way, http://www.mazepath.com/uncleal/effete3.png http://www.mazepath.com/uncleal/sunshine.jpg http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24 GPS satellites carries either four cesium atomic clocks or three rubidum atomic clocks in orbit, with full relativistic corrections being applied. Internal inconsistencies in SR (meaning inconsistencies of a purely mathematical logical nature) automatically lead to contradictions in number theory, itself, and arithmetic, since the mathematics of Minkowski geometry is equiconsistent with the theory of real numbers and with arithmetic. Mathematics of gravitation Equivalence Principle testing http://arXiv.org/abs/hep-th/0111236 Geometric structure of reality http://arxiv.org/abs/gr-qc/0103044 http://arXiv.org/abs/hep-th/0307140 GR structure, especially Part 4/p. 7 http://arXiv.org/abs/gr-qc/0311039 Experimental constraints on General Relativity http://www.eftaylor.com/pub/projecta.pdf Relativity in the GPS system http://arXiv.org/abs/gr-qc/9909014 falling light http://metrologyforum.tm.agilent.com/cesium.shtml http://arxiv.org/abs/physics/0008012 Hafele-Keating Experiment http://www.hawaii.edu/suremath/SRtwinParadox.html Twin Paradox http://arXiv.org/abs/astro-ph/0401086 http://arxiv.org/abs/astro-ph/0312071 Deeply relativistic neutron star binaries http://arxiv.org/abs/hep-th/0405160 Black hole evaporation http://physicstoday.org/vol-57/iss-7/p40.shtml No aether http://fsweb.berry.edu/academic/mans/clane/ No Lorentz violation http://arXiv.org/abs/gr-qc/0409089 Spin-2 gravitons have problems (so does the proposal) http://arXiv.org/abs/gr-qc/0411113 http://arXiv.org/abs/gr-qc/0301024 Nordtvedt Effect http://map.gsfc.nasa.gov/ http://arxiv.org/abs/astro-ph/0403292 http://arXiv.org/abs/astro-ph/0310723 WMAP + Sloane Digital Sky Survey http://arxiv.org/abs/hep-ph/0404175 Dark matter candidates Carroll on what it all means. Special Relativity is physics on a topologically trivial Lorentzian manifold with a metric whose curvature tensor is zero. This is a perfectly diffeomorphism-invariant condition and does not require any particular coordinate choice. It is invariant under the full group of diffeomorphisms. The Poincare group is the group of *isometries* of the metric in special relativity. The Special Relativity metric is *non-dynamical* (unlike GR). It defines the coupling *constants* of your theory. If you change the metric in any nontrivial way you are changing your theory. An operation can only be called a symmetry of a special-relativistic (non-gravitational) theory if it preserves the metric, and therefore the symmetry of special-relativistic theories is the Poincare group only. General Relativity (gravitation) has a dynamic metric. NIM A 355 537 (1995) Physics Letters B 328 103 (1994) Physical Review Letters 64 1697 (1990) Physical Review Letters 39 1051 (1977) Physical Review 135 B1071 (1964) Physics Letters 12 260 (1964) Europhysics Letters 56(2) 170-174 (2001) General Relativity and Gravitation 34(9) 1371 (2002) http://fourmilab.to/etexts/einstein/specrel/specrel.pdf Longitudinal and transverse mass Physics Today 58(3) 34 (2005) Time passage, equator vs. poles http://arxiv.org/abs/gr-qc/0306076.pdf http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm http://www.trimble.com/gps/index.html http://sirius.chinalake.navy.mil/satpred/ http://www.phys.lsu.edu/mog/mog9/node9.html http://egtphysics.net/GPS/RelGPS.htm http://www.schriever.af.mil/gps/Current/current.oa1 http://edu-observatory.org/gps/gps_books.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf === Subject: homeomorphism vs isomorphism William Elliot summarised: > Catagory Theory morphic > Philosophy identical > Common sense same > Statistics about the same > Politics comparable Not bad. Though I think in cat theory it's still isomorphic, isn't it? I like to tell my first year classes (after giving them a definition), that two things are whatnot-morphic when the difference doesn't make any difference! ---------------------------------------------------------------------------- -- Bill Taylor W.Taylor@math.canterbury.ac.nz ---------------------------------------------------------------------------- -- The Physical Turing Machine is to computer science as the perpetual motion machine once was to physics. ---------------------------------------------------------------------------- -- === Subject: Re: Now how did we end up with this genius for President? > Bush, The Spoiled Man-Child > What causes the fall of empires? Why, stubborn leaders who speak like > toddlers and never admit mistakes > - By Mark Morford, SF Gate Columnist > Friday, June 3, 2005 > But not BushCo. This is the hilarious thing. This is the appalling > thing, still. How can this man remain so blindly, staggeringly > resolute? How can he be so appallingly ignorant of fact, of truth, of > evidence, of deep thought? In short, what the hell is wrong with > George W. Bush? A recent comparison of President Bush's grades at Yale with those of John Kerry showed the President's grade point average to be slightly higher. Does the country do better when it has a smart President like Grant, Hoover, or Carter? -- Ron === Subject: Re: Now how did we end up with this genius for President? > Bush, The Spoiled Man-Child > What causes the fall of empires? Why, stubborn leaders who speak like > toddlers and never admit mistakes > - By Mark Morford, SF Gate Columnist > Friday, June 3, 2005 But not BushCo. This is the hilarious thing. This is the appalling > thing, still. How can this man remain so blindly, staggeringly > resolute? How can he be so appallingly ignorant of fact, of truth, of > evidence, of deep thought? In short, what the hell is wrong with > George W. Bush? A recent comparison of President Bush's grades at Yale with those of > John Kerry showed the President's grade point average to be slightly > higher. Does the country do better when it has a smart President like Grant, > Hoover, or Carter? Those people had 'aquired' information through schools. Others have brains. -- > Ron > === Subject: Re: Now how did we end up with this genius for President? A recent comparison of President Bush's grades at Yale with those of > John Kerry showed the President's grade point average to be slightly > higher. Tee hee. But only the very silly (who vote democRAT anyway) believed for a second that Kerry was some kind of genius and W was some kind of idiot. The funny thing as I understand is was that the real reason Kerry held of what the Navy said about him but that the Navy records included his college records! That's what happens when you run a campaign based on nonsense. Does the country do better when it has a smart President like Grant, > Hoover, or Carter? -- > Ron > === Subject: Re: Now how did we end up with this genius for President? Basically your analogy about 'GW Bush' is entirely right. However, I believe at least one if not the entire collective of incest cloned Borgs broke lose with such a horrific wind, and that's the sort of flatulence where our resident warlord(GW Bush) came from. The easily persuaded and enforcible military vote, plus counting upon all that's related in support of their associated partners in crimes against humanity isn't actually all that hard to identify. The matter of fact that their own 'Skull and Bones' cult member Kerry did little or nothing as to challenge so much as one of the state returns is further proof positive of the power of such cultism. If it worked good enough for Jews, almost worked for Hitler and before that of nicely accommodating a couple of Popes going postal over Cathars, then it'll certainly function just fine and dandy on behalf of our very own 'Skull and Bones' team from hell that pretends to be closely associated with a very white and male God. Of course, once we started off with perpetrating such a horrific cold-war in order to profit from the demise of others while disqualifying the matter of fact that it was actually the USSR of Russian troops that accomplished 90% of wining WW-II, whereas subsequently the USSR was more than willing to return the warm and fuzzy cloak and dagger favor with more of the same cold-war tit for tats, whereas after that there was absolutely no simple method of turning back. Ever since then it has been down hill and nowadays situated well within the nearest space-toilet. Thus morality and whatever remorse are entirely out the window and, it seems there's not ever been a perpetrated cold-war rule in sight. Thus the results of incest cloning from the DNA/RNA remains of Hitler into becoming the likes of GW Bush are free to roam about the country, as well as to plunder, pillage and rape the world as based entirely upon liars telling lies until them NASA/Apollo cows come home. ~ My GUTH Venus township, bridge and ET Park-n-Ride tarmac: http://guthvenus.tripod.com/gv-town.htm The Russian LSE-CM/ISS (Lunar Space Elevator) http://guthvenus.tripod.com/lunar-space-elevator.htm A few other hot & testy topics by; Brad Guth / GASA-IEIS http://guthvenus.tripod.com/gv-topics.htm === Subject: Re: Now how did we end up with this genius for President? Enough sane people voted for him. There were fewer insane voters than sane voters. jt -- Without the second amendment the first amendment means nil. www.townhall.com www.newsmax.com www.nranews.org === Subject: Re: Now how did we end up with this genius for President? >... people voted ... The people's votes weren't counted. Why do you hate America? === Subject: Re: Now how did we end up with this genius for President? ... people voted ... The people's votes weren't counted. Why do you hate America? I don't hate any person or country. I just hate lies and communism or communism lite. You know, what you do? jt -- Without the second amendment the first amendment means nil. www.townhall.com www.newsmax.com www.nranews.org === Subject: Re: Now how did we end up with this genius for President? >... I just hate ... You must even hate yourself, to support Bush. He's harming you, too, whether you're aware of it or not. He's also harming the USA, so you effectively hate America. >... people voted ... The people's votes weren't counted. Why do you hate America? === Subject: Re: Now how did we end up with this genius for President? He uses the word science once. The Sci in sci.math stands for science. Mathematics is a Science, and Scientists always appreciate well-formulated thoughts, reasonings and argumentations whatever the source is, be it from Mumford, Morford, Bush or you. === Subject: Re: Now how did we end up with this genius for President? > Know what real men do? They admit their mistakes. Know what real > people do in times of great stress and strife and economic downturn? > They seek help, understand they don't know all the answers, realize > they might not've been asking the right questions in the first place. Maybe real men in San Francisco do that. Real Leaders get the information from the best available sources availble and then ACT. Know what great leaders, great nations do at times of war and fracture > and massive bludgeoning debt? All of the above, all the time, with > great intelligence and humility and grace and awareness and shared > humanity. Or they die. Frankly, you have your head up your ass. You certainly are describing the actions of any successful national leader I know of. It doesn't describe FDR, LFJ, Lincoln, Washington or the various successful leaders in business. (RR was asked if he had ever been wrong. He admitted that he had been because he had once been a democRAT.) You can't change the past. Folks with common sense look forward. Great leaders make mistakes but they don't let themselves he dragged down by them and the don't accept the judgments of their critics. If the live a LONG time after leaving office they might look back with some objectivity (e.g.: US Grant) but most die in harness or retire and keep quiet. === Subject: Re: Now how did we end up with this genius for President? >This type of noise is acceptable. >I give it the thumbs up. > Morons applaud morons. Mati Meron | When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same === Subject: Re: Now how did we end up with this genius for President? >>This type of noise is acceptable. >>I give it the thumbs up. >Morons applaud morons. You're saying you admire bushworshippers? >Mati Meron | When you argue with a fool, >meron@cars.uchicago.edu | chances are he is doing just the same Bush despises science and scientists. You'd expect a qualified scientist to know better than to support Bush. http://www.guardian.co.uk/usa/story/0,12271,1443198,00.html http://abcnews.go.com/Technology/wireStory?id=517770 http://www.commondreams.org/views05/0322-25.htm http://www.commondreams.org/headlines05/0221-27.htm http://www.usatoday.com/news/washington/2005-02-20-bush-science_x.htm http://www.americanhumanist.org/press/NFBushScience.html The following really isn't 'noise' at all, but reality: >Bush, The Spoiled Man-Child >What causes the fall of empires? Why, stubborn leaders who speak like >toddlers and never admit mistakes >- By Mark Morford, SF Gate Columnist >Friday, June 3, 2005 Know what real men do? They admit their mistakes. Know what real >people do in times of great stress and strife and economic downturn? >They seek help, understand they don't know all the answers, realize >they might not've been asking the right questions in the first place. Know what great leaders, great nations do at times of war and fracture >and massive bludgeoning debt? All of the above, all the time, with >great intelligence and humility and grace and awareness and shared >humanity. Or they die. But not BushCo. This is the hilarious thing. This is the appalling >thing, still. How can this man remain so blindly, staggeringly >resolute? How can he be so appallingly ignorant of fact, of truth, of >evidence, of deep thought? In short, what the hell is wrong with >George W. Bush? Here it is, another bumbling, barely articulate press conference by >Dubya, one of few he ever gives because he clearly hates the things >and is deeply troubled by them, hates reporters who ask complicated >questions and hates people who dare doubt his simple mindset, his >effectiveness, his policies, his lopsided myopic one-way black/white >good/evil worldview. Bush hates press conferences because can't speak extemporaneously and >can't form a complete sentence without mashing up the language like a >five-year-old and can't express a complex idea to save his life and >somewhere deep down, he knows it, and he knows we know it, and it >makes him mumble and stutter and wish he could be somewhere else, >anywhere else, like sittin' on the back porch in Texas eatin' ribs and >dreamin' 'bout baseball. Ahhh, there now. That's better. But here he is, instead, stuck like a pinned bug in the Rose Garden, >struggling to answer tricky, multisyllabic questions from the >godforsaken press. Go ahead, read the Q&A, linked above. It's sort of >staggering. It's also very impressive, in a soul-stabbing, nauseating >way. Bush is, to be sure and in a word, unyielding. Determined. Immovable. >Also, deeply confused. Myopic as hell. Frighteningly narrow minded. >Weirdly random. Childish in a way that would make any good parent >seriously question whether it might be time to get their child some >Ritalin and an emetic. Unlike you or me or any human anywhere who happens to be in possession >of humility or subtlety of mind, Bush, to this day, admits zero >mistakes. He refuses help, rejects suggestions that everything is not >dandy and swell. He is confounded by questions that dare suggest he >might be somewhat inept, or failing. And he absolutely insists that >America exists in some sort of bizarre utopian vacuum, isolated and >virtuous and towering like a mad hobbled king over our enemies and >allies alike. He is, in other words, our downfall. Iraq? Going smoothly, Bush says, happy with the progress there, >despite huge surges in insurgent violence and endless uptick of the >U.S. death toll and the utter wasteland we've made of that poor, >shredded nation. Iran, North Korea and Egypt? Just dandy. No serious problems at all. >Gotta talk more with that North Korean guy though, sort out the >nukuler problem. Sneering thug John Bolton for U.N. ambassador? You >betcha, still on track, a good man, despite what everybody -- and I do >mean everybody -- says. Overhaul Social Security, despite an enormous lack of support from >Dems and Repubs and the vast majority of the American people? Just a >matter of time, Bush mutters, completely blinded to the fact that >it's an enormous mistake. His deeply hypocritical stance on stem-cell >research that kow-tows to the deeply ignorant Christian Right? No real >answer there. Doesn't compute. Just shrug that sucker right off. Notice, when you read: There is no eloquent, deeply felt defense of >ideas. There is no intellectual breakdown of opinion, no multifaceted >explanation, no passionate clarification. And there is certainly no >reference to outside ideas, a confession that we might need help, >input, wisdom from our neighbors, from science, from the wise and the >experienced. It's a fact we've known all along but which keeps hammering at us like >a drunk gorilla hammers at a dead mouse: Bush is able to speak only at >one level, to one level. The level of a child. The level of a >simpleton. The level of a sweet, bumbling, small-town mayor, >addressing a PTA meeting, everyone in soft plaids and everyone >drinking light beer and everyone wondering about just what the heck to >do about the rusty swing sets and the busted stoplight. Bush is, of course, not talking to you or me or anyone with a remotely >active imagination when he speaks at press conferences, or at his >staged, pre-screened, sycophant-rich town hall meetings, so full of >plain, everyday folk hand-selected for their blind love of Shrub and >lack of ability to ask hard questions (read this transcript of a >recent town hall on Social Security, and come away stupefied at the >man's shocking ability to appear just exactly as gullible and >uneducated as his questioners). He is not even speaking to conservative Democrats or moderate >Republicans. He's certainly not speaking to highly educated people who >harbor a sincere curiousity for and tenuous understanding of the >complexities of the world. Bush is, of course, speaking to children. He is speaking to babies. It >is a decidedly shallow and hollow and oddly deflated type of language >that offers not a single nutritious or substantive thought to the >political or cultural dialogue, other than to expand his staggering >collection of embarrassing Bushisms. It's all merely a crayon drawing, an intellectual wading pool, a big >messy cartoon world populated by manly white good guys and fanged dark >evil guys and we are good and They are evil and that's all there is to >it so please stop asking weird tricky polysyllabic questions. Maybe this is appropriate. Maybe this is as it should be. After all, >we are, by and large, a nation that refuses to grow up, refuses to >take responsibility for our gluttony and its global effects, refuses >to see the world as it is now, a mad tangle of interconnected >humanity, a global marketplace, a hodgepodge of variegated religions >all stemming from the same source and which therefore all require a >nimble and nuanced and deeply intelligent leadership, to navigate. >Qualities which our current leadership has, well, not at all. The U.S. still behaves, when all is said and done, like one of those >scared wild monkeys, clinging desperately to a shiny object despite >the trap closing in all around us, unable to let go of this old, >silly, faux-cowboy mentality of boom boom kill kill God is your daddy >now sit down and shut up. What causes the downfall of empires? What causes the implosion of >leadership, the slide of great nations into the deep muck of recession >and war and mediocrity and numb irrelevance? That's easy. Stagnation. >Refusal to change. Refusal to adapt, to progress. Refusal to grow the >hell up, to take responsibility for our shortcomings and failures, as >well as our successes. Indeed, George W. Bush would make a great small-town mayor, somewhere >deep in a dusty, forgotten part of Texas. His still-appalling >inability to speak with any depth or resonance, coupled with his brand >of personable, aww-shucks, none-too-bright simpleton worldview is >perfect for some cute, redneck, tiny burg. It really is. But for a major world power caught in the throes of a desperate need >to change and grow and evolve, he is, of course, imminent death, >leading us deeper into a regressive ideological tar pit from which we >may never emerge. --------------------------------------------------------------------------- ----- === Subject: Re: Now how did we end up with this genius for President? <04q5a1952fcnhsk6tqagutvibl01pkqrht@4ax.com> In <04q5a1952fcnhsk6tqagutvibl01pkqrht@4ax.com>, on 06/05/2005 >The following really isn't 'noise' at all, but reality: It may be reality, but when it's posted to off-topic groups then it's still noise. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Now how did we end up with this genius for President? >... off-topic ... Yes, your post is offtopic on all the groups to which you posted it. Not a one of them is about you or your failure to discern genuine relevance at all. The discussion here is the way mathematics and science are being ignored, and worse, by corrupt politicians. Destroying the Life and Career.of a Valued Physician-Scientist http://www.promedmail.org/pls/promed/f?p=2400:1001:5120297554616370640::NO:: F2400_P1001_BACK_PAGE,F2400_P1001_PUB_MAIL_ID:1000,29134 >>This type of noise is acceptable. >>I give it the thumbs up. >Morons applaud morons. You're saying you admire bushworshippers? >Mati Meron | When you argue with a fool, >meron@cars.uchicago.edu | chances are he is doing just the same Bush despises science and scientists. You'd expect a qualified scientist to know better than to support Bush. http://www.guardian.co.uk/usa/story/0,12271,1443198,00.html http://abcnews.go.com/Technology/wireStory?id=517770 http://www.commondreams.org/views05/0322-25.htm http://www.commondreams.org/headlines05/0221-27.htm http://www.usatoday.com/news/washington/2005-02-20-bush-science_x.htm http://www.americanhumanist.org/press/NFBushScience.html The following really isn't 'noise' at all, but reality: >Bush, The Spoiled Man-Child >What causes the fall of empires? Why, stubborn leaders who speak like >toddlers and never admit mistakes >- By Mark Morford, SF Gate Columnist >Friday, June 3, 2005 Know what real men do? They admit their mistakes. Know what real >people do in times of great stress and strife and economic downturn? >They seek help, understand they don't know all the answers, realize >they might not've been asking the right questions in the first place. Know what great leaders, great nations do at times of war and fracture >and massive bludgeoning debt? All of the above, all the time, with >great intelligence and humility and grace and awareness and shared >humanity. Or they die. But not BushCo. This is the hilarious thing. This is the appalling >thing, still. How can this man remain so blindly, staggeringly >resolute? How can he be so appallingly ignorant of fact, of truth, of >evidence, of deep thought? In short, what the hell is wrong with >George W. Bush? Here it is, another bumbling, barely articulate press conference by >Dubya, one of few he ever gives because he clearly hates the things >and is deeply troubled by them, hates reporters who ask complicated >questions and hates people who dare doubt his simple mindset, his >effectiveness, his policies, his lopsided myopic one-way black/white >good/evil worldview. Bush hates press conferences because can't speak extemporaneously and >can't form a complete sentence without mashing up the language like a >five-year-old and can't express a complex idea to save his life and >somewhere deep down, he knows it, and he knows we know it, and it >makes him mumble and stutter and wish he could be somewhere else, >anywhere else, like sittin' on the back porch in Texas eatin' ribs and >dreamin' 'bout baseball. Ahhh, there now. That's better. But here he is, instead, stuck like a pinned bug in the Rose Garden, >struggling to answer tricky, multisyllabic questions from the >godforsaken press. Go ahead, read the Q&A, linked above. It's sort of >staggering. It's also very impressive, in a soul-stabbing, nauseating >way. Bush is, to be sure and in a word, unyielding. Determined. Immovable. >Also, deeply confused. Myopic as hell. Frighteningly narrow minded. >Weirdly random. Childish in a way that would make any good parent >seriously question whether it might be time to get their child some >Ritalin and an emetic. Unlike you or me or any human anywhere who happens to be in possession >of humility or subtlety of mind, Bush, to this day, admits zero >mistakes. He refuses help, rejects suggestions that everything is not >dandy and swell. He is confounded by questions that dare suggest he >might be somewhat inept, or failing. And he absolutely insists that >America exists in some sort of bizarre utopian vacuum, isolated and >virtuous and towering like a mad hobbled king over our enemies and >allies alike. He is, in other words, our downfall. Iraq? Going smoothly, Bush says, happy with the progress there, >despite huge surges in insurgent violence and endless uptick of the >U.S. death toll and the utter wasteland we've made of that poor, >shredded nation. Iran, North Korea and Egypt? Just dandy. No serious problems at all. >Gotta talk more with that North Korean guy though, sort out the >nukuler problem. Sneering thug John Bolton for U.N. ambassador? You >betcha, still on track, a good man, despite what everybody -- and I do >mean everybody -- says. Overhaul Social Security, despite an enormous lack of support from >Dems and Repubs and the vast majority of the American people? Just a >matter of time, Bush mutters, completely blinded to the fact that >it's an enormous mistake. His deeply hypocritical stance on stem-cell >research that kow-tows to the deeply ignorant Christian Right? No real >answer there. Doesn't compute. Just shrug that sucker right off. Notice, when you read: There is no eloquent, deeply felt defense of >ideas. There is no intellectual breakdown of opinion, no multifaceted >explanation, no passionate clarification. And there is certainly no >reference to outside ideas, a confession that we might need help, >input, wisdom from our neighbors, from science, from the wise and the >experienced. It's a fact we've known all along but which keeps hammering at us like >a drunk gorilla hammers at a dead mouse: Bush is able to speak only at >one level, to one level. The level of a child. The level of a >simpleton. The level of a sweet, bumbling, small-town mayor, >addressing a PTA meeting, everyone in soft plaids and everyone >drinking light beer and everyone wondering about just what the heck to >do about the rusty swing sets and the busted stoplight. Bush is, of course, not talking to you or me or anyone with a remotely >active imagination when he speaks at press conferences, or at his >staged, pre-screened, sycophant-rich town hall meetings, so full of >plain, everyday folk hand-selected for their blind love of Shrub and >lack of ability to ask hard questions (read this transcript of a >recent town hall on Social Security, and come away stupefied at the >man's shocking ability to appear just exactly as gullible and >uneducated as his questioners). He is not even speaking to conservative Democrats or moderate >Republicans. He's certainly not speaking to highly educated people who >harbor a sincere curiousity for and tenuous understanding of the >complexities of the world. Bush is, of course, speaking to children. He is speaking to babies. It >is a decidedly shallow and hollow and oddly deflated type of language >that offers not a single nutritious or substantive thought to the >political or cultural dialogue, other than to expand his staggering >collection of embarrassing Bushisms. It's all merely a crayon drawing, an intellectual wading pool, a big >messy cartoon world populated by manly white good guys and fanged dark >evil guys and we are good and They are evil and that's all there is to >it so please stop asking weird tricky polysyllabic questions. Maybe this is appropriate. Maybe this is as it should be. After all, >we are, by and large, a nation that refuses to grow up, refuses to >take responsibility for our gluttony and its global effects, refuses >to see the world as it is now, a mad tangle of interconnected >humanity, a global marketplace, a hodgepodge of variegated religions >all stemming from the same source and which therefore all require a >nimble and nuanced and deeply intelligent leadership, to navigate. >Qualities which our current leadership has, well, not at all. The U.S. still behaves, when all is said and done, like one of those >scared wild monkeys, clinging desperately to a shiny object despite >the trap closing in all around us, unable to let go of this old, >silly, faux-cowboy mentality of boom boom kill kill God is your daddy >now sit down and shut up. What causes the downfall of empires? What causes the implosion of >leadership, the slide of great nations into the deep muck of recession >and war and mediocrity and numb irrelevance? That's easy. Stagnation. >Refusal to change. Refusal to adapt, to progress. Refusal to grow the >hell up, to take responsibility for our shortcomings and failures, as >well as our successes. Indeed, George W. Bush would make a great small-town mayor, somewhere >deep in a dusty, forgotten part of Texas. His still-appalling >inability to speak with any depth or resonance, coupled with his brand >of personable, aww-shucks, none-too-bright simpleton worldview is >perfect for some cute, redneck, tiny burg. It really is. But for a major world power caught in the throes of a desperate need >to change and grow and evolve, he is, of course, imminent death, >leading us deeper into a regressive ideological tar pit from which we >may never emerge. --------------------------------------------------------------------------- ----- === Subject: Re: Now how did we end up with this genius for President? <04q5a1952fcnhsk6tqagutvibl01pkqrht@4ax.com> <42a372ef$2$fuzhry+tra$mr2ice@news.patriot.net> In , on 06/06/2005 >The discussion here is the way mathematics and science >are being ignored, and worse, by corrupt politicians. Really, tonto? Have you been taking logic lessons from Carl Rove? Take a closer look at the title you posted: >Physician-Scientist That's a strange way to spell Mathematician. sci.med or sci.misc would have been appropriate; sci.math was not. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Now how did we end up with this genius for President? >... tonto? ... Feeling 'superior', Kemosabe? >... a strange way to spell Mathematician ... Mathematics is the language of many sciences. It improves one's awareness of the maths to be open to those areas in which it is applied. >... off-topic ... Yes, your post is offtopic on all the groups to which you posted it. Not a one of them is about you or your failure to discern genuine relevance at all. The discussion here is the way mathematics and science are being ignored, and worse, by corrupt politicians. Destroying the Life and Career.of a Valued Physician-Scientist http://www.promedmail.org/pls/promed/f?p=2400:1001:5120297554616370640::NO:: F2400_P1001_BACK_PAGE,F2400_P1001_PUB_MAIL_ID:1000,29134 >>This type of noise is acceptable. >>I give it the thumbs up. >Morons applaud morons. You're saying you admire bushworshippers? >Mati Meron | When you argue with a fool, >meron@cars.uchicago.edu | chances are he is doing just the same Bush despises science and scientists. You'd expect a qualified scientist to know better than to support Bush. http://www.guardian.co.uk/usa/story/0,12271,1443198,00.html http://abcnews.go.com/Technology/wireStory?id=517770 http://www.commondreams.org/views05/0322-25.htm http://www.commondreams.org/headlines05/0221-27.htm http://www.usatoday.com/news/washington/2005-02-20-bush-science_x.htm http://www.americanhumanist.org/press/NFBushScience.html The following really isn't 'noise' at all, but reality: >Bush, The Spoiled Man-Child >What causes the fall of empires? Why, stubborn leaders who speak like >toddlers and never admit mistakes >- By Mark Morford, SF Gate Columnist >Friday, June 3, 2005 Know what real men do? They admit their mistakes. Know what real >people do in times of great stress and strife and economic downturn? >They seek help, understand they don't know all the answers, realize >they might not've been asking the right questions in the first place. Know what great leaders, great nations do at times of war and fracture >and massive bludgeoning debt? All of the above, all the time, with >great intelligence and humility and grace and awareness and shared >humanity. Or they die. But not BushCo. This is the hilarious thing. This is the appalling >thing, still. How can this man remain so blindly, staggeringly >resolute? How can he be so appallingly ignorant of fact, of truth, of >evidence, of deep thought? In short, what the hell is wrong with >George W. Bush? Here it is, another bumbling, barely articulate press conference by >Dubya, one of few he ever gives because he clearly hates the things >and is deeply troubled by them, hates reporters who ask complicated >questions and hates people who dare doubt his simple mindset, his >effectiveness, his policies, his lopsided myopic one-way black/white >good/evil worldview. Bush hates press conferences because can't speak extemporaneously and >can't form a complete sentence without mashing up the language like a >five-year-old and can't express a complex idea to save his life and >somewhere deep down, he knows it, and he knows we know it, and it >makes him mumble and stutter and wish he could be somewhere else, >anywhere else, like sittin' on the back porch in Texas eatin' ribs and >dreamin' 'bout baseball. Ahhh, there now. That's better. But here he is, instead, stuck like a pinned bug in the Rose Garden, >struggling to answer tricky, multisyllabic questions from the >godforsaken press. Go ahead, read the Q&A, linked above. It's sort of >staggering. It's also very impressive, in a soul-stabbing, nauseating >way. Bush is, to be sure and in a word, unyielding. Determined. Immovable. >Also, deeply confused. Myopic as hell. Frighteningly narrow minded. >Weirdly random. Childish in a way that would make any good parent >seriously question whether it might be time to get their child some >Ritalin and an emetic. Unlike you or me or any human anywhere who happens to be in possession >of humility or subtlety of mind, Bush, to this day, admits zero >mistakes. He refuses help, rejects suggestions that everything is not >dandy and swell. He is confounded by questions that dare suggest he >might be somewhat inept, or failing. And he absolutely insists that >America exists in some sort of bizarre utopian vacuum, isolated and >virtuous and towering like a mad hobbled king over our enemies and >allies alike. He is, in other words, our downfall. Iraq? Going smoothly, Bush says, happy with the progress there, >despite huge surges in insurgent violence and endless uptick of the >U.S. death toll and the utter wasteland we've made of that poor, >shredded nation. Iran, North Korea and Egypt? Just dandy. No serious problems at all. >Gotta talk more with that North Korean guy though, sort out the >nukuler problem. Sneering thug John Bolton for U.N. ambassador? You >betcha, still on track, a good man, despite what everybody -- and I do >mean everybody -- says. Overhaul Social Security, despite an enormous lack of support from >Dems and Repubs and the vast majority of the American people? Just a >matter of time, Bush mutters, completely blinded to the fact that >it's an enormous mistake. His deeply hypocritical stance on stem-cell >research that kow-tows to the deeply ignorant Christian Right? No real >answer there. Doesn't compute. Just shrug that sucker right off. Notice, when you read: There is no eloquent, deeply felt defense of >ideas. There is no intellectual breakdown of opinion, no multifaceted >explanation, no passionate clarification. And there is certainly no >reference to outside ideas, a confession that we might need help, >input, wisdom from our neighbors, from science, from the wise and the >experienced. It's a fact we've known all along but which keeps hammering at us like >a drunk gorilla hammers at a dead mouse: Bush is able to speak only at >one level, to one level. The level of a child. The level of a >simpleton. The level of a sweet, bumbling, small-town mayor, >addressing a PTA meeting, everyone in soft plaids and everyone >drinking light beer and everyone wondering about just what the heck to >do about the rusty swing sets and the busted stoplight. Bush is, of course, not talking to you or me or anyone with a remotely >active imagination when he speaks at press conferences, or at his >staged, pre-screened, sycophant-rich town hall meetings, so full of >plain, everyday folk hand-selected for their blind love of Shrub and >lack of ability to ask hard questions (read this transcript of a >recent town hall on Social Security, and come away stupefied at the >man's shocking ability to appear just exactly as gullible and >uneducated as his questioners). He is not even speaking to conservative Democrats or moderate >Republicans. He's certainly not speaking to highly educated people who >harbor a sincere curiousity for and tenuous understanding of the >complexities of the world. Bush is, of course, speaking to children. He is speaking to babies. It >is a decidedly shallow and hollow and oddly deflated type of language >that offers not a single nutritious or substantive thought to the >political or cultural dialogue, other than to expand his staggering >collection of embarrassing Bushisms. It's all merely a crayon drawing, an intellectual wading pool, a big >messy cartoon world populated by manly white good guys and fanged dark >evil guys and we are good and They are evil and that's all there is to >it so please stop asking weird tricky polysyllabic questions. Maybe this is appropriate. Maybe this is as it should be. After all, >we are, by and large, a nation that refuses to grow up, refuses to >take responsibility for our gluttony and its global effects, refuses >to see the world as it is now, a mad tangle of interconnected >humanity, a global marketplace, a hodgepodge of variegated religions >all stemming from the same source and which therefore all require a >nimble and nuanced and deeply intelligent leadership, to navigate. >Qualities which our current leadership has, well, not at all. The U.S. still behaves, when all is said and done, like one of those >scared wild monkeys, clinging desperately to a shiny object despite >the trap closing in all around us, unable to let go of this old, >silly, faux-cowboy mentality of boom boom kill kill God is your daddy >now sit down and shut up. What causes the downfall of empires? What causes the implosion of >leadership, the slide of great nations into the deep muck of recession >and war and mediocrity and numb irrelevance? That's easy. Stagnation. >Refusal to change. Refusal to adapt, to progress. Refusal to grow the >hell up, to take responsibility for our shortcomings and failures, as >well as our successes. Indeed, George W. Bush would make a great small-town mayor, somewhere >deep in a dusty, forgotten part of Texas. His still-appalling >inability to speak with any depth or resonance, coupled with his brand >of personable, aww-shucks, none-too-bright simpleton worldview is >perfect for some cute, redneck, tiny burg. It really is. But for a major world power caught in the throes of a desperate need >to change and grow and evolve, he is, of course, imminent death, >leading us deeper into a regressive ideological tar pit from which we >may never emerge. --------------------------------------------------------------------------- ----- === Subject: Re: Now how did we end up with this genius for President? <04q5a1952fcnhsk6tqagutvibl01pkqrht@4ax.com> <42a372ef$2$fuzhry+tra$mr2ice@news.patriot.net> <42a5c1a4$36$fuzhry+tra$mr2ice@news.patriot.net> In , on 06/07/2005 at 06:56 PM, * US * said: >Feeling 'superior', Kemosabe? Certainly, tonto, and you've just proven me right. It went right over your head. >Mathematics is the language of many sciences. So are English, French, Russian and German; that wouldn't justify crossposting to news groups for them. This thread has nothing to do with Mathematics. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not === Subject: Re: Now how did we end up with this genius for President? >Certainly... Your 'pride' is noted, as anticipated. >So are English, French, Russian and German; that wouldn't justify >crossposting to news groups for them. This thread has nothing to do >with Mathematics. accurate, or flawed? Show your work. >... tonto? ... Feeling 'superior', Kemosabe? >... a strange way to spell Mathematician ... Mathematics is the language of many sciences. It improves one's awareness of the maths to be open to those areas in which it is applied. >... off-topic ... Yes, your post is offtopic on all the groups to which you posted it. Not a one of them is about you or your failure to discern genuine relevance at all. The discussion here is the way mathematics and science are being ignored, and worse, by corrupt politicians. Destroying the Life and Career.of a Valued Physician-Scientist http://www.promedmail.org/pls/promed/f?p=2400:1001:5120297554616370640::NO:: F2400_P1001_BACK_PAGE,F2400_P1001_PUB_MAIL_ID:1000,29134 >>This type of noise is acceptable. >>I give it the thumbs up. >Morons applaud morons. You're saying you admire bushworshippers? >Mati Meron | When you argue with a fool, >meron@cars.uchicago.edu | chances are he is doing just the same Bush despises science and scientists. You'd expect a qualified scientist to know better than to support Bush. http://www.guardian.co.uk/usa/story/0,12271,1443198,00.html http://abcnews.go.com/Technology/wireStory?id=517770 http://www.commondreams.org/views05/0322-25.htm http://www.commondreams.org/headlines05/0221-27.htm http://www.usatoday.com/news/washington/2005-02-20-bush-science_x.htm http://www.americanhumanist.org/press/NFBushScience.html The following really isn't 'noise' at all, but reality: >Bush, The Spoiled Man-Child >What causes the fall of empires? Why, stubborn leaders who speak like >toddlers and never admit mistakes >- By Mark Morford, SF Gate Columnist >Friday, June 3, 2005 Know what real men do? They admit their mistakes. Know what real >people do in times of great stress and strife and economic downturn? >They seek help, understand they don't know all the answers, realize >they might not've been asking the right questions in the first place. Know what great leaders, great nations do at times of war and fracture >and massive bludgeoning debt? All of the above, all the time, with >great intelligence and humility and grace and awareness and shared >humanity. Or they die. But not BushCo. This is the hilarious thing. This is the appalling >thing, still. How can this man remain so blindly, staggeringly >resolute? How can he be so appallingly ignorant of fact, of truth, of >evidence, of deep thought? In short, what the hell is wrong with >George W. Bush? Here it is, another bumbling, barely articulate press conference by >Dubya, one of few he ever gives because he clearly hates the things >and is deeply troubled by them, hates reporters who ask complicated >questions and hates people who dare doubt his simple mindset, his >effectiveness, his policies, his lopsided myopic one-way black/white >good/evil worldview. Bush hates press conferences because can't speak extemporaneously and >can't form a complete sentence without mashing up the language like a >five-year-old and can't express a complex idea to save his life and >somewhere deep down, he knows it, and he knows we know it, and it >makes him mumble and stutter and wish he could be somewhere else, >anywhere else, like sittin' on the back porch in Texas eatin' ribs and >dreamin' 'bout baseball. Ahhh, there now. That's better. But here he is, instead, stuck like a pinned bug in the Rose Garden, >struggling to answer tricky, multisyllabic questions from the >godforsaken press. Go ahead, read the Q&A, linked above. It's sort of >staggering. It's also very impressive, in a soul-stabbing, nauseating >way. Bush is, to be sure and in a word, unyielding. Determined. Immovable. >Also, deeply confused. Myopic as hell. Frighteningly narrow minded. >Weirdly random. Childish in a way that would make any good parent >seriously question whether it might be time to get their child some >Ritalin and an emetic. Unlike you or me or any human anywhere who happens to be in possession >of humility or subtlety of mind, Bush, to this day, admits zero >mistakes. He refuses help, rejects suggestions that everything is not >dandy and swell. He is confounded by questions that dare suggest he >might be somewhat inept, or failing. And he absolutely insists that >America exists in some sort of bizarre utopian vacuum, isolated and >virtuous and towering like a mad hobbled king over our enemies and >allies alike. He is, in other words, our downfall. Iraq? Going smoothly, Bush says, happy with the progress there, >despite huge surges in insurgent violence and endless uptick of the >U.S. death toll and the utter wasteland we've made of that poor, >shredded nation. Iran, North Korea and Egypt? Just dandy. No serious problems at all. >Gotta talk more with that North Korean guy though, sort out the >nukuler problem. Sneering thug John Bolton for U.N. ambassador? You >betcha, still on track, a good man, despite what everybody -- and I do >mean everybody -- says. Overhaul Social Security, despite an enormous lack of support from >Dems and Repubs and the vast majority of the American people? Just a >matter of time, Bush mutters, completely blinded to the fact that >it's an enormous mistake. His deeply hypocritical stance on stem-cell >research that kow-tows to the deeply ignorant Christian Right? No real >answer there. Doesn't compute. Just shrug that sucker right off. Notice, when you read: There is no eloquent, deeply felt defense of >ideas. There is no intellectual breakdown of opinion, no multifaceted >explanation, no passionate clarification. And there is certainly no >reference to outside ideas, a confession that we might need help, >input, wisdom from our neighbors, from science, from the wise and the >experienced. It's a fact we've known all along but which keeps hammering at us like >a drunk gorilla hammers at a dead mouse: Bush is able to speak only at >one level, to one level. The level of a child. The level of a >simpleton. The level of a sweet, bumbling, small-town mayor, >addressing a PTA meeting, everyone in soft plaids and everyone >drinking light beer and everyone wondering about just what the heck to >do about the rusty swing sets and the busted stoplight. Bush is, of course, not talking to you or me or anyone with a remotely >active imagination when he speaks at press conferences, or at his >staged, pre-screened, sycophant-rich town hall meetings, so full of >plain, everyday folk hand-selected for their blind love of Shrub and >lack of ability to ask hard questions (read this transcript of a >recent town hall on Social Security, and come away stupefied at the >man's shocking ability to appear just exactly as gullible and >uneducated as his questioners). He is not even speaking to conservative Democrats or moderate >Republicans. He's certainly not speaking to highly educated people who >harbor a sincere curiousity for and tenuous understanding of the >complexities of the world. Bush is, of course, speaking to children. He is speaking to babies. It >is a decidedly shallow and hollow and oddly deflated type of language >that offers not a single nutritious or substantive thought to the >political or cultural dialogue, other than to expand his staggering >collection of embarrassing Bushisms. It's all merely a crayon drawing, an intellectual wading pool, a big >messy cartoon world populated by manly white good guys and fanged dark >evil guys and we are good and They are evil and that's all there is to >it so please stop asking weird tricky polysyllabic questions. Maybe this is appropriate. Maybe this is as it should be. After all, >we are, by and large, a nation that refuses to grow up, refuses to >take responsibility for our gluttony and its global effects, refuses >to see the world as it is now, a mad tangle of interconnected >humanity, a global marketplace, a hodgepodge of variegated religions >all stemming from the same source and which therefore all require a >nimble and nuanced and deeply intelligent leadership, to navigate. >Qualities which our current leadership has, well, not at all. The U.S. still behaves, when all is said and done, like one of those >scared wild monkeys, clinging desperately to a shiny object despite >the trap closing in all around us, unable to let go of this old, >silly, faux-cowboy mentality of boom boom kill kill God is your daddy >now sit down and shut up. What causes the downfall of empires? What causes the implosion of >leadership, the slide of great nations into the deep muck of recession >and war and mediocrity and numb irrelevance? That's easy. Stagnation. >Refusal to change. Refusal to adapt, to progress. Refusal to grow the >hell up, to take responsibility for our shortcomings and failures, as >well as our successes. Indeed, George W. Bush would make a great small-town mayor, somewhere >deep in a dusty, forgotten part of Texas. His still-appalling >inability to speak with any depth or resonance, coupled with his brand >of personable, aww-shucks, none-too-bright simpleton worldview is >perfect for some cute, redneck, tiny burg. It really is. But for a major world power caught in the throes of a desperate need >to change and grow and evolve, he is, of course, imminent death, >leading us deeper into a regressive ideological tar pit from which we >may never emerge. --------------------------------------------------------------------------- ----- === Subject: Re: Now how did we end up with this genius for President? <04q5a1952fcnhsk6tqagutvibl01pkqrht@4ax.com> Food for thought: The first principle is that you must not fool yourself - and you are the easiest person to fool. - Richard Feynman, 1974 Caltech commencement address What luck for rulers, that men do not think. - Adolf Hitler === Subject: Re: Now how did we end up with this genius for President? >Food for thought: The first principle is that you must not fool yourself - and you are >the easiest person to fool. >- Richard Feynman, 1974 Caltech commencement address What luck for rulers, that men do not think. >- Adolf Hitler Feynman's one of my favorites. Here's some more food for thought: the follower of Bush fools himself by believing a known liar. >>This type of noise is acceptable. >>I give it the thumbs up. >Morons applaud morons. You're saying you admire bushworshippers? >Mati Meron | When you argue with a fool, >meron@cars.uchicago.edu | chances are he is doing just the same Bush despises science and scientists. You'd expect a qualified scientist to know better than to support Bush. http://www.guardian.co.uk/usa/story/0,12271,1443198,00.html http://abcnews.go.com/Technology/wireStory?id=517770 http://www.commondreams.org/views05/0322-25.htm http://www.commondreams.org/headlines05/0221-27.htm http://www.usatoday.com/news/washington/2005-02-20-bush-science_x.htm http://www.americanhumanist.org/press/NFBushScience.html The following really isn't 'noise' at all, but reality: >Bush, The Spoiled Man-Child >What causes the fall of empires? Why, stubborn leaders who speak like >toddlers and never admit mistakes >- By Mark Morford, SF Gate Columnist >Friday, June 3, 2005 Know what real men do? They admit their mistakes. Know what real >people do in times of great stress and strife and economic downturn? >They seek help, understand they don't know all the answers, realize >they might not've been asking the right questions in the first place. Know what great leaders, great nations do at times of war and fracture >and massive bludgeoning debt? All of the above, all the time, with >great intelligence and humility and grace and awareness and shared >humanity. Or they die. But not BushCo. This is the hilarious thing. This is the appalling >thing, still. How can this man remain so blindly, staggeringly >resolute? How can he be so appallingly ignorant of fact, of truth, of >evidence, of deep thought? In short, what the hell is wrong with >George W. Bush? Here it is, another bumbling, barely articulate press conference by >Dubya, one of few he ever gives because he clearly hates the things >and is deeply troubled by them, hates reporters who ask complicated >questions and hates people who dare doubt his simple mindset, his >effectiveness, his policies, his lopsided myopic one-way black/white >good/evil worldview. Bush hates press conferences because can't speak extemporaneously and >can't form a complete sentence without mashing up the language like a >five-year-old and can't express a complex idea to save his life and >somewhere deep down, he knows it, and he knows we know it, and it >makes him mumble and stutter and wish he could be somewhere else, >anywhere else, like sittin' on the back porch in Texas eatin' ribs and >dreamin' 'bout baseball. Ahhh, there now. That's better. But here he is, instead, stuck like a pinned bug in the Rose Garden, >struggling to answer tricky, multisyllabic questions from the >godforsaken press. Go ahead, read the Q&A, linked above. It's sort of >staggering. It's also very impressive, in a soul-stabbing, nauseating >way. Bush is, to be sure and in a word, unyielding. Determined. Immovable. >Also, deeply confused. Myopic as hell. Frighteningly narrow minded. >Weirdly random. Childish in a way that would make any good parent >seriously question whether it might be time to get their child some >Ritalin and an emetic. Unlike you or me or any human anywhere who happens to be in possession >of humility or subtlety of mind, Bush, to this day, admits zero >mistakes. He refuses help, rejects suggestions that everything is not >dandy and swell. He is confounded by questions that dare suggest he >might be somewhat inept, or failing. And he absolutely insists that >America exists in some sort of bizarre utopian vacuum, isolated and >virtuous and towering like a mad hobbled king over our enemies and >allies alike. He is, in other words, our downfall. Iraq? Going smoothly, Bush says, happy with the progress there, >despite huge surges in insurgent violence and endless uptick of the >U.S. death toll and the utter wasteland we've made of that poor, >shredded nation. Iran, North Korea and Egypt? Just dandy. No serious problems at all. >Gotta talk more with that North Korean guy though, sort out the >nukuler problem. Sneering thug John Bolton for U.N. ambassador? You >betcha, still on track, a good man, despite what everybody -- and I do >mean everybody -- says. Overhaul Social Security, despite an enormous lack of support from >Dems and Repubs and the vast majority of the American people? Just a >matter of time, Bush mutters, completely blinded to the fact that >it's an enormous mistake. His deeply hypocritical stance on stem-cell >research that kow-tows to the deeply ignorant Christian Right? No real >answer there. Doesn't compute. Just shrug that sucker right off. Notice, when you read: There is no eloquent, deeply felt defense of >ideas. There is no intellectual breakdown of opinion, no multifaceted >explanation, no passionate clarification. And there is certainly no >reference to outside ideas, a confession that we might need help, >input, wisdom from our neighbors, from science, from the wise and the >experienced. It's a fact we've known all along but which keeps hammering at us like >a drunk gorilla hammers at a dead mouse: Bush is able to speak only at >one level, to one level. The level of a child. The level of a >simpleton. The level of a sweet, bumbling, small-town mayor, >addressing a PTA meeting, everyone in soft plaids and everyone >drinking light beer and everyone wondering about just what the heck to >do about the rusty swing sets and the busted stoplight. Bush is, of course, not talking to you or me or anyone with a remotely >active imagination when he speaks at press conferences, or at his >staged, pre-screened, sycophant-rich town hall meetings, so full of >plain, everyday folk hand-selected for their blind love of Shrub and >lack of ability to ask hard questions (read this transcript of a >recent town hall on Social Security, and come away stupefied at the >man's shocking ability to appear just exactly as gullible and >uneducated as his questioners). He is not even speaking to conservative Democrats or moderate >Republicans. He's certainly not speaking to highly educated people who >harbor a sincere curiousity for and tenuous understanding of the >complexities of the world. Bush is, of course, speaking to children. He is speaking to babies. It >is a decidedly shallow and hollow and oddly deflated type of language >that offers not a single nutritious or substantive thought to the >political or cultural dialogue, other than to expand his staggering >collection of embarrassing Bushisms. It's all merely a crayon drawing, an intellectual wading pool, a big >messy cartoon world populated by manly white good guys and fanged dark >evil guys and we are good and They are evil and that's all there is to >it so please stop asking weird tricky polysyllabic questions. Maybe this is appropriate. Maybe this is as it should be. After all, >we are, by and large, a nation that refuses to grow up, refuses to >take responsibility for our gluttony and its global effects, refuses >to see the world as it is now, a mad tangle of interconnected >humanity, a global marketplace, a hodgepodge of variegated religions >all stemming from the same source and which therefore all require a >nimble and nuanced and deeply intelligent leadership, to navigate. >Qualities which our current leadership has, well, not at all. The U.S. still behaves, when all is said and done, like one of those >scared wild monkeys, clinging desperately to a shiny object despite >the trap closing in all around us, unable to let go of this old, >silly, faux-cowboy mentality of boom boom kill kill God is your daddy >now sit down and shut up. What causes the downfall of empires? What causes the implosion of >leadership, the slide of great nations into the deep muck of recession >and war and mediocrity and numb irrelevance? That's easy. Stagnation. >Refusal to change. Refusal to adapt, to progress. Refusal to grow the >hell up, to take responsibility for our shortcomings and failures, as >well as our successes. Indeed, George W. Bush would make a great small-town mayor, somewhere >deep in a dusty, forgotten part of Texas. His still-appalling >inability to speak with any depth or resonance, coupled with his brand >of personable, aww-shucks, none-too-bright simpleton worldview is >perfect for some cute, redneck, tiny burg. It really is. But for a major world power caught in the throes of a desperate need >to change and grow and evolve, he is, of course, imminent death, >leading us deeper into a regressive ideological tar pit from which we >may never emerge. --------------------------------------------------------------------------- ----- === Subject: Re: Now how did we end up with this genius for President? > Bush despises science and scientists. I despise anonymous posters. If information wants to be free that includes the information of who you are and why should we take you seriously. > You'd expect a qualified scientist to know better than to support > Bush. I regret to say that he's no Reagan. Reagan, after all, was able to point out that the most abundant form of toxic waste in the atmosphere was produced by green plants. On the other hand, in 2008 I might be able to vote for Professor Newt Gingrich. -- http://hertzlinger.blogspot.com === Subject: Re: Now how did we end up with this genius for President? Joseph Hertzlinger Bush despises science and scientists. I despise anonymous posters. I don'tthink Bush despises scientists but I'm sure he is sceptical of them because they are wrong so much. They advance an imaginary theory and get angry with anyone who challenges it before it is thoroughly vetted! jt -- Without the second amendment the first amendment means nil. www.townhall.com www.newsmax.com www.nranews.org > On the other hand, in 2008 I might be able to vote for Professor Newt > Gingrich. -- > http://hertzlinger.blogspot.com === Subject: Re: Now how did we end up with this genius for President? A bipartisan, all-star roster of Nobel Prize winners and former federal science officials accused the Bush administration Wednesday of politicizing science. >I don'tthink ... >jt You're afraid to think, even if you had the capacity to do so. === Subject: Re: Now how did we end up with this genius for President? Linux platform NewsFleX homepage: http://panteltje.com/panteltje/newsflex/ and ftp download ftp://sunsite.unc.edu/pub/linux/system/news/readers/ listed above. : >A bipartisan, all-star roster of Nobel Prize winners and former federal science officials >accused the Bush administration Wednesday of politicizing science. >I don'tthink ... >>jt You're afraid to think, even if you had the capacity to do so. hear hear. === Subject: Re: Now how did we end up with this genius for President? >: >A bipartisan, all-star roster of Nobel Prize winners and former federal science officials >>accused the Bush administration Wednesday of politicizing science. >I don'tthink ... >jt >>You're afraid to think, even if you had the capacity to do so. >hear hear. I used to wonder, such a long time ago, how it came to be that the Germans allowed such harm to be done by those in their government that the rest of the world had to step in and stop it. To my dismay, I am now observing more directly how that occurs. The connection is also far more direct than many people realize, yet. http://www.takebackthemedia.com/bushnonazi.html === Subject: Re: Now how did we end up with this genius for President? > A bipartisan, all-star roster of Nobel Prize winners and former federal science officials > accused the Bush administration Wednesday of politicizing science. > Well, well, well. All that W is doing is using his legal authority to affect how public money is spent. The spending of public money is definitely subject to politicizing. If anyone is pppoliticizing the issue, however, it is those scientists who are being shameless is claiming that: 1) the questioned research would nearly certain lead to cures of everything from bad breath to cancer; 2) the results of the reserach will lead to great economic advantages to the country that pays for it; but 3) that without federal government support the research would never be done. This sort of reminds me how the homosexual community (and its fellow travelers) claimed that the reason HIV killed so many folks was that RR decided that the victims brought the disease upon themselves. IOW: RR somehow wasted 8 years of potential development of a cure. But RR has been out of office for 12 years. No NIV cure. But the queers and butt f*cking each other as much as effort. > I don'tthink ... >jt You're afraid to think, even if you had the capacity to do so. === Subject: Re: Now how did we end up with this genius for President? ...science and technology are crucial building blocks for American prosperity that have not be adequately managed in the last four years... http://scientistsandengineersforchange.org/index.php money is spent. You go ahead and believe that, if it makes your bedwetting diminish. Let the competent folks deal with reality. >... pppoliticizing ... There you go with your pp problem, again. A bipartisan, all-star roster of Nobel Prize winners and former federal science officials accused the Bush administration Wednesday of politicizing science. >I don'tthink ... >jt You're afraid to think, even if you had the capacity to do so. === Subject: Re: Now how did we end up with this genius for President? > ...science and technology are crucial building blocks for American > prosperity that have not be adequately managed in the last four years... Oh, yeah. That's a variation of: We get back N times what we spend on space research in benefits for the civilian economy. But when public money is spent, the ENTIRE public has a right to participate in the decision on how to spend the money. That's not complicated. It's how a democratic-republic is supposed to operate. When what these scientists and engineers are saying is that the public should just hand over the cash and let the scientists and engineers decide what's best for us. All that W is doing is using his legal authority to affect how public >money is spent. You go ahead and believe that, if it makes your bedwetting diminish. My, my. You believe that the POTUS should NOT use his authority to decide how public money is spent? Seems to me that you are the bedwetter here. === Subject: Re: Now how did we end up with this genius for President? in the decision on how to spend the money. So you should object to the fact that Bush is plundering the US Treasury to load his own and Cheney's pockets with their treasonous war profiteering. >When what these scientists and engineers are saying is that the public >should just hand over the cash and let the scientists and engineers decide >what's best for us. Why do you imagine that? Science doesn't work that way. You should learn about it, if you ever gain the capacity. What is being said, were you able to read for comprehension, is that valid scientific results are being ignored/thwarted by those who'd prefer to let the citizens come to harm thereby, since it's profitable to the corrupt in those instances. >You believe that the POTUS should NOT use his authority to decide how public >money is spent? You merely fail to comprehend the fact that the occupying fascist Bush is _misusing_ that 'authority'. The difference, significant as it is, eludes you, along with so much else, as usual. ...science and technology are crucial building blocks for American prosperity that have not be adequately managed in the last four years... http://scientistsandengineersforchange.org/index.php money is spent. You go ahead and believe that, if it makes your bedwetting diminish. Let the competent folks deal with reality. >... pppoliticizing ... There you go with your pp problem, again. A bipartisan, all-star roster of Nobel Prize winners and former federal science officials accused the Bush administration Wednesday of politicizing science. >I don'tthink ... >jt You're afraid to think, even if you had the capacity to do so. === Subject: Re: Now how did we end up with this genius for President? But when public money is spent, the ENTIRE public has a right to participate >in the decision on how to spend the money. So you should object to the fact that Bush is plundering > the US Treasury to load his own and Cheney's pockets > with their treasonous war profiteering. When what these scientists and engineers are saying is that the public >should just hand over the cash and let the scientists and engineers decide >what's best for us. Why do you imagine that? Science doesn't work that way. Really? BIG SCIENCE works EXACTLY that way. You should learn about it, if you ever gain the capacity. My, my. You mother turned her back and leet you get on the computer again! What is being said, were you able to read for comprehension, > is that valid scientific results are being ignored/thwarted by > those who'd prefer to let the citizens come to harm thereby, > since it's profitable to the corrupt in those instances. So, what's being SAID is that W should permit essentiallly un-restricted stem cell reserach functed by federal government (i.e.: taxpayer) money. All W is doing is placing some restrictions on the research funded by the federal government. That's all. Severa states have decided to fund such research and so long as the research doesn't use federal funds (or, in certain circumstances) equipment paid for with federal funds, the researchs can play with LIFE all they want. You believe that the POTUS should NOT use his authority to decide how public >money is spent? You merely fail to comprehend the fact that the occupying > fascist Bush is _misusing_ that 'authority'. Not at all. It's a proper use of the authority. You are being a baby and saying that whenever the POTUS takes a decision with which you don't agree then the POTUS is misusing his authority. That's nonsense. The difference, significant as it is, eludes you, along with > so much else, as usual. Yeah, yeah. Now eat the lunch your mother prepared and take your afternoon map.