mm-5854 === Subject: Re: Multiplication and convolution question > I have a question about finding a time-domain series corresponding to multiplication and convolution. Basically, consider the following scenario: A(t)xB(t) = A(t)*C(t) Here 'x' denotes multiplication and '*' denotes convolution. I know A(t) and B(t). Is there any method to find C(t)? a mathematical approach? > Try Laplace transforms, or Fourier transforms. R.G. Vickson === Subject: Re: Projecting 3D coplanar points to 2D I have 4 arbitrary points in 3D, which have been determined to be > coplanar. The plane that they lie in is not parallel to any of the 3 > coordinate planes (not parallel to XY plane, XZ plane, or YZ > plane). > I would like to come up with an analogous set of 4 2D points that > have > exactly the same relationships among themselves that the original 3D > points do. In other words, each of the points is the same distance from the > others, and if I took vectors from one of the points to each of the > other 3, the angles between these vectors would be the same as in the > original points. How can it be done!? > Label these 4 points as X, A, B, C. Pick one, say X, as the 'origin'. The vectors XA, XB span the the affine plane anchored at X. Orthonormalize the vector XA and XB to generate an orthonormal base (e A, e B). Since your 4 points are coplanar, XC is a linear combination of e A, e B. You can work out XC's coordinate in this base by taking inner products with e A, e B. ( which can be expressed using inner products and norms among XA, XB, XC. ) === Subject: Re: Pi Reward?! > A better contest would have been to find the rational number with the > smallest denominator which approximates pi better than 355/113. > (Answer: 52163/16604) A better contest (IMHO) would be to find the rational number whose numerator and denominator are both primes, such that the absolute value of the product of the denominator and the error is minimised. That should help keep people away from continued fractions, which are the magic bullet that's always rolled out in situations like this. Phil -- I tried the Vista speech recognition by running the tutorial. I was amazed, it was awesome, recognised every word I said. Then I said the wrong word ... and it typed the right one. It was actually just detecting a sound and printing the expected word! -- pbhj on /. === Subject: Re: convex polyhedron so, the correct answer is 104, am i right ? === Subject: Re: Sequence > > On 14 maalis, 16:30, dark.sorrow.myst...@gmail.com > Hi I am cant seem to find the formula for the sequence 0, 0 , 1/2 , > 1/4 , 3/4 , 3/8 , 7/8 , 7/16 , 15/16 , 15/32, 31/32 ... > I can see that you are adding 1/2 the multiplying by 1/2 etc... > > It looks like 0,... then (2^(n/2) - 1)/2^(n/2), n = 2t, t /in Z_+, (2^ > ((n - 1)/2 - 1)/ 2^n , if n = 2t - 1 t /in Z_+, but I didn`t proof > it. > Typo. It looks like 0,... then (2^(n/2) - 1)/2^(n/2), n = 2t, t /in Z_ > +, (2^ > (n - 1)/2 - 1)/ 2^n , if n = 2t - 1 t /in Z_+, but I didn`t proof > it, didn`t have the time to check, maybe this helps the OP? > Sigh. I will correct this one more time and try to proof it. > It looks like 0,... then (2^(n/2) - 1)/2^(n/2), n = 2t, t /in Z_ > +, (2^(n - 1)/2 - 1)/ 2^(n + 1)/2 , if n = 2t - 1 t /in Z_+. > Proof: by induction first when n = 2t - 1, t /in Z_+ > base should be OK. induction hypothesis (2^(n - 1)/2 - 1)/ 2^(n +1)/ > 2 , if n = 2t_0 - 1 t_0 /in Z > now ((2^(n - 1)/2 - 1)/ (2^(n + 1)/2)) + 1/2)*1/2 = ((2^(n - 1)/2 - 1 > + 2^((n + 1)/2 - 1) / 2^(n +1)/2 + 1) = ((2^t_0 - 1 + 2^(t_0)) / 2^(n > + 1)/2 + 1) = (2^ (t_0 + 1) - 1/ > 2^(t_0 + 1) = (2^(n + 1)/2 - 1)/ 2^(n + 3)/2. > Second induction: n = 2t, t /in Z_+, base should be clear, now (((2^(n/ > 2) - 1)/2^(n/2)) + 1/2)*1/2 = (2^(n/2) - 1 + 2^((n/2) - 1))/ 2^((n/2) > + 1) = 2^(n) - 1/ 2^((n)/2) = 2^((n + 1)/2) - 1)/(2^(n + 3)/2). > Hope this is now right. > insight -- Michael Press === Subject: Rant about The Creator's Glory Rant about The Creator's Glory as reflected in how light behaves (Relativity). When He made this World as it is, He *never* *meant* for humans to be the OVERSEERS (or stewards) of His Creation. Mankind has been following a false avenue all these centuries and millenia, thinking that it/he can behold ALL there is of The Creation, rather if not literally behold at least fully grok the portion which is beyond the range of his most powerful telescopes ...a false avenue because that grokking just wasn't meant to be! It's impossible to grasp the entirety as it stands because there is no meaningful master time continuum so there can be no momentary stasis to behold. Put even more simply, there is no taking of a mental image snapshot of the cosmos-at-a-juncture, because that implies a moment in universal time. We now know that Reality neither conforms nor defers to any such Universal Time. So WTF do I mean by bringing God into all this? Silly I suppose, but it's His Almighty Surprise Factor that flips my twig. Hehe, the joke's on Humanity, ha-ha, ho-ho. End of rant === Subject: Re: Rant about The Creator's Glory Distribution: world >Rant about The Creator's Glory as reflected in how light behaves (Relativity). When He made this World as it is, He *never* *meant* for humans to be the OVERSEERS >(or stewards) of His Creation. Oh, yeah? Try reading Genesis 1:26-28. -- Michael F. Stemper #include 2 + 2 = 5, for sufficiently large values of 2 === Subject: Re: Rant about The Creator > Rant about The Creator's Glory as reflected in how light behaves > (Relativity). Rants about The Creator, whether pro or con, do not belong in sci.math. There are plenty of NGs more appropriate. === Subject: Re: Rant about The Creator's Glory When He made this World as it is, Who did? I mean there are so many God-wannabe > e entities out there > that one wouldn't know which one you mean. Care to > clarify? > Please: not another post about JSH :) . === Subject: Re: Rant about The Creator's Glory > When He made this World as it is, Who did? I mean there are so many God-wannabe entities out there > that one wouldn't know which one you mean. Care to clarify? I clarified somewhat in my later posts, this thread. The World is the way it is and we'll never be able to surmount certain (like relativistic) constraints. And so, just like the insurance companies do in cases like that, it's refered to as an Act of God, a known symbolic reference, ergo applicable to my rant. I don't embrace shamanism, or god-wannabe icons of any kind; only His Honor, The Almighty, The Actual Creator, however nebulously you take that to mean. === Subject: Re: Rant about The Creator's Glory posting-account=7bF0GwoAAABMFHX6V4fON4-1F6LFJ834 .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; InfoPath.2; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Rant about The Creator's Glory as reflected in how > light behaves (Relativity). ... > So WTF do I mean by bringing God into all this? > Silly I suppose, but it's His Almighty Surprise > Factor that flips my twig. Hehe, the joke's on > Humanity, ha-ha, ho-ho. End of rant You might want to read Star Maker... David A. Smith === Subject: Re: Rant about The Creator's Glory >Rant about The Creator's Glory as reflected in how light behaves (Relativity). When He made this World as it is, He *never* *meant* for humans to be the OVERSEERS >(or stewards) of His Creation. Mankind has been following a false avenue all these centuries and millenia, thinking >that it/he can behold ALL there is of The Creation, rather if not literally behold at >least fully grok the portion which is beyond the range of his most powerful telescopes >...a false avenue because that grokking just wasn't meant to be! It's impossible to >grasp the entirety as it stands because there is no meaningful master time continuum >so there can be no momentary stasis to behold. Put even more simply, there is no >taking of a mental image snapshot of the cosmos-at-a-juncture, because that implies >a moment in universal time. We now know that Reality neither conforms nor defers to >any such Universal Time. So WTF do I mean by bringing God into all this? Silly I suppose, but it's His Almighty >Surprise Factor that flips my twig. Hehe, the joke's on Humanity, ha-ha, ho-ho. End of rant > It isn't a joke. It is an opportunity to learn, so we won't make the same mistake Lucifer made, after we've been granted immortality and absolute sovereignty. How else could God have prepared us for immortality and absolute sovereignty without risking a bunch of failures such as Lucifer's? How else could God have given each of us the unfettered opportunity to go along with His plan, or to opt out as we choose? Keep in mind that God's temporal frame (eternity) is not the same as our temporal frame (time). This on-going process that, from our current perspective, seem to be taking a VERY long time, is completed almost instantaneously from God's temporal perspective. It is a hands on learning process that lets us make our own choices instead of having been pre-programmed for absolute obedience like a bunch of puppet robots. Gordon === Subject: Re: Rant about The Creator's Glory > It isn't a joke. ...we've been granted immortality and absolute sovereignty. Each of those is a physical impossibility, not to mention undesirable. I agree with the other poster that greed and blindness conspire to provoke such beliefs. When you, Gordon, said God you must have meant god, because in my rant I was referring to The Highest & Mightiest No Less, and what interest would He have in pandering to some 3rd rate species on some 3rd rate rock circling some 3rd rate star in some out-of-the-way 3rd rate galaxy, hmmm? None. So I was referring to The Actual Creator Himself and I congratulate His Honor for making Relativity the scheme of things. Men can never be the OVERSEERS, nor have sovereignty nor stewardship nor eternal life. Ha-ha! Because relativity shows that there is no such animal as a cosmic OVERVIEW. Those who fully grasp the science know precisely what that truth. === Subject: Re: Rant about The Creator's Glory > It isn't a joke. ...we've been granted immortality and absolute sovereignty. Each of those is a physical impossibility, not to mention undesirable. I agree with the other poster that greed and blindness conspire to provoke such >beliefs. When you, Gordon, said God you must have meant god, because in my rant I was >referring to The Highest & Mightiest No Less, and what interest would He have in >pandering to some 3rd rate species on some 3rd rate rock circling some 3rd rate >star in some out-of-the-way 3rd rate galaxy, hmmm? > God isn't pandering to us. God created us and, from our temporal eternity temporal perspective this project was finished almost instantly. The only other option would have been for God to have skipped this temporal stage wherein we are now developing by our own experiences and by the experiences of those we observe. That is, He could have crated us already perfected and completely subservient...as pre-programmed robots, but not as genuinely sovereign beings. None. So I was referring to The Actual Creator Himself and I congratulate His Honor for >making Relativity the scheme of things. Men can never be the OVERSEERS, nor >have sovereignty nor stewardship nor eternal life. Ha-ha! Because relativity shows >that there is no such animal as a cosmic OVERVIEW. Those who fully grasp the >science know precisely what that truth. > Humans will continue to understand more and more about God and His creation...Super String multiverse...levels of Heaven...but we will never be able to comprehend it entirely, as mortals. We simply do not have enough brain cells, nor do we have the mental speed and agility that would be required. Our present assignment is to fully explore all those things that were so alluring to Lucifer. Then, once all this has been fully explored and we have reached the firm conclusion that nothing in this realm can lead to a better state of being for us or for anyone else, we will be ready for immortality and absolute sovereignty. Gordon === Subject: Re: Rant about The Creator's Glory > It isn't a joke. ...we've been granted immortality and absolute > sovereignty. > Each of those is a physical impossibility, not to mention > undesirable. > I agree with the other poster that greed and blindness conspire to > provoke such beliefs. > When you, Gordon, said God you must have meant god, because in my > rant I was referring to The Highest & Mightiest No Less, and what > interest would He have in pandering to some 3rd rate species on some > 3rd rate rock circling some 3rd rate star in some out-of-the-way 3rd > rate galaxy, hmmm? > God isn't pandering to us. You claim He offers men the world, salvation, sovereignty, stewardship and magical soul transmigration, etc -- and that isn't pandering?? > None. > So I was referring to The Actual Creator Himself and I congratulate > His Honor for making Relativity the scheme of things. Men can never > be the OVERSEERS, nor > have sovereignty nor stewardship nor eternal life. Ha-ha! Because > relativity shows that there is no such animal as a cosmic OVERVIEW. > Those who fully grasp the science know precisely what that truth. > Humans will continue to understand more and more about God and His > creation...Super String multiverse...levels of Heaven...but we will > never be able to comprehend it entirely, as mortals. We simply do not > have enough brain cells, nor do we have the mental speed and agility > that would be required. If humans continue with inane pursuits such as those you cite, the animal kingdoms will (continue to) get trampled, the forests denuded and the ecosphere despoiled. > Our present assignment is to fully explore all those things that were > so alluring to Lucifer. Then, once all this has been fully explored > and we have reached the firm conclusion that nothing in this realm can > lead to a better state of being for us or for anyone else, we will be > ready for immortality and absolute sovereignty. I'd readily agree to that last paragraph if the word slaughtering replaces your phrase, immortatility and absolute sovereignty. === Subject: Re: Rant about The Creator's Glory > It isn't a joke. ...we've been granted immortality and absolute > sovereignty. > Each of those is a physical impossibility, not to mention > undesirable. > I agree with the other poster that greed and blindness conspire to > provoke such beliefs. > When you, Gordon, said God you must have meant god, because in my > rant I was referring to The Highest & Mightiest No Less, and what > interest would He have in pandering to some 3rd rate species on some > 3rd rate rock circling some 3rd rate star in some out-of-the-way 3rd > rate galaxy, hmmm? > God isn't pandering to us. You claim He offers men the world, salvation, sovereignty, stewardship >and magical soul transmigration, etc -- and that isn't pandering?? > Nature offers us fruits, vegetables and other necessities for life. Is Nature pandering us? Or, are the bounties of nature simply available to us if we choose to make prudent use of them and not mess the ecosystem up to the point that these things are no longer available to us. > None. > So I was referring to The Actual Creator Himself and I congratulate > His Honor for making Relativity the scheme of things. Men can never > be the OVERSEERS, nor > have sovereignty nor stewardship nor eternal life. Ha-ha! Because > relativity shows that there is no such animal as a cosmic OVERVIEW. > Those who fully grasp the science know precisely what that truth. > Humans will continue to understand more and more about God and His > creation...Super String multiverse...levels of Heaven...but we will > never be able to comprehend it entirely, as mortals. We simply do not > have enough brain cells, nor do we have the mental speed and agility > that would be required. If humans continue with inane pursuits such as those you cite, the animal >kingdoms will (continue to) get trampled, the forests denuded and >the ecosphere despoiled. > I agree, for the most part, but I also hope that sometime soon we will mature above this wasteful state that has led us to the point you describe. Maybe some rapid advances in our intelligence and self control will save us from self extinction. What would this planet be like in a few years if we could somehow develop robots or complex machines that would clean up all the land fills and re-cycle the materials that have been wasted over the past 100 years or so? Could we hope to survive if we could make a break-through in cold hydrogen fusion and eliminate the need for burning fossil fuels entirely? My assessment of today's situation is that we are at or very near a fork in the road. If we take the wrong fork we will probably end up extinct. But, if we take the right fork I think we have a LONG way to go and a MUCH better level of existence to look forward to. > Our present assignment is to fully explore all those things that were > so alluring to Lucifer. Then, once all this has been fully explored > and we have reached the firm conclusion that nothing in this realm can > lead to a better state of being for us or for anyone else, we will be > ready for immortality and absolute sovereignty. I'd readily agree to that last paragraph if the word slaughtering >replaces your phrase, immortatility and absolute sovereignty. > I don't take the same negative view that you seem to embrace. I truly think God is still in charge and that he is managing things very well, indeed. We are learning, jointly and severally, and when this mortal phase of our existence ends we will move ahead into a much better state of being. Super String theory...multiverse...levels of Heaven all seem to be in harmony with the Word of God, and I'm quite comfortable with the situation. Gordon === Subject: Re: Rant about The Creator's Glory > ......I think God is still in charge and that he is managing > things very well, > indeed. Yes: Sudan, the holocaust, injustice at all levels. Great job indeed. I used to visit near a place for people with physical deformities. Maybe you can remind them of the great job your boss is doing. Remind them that your boss is all-knowing, all-capable, yet chooses to do nothing about their suffering. BTW: I knew of someone like you--someone who believed without understanding /questioning. He told me that suffering was a gift from god, a sign of god's love. So I kicked him in the balls and told him: god sends you his love! We are learning, jointly and severally, and > when this mortal > phase of our existence ends we will move ahead into a > much better > state of being. Super String > theory...multiverse...levels of Heaven > all seem to be in harmony with the Word of God, and > I'm quite > comfortable with the situation. > Yes, because you're not eating at the wrong end of the stick, and you don't care to stand for those that do, and it does not bother you that your god is not doing anything about it. You'll make a good republican. > Gordon How submissive can one get to just follow what their told, like you have? === Subject: Re: Rant about The Creator's Glory > God isn't pandering to us. > You claim He offers men the world, salvation, sovereignty, > stewardship and magical soul transmigration, etc -- and that isn't > pandering?? > Nature offers us fruits, vegetables and other necessities for life. Is > Nature pandering us? Or, are the bounties of nature simply available > to us if we choose to make prudent use of them and not mess the > ecosystem up to the point that these things are no longer available to > us. Sure yes, Nature panders to our physical needs because our physiques evolved in symbiosis with the natural world, just so. Not so the imaginary world of deities, for that is some spookiness only, not a crutch or gift and not even benificent. Though I still occasionally will refer to God because He is more than a mere deity or demigod. He is The World, The Glory! > So I was referring to The Actual Creator Himself and I congratulate > His Honor for making Relativity the scheme of things. > If humans continue with inane pursuits such as those you cite, the > animal kingdoms will (continue to) get trampled, the forests denuded > and the ecosphere despoiled. > I agree, for the most part, but I also hope that sometime soon we will > mature above this wasteful state that has led us to the point you > describe. Maybe some rapid advances in our intelligence and self > control will save us from self extinction. What would this planet be like in a few years if we could somehow > develop robots or complex machines that would clean up all the land > fills and re-cycle the materials that have been wasted over the past > 100 years or so? Could we hope to survive if we could make a > break-through in cold hydrogen fusion and eliminate the need for > burning fossil fuels entirely? My assessment of today's situation is that we are at or very near a > fork in the road. If we take the wrong fork we will probably end up > extinct. But, if we take the right fork I think we have a LONG way to > go and a MUCH better level of existence to look forward to. We took the WRONG fork eons ago and all is irrevocably lost. Good news for blessed Earth that we are leaving anon! === Subject: Re: Rant about The Creator's Glory <84jsr4dbccrdk2pa7v9k3t0n9lt8hkfjjc@4ax.com> <49be6b47$0$29990$822641b3@news.adtechcomputers.com> posting-account=6eN7JQoAAADXmr44mvgiyML4zUx3pABg 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > So I was referring to The Actual Creator Himself and I congratulate His Honor for > making Relativity the scheme of things. Men can never be the OVERSEERS, nor > have sovereignty nor stewardship nor eternal life. Ha-ha! Because relativity shows > that there is no such animal as a cosmic OVERVIEW. Those who fully grasp the > science know precisely what that truth. Not inconceivably it's relativity which will ultimately prove to be the greatest joke on mankind. The same people that tell us nothing can travel faster than light are the very same people who turn right around and tell us that because of spin, two matched subatomic across the universe. === Subject: Re: Rant about The Creator's Glory as an expression of Extreme Avarice and Malice >... immortality and >absolute sovereignty. So you're in it for your greed. >... lets us make our own choices... You can't show that you'd ever chosen anything, though. Why are you such a sucker for falsehoods? Oh, wait, it's the greed. === Subject: Re: Rant about The Creator's Glory as an expression of Extreme Avarice and Malice >... immortality and >absolute sovereignty. So you're in it for your greed. >... lets us make our own choices... You can't show that you'd ever chosen anything, though. Why are you such a sucker for falsehoods? Oh, wait, it's the greed. > *US* you must feel terribly insecure and angry with yourself to respond the way you do to this and other posts. What is it that is making you feel so threatened? === Subject: Re: Rant about The Creator's Glory as an expression of Extreme Avarice and Malice >... feel terribly insecure and angry ... No wonder you let your greed overrule any reason you may have. Your failure to dispute the fact that you are greedy remains, of course. >... immortality and >absolute sovereignty. So you're in it for your greed. >... lets us make our own choices... You can't show that you'd ever chosen anything, though. Why are you such a sucker for falsehoods? Oh, wait, it's the greed. === Subject: Re: bottles vs. cartons > Have fun explaining > http://onelook.com/?w=soft+drink > and the Oxford dictionary. The Oxford dictionary? Until this moment, Rod Speed, I think I have never really gauged your > man who is starting what looks to be a brilliant career with usenet. > Little did I dream you could be so reckless and so cruel as to do an > injury to that lad. It is true that he will continue to be with > sci.math, alt.usage.english, rec.uk.waterways, and > uk.media.radio.archers. It is, I regret to say, equally true that I > fear he shall always bear a scar needlessly inflicted by you. If it > were in my power to forgive you for your reckless cruelty I would do > so. I like to think that I am a gentle man, but your forgiveness will > have to come from someone other than me. The young's a nice compliment, and I've only been posting for around 10 years, so am relatively new in what's left of Usenet these days. But I hold fast to my claim, pace the OED, that soft drink is common UK English for a non-alcoholic drink and that fruit-juice fits that to a T. Why milk doesn't is, I admit, inexplicable. I'd cut the cross-postings, but don't know which group the main posters to the thread are reading it in. -- Online waterways route planner: http://canalplan.org.uk development version: http://canalplan.eu === Subject: Re: bottles vs. cartons > > Have fun explaining > http://onelook.com/?w=soft+drink > and the Oxford dictionary. > The Oxford dictionary? > Until this moment, Rod Speed, I think I have never really gauged your > man who is starting what looks to be a brilliant career with usenet. > Little did I dream you could be so reckless and so cruel as to do an > injury to that lad. It is true that he will continue to be with > sci.math, alt.usage.english, rec.uk.waterways, and > uk.media.radio.archers. It is, I regret to say, equally true that I > fear he shall always bear a scar needlessly inflicted by you. If it > were in my power to forgive you for your reckless cruelty I would do > so. I like to think that I am a gentle man, but your forgiveness will > have to come from someone other than me. The young's a nice compliment, and I've only been posting for around > 10 years, so am relatively new in what's left of Usenet these days. But I hold fast to my claim, pace the OED, that soft drink is > common UK English for a non-alcoholic drink and that fruit-juice fits > that to a T. Why milk doesn't is, I admit, inexplicable. > Equally I would hold to my claim that many non-alcoholic drinks are not soft-drinks. For example, milk, tea, coffee, mango lassi, kava, tomato soup, vichyssoise, water, tomatoe juic, hot chocolate. You seem to consider soft-drink as synonomous to 'non-alcoholic-beverage', but that just doesn't seem to be the case. Mike === Subject: Re: bottles vs. cartons > Equally I would hold to my claim that many non-alcoholic drinks are not > soft-drinks. For example, milk, tea, coffee, mango lassi, kava, tomato > soup, vichyssoise, Vichysoisse is a drink? -- Ted S. fedya at hughes dot net Now blogging at http://justacineast.blogspot.com === Subject: Re: bottles vs. cartons Equally I would hold to my claim that many non-alcoholic drinks are not > soft-drinks. For example, milk, tea, coffee, mango lassi, kava, tomato > soup, vichyssoise, Vichysoisse is a drink? > The world can probably be divided into those people who might say Please drink your soup, and those who might say Please eat your soup (of course, to be pedantic, there will be a third group of people who are either less polite or who just don't want to talk about soup). I consider myself part of the first group, so my answer is Yes, although I admit it would be difficult to consume it with a straw. Mike === Subject: Re: bottles vs. cartons > > Have fun explaining > http://onelook.com/?w=soft+drink > and the Oxford dictionary. > The Oxford dictionary? > Until this moment, Rod Speed, I think I have never really gauged your > man who is starting what looks to be a brilliant career with usenet. > Little did I dream you could be so reckless and so cruel as to do an > injury to that lad. It is true that he will continue to be with > sci.math, alt.usage.english, rec.uk.waterways, and > uk.media.radio.archers. It is, I regret to say, equally true that I > fear he shall always bear a scar needlessly inflicted by you. If it > were in my power to forgive you for your reckless cruelty I would do > so. I like to think that I am a gentle man, but your forgiveness will > have to come from someone other than me. The young's a nice compliment, and I've only been posting for around > 10 years, so am relatively new in what's left of Usenet these days. But I hold fast to my claim, pace the OED, that soft drink is > common UK English for a non-alcoholic drink and that fruit-juice fits > that to a T. Why milk doesn't is, I admit, inexplicable. Yes, my OED simply says it's a non-alcoholic drink. The term soft drink came into use because drink commonly meant alcoholic drink. It's usually used to describe nonalcoholic servings of drinks that are often alcoholic, such as carbonated beverages or punch. I'd cut the cross-postings, but don't know which group the main posters > to the thread are reading it in. I'm from the puzzles group, and here's the answer: http://www.americanrhetoric.com/speeches/welch-mccarthy.html If you scroll halfway down the page, you'll see two big paragraphs that start, Mr Welch. === === Subject: Re: Shuttle launch tonight at 7:43 EDT >I'd say it was certainly as bright as I've seen Venus, also, I'm >informed, with good eyes, one can resolve it beyond a point. No. Not even with basic binoculars. Brian === === Subject: Re: Shuttle launch tonight at 7:43 EDT > I'd say it was certainly as bright as I've seen Venus, also, I'm > informed, with good eyes, one can resolve it beyond a point. > No. Not even with basic binoculars. > Sorry Brian, you're out classed :-). > A professional associate did the arc visual acuity calculations > and I found his computations to be correct. > I'll help you out if you have any notions of what binoculars are. > Does personal experience count? > Not much, it's science. > Have you actually tried to make out > more than a point? > No. > I have. Not in the real world, you can't. > Wish it were so, but it isn't. :-) > Brian > The person I refer to has good eyes and is a fellow scientist. > I'll ask him to put a paragraph together and I'll post it, but > Brian I really wish you'd do your own math, for your good. > Ken People with good eyesight can resolve things about one arc-minute > apart. That's 1/3500 of a radian. So if the spacecraft are directly > overhead, 350 km high, they could be resolved if they're 100 metres > apart. So I doubt that the ISS and shuttle can be resolved while > they're docked together, but they should certainly be resolvable when > they're flying in close formation. > Ken There's a difference between detection and resolution. Once I watched Mir, the shuttle and a Soyuz (?) go overhead. It was 4 July several years ago, I can't remember the year. I wasn't using any form of optics. Had I used binoculars as you suggested I still couldn't have resolved any of the objects. Dan, U.S. Air Force, retired === Subject: Re: Shuttle launch tonight at 7:43 EDT The person I refer to has good eyes and is a fellow scientist. > I'll ask him to put a paragraph together and I'll post it, but > Brian I really wish you'd do your own math, for your good. > Ken You know, you're reminding me of a guy in my Freshman year that proved to me that it was impossible to see Long Island from the Connecticut shoreline. Despite the fact that I had done so numerous times. While in a strictly atmosphereless situation you and your friend are of course right, atmospheric diffraction really makes a huge difference here. That said, I am going to have to try this for myself. -- Greg Moore Ask me about lily, an RPI based CMC. === Subject: Re: Shuttle launch tonight at 7:43 EDT > The person I refer to has good eyes and is a fellow scientist. > I'll ask him to put a paragraph together and I'll post it, but > Brian I really wish you'd do your own math, for your good. > Ken You know, you're reminding me of a guy in my Freshman year that proved to > me that it was impossible to see Long Island from the Connecticut shoreline. > Despite the fact that I had done so numerous times. While in a strictly atmosphereless situation you and your friend are of > course right, atmospheric diffraction really makes a huge difference here. That said, I am going to have to try this for myself. I've also been informed Venus when bright and close, ie cresent, can be resolved, with good naked eyes, beyond point-like. Ken === Subject: Re: Shuttle launch tonight at 7:43 EDT > I'd say it was certainly as bright as I've seen Venus, also, I'm > informed, with good eyes, one can resolve it beyond a point. > No. Not even with basic binoculars. > Brian Sorry Brian, you're out classed :-). > A professional associate did the arc visual acuity calculations > and I found his computations to be correct. > I'll help you out if you have any notions of what binoculars are. > Ken It depends on the definition of resolution. The atmosphere alone limits resolution. Dan, U.S. Air Force, retired === > Trig doesn't account for air density variations. If you haven't noticed lenses with focal lengths similar to those found in binoculars can't resolve buildings from the space station. Why do you think recon satellites have focal lengths on the order of several feet? Contrary to myth the Great Wall of China can't be seen from space with the naked eye. Dan, U.S. Air Force, retired === === Subject: Tips on visualizing algebraic curves and algebraic varieties I am ashamed to say that to this date my understanding of algebraic geoemetry has more focused in the algebraic side rather than the geometric side. Now I'd like to improve myself in the geometric aspects of this area. So I am trying to be more involved in the beautiful field of algebraic curves. But as I read reference on this area, I realize how little I know about the geometry of algebraic geometry. So I come here again so that maybe a few wiser ones could give me a little tip. I'd like to visualize things I know now.. for instance, how do I visualize a prime ideal geometrically (lets work only with polynomials of at most 3 variables over an algebraically or even not algebraically closed field)? I know prime ideals very well in the algebraic level.. but what about geometrically? Could I say.. If I have a prime ideal over the polynomials.. I can make a variety that is smooth and nonsingular? Ive been working with prime ideals during 5 years of my Phd and unfortunately done very little with them geometrically (at least in a level I could visualize them geometrically). What if I don't deal with algebraically closed fields and only fields.. What are the weaker forms of say Bezout's Theorem and is there a weaker form of Hilbert's Nullstellensatz? And how do we visualize them geometrically? I know all these only at an algebraic level but I do know that they are much more important geometrically. As for algebraic curves.. is there a rule of thumb by which I could imagine how they are ploted and traced. Supposing I have a polynomial in A^2 (affine plane) or even A^3. It does look like a highschool What are the basic ideas one can visualize an implicite plot of the algebraic curve formed by this polynomial. And what tricks one can make use of in finding the singular points (I know the rule with taking partial derivatives and finding zeroes at points of the curve, but finding points of the curve itself dont seem to be a trivial stuff). What I can instinctively say is for instance.. once I can imagine how this polynomial is traced, the singular points are points where the curve is no longer smooth or has multiple intersections, is this way of thinking correct here? So the problem reduces in actually tracing the curve in my mind, no? A little motivational response would do me good here. I can read pages after pages of the work of Grothendieck but I believe he works rather too algebraic and less geometric. Right now I am trying to go back to the field of elliptic curves and expand my knowledge. The works of Fulton, Silvermann and Milton are what I read currently. Does anyone have any suggestion for a person who has been in the field of algebraic geometry but has not been exposed with a lot of algebraic curves or geometry? Jose Capco === Subject: Re: Tips on visualizing algebraic curves and algebraic varieties Ok I think to give an idea of myself and others regarding plotting an algebraic curve given by one polynomial. Supposing say I take the example from Silverman.. the curve 4x^2y^2 = (x^2 + y^2)^3 in A^2(R) (R being the real numbers) 1. I would look at the equation then realize.. ok.. the values on both side take positive values. 2. I'd try to realize the boundaries of the curves.. if ever.. in this case I'd see that values for x and y exceeding 1 cannot happen as the right hand side grows much faster than the left hand side for such values. So I am thus working in a square bounded by (-1,1) and (-1,1) for both x and y values.. 3. I'd find the singular points by taking partial derivatives and equating to 0. Im not sure why but I see only (0,0) here. So these are the steps I make in visualizing curves that are like these.. For elliptic curves I know exactly how to deal with them, because I know things about the discriminant and etc. But for any wild curve this could be more complicated .. but this is at least my rule of thumb.. it doesnt seem to be the most effective though.. One quite easy way is of course to plot in a math software like Maple, but its much important to realize in my head why and how the curves are formed. Jose Capco === Subject: Proving that these roots are real I have a problem that I'm not able to completely solve yet. It reads: 'Show that the roots of the equation 4(m + 1)x^2 - 4(m - 1)x - 3 = 0 are real for all real m.' I've calculated the discriminant of this equation. However, I'm not *entirely* sure as to how it can be used to solve the above problem (yet). I can see that the discriminant of the discriminant [briefly discussed in the above paragraph] is >= 0 so m is real. It doesn't seem constructive to the main problem though. As somehow implied from all the above, I haven't come up with any plan (really) that will attempt to solve the problem. Please help me come up with a non-futile one. Albert === Subject: Re: Proving that these roots are real I have a problem that I'm not able to completely solve yet. It reads: 'Show that the roots of the equation 4(m + 1)x^2 - 4(m - 1)x - 3 = 0 are > real for all real m.' I've calculated the discriminant of this equation. However, I'm not > *entirely* sure as to how it can be used to solve the above problem (yet). > I can see that the discriminant of the discriminant [briefly discussed > in the above paragraph] is >= 0 so m is real. It doesn't seem > constructive to the main problem though. As somehow implied from all the above, I haven't come up with any plan > (really) that will attempt to solve the problem. Please help me come up > with a non-futile one. Albert Hint: Consider a random expression like (m + 1/2)^2 Why is this expression alwyas non-negative for real m? Next consider e.g. (m + 1/2)^2 + 15/4. Why is this always strictly positive for real m? Can you somehow apply such reasoning to your original problem? === Subject: Re: Proving that these roots are real > I have a problem that I'm not able to completely solve yet. It reads: 'Show that the roots of the equation 4(m + 1)x^2 - 4(m - 1)x - 3 = 0 are > real for all real m.' I've calculated the discriminant of this equation. And what did you get? > However, I'm not > *entirely* sure as to how it can be used to solve the above problem (yet). > I can see that the discriminant of the discriminant [briefly discussed > in the above paragraph] is >= 0 so m is real. Since the problem *assumes* that _m_ is real, I fail to see why do you want to prove it. > As somehow implied from all the above, I haven't come up with any plan > (really) that will attempt to solve the problem. Please help me come up > with a non-futile one. Use the fact that all the roots of a second degree equation are real if and only if the discriminant of the equation is equal or greater than 0. Jose Carlos Santos === Subject: Re: Proving that these roots are real Jos.8e Carlos Santos a .8ecrit : Show that the roots of the equation 4(m + 1)x^2 - 4(m - 1)x - 3 = 0 > are real for all real m. I've calculated the discriminant of this equation. And what did you get? > However, I'm not *entirely* sure as to how it can be used to solve > the above problem (yet). > I can see that the discriminant of the discriminant [briefly > discussed in the above paragraph] is >= 0 so m is real. Since the problem *assumes* that _m_ is real, I fail to see why do > you want to prove it. > NOPE, what gives you the discriminant of the discriminant ? a way to solve for m ?????? to solve what ? and what is your aim in solving that ? However I'm not shure this discriminant of discriminant is >= 0 as BTW some people hate discriminants, and they prefer allways to complete the squares, may be it's better here, and prevents you to go straightforward lost in equations about equations about equations... -- Philippe Ch., mail : chephip+news@free.fr site : http://mathafou.free.fr/ (recreational mathematics) === Subject: Re: Proving that these roots are real > Show that the roots of the equation 4(m + 1)x^2 - 4(m - 1)x - 3 = 0 > are real for all real m. > I've calculated the discriminant of this equation. > And what did you get? > However, I'm not *entirely* sure as to how it can be used to solve > the above problem (yet). > I can see that the discriminant of the discriminant [briefly > discussed in the above paragraph] is >= 0 so m is real. > Since the problem *assumes* that _m_ is real, I fail to see why do > you want to prove it. NOPE, what gives you the discriminant of the discriminant ? Well, this makes sense in this case, because the discriminant is a second degree polynomial in _m_. Jose Carlos Santos === Subject: Re: Proving that these roots are real Jos.8e Carlos Santos a .8ecrit : NOPE, what gives you the discriminant of the discriminant ? Well, this makes sense in this case, because the discriminant is a > second degree polynomial in _m_. > I know ;-) But this makes sense to my question : what is the *aim* to calculate the discriminant of discriminant ? Of course this question is to _Albert_, I think you know. And this is why I induced _Albert_ not to react at once by first calculating the discriminant of whatever he sees, but to *think* about what he wants to reach, equations and discriminants are just a mean to reach this goal. The goal is to proove the initial equation always has real roots. An intermediate step is to proove that the discriminant of this equation is >= 0. That is, a new sub problem arises : how to proove that some expression f(m) = discriminant is allways >=0 ? As this expression is a quadratic in m, you may try to solve it for f(m) = 0, because you (_Albert_) 'know' that the roots of this quadratic separate the values of m into ranges where f(m) > 0 and ranges where f(m) < 0. But may be it is simpler to directly proove that f(m) > 0 without heavy techniques, this preventing _Albert_ from calculating a discriminant, just _because_he_sees_ a quadratic... and be lost because he doesn't know where to go then (forgot the goal). -- Philippe Ch., mail : chephip+news@free.fr site : http://mathafou.free.fr/ (recreational mathematics) === Subject: why tensor ? why not vectors in 100 words. posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) well, I'm investigating about 'Tensors' ____ Can you describe.., a) what are 'Tensors uses' ? in 100 words or so.... b) what are the difficulties we have to face with out the concept of Tensors? please, Any reference books on this topic. Why should I refuse a good dinner simply because I don't understand the digestive processes involved. Oliver Heaviside === Subject: Re: why tensor ? why not vectors in 100 words. Distribution: world > well, > I'm investigating about 'Tensors' > Can you describe.., > a) what are 'Tensors uses' ? in 100 words or so.... > b) what are the difficulties we have to face with out > the concept of Tensors? > please, > Any reference books on this topic. Try _The Demolished Man_ by Alfred Bester. >As I read your request, I got tensor and tensor. Tension, apprehension, and dissension have begun. -- Michael F. Stemper #include This sentence no verb. === Subject: Re: why tensor ? why not vectors in 100 words. Distribution: world posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) On Mar 17, 10:48pm, mstem...@walkabout.empros.com (Michael Stemper) > well, > I'm investigating about 'Tensors' > Can you describe.., > a) what are 'Tensors uses' ? in 100 words or so.... > b) what are the difficulties we have to face with out > the concept of Tensors? > please, > Any reference books on this topic. Try The Demolished Man by Alfred Bester. Sorry; Is this a 'Math' book on Tensors ? or just a Novel >As I read your request, I got tensor and tensor. Tension, apprehension, and dissension have begun. -- > Michael F. Stemper > #include On Mar 17, 10:48pm, mstem...@walkabout.empros.com (Michael Stemper) > Try _The Demolished Man_ by Alfred Bester. Sorry; > Is this a 'Math' book on Tensors ? or just a Novel It's one of Alfred Bester's better novels. The Finnish radio adaptation is also very nice. Give it a try. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: why tensor ? why not vectors in 100 words. <87k56oxa8v.fsf@alatheia.dsl.inet.fi> posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > On Mar 17, 10:48pm, mstem...@walkabout.empros.com (Michael Stemper) > Try The Demolished Man by Alfred Bester. > Sorry; > Is this a 'Math' book on Tensors ? or just a Novel It's one of Alfred Bester's better novels. The Finnish radio > adaptation is also very nice. Give it a try. Sure; I'll share my thoughts; Once I finish it. for the recommendation. === Subject: Re: why tensor ? why not vectors in 100 words. > well, > I'm investigating about 'Tensors' > please, > Any reference books on this topic. > J. F. Nye, Physical properties of crystals, their representation by tensors and matrices -- *********** To reply by e-mail, make w single in address ************** === Subject: Re: why tensor ? why not vectors in 100 words. > well, > I'm investigating about 'Tensors' > ____ Can you describe.., a) what are 'Tensors uses' ? in 100 words or so.... concept of a vector to physical properties that require more than just magnitude and direction for their characterization. For a mechanics exanple, work is a number (scalar), force is a vector, and stress, in general, is a tensor. In electromagnetics permittivity and permeability are, in general, tensors. As an EE I tend to work with either scalars or vectors as input and output quantitites. In those situations a tensor can be viewed as something that operates on the input to produce an output. > b) what are the difficulties we have to face with out > the concept of Tensors? You might as well ask where modern math would be without the calculus. John Wood (Code 5550) e-mail: wood@itd.nrl.navy.mil Naval Research Laboratory 4555 Overlook Avenue, SW Washington, DC 20375-5337 === Subject: Re: why tensor ? why not vectors in 100 words. posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) Can you describe.., a) what are 'Tensors uses' ? in 100 words or so.... On R^n, there are geometric objects that doesn't transform like vectors under symmetry operations of R^n (the rotations). e.g. the surface element when you integrate over a 2-dim surface embedded in 5-dim space. A way to simplify the analysis is to include objects that transform like outer products of vectors, hence the tensors. > b) what are the difficulties we have to face with out > the concept of Tensors? The concept of 'tensor' is just a tool. If you don't use this when it is appropriate, you simply waste time in checking boring details instead of spending time on your real problem. === S === Subject: Re: Surely You're Joking, Mr. Ullrich ! > >?? Another kind of counter intuitive mathematics again ?? I'm sure TU Delft has courses in measure theory. Take one. It's fun. > This sort of counter-intuitive fact will come up even in a one semester > course. Guess I'm already too old to learn :-( Han de Bruijn === Subject: Re: Surely You're Joking, Mr. Ullrich ! >?? Another kind of counter intuitive mathematics again ?? I'm sure TU Delft has courses in measure theory. Take one. It's fun. > This sort of counter-intuitive fact will come up even in a one semester > course. Guess I'm already too old to learn :-( That seems to sum up the pointlessness of these discussions. -- People make mistakes. Better to live today and learn the truth, than to be one of those poor saps who died deluded, thinking they knew certain things that they just didn't. Thinking they had proofs that they didn't. --James S. Harris, almost too sad for a .sig === Subject: Re: Surely You're Joking, Mr. Ullrich ! > >?? Another kind of counter intuitive mathematics again ?? >I'm sure TU Delft has courses in measure theory. Take one. It's fun. >This sort of counter-intuitive fact will come up even in a one semester >course. >Guess I'm already too old to learn :-( That seems to sum up the pointlessness of these discussions. Apart from the smiley .. But _this_ discussion will end soon, as far as I am concerned. David Ullrich's book has been an eye-opener, sort of .. Han de Bruijn === Subject: Re: Surely You're Joking, Mr. Ullrich ! <1iwh84h.17wntivun4eN%see@sig.for.address> <711ee$49be225d$82a1e228$6888@news1.tudelft.nl> posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e 2.0.50727),gzip(gfe),gzip(gfe) On Mar 16, 11:56am, Han de Bruijn ?? Another kind of counter intuitive mathematics again ?? > I'm sure TU Delft has courses in measure theory. Take one. It's fun. > This sort of counter-intuitive fact will come up even in a one semester > course. Guess I'm already too old to learn :-( > == Yes, you are...and you've proved this time after time after time... Tonio > Han de Bruijn === Subject: Re: Surely You're Joking, Mr. Ullrich ! > And about meeloper: it seems to be a person who places expediency > above principle, according to > http://lookwayup.com/lwu.exe/lwu/toEng?s=d&w=meeloper&slang=Nld So hanger-on is NOT meeloper, and more interesting: you seem to think > that either meeloper or hanger-on is an appropiate name to call me, > and manyh others, when we try to educate you and correct your stupid > ideas about mathematics. > Well...ok, I suppose. As long as you feel fine with that. 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Full details: http://jobs.phds.org/job/12906/delft-university-of-technology/phd-student-dr o plet-turbulence -------------------------------------------------------------------- Post your job (free!): http://jobs.phds.org/job/post PhDs.org: Science, Math, and Engineering Career Resources --------------------------------------------------------- * Job Listings: http://jobs.phds.org/ - Job board with hundreds of listings for Ph.D.s - Reach tens of thousands of Ph.D.s each month * Graduate School Rankings: http://graduate-school.phds.org/ - Comprehensive, customizable rankings of graduate programs * Career Resources: http://www.phds.org/ - Pointers to the best resources on the web for: + getting into graduate school + writing your dissertation + jobs for Ph.D.s in academia and industry * Engineering Science Weblog: http://blog.phds.org/ - Building better scientists and engineers === Subject: Re: The only angle is theta! - Wackypedia Expires: 60 days >Smooth them out using a Gaussian convolution filter. >Wait... you wouldn't know what that was. > http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm > Why would I want one of those when I produce perfectly smooth curves > already? > You can't even run my program so why should I take any notice of your > criticisms? You are just being silly again. Your method sucks, you invented h-aether and uniation. You are >incompetent and you argue idiotic bull >No need. The primary (that's the star itself) has to move about a >common barycentre. > Yes......and that causes the brightness variation, as we know. >Right. So all you need to do it pitch the orbit, that'll give the >ball park distance and no need to invent something as stupid >as uniation. > The program needs an input figure for orbital velocity. Mine uses the > maximum > at the perihelion. Hint: The ISS orbits the Earth in 45 minutes at 200 miles high, >a geostationary satellite in 24 hours at 23,500 miles high, the Moon >in a month at 238,000 miles high. >Mercury takes 88 days to orbit the Sun, >Venus takes 225 days, >Earth takes 365 days, >Jupiter takes 12 years, >Pluto takes 208 years. >There is a clear relation between period and altitude. >If you know the altitude you know the velocity (2pi.r/period), >if you know the period you know the altitude. >Look it up. Sure, if you know the mass of the main body. ...but engineers don't learn physics past first year... > Velocity curves based on doppler shift are published for many variables. > What > figure do you use for Algol? There isn't any data for a velocity curve, Algol is face-on and >hence uniated by inclination of its orbit to the celestial plane >(but not by h-aether magic or Fritzian extinction). That; why none >has been published. I could believe that if it didn't come from a silly old pom. > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls It doesn't work. My ellipses are better than yours anyway. >Of course if Algol were really eclipsing then there damn well >ought to be, but Goodricke and his wooden telescope in 1792 >had no way of knowing. ing theorists jump to the first >thing that pops into their head, and then they name a college >after the little prick in York. him. > http://www.yorkconferences.com/upload_files/aerial_view_campus_1_1.jpg > http://farm1.static.flickr.com/170/373437849_a17379f8a1.jpg?v=0 Maybe they'll name the house after YOU. >Mind you, I did some good humping there in my student days. I hope there are no illegitimates around like you. >Later I'll produce the luminosity curve but it takes time, I can't >index arrays easily on a spreadsheet and it is a very tedious >task. I'll sell you a good program. i have been working on it again lately. It is improving all the time. I will have to write a proper paper about BaTh soon or will run out of time. > You seem to be continually confusing Australians with New Zealanders. > WE still prefer women...even though some are a bit hairy. Is that why you changed your name from Henry to Henri to Hairy? >I thought Hairy Wilson suited an old sheep shagger. The sheep >are certainly hairy, although we usually say Woolly. How about >Woolly Wilson? That will do. Woolly Wilson's Wobbly Worbits >with WCH's. Wuck off! >there was a systematic variation in the arrival time of the pulses. >Sometimes, the pulses were received a little sooner than expected; >sometimes, later than expected. These variations changed in a smooth and >repetitive manner, with a period of 7.75 hours. They realized that such >behavior is predicted if the pulsar were in a binary orbit with another >star. >7.75 hours is a damned short period for something the size of a star. >Can you model it? > I already have. > The pulsar is wobbling around a barycentre, presumably that caused by a > lump of > accumulated matter pretty close to the pulsar. > I have reproduced its curve. See RHS: > http://www.users.bigpond.com/hewn/group1.jpg Ok, what I was looking for is something like this: > http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF >Along the top as the pulses arrive Sometimes, the pulses were received a >little sooner than expected; sometimes, later than expected. These >variations changed in a smooth and repetitive manner, with a period of 7.75 >hours. You didn't include unification....otherwise it is great. It's simple case of a light emitter orbiting a barycentre. I would say it is a binary orbiting an larger mass centre...hence the cyclic doppler shift. > Can YOU produce any of those curves with YOUR program? Now you ARE being silly. I've been doing that since 1993. You can't plug in any old curve and match it like I can. It has taken me more than ten years on and off to write my program. Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: The only angle is theta! - Wackypedia > Smooth them out using a Gaussian convolution filter. >Wait... you wouldn't know what that was. > http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm > Why would I want one of those when I produce perfectly smooth curves > already? > You can't even run my program so why should I take any notice of your > criticisms? You are just being silly again. >Your method sucks, you invented h-aether and uniation. You are >incompetent and you argue idiotic bull I don't want to show you my new luminosity curve with just 100 points. You'll only be jealous. >No need. The primary (that's the star itself) has to move about a >common barycentre. > Yes......and that causes the brightness variation, as we know. >Right. So all you need to do it pitch the orbit, that'll give the >ball park distance and no need to invent something as stupid >as uniation. > The program needs an input figure for orbital velocity. Mine uses the > maximum > at the perihelion. >Hint: The ISS orbits the Earth in 45 minutes at 200 miles high, >a geostationary satellite in 24 hours at 23,500 miles high, the Moon >in a month at 238,000 miles high. >Mercury takes 88 days to orbit the Sun, >Venus takes 225 days, >Earth takes 365 days, >Jupiter takes 12 years, >Pluto takes 208 years. >There is a clear relation between period and altitude. >If you know the altitude you know the velocity (2pi.r/period), >if you know the period you know the altitude. >Look it up. Sure, if you know the mass of the main body. > ...but engineers don't learn physics past first year... Sure, they teach relativity the second year, why bother with that ? Physicists never learn engineering, they are all theory and no practical experience. How's your old pal Einstein doing these days? Did he ever get his electrical engineering diploma from Eidgen.9assische Technische Hochschule in Zurich or did he remain a clerk in the patent office? > Velocity curves based on doppler shift are published for many variables. > What > figure do you use for Algol? >There isn't any data for a velocity curve, Algol is face-on and >hence uniated by inclination of its orbit to the celestial plane >(but not by h-aether magic or Fritzian extinction). That; why none >has been published. I could believe that if it didn't come from a silly old pom. > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls It doesn't work. My ellipses are better than yours anyway. I don't want to show you my new luminosity curve with just 100 points. You'll only be jealous. >Of course if Algol were really eclipsing then there damn well >ought to be, but Goodricke and his wooden telescope in 1792 >had no way of knowing. ing theorists jump to the first >thing that pops into their head, and then they name a college >after the little prick in York. him. He's one yours, another theoretical physicist. > http://www.yorkconferences.com/upload_files/aerial_view_campus_1_1.jpg > http://farm1.static.flickr.com/170/373437849_a17379f8a1.jpg?v=0 Maybe they'll name the house after YOU. Touch a nerve, did I? >Mind you, I did some good humping there in my student days. I hope there are no illegitimates around like you. >Later I'll produce the luminosity curve but it takes time, I can't >index arrays easily on a spreadsheet and it is a very tedious >task. I'll sell you a good program. > i have been working on it again lately. It is improving all the time. > I will have to write a proper paper about BaTh soon or will run out of > time. > Does it have 100 points and run on a spreadsheet? > You seem to be continually confusing Australians with New Zealanders. > WE still prefer women...even though some are a bit hairy. >Is that why you changed your name from Henry to Henri to Hairy? >I thought Hairy Wilson suited an old sheep shagger. The sheep >are certainly hairy, although we usually say Woolly. How about >Woolly Wilson? That will do. Woolly Wilson's Wobbly Worbits >with WCH's. Wuck off! Oh, so you DO like it. Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. >there was a systematic variation in the arrival time of the pulses. >Sometimes, the pulses were received a little sooner than expected; >sometimes, later than expected. These variations changed in a smooth and >repetitive manner, with a period of 7.75 hours. They realized that such >behavior is predicted if the pulsar were in a binary orbit with another >star. >7.75 hours is a damned short period for something the size of a star. >Can you model it? > I already have. > The pulsar is wobbling around a barycentre, presumably that caused by a > lump of > accumulated matter pretty close to the pulsar. > I have reproduced its curve. See RHS: > http://www.users.bigpond.com/hewn/group1.jpg >Ok, what I was looking for is something like this: > http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF >Along the top as the pulses arrive Sometimes, the pulses were received a >little sooner than expected; sometimes, later than expected. These >variations changed in a smooth and repetitive manner, with a period of >7.75 >hours. You didn't include unification....otherwise it is great. It's simple case > of a > light emitter orbiting a barycentre. I would say it is a binary orbiting > an > larger mass centre...hence the cyclic doppler shift. > Oh yeah, Earth and Moon are a binary, right? Are you and your sheila a binary? > Can YOU produce any of those curves with YOUR program? >Now you ARE being silly. I've been doing that since 1993. You can't plug in any old curve and match it like I can. > It has taken me more than ten years on and off to write my program. BWAHAHAHAHA! This is 2009, Wilson, you didn't start until 2000 after I told you about it. You've wasted all that time arguing with dorks, trying to inflate your ego. Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. === Subject: Re: The only angle is theta! - Wackypedia Expires: 60 days > I don't want to show you my new luminosity curve with just 100 points. >You'll only be jealous. My program includes two independent methods for calculating brightness curves. If you could run it you would discover that they both produce almost the same curves. The second one, named after George Dishman (who suggested it but is unfortunately no longer here) uses only about 330 points around the ellipse although the latter is still established with ~33000. >Hint: The ISS orbits the Earth in 45 minutes at 200 miles high, >a geostationary satellite in 24 hours at 23,500 miles high, the Moon >in a month at 238,000 miles high. >Mercury takes 88 days to orbit the Sun, >Venus takes 225 days, >Earth takes 365 days, >Jupiter takes 12 years, >Pluto takes 208 years. >There is a clear relation between period and altitude. >If you know the altitude you know the velocity (2pi.r/period), >if you know the period you know the altitude. >Look it up. > Sure, if you know the mass of the main body. > ...but engineers don't learn physics past first year... Sure, they teach relativity the second year, why bother with that ? > Physicists never learn engineering, they are all theory and no practical >experience. >How's your old pal Einstein doing these days? Did he ever get >his electrical engineering diploma from Eidgen.9assische Technische Hochschule >in Zurich or did he remain a clerk in the patent office? > Velocity curves based on doppler shift are published for many variables. > What > figure do you use for Algol? >There isn't any data for a velocity curve, Algol is face-on and >hence uniated by inclination of its orbit to the celestial plane >(but not by h-aether magic or Fritzian extinction). That; why none >has been published. > I could believe that if it didn't come from a silly old pom. > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls > It doesn't work. My ellipses are better than yours anyway. I don't want to show you my new luminosity curve with just 100 points. >You'll only be jealous. >Of course if Algol were really eclipsing then there damn well >ought to be, but Goodricke and his wooden telescope in 1792 >had no way of knowing. ing theorists jump to the first >thing that pops into their head, and then they name a college >after the little prick in York. > him. He's one yours, another theoretical physicist. > http://www.yorkconferences.com/upload_files/aerial_view_campus_1_1.jpg > http://farm1.static.flickr.com/170/373437849_a17379f8a1.jpg?v=0 > Maybe they'll name the house after YOU. Touch a nerve, did I? >Mind you, I did some good humping there in my student days. > I hope there are no illegitimates around like you. >Later I'll produce the luminosity curve but it takes time, I can't >index arrays easily on a spreadsheet and it is a very tedious >task. > I'll sell you a good program. > i have been working on it again lately. It is improving all the time. > I will have to write a proper paper about BaTh soon or will run out of > time. Does it have 100 points and run on a spreadsheet? It has ample points and runs on any windows based computer. Yours wont run it, obviously. >Is that why you changed your name from Henry to Henri to Hairy? >I thought Hairy Wilson suited an old sheep shagger. The sheep >are certainly hairy, although we usually say Woolly. How about >Woolly Wilson? That will do. Woolly Wilson's Wobbly Worbits >with WCH's. > Wuck off! Oh, so you DO like it. Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. Wuck off again > The pulsar is wobbling around a barycentre, presumably that caused by a > lump of > accumulated matter pretty close to the pulsar. > I have reproduced its curve. See RHS: > http://www.users.bigpond.com/hewn/group1.jpg >Ok, what I was looking for is something like this: > http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF >Along the top as the pulses arrive Sometimes, the pulses were received a >little sooner than expected; sometimes, later than expected. These >variations changed in a smooth and repetitive manner, with a period of >7.75 >hours. > You didn't include unification....otherwise it is great. It's simple case > of a > light emitter orbiting a barycentre. I would say it is a binary orbiting > an > larger mass centre...hence the cyclic doppler shift. >Oh yeah, Earth and Moon are a binary, right? Are you and your sheila >a binary? > Can YOU produce any of those curves with YOUR program? >Now you ARE being silly. I've been doing that since 1993. > You can't plug in any old curve and match it like I can. > It has taken me more than ten years on and off to write my program. BWAHAHAHAHA! >This is 2009, Wilson, you didn't start until 2000 after I told you about it. >You've wasted all that time arguing with dorks, trying to inflate your ego. >Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. I was already producing brightness curves for circular orbits before I read any of your ty messages. Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: The only angle is theta! - Wackypedia > I don't want to show you my new luminosity curve with just 100 points. >You'll only be jealous. My program includes two independent methods for calculating brightness > curves. > If you could run it you would discover that they both produce almost the > same > curves. > The second one, named after George Dishman (who suggested it but is > unfortunately no longer here) uses only about 330 points around the > ellipse > although the latter is still established with ~33000. > Dishwater was a clot and so are you for listening to the idiot. Delta-T, as shown in http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF is the arrival time between two photons that departed delta-t apart. The larger the value of delta-T, the fewer photons arrive per second. Therefore the number of photons arriving per second is inversely proportional to delta-T. So, by sorting the array of arrival times so as to be monotonic, then plotting the inverse (logarithmically) against delta-T, we have a luminosity curve. >Hint: The ISS orbits the Earth in 45 minutes at 200 miles high, >a geostationary satellite in 24 hours at 23,500 miles high, the Moon >in a month at 238,000 miles high. >Mercury takes 88 days to orbit the Sun, >Venus takes 225 days, >Earth takes 365 days, >Jupiter takes 12 years, >Pluto takes 208 years. >There is a clear relation between period and altitude. >If you know the altitude you know the velocity (2pi.r/period), >if you know the period you know the altitude. >Look it up. > Sure, if you know the mass of the main body. > ...but engineers don't learn physics past first year... >Sure, they teach relativity the second year, why bother with that ? > Physicists never learn engineering, they are all theory and no practical >experience. >How's your old pal Einstein doing these days? Did he ever get >his electrical engineering diploma from Eidgen.9assische Technische >Hochschule >in Zurich or did he remain a clerk in the patent office? > Velocity curves based on doppler shift are published for many > variables. > What > figure do you use for Algol? >There isn't any data for a velocity curve, Algol is face-on and >hence uniated by inclination of its orbit to the celestial plane >(but not by h-aether magic or Fritzian extinction). That; why none >has been published. > I could believe that if it didn't come from a silly old pom. > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls > It doesn't work. My ellipses are better than yours anyway. >I don't want to show you my new luminosity curve with just 100 points. >You'll only be jealous. >Of course if Algol were really eclipsing then there damn well >ought to be, but Goodricke and his wooden telescope in 1792 >had no way of knowing. ing theorists jump to the first >thing that pops into their head, and then they name a college >after the little prick in York. > him. >He's one yours, another theoretical physicist. > http://www.yorkconferences.com/upload_files/aerial_view_campus_1_1.jpg > http://farm1.static.flickr.com/170/373437849_a17379f8a1.jpg?v=0 > Maybe they'll name the house after YOU. >Touch a nerve, did I? >Mind you, I did some good humping there in my student days. > I hope there are no illegitimates around like you. >Later I'll produce the luminosity curve but it takes time, I can't >index arrays easily on a spreadsheet and it is a very tedious >task. > I'll sell you a good program. > i have been working on it again lately. It is improving all the time. > I will have to write a proper paper about BaTh soon or will run out of > time. >Does it have 100 points and run on a spreadsheet? It has ample points and runs on any windows based computer. Yours wont run > it, > obviously. True. I tried to load it but my computer puked up, I had a hell of mess to clean. Bits of code mixed with constants all over the floor, even the cat turned his nose up and went out for the day. I expect you eat pickled onions in red wine and ice cream on fried mutton with a chocolate sauce judging from the way you write programs. What the is elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) supposed to be? like that if he worked for me. Sheesh, I've never seen such woolly-headed crap. Anyone can draw an ellipse (except Wilson) - Woolly Wilson. NEVER embed numbers in code. Not even pi. If you mistype it once you'll have hell of a time finding it. pi = 3.14159265 pi2 = 3.14159265 *2 circumference = 2 * 3.14169265 * radius ' not ok, 6 instead of 5. circumference = 2 * pi * radius ' ok circumference = pi2 * radius ' better and faster Then later you can change it to pi = 3.1415926535897932384626433832795 to be more accurate and never have to change it anywhere else in the code. Simple and readable. This makes life easier for YOU, Wilson. Bodging never does. >Is that why you changed your name from Henry to Henri to Hairy? >I thought Hairy Wilson suited an old sheep shagger. The sheep >are certainly hairy, although we usually say Woolly. How about >Woolly Wilson? That will do. Woolly Wilson's Wobbly Worbits >with WCH's. > Wuck off! >Oh, so you DO like it. > Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. Wuck off again How about Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's then? > The pulsar is wobbling around a barycentre, presumably that caused by > a > lump of > accumulated matter pretty close to the pulsar. > I have reproduced its curve. See RHS: > http://www.users.bigpond.com/hewn/group1.jpg >Ok, what I was looking for is something like this: > http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF >Along the top as the pulses arrive Sometimes, the pulses were received >a >little sooner than expected; sometimes, later than expected. These >variations changed in a smooth and repetitive manner, with a period of >7.75 >hours. > You didn't include unification....otherwise it is great. It's simple > case > of a > light emitter orbiting a barycentre. I would say it is a binary orbiting > an > larger mass centre...hence the cyclic doppler shift. >Oh yeah, Earth and Moon are a binary, right? Are you and your sheila >a binary? > Can YOU produce any of those curves with YOUR program? >Now you ARE being silly. I've been doing that since 1993. > You can't plug in any old curve and match it like I can. > It has taken me more than ten years on and off to write my program. >BWAHAHAHAHA! >This is 2009, Wilson, you didn't start until 2000 after I told you about >it. >You've wasted all that time arguing with dorks, trying to inflate your >ego. >Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. I was already producing brightness curves for circular orbits before I > read any > of your ty messages. Yeah, yeah.... Wasted years talking to Dishwater and produced BaThwater. Everyone reckons your overlays are hand-drawn anyway. It would go hand-in-glove with your doctorate, a ing cheat. The only one you fool is yourself. Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's. far superior elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) And what was your far superior G again? BWAHAHAHAHAHAHAHA! === Subject: Re: The only angle is theta! - Wackypedia Expires: 60 days >I don't want to show you my new luminosity curve with just 100 points. >You'll only be jealous. > My program includes two independent methods for calculating brightness > curves. > If you could run it you would discover that they both produce almost the > same > curves. > The second one, named after George Dishman (who suggested it but is > unfortunately no longer here) uses only about 330 points around the > ellipse > although the latter is still established with ~33000. >Dishwater was a clot and so are you for listening to the idiot. Delta-T, as shown in > http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF >is the arrival time between two photons that departed delta-t apart. >The larger the value of delta-T, the fewer photons arrive per second. >Therefore the number of photons arriving per second is inversely >proportional to delta-T. >So, by sorting the array of arrival times so as to be monotonic, >then plotting the inverse (logarithmically) against delta-T, we have a luminosity curve. That's roughly the way. Dishman pointed out that if the arrival interval between pulses that were emitted say x seconds apart was monitored for about 500 equally time spaced pairs of points around the orbit, the inverse would also produce the bunching factor. I was subsequently able to programmed the method successfully because I had all the time based data for the ellipse already. It's a lot faster than setting up arrays of arrival times for all the emitted pulses but its also pretty hard to program. > I'll sell you a good program. > i have been working on it again lately. It is improving all the time. > I will have to write a proper paper about BaTh soon or will run out of > time. >Does it have 100 points and run on a spreadsheet? > It has ample points and runs on any windows based computer. Yours wont run > it, > obviously. True. I tried to load it but my computer puked up, I had a hell of mess >to clean. Bits of code mixed with constants all over the floor, even the >cat turned his nose up and went out for the day. I expect you eat pickled >onions in red wine and ice cream on fried mutton with a chocolate sauce >judging from the way you write programs. >What the is elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) supposed >to be? Ah! I thought you might have some difficulty with that. I had to find a relationship that gave me the right sized ellipse and about the right number of points when I generated it with Newton's GM/r^2. I arrived at the about formula after a lot of trial and error. Same with Xstart and G. Here's an upgraded version...including diagrams for the ellipse (with foci) and velocities. ************* If ecc = 0 Then r = CMaxvel * falsep / twopi 'circle radius, lightdays points = 33402 Else 'GENERATE ELLIPSE Orbit.Cls If pointindex = 20000 Then pointnumber = 3.2 If pointindex = 33000 Then pointnumber = 5 If pointindex = 60000 Then pointnumber = 9.2 p = 0: pmax = 0: Minax = 0: maxax = 0 xstart = pointnumber * (1 - ecc) ^ (5 / 3) 'empirically determined to give the about the right number of points G = xstart / (1 + ecc) / (10 ^ 6) 'ditto elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) 'empirically adjusts print size Ystart = 0: Xtemp = -xstart: Ytemp = 0 RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) Radvector = (RADSQ) ^ 0.5 'length of radius vector vellx = 0.00000000001: velly = 0.001 'this introduces a factor of 0.001 Force = G / RADSQ '(Radvector ^ 2) 'DrawWidth = 1 While Ytemp >= 0 'determines apastron If p Mod 4 = 0 Then compare.PSet (200 + (elipsize * Xtemp / 5), 250 + (Ytemp * elipsize / 5)), RGB(255, 255, 255) 'draw ellipse compare.PSet (200 + (elipsize * Xtemp / 5), 250 - (Ytemp * elipsize / 5)), RGB(255, 255, 255) End If velocity(p) = (((vellx ^ 2) + (velly ^ 2)) ^ 0.5) * 1000 If vellx <> 0 Then x = (velly / vellx) Vangle(p) = (pi / 2) - Atn(x) 'last reading at pmax End If RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) Radvector = RADSQ ^ 0.5 'radv(p) = Radvector Xtemp = Xtemp + vellx '+ (0.5 * Xacc) Ytemp = Ytemp + velly '- (0.5 * Yacc) Xacc = Force * (-Xtemp) / Radvector Yacc = Force * (Ytemp) / Radvector vellx = vellx + Xacc velly = velly - Yacc Force = G / RADSQ If Xtemp > maxax Then maxax = Xtemp If Ytemp > Minax Then Minax = Ytemp p = p + 1 Wend pmax = p - 1 points = (2 * pmax) '+ 1 VVoverP = VVorbs / points focX = (((((maxax + xstart) / 2) ^ 2) - (Minax ^ 2)) ^ 0.5) * elipsize / 5 'length of base 'c' trueecc = focX / ((maxax + xstart) / 2) / elipsize * 5 compare.DrawWidth = 3 compare.PSet (200 - (elipsize * xstart / 5), 250), 255155 'Left compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10), 250), 255155 'midpoint compare.PSet (200 + (Xtemp * elipsize / 5), 250), 255155 'right compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) + focX, 250), 255155 'Rfocus compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) - focX, 250), 255155 'Lfocus compare.DrawWidth = 1 compare.Print: compare.Print True Eccentricity = ; trueecc compare.Print Number of Points = ; points For j = 1 To pmax 'other half of ellipse velocity(pmax + j) = velocity(pmax - j) Vangle(pmax + j) = (twopi) - Vangle(pmax - j) ' Next Gmod = G * 80000000 * (ecc + 0.1) / points Orbit.Show For j = 0 To points Step 20 ''velocity v/s time graph Orbit.PSet (50 + (j * 100 / p), 300 - (0.1 / Gmod * velocity(j))), RGB(0, 0, 255) 'blue Orbit.PSet (50 + (j * 100 / p), 200 - (0.05 / Gmod * velocity(j) * Cos(Vangle(j) - piyaw))), RGB(255, 255, 0) Orbit.PSet (50 + (j * 100 / p), 150 - (20 * Vangle(j))), RGB(255, 0, 0) 'red Next velocity(0) = 1 Vangle(0) = 0: Vangle(pmax) = pi Gmod = G * 80000000 * (ecc + 0.1) / points End If Call diagram 10: End If ************* 'Compare' and 'orbit' are separate forms. Remember my YAW angle is for edge on orbits. My pitch would be the angle of rotation of the orbit plane around the unique axis that is both perpendicular to the LOS and lies in the orbit plane. Instead of including pitch, I simply reduce my velocity input figure. This has the same effect. >like that if he worked for me. Sheesh, I've never seen such woolly-headed >crap. Anyone can draw an ellipse (except Wilson) - Woolly Wilson. NEVER embed numbers in code. Not even pi. >If you mistype it once you'll have hell of a time finding it. pi = 3.14159265 >pi2 = 3.14159265 *2 circumference = 2 * 3.14169265 * radius ' not ok, 6 instead of 5. ing useless engineer...No wonder the Concorde crashed.... Check Google for pi....and hope Greene doesn't find out how silly you are. >circumference = 2 * pi * radius ' ok >circumference = pi2 * radius ' better and faster Then later you can change it to >pi = 3.1415926535897932384626433832795 >to be more accurate and never have to change it anywhere else in the code. >Simple and readable. This makes life easier for YOU, Wilson. Bodging >never does. I set pi, 2p, pi/2 etc at the start. What the hell is wrong with that? Are you raving again? my program. >BWAHAHAHAHA! >This is 2009, Wilson, you didn't start until 2000 after I told you about >it. >You've wasted all that time arguing with dorks, trying to inflate your >ego. >Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. > I was already producing brightness curves for circular orbits before I > read any > of your ty messages. Yeah, yeah.... Wasted years talking to Dishwater and produced BaThwater. >Everyone reckons your overlays are hand-drawn anyway. It would go >hand-in-glove with your doctorate, a ing cheat. The only one you >fool is yourself. >Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's. >far superior elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >And what was your far superior G again? >BWAHAHAHAHAHAHAHA! the fact that this is a simple relationship means there is probably a simple mathematical reason for it. I couldn't be bothered looking Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: The only angle is theta! - Wackypedia > I don't want to show you my new luminosity curve with just 100 points. >You'll only be jealous. > My program includes two independent methods for calculating brightness > curves. > If you could run it you would discover that they both produce almost the > same > curves. > The second one, named after George Dishman (who suggested it but is > unfortunately no longer here) uses only about 330 points around the > ellipse > although the latter is still established with ~33000. >Dishwater was a clot and so are you for listening to the idiot. >Delta-T, as shown in > http://www.androcles01.pwp.blueyonder.co.uk/Doolin'sStar.GIF >is the arrival time between two photons that departed delta-t apart. >The larger the value of delta-T, the fewer photons arrive per second. >Therefore the number of photons arriving per second is inversely >proportional to delta-T. >So, by sorting the array of arrival times so as to be monotonic, >then plotting the inverse (logarithmically) against delta-T, we have a >luminosity curve. That's roughly the way. Dishman pointed out that if the arrival interval between pulses that were > emitted say x seconds apart was monitored for about 500 equally time > spaced > pairs of points around the orbit, the inverse would also produce the > bunching > factor. I was subsequently able to programmed the method successfully > because I > had all the time based data for the ellipse already. It's a lot faster than setting up arrays of arrival times for all the > emitted > pulses but its also pretty hard to program. > If you compute distance/(c+v) + t_emit you get the arrival time. FOR t_emit = 0 TO Period STEP Period/N_points. Arrival time = distance/(c+v) + t_emit ... Now... if you compute distance/c + t_emit you are just adding a constant to t_emit. So: Delta_T = distance/(c+v) - distance/c + t_emit gives an early, on-time or late arrival. The problem is overlap, where slower light is passed by faster light at what we've called critical distance. One full period of arrival is not equal to one full period of emission, there has to be overlapping. > I'll sell you a good program. > i have been working on it again lately. It is improving all the time. > I will have to write a proper paper about BaTh soon or will run out of > time. >Does it have 100 points and run on a spreadsheet? > It has ample points and runs on any windows based computer. Yours wont > run > it, > obviously. >True. I tried to load it but my computer puked up, I had a hell of mess >to clean. Bits of code mixed with constants all over the floor, even the >cat turned his nose up and went out for the day. I expect you eat pickled >onions in red wine and ice cream on fried mutton with a chocolate sauce >judging from the way you write programs. >What the is elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >supposed >to be? Ah! I thought you might have some difficulty with that. > I had to find a relationship that gave me the right sized ellipse and > about the > right number of points when I generated it with Newton's GM/r^2. > I arrived at the about formula after a lot of trial and error. Same with > Xstart > and G. Here's an upgraded version...including diagrams for the ellipse (with > foci) and > velocities. > ************* > If ecc = 0 Then > r = CMaxvel * falsep / twopi 'circle radius, lightdays > points = 33402 > Else 'GENERATE ELLIPSE > Orbit.Cls > If pointindex = 20000 Then pointnumber = 3.2 > If pointindex = 33000 Then pointnumber = 5 > If pointindex = 60000 Then pointnumber = 9.2 > p = 0: pmax = 0: Minax = 0: maxax = 0 > xstart = pointnumber * (1 - ecc) ^ (5 / 3) 'empirically > determined to give the about the right number of points > G = xstart / (1 + ecc) / (10 ^ 6) 'ditto > elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) 'empirically > adjusts print size > Ystart = 0: Xtemp = -xstart: Ytemp = 0 > RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) > Radvector = (RADSQ) ^ 0.5 'length of radius vector > vellx = 0.00000000001: velly = 0.001 'this > introduces a factor of 0.001 > Force = G / RADSQ '(Radvector ^ 2) > 'DrawWidth = 1 > While Ytemp >= 0 'determines apastron > If p Mod 4 = 0 Then > compare.PSet (200 + (elipsize * Xtemp / 5), 250 + (Ytemp * > elipsize / 5)), RGB(255, 255, 255) 'draw ellipse > compare.PSet (200 + (elipsize * Xtemp / 5), 250 - (Ytemp * > elipsize / 5)), RGB(255, 255, 255) > End If > velocity(p) = (((vellx ^ 2) + (velly ^ 2)) ^ 0.5) * 1000 > If vellx <> 0 Then > x = (velly / vellx) > Vangle(p) = (pi / 2) - Atn(x) 'last reading at pmax > End If > RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) > Radvector = RADSQ ^ 0.5 > 'radv(p) = Radvector > Xtemp = Xtemp + vellx '+ (0.5 * Xacc) > Ytemp = Ytemp + velly '- (0.5 * Yacc) > Xacc = Force * (-Xtemp) / Radvector > Yacc = Force * (Ytemp) / Radvector > vellx = vellx + Xacc > velly = velly - Yacc > Force = G / RADSQ > If Xtemp > maxax Then maxax = Xtemp > If Ytemp > Minax Then Minax = Ytemp > p = p + 1 > Wend > pmax = p - 1 > points = (2 * pmax) '+ 1 > VVoverP = VVorbs / points > focX = (((((maxax + xstart) / 2) ^ 2) - (Minax ^ 2)) ^ 0.5) * > elipsize > / 5 'length of base 'c' > trueecc = focX / ((maxax + xstart) / 2) / elipsize * 5 compare.DrawWidth = 3 > compare.PSet (200 - (elipsize * xstart / 5), 250), 255155 > 'Left > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10), 250), > 255155 > 'midpoint > compare.PSet (200 + (Xtemp * elipsize / 5), 250), 255155 > 'right > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) + focX, > 250), > 255155 'Rfocus > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) - focX, > 250), > 255155 'Lfocus > compare.DrawWidth = 1 > compare.Print: compare.Print True > Eccentricity = ; trueecc > compare.Print Number of Points = ; points > For j = 1 To pmax 'other half of ellipse > velocity(pmax + j) = velocity(pmax - j) > Vangle(pmax + j) = (twopi) - Vangle(pmax - j) ' > Next > Gmod = G * 80000000 * (ecc + 0.1) / points > Orbit.Show > For j = 0 To points Step 20 ''velocity v/s > time > graph > Orbit.PSet (50 + (j * 100 / p), 300 - (0.1 / Gmod * velocity(j))), > RGB(0, > 0, 255) 'blue > Orbit.PSet (50 + (j * 100 / p), 200 - (0.05 / Gmod * velocity(j) * > Cos(Vangle(j) - piyaw))), RGB(255, 255, 0) > Orbit.PSet (50 + (j * 100 / p), 150 - (20 * Vangle(j))), RGB(255, 0, 0) > 'red > Next > velocity(0) = 1 > Vangle(0) = 0: > Vangle(pmax) = pi > Gmod = G * 80000000 * (ecc + 0.1) / points > End If > Call diagram > 10: > End If ************* > 'Compare' and 'orbit' are separate forms. I'm still not going to eat pickles and strawberry ice cream. And you left out pitch again. Remember my YAW angle is for edge on orbits. Woolly Wilson's Wobby Wedge-on Worbits are the only kind you've got, how could I forget? My pitch would be the angle of > rotation of the orbit plane around the unique axis that is both > perpendicular > to the LOS and lies in the orbit plane. If you had any. Instead of including pitch, I simply reduce my velocity input figure. This > has > the same effect. ing hopeless. V = c + * cos (pitch) * cos (yaw) When edge on, V = c+ v * 1 * cos (yaw) ' = c+ v. cos(yaw) When face on, V = c+ v * 0 * cos (yaw) ' = c+ 0, total uniation. >like that if he worked for me. Sheesh, I've never seen such woolly-headed >crap. Anyone can draw an ellipse (except Wilson) - Woolly Wilson. >NEVER embed numbers in code. Not even pi. >If you mistype it once you'll have hell of a time finding it. >pi = 3.14159265 >pi2 = 3.14159265 *2 >circumference = 2 * 3.14169265 * radius ' not ok, 6 instead of 5. ing useless engineer...No wonder the Concorde crashed.... > Check Google for pi....and hope Greene doesn't find out how silly you are. I used my desktop calculator, ing useless sheep shagger. >circumference = 2 * pi * radius ' ok >circumference = pi2 * radius ' better and faster >Then later you can change it to >pi = 3.1415926535897932384626433832795 >to be more accurate and never have to change it anywhere else in the code. >Simple and readable. This makes life easier for YOU, Wilson. Bodging >never does. I set pi, 2p, pi/2 etc at the start. What the hell is wrong with that? Are > you > raving again? Pity you don't set G * 80000000 * (ecc + 0.1) / points and 750 / xstart * ((1 - ecc) ^ (2 / 3)) at the start, stupid old git. What the is xstart anyway? xstart = pointnumber * (1 - ecc) ^ (5 / 3) Oh wait, before I leave my house I need to know how many turns I'll need to get to your house, and I'll leave from a nearby street if I have to turn left at Albuquerque. You are round the ing twist. > my program. >BWAHAHAHAHA! >This is 2009, Wilson, you didn't start until 2000 after I told you about >it. >You've wasted all that time arguing with dorks, trying to inflate your >ego. >Woolly Wilson's War Wuperior Wobbly Worbits with WCH's. > I was already producing brightness curves for circular orbits before I > read any > of your ty messages. >Yeah, yeah.... Wasted years talking to Dishwater and produced BaThwater. >Everyone reckons your overlays are hand-drawn anyway. It would go >hand-in-glove with your doctorate, a ing cheat. The only one you >fool is yourself. >Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's. >far superior elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >And what was your far superior G again? >BWAHAHAHAHAHAHAHA! the fact that this is a simple relationship means there is probably a > simple > mathematical reason for it. I couldn't be bothered looking Couldn't be bothered looking is called the far superior method of pulling it out of your arse. I've got to go into London today, medical check up. Can I bring you back anything? An education, maybe? === Subject: Re: The only angle is theta! - Wackypedia Expires: 60 days > That's roughly the way. > Dishman pointed out that if the arrival interval between pulses that were > emitted say x seconds apart was monitored for about 500 equally time > spaced > pairs of points around the orbit, the inverse would also produce the > bunching > factor. I was subsequently able to programmed the method successfully > because I > had all the time based data for the ellipse already. > It's a lot faster than setting up arrays of arrival times for all the > emitted > pulses but its also pretty hard to program. >If you compute distance/(c+v) + t_emit you get the arrival time. FOR t_emit = 0 TO Period STEP Period/N_points. >Arrival time = distance/(c+v) + t_emit >... Now... if you compute distance/c + t_emit you are just adding a constant >to t_emit. >So: >Delta_T = distance/(c+v) - distance/c + t_emit gives an early, on-time or >late >arrival. >The problem is overlap, where slower light is passed by faster light at what >we've called critical distance. One full period of arrival is not equal to >one >full period of emission, there has to be overlapping..... ...and multiple imagery would occur.....but it is never observed....SO the answer is unification..not high pitch angles for every bloody orbit in the universe.. >True. I tried to load it but my computer puked up, I had a hell of mess >to clean. Bits of code mixed with constants all over the floor, even the >cat turned his nose up and went out for the day. I expect you eat pickled >onions in red wine and ice cream on fried mutton with a chocolate sauce >judging from the way you write programs. >What the is elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >supposed >to be? > Ah! I thought you might have some difficulty with that. > I had to find a relationship that gave me the right sized ellipse and > about the > right number of points when I generated it with Newton's GM/r^2. > I arrived at the about formula after a lot of trial and error. Same with > Xstart > and G. > Here's an upgraded version...including diagrams for the ellipse (with > foci) and > velocities. > ************* > If ecc = 0 Then > r = CMaxvel * falsep / twopi 'circle radius, lightdays > points = 33402 > Else 'GENERATE ELLIPSE > Orbit.Cls > If pointindex = 20000 Then pointnumber = 3.2 > If pointindex = 33000 Then pointnumber = 5 > If pointindex = 60000 Then pointnumber = 9.2 > p = 0: pmax = 0: Minax = 0: maxax = 0 > xstart = pointnumber * (1 - ecc) ^ (5 / 3) 'empirically > determined to give the about the right number of points > G = xstart / (1 + ecc) / (10 ^ 6) 'ditto > elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) 'empirically > adjusts print size > Ystart = 0: Xtemp = -xstart: Ytemp = 0 > RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) > Radvector = (RADSQ) ^ 0.5 'length of radius vector > vellx = 0.00000000001: velly = 0.001 'this > introduces a factor of 0.001 > Force = G / RADSQ '(Radvector ^ 2) > 'DrawWidth = 1 > While Ytemp >= 0 'determines apastron > If p Mod 4 = 0 Then > compare.PSet (200 + (elipsize * Xtemp / 5), 250 + (Ytemp * > elipsize / 5)), RGB(255, 255, 255) 'draw ellipse > compare.PSet (200 + (elipsize * Xtemp / 5), 250 - (Ytemp * > elipsize / 5)), RGB(255, 255, 255) > End If > velocity(p) = (((vellx ^ 2) + (velly ^ 2)) ^ 0.5) * 1000 > If vellx <> 0 Then > x = (velly / vellx) > Vangle(p) = (pi / 2) - Atn(x) 'last reading at pmax > End If > RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) > Radvector = RADSQ ^ 0.5 > 'radv(p) = Radvector > Xtemp = Xtemp + vellx '+ (0.5 * Xacc) > Ytemp = Ytemp + velly '- (0.5 * Yacc) > Xacc = Force * (-Xtemp) / Radvector > Yacc = Force * (Ytemp) / Radvector > vellx = vellx + Xacc > velly = velly - Yacc > Force = G / RADSQ > If Xtemp > maxax Then maxax = Xtemp > If Ytemp > Minax Then Minax = Ytemp > p = p + 1 > Wend > pmax = p - 1 > points = (2 * pmax) '+ 1 > VVoverP = VVorbs / points > focX = (((((maxax + xstart) / 2) ^ 2) - (Minax ^ 2)) ^ 0.5) * > elipsize > / 5 'length of base 'c' > trueecc = focX / ((maxax + xstart) / 2) / elipsize * 5 > compare.DrawWidth = 3 > compare.PSet (200 - (elipsize * xstart / 5), 250), 255155 > 'Left > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10), 250), > 255155 > 'midpoint > compare.PSet (200 + (Xtemp * elipsize / 5), 250), 255155 > 'right > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) + focX, > 250), > 255155 'Rfocus > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) - focX, > 250), > 255155 'Lfocus > compare.DrawWidth = 1 > compare.Print: compare.Print True > Eccentricity = ; trueecc > compare.Print Number of Points = ; points > For j = 1 To pmax 'other half of ellipse > velocity(pmax + j) = velocity(pmax - j) > Vangle(pmax + j) = (twopi) - Vangle(pmax - j) ' > Next > Gmod = G * 80000000 * (ecc + 0.1) / points > Orbit.Show > For j = 0 To points Step 20 ''velocity v/s > time > graph > Orbit.PSet (50 + (j * 100 / p), 300 - (0.1 / Gmod * velocity(j))), > RGB(0, > 0, 255) 'blue > Orbit.PSet (50 + (j * 100 / p), 200 - (0.05 / Gmod * velocity(j) * > Cos(Vangle(j) - piyaw))), RGB(255, 255, 0) > Orbit.PSet (50 + (j * 100 / p), 150 - (20 * Vangle(j))), RGB(255, 0, 0) > 'red > Next > velocity(0) = 1 > Vangle(0) = 0: > Vangle(pmax) = pi > Gmod = G * 80000000 * (ecc + 0.1) / points > End If > Call diagram > 10: > End If > ************* > 'Compare' and 'orbit' are separate forms. I'm still not going to eat pickles and strawberry ice cream. >And you left out pitch again. That part is just the ellipse generator. > Remember my YAW angle is for edge on orbits. Woolly Wilson's Wobby Wedge-on Worbits are the only kind you've got, >how could I forget? Can't an engineer get into his head that if you look at any edge on orbit, you can rotate it around an axis that is both normal to the LOS and lies in he otrbit plane and in that way, you can get ALL possible orbit orientations. >My pitch would be the angle of > rotation of the orbit plane around the unique axis that is both > perpendicular > to the LOS and lies in the orbit plane. If you had any. Of course I have a ing orbit plane... you old dope. > Instead of including pitch, I simply reduce my velocity input figure. This > has > the same effect. ing hopeless. >V = c + * cos (pitch) * cos (yaw) >When edge on, >V = c+ v * 1 * cos (yaw) ' = c+ v. cos(yaw) >When face on, >V = c+ v * 0 * cos (yaw) ' = c+ 0, total uniation. Your problem is that you think you are still in a flight simulator.... For our purposes, the third axis of rotation is not required. ...and by redefining pitch or whatever you want to call it, the same result can be achieved by simply reducing velocity or distance. >like that if he worked for me. Sheesh, I've never seen such woolly-headed >crap. Anyone can draw an ellipse (except Wilson) - Woolly Wilson. >NEVER embed numbers in code. Not even pi. >If you mistype it once you'll have hell of a time finding it. >pi = 3.14159265 >pi2 = 3.14159265 *2 >circumference = 2 * 3.14169265 * radius ' not ok, 6 instead of 5. > ing useless engineer...No wonder the Concorde crashed.... > Check Google for pi....and hope Greene doesn't find out how silly you are. I used my desktop calculator, ing useless sheep shagger. >circumference = 2 * pi * radius ' ok >circumference = pi2 * radius ' better and faster >Then later you can change it to >pi = 3.1415926535897932384626433832795 >to be more accurate and never have to change it anywhere else in the code. >Simple and readable. This makes life easier for YOU, Wilson. Bodging >never does. > I set pi, 2p, pi/2 etc at the start. What the hell is wrong with that? Are > you > raving again? >Pity you don't set > G * 80000000 * (ecc + 0.1) / points >and > 750 / xstart * ((1 - ecc) ^ (2 / 3)) >at the start, stupid old git. I did. >What the is xstart anyway? > xstart = pointnumber * (1 - ecc) ^ (5 / 3) I've forgotten. It is related to the distance between the focus and the perihelion. >Oh wait, before I leave my house I need to know how many >turns I'll need to get to your house, and I'll leave from a nearby >street if I have to turn left at Albuquerque. >You are round the ing twist. ......Takes one to know one.... >Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's. >far superior elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >And what was your far superior G again? >BWAHAHAHAHAHAHAHA! > the fact that this is a simple relationship means there is probably a > simple > mathematical reason for it. I couldn't be bothered looking Couldn't be bothered looking is called the far superior method of >pulling it out of your arse. I've got to go into London today, medical check up. ...don't let 'em examine your brain.... >Can I bring you back anything? An education, maybe? ..you still owe me that bottle of red.... Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: The only angle is theta! - Wackypedia > That's roughly the way. > Dishman pointed out that if the arrival interval between pulses that > were > emitted say x seconds apart was monitored for about 500 equally time > spaced > pairs of points around the orbit, the inverse would also produce the > bunching > factor. I was subsequently able to programmed the method successfully > because I > had all the time based data for the ellipse already. > It's a lot faster than setting up arrays of arrival times for all the > emitted > pulses but its also pretty hard to program. >If you compute distance/(c+v) + t_emit you get the arrival time. >FOR t_emit = 0 TO Period STEP Period/N_points. >Arrival time = distance/(c+v) + t_emit >... >Now... if you compute distance/c + t_emit you are just adding a constant >to t_emit. >So: >Delta_T = distance/(c+v) - distance/c + t_emit gives an early, on-time or >late >arrival. >The problem is overlap, where slower light is passed by faster light at >what >we've called critical distance. One full period of arrival is not equal to >one >full period of emission, there has to be overlapping..... ...and multiple imagery would occur.....but it is never observed.... What's this then, a real tail on a star? http://antwrp.gsfc.nasa.gov/apod/ap010121.html You are just the sort of dozy bastard who'd say this pencil is bent: http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg I've got news for you, Wanker Woolly Wilson. Stars are spherical and pencils are straight, no matter what they look like. You must be a relativist. SO the > answer is unification..not high pitch angles for every bloody orbit in the > universe.. Stupid old sheep shagger, makes up silly numbers for G, doesn't trust his own calculations and then invents crackpot theories! You must be a relativist. Wanker Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's and probably a simple mathematical reason for it but couldn't be bothered looking. Recorded for posterity in message >True. I tried to load it but my computer puked up, I had a hell of mess >to clean. Bits of code mixed with constants all over the floor, even the >cat turned his nose up and went out for the day. I expect you eat >pickled >onions in red wine and ice cream on fried mutton with a chocolate sauce >judging from the way you write programs. >What the is elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >supposed >to be? > Ah! I thought you might have some difficulty with that. > I had to find a relationship that gave me the right sized ellipse and > about the > right number of points when I generated it with Newton's GM/r^2. > I arrived at the about formula after a lot of trial and error. Same with > Xstart > and G. > Here's an upgraded version...including diagrams for the ellipse (with > foci) and > velocities. > ************* > If ecc = 0 Then > r = CMaxvel * falsep / twopi 'circle radius, lightdays > points = 33402 > Else 'GENERATE ELLIPSE > Orbit.Cls > If pointindex = 20000 Then pointnumber = 3.2 > If pointindex = 33000 Then pointnumber = 5 > If pointindex = 60000 Then pointnumber = 9.2 > p = 0: pmax = 0: Minax = 0: maxax = 0 > xstart = pointnumber * (1 - ecc) ^ (5 / 3) 'empirically > determined to give the about the right number of points > G = xstart / (1 + ecc) / (10 ^ 6) 'ditto > elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) 'empirically > adjusts print size > Ystart = 0: Xtemp = -xstart: Ytemp = 0 > RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) > Radvector = (RADSQ) ^ 0.5 'length of radius vector > vellx = 0.00000000001: velly = 0.001 'this > introduces a factor of 0.001 > Force = G / RADSQ '(Radvector ^ 2) > 'DrawWidth = 1 > While Ytemp >= 0 'determines apastron > If p Mod 4 = 0 Then > compare.PSet (200 + (elipsize * Xtemp / 5), 250 + (Ytemp > * > elipsize / 5)), RGB(255, 255, 255) 'draw ellipse > compare.PSet (200 + (elipsize * Xtemp / 5), 250 - (Ytemp > * > elipsize / 5)), RGB(255, 255, 255) > End If > velocity(p) = (((vellx ^ 2) + (velly ^ 2)) ^ 0.5) * 1000 > If vellx <> 0 Then > x = (velly / vellx) > Vangle(p) = (pi / 2) - Atn(x) 'last reading at pmax > End If > RADSQ = (Xtemp ^ 2) + (Ytemp ^ 2) > Radvector = RADSQ ^ 0.5 > 'radv(p) = Radvector > Xtemp = Xtemp + vellx '+ (0.5 * Xacc) > Ytemp = Ytemp + velly '- (0.5 * Yacc) > Xacc = Force * (-Xtemp) / Radvector > Yacc = Force * (Ytemp) / Radvector > vellx = vellx + Xacc > velly = velly - Yacc > Force = G / RADSQ > If Xtemp > maxax Then maxax = Xtemp > If Ytemp > Minax Then Minax = Ytemp > p = p + 1 > Wend > pmax = p - 1 > points = (2 * pmax) '+ 1 > VVoverP = VVorbs / points > focX = (((((maxax + xstart) / 2) ^ 2) - (Minax ^ 2)) ^ 0.5) * > elipsize > / 5 'length of base 'c' > trueecc = focX / ((maxax + xstart) / 2) / elipsize * 5 > compare.DrawWidth = 3 > compare.PSet (200 - (elipsize * xstart / 5), 250), 255155 > 'Left > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10), 250), > 255155 > 'midpoint > compare.PSet (200 + (Xtemp * elipsize / 5), 250), 255155 > 'right > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) + focX, > 250), > 255155 'Rfocus > compare.PSet (200 + ((Xtemp - xstart) * elipsize / 10) - focX, > 250), > 255155 'Lfocus > compare.DrawWidth = 1 > compare.Print: compare.Print True > Eccentricity = ; trueecc > compare.Print Number of Points = ; points > For j = 1 To pmax 'other half of > ellipse > velocity(pmax + j) = velocity(pmax - j) > Vangle(pmax + j) = (twopi) - Vangle(pmax - j) ' > Next > Gmod = G * 80000000 * (ecc + 0.1) / points > Orbit.Show > For j = 0 To points Step 20 ''velocity > v/s > time > graph > Orbit.PSet (50 + (j * 100 / p), 300 - (0.1 / Gmod * velocity(j))), > RGB(0, > 0, 255) 'blue > Orbit.PSet (50 + (j * 100 / p), 200 - (0.05 / Gmod * velocity(j) * > Cos(Vangle(j) - piyaw))), RGB(255, 255, 0) > Orbit.PSet (50 + (j * 100 / p), 150 - (20 * Vangle(j))), RGB(255, 0, > 0) > 'red > Next > velocity(0) = 1 > Vangle(0) = 0: > Vangle(pmax) = pi > Gmod = G * 80000000 * (ecc + 0.1) / points > End If > Call diagram > 10: > End If > ************* > 'Compare' and 'orbit' are separate forms. >I'm still not going to eat pickles and strawberry ice cream. >And you left out pitch again. That part is just the ellipse generator. I'm still not going to eat pickles and strawberry ice cream. And you left out pitch again. > Remember my YAW angle is for edge on orbits. >Woolly Wilson's Wobby Wedge-on Worbits are the only kind you've got, >how could I forget? Can't an engineer get into his head that if you look at any edge on orbit, > you > can rotate it around an axis that is both normal to the LOS and lies in he > otrbit plane and in that way, you can get ALL possible orbit orientations. There is probably a simple Woolly Wilson the Wanker reason for it but having modelled it correctly in http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls I couldn't be bothered looking. >My pitch would be the angle of > rotation of the orbit plane around the unique axis that is both > perpendicular > to the LOS and lies in the orbit plane. >If you had any. Of course I have a ing orbit plane... you old dope. It's a Wedge-on Wonly Wobbly Worbit with fake Welocity. > Instead of including pitch, I simply reduce my velocity input figure. > This > has > the same effect. >ing hopeless. >V = c + v * cos (pitch) * cos (yaw) >When edge on, >V = c+ v * 1 * cos (yaw) ' = c+ v. cos(yaw) >When face on, >V = c+ v * 0 * cos (yaw) ' = c+ 0, total uniation. Your problem is that you think you are still in a flight simulator.... Nope, I live in a 3D universe and I don't fake Welocity in my humbly correct method. Your problem is you have no clue what you are doing and you bodge. There is probably a simple Woolly Wilson the Wanker reason for it - incompetence. You can't be bothered doing it right because you don't know how. > For our purposes, the third axis of rotation is not required. We've already discussed roll, Squirming Wanker Woolly Wilson. > ...and by redefining pitch or whatever you want to call it, the same > result can > be achieved by simply reducing velocity or distance. Yeah, sure, reduce distance! Clever that, must be Lorentz contraction. You are a relativist. >like that if he worked for me. Sheesh, I've never seen such >woolly-headed >crap. Anyone can draw an ellipse (except Wilson) - Woolly Wilson. >NEVER embed numbers in code. Not even pi. >If you mistype it once you'll have hell of a time finding it. >pi = 3.14159265 >pi2 = 3.14159265 *2 >circumference = 2 * 3.14169265 * radius ' not ok, 6 instead of 5. > ing useless engineer...No wonder the Concorde crashed.... > Check Google for pi....and hope Greene doesn't find out how silly you > are. >I used my desktop calculator, ing useless sheep shagger. >circumference = 2 * pi * radius ' ok >circumference = pi2 * radius ' better and faster >Then later you can change it to >pi = 3.1415926535897932384626433832795 >to be more accurate and never have to change it anywhere else in the >code. >Simple and readable. This makes life easier for YOU, Wilson. Bodging >never does. > I set pi, 2p, pi/2 etc at the start. What the hell is wrong with that? > Are > you > raving again? >Pity you don't set > G * 80000000 * (ecc + 0.1) / points >and > 750 / xstart * ((1 - ecc) ^ (2 / 3)) >at the start, stupid old git. I did. >What the is xstart anyway? > xstart = pointnumber * (1 - ecc) ^ (5 / 3) I've forgotten. BWAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA! You've forgotten you pulled it out of your arse! > It is related to the distance between the focus and the perihelion. It is apoapsis, you dork! Your points get gradually further apart as they leave xstart. apsis: the point in an astronomical orbit at which the distance of the body from the center of attraction is either greatest or least http://www.merriam-webster.com/dictionary/apsis Periapsis: closest to the focus. Apoapsis: furthest from the focus. It has sweet -all to do with how many points you arbitrarily choose in your far superior method. >Oh wait, before I leave my house I need to know how many >turns I'll need to get to your house, and I'll leave from a nearby >street if I have to turn left at Albuquerque. >You are round the ing twist. ......Takes one to know one.... http://www.youtube.com/watch?v=e8TUwHTfOOU Bugs shoulda started at a different place. >Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits with WCH's. >far superior elipsize = 750 / xstart * ((1 - ecc) ^ (2 / 3)) >And what was your far superior G again? >BWAHAHAHAHAHAHAHA! > the fact that this is a simple relationship means there is probably a > simple > mathematical reason for it. I couldn't be bothered looking > Couldn't be bothered looking is called the far superior method of >pulling it out of your arse. >I've got to go into London today, medical check up. ...don't let 'em examine your brain.... >Can I bring you back anything? An education, maybe? ..you still owe me that bottle of red.... It turned left at Albukoykee. === Subject: Re: The only angle is theta! - Wackypedia Expires: 60 days >Now... if you compute distance/c + t_emit you are just adding a constant >to t_emit. >So: >Delta_T = distance/(c+v) - distance/c + t_emit gives an early, on-time or >late >arrival. >The problem is overlap, where slower light is passed by faster light at >what >we've called critical distance. One full period of arrival is not equal to >one >full period of emission, there has to be overlapping..... > ...and multiple imagery would occur.....but it is never observed.... What's this then, a real tail on a star? > http://antwrp.gsfc.nasa.gov/apod/ap010121.html That's not a double image. It is probably a c+v effect though. >You are just the sort of dozy bastard who'd say this pencil is bent: > http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg >I've got news for you, Wanker Woolly Wilson. Stars are spherical and >pencils are straight, no matter what they look like. >You must be a relativist. SO the > answer is unification..not high pitch angles for every bloody orbit in the > universe.. Stupid old sheep shagger, makes up silly numbers for G, doesn't trust his >own calculations and then invents crackpot theories! >You must be a relativist. My 'G' is not Newton's G. >Wanker Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits >with WCH's and probably a simple mathematical reason for it but >couldn't be bothered looking. Recorded for posterity in message OK smartarse engineer, how does your version of emission theory account for molecular source speeds? They should completely destroy your Algol calculations since at 10000K they are about 0.001c. > ************* > 'Compare' and 'orbit' are separate forms. >I'm still not going to eat pickles and strawberry ice cream. >And you left out pitch again. > That part is just the ellipse generator. I'm still not going to eat pickles and strawberry ice cream. >And you left out pitch again. Pitch is not needed. My velocity figures ALL include the same cos(pitch) factor. > Remember my YAW angle is for edge on orbits. >Woolly Wilson's Wobby Wedge-on Worbits are the only kind you've got, >how could I forget? > Can't an engineer get into his head that if you look at any edge on orbit, > you > can rotate it around an axis that is both normal to the LOS and lies in he > otrbit plane and in that way, you can get ALL possible orbit orientations. There is probably a simple Woolly Wilson the Wanker reason for it but >having modelled it correctly in > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls >I couldn't be bothered looking. If you don't watch out, I'll tell Greene that you insisted pi was 3.1416... and not 3.1415... >My pitch would be the angle of > rotation of the orbit plane around the unique axis that is both > perpendicular > to the LOS and lies in the orbit plane. >If you had any. > Of course I have a ing orbit plane... you old dope. It's a Wedge-on Wonly Wobbly Worbit with fake Welocity. I can feel a plonk coming on.... >V = c+ v * 1 * cos (yaw) ' = c+ v. cos(yaw) >When face on, >V = c+ v * 0 * cos (yaw) ' = c+ 0, total uniation. > Your problem is that you think you are still in a flight simulator.... Nope, I live in a 3D universe and I don't fake Welocity in my humbly >correct method. Your problem is you have no clue what you are doing >and you bodge. There is probably a simple Woolly Wilson the Wanker >reason for it - incompetence. >You can't be bothered doing it right because you don't know how. Get out of your flight simulator before you make any more blunders. > For our purposes, the third axis of rotation is not required. We've already discussed roll, Squirming Wanker Woolly Wilson. > ...and by redefining pitch or whatever you want to call it, the same > result can > be achieved by simply reducing velocity or distance. Yeah, sure, reduce distance! Clever that, must be Lorentz contraction. >You are a relativist. Get out of your flight simulator >Pity you don't set > G * 80000000 * (ecc + 0.1) / points >and > 750 / xstart * ((1 - ecc) ^ (2 / 3)) >at the start, stupid old git. > I did. >What the is xstart anyway? > xstart = pointnumber * (1 - ecc) ^ (5 / 3) > I've forgotten. BWAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA! >You've forgotten you pulled it out of your arse! > It is related to the distance between the focus and the perihelion. It is apoapsis, you dork! Periapsis, you bigger dork >Your points get gradually further apart as they leave xstart. My points are equi-temporal, dopey pommie engineer. The factors G, Xstart and ellipsize were determined solely to make the diagram fit on ghe screen for all eccentricity values and point numbers. >apsis: the point in an astronomical orbit at which the distance of the body >from the center of attraction is either greatest or least http://www.merriam-webster.com/dictionary/apsis Periapsis: closest to the focus. I use perihelion....just a habit. >Apoapsis: furthest from the focus. If it will shut you up I will endeavour to use periapsis and apoapsis in future. I don't see that it is very important. All stars are suns. >It has sweet -all to do with how many points you arbitrarily >choose in your far superior method. If you buy a decent computer and run my program you will soon see how good it is. >Oh wait, before I leave my house I need to know how many >turns I'll need to get to your house, and I'll leave from a nearby >street if I have to turn left at Albuquerque. >You are round the ing twist. > ......Takes one to know one.... http://www.youtube.com/watch?v=e8TUwHTfOOU Bugs shoulda started at a different place. ...silly old engineer....watches kids' comics now.... Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: The only angle is theta! - Wackypedia > Now... if you compute distance/c + t_emit you are just adding a constant >to t_emit. >So: >Delta_T = distance/(c+v) - distance/c + t_emit gives an early, on-time >or >late >arrival. >The problem is overlap, where slower light is passed by faster light at >what >we've called critical distance. One full period of arrival is not equal >to >one >full period of emission, there has to be overlapping..... > ...and multiple imagery would occur.....but it is never observed.... >What's this then, a real tail on a star? > http://antwrp.gsfc.nasa.gov/apod/ap010121.html That's not a double image. It is probably a c+v effect though. >You are just the sort of dozy bastard who'd say this pencil is bent: > http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg >I've got news for you, Wanker Woolly Wilson. Stars are spherical and >pencils are straight, no matter what they look like. >You must be a relativist. >SO the > answer is unification..not high pitch angles for every bloody orbit in > the > universe.. >Stupid old sheep shagger, makes up silly numbers for G, doesn't trust his >own calculations and then invents crackpot theories! >You must be a relativist. My 'G' is not Newton's G. I never imagine it was for a moment. Marvellous how so many of you relativists can say what things are not. You learned that from Diaper, didn't you? A horse is not an English breakfast. Sydney Harbour Bridge is not a town called Alice. The USA is not in Western Australia. Wilson is not a software engineer. Why don't you make a big list of what things are not, Woolly Wilson, and then we can just refer to it quickly to find out what your G isn't. It won't help anyone know what it is, though. >Wanker Woolly Wilson's War Wuperior Wucked-Up Wobbly Worbits >with WCH's and probably a simple mathematical reason for it but >couldn't be bothered looking. Recorded for posterity in message OK smartarse engineer, how does your version of emission theory account > for > molecular source speeds? > They should completely destroy your Algol calculations since at 10000K > they are > about 0.001c. > You must be a relativist who's never seen a bell curve. They look like this: You want me to worry about the ends and forget the middle, right? I'm not counting molecules, Wilson, I'm looking at a single star. That's the high bit in the middle of the bell curve, where the mean is zero. Dishwater teach you that, did he? Wilson, you are so dense your blood type is ragu. No wonder you need red wine to thin it down. http://thecourier.typepad.com/ontheside/images/2007/10/08/ragu.jpg > ************* > 'Compare' and 'orbit' are separate forms. >I'm still not going to eat pickles and strawberry ice cream. >And you left out pitch again. > That part is just the ellipse generator. >I'm still not going to eat pickles and strawberry ice cream. >And you left out pitch again. Pitch is not needed. > My velocity figures ALL include the same cos(pitch) factor. I'm still not going to eat boiled mutton and black forest gateau in sheep shagger G sauce that is not Newton's G, no matter how tasty you say it is. And you left out pitch again. > Remember my YAW angle is for edge on orbits. >Woolly Wilson's Wobby Wedge-on Worbits are the only kind you've got, >how could I forget? > Can't an engineer get into his head that if you look at any edge on > orbit, > you > can rotate it around an axis that is both normal to the LOS and lies in > he > otrbit plane and in that way, you can get ALL possible orbit > orientations. >There is probably a simple Woolly Wilson the Wanker reason for it but >having modelled it correctly in > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls >I couldn't be bothered looking. If you don't watch out, I'll tell Greene that you insisted pi was > 3.1416... and > not 3.1415... Tell him what you like, he's a thick bastard just like you. >My pitch would be the angle of > rotation of the orbit plane around the unique axis that is both > perpendicular > to the LOS and lies in the orbit plane. >If you had any. > Of course I have a ing orbit plane... you old dope. >It's a Wedge-on Wonly Wobbly Worbit with fake Welocity. I can feel a plonk coming on.... You've got that right. I can always chat with Tom Davidson. === Subject: Need a favour Tom, I'm asking a favour of you. I've published a spreadsheet and Henry Wilson says he cannot change the initial variables. Since I can and have no other way to find what the problem is, could you please check to see if what he's saying is generally the case or if he's got some quirk in his software? http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls Sheets 1, 2 and Analysis. What I'm trying to do is show how him the correct method, but he's a cantankerous old guy. http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls Androcles No problem, Androcles - I downloaded both spreadsheets. I am able to change the values in the yellow cells, but I had to *double-click* to select the unprotected cells for data entry. Ask Henry if he has tried that. Otherwise, I had no trouble. All seems to work correctly, and produce reasonable results. BTW, Nice ellipses. I have done more than my share of numerical simulations, and I appreciate the fact that errors propagate through iterative procedures, so whenever explicit calculations can be performed using an analytical formula, it is always to be preferred over the kind of calculate-the-next-result-based-on-the-result-we-got-from-the-last-calcula t ion method that characterized so many numerical models. Back in the 1980's when I was in the team analyzing atmospheric helium and demonstrating empirically the rapid mixing at sea level, I had the opportunity to examine a strategy for a numerical simulation of a body of compressible gas with various variables (P, T, local velocity, specific heat, heat input and radiation, adiabatic coefficient, etc.) that used a modified volumetric cell array. The strategy *appeared* sound, but the programmers had overlooked a critical detail: digital computers do not have an optimal rounding algorithm. When the last decimal digit of a number is 5, computers invariably rounded up at that time, whereas the procedure recommended by mathematicians and engineers (ASTM, at least) is to round terminal 5s up exactly half the time, and down the other half of the time. The ASTM procedure in particular instructs that *bias* in rounding may be eliminated by rounding up when the digit preceding the 5 is odd, and down when that digit is even. This eliminates what the mathematicians call propagation of round-off error. In modeling small systems this is normally not a problem, and it can be avoided by using extended precision in the calculations. However in large systems in which there are large numbers of iterations (due to high data resolution in spatial and/or temporal dimensions) an error of one part in a billion consistently *added* to one number of every twenty can produce significant errors. When I learned that the modelers either had no appreciation for the accumulation of round-off error, or did not consider it a serious issue, or (in at least one case) considered the consequences of enduring such an error to be preferable to delaying the publication of results when corrective measures were implemented, I lost all faith in climate modeling. It was not long afterward that it was discovered that their model invariably predicted overall warming of the atmosphere, even when the calculations were run for *reduced* CO2, or when calculating *backwards* in time, the average temperatures also increased monotonically with the amount of time regressed. Little was said publicly about these results. It seemed obvious to me that the ever-increasing temperatures were accumulating round-off error from thousands of time iterations on millions of cells. I have not spoken with them since. I hope I've said something helpful. Tom >V = c+ v * 1 * cos (yaw) ' = c+ v. cos(yaw) >When face on, >V = c+ v * 0 * cos (yaw) ' = c+ 0, total uniation. > Your problem is that you think you are still in a flight simulator.... >Nope, I live in a 3D universe and I don't fake Welocity in my humbly >correct method. Your problem is you have no clue what you are doing >and you bodge. There is probably a simple Woolly Wilson the Wanker >reason for it - incompetence. >You can't be bothered doing it right because you don't know how. Get out of your flight simulator before you make any more blunders. > For our purposes, the third axis of rotation is not required. >We've already discussed roll, Squirming Wanker Woolly Wilson. > ...and by redefining pitch or whatever you want to call it, the same > result can > be achieved by simply reducing velocity or distance. >Yeah, sure, reduce distance! Clever that, must be Lorentz contraction. >You are a relativist. Get out of your flight simulator >Pity you don't set > G * 80000000 * (ecc + 0.1) / points >and > 750 / xstart * ((1 - ecc) ^ (2 / 3)) >at the start, stupid old git. > I did. >What the is xstart anyway? > xstart = pointnumber * (1 - ecc) ^ (5 / 3) > I've forgotten. >BWAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA! >You've forgotten you pulled it out of your arse! > It is related to the distance between the focus and the perihelion. >It is apoapsis, you dork! Periapsis, you bigger dork BWHAHAHAHAHAHAHAHAHA! >Your points get gradually further apart as they leave xstart. My points are equi-temporal, dopey pommie engineer. The factors G, Xstart > and > ellipsize were determined solely to make the diagram fit on ghe screen for > all > eccentricity values and point numbers. BWHAHAHAHAHAHAHAHAHA! >apsis: the point in an astronomical orbit at which the distance of the >body >from the center of attraction is either greatest or least >http://www.merriam-webster.com/dictionary/apsis >Periapsis: closest to the focus. I use perihelion....just a habit. Your xstart is still furthest from the focus, not closest. >Apoapsis: furthest from the focus. If it will shut you up I will endeavour to use periapsis and apoapsis in > future. I don't see that it is very important. All stars are suns. >It has sweet -all to do with how many points you arbitrarily >choose in your far superior method. If you buy a decent computer and run my program you will soon see how good > it > is. I've seen how bad it is. http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls On Sheet 2 you only have to change vellx to 0.000000001 to see you don't have an ellipse no matter how many points you add. in' useless. >Oh wait, before I leave my house I need to know how many >turns I'll need to get to your house, and I'll leave from a nearby >street if I have to turn left at Albuquerque. >You are round the ing twist. > ......Takes one to know one.... > http://www.youtube.com/watch?v=e8TUwHTfOOU >Bugs shoulda started at a different place. ...silly old engineer....watches kids' comics now.... Yeah, that's why I won't watch Woolly Wilson's Wobbly Worbits, they are kid's comics without being funny. === Subject: Re: The only angle is theta! - Wackypedia Expires: 60 days > My 'G' is not Newton's G. I never imagine it was for a moment. Marvellous how so many of you >relativists can say what things are not. You learned that from Diaper, >didn't you? You can call me a relativist...but not of the Einsteinian type. >A horse is not an English breakfast. .... but a bottle of glenlivet is. >Sydney Harbour Bridge is not a town called Alice. >The USA is not in Western Australia. >Wilson is not a software engineer. >Why don't you make a big list of what things are not, Woolly Wilson, >and then we can just refer to it quickly to find out what your G isn't. Jealous old bastard... > OK smartarse engineer, how does your version of emission theory account > for > molecular source speeds? > They should completely destroy your Algol calculations since at 10000K > they are > about 0.001c. You must be a relativist who's never seen a bell curve. >They look like this: You want me to worry about the ends and forget the middle, right? >I'm not counting molecules, Wilson, I'm looking at a single star. >That's the high bit in the middle of the bell curve, where the mean is >zero. You don't even know what I'm talking about.... >There is probably a simple Woolly Wilson the Wanker reason for it but >having modelled it correctly in > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls >I couldn't be bothered looking. > If you don't watch out, I'll tell Greene that you insisted pi was > 3.1416... and > not 3.1415... Tell him what you like, he's a thick bastard just like you. no wonder the Concorde crashed.... > Of course I have a ing orbit plane... you old dope. >It's a Wedge-on Wonly Wobbly Worbit with fake Welocity. > I can feel a plonk coming on.... You've got that right. I can always chat with Tom Davidson. > === >Subject: Need a favour >Tom, I'm asking a favour of you. >I've published a spreadsheet and Henry Wilson says >he cannot change the initial variables. Since I can >and have no other way to find what the problem >is, could you please check to see if what he's saying >is generally the case or if he's got some quirk in his >software? http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls Sheets 1, 2 and Analysis. >What I'm trying to do is show how him the correct method, >but he's a cantankerous old guy. > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls When I increase the points, I get a small section of an ellipse. You program is plain stupid. > It is related to the distance between the focus and the perihelion. >It is apoapsis, you dork! > Periapsis, you bigger dork BWHAHAHAHAHAHAHAHAHA! >Your points get gradually further apart as they leave xstart. > My points are equi-temporal, dopey pommie engineer. The factors G, Xstart > and > ellipsize were determined solely to make the diagram fit on ghe screen for > all > eccentricity values and point numbers. BWHAHAHAHAHAHAHAHAHA! >apsis: the point in an astronomical orbit at which the distance of the >body >from the center of attraction is either greatest or least >http://www.merriam-webster.com/dictionary/apsis >Periapsis: closest to the focus. > I use perihelion....just a habit. Your xstart is still furthest from the focus, not closest. An ellipse has TWO foci, dopey old engineer.. >Apoapsis: furthest from the focus. > If it will shut you up I will endeavour to use periapsis and apoapsis in > future. I don't see that it is very important. All stars are suns. >It has sweet -all to do with how many points you arbitrarily >choose in your far superior method. > If you buy a decent computer and run my program you will soon see how good > it > is. I've seen how bad it is. > http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls On Sheet 2 you only have to change vellx to 0.000000001 to see you >don't have an ellipse no matter how many points you add. in' useless. I told you, I have deliberatelty distorted my ellipses by a considerable amount to see the effect on brighness curves. It was negligible. Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: The only angle is theta! - Wackypedia > My 'G' is not Newton's G. >I never imagine it was for a moment. Marvellous how so many of you >relativists can say what things are not. You learned that from Diaper, >didn't you? You can call me a relativist...but not of the Einsteinian type. Very much so, he was full of bull too. Einstein: The velocity of light is not source dependent. Einstein: We'll alter time to make lightspeed have the same c for everyone. Wilson: We'll uniate light speed to make it have the same c for everyone. Wilson: My 'G' is not Newton's G. Einstein: These two postulates suffice for the attainment of a simple and consistent theory Einstein: I'm a prominent theoretical physicist. Wilson: xstart depends on how many points I want. Wilson: My ellipses are beautiful, I said so. Wilson: I'm a prominent theoretical physicist. No fundamental difference at all, you are exactly like Einstein. You both theories out of your arse faster than Superman can fly around the Earth. You are even proud of your far superior theories. I have to hand it to you, Wilson, your bull is far superior to anyone's. >A horse is not an English breakfast. .... but a bottle of glenlivet is. >Sydney Harbour Bridge is not a town called Alice. >The USA is not in Western Australia. >Wilson is not a software engineer. >Why don't you make a big list of what things are not, Woolly Wilson, >and then we can just refer to it quickly to find out what your G isn't. Jealous old bastard... Bull doesn't make me jealous, Wilson. > OK smartarse engineer, how does your version of emission theory account > for > molecular source speeds? > They should completely destroy your Algol calculations since at 10000K > they are > about 0.001c. >You must be a relativist who's never seen a bell curve. >They look like this: >You want me to worry about the ends and forget the middle, right? >I'm not counting molecules, Wilson, I'm looking at a single star. >That's the high bit in the middle of the bell curve, where the mean is >zero. You don't even know what I'm talking about.... And you do? BWAHAHAHAHAHAHAHAHA! >There is probably a simple Woolly Wilson the Wanker reason for it but >having modelled it correctly in > http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls >I couldn't be bothered looking. > If you don't watch out, I'll tell Greene that you insisted pi was > 3.1416... and > not 3.1415... >Tell him what you like, he's a thick bastard just like you. no wonder the Concorde crashed.... > Of course I have a ing orbit plane... you old dope. >It's a Wedge-on Wonly Wobbly Worbit with fake Welocity. > I can feel a plonk coming on.... >You've got that right. I can always chat with Tom Davidson. > No point in you interrupting a conversation between Tom and I, Wilson, and snipping his reply is just sticking your head up your jealous arse. Tom, I'm asking a favour of you. I've published a spreadsheet and Henry Wilson says he cannot change the initial variables. Since I can and have no other way to find what the problem is, could you please check to see if what he's saying is generally the case or if he's got some quirk in his software? http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls Sheets 1, 2 and Analysis. What I'm trying to do is show how him the correct method, but he's a cantankerous old guy. http://www.androcles01.pwp.blueyonder.co.uk/Orbit.xls Androcles No problem, Androcles - I downloaded both spreadsheets. I am able to change the values in the yellow cells, but I had to *double-click* to select the unprotected cells for data entry. Ask Henry if he has tried that. Otherwise, I had no trouble. All seems to work correctly, and produce reasonable results. BTW, Nice ellipses. I have done more than my share of numerical simulations, and I appreciate the fact that errors propagate through iterative procedures, so whenever explicit calculations can be performed using an analytical formula, it is always to be preferred over the kind of calculate-the-next-result-based-on-the-result-we-got-from-the-last-calcula tion method that characterized so many numerical models. Back in the 1980's when I was in the team analyzing atmospheric helium and demonstrating empirically the rapid mixing at sea level, I had the opportunity to examine a strategy for a numerical simulation of a body of compressible gas with various variables (P, T, local velocity, specific heat, heat input and radiation, adiabatic coefficient, etc.) that used a modified volumetric cell array. The strategy *appeared* sound, but the programmers had overlooked a critical detail: digital computers do not have an optimal rounding algorithm. When the last decimal digit of a number is 5, computers invariably rounded up at that time, whereas the procedure recommended by mathematicians and engineers (ASTM, at least) is to round terminal 5s up exactly half the time, and down the other half of the time. The ASTM procedure in particular instructs that *bias* in rounding may be eliminated by rounding up when the digit preceding the 5 is odd, and down when that digit is even. This eliminates what the mathematicians call propagation of round-off error. In modeling small systems this is normally not a problem, and it can be avoided by using extended precision in the calculations. However in large systems in which there are large numbers of iterations (due to high data resolution in spatial and/or temporal dimensions) an error of one part in a billion consistently *added* to one number of every twenty can produce significant errors. When I learned that the modelers either had no appreciation for the accumulation of round-off error, or did not consider it a serious issue, or (in at least one case) considered the consequences of enduring such an error to be preferable to delaying the publication of results when corrective measures were implemented, I lost all faith in climate modeling. It was not long afterward that it was discovered that their model invariably predicted overall warming of the atmosphere, even when the calculations were run for *reduced* CO2, or when calculating *backwards* in time, the average temperatures also increased monotonically with the amount of time regressed. Little was said publicly about these results. It seemed obvious to me that the ever-increasing temperatures were accumulating round-off error from thousands of time iterations on millions of cells. I have not spoken with them since. I hope I've said something helpful. Tom See, Tom Davidson is a rational scientist, whereas Woolly Wilson is just another ing idiot. Now plonk that, sheep shagging moron. > It is related to the distance between the focus and the perihelion. >It is apoapsis, you dork! > Periapsis, you bigger dork >BWHAHAHAHAHAHAHAHAHA! >Your points get gradually further apart as they leave xstart. > My points are equi-temporal, dopey pommie engineer. The factors G, > Xstart > and > ellipsize were determined solely to make the diagram fit on ghe screen > for > all > eccentricity values and point numbers. >BWHAHAHAHAHAHAHAHAHA! >apsis: the point in an astronomical orbit at which the distance of the >body >from the center of attraction is either greatest or least >http://www.merriam-webster.com/dictionary/apsis >Periapsis: closest to the focus. > I use perihelion....just a habit. >Your xstart is still furthest from the focus, not closest. An ellipse has TWO foci, dopey old engineer.. Oh sure, and the Solar system has two suns, one of which is invisible, right? So your xstart is closer to the one we can't see. That plonk you feel coming on is getting ever more enticing. >Apoapsis: furthest from the focus. > If it will shut you up I will endeavour to use periapsis and apoapsis in > future. I don't see that it is very important. All stars are suns. >It has sweet -all to do with how many points you arbitrarily >choose in your far superior method. > If you buy a decent computer and run my program you will soon see how > good > it > is. >I've seen how bad it is. > http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls >On Sheet 2 you only have to change vellx to 0.000000001 to see you >don't have an ellipse no matter how many points you add. in' useless. I told you, I have deliberatelty distorted my ellipses by a considerable > amount > to see the effect on brighness curves. It was negligible. You can tell me 'til the ing cows come home, your ellipses are still half-polygons mirrored. Go back to shagging sheep where you belong. http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls On Sheet 2 you only have to change vellx to 0.000000001 to see you don't have an ellipse no matter how many points you add. in' useless. === Subject: Generation of cyclic functions posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) Bonjour .88 tous, Do you know means of building, on purpose, real continuous functions of a given cycle n , 'n' any positive integer >1 . There are two over-beated cases: conjugate of a cyclic one, and produce of symmetrical expressions like: 1/f + 1/x = 4 , yielding involutive functions such as f(x) =x/(4x-1) I've also noticed some equations leading to cycles : Example: in f(f(x)/(1+f(x)) = x/(1-x) f(x) possesses a general solution k(x)/(1-k(x)) where k(x) is involutive (cycle=2) Welcome to you and your ideas, Alain === Subject: Re: Generation of cyclic functions posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On 16 Mrz., 11:42, alainvergh...@gmail.com continuous functions of a given cycle n , 'n' any positive > integer >1 . > There are two over-beated cases: conjugate of a cyclic one, > and produce of symmetrical expressions like: > 1/f + 1/x = 4 , yielding involutive functions such as > f(x) =x/(4x-1) I've also noticed some equations leading to cycles : > Example: in f(f(x)/(1+f(x)) = x/(1-x) > f(x) possesses a general solution k(x)/(1-k(x)) > where k(x) is involutive (cycle=2) Welcome to you and your ideas, Alain Given a matrix A = ((a b) (c d)), we have f A : x |-> (ax+b)/(cx+d) and note that f (A*B) = f A o f B Hence look for matrix A with A^n = 1, e.g. A = ((cos t sin t) (-sin t cos t)) with t=2pi/n === Subject: Re: Generation of cyclic functions posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) > On 16 Mrz., 11:42, alainvergh...@gmail.com Bonjour .88 tous, > Do you know means of building, on purpose, real > continuous functions of a given cycle n , 'n' any positive > integer >1 . > There are two over-beated cases: conjugate of a cyclic one, > and produce of symmetrical expressions like: > 1/f + 1/x = 4 , yielding involutive functions such as > f(x) =x/(4x-1) > I've also noticed some equations leading to cycles : > Example: in f(f(x)/(1+f(x)) = x/(1-x) > f(x) possesses a general solution k(x)/(1-k(x)) > where k(x) is involutive (cycle=2) > Welcome to you and your ideas, > Alain Given a matrix A = ((a b) (c d)), we have > f A : x |-> (ax+b)/(cx+d) > and note that f (A*B) = f A o f B > Hence look for matrix A with A^n = 1, e.g. > A = ((cos t sin t) (-sin t cos t)) > with t=2pi/n- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Bonjour Hagman, Well, I did not mention homographic functions (fractionnal) three cases: Identity h(x) = x , lines l(x) = a -x functions h | (h^[n](x)-x1)/(h^[n](x)-x2)=a^n*(x-x1)/(x-x2) x1 and x2 fixed points , when cyclic , factor 'a' is root of unity, n non null integer, Alain === Subject: Re: Geometric series problem (1) > Question : Find the sum of n consecutive geometric terms which can be > inserted between 1 and 2. > How do you construct an equation to solve this? The answer is > supposed to be (2 - 2^(1/(n+1)) )/( 2^(1/(n+1)) - 1) > How does one arrive at this answer? > *********************************************************** > We suppose 1, a_1,...,a_n, 2 is a geom. sequence, and not only the n > elements a_1,...,a_n, otherwise the problem has infinite number of > solutions, but then: > a_1/1 = a_1 = r, and also 2/a_n = r ==> use the formula for the n-th > element in a geom, seq. and find that r^(n+1) = 2. > Now use the formula for the sum of the n consecutive elements of a > geom. seq. a_1 +...+ a_n, substitute and get the result. > Tonio > don't really understand what you mean by the above. Could you rephrase > it a little? > You have 1 < a_1 < a_2 < ... < a_n < 2, you know that this is a > geometrical sequence and your goal is to find a_1 + a_2 + ... + a_n. > Now, let let r = a_1/1 = 1. Then a_2/a_1 = r, a_3/a_2 = r, and so on > until 2/a_n = r. Then > 2 = (2/a_n)*(a_n/a_{n - 1})*... *(a_2/a_1)*(a_1/1) = r^{n + 1}. > Now you know the value of _r_ and it should be easy for you to compute > a_1 + a_2 + ... + a_n. We know that S_n = a(1-r^n)/(1-r) > What's a, the first term in this case? By putting r = 2^(1/n+1) back > into the equation, it doesn't give me (2 - 2^(1/(n+1)) )/( 2^(1/(n+1)) > - 1). The first term of the sum a_1 + a_2 + ... + a_n is a_1, obviously, and, r(1 - r^n)/(1 - r) = (r - r^{n + 1})/(1 - r) = (2^{1/(n + 1)} - 2)/(1 - 2^{1/(n + 1)}). Jose Carlos Santos === Subject: About confidence intervals posting-account=GBCVaAoAAABLGAL92uIOBLrEf_j0nkgM Gecko/2008050509 Firefox/3.0b5,gzip(gfe),gzip(gfe) I have the following problem. I want to estimate two parameters from a certain population, let's say A and B. Then I want to compute the following relation between them: C = (A-B)/A My question is: How can I compute the confidence intervals of C ? Daniel === Subject: Re: Wombat Wilson's Wobbly Worbits revisited. Expires: 60 days > http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls In it's simplest form with all constants removed, sheet 1 is supposed to >be a circle. Wilson computes half-way round and mirrors the other half, >which I have duplicated. Some of Wilson's actual code has been converted to spreadsheet form >and is shown on sheet 2. Naturally I'm not about to create a 100,000 >element array on a spreadsheet, but the part of the curve shown speaks >for itself. Feel free to modify the initial values in the yellow boxes. Wilson seems to be under the illusion that he can generate an ellipse >solely from Newtonian Mechanical extrapolation but Newtonian >Mechanics also allows for precession, which is what we have. Wilson is clearly quite insane if he thinks that is far superior >to http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.xls >which uses Kepler's equation. Perhaps some kind soul will explain his error to the poor boy (or put >him in a straight jacket where he belongs). You are already threatened with one defamation case, why try to get yourself another? Your professional jealousy will get you into a lot of trouble before you're much older. Accept it, your variable star program is compared with mine. Harry Wilson. ASTC,BSc,DSc(T) www.users.bigpond.com/hewn/index.htm. ..... === Subject: Re: Wombat Wilson's Wobbly Worbits revisited. > http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls >In it's simplest form with all constants removed, sheet 1 is supposed to >be a circle. Wilson computes half-way round and mirrors the other half, >which I have duplicated. >Some of Wilson's actual code has been converted to spreadsheet form >and is shown on sheet 2. Naturally I'm not about to create a 100,000 >element array on a spreadsheet, but the part of the curve shown speaks >for itself. Feel free to modify the initial values in the yellow boxes. >Wilson seems to be under the illusion that he can generate an ellipse >solely from Newtonian Mechanical extrapolation but Newtonian >Mechanics also allows for precession, which is what we have. >Wilson is clearly quite insane if he thinks that is far superior >to http://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.xls >which uses Kepler's equation. >Perhaps some kind soul will explain his error to the poor boy (or put >him in a straight jacket where he belongs). You are already threatened with one defamation case, why try to get > yourself > another? > Your professional jealousy will get you into a lot of trouble before > you're > much older. > Accept it, your variable star program is compared with mine. Wilson, and you are a ing liar. Sue me. === Subject: Re: Wombat Wilson's Wobbly Worbits revisited. posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > http://www.androcles01.pwp.blueyonder.co.uk/WilsonMethod.xls >In it's simplest form with all constants removed, sheet 1 is supposed to >be a circle. Wilson computes half-way round and mirrors the other half, >which I have duplicated. >Some of Wilson's actual code has been converted to spreadsheet form >and is shown on sheet 2. Naturally I'm not about to create a 100,000 >element array on a spreadsheet, but the part of the curve shown speaks >for itself. Feel free to modify the initial values in the yellow boxes. >Wilson seems to be under the illusion that he can generate an ellipse >solely from Newtonian Mechanical extrapolation but Newtonian >Mechanics also allows for precession, which is what we have. >Wilson is clearly quite insane if he thinks that is far superior >tohttp://www.androcles01.pwp.blueyonder.co.uk/Orbit/Orbit.xls >which uses Kepler's equation. >Perhaps some kind soul will explain his error to the poor boy (or put >him in a straight jacket where he belongs). You are already threatened with one defamation case, why try to get yourself > another? > Your professional jealousy will get you into a lot of trouble before you're > much older. > Accept it, your variable star program is compared with mine. It is like comparing a cat turd with a dog turd. The dog will eat the cat turd, but it is still a turd. Harry Wilson. ASTC,BSc,DSc(T) Did you update all your fake certifications with your new name? www.users.bigpond.com/hewn/index.htm. ..... === Subject: Prescribed distance function posting-account=I6hi8AoAAAD3vgxikS-QN7ej64-ZP9WT Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) I have the following problem: Let $M$ be a differentiable manifold (compact if needed), given a distance function $d(x,y)$ on $M$ is there a Riemannian metric that gives raise to this distance? Any help or pointers are appreciated. SK === Subject: Re: Prescribed distance function > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given a distance function $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to this distance? Question: what if _d_ is the discrete metric? Besides, a Rimannian metric does not give rise to a given distance. Either they are equal or they are different. Jose Carlos Santos === Subject: Re: Prescribed distance function > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given a distance function $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to this distance? > Question: what if _d_ is the discrete metric? > Besides, a Rimannian metric does not give rise to a given distance. > Either they are equal or they are different. ??? Certainly a riemannian metric gives rise to, or leads to, > or is naturally associated with, a distance function. It's unfortunate that the word metric means two different > things. Indeed. I interpreted Riemannian metric as a metric (in the topological sense) induced by a family of (positive definite) inner products defined on the tangent spaces of M, with the properties that you are aware of. > Let's say a riemannian metric is an r-metric, > while a metric in the sense of map from XxX to (0,infinity) > that satisfies the triangle inequality, etc is a d-metric; > a d-metric is what's being called a distance function > here. An r-metric and a d-metric are very different things; > an r-metric is a quadratic form on the tangent space > of a manifold. An r-metric gives a definition of the > length of a differentiable curve (the integral of > the norm of the derivative, with the norm > determined by the r-metric). And then that notion > of the length of a curve leads to a d-metric, > namely d(p,q) = the inf of the length of a curve > from p to q. In particular an r-metric is not a d-metric, so > it cannot equal a d-metric, but it certainly > gives rise to a d-metric. In spite of my mistake, it is still true that the discrete metric cannot be induced by a Riemannian metric. Jose Carlos Santos === Subject: Re: Prescribed distance function <726to9Fo8qf1U2@mid.individual.net> posting-account=I6hi8AoAAAD3vgxikS-QN7ej64-ZP9WT Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given a distance function $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to this distance? Question: what if d is the discrete metric? Besides, a Rimannian metric does not give rise to a given distance. > Either they are equal or they are different. > Jose Carlos Santos By Riemannian metric, I meant a positive-definite quadratic form (well the word metric is used for two different entities unfortunately). I am interested in the case where (M,d) is a length space, and In general I exclude all kinds of pathologies, the question being raised by applicative concerns and not purely mathematical. SK === Subject: Re: Prescribed distance function > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given a distance function $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to this distance? Any help or pointers are appreciated. > SK No, not even if M is the plane (or the 2-torus if compactness is needed). There is d that is not infinitesimally Euclidean. === Subject: Re: Prescribed distance function <160320090807363749%anniel@nym.alias.net.invalid> posting-account=I6hi8AoAAAD3vgxikS-QN7ej64-ZP9WT Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given a distance function $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to this distance? > Any help or pointers are appreciated. > SK No, not even if M is the plane (or the 2-torus if compactness is > needed). There is d that is not infinitesimally Euclidean. necessary condition, but is is sufficient, given that the metric is an induced intrinsic metric (i.e. (M,d) is a length space) ? SK === Subject: Re: Prescribed distance function <0fnsr4lcpult799rq1inia94pe9gomk7en@4ax.com> posting-account=I6hi8AoAAAD3vgxikS-QN7ej64-ZP9WT Gecko/2008121621 Ubuntu/8.04 (hardy) Firefox/3.0.5,gzip(gfe),gzip(gfe) > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given adistancefunction $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to thisdistance? > Any help or pointers are appreciated. > SK > No, not even if M is the plane (or the 2-torus if compactness is > needed). There is d that is not infinitesimally Euclidean. >necessary condition, but is is sufficient, given that the metric is an >induced intrinsic metric (i.e. (M,d) is a length space) ? I'm no doubt going to get the terminology wrong... Surely you the following is the condition you want. > Given a point p and a tangent vector v at p, there is > a curve c v(t) with c v(0) = p and c v'(0) = v, defined by > the exponential map, right? Now given adistancefunction > d, attempt to define a quadratic form Q by Q p(v) = lim {t->0} d(p, c v(t)) / t. If that is a quadratic form, and varies continuously > from point to point, then surely the d-length of a > curve c is given by the integral of Q {c(t)}(c'(t))? >SK David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) it other than to check for Q being quadratic and smooth. The existence of a norm on each tangent space that satisfies f(v)=lim {t->0} d(p, c v (t)) / t and varies smoothly only guarantees the manifold to be Finslerian. But I think adding to this the requirement of being infinitesimally Euclidean can be a sufficient condition for being Riemannian. Remains to check this... SK === Subject: Re: Prescribed distance function posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) it other than to check for Q being quadratic and smooth. The existence > of a norm on each tangent space that satisfies f(v)=lim {t->0} d(p, > c v(t)) / t and varies smoothly only guarantees the manifold to be > Finslerian. But I think adding to this the requirement of being > infinitesimally Euclidean can be a sufficient condition for being > Riemannian. Remains to check this... > SK If being Riemannian you mean the distance function d(p,q) is the length of a geodesic joining p to q wrt your Riemannian metric defined on the tangent spaces, then I don't think your condition is sufficient. This is because for any increasing concave smooth function g: [0,inf) -> [0,inf) such that g(x) = 0 iff x = 0, AND g(x) = x on a small neighbour of 0. g(d(p,q)) is again a metric on your space which gives the same Riemannian metric on tangent spaces as your original d(p,q). === Subject: Re: Prescribed distance function <0fnsr4lcpult799rq1inia94pe9gomk7en@4ax.com> posting-account=TFySpAoAAACHhjHEqw8aQoxuQ_UD1wou Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > I have the following problem: Let $M$ be a differentiable manifold > (compact if needed), given a distance function $d(x,y)$ on $M$ is > there a Riemannian metric that gives raise to this distance? > Any help or pointers are appreciated. > SK > No, not even if M is the plane (or the 2-torus if compactness is > needed). There is d that is not infinitesimally Euclidean. >necessary condition, but is is sufficient, given that the metric is an >induced intrinsic metric (i.e. (M,d) is a length space) ? I'm no doubt going to get the terminology wrong... Surely you the following is the condition you want. > Given a point p and a tangent vector v at p, there is > a curve c v(t) with c v(0) = p and c v'(0) = v, defined by > the exponential map, right? Now given a distance function > d, attempt to define a quadratic form Q by Q p(v) = lim {t->0} d(p, c v(t)) / t. If that is a quadratic form, and varies continuously > from point to point, then surely the d-length of a > curve c is given by the integral of Q {c(t)}(c'(t))? >SK David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) it other than to check for Q being quadratic and smooth. The existence of a norm on each tangent space that satisfies f(v)=lim {t->0} d(p, c v (t)) / t and varies smoothly only guarantees the manifold to be Finslerian. But I think adding to this the requirement of being infinitesimally Euclidean can be a sufficient condition for being Riemannian. Remains to check this... SK === 8th solutions manual (To search click in keyboard Ctrl+F) Solutions Manuals in Electronic (PDF)Format! Just contact with , getsolutionmanual (at) hotmail.com (my email address,getsolutionmanual@hotmail.com ), these are parts of our solutions, if the solution you want is on the list, please email to me. NOTICE: if the solutions manual that in my list ,please note it in your email . Instructor Solutions manual to : Solutions manual to Thermodynamics: An Engineering Approach,6th Ed. by Cengel Solutions manual to Introduction to Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} Solutions manual to Macroeconomics, 4E Olivier Blanchard instructor manual Solutions manual to Vector Mechanics for Engineers; Statics 8th Beer Johnston Solutions manual to Mechanics of Materials, 7th James M. 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Roberts === Subject: Re: New Lower Limit on Higgs Boson Mass > Are they saying that the Higgs could be between 114-160 GeV or > between 170-185 GeV? > Anyways, the LHC folks must feel like they're in the Olympics and > they have a broken leg. > Yousuf Khan IMHO, the game is not over yet. It will be more interesting > if the Fermilab folks can rule out the existence of Higgs > range. This will force the theorist to look for a more > satisfactory mass generation mechanism for the zoo of Does anyone know if we assume Higgs is some form of > what is the mass limit (if that make sense) posed by > current experimental results? I don't understand how the standard model makes any statement at all, about the Higgs mass. When I studied the standard model, it was six quarks, six leptons and the various resulting bosons that you get from all the different pairings of all those twelve fermions. The fermions are arranged onto a hexagon and the bosons onto a triangle. All that has nothing to do with Higgs, which seems to be some kind of an add-on that they just forced in later, with a shoehorn. Or a crowbar. :P === Subject: Re: New Lower Limit on Higgs Boson Mass <49bd4ddc$1@news.bnb-lp.com> posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Are they saying that the Higgs could be between 114-160 GeV or > between 170-185 GeV? > Anyways, the LHC folks must feel like they're in the Olympics and > they have a broken leg. > Yousuf Khan > IMHO, the game is not over yet. It will be more interesting > if the Fermilab folks can rule out the existence of Higgs > range. This will force the theorist to look for a more > satisfactory mass generation mechanism for the zoo of > Does anyone know if we assume Higgs is some form of > what is the mass limit (if that make sense) posed by > current experimental results? I don't understand how the standard model makes any statement at all, > about the Higgs mass. When I studied the standard model, it was six > quarks, six leptons and the various resulting bosons that you get from > all the different pairings of all those twelve fermions. The fermions > are arranged onto a hexagon and the bosons onto a triangle. All that has nothing to do with Higgs, which seems to be some kind of an > add-on that they just forced in later, with a shoehorn. Or a crowbar. :P Higgs boson because it is the only known mass generating mechanism that works with the gauge symmetries ( which are essential to keep the theory renormalizable ). I'll be happy to know other more compelling reasons why Higgs boson should exist. === Subject: Re: New Lower Limit on Higgs Boson Mass > Other than more power, what's there at the LHC that isn't there at > Fermilab? If they've already narrowed it down to a range that > Fermilab can produce, then what more can LHC possibly bring to the > search? > Assuming that the Higgs is found at 185 gev, the higher energy at LHC > can produce more Higgs bosons faster, allowing them to tighten the > resolution of their measurement of its mass into a narrower band than > Tevatron can. Oh, I see, that makes some sense. > > If this Higgs is not found at 185 gev, then LHC can reach up to a > higher, ultimate energy than Tevatron, as they grope around, looking > for it. Well, aren't they saying they are 95% certain that it's below 185 > GeV? > Fermilab Provides More Constraints on the Elusive Higgs Boson: > Scientific American > Previous collider experiments had placed a lower bound of 114 giga- > the Higgs, and theoretical calculations require it to be less than 185 > GeV. This contradicts what that lady said on NPR. She said it would be *at* 185 gev, a HUGE difference. If the standard model only predicts that it be at or above 185 gev, then I feel no uncertainty in predicting that they're not going to find it there. That's just a lower bound, with the energy range above it being just as infinite as before they chopped off the lower part of the range. :P~ > The new Fermilab results, from its Tevatron collider, rule out a > Higgs mass between 160 and 170 GeV. (All of these constraints are at > the 95 percent confidence level, according to Fermilab.) tevatron Are they saying that the Higgs could be between 114-160 GeV or between > 170-185 GeV? Both. They skipped 114-160, because of their confidence in the standard model, which has been unbelieeeevably successful. If they can't find it at 185, 114-160 is the first place they'll look after that. === Subject: Re: New Lower Limit on Higgs Boson Mass > > Both. They skipped 114-160, because of their confidence in the standard > model, which has been unbelieeeevably successful. If they can't find it > at 185, 114-160 is the first place they'll look after that. No, that's not right, either. > The Standard Model supports both a Higgs at 170-185 or one at 114-160 > GeV. What's the next range of masses up beyond 185 GeV where a Higgs could possibly be, according to theory? > A Higgs at 183 GeV would decay into a pair of Z bosons, which would > have a very clean experimental signature and would stand out like a > sore thumb. A Higgs a between 170 and 180 GeV could in principle decay to a single > top quark and other stuff, which would be much harder to pick out but > still feasible. This is why DZero's single top quark measurement > announced a few days ago is of such interest. (This is the straw for > the needle in this case.) Ah okay, so I was wondering why they were so excited about finding a single Top quark, when they had already discovered double Top quarks in experiments previously. This is on the doorstep to Higgs. Funny how none Yousuf Khan === Subject: Re: New Lower Limit on Higgs Boson Mass <49bd4ddc$1@news.bnb-lp.com> posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > Both. They skipped 114-160, because of their confidence in the standard > model, which has been unbelieeeevably successful. If they can't find it > at 185, 114-160 is the first place they'll look after that. No, that's not right, either. > The Standard Model supports both a Higgs at 170-185 or one at 114-160 > GeV. > easier to identify. A Higgs at 183 GeV would decay into a pair of Z bosons, which would > have a very clean experimental signature and would stand out like a > sore thumb. A Higgs a between 170 and 180 GeV could in principle decay to a single > top quark and other stuff, which would be much harder to pick out but > still feasible. This is why DZero's single top quark measurement > announced a few days ago is of such interest. (This is the straw for > the needle in this case.) A Higgs below 140 GeV would decay predominantly into a pair of b > mesons, which would then be produced in copious quantities, but b > mesons are produced by the gazillions anyway. So you'd be talking > about an itty bitty signal bump on top of a giant background. The > equivalent would be like getting a report that someone just fell into > the ocean and needs help, and the way you are given to look for him is > the ripple from where he fell in. In this realm, the background at the > LHC is orders of magnitude worse than it is at Fermilab, where it's > still tough to deal with. PD The way you describe it, it sounds like we could have already seen the signature but have had it dumped as noise. === Subject: Re: New Lower Limit on Higgs Boson Mass <49bd4ddc$1@news.bnb-lp.com> posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > The way you describe it, it sounds like we could have already seen the > signature but have had it dumped as noise. Well, yes, of course. There are 300 trillion collisions in the dataset > already analyzed, and another 350 trillion in the dataset not yet > combed through. The Higgs cross-section, if there is a Higgs at all, > tells you how many Higgs bosons have been created and are sitting in > that pile somewhere. But the art is finding distinguishing footprints. For that you have to > choose a decay channel that provides a signature that is more easily > distinguishable, which means that you are choosing only a fraction of > the Higgs bosons that are created. (And the branching ratio of decays > to that channel strongly depends on the Higgs mass.) And even then, the signature is produced by a variety of processes > that happen way, way more frequently than Higgs boson production. But > in most of those cases, the background for that signature has a broad > and predictable spectrum for some kinematic variable (like > reconstructed mass, or missing transverse energy, or rapidity of > leading jets, or some such), while the Higgs signature should present > some excess or bump in a region of that spectrum. But of course, the > background doesn't have a completely smooth spectrum -- it also has > statistical fluctuations that look like bumps. So you do a > chemotherapy-in-reverse approach -- you cut the data some more with > some poison that kills both background and Higgs signal, but hopefully > kills the Higgs signal a little less, so that it stands out a little > more against the background. So, if they are there at all, there are Higgs bosons scattered > throughout the data. But most of them decay into channels that are > indistinguishable from other processes, or most of them have signature > kinematic variables that are spread out enough that they don't rise > above background, or the cuts you've applied to the data have killed > most of the Higgs. The good news is that you don't have to find all > the Higgs bosons in the data. You only need to find enough of them > that you can say with statistical confidence that there are more > events in this little bunch right here than can be accounted for by > background alone. In that little bunch, you won't even be able to say > which of those are background and which are Higgs bosons, because they > still look alike. But you'd be able to say that surely some of those > are Higgs bosons, and this is enough to declare discovery. Fun stuff. Really, really, really hard. PD ------------------ with that 'philosophy' you already found my and yous Mother in law in those experiments!! 2 suddenly the Higgs has mass ?? no more in shell out shell ??? stop fooling yourself and others and wasting your precious time (unless you dont mind stiing all your life and mumbling) Y.Porat ---------------------------- === Subject: Re: New Lower Limit on Higgs Boson Mass > Other than more power, what's there at the LHC that isn't there > at Fermilab? If they've already narrowed it down to a range that > Fermilab can produce, then what more can LHC possibly bring to > the search? > Assuming that the Higgs is found at 185 gev, the higher energy at > LHC can produce more Higgs bosons faster, allowing them to tighten > the resolution of their measurement of its mass into a narrower > band than Tevatron can. > Oh, I see, that makes some sense. > If this Higgs is not found at 185 gev, then LHC can reach up to a > higher, ultimate energy than Tevatron, as they grope around, > looking for it. > Well, aren't they saying they are 95% certain that it's below 185 > GeV? > Fermilab Provides More Constraints on the Elusive Higgs Boson: > Scientific American > Previous collider experiments had placed a lower bound of 114 > mass, on the Higgs, and theoretical calculations require it to be > less than 185 GeV. > This contradicts what that lady said on NPR. She said it would be > *at* 185 gev, a HUGE difference. Forgive me, but the lady at NPR doesn't know what she's talking about. With that attitude, you'll never get your PhD, Patrick. === Subject: Re: New Lower Limit on Higgs Boson Mass > Other than more power, what's there at the LHC that isn't > there at Fermilab? If they've already narrowed it down to a > range that Fermilab can produce, then what more can LHC > possibly bring to the search? > Assuming that the Higgs is found at 185 gev, the higher energy > at LHC can produce more Higgs bosons faster, allowing them to > tighten the resolution of their measurement of its mass into a > narrower band than Tevatron can. > Oh, I see, that makes some sense. > If this Higgs is not found at 185 gev, then LHC can reach up to > a higher, ultimate energy than Tevatron, as they grope around, > looking for it. > Well, aren't they saying they are 95% certain that it's below > 185 GeV? > Fermilab Provides More Constraints on the Elusive Higgs Boson: > Scientific American > Previous collider experiments had placed a lower bound of 114 > giga- electron volts (GeV), a measure that can be used for > require it to be less than 185 GeV. > This contradicts what that lady said on NPR. She said it would be > *at* 185 gev, a HUGE difference. > Forgive me, but the lady at NPR doesn't know what she's talking > about. > With that attitude, you'll never get your PhD, Patrick. Who's Patrick? And do I have to give the PhD back? Yes. What's the 'P' stand for? === Subject: Re: New Lower Limit on Higgs Boson Mass <49bd4ddc$1@news.bnb-lp.com> posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > Other than more power, what's there at the LHC that isn't there at > Fermilab? If they've already narrowed it down to a range that Fermilab > can produce, then what more can LHC possibly bring to the search? > Assuming that the Higgs is found at 185 gev, the higher energy at LHC > can produce more Higgs bosons faster, allowing them to tighten the > resolution of their measurement of its mass into a narrower band than > Tevatron can. > Oh, I see, that makes some sense. > If this Higgs is not found at 185 gev, then LHC can reach up to a > higher, ultimate energy than Tevatron, as they grope around, looking for > it. > Well, aren't they saying they are 95% certain that it's below 185 > GeV? > Fermilab Provides More Constraints on the Elusive Higgs Boson: > Scientific American > Previous collider experiments had placed a lower bound of 114 giga- > the Higgs, and theoretical calculations require it to be less than 185 > GeV. The new Fermilab results, from its Tevatron collider, rule out a > Higgs mass between 160 and 170 GeV. (All of these constraints are at > Are they saying that the Higgs could be between 114-160 GeV or between > 170-185 GeV? > Anyways, the LHC folks must feel like they're in the Olympics and they > have a broken leg. > Yousuf Khan ----------------- > not only the leg > the neck as well > a huge waist of human resources !! > and not less-- invaluable time as well Y.Porat > ------------------------------ Is there a particular reason you felt that you had to express your belief that science is a waste of time in your typical gibberish? === Subject: Re: New Lower Limit on Higgs Boson Mass <49bd4ddc$1@news.bnb-lp.com> posting-account=5GUrzQkAAADun29oaK3p_W_saUVxxHUF Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Other than more power, what's there at the LHC that isn't there at > Fermilab? If they've already narrowed it down to a range that Fermilab > can produce, then what more can LHC possibly bring to the search? > Assuming that the Higgs is found at 185 gev, the higher energy at LHC > can produce more Higgs bosons faster, allowing them to tighten the > resolution of their measurement of its mass into a narrower band than > Tevatron can. > Oh, I see, that makes some sense. > If this Higgs is not found at 185 gev, then LHC can reach up to a > higher, ultimate energy than Tevatron, as they grope around, looking for > it. > Well, aren't they saying they are 95% certain that it's below 185 > GeV? > Fermilab Provides More Constraints on the Elusive Higgs Boson: > Scientific American > Previous collider experiments had placed a lower bound of 114 giga- > the Higgs, and theoretical calculations require it to be less than 185 > GeV. The new Fermilab results, from its Tevatron collider, rule out a > Higgs mass between 160 and 170 GeV. (All of these constraints are at > Are they saying that the Higgs could be between 114-160 GeV or between > 170-185 GeV? > Anyways, the LHC folks must feel like they're in the Olympics and they > have a broken leg. > Yousuf Khan > ----------------- > not only the leg > the neck as well > a huge waist of human resources !! > and not less-- invaluable time as well > Y.Porat > ------------------------------ Is there a particular reason you felt that you had to express your > belief that science is a waste of time in your typical gibberish? ----------- -psychopath ---------------- === Subject: Re: New Lower Limit on Higgs Boson Mass reply-type=response Interesting post. collisions as well, and these also have mass. You may need a far more imply. === Subject: Re: New Lower Limit on Higgs Boson Mass > Interesting post. mass 180 GeV. Various conservation laws generally require other > its rest mass alone would imply. are precisely identical, to very many decimal places, and the scattering angle is precisely zero, to very many decimal places. Only when those two parameter fall precisely into a very tiny range do they get the event they're looking for. The rest of the time, they get a useless shower of junk, and they've had to develop some unbelievable computer algorithms to winnow out the garbage. In the seventies, they used to do that task by hand, but nowadays, that would never work. It's amazing that they can do it at all. :D~ === Subject: Re: New Lower Limit on Higgs Boson Mass <49bd4ddc$1@news.bnb-lp.com> <49bdf09d$0$3799$afc38c87@news.optusnet.com.au> posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 16, 2:24pm, Peter Webb > Interesting post. collisions as well, and these also have mass. You may need a far more > imply. and conservation law should not be an issue. In Standard mass, that means there is a lot of channel to create a Higgs bound to happen. === Subject: Marginal density of normal+beta random variable Suppose this error term in a regression: Z = X + Y where X is distributed as normal(0, sigma^2) and 0 < Y < 1 is distributed as beta(a, b). The zi can be estimated in each observation but xi and yi cannot be separated from each other. I need the marginal density f(z). I can find the joint density of Z and Y as f(z, y) = ((1 - y)^(b -1)*y^(a - 1)*Gamma[a + b])/(E^((y + z)^2/(2*Sigma^2))* (Sqrt[2*Pi]*Sigma*Gamma[a]*Gamma[b])) I cannot find a way to integrate out Y from f(z, y) to give me f(z). Can someone show me how to evaluate this integral so I can obtain a closed form result? Alternatively, is there another approach that will give me a closed form for f(z)? Richard CC: Stephen J. Herschkorn === Subject: Re: Marginal density of normal+beta random variable >Suppose this error term in a regression: >Z = X + Y >where X is distributed as normal(0, sigma^2) and 0 < Y < 1 is distributed as beta(a, b). The zi can be estimated in each observation but xi and yi cannot be separated from each other. I need the marginal density f(z). I can find the joint density of Z and Y as >f(z, y) = ((1 - y)^(b -1)*y^(a - 1)*Gamma[a + b])/(E^((y + z)^2/(2*Sigma^2))* > (Sqrt[2*Pi]*Sigma*Gamma[a]*Gamma[b])) I cannot find a way to integrate out Y from f(z, y) to give me f(z). Can someone show me how to evaluate this integral so I can obtain a closed form result? Alternatively, is there another approach that will give me a closed form for f(z)? > > I assume, as your formula indicates, that X and Y are independent. By convolution, the marginal density f for Z is f(z) = G(a+b)/[G(a)G(b) sqrt(2pi v)] integral(y=0..1, exp(-(z-y)^2 / (2v)) y^(a-1) (1-y)^(b-1)) where G is the gamma function and v is the variance sigma^2. You can write this as an expectation: f(z) = G(a+b)/[G(a)G(b)] E[(sigma W+z)^(a-1) (1 - (sigma W + z))^(b-1) 1_{-z/sigma posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) On Mar 13, 8:36am, Paul B. Andersen a violation of the laws of physics? > How can a sane person claim an experimentally proven fact of the sun revolving around the earth is a violation of the laws of physics? For starters, observation is not equal to experimental fact. That you directly observe stellar aberration does not mean it is an experimental fact. In tha same manner, that you directly observe the sun go around the earth does not mean it is an experimental fact. The larger mass of the sun precludes it from revolving around the earth. Similarly, the principle of relativity precludes that aberration be causable by earth motion but uncausable by star motion. But then I'm arguing with morons so this violation of the laws of physics is acceptable as long as their visual 'facts' are maintained. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=LxihSQoAAABzdzEeG7JudGr6Yl-Mh-CT InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > GP-B was experimental fact that proved relativity still has a square > peg kind of problem or two, of fitting into that round hole. ~ BG- Here is another experimental fact in line with paradox #2 above that relativity is indeed a square peg in the round hole of reality: http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Notice how the relativists choose to close their eyes and bite their lips while waiting for this storm to pass over... === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > GP-B was experimental fact that proved relativity still has a square > peg kind of problem or two, of fitting into that round hole. > ~ BG- Here is another experimental fact in line with paradox #2 above that > relativity is indeed a square peg in the round hole of reality: http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Notice how the relativists choose to close their eyes and bite their > lips while waiting for this storm to pass over... Are you trying to emulate Pencho Valev, David? === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > GP-B was experimental fact that proved relativity still has a square > peg kind of problem or two, of fitting into that round hole. > ~ BG- Here is another experimental fact in line with paradox #2 above that > relativity is indeed a square peg in the round hole of reality: http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 or the BB. How you YOU see it related to relativity David? Notice how the relativists choose to close their eyes and bite their > lips while waiting for this storm to pass over... === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=3CnWfgoAAADOSnwZZuOMJVm57N_DDT98 InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 The answer is simple. It disproves relativity. The measured quantum posted speed limit of light as promulgated by Einstein's relativity. Here is what the authors say: We conclude that with our measurement we can put an upper limit of 34as on a delta-t D in the nonadiabatic tunnelling regime with a gamma ranging from 1.45 to 1.17. Quantum mechanical simulation using time- dependent Schrodinger equation predict instantaneous ionization with no angular delay... The measured upper limit of the tunneling delay time is much shorter than the Buttiker-Landauer traversal time delta- t T which for present conditions is predicted to range between 450 and 560as... Our experimental results give a strong indication that there is no real tunnelling delay time and we expect that this conclusion will shed some light on the ongoing theoretical discussion on tunneling time. http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... For the intellectually challenged, that simply means... INSTANTANEOUS. For the Einstein groupee subset, that also means... FASTER THAN THE SPEED OF LIGHT. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 The answer is simple. It disproves relativity. The measured quantum posted speed limit of light as promulgated by Einstein's relativity. Here is what the authors say: We conclude that with our measurement we can put an upper limit of 34as on a delta-t_D in the nonadiabatic tunnelling regime with a gamma ranging from 1.45 to 1.17. Quantum mechanical simulation using time- dependent Schrodinger equation predict instantaneous ionization with no angular delay... The measured upper limit of the tunneling delay time is much shorter than the Buttiker-Landauer traversal time delta- t_T which for present conditions is predicted to range between 450 and 560as... Our experimental results give a strong indication that there is no real tunnelling delay time and we expect that this conclusion will shed some light on the ongoing theoretical discussion on tunneling time. http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... For the intellectually challenged, that simply means... INSTANTANEOUS. For the Einstein groupee subset, that also means... FASTER THAN THE SPEED OF LIGHT. Speed? Velocity? Space? Time? cccccccccccccccccccccccccccc | | | | | | | | | | | | | | | | | | | | | | | | | | | | vvvvvvvvvvvvvvvvvvvvvvvvvvvv ------------> c ---------------> <------------ c <--------------- {{-------> traveler --------->}} <------------ c <--------------- ------------> c ---------------> ^^^^^^^^^^^^^^^^^^^^^^^^ | | | | | | | | | | | | | | | | | | | | | | | | | | | ccccccccccccccccccccccccccc GLB === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 The answer is simple. It disproves relativity. The measured quantum > posted speed limit of light as promulgated by Einstein's relativity. I don't see how... Perhaps you might want to do some self-education concerning quantum tunneling. These should get you started... do follow up with the references. Quantum tunneling http://en.wikipedia.org/wiki/Quantum_tunneling http://en.wikipedia.org/wiki/Faster-than-light#Quantum_mechanics Does instantaneous quantum tunneling constitute a violation of special relativity? http://askville.amazon.com/instantaneous-quantum-tunneling-constitute-violat ion-special-relativity/AnswerViewer.do?requestId=3819593 === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole reply-type=response > http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 > The answer is simple. It disproves relativity. The measured quantum > posted speed limit of light as promulgated by Einstein's relativity. > I don't see how... Perhaps you might want to do some self-education concerning quantum > tunneling. These should get you started... do follow up with the > references. Quantum tunneling > http://en.wikipedia.org/wiki/Quantum_tunneling > http://en.wikipedia.org/wiki/Faster-than-light#Quantum_mechanics Does instantaneous quantum tunneling constitute a violation of special > relativity? http://askville.amazon.com/instantaneous-quantum-tunneling-constitute-violat i on-special-relativity/AnswerViewer.do?requestId=3819593 Who are you addressing? GLB === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >The answer is simple. It disproves relativity. The measured quantum >posted speed limit of light as promulgated by Einstein's relativity. >I don't see how... > Perhaps you might want to do some self-education concerning quantum > tunneling. These should get you started... do follow up with the references. > Quantum tunneling > http://en.wikipedia.org/wiki/Quantum_tunneling > http://en.wikipedia.org/wiki/Faster-than-light#Quantum_mechanics > Does instantaneous quantum tunneling constitute a violation of special relativity? >http://askville.amazon.com/instantaneous-quantum-tunneling-constitute... > What's quantum about real world objective measurements? ~ BG === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 The answer is simple. It disproves relativity. The measured quantum > posted speed limit of light as promulgated by Einstein's relativity. Here is what the authors say: > We conclude that with our measurement we can put an upper limit of > 34as on a delta-t_D in the nonadiabatic tunnelling regime with a gamma > ranging from 1.45 to 1.17. Quantum mechanical simulation using time- > dependent Schrodinger equation predict instantaneous ionization with > no angular delay... The measured upper limit of the tunneling delay > time is much shorter than the Buttiker-Landauer traversal time delta- > t_T which for present conditions is predicted to range between 450 and > 560as... Our experimental results give a strong indication that there > is no real tunnelling delay time and we expect that this conclusion > will shed some light on the ongoing theoretical discussion on > tunneling time. > http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... For the intellectually challenged, that simply means... > INSTANTANEOUS. For the Einstein groupee subset, that also means... > FASTER THAN THE SPEED OF LIGHT. is nothing to challenge relativity in it. You really need to study quantum mechanics. Well you need to study almost anything related to physics. Strich has another massive failure. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole > >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >The answer is simple. It disproves relativity. The measured quantum >posted speed limit of light as promulgated by Einstein's relativity. >Here is what the authors say: >We conclude that with our measurement we can put an upper limit of >34as on a delta-t_D in the nonadiabatic tunnelling regime with a gamma >ranging from 1.45 to 1.17. Quantum mechanical simulation using time- >dependent Schrodinger equation predict instantaneous ionization with >no angular delay... The measured upper limit of the tunneling delay >time is much shorter than the Buttiker-Landauer traversal time delta- >t_T which for present conditions is predicted to range between 450 and >560as... Our experimental results give a strong indication that there >is no real tunnelling delay time and we expect that this conclusion >will shed some light on the ongoing theoretical discussion on >tunneling time. >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... >For the intellectually challenged, that simply means... >INSTANTANEOUS. For the Einstein groupee subset, that also means... >FASTER THAN THE SPEED OF LIGHT. >is nothing to challenge relativity in it. You really need to study >quantum mechanics. Well you need to study almost anything related >to physics. Strich has another massive failure. > And your intellectual fart has meaning? If the coax, waveguide, fiber optic or whatever conduit exist, and the > tunneling is objectively capable of near INSTANTANEOUS throughput, > then where's the objective argument that it's not real? Read some quantum mechanics. You will not because you prefer ignorance. We are not responsible for your education. ~ BG === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >The answer is simple. It disproves relativity. The measured quantum >posted speed limit of light as promulgated by Einstein's relativity. >Here is what the authors say: >We conclude that with our measurement we can put an upper limit of >34as on a delta-t D in the nonadiabatic tunnelling regime with a gamma >ranging from 1.45 to 1.17. Quantum mechanical simulation using time- >dependent Schrodinger equation predict instantaneous ionization with >no angular delay... The measured upper limit of the tunneling delay >time is much shorter than the Buttiker-Landauer traversal time delta- >t T which for present conditions is predicted to range between 450 and >560as... Our experimental results give a strong indication that there >is no real tunnelling delay time and we expect that this conclusion >will shed some light on the ongoing theoretical discussion on >tunneling time. >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... >For the intellectually challenged, that simply means... >INSTANTANEOUS. For the Einstein groupee subset, that also means... >FASTER THAN THE SPEED OF LIGHT. >is nothing to challenge relativity in it. You really need to study >quantum mechanics. Well you need to study almost anything related >to physics. Strich has another massive failure. > And your intellectual fart has meaning? > If the coax, waveguide, fiber optic or whatever conduit exist, and the > tunneling is objectively capable of near INSTANTANEOUS throughput, > then where's the objective argument that it's not real? > Read some quantum mechanics. You will not because you prefer > ignorance. We are not responsible for your education. What's quantum about real world objective measurements? ~ BG You may wish to investigate all of 20th century physics, guthball. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 The answer is simple. It disproves relativity. The measured quantum > posted speed limit of light as promulgated by Einstein's relativity. I don't see how... Perhaps you might want to do some self-education concerning quantum tunneling. These should get you started... do follow up with the references. Quantum tunnelling http://en.wikipedia.org/wiki/Quantum_tunneling http://en.wikipedia.org/wiki/Faster-than-light#Quantum_mechanics Does instantaneous quantum tunneling constitute a violation of special relativity? http://askville.amazon.com/instantaneous-quantum-tunneling-constitute-violat ion-special-relativity/AnswerViewer.do?requestId=3819593 Here is what the authors say: > We conclude that with our measurement we can put an upper limit of > 34as on a delta-t_D in the nonadiabatic tunnelling regime with a gamma > ranging from 1.45 to 1.17. Quantum mechanical simulation using time- > dependent Schrodinger equation predict instantaneous ionization with > no angular delay... The measured upper limit of the tunneling delay > time is much shorter than the Buttiker-Landauer traversal time delta- > t_T which for present conditions is predicted to range between 450 and > 560as... Our experimental results give a strong indication that there > is no real tunnelling delay time and we expect that this conclusion > will shed some light on the ongoing theoretical discussion on > tunneling time. > http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... For the intellectually challenged, that simply means... > INSTANTANEOUS. For the Einstein groupee subset, that also means... > FASTER THAN THE SPEED OF LIGHT. === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole posting-account=7GQ4GwoAAABB4i_LSu__bqc3eTgaXgjV 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > The answer is simple. It disproves relativity. The measured quantum > posted speed limit of light as promulgated by Einstein's relativity. Here is what the authors say: > We conclude that with our measurement we can put an upper limit of > 34as on a delta-t D in the nonadiabatic tunnelling regime with a gamma > ranging from 1.45 to 1.17. Quantum mechanical simulation using time- > dependent Schrodinger equation predict instantaneous ionization with > no angular delay... The measured upper limit of the tunneling delay > time is much shorter than the Buttiker-Landauer traversal time delta- > t T which for present conditions is predicted to range between 450 and > 560as... Our experimental results give a strong indication that there > is no real tunnelling delay time and we expect that this conclusion > will shed some light on the ongoing theoretical discussion on > tunneling time.http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Let me requote that: ... There is NO REAL TUNNELING DELAY TIME ... For the intellectually challenged, that simply means... > INSTANTANEOUS. For the Einstein groupee subset, that also means... > FASTER THAN THE SPEED OF LIGHT. A simple concept which the establishment physics wishes to ignore. Of course, there are the usual cyborgs that have been programmed to spout their indifference to any righteous technology being black- budgeted, mainly because black might also refer to being not quite in the red, as most Bolsheviks prefer. Yet these are the things that deserve our respect and curiousity, esp. if respect and curiousity were not attributed to placing dice in the box of establishment physics for just another throw. The impression one must achieve IMO would have to correlate to how the human mind achieves imprinting, or memory - possibly in short term hops as FTL velocities are supposed to travel back in time[1]. American Time might be defined here as also meaning spacetime, esp. as it relates also to how phonons become radiated longitudinally === Subject: Re: R E L A T I V I T Y: Fitting a Square Peg into a Round Hole On Mar 13, 8:36 am, Paul B. Andersen a violation of the laws of physics? > How can a sane person claim an experimentally proven fact of the sun revolving around the earth is a violation of the laws of physics? For starters, observation is not equal to experimental fact. That you directly observe stellar aberration does not mean it is an experimental fact. In tha same manner, that you directly observe the sun go around the earth does not mean it is an experimental fact. The larger mass of the sun precludes it from revolving around the earth. Similarly, the principle of relativity precludes that aberration be causable by earth motion but uncausable by star motion. But then I'm arguing with morons so this violation of the laws of physics is acceptable as long as their visual 'facts' are maintained. Tusseladd hasn't been claiming he's sane again, has he? I suppose he has to, given there is so much room for doubt. === Subject: Re: WM lying as usual > Those numbers cannot be > named, used, thought of (as individuals). You name those numbers by saying those numbers. You use those numbers by falsely critizising them. You think of those numbers. You attach certain properties by saying numbers. They are distinguished by your very own wording. Therefore you bring them into existence and prove yourself wrong. Viele Gr.9f¤e Klaus === Subject: Re: WM lying as usual <7273thFo565gU1@mid.uni-berlin.de> posting-account=1EN5bAoAAACeeTnVeFpiUczw-ZOqTKWg Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Those numbers cannot be > named, used, thought of (as individuals). You name those numbers by saying those numbers. > You use those numbers by falsely critizising them. > You think of those numbers. You attach certain properties by saying numbers. > They are distinguished by your very own wording. Therefore you bring them into existence and prove yourself wrong. Viele Gr.9f¤e > Klaus Wooooooooow! I don't know the specifics of the debate going on between you and your friend but HOLD ON A MINUTE! Do you realize what you're saying? Since when naming something brings that thing into existence? o O A billion dollars. === Subject: Re: Factoring problem solved, remaining issues resolved Nntp-Posting-Host: hera.cwi.nl ... > Your rule was abs(r(v)) < D. Now you are changing that to abs(r(v)) < > D/2? With your method, that changes the results to: > > v exists for d in > {15,35,39,51,55,65,69,77,87,91,95,115,119,143,155,187,203,209,247,299,319 > ,391,403,493,527,551,589,713} > > v does NOT exist for d in > {21,33,57,85,93,133,145,161,217,221,253,323,341,377,437,667,899} > > Not only does it have to exist, I can figure it out quickly. If you do not know the factors of D? > For 21, the minimum r = (7+3)/2 = 5, but r(v) has to be multiplied > times the smaller factor, so a solution exists with: Ah, you need to know a factor of D before your algorithm factorises it. Great. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Factoring problem solved, remaining issues resolved Nntp-Posting-Host: hera.cwi.nl > ... > Your rule was abs(r(v)) < D. Now you are changing that to abs(r(v)) < > D/2? With your method, that changes the results to: > > v exists for d in > {15,35,39,51,55,65,69,77,87,91,95,115,119,143,155,187,203,209,247,299,319 > ,391,403,493,527,551,589,713} > > v does NOT exist for d in > {21,33,57,85,93,133,145,161,217,221,253,323,341,377,437,667,899} > > Not only does it have to exist, I can figure it out quickly. > > If you do not know the factors of D? > > For 21, the minimum r = (7+3)/2 = 5, but r(v) has to be multiplied > times the smaller factor, so a solution exists with: > > Ah, you need to know a factor of D before your algorithm factorises it. > Great. > > It's not even that good. Ah, you misunderstand James. He changed the algorithm again. Find some r(v), next multiply it with a factor of D and that r will factorise D. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Factoring problem solved, remaining issues resolved sha1:as2s0hVLmDIM+hAtRSPqij/bMcE= > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). As a noun. As a verb, the only people I hear it from are the less > educated and darker skinned. No matter who you hear it from, it has been used *as a verb* since the early 1600s. Frankly, this fact surprised me when I learned it. In any case, your correction was both racist and butt-wrong. -- Meaningless movies on the screen behind the band that's blowing Waterboys, throwing shapes My Love is My Rock Half of the music is on tape in the Weary Land === Subject: Re: Factoring problem solved, remaining issues resolved > > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are the less > educated and darker skinned. No matter who you hear it from, it has been used *as a verb* since the > early 1600s. Frankly, this fact surprised me when I learned it. In any case, your > correction was both racist and butt-wrong. I never said it wasn't a verb since any point in time just that it is most commonly used by A-A, those that are less educated and those who are darker skinned. The same people who have comprehension issues as you do and run around shouting *RACIST* whenever those words appear in the same sentence. Clue 2: The dumb whiggers and near illiterate Caucasians who can't comprehend with linearity, I, for one, am troubling myself with comprehending which class you fall into. I'm betting whigger. -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: Factoring problem solved, remaining issues resolved <87mybl3d8w.fsf@phiwumbda.org> posting-account=WttvjgoAAABWTM7Oa0VLZ7n9CawA1j15 Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are the less > educated and darker skinned. > No matter who you hear it from, it has been used *as a verb* since the > early 1600s. > Frankly, this fact surprised me when I learned it. In any case, your > correction was both racist and butt-wrong. I never said it wasn't a verb since any point in time just that it is > most commonly used by A-A, those that are less educated and those who > are darker skinned. The same people who have comprehension issues as you do and run around > shouting *RACIST* whenever those words appear in the same sentence. Clue 2: The dumb whiggers and near illiterate Caucasians who can't > comprehend with linearity, I, for one, am troubling myself with > comprehending which class you fall into. I'm betting whigger. Wow! You really put the kkk in netkkkop! === Subject: Re: Factoring problem solved, remaining issues resolved sha1:BxNX4sJV4Vp2NcBcNRWRbFZ1E/M= > > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are the less > educated and darker skinned. No matter who you hear it from, it has been used *as a verb* since the > early 1600s. Frankly, this fact surprised me when I learned it. In any case, your > correction was both racist and butt-wrong. I never said it wasn't a verb since any point in time just that it is > most commonly used by A-A, those that are less educated and those who > are darker skinned. Oh. How odd that I misinterpreted the following statement: > Clue: This is not a word in a classical sense unless you are a > way kewl African-American Sure looks to me like you were claiming that disrespected is not a word, aside from African-American slang. But you say you meant no such thing, so surely I'm mistaken. > The same people who have comprehension issues as you do and run around > shouting *RACIST* whenever those words appear in the same sentence. Clue 2: The dumb whiggers and near illiterate Caucasians who can't > comprehend with linearity, I, for one, am troubling myself with > comprehending which class you fall into. I'm betting whigger. You sure have a funny way of avoiding claims of racism. -- Jesse F. Hughes I often told you of the dangers of hubris, and most importantly of all, I TOLD you that I wanted to change the institution of mathematics worldwide. -- James Harris, on the evils of pride === Subject: Re: Factoring problem solved, remaining issues resolved > No, most of the time integer r(v) < D has gcd(r(v),D) = 1 or D - which > is useless. Plenty of counterexamples to your unsupported assertion Uhm...if r(v) < D, I don't think gcd(r(v),D) is going to ever be D. :-) Yes, thank you. Sloppy editing on my part, as I was just restating the definition of trivial factorization. Now, of course, he insists on r(v) < D/2 which gives even more counterexamples to his claims. No doubt he'll add some new variable, change the conditions, and claim that's what he meant all along. Again. (And *still* he doesn't give an algorithm for finding v) - Tim === Subject: Re: Factoring problem solved, remaining issues resolved > On Mar 14, 8:24pm, russell kym horsell factoring problem by using Pell's Equation and posters have argued > with me. Well it turns out they were arguing over details of > implementation, and ignoring the proof. > ... > If you insist on cross-posting to sci.physics then you can shut up your > detractors there by simply writing a program and demonstrating with a clock that > it does general (or even Mersenne) factoring faster than published methods. > Even factoring a few numbers on the various to do lists on the 'net would > be something (even if you couldn't demon they were done quickly). Implementation is not necessarily trivial even with theory. But mathematical proof is supposed to be good enough. Note all the noise recently about quantum computing. It has managed to, what? Factor 15. No rules there about needing to be faster than published methods. Part of my point is that the current academic system is broken. Even physics people should care if the factoring problem is solved as > you're in the same world as everyone else. And you know enough math to understand the solution, so you doing > nothing is a big point. I want it clear that multiple communities failed here. with things in this area, to the computer science people who > supposedly are experts in this area, to math people, and yes physics > people. The point is, you all failed. I'm posting here not to convince you of anything but to give you a > chance, so as you fail, later when I say the academic world is broken > and we have to destroy tenure and we have to shred funding across the > board to force a survival of the fittest and you whine about it and > claim it will ruin scientific development, I'll point back to this > case. And your money will be taken away. I want you all to start working for a living again, versus living on > what I call white-collar welfare. You need to be right, to earn a living as an academic. And you need > to be aware. What can we do to avert this state of affairs? -- Michael Press === Subject: Re: Factoring problem solved, remaining issues resolved > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are [racism > deleted] FOAD. I see, Less educated and darker skinned, one not necessarily intrinsically linked to the other, is racist. Racism is defined as determining that a particular (in)capability is due entirely to race. I indicated no lack of capability in the use of the word. The word disrespect, ime, is used by A-As in slang. This thread has shown no A-A slang persuasion. With your post, you have accomplished to interject the first hint of idiocy. I hope others, other idiots, willnot be persuaded to follow your lead. Only time will tell. -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: Factoring problem solved, remaining issues resolved posting-account=WttvjgoAAABWTM7Oa0VLZ7n9CawA1j15 Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are [racism > deleted] > FOAD. [numerous vicious insults deleted] No, you're the stupid one. (And before you, JSH was the first to inject idiocy into this thread, right back when he started it!) None of the nasty things that you have said or implied about me are at all true. === Subject: Re: Factoring problem solved, remaining issues resolved > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are [racism > deleted] > FOAD. > [numerous vicious insults reinstated] > I see, Less educated and darker skinned, one not necessarily > intrinsically linked to the other, is racist. > Racism is defined as determining that a particular (in)capability is due > entirely to race. I indicated no lack of capability in the use of the > word. The word disrespect, ime, is used by A-As in slang. This thread > has shown no A-A slang persuasion. > With your post, you have accomplished to interject the first hint of > idiocy. > I hope others, other idiots, will not be persuaded to follow your lead. > Only time will tell. > No, you're the stupid one. (And before you, JSH was the first to > inject idiocy into this thread, right back when he started it!) None of the nasty things that you have said or implied about me are at > all true. ______________ / | WHAAAAAAAAAAA! | __ _________/ / ,' _.~._ /,' ,~'.~@~.`~. / : _..._ : { :,''`.: } `C) 0 _ 0 (--.._,--.__ ( ) @ ( ) `. `-.-_-.-' ,' / ,` ;`-._,-. ,' ,'/ ,' `---t.,-. _ ,--.,',' ,'----.__ _( ----' '///,`,--.,' `-.__.--' `. ) '///,' `-` === Subject: Re: Factoring problem solved, remaining issues resolved posting-account=WttvjgoAAABWTM7Oa0VLZ7n9CawA1j15 Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Decker disrespects > Clue: This is not a word in a classical sense unless you are a way kewl > African-American > You should really check a dictionary before making statements like that. > (Hint: disrespect has been used at least as far back as the early > 1600's, in the highest levels of literary and academic writing). > As a noun. As a verb, the only people I hear it from are [racism > deleted] > FOAD. > [numerous vicious insults reinstated] > [misquotes and viciously insults me] Do not misquote me again. Your post contained supposed quoted material that did not occur in the post that you followed up to nor summarize material that did. That is incorrect. Stop being dishonest. You're the stupid one. None of the nasty things that you have said or implied about me are at all true. > No, you're the stupid one. (And before you, JSH was the first to > inject idiocy into this thread, right back when he started it!) > None of the nasty things that you have said or implied about me are at > all true. [implied serious insult deleted] No, you're the infant. None of the nasty things that you have said or implied about me are at all true. === Subject: Re: A Note on the Collatz Conjecture I've got an explanation for the trivial and not-so-trival loops (in the framework of a unified 3n+c approach) for the known loops for c=1, -1, and 5 (at least the ones I've heard about) at the 3n+c website http://home.graysoncable.com/dkcox. === Jerusalem. According to the Hebrew Bible, my date of birth can be calculated. I am a hero. I will tell you what is Armageddon. I think that Chinese people like dogs. I will take the yellow people and the black people into concentration camps. When you see me, I will make you feel Speechless. I will take Barack Obama and Condoleezza Rice into concentration camps, I think that the black people and Latino like dogs. posting-account=u8iZFQoAAAAKeUjG5DiutDtd9i25ADp3 Presto/2.1.1,gzip(gfe),gzip(gfe) All English can see what is happening to China, China has been become a democracy. The Chinese government meetings are already televised live. For explem: Each Cantonese can make a telephone call to talk with the Cantonese senior officials, it is televised live. http://www.gdhotline.net/ Isaac Newton Since 25th December, 2008 === Subject: Stepping By Divisors -- Grid Game posting-account=dGiPYgkAAABSJ3xUlNLViQdT0h489hR6 AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) Here is a game for any plural number of players. Start with an m-by-m grid drawn on paper. (I suggest that m be about 8 to 10 for beginners.) Draw the grid large enough so that two integers can be written in each square. In the first phase of the game, players take turns writing the positive integers 1 to m^2 in order into the squares of the grid. One number is placed in any empty square of the grid on each move. (So, if Let the variable d (d for 'divisor') start the second phase of the game with a value of 1. value of d, which is 1, alongside any number in the grid (in the same square as the number). The players thereafter continue to take turns. On a move, a player chooses any square of the grid that has not yet had a second number written in it, but is adjacent to (in the direction of above, below, right of, or left of) any square that has had a second number written in it. divisor of the number in that square. The variable d then becomes that divisor. * The value of d, however, must change each move. The same divisor number cannot be written in two squares on two consecutive moves. The absolute value of the difference between the older recent value of d (the divisor written by the previous player to move) and the new value of d (the divisor written by the current player moving) is then added to the currently moving player's score. Note: The goal of the game is to get the LOWEST score. So, it is advantageous to change the value of d by as little as possible on a move. (Changing the value of d by 1 is the best a player can hope for on a move.) The game continues until each square has exactly two numbers in it. (So, there are a total of m^2 moves in the first phase of the game, and m^2 moves in the second phase of the game.) As I said before, the player with the lowest score wins. I would suggest that the divisor numbers (the values of d) be written smaller than the numbers written during phase 1 of the game, or be written in another color than the first numbers placed in the squares. Leroy Quet === Subject: Re: Stepping By Divisors -- Grid Game posting-account=dGiPYgkAAABSJ3xUlNLViQdT0h489hR6 AppleWebKit/523.10.3 (KHTML, like Gecko) Version/3.0.4 Safari/523.10,gzip(gfe),gzip(gfe) > Here is a game for any plural number of players. Start with an m-by-m > grid drawn on paper. (I suggest that m be about 8 to 10 for > beginners.) Draw the grid large enough so that two integers can be > written in each square. In the first phase of the game, players take turns writing the > positive integers 1 to m^2 in order into the squares of the grid. One > number is placed in any empty square of the grid on each move. (So, if Let the variable d (d for 'divisor') start the second phase of the > game with a value of 1. value of d, which is 1, alongside any number in the grid (in the same > square as the number). The players thereafter continue to take turns. On a move, a player > chooses any square of the grid that has not yet had a second number > written in it, but is adjacent to (in the direction of above, below, > right of, or left of) any square that has had a second number written > in it. > divisor of the number in that square. > The variable d then becomes that divisor. > * The value of d, however, must change each move. The same divisor > number cannot be written in two squares on two consecutive moves. The absolute value of the difference between the older recent value of > d (the divisor written by the previous player to move) and the new > value of d (the divisor written by the current player moving) is then > added to the currently moving player's score. > Note: The goal of the game is to get the LOWEST score. So, it is > advantageous to change the value of d by as little as possible on a > move. (Changing the value of d by 1 is the best a player can hope for > on a move.) The game continues until each square has exactly two numbers in it. > (So, there are a total of m^2 moves in the first phase of the game, > and m^2 moves in the second phase of the game.) As I said before, the player with the lowest score wins. I would suggest that the divisor numbers (the values of d) be written > smaller than the numbers written during phase 1 of the game, or be > written in another color than the first numbers placed in the squares. Leroy Quet The only problem I can see with this game is if the last square to get a second number has a 1 in it, and the previous (next to last) player to move placed a 1 as the second (divisor) number in some square. (This is a problem because d must change each move.) Then, in that case, the second phase of the game ends after m^2 - 1 moves. Leroy Quet === Subject: Coogi,BAPE and BBC Apparels - discount posting-account=BvWCTgoAAADXCKMX13d90pQ-zMEuLX4s Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; Embedded Web Browser from: http://bsalsa.com/),gzip(gfe),gzip(gfe) Want to buy cheap and high quality Coogi,BAPE and BBC Apparels,please view our store (www.luxury-fashion.org) Our goods are the fine quality. You can check them here: http://www.luxury-fashion.org/static/Apparels/Coogi.html http://www.luxury-fashion.org/static/Apparels/BBC.html http://www.luxury-fashion.org/static/Apparels/Bape.html Welcome check our site and feel free contact us. Believe You can find what do you want here! === Subject: Basic calculus problem - is this approach correct? posting-account=hlsuLgoAAABdRR1Wo-FQwG-MHXfO4_GV 1.1.4322),gzip(gfe),gzip(gfe) I'm self teaching and working on the following question: The curve y = ax^2 + bx + c crosses the y-axis at the point (0,3) and has a stationary point at (1,2). Find the values of a, b and c. I can find that c = 3 easily. That's revealed by the point (0,3). a and b are causing me difficulty though. My text has taught me that the derivitive function will equal zero at a stationary point. Therefore: 2ax + b = 0 at the stationary point. I know x = 1 at one of the stationary points. Therefore 2a(1) + b = 0 and therefore b = -2a. I want to know if the following step is valid or not: plugging b = -2a into the original equation for when x = 1 to get a as follows: 2 = a(1)^2 - 2a(1) + 3 ---> a = 1. and then finding b using: 2 = -1(1)^2 + b(1) + 3 ---> b = -2 To rephrase my question, does the relationship b = -2a found in the derivative function also apply to the original function? Peter Barker === Subject: Re: Basic calculus problem - is this approach correct? I'm self teaching and working on the following question: The curve y = ax^2 + bx + c crosses the y-axis at the point (0,3) and >has a stationary point at (1,2). Find the values of a, b and c. I can find that c = 3 easily. That's revealed by the point (0,3). a and b are causing me difficulty though. My text has taught me that >the derivitive function will equal zero at a stationary point. >Therefore: 2ax + b = 0 at the stationary point. I know x = 1 at one of the >stationary points. Therefore 2a(1) + b = 0 and therefore b = -2a. I want to know if the following step is valid or not: plugging b = -2a >into the original equation for when x = 1 to get a as follows: 2 = a(1)^2 - 2a(1) + 3 ---> a = 1. and then finding b using: 2 = -1(1)^2 + b(1) + 3 ---> b = -2 The -1 above should be 1. But to find b, instead of substituting a = 1, c = 3, x = 1, y = 2 in the quadratic y = ax^2 + bx + c, you can just substitute a = 1 in the equation b = -2a. >To rephrase my question, does the relationship b = -2a found in the >derivative function also apply to the original function? Let's look at the problem again ... Using the given information (0,3) on the curve => f(0) = 3 => c = 3 (1,2) on the curve => f(1) = 2 => a + b + c = 2 (1,2) stationary => f'(1) = 0 => 2a + b = 0 Thus, you have 3 equations c = 3 a + b + c = 0 2a + b = 0 relating the 3 unknowns a,b,c. But once you solve -- that it -- they're no longer unknown. quasi === Subject: Re: Basic calculus problem - is this approach correct? >I'm self teaching and working on the following question: >The curve y = ax^2 + bx + c crosses the y-axis at the point (0,3) and >has a stationary point at (1,2). Find the values of a, b and c. >I can find that c = 3 easily. That's revealed by the point (0,3). >a and b are causing me difficulty though. My text has taught me that >the derivitive function will equal zero at a stationary point. >Therefore: >2ax + b = 0 at the stationary point. I know x = 1 at one of the >stationary points. Therefore 2a(1) + b = 0 and therefore b = -2a. >I want to know if the following step is valid or not: plugging b = -2a >into the original equation for when x = 1 to get a as follows: >2 = a(1)^2 - 2a(1) + 3 ---> a = 1. >and then finding b using: >2 = -1(1)^2 + b(1) + 3 ---> b = -2 The -1 above should be 1. But to find b, instead of substituting a = 1, c = 3, x = 1, y = 2 in >the quadratic y = ax^2 + bx + c, you can just substitute a = 1 in the >equation b = -2a. >To rephrase my question, does the relationship b = -2a found in the >derivative function also apply to the original function? Let's look at the problem again ... Using the given information (0,3) on the curve => f(0) = 3 => c = 3 (1,2) on the curve => f(1) = 2 => a + b + c = 2 (1,2) stationary => f'(1) = 0 => 2a + b = 0 Thus, you have 3 equations c = 3 a + b + c = 0 2a + b = 0 relating the 3 unknowns a,b,c. But once you solve -- that it -- they're no longer unknown. Let me highlight one thing ... For this problem, a,b,c represent unknown _constants_. quasi === Subject: Re: Basic calculus problem - is this approach correct? posting-account=hlsuLgoAAABdRR1Wo-FQwG-MHXfO4_GV 1.1.4322),gzip(gfe),gzip(gfe) > Let me highlight one thing ... For this problem, a,b,c represent unknown _constants_. quasi The bit about constants really helped. Obvious in hindsight but when learning this stuff there's so much to take in and it gets a bit bewildering. My mind was thinking about when you've got a derivative, then the relationship between all the variables changes. It's like you're working in another system. I was just a bit muddled about the whole thing and can now see more clearly. Amazed and excited at the power of calculus and I know I've only scratched the surface. Watch this space for more questions! Pete === Subject: Re: Basic calculus problem - is this approach correct? posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; GTB5; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) I'm self teaching and working on the following question: The curve y = ax^2 + bx + c crosses the y-axis at the point (0,3) and > has a stationary point at (1,2). Find the values of a, b and c. I can find that c = 3 easily. That's revealed by the point (0,3). a and b are causing me difficulty though. My text has taught me that > the derivitive function will equal zero at a stationary point. > Therefore: 2ax + b = 0 at the stationary point. I know x = 1 at one of the > stationary points. Therefore 2a(1) + b = 0 and therefore b = -2a. I want to know if the following step is valid or not: plugging b = -2a > into the original equation for when x = 1 to get a as follows: 2 = a(1)^2 - 2a(1) + 3 ---> a = 1. and then finding b using: 2 = -1(1)^2 + b(1) + 3 ---> b = -2 To rephrase my question, does the relationship b = -2a found in the > derivative function also apply to the original function? Your function y = ax^2 + bx + c satisfies three conditions: y(0) = 3 y(1) = 2 y'(1) = 0 You have written these three conditions in terms of a, b, and c: c = 3 a + b + c = 2 2a + b = 0 The conditions are on a, b, and c, not on the function or its derivative, so your question doesn't make much sense. You then solve the three equations to get a = 1, b = -2, and c = 3, and substitute these values into y = ax^2 + bx + c, giving y = x^2 - 2x + 3. Dave === Subject: Re: Basic calculus problem - is this approach correct? posting-account=hlsuLgoAAABdRR1Wo-FQwG-MHXfO4_GV 1.1.4322),gzip(gfe),gzip(gfe) > Your function y = ax^2 + bx + c satisfies three conditions: > y(0) = 3 > y(1) = 2 > y'(1) = 0 You have written these three conditions in terms of a, b, and c: > c = 3 > a + b + c = 2 > 2a + b = 0 The conditions are on a, b, and c, not on the function or its > derivative, so your question doesn't make much sense. You then solve > the three equations to get a = 1, b = -2, and c = 3, and substitute > these values into y = ax^2 + bx + c, giving y = x^2 - 2x + 3. Dave- Hide quoted text - Dave, function and its derivative. Pete === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > Withough advanced math, airplanes wouldn't fly and > computers wouldn't connect you to the Usenet. > That's an argument in favor of banning math, huh? > This is America, you can practice any religion you want... > Any sufficiently advanced science is indistinguishable from > magic. Algebra is so advanced for you that it appears to > be a superstition. > To him, tying one's shoes appears to be magic. > Tying a knot is a mathematical operation. > Operating a light switch is an excercies in binary math. > Obviously beyond him. > Is that the probem I was having the other night? I was at this > girl's house, and the police shows up, and tasred your ass, and you're posting from your cell. Right? -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Starmaker is my bitch forever! Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > .17 .10 2: > Gutless Umbrella Carrying Sissy > 0: > Jesus forgives sinners, not criminals. > If > S = the set of all sinners, > and > C = the set of all criminals, > and > A = the intersection operator, > and > S A C != an Air Force base under Cheyenne > Mountain, > then > S A C = C; > Quantum Electro-Dynamics (QED). ;D > Mathematics does not and cannot explain > people, or where people come from. > Mathematics is just a religious Bible > upgraded for the information > age. > Every DNA codon contains two bits of > information and two more redundancy bits for > error correction. > And we *still* get defectives like Starmaker. > When I look at the percentage of people who have > a grasp of higher math to those who don't, > then...those with the grasp of higher math *are* > the defectives ones, because their numbers are > way smaller. You're a mistake. You're the > defective one, don't you get it? > Like everything else, people are distributed along > a bell curve, which is symmetrical, making the > number and distribution of the borderline retarded > people identical to the number and distribution of > high overachiers. > Bees, flowers, cats and fishes don't know math > and they seem to get along fine without it. And > most people on the planet get along without > it...it's just you guys in the sci.math class > that are spinning around in circles... > Withough advanced math, airplanes wouldn't fly and > computers wouldn't connect you to the Usenet. > What does a bee need an airplane for? > What does the world need you for? Nothing. In fact, > you're much like a tumor, and should be cut out or > dosed with radiation. > -- > Terry Austin > Terry Austin: like the polio vaccine, only with more > asshole. > -- David Bilek > You're really *into* medicine, aren't you? You know, if > you re-arrange your name Terry Austin, you get -- > Urinary Test. > And yours becomes retarded troll. Oh, what, that's not > rearranging your name, that *is* your name. > That is what I mean about 'limited intelligence'... > It's good that you know your own limitations. In fact, it's > accomplishment that you know your own name. > Actually, I don't even know my own name. I believe you. You are that stupid. And, you're my bitch. > That's a first, a sissy calling me a bitch! Is Terry a girls name? Anybody with a name like Terry, and a handle name Sissy--I > suspect is a girlish person. You know, those people they call > gay. Those people are gay because of a genetic defect... Is > that you, ...gay? > Gee, I haven't heard that insult before. Well, not since the third grade, at any rate. You masturbate a lot, don't you? And by a lot, I mean, well, pretty much constantly. Cuz you've never been allowed to touch an actual gurl, ever, with with Mummy's credit card, have you? -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > 115 .17 .10 2: > The Starmaker Gutless Umbrella Carrying Sissy > 6.5 0: > Jesus forgives sinners, not criminals. > If > S = the set of all sinners, > and > C = the set of all criminals, > and > A = the intersection operator, > and > S A C != an Air Force base under Cheyenne > Mountain, > then > S A C = C; > Quantum Electro-Dynamics (QED). ;D > Mathematics does not and cannot explain > people, or where people come from. > Mathematics is just a religious Bible > upgraded for the information > age. > Every DNA codon contains two bits of > information and two more redundancy bits > for error correction. > And we *still* get defectives like Starmaker. > When I look at the percentage of people who > have a grasp of higher math to those who > don't, then...those with the grasp of higher > math *are* the defectives ones, because their > numbers are way smaller. You're a mistake. > You're the defective one, don't you get it? > Like everything else, people are distributed > along a bell curve, which is symmetrical, making > the number and distribution of the borderline > retarded people identical to the number and > distribution of high overachiers. > Bees, flowers, cats and fishes don't know math > and they seem to get along fine without it. > And most people on the planet get along > without it...it's just you guys in the > sci.math class that are spinning around in > circles... > Withough advanced math, airplanes wouldn't fly > and computers wouldn't connect you to the > Usenet. > What does a bee need an airplane for? > What does the world need you for? Nothing. In fact, > you're much like a tumor, and should be cut out or > dosed with radiation. > -- > Terry Austin > Terry Austin: like the polio vaccine, only with > more asshole. > -- David Bilek > You're really *into* medicine, aren't you? You know, > if you re-arrange your name Terry Austin, you get -- > Urinary Test. > And yours becomes retarded troll. Oh, what, that's > not rearranging your name, that *is* your name. > That is what I mean about 'limited intelligence'... > It's good that you know your own limitations. In fact, > it's accomplishment that you know your own name. > Actually, I don't even know my own name. > I believe you. You are that stupid. > And, you're my bitch. > That's a first, a sissy calling me a bitch! > Is Terry a girls name? > Anybody with a name like Terry, and a handle name Sissy--I > suspect is a girlish person. You know, those people they call > gay. Those people are gay because of a genetic defect... Is > that you, ...gay? > Gee, I haven't heard that insult before. Well, not since the > third grade, at any rate. I'm sorry, I wasn't trying to be insulting.. Bad liar. You're not even trying. But then, you *are* that retarded. -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > 115 .17 .10 2: > The Starmaker Gutless Umbrella Carrying Sissy > 6.5 0: > Jesus forgives sinners, not criminals. > If > S = the set of all sinners, > and > C = the set of all criminals, > and > A = the intersection operator, > and > S A C != an Air Force base under Cheyenne > Mountain, > then > S A C = C; > Quantum Electro-Dynamics (QED). ;D > Mathematics does not and cannot explain > people, or where people come from. > Mathematics is just a religious Bible > upgraded for the information > age. > Every DNA codon contains two bits of > information and two more redundancy bits > for error correction. > And we *still* get defectives like Starmaker. > When I look at the percentage of people who > have a grasp of higher math to those who > don't, then...those with the grasp of higher > math *are* the defectives ones, because their > numbers are way smaller. You're a mistake. > You're the defective one, don't you get it? > Like everything else, people are distributed > along a bell curve, which is symmetrical, making > the number and distribution of the borderline > retarded people identical to the number and > distribution of high overachiers. > Bees, flowers, cats and fishes don't know math > and they seem to get along fine without it. > And most people on the planet get along > without it...it's just you guys in the > sci.math class that are spinning around in > circles... > Withough advanced math, airplanes wouldn't fly > and computers wouldn't connect you to the > Usenet. > What does a bee need an airplane for? > What does the world need you for? Nothing. In fact, > you're much like a tumor, and should be cut out or > dosed with radiation. > -- > Terry Austin > Terry Austin: like the polio vaccine, only with > more asshole. > -- David Bilek > You're really *into* medicine, aren't you? You know, > if you re-arrange your name Terry Austin, you get -- > Urinary Test. > And yours becomes retarded troll. Oh, what, that's > not rearranging your name, that *is* your name. > That is what I mean about 'limited intelligence'... > It's good that you know your own limitations. In fact, > it's accomplishment that you know your own name. > Actually, I don't even know my own name. > I believe you. You are that stupid. > And, you're my bitch. > That's a first, a sissy calling me a bitch! > Is Terry a girls name? > Anybody with a name like Terry, and a handle name Sissy--I > suspect is a girlish person. You know, those people they call > gay. Those people are gay because of a genetic defect... Is > that you, ...gay? > Gee, I haven't heard that insult before. Well, not since the > third grade, at any rate. > I'm sorry, I wasn't trying to be insulting.. Bad liar. You're not even trying. But then, you *are* that retarded. Do you believe intelligent life exist on Earth? Not in your house, Prof. Math-Is-A-Lie. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > 207. > 115 .17 .10 2: > The Starmaker Gutless Umbrella Carrying Sissy 69.16.18 > 6.5 0: > Jesus forgives sinners, not criminals. > If > S = the set of all sinners, > and > C = the set of all criminals, > and > A = the intersection operator, > and > S A C != an Air Force base under Cheyenne > Mountain, > then > S A C = C; > Quantum Electro-Dynamics (QED). ;D > Mathematics does not and cannot explain > people, or where people come from. > Mathematics is just a religious Bible > upgraded for the information > age. > Every DNA codon contains two bits of > information and two more redundancy bits > for error correction. > And we *still* get defectives like Starmaker. > When I look at the percentage of people who > have a grasp of higher math to those who > don't, then...those with the grasp of higher > math *are* the defectives ones, because their > numbers are way smaller. You're a mistake. > You're the defective one, don't you get it? > Like everything else, people are distributed > along a bell curve, which is symmetrical, making > the number and distribution of the borderline > retarded people identical to the number and > distribution of high overachiers. > Bees, flowers, cats and fishes don't know math > and they seem to get along fine without it. > And most people on the planet get along > without it...it's just you guys in the > sci.math class that are spinning around in > circles... > Withough advanced math, airplanes wouldn't fly > and computers wouldn't connect you to the > Usenet. > What does a bee need an airplane for? > What does the world need you for? Nothing. In fact, > you're much like a tumor, and should be cut out or > dosed with radiation. > -- > Terry Austin > Terry Austin: like the polio vaccine, only with > more asshole. > -- David Bilek > You're really *into* medicine, aren't you? You know, > if you re-arrange your name Terry Austin, you get -- > Urinary Test. > And yours becomes retarded troll. Oh, what, that's > not rearranging your name, that *is* your name. > That is what I mean about 'limited intelligence'... > It's good that you know your own limitations. In fact, > it's accomplishment that you know your own name. > Actually, I don't even know my own name. > I believe you. You are that stupid. > And, you're my bitch. > That's a first, a sissy calling me a bitch! > Is Terry a girls name? > Anybody with a name like Terry, and a handle name Sissy--I > suspect is a girlish person. You know, those people they call > gay. Those people are gay because of a genetic defect... Is > that you, ...gay? > Gee, I haven't heard that insult before. Well, not since the > third grade, at any rate. > I'm sorry, I wasn't trying to be insulting.. > Bad liar. You're not even trying. > But then, you *are* that retarded. > Do you believe intelligent life exist on Earth? Not in your house, Oh, you mean next door maybe? Or maybe down the block?? Around the > corner??? > > Prof. Math-Is-A-Lie. I *never* said math is a lie, I said it's an invention by man... You never said Math is an invention by man. You said Mathematics is just a religious Bible upgraded for the information age. Make up your mind. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > > The Starmaker The Starmaker in > ak@ > 207. > 115 .17 .10 2: > The Starmaker > > Gutless Umbrella Carrying Sissy > 69.16.18 > 6.5 0: > Jesus forgives sinners, not > criminals. > If > S = the set of all sinners, > and > C = the set of all criminals, > and > A = the intersection operator, > and > S A C != an Air Force base under > Cheyenne > Mountain, > then > S A C = C; > Quantum Electro-Dynamics (QED). > ;D > Mathematics does not and cannot > explain > people, or where people come from. > Mathematics is just a religious > Bible > upgraded for the information > age. > Every DNA codon contains two bits of > information and two more redundancy > bits for error correction. > And we *still* get defectives like > Starmaker. > When I look at the percentage of people > who have a grasp of higher math to > those who don't, then...those with the > grasp of higher > math *are* the defectives ones, because > their numbers are way smaller. You're a > mistake. You're the defective one, > don't you get it? > Like everything else, people are > distributed along a bell curve, which is > symmetrical, making > the number and distribution of the > borderline retarded people identical to > the number and distribution of high > overachiers. > Bees, flowers, cats and fishes don't > know math and they seem to get along > fine without it. > And most people on the planet get along > without it...it's just you guys in the > sci.math class that are spinning around > in circles... > Withough advanced math, airplanes > wouldn't fly and computers wouldn't > connect you to the > Usenet. > What does a bee need an airplane for? > What does the world need you for? Nothing. > In fact, you're much like a tumor, and > should be cut out or dosed with radiation. > -- > Terry Austin > Terry Austin: like the polio vaccine, only > with more asshole. > -- David Bilek > You're really *into* medicine, aren't you? > You know, if you re-arrange your name Terry > Austin, you get -- Urinary Test. > And yours becomes retarded troll. Oh, what, > that's not rearranging your name, that *is* > your name. > That is what I mean about 'limited > intelligence'... > It's good that you know your own limitations. In > fact, it's accomplishment that you know your own > name. > Actually, I don't even know my own name. > I believe you. You are that stupid. > And, you're my bitch. > That's a first, a sissy calling me a bitch! > Is Terry a girls name? > Anybody with a name like Terry, and a handle name > Sissy--I suspect is a girlish person. You know, those > people they call gay. Those people are gay because > of a genetic defect... Is that you, ...gay? > Gee, I haven't heard that insult before. Well, not since > the third grade, at any rate. > I'm sorry, I wasn't trying to be insulting.. > Bad liar. You're not even trying. > But then, you *are* that retarded. > Do you believe intelligent life exist on Earth? > Not in your house, Oh, you mean next door maybe? Or maybe down the block?? Around > the corner??? > Prof. Math-Is-A-Lie. I *never* said math is a lie, I said it's an invention by > man... You never said Math is an invention by man. You said > Mathematics is just a religious Bible upgraded for the > information age. Make up your mind. > Which means he said that God was invented by man. His words. No other possible way to interpret them. -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Starmaker still my bitch! Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) Starmaker still my bitch! -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. - David Bilek Jesus forgives sinners, not criminals. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > Withough advanced math, airplanes wouldn't fly and > computers wouldn't connect you to the Usenet. > That's an argument in favor of banning math, huh? > This is America, you can practice any religion you want... > Any sufficiently advanced science is indistinguishable from > magic. Algebra is so advanced for you that it appears to be a > superstition. > To him, tying one's shoes appears to be magic. Tying a knot is a mathematical operation. >Operating a light switch is an excercies in binary math. Obviously > beyond him. amateurs, back in the seventies. Sadly, I can't find a link to a book by him, with the word knot in the title, to prove it. Apparently it was about the last, really important result from quantum mechanics, === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > Withough advanced math, airplanes wouldn't fly and > computers wouldn't connect you to the Usenet. > That's an argument in favor of banning math, huh? > This is America, you can practice any religion you want... > Any sufficiently advanced science is indistinguishable from > magic. Algebra is so advanced for you that it appears to be > a superstition. > To him, tying one's shoes appears to be magic. > Tying a knot is a mathematical operation. > Operating a light switch is an excercies in binary math. > Obviously beyond him. brainy amateurs, back in the seventies. Sadly, I can't find a > link to a book by him, with the word knot in the title, to > prove it. Apparently it was about the last, really important > result from quantum mechanics, before it was supplanted by > http://www.amazon.com/exec/obidos/ISBN=0716717999/ctksoftwareincA/ perhaps? Googling on his name and knot theory also produces a couple of puzzle books. -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > Withough advanced math, airplanes wouldn't fly and > computers wouldn't connect you to the Usenet. > That's an argument in favor of banning math, huh? > This is America, you can practice any religion you want... > Any sufficiently advanced science is indistinguishable from > magic. Algebra is so advanced for you that it appears to be > a superstition. > To him, tying one's shoes appears to be magic. > Tying a knot is a mathematical operation. > Operating a light switch is an excercies in binary math. > Obviously beyond him. brainy amateurs, back in the seventies. Sadly, I can't find a > link to a book by him, with the word knot in the title, to > prove it. Apparently it was about the last, really important > result from quantum mechanics, before it was supplanted by http://www.amazon.com/exec/obidos/ISBN=0716717999/ctksoftwareincA/ perhaps? Googling on his name and knot theory also produces a > couple of puzzle books. === Subject: Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > Withough advanced math, airplanes wouldn't fly and > computers wouldn't connect you to the Usenet. > That's an argument in favor of banning math, huh? > This is America, you can practice any religion you want... > Any sufficiently advanced science is indistinguishable from > magic. Algebra is so advanced for you that it appears to be > a superstition. > To him, tying one's shoes appears to be magic. > Tying a knot is a mathematical operation. > Operating a light switch is an excercies in binary math. > Obviously beyond him. > brainy amateurs, back in the seventies. Sadly, I can't find a > link to a book by him, with the word knot in the title, to > prove it. Apparently it was about the last, really important > result from quantum mechanics, before it was supplanted by > http://www.amazon.com/exec/obidos/ISBN=0716717999/ctksoftwareincA/ > perhaps? Googling on his name and knot theory also produces a > couple of puzzle books. You let a Gutless Umbrella Carrying Sissy show you how to use Google? > What's the world coming too!! Is this some kind of wierd club or > something? Buzz off, dorkwad. === Subject: Starmaker is my bitch forever! Re: My Mathematical Proof of the Week (Was: Report: Rihanna Hit First, So Chris Brown Wants A Misdemeanor) > Gutless Umbrella Carrying Sissy -- Terry Austin Terry Austin: like the polio vaccine, only with more asshole. -- David Bilek Jesus forgives sinners, not criminals. === Subject: Re: SUBTHREAD : fixed point <30127591.1237067260324.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > 1. Extensionality: Ax (Ay (x=y <-> (Az (xcz <-> ycz)))) > 2. Reflexivity: Ax (xcx) > 3. Antisymmetry: Ax (Ay ((xcy & ycx) -> x=y) > 4. Transitivity: Ax (Ay (Az ((xcy & ycz) -> xcz))) > 5. Bottom: Ex (Ay (ycx -> x=y) > 6. Top: Ex (Ay (ycx)) > 7. Union: Aa (Ab (Ex (Ay (ycx <-> (yca or ycb))))) > 8. Intersection: Aa (Ab (Ex (Ay (ycx <-> (yca & ycb))))) The object whose existence is guaranteed by I.5 may be > called Bottom or []. I'm lazy. Please show me your proof that there exists a UNIQUE x such that Ay(ycx -> x=y) to justify calling referring to the such object. MoeBlee MoeBlee === Subject: Re: SUBTHREAD : fixed point <30127591.1237067260324.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > 1. Extensionality: Ax (Ay (x=y <-> (Az (xcz <-> ycz)))) > 2. Reflexivity: Ax (xcx) > 3. Antisymmetry: Ax (Ay ((xcy & ycx) -> x=y) > 4. Transitivity: Ax (Ay (Az ((xcy & ycz) -> xcz))) > 5. Bottom: Ex (Ay (ycx -> x=y) > 6. Top: Ex (Ay (ycx)) > 7. Union: Aa (Ab (Ex (Ay (ycx <-> (yca or ycb))))) > 8. Intersection: Aa (Ab (Ex (Ay (ycx <-> (yca & ycb))))) > The object whose existence is guaranteed by I.5 may be > called Bottom or []. > I'm lazy. Please show me your proof that there exists a UNIQUE x such > that Ay(ycx -> x=y) to justify calling referring to the such object. MoeBlee's pointed out an obvious error. Since it appears in this mereology section, let me go back to the ultimate source, which is the Stanford site, to see how to correct it. Here's the correct formulation for Bottom according to Stanford: Bottom: Ex (Ay (xcy)) That is, Bottom is not defined as an object with no proper parts, but an object that is part of every other object. But notice that MoeBlee's objection is still not addressed. In fact, we go back to Stanford: Two exceptions are Martin 1965 and Bunt 1985; see also Bunge 1966 for a theory with several null individuals. Thus in Bunge's 1966 mereology, Bottom is not unique, but there can be several such objects! But this is tommy1729's theory, not Bunge's. And tommy1729, by using the notation [], implies that he, unlike Bunge, does want his Bottom object to be unique. So it appears that we have no way to make it unique, except to force it: I. Merelogy 6. Bottom: E!x (Ay (xcy)) does have no proper parts: Proof: Transitivity that zcy. Thus Ay (zcy) -- and by uniqueness, there is a unique element y such that Ay (zcy) -- Bottom itself. Thus we conclude that x = y. QED We can rewrite the definition of atomic, using the correct definition of Bottom: x atomic <-> (Ew (wcx & ~w=x) & Ay (ycx <-> (y=x or Az (ycz)))) Finally, since MoeBlee has inquired about the uniqueness of Bottom, one might ask about the uniqueness of Top. As it turns out, the axiom is correct as written. According to Stanford, the uniqueness of Top can be shown using Extensionality. Proof: Let x = Top, and suppose Ay (ycz). Then since Ay (ycx), x and z would have all the same parts (namely every object). Therefore we conclude that x = z. QED But all of this shows the problem with axiomatization. We're still trying to figure out how to make Bottom work (a concept first mentioned on sci.math by galathaea, our mereology expert), so we're still miles away from aleph oo, which is what tommy1729 was trying to define. By the time we're able to define aleph oo rigorously, the standard set theorists most likely will have stopped reading this axiomatization. === Subject: Re: SUBTHREAD : fixed point <30127591.1237067260324.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Most of the time, whenever I propose an > axiomatization for > TST, the post is ignored, so I don't want to give yet > another long list of axioms just yet. The last time I saw you give an axiomatization, a thread of many posts resulted. Your axioms were not at all ignored, but rather discussed in detail. I don't know what posting of axioms you refer to that was ignored. MoeBlee === Subject: What are binodal points ? posting-account=sKfmEQkAAAC8kI3Pv6_U_nt9sVsxZ_ou 1.1.4322),gzip(gfe),gzip(gfe) What are the binodal points of the cubic surface X^3 +AY^3 +AAZ^3 -3AXYZ = m ? In 19th century papers, I've come across a number of references to hyperbolas that are producrs of complex lines, complex planes, complex cyliners, etc. It is always assumed that the reader is familar with complex asymtotes, binodal points, unicursals, szyzygies and so on. Where could I find out more about this once widely known terminology and the techniques used to interpret complex surfaces ? === Subject: Re: How does an EM wave progagate? posting-account=d-ESTAkAAAAG0l03yI1WJgsTVXx4ebeJ Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > Do not beg to lick my boots by arguing that nonexistent b are > nonsense, because such b are certainly not nonsense. If you can point > to an empty cup and call it zero water then nothingness is water > _trivially_ . For the exact same reason we can COMFORTABLY work with > trivial magnitudes which likewise do not exist. Lick your boots? I don't think so. However, you are arguing words and mathematics not physics. Your physics is totally non-existant, but I can comfortably work with that so long as you call it math. In math anything that can be imagined is valid. I physics (and the real world) saying that things that don't exist have properties is nonsense. The zero water in an empty cup is wet only in your mind! Sure lots of Mensians love word games, and are even COMFORTABLE with them, but they rarely produce enlightenment or insight! === Subject: Re: How does an EM wave progagate? > Do not beg to lick my boots by arguing that nonexistent b are > nonsense, because such b are certainly not nonsense. If you can point > to an empty cup and call it zero water then nothingness is water > trivially . For the exact same reason we can COMFORTABLY work with > trivial magnitudes which likewise do not exist. Lick your boots? I don't think so. However, you are arguing words and > mathematics not physics. Your physics is totally non-existant, but I > can comfortably work with that so long as you call it math. In math > anything that can be imagined is valid. I physics (and the real > world) saying that things that don't exist have properties is > nonsense. The zero water in an empty cup is wet only in your > mind! Sure lots of Mensians love word games, and are even COMFORTABLE > with them, but they rarely produce enlightenment or insight! I am modelling conjecturally. My models are conjectural with respect to mathematics which is assumed to be truth (in some sense). I am arguing that mathematics is not the exclusive tool for modelling physics. There is another tool, and that tool is conjecture. I woul also argue that this methodology is: qualitative quantitative falsifiable reproducible, and predictive Just like math in ways, but it is not mathematics. Math is of no use to me except in confirming that my conjectures are consistent with respect to one another, because each individual conjecture must be transformable into a mathematical statement. So, thats all that math is really good for to me. Math proves that conjectures are consistent with each other. My boots are drying out......ahem...... === Subject: Re: How does an EM wave progagate? > I am arguing that mathematics is not the exclusive tool for modelling > physics. There is another tool, and that tool is conjecture. I woul also argue that this methodology is: > qualitative > quantitative > falsifiable > reproducible, and > predictive I've heard this story (out of you) before. So how about verifiable? Just where is the data that proves your conjecture that zero water is wet'? Haven't seen it yet. Or are you operating under the rule: I think, therefore I am! ? > My boots are drying out......ahem...... You haven't even proved your zero boots are wet yet! === Subject: Re: How does an EM wave progagate? posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > I am arguing that mathematics is not the exclusive tool for modelling > physics. There is another tool, and that tool is conjecture. > I woul also argue that this methodology is: > qualitative > quantitative > falsifiable > reproducible, and > predictive I've heard this story (out of you) before. So how about verifiable? > Just where is the data that proves your conjecture that zero water where are.. prove > is wet'? Haven't seen it yet. Or are you operating under the rule: I > think, therefore I am! ? nouht water is nouhtly wet === Subject: Re: How does an EM wave progagate? > Do not beg to lick my boots by arguing that nonexistent b are > nonsense, because such b are certainly not nonsense. If you can point > to an empty cup and call it zero water then nothingness is water > trivially . For the exact same reason we can COMFORTABLY work with > trivial magnitudes which likewise do not exist. Lick your boots? I don't think so. However, you are arguing words and > mathematics not physics. Your physics is totally non-existant, but I > can comfortably work with that so long as you call it math. In math > anything that can be imagined is valid. I physics (and the real > world) saying that things that don't exist have properties is > nonsense. The zero water in an empty cup is wet only in your > mind! Sure lots of Mensians love word games, and are even COMFORTABLE > with them, but they rarely produce enlightenment or insight! Mediumless wave of electric energy. Mitch Raemsch === WELL ORDER, PLEASE READ! DON'T LET THE CAPS LOCK KEY SCARE YOU AWAY! posting-account=fWSjlAoAAABhdvLz9gHpERiqVNX5yD3B 98),gzip(gfe),gzip(gfe) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% LET (M,<) BE A LINEAR ORDER, LET .85 BE A PART OF M. DEFINITION: .85 IS FULL TO THE LEFT IN (M,<), IF FOR ALL x,y, in M: ((y IN .85) AND (x (x IN .85) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%% LET (M,<) BE A LINEAR ORDER, LET C M(.85) BE THE COMPLEMENT OF .85 WITH RESPECT TO M. DEFINITION: (M,<) IS A FINE ORDER, IF FOR ALL SUBSETS, .85 OF M: IF, .85 IS FULL TO THE LEFT IN (M,<) AND C M(.85) IS NON EMPTY THEN: C M(.85) HAS A LEAST ELEMENT. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%% DEFINITION: (M,<) IS A WELL ORDER, IF FOR ALL SUBSETS, .85 OF M: IF, .85 IS NON EMPTY THEN: .85 HAS A LEAST ELEMENT. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% THEOREM: LET (M,<) BE A LINEAR ORDER, THEN: (M,<) IS A FINE ORDER <---> (M,<) IS A WELL ORDER PROOF: THE IMPLIKATION <--- IS TRIVIAL, THE IMPLIKATION ---> IS ALSO TRIVIAL IF M IS EMPTY. SO, ASSUME THAT (M,<) IS A FINE ORDER, BUT NOT A WELL ORDER. AND THAT M IS NON EMPTY. LET B BE A NON EMPTY SUBSET OF M THAT DON'T HAVE A LEAST ELEMENT, THEN THERE EXIST A SEQUENZE OF ELEMENTS IN B: .....< b 5 < b 4 < b 3 < b 2 < b 1 < b 0 THE SET: O = {x IN M; x < b j j=0,1,2,3,4,5,..... } IS FULL TO THE LEFT, BUT THEN, AS (M,<) IS A FINE ORDER, C M(O) HAS A LEAST ELEMENT, SAY C. C IS IN C M(O) ---> SOME,j, b j <= C BUT IF b i <= C THEN b (i+1) < C, AND b (i+1) IS IN C M(O), SO, C IS NOT THE LEAST ELEMENT IN C M(O) CONTRADICTION! THE THEOREM IS PROVEN! ;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% === OF WELL ORDER, PLEASE READ! Is there a reason you're captain capital? As all caps make for harsh reading, I'll review your post by transcribing it. Is this a correct transcription? Let (M,<=) be a linear order. A is lower set when for all x, if some a in A with x <= a, then x in A. A is a full to the left subset of M when A is lower set. M fine order when for all A proper subset M, if A is lower set, then, MA has least element. M well order when for all nonnul A subset M, A has least element. Linear order M ==> M fine order iff M well order Consider the negative integers. They are not well ordered. They are however a fine order. Have I misunderstood something? Please, do not use cap lock when you reply. ---- === OF WELL ORDER, PLEASE READ! <20090317030544.C19170@agora.rdrop.com> posting-account=fWSjlAoAAABhdvLz9gHpERiqVNX5yD3B 98),gzip(gfe),gzip(gfe) William Elliot skrev: Is there a reason you're captain capital? As all caps make for harsh > reading, I'll review your post by transcribing it. Is this a correct > transcription? Let (M,<=) be a linear order. > It's not supposed to be <= , only < not less than or equal to but less than > A is lower set when for all x, if some a in A with x <= a, then x in A. > A is a full to the left subset of M when A is lower set. M fine order when for all A proper subset M, if A is lower set, > then, MA has least element. M well order when for all nonnul A subset M, A has least element. Linear order M == M fine order iff M well order Consider the negative integers. They are not well ordered. > They are however a fine order. Have I misunderstood something? > The empty set is full to the left. The negative integers are not a fine order, the complement to the empty set is the negative integers in this case, but they don't have a least element. > Please, do not use cap lock when you reply. ---- === OF WELL ORDER, PLEASE READ! <20090317030544.C19170@agora.rdrop.com William Elliot skrev: > Is there a reason you're captain capital? As all caps make for harsh > reading, I'll review your post by transcribing it. Is this a correct > transcription? > Let (M,<=) be a linear order. It's not supposed to be <= , only < > not less than or equal to but less than > It'll make no difference other than the refexive order <=, is easier to work with than the irreflexive order <. > A is lower set when for all x, if some a in A with x <= a, then x in A. > A is a full to the left subset of M when A is lower set. > M fine order when for all A proper subset M, if A is lower set, > then, MA has least element. > M well order when for all nonnul A subset M, A has least element. > Linear order M ==> M fine order iff M well order > Direct Proof. Assume A nonnul subset M. Thus B = { x | x lower bound A } - A proper subset M. As B is a lower set, let a = least MB. Since A subset B, a is a lower bound for A, Since a not in B, a in A. Thus a = least A. === Subject: Slightly OT: Does drinking alcohol effect long term ability to do good math? I know, this sounds like a vaguely troll-ish topic but this is something I thought about the other night while drinking. ;) Suppose one has a couple of glasses of wine with dinner each night...maybe has several drinks to the point of being tipsy once every week or two. Does this sound like a recipe for disaster in disrupting thoughtful abilities? Does anybody here specifically choose not to drink for fear that it may effect their math abilities? === Subject: Re: Slightly OT: Does drinking alcohol effect long term ability to do good math? > I know, this sounds like a vaguely troll-ish topic but this is something > I thought about the other night while drinking. ;) > Suppose one has a couple of glasses of wine with dinner each > night...maybe has several drinks to the point of being tipsy once every > week or two. Does this sound like a recipe for disaster in disrupting > thoughtful abilities? Oh supposed one, I hear the sound of an alcohol problem. > Does anybody here specifically choose not to drink for fear that it may > effect their math abilities? > No. I don't drink because it's a health drag. Occasionally I'd have _one_ glass of wine with dinner. More than that is an alcohol problem and will affect your health. === Subject: Re: Slightly OT: Does drinking alcohol effect long term ability to do good math? > I know, this sounds like a vaguely troll-ish topic but this is something > I thought about the other night while drinking. ;) > Suppose one has a couple of glasses of wine with dinner each > night...maybe has several drinks to the point of being tipsy once every > week or two. Does this sound like a recipe for disaster in disrupting > thoughtful abilities? > Oh supposed one, I hear the sound of an alcohol problem. > Does anybody here specifically choose not to drink for fear that it may > effect their math abilities? > No. I don't drink because it's a health drag. > Occasionally I'd have _one_ glass of wine with dinner. > More than that is an alcohol problem and will affect your health. I think it does affect your math abilities. Just look at Goedel. I guess I don't know anything about G.9adel's personal life other than that he went nuts and starved himself to death. What is the story with him and alcohol? === Subject: Re: Slightly OT: Does drinking alcohol effect long term ability to do good math? > I know, this sounds like a vaguely troll-ish topic but this is something > I thought about the other night while drinking. ;) > Suppose one has a couple of glasses of wine with dinner each > night...maybe has several drinks to the point of being tipsy once every > week or two. Does this sound like a recipe for disaster in disrupting > thoughtful abilities? > Oh supposed one, I hear the sound of an alcohol problem. > Does anybody here specifically choose not to drink for fear that it may > effect their math abilities? > No. I don't drink because it's a health drag. > Occasionally I'd have _one_ glass of wine with dinner. > More than that is an alcohol problem and will affect your health. I think it does affect your math abilities. Just look at Goedel. Amphetamines are a better choice -- just look at Erdos. quasi === Subject: Hex KB - Klein bottle game posting-account=uEOgRAoAAAASMp5oEBx_0d7qfHMcYtcE Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Hex KB is a game, but this document is mainly a study of the Klein bottle and loops drawn on the Klein bottle. http://www.marksteeregames.com/Hex_KB_rules.html Mark Steere Games http://www.marksteeregames.com/index.html === Subject: Re: That continuous iteration of quadratic maps thingy again. posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 15, 8:54pm, Mariano Su.87rez-Alvarez > On Mar 7, 5:35am, alainvergh...@gmail.com I always wished getting out of these heavy representations, > Alain > How about if one used a simpler Riemann surface, namely that of the > inverse > of z^2 + c, i.e. that of sqrt(z - c)? This is simpler as it has only 2 > leaves. > Note that sqrt(z - c) sends points on the Riemann surface to points on > the > z-plane, and the map z^2 + c could then be thought of as sending > points on > the z-plane to points on the Riemann surface. The rub here would then > be: > 1. finding a simple, easy representation for the Riemann surface's > points Let c be in C. Then the Riemann surface of f(z) = sqrt(c - z) > is simply the set S = { (z, w) in C x C : w^2 + c = z } The complete function corresponding to f (that is, > the extension of f to its Riemann surface) is the > function F : S --> C such that F(z, w) = w. The covering p : S --> C is given by p(z, w) = z, > and it is (outside of the ramification point 0) > a two-sheeted covering. > But this doesn't solve the problem... how to represent the dynamics of z^2 + c in such a way that the inverse map is single valued as well. This involves iteration (repeated application) of both z^2 + c and sqrt (z - c). === Subject: Re: That continuous iteration of quadratic maps thingy again. > On Mar 7, 5:35am, alainvergh...@gmail.com I always wished getting out of these heavy representations, > Alain > How about if one used a simpler Riemann surface, namely that of the > inverse > of z^2 + c, i.e. that of sqrt(z - c)? This is simpler as it has only 2 > leaves. > Note that sqrt(z - c) sends points on the Riemann surface to points on > the > z-plane, and the map z^2 + c could then be thought of as sending > points on > the z-plane to points on the Riemann surface. The rub here would then > be: > 1. finding a simple, easy representation for the Riemann surface's > points > Let c be in C. Then the Riemann surface of f(z) = sqrt(c - z) > is simply the set > S = { (z, w) in C x C : w^2 + c = z } > The complete function corresponding to f (that is, > the extension of f to its Riemann surface) is the > function F : S --> C such that F(z, w) = w. > The covering p : S --> C is given by p(z, w) = z, > and it is (outside of the ramification point 0) > a two-sheeted covering. But this doesn't solve the problem... how to represent the dynamics > of z^2 + c in such a way that the inverse map is single valued as > well. > This involves iteration (repeated application) of both z^2 + c and sqrt > (z - c). I never claimed to solve the problem. In fact, I do not even understand *what* the problem is. I just wanted to show you that the Riemann surface has a very simple description in this case. -- m === Subject: Re: That continuous iteration of quadratic maps thingy again. posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009020407 Iceweasel/3.0.6 (Debian-3.0.6-1),gzip(gfe),gzip(gfe) On Mar 16, 5:40pm, Mariano Su.87rez-Alvarez > On Mar 15, 8:54pm, Mariano Su.87rez-Alvarez > On Mar 7, 5:35am, alainvergh...@gmail.com I always wished getting out of these heavy representations, > Alain > How about if one used a simpler Riemann surface, namely that of the > inverse > of z^2 + c, i.e. that of sqrt(z - c)? This is simpler as it has only 2 > leaves. > Note that sqrt(z - c) sends points on the Riemann surface to points on > the > z-plane, and the map z^2 + c could then be thought of as sending > points on > the z-plane to points on the Riemann surface. The rub here would then > be: > 1. finding a simple, easy representation for the Riemann surface's > points > Let c be in C. Then the Riemann surface of f(z) = sqrt(c - z) > is simply the set > S = { (z, w) in C x C : w^2 + c = z } > The complete function corresponding to f (that is, > the extension of f to its Riemann surface) is the > function F : S --> C such that F(z, w) = w. > The covering p : S --> C is given by p(z, w) = z, > and it is (outside of the ramification point 0) > a two-sheeted covering. > But this doesn't solve the problem... how to represent the dynamics > of z^2 + c in such a way that the inverse map is single valued as > well. > This involves iteration (repeated application) of both z^2 + c and sqrt > (z - c). I never claimed to solve the problem. In fact, I do > not even understand *what* the problem is. > I just wanted to show you that the Riemann surface > has a very simple description in this case. > OK. Hmm... === Subject: Re: That continuous iteration of quadratic maps thingy again. posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009020407 Iceweasel/3.0.6 (Debian-3.0.6-1),gzip(gfe),gzip(gfe) > On Mar 16, 5:40pm, Mariano Su.87rez-Alvarez > On Mar 15, 8:54pm, Mariano Su.87rez-Alvarez > On Mar 7, 5:35am, alainvergh...@gmail.com I always wished getting out of these heavy representations, > Alain > How about if one used a simpler Riemann surface, namely that of the > inverse > of z^2 + c, i.e. that of sqrt(z - c)? This is simpler as it has only 2 > leaves. > Note that sqrt(z - c) sends points on the Riemann surface to points on > the > z-plane, and the map z^2 + c could then be thought of as sending > points on > the z-plane to points on the Riemann surface. The rub here would then > be: > 1. finding a simple, easy representation for the Riemann surface's > points > Let c be in C. Then the Riemann surface of f(z) = sqrt(c - z) > is simply the set > S = { (z, w) in C x C : w^2 + c = z } > The complete function corresponding to f (that is, > the extension of f to its Riemann surface) is the > function F : S --> C such that F(z, w) = w. > The covering p : S --> C is given by p(z, w) = z, > and it is (outside of the ramification point 0) > a two-sheeted covering. > But this doesn't solve the problem... how to represent the dynamics > of z^2 + c in such a way that the inverse map is single valued as > well. > This involves iteration (repeated application) of both z^2 + c and sqrt > (z - c). > I never claimed to solve the problem. In fact, I do > not even understand *what* the problem is. > I just wanted to show you that the Riemann surface > has a very simple description in this case. OK. Hmm... Riemann surface, though. By the way, the problem is this. f(z) z^2 + c is not an injective map, because z^2 is not an injective map. This means it has no proper inverse map. Therefore, one asks, is there some domain D on which we can define a bijective function G: D->D such that c(G(u)) = f(c(u)), where c(u) is a surjective function c: D->C? (This function gives the complex number corresponding to a point in D. Note that it itself need not be injective. f(z) on the z-plane loses information, you know.) That way, iteration of G, i.e. G(u), G(G(u)), G(G(G(u))), etc. provides a dynamical system that could possibly be turned into a flow somehow. And I was wondering if some Riemann surface could be used for this domain D, maybe that of f^-1(z). This investigation was inspired by this web page: http://www.xs4all.nl/~westy31/ContFract/Continuous iteration of fractals.html and I was wondering if there was any way to do it without the discontinuity, or at least to minimize arbitrary choices as much as possible (the location of said discontinuity was chosen arbitrarily by the arctan2 branch used in computing the sum of points on the surface when represented as polars (r 1, theta 1) and (r 2, theta 2) with unbounded theta.). Addendum: Now that I think about it, I don't think the Riemann surface of f^-1 is suitable. Consider two applications of f: f(f(z)). The inverse now needs a Riemann surface that is different, having 4 leaves. It would seem that for the general problem, we'd need one with infinitely many leaves, like the one mentioned on the web page. Although then comes the problem of suitably defining addition which is needed to extend the map... === Subject: Powerset of a set is not its member posting-account=5t-ZfgkAAACU7ydoC4Cq-xVNAFsq481f Gecko/2009031120 Mandriva/1.9.0.7-0.1mdv2009.0 (2009.0) Firefox/3.0.7,gzip(gfe),gzip(gfe) I think in ZF (without the axiom of regularity) can be proved: The powerset of a set is not its member (2^Z notin Z). How this can be proved? (Or indeed it cannot be proved?) === Subject: Re: Powerset of a set is not its member > I think in ZF (without the axiom of regularity) can be proved: > The powerset of a set is not its member (2^Z notin Z). Interesting question. It's not immediately obvious to me which way that goes. It's pretty quickly provable with regularity. I think it is not provable without. It seems that the Anti-Foundation Axiom is consistent with ZF without Axiom of Regularity, and asserts that sets exist corresponding to arbitrary membership relation graphs. With the graph A---<->---B--->---0, we have the relations 0 in B, A in B, and B in A. It is readily verified that A has only two subsets: 0 and A, and B has exactly those as elements. Thus B = P(A), and B in A. So unless I have misinterpreted something (not unlikely!), it cannot be proven that 2^Z notin Z without the Axiom of Regularity in ZF. - Tim === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > There are devotionals to Saint Albert and Saint Albert hymns and other > that were created for the express purpose of worshiping Albert > Einstein. > I'm looking to compile an extensive list. Please share your favorite > references. > Shubee > http://www.everythingimportant.org/Einstein worship > Eugene, is there any known flaw in the equations of special > or general relativity, in your opinion? > Is there any known flaw in my equations? > http://www.everythingimportant.org/relativity/special.pdf > Shubee So your complaint is that you want the same attention as Einstein > gets? As though you're entitled to it? PD I claim that the essence, beauty and practically of relativity is primarily Lorentz invariance and that the occult science that Einstein made out of the physics of Lorentz and Poincar.8e is worthless, consequently, that Henri Poincar.8e is the true father of relativity. http://www.everythingimportant.org/relativity/directory.htm To the same degree that the physics community worships Einstein and his legacy, to that same degree I expect to receive threats and all manner of abuse. Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) >http://www.everythingimportant.org/relativity/directory.htm > To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. Yes, I know, you consider yourself a Martyr 3rd Class, and you are > hoping that this pursuit will allow you to petition for elevation of > status to Martyr 2nd Class. PD That doesn't seem fair. I think my fate should be decided by what the rabble wants. Hasn't it always been that way? My impression is that Eric Gisse wants to see me crucified because, in his opinion, I have the same character flaw as Jesus of Nazareth. Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) >http://www.everythingimportant.org/relativity/directory.htm > To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. > Yes, I know, you consider yourself a Martyr 3rd Class, and you are > hoping that this pursuit will allow you to petition for elevation of > status to Martyr 2nd Class. > PD > That doesn't seem fair. I think my fate should be decided by what the > rabble wants. And what happens to folks that the rabble doesn't particularly care > about one way or the other? What happens to them? You're part of the rabble. Just look within yourself for the answer. > Hasn't it always been that way? My impression is that > Eric Gisse wants to see me crucified because, in his opinion, I have > the same character flaw as Jesus of Nazareth. > Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) >http://www.everythingimportant.org/relativity/directory.htm > To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. > Yes, I know, you consider yourself a Martyr 3rd Class, and you are > hoping that this pursuit will allow you to petition for elevation of > status to Martyr 2nd Class. > PD > That doesn't seem fair. I think my fate should be decided by what the > rabble wants. And what happens to folks that the rabble doesn't particularly care > about one way or the other? What happens to them? They become like shooby - feverishly looking for a reason for the universe to care about them. [...] === Subject: Re: Compiling Undeniable Evidence of Einstein Worship >http://www.everythingimportant.org/relativity/directory.htm > To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. > Yes, I know, you consider yourself a Martyr 3rd Class, and you are > hoping that this pursuit will allow you to petition for elevation of > status to Martyr 2nd Class. > PD That doesn't seem fair. I think my fate should be decided by what the > rabble wants. Hasn't it always been that way? My impression is that > Eric Gisse wants to see me crucified because, in his opinion, I have > the same character flaw as Jesus of Nazareth. Shubee You are a confused soul. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) [...] > I claim that the essence, beauty and practically of relativity is > primarily Lorentz invariance and that the occult science that Einstein > made out of the physics of Lorentz and Poincar.8e is worthless, > consequently, that Henri Poincar.8e is the true father of relativity. Occult? Well, I guess a devoted 7th day adventist would know it when he sees it... Why don't you take a minute from the persecution complex and notice how modern physics is taught. Einstein is given credit for relativity but Minkoski's formalism is the one that is actually used. http://www.everythingimportant.org/relativity/directory.htm To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. Ah so you expect abuse every time you post. Yet you persist regardless. What does that say about you? Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) [...] > I claim that the essence, beauty and practically of relativity is > primarily Lorentz invariance and that the occult science that Einstein > made out of the physics of Lorentz and Poincar.8e is worthless, > consequently, that Henri Poincar.8e is the true father of relativity. Occult? Well, I guess a devoted 7th day adventist would know it when > he sees it... I'm a Millerite Christian, not a Seventh-day Adventist. > Why don't you take a minute from the persecution complex and notice > how modern physics is taught. Einstein is given credit for relativity > but Minkoski's formalism is the one that is actually used. Correct. And history testifies that when Einstein first heard Minkowski lecture on the geometric unification of space and time, Einstein whined about the concept saying that it was too difficult. http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf A more interesting historical detail about the Cologne lecture of 1908 is that Minkowski claimed scientific priority for his so-called great, new, geometric theory of relativity but it was based largely on the work of Poincar.8e. Poincar.8e was purposely excluded from the meeting. http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf > http://www.everythingimportant.org/relativity/directory.htm > To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. Ah so you expect abuse every time you post. Yet you persist > regardless. What does that say about you? That maybe I believe that I know how to escape the final judgment? Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship > I claim that the essence, beauty and practically of relativity is > primarily Lorentz invariance and that the occult science that Einstein > made out of the physics of Lorentz and Poincar.8e is worthless, > consequently, that Henri Poincar.8e is the true father of relativity. > Occult? Well, I guess a devoted 7th day adventist would know it when > he sees it... I'm a Millerite Christian, not a Seventh-day Adventist. > Why don't you take a minute from the persecution complex and notice > how modern physics is taught. Einstein is given credit for relativity > but Minkoski's formalism is the one that is actually used. Correct. Great! Now that you understand and acknowledge that Einstein's formalism is not relevant, could you finally shut the hell up about it and move on? >And history testifies that when Einstein first heard > Minkowski lecture on the geometric unification of space and time, > Einstein whined about the concept saying that it was too difficult. http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf Feel free to show where Einstein whined. A more interesting historical detail about the Cologne lecture of 1908 > is that Minkowski claimed scientific priority for his so-called great, > new, geometric theory of relativity but it was based largely on the > work of Poincar.8e. Poincar.8e was purposely excluded from the meeting. http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf Feel free to show where it says Poincare was banned. >http://www.everythingimportant.org/relativity/directory.htm > To the same degree that the physics community worships Einstein and > his legacy, to that same degree I expect to receive threats and all > manner of abuse. > Ah so you expect abuse every time you post. Yet you persist > regardless. > What does that say about you? That maybe I believe that I know how to escape the final judgment? Shubee I worship the worlds largest pine cone. When the universe-ending firestorm comes, His Seeds Will Sprout Forth And Bring New Life. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship > Great! Now that you understand and acknowledge that Einstein's > formalism is not relevant Einstein didn't have a formalism. He stole everything. Even Einstein's summation convention wasn't his. >And history testifies that when Einstein first heard > Minkowski lecture on the geometric unification of space and time, > Einstein whined about the concept saying that it was too difficult. > http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf Feel free to show where Einstein whined. Einstein whined in writing (page 48-49 of the cited paper): In April 1908, Minkowski published a technically accomplished paper on the electromagnetic processes in moving bodies (ñDie Grundgleichungen fur die electromagnetischen Vorgange in bewegten Korpern,î hereafter field equations of relativistic electrodynamics in four-dimensional form, using Arthur CayleyÍs matrix calculus. He also derived the equations of electrodynamics of moving media, and formulated the basis of a mechanics appropriate to four-dimensional space with an indefinite squared interval. MinkowskiÍs study represented the first elaboration of the principle of relativity by a mathematician in Germany. Soon after its publication, the Grundgleichungen sustained restrained comment from MinkowskiÍs former students Albert Einstein and Jakob Laub (1908a, 1908b). These authors rejected out of hand the four- dimensional apparatus of MinkowskiÍs paper, the inclusion of which, (1908a: 532). No other reaction to MinkowskiÍs work was published before the Cologne meeting. Page 69: The initial response by Einstein and Laub to the Grundgleichungen,we mentioned earlier, dismissed the four-dimensional approach, and criticized MinkowskiÍs formula for ponderomotive force density. Others were more appreciative of MinkowskiÍs formalism, including the coeditors of the Annalen der Physik, Max Planck and Willy Wien. According to Planck and Wien, Minkowski had put EinsteinÍs theory in a very elegant mathematical form (Wien 1909a: 37; Planck 1910a: 110). === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > Great! Now that you understand and acknowledge that Einstein's > formalism is not relevant Einstein didn't have a formalism. He stole everything. Even > Einstein's summation convention wasn't his. >And history testifies that when Einstein first heard > Minkowski lecture on the geometric unification of space and time, > Einstein whined about the concept saying that it was too difficult. >http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf > Feel free to show where Einstein whined. Einstein whined in writing (page 48-49 of the cited paper): [...] No such whining is present. You see that which you wish to see. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf > Feel free to show where Einstein whined. > Einstein whined in writing (page 48-49 of the cited paper): [...] No such whining is present. You see that which you wish to see. The key judgment against Albert Einstein and Jakob Laub (1908a, 1908b) states: These authors rejected out of hand the four-dimensional would have placed ñrather great demandsî on their readers (1908a: 532). Translation: Thinking about 4-dimensions is too difficult for us physicists. We hereby formally object with feelings of terrible inadequacy, tears and tantrums. Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) >http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf > Feel free to show where Einstein whined. > Einstein whined in writing (page 48-49 of the cited paper): > [...] > No such whining is present. You see that which you wish to see. The key judgment against Albert Einstein and Jakob Laub (1908a, 1908b) > states: These authors rejected out of hand the four-dimensional > would have placed ñrather great demandsî on their readers (1908a: > 532). Translation: Thinking about 4-dimensions is too difficult for us > physicists. We hereby formally object with feelings of terrible > inadequacy, tears and tantrums. Shubee This is called projection. YOU are unable to understand the four dimensional formulation of special relativity, so you project YOUR confusion on Einstein. Einstein had a bachelors and a PhD in physics by that point in time, so the criticism is both completely unfounded and completely silly. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506; Media Center PC 5.0; InfoPath.2),gzip(gfe),gzip(gfe) > The key judgment against Albert Einstein and Jakob Laub (1908a, 1908b) > states: These authors rejected out of hand the four-dimensional > would have placed ñrather great demandsî on their readers (1908a: > 532). > Translation: Thinking about 4-dimensions is too difficult for us > physicists. We hereby formally object with feelings of terrible > inadequacy, tears and tantrums. This is called projection. YOU are unable to understand the four > dimensional formulation of special relativity, so you project YOUR > confusion on Einstein. That is why Gisse is a college drop-out. His mind is totally fvcked up. so the criticism is both completely unfounded and completely silly. It does not how any degrees Einstein had. Einstein was still a nitwit, a plagiarist, and a liar. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > The key judgment against Albert Einstein and Jakob Laub (1908a, 1908b) > states: These authors rejected out of hand the four-dimensional > would have placed ñrather great demandsî on their readers (1908a: > 532). > Translation: Thinking about 4-dimensions is too difficult for us > physicists. We hereby formally object with feelings of terrible > inadequacy, tears and tantrums. > This is called projection. YOU are unable to understand the four > dimensional formulation of special relativity, so you project YOUR > confusion on Einstein. > That is why Gisse is a college drop-out. His mind is totally fvcked > up. Einstein had a bachelors and a PhD in physics by that point in time, > so the criticism is both completely unfounded and completely silly. > It does not how any degrees Einstein had. Einstein was still a > nitwit, a plagiarist, and a liar. Put a sock in it , Mother-er. Get a ing life. Become a > ing whore. Contribute to society for once in your ing life. Sorry about thta, but you asshole going round and round and round and > round about this inconsequential crap (just as Godel's Incompleteness > theorem is inconsequential) just gets old, I mean to the point of > making your reader swant to ing barf after awhile, i eman, someoen > needs to come along and knock the ing needle over to the next > track, to use a metaphor alonsy no one would understand n e more, and > like, it really shouldn matter, after all, who gives a fci if you > cocksuckerwaste your worthleive sing with each other, but dammit, > you asshole could be running in a gioant cage to genrate electricity > or the like an d at least do some good, but youd prolly finad a way to > write ing whilst running, and anyway, who gives a about > anything anymore, Geral Chilton willprolly give us all the way out, > and like hasgeorge, no relies will be read. isomorphic to a shooter > who has his fun and then runs off and hidesin the forest. all of > you. have a nice day. - Don PS usenet. He does get repetitive with his nonsense, doesn't he? Does make refuting it easier - just point to something written 3 years ago. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship > On Mar 15, 5:13 am, Dirk Van de moortel > There are devotionals to Saint Albert and Saint Albert hymns and other > that were created for the express purpose of worshiping Albert > Einstein. > I'm looking to compile an extensive list. Please share your favorite > references. > Shooby nee Eugene Shubert > Androcles nee John Parker > Kooby Wublee nee whatever > NoEinstein nee John Armisted Correction: John Armistead > http://www.jurgita.com/scouts-id275378.html > Flirt zone: > I am looking for: (female personals) > My purpose is: Socializing > I am interested in: Art > I love to listen to: Good Oldies > Religion: Other Christian Oh my - > I am the casting agent for a major dramatic movie for international > distribution. I wish to contact new face actors who catch my eye, > rather than have casting calls. I will give details about the roles to > those contacts who are available and interested to learn more. The > financial rewards are tops. > I wonder if he wears a leisure suit when conducting auditions. Let's hope he does. Dirk Vdm === Subject: Re: Compiling Undeniable Evidence of Einstein Worship > There are devotionals to Saint Albert and Saint Albert hymns and other > that were created for the express purpose of worshiping Albert > Einstein. > I'm looking to compile an extensive list. Please share your favorite > references. >Shooby nee Eugene Shubert >Androcles nee John Parker >Kooby Wublee nee whatever >NoEinstein nee John Armisted >These people can't shut the up about Einstein. This is so funny. If not for all the posts by the anti-relativity nuts so obsessed with trying to disprove relativity and discredit Einstein, and for all the replies they generate, there really wouldn't be all that much mention of Einstein in the sci.physics groups. After all, he's been dead for over half a century, and isn't exactly coming up with anything new. === Subject: Gamblers in casinos, Chistians in church, sci-fi nuts in Sci.Physics. Peopleare still talking about Darwin, because he's a symbol. Same goes for Einstein, but even more so. Einstein gave us the origin of the cosmos, not just the origin of the species. We crave hope, no matter how preposterous. For example: gamblers in casinos, Chistians in church, and .81 last but not least .81 sci-fi nuts in Sci.Physics. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship > There are devotionals to Saint Albert and Saint Albert hymns and other > that were created for the express purpose of worshiping Albert > Einstein. > I'm looking to compile an extensive list. Please share your favorite > references. > Shubee > http://www.everythingimportant.org/Einstein_worship > Eugene, is there any known flaw in the equations of special > or general relativity, in your opinion? Is there any known flaw in my equations? > http://www.everythingimportant.org/relativity/special.pdf Shubee So, no, you have not found any flaws in the equations of special or general relativity, as far as you understand them. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship On Mar 15, 6:35 pm, Peter Webb > Your paper goes to some lengths to derive the Lorentz transformation, > which > is the basis of SR. It seems to predict identical results to SR (because > it > uses the same transformations), and in fact seems to be nothing more than > a > poorly thought through derivation of SR. Einstein gave a much better one > over 100 years ago. The world doesn't need any more proof that SR is correct; it is proved But good of you to try to derive the Lorentz transformation by another > means, however crappy that other means is. You are mistaken on several levels. The axioms assumed in http://www.everythingimportant.org/relativity/special.pdf do not include the principle of relativity or the constancy of the speed of light. *********************** It therefore is SR. If it does not produce identical results for inertial reference frames as does SR, you should explain how the results differ, with a numeric example. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship > You are mistaken on several levels. The axioms assumed in > http://www.everythingimportant.org/relativity/special.pdf do not > include the principle of relativity or the constancy of the speed of > light. It therefore is SR. If it does not produce identical results for inertial reference frames as > does SR, you should explain how the results differ, with a numeric example. Absolutely, but I can't do everything at once. I have too many things to do in real life. That's why I'm writing the paper piecemeal. You should start seeing major differences and advantages over ordinary relativity in the next edition. Shubee === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=LxihSQoAAABzdzEeG7JudGr6Yl-Mh-CT InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) Shubee, here is another evidence of Einstein worship. It is Eric trying to pass off some new preliminary GPB result as the official positive result. You can use the GPB website as an evolving evidence. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > Shubee, here is another evidence of Einstein worship. It is Eric > trying to pass off some new preliminary GPB result as the official > positive result. You can use the GPB website as an evolving evidence. > Is there something you disagree with in particular, or are you shrieking for no specific reason beyond that of being anti-relativity? === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > Shubee, here is another evidence of Einstein worship. It is Eric > trying to pass off some new preliminary GPB result as the official > positive result. You can use the GPB website as an evolving evidence. > Is there something you disagree with in particular, or are you > shrieking for no specific reason beyond that of being anti-relativity? Forgive Eric for being incredibly stupid. May he re-enroll in a community college, obtain a janitorial diploma, and do something worthwhile. For the record, I am merely against pseudoscience. Eric it seems, is against logic and intellect. Thus his doctoral in crookedness and flunkieship. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > Shubee, here is another evidence of Einstein worship. It is Eric > trying to pass off some new preliminary GPB result as the official > positive result. You can use the GPB website as an evolving evidence. > Is there something you disagree with in particular, or are you > shrieking for no specific reason beyond that of being anti-relativity? Forgive Eric for being incredibly stupid. May he re-enroll in a > community college, obtain a janitorial diploma, and do something > worthwhile. For the record, I am merely against pseudoscience. Eric it seems, is > against logic and intellect. Thus his doctoral in crookedness and > flunkieship. Ah, so you can't identify the source of disagreement. You just know you do not agree. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > There are devotionals to Saint Albert and Saint Albert hymns and other > that were created for the express purpose of worshiping Albert > Einstein. > I'm looking to compile an extensive list. Please share your favorite > references. > Shooby nee Eugene Shubert > Androcles nee John Parker > Kooby Wublee nee whatever > NoEinstein nee John Armisted > These people can't shut the up about Einstein. Just because yours truly exposed your messiah Einstein the nitwit, the > plagiarist, and the liar as nothing but a nitwit, a plagiarist, and a > lair, you donÍt have to throw a fit like that, college drop-out. > finished saying you couldn't stop whining about Einstein. I will admit the nonsense in SR if you can show me valid mathematical > proof in the resolution to the twinÍs paradox. You need to show so > from the two framesÍ points of view. Tell me why your opinion should matter to me. [...] So, punk, the college drop-out. Put up or shut up! The irony is staggering. Several years of asking you to back up your asinine claims with that exact phrase obtained nothing but further idiocies. Let's revisit the last one. You've had nearly two years - are you yet able to produce one literature reference that agrees with you? === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; InfoPath.2),gzip(gfe),gzip(gfe) > Just because yours truly exposed your messiah Einstein the nitwit, the > plagiarist, and the liar as nothing but a nitwit, a plagiarist, and a > lair, you donÍt have to throw a fit like that, college drop-out. > [Irrelevant whining crap snipped] > I will admit the nonsense in SR if you can show me valid mathematical > proof in the resolution to the twinÍs paradox. You need to show so > from the two framesÍ points of view. Tell me why your opinion should matter to me. [More irrelevant whining crap snipped] The Lorentz transform manifests the following two properties: ** The principle of relativity > ** Time dilation > The twinÍs paradox results in the very combination of the two these > properties. To resolve the twinÍs paradox, you must show either or > both of the properties invalid. In doing so, you disprove the Lorentz > transform. Thus, the paradox exists. Claiming any resolution to the > paradox is like claiming to have invented another perpetual motion > machine. So, punk, the college drop-out. Put up or shut up! [Yet more irrelevant whining crap snipped] The college drop-out can still not produce anything to resolve the twinÍs paradox as expected. The Lorentz transform manifests the following two properties: ** The principle of relativity ** Time dilation The twinÍs paradox results in the very combination of the two these properties. To resolve the twinÍs paradox, you must show either or both of the properties invalid. In doing so, you disprove the Lorentz transform. Thus, the paradox exists. Claiming any resolution to the paradox is like claiming to have invented another perpetual motion machine. === Subject: Re: Compiling Undeniable Evidence of Einstein Worship posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) [irrelevant whining snipped] Nothing left. === Subject: Re: JSH: Factoring solution test run, Fermat primes gcd with a function I call r_c(v), where: r_c(v) = 2((D+1)v^2 - 2f_1*v + f_1^2) > [...] > If you can never find a rational v in range such that r_c(v) is an > integer, for any f_1 where again that is a factor of D-1, which > includes 1 as a possibility, then D is guaranteed to be prime. There are infinitely many rational v in range. What is your method for restricting the search to a small number of possibilities for v? - Tim === Subject: Re: JSH: Factoring solution test run, Fermat primes posting-account=DkG3nAkAAAAVuxctYYjlIz6_Yb78PVNd rv:1.8.1.3) Gecko/20070309 Firefox/2.0.0.3,gzip(gfe),gzip(gfe) > In case you missed it, I've found what I claim is a solution to the > factoring problem involving factor D-1 in order to factor a target > composite D, where I used Pell's Equation. > It was brought to my attention by Penny Hassett in a comment on my > math blog that Fermat primes might be a good area to bring this new > solution to bear, as factoring D-1 is then trivial. > The possibility here is in finding the next Fermat prime. Here is the > factoring algorithm: > Given an odd composite D, to be factored, you factor it by taking its > gcd with a function I call r_c(v), where: > r_c(v) = 2((D+1)v^2 - 2f_1*v + f_1^2) > and f_1 is a factor of D-1, so with Fermat numbers, it is always just > 2 raised to some natural number power, where you find rational v, such > that v is in the following range: > (f_1 - sqrt(f_1^2 - [f_1^2 - D/2](D+1)))/(D+1) < v < (f_1 + sqrt(f_1^2 > - [f_1^2 - D/2](D+1)))/(D+1) You're restricting yourself in two bad ways. First, by requiring |r (v)| < D you have essentially limited your range for v to v = -1/2, 0, 1/2, as mike3 has already pointed out (plug in some actual values for D and f_1 above and you'll see that). > and r_c(v) is an integer, where if that range gives an integer v, then > you're done, as you just plug that into r_c(v), and you're guaranteed > have a factorization of D, from the gcd. Here's your second bad choice. Requiring r_c(v) to be an integer will almost never yield a useful factor, especially for a Fermat prime. Observe that gcd(r_c(v), D) = gcd(2((D+1)v^2 - 2 v f_1 + f_1^2) = gcd(2((v - f_1)^2 + D v^2, D) = gcd(2(v - f_1)^2, D) = gcd((v - f_1)^2, D) since we may assume D is odd. But now even without your restriction on the range of v, we are basically looking at nothing but trial division to find a suitable v. If we relax the restriction that v be an integer or half an integer, we can indeed get nontrivial divisors for D. Suppose, for example, we wanted to test the primality of F_5 = 2^32 + 1. By Lucas' result we need only use f_1 = 128 (since g will be a factor of F_n only if g = 1 mod (2^{n+2})) and we find that v = -1/5 will yield r_c(-1/5) = 2((-1/10 - 128) + (2^32 + 1)/100) and the numerator of that fraction has a factor of 641, which we know divides 2^32 + 1. > If no integers are available for v, not to worry! Turns out a > rational solution MUST exist if there is rational range at all, and > it's denominator is, 2. Actually, no. There will be a rational solution (where the numerator has a factor dividing D), but its denominator won't in general be 2. Rick === Subject: Re: JSH: Factoring solution test run, Fermat primes Nntp-Posting-Host: hera.cwi.nl ... > Given D = 2^k + 1, you have that D-1 = 2^k, so f_1 = 1, or f_1 = 2^= > c, > where c is a natural number up to k potentially, but you will not have > rational solutions that far up. The smallest k for which it is unknown whether it is prime or not is 2^33, or 8589934592. > Then you just check the range of possible rational v's with: > > (f_1 - sqrt(f_1^2 - [f_1^2 - D/2](D+1)))/(D+1) < v < (f_1 + sqrt(f_1^2 > - [f_1^2 - D/2](D+1)))/(D+1) > > where you loop through every f_1 for which you have rational > solutions. Notice that once f_1 > sqrt(D/2) you have no more rational > solutions. Aha, so we have to loop only to f_1 = 2^4294967296. Helps a lot! I think it will take a bit of time to do all those calculations. Good luck. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Factoring solution test run, Fermat primes posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > In case you missed it, I've found what I claim is a solution to the > factoring problem involving factor D-1 in order to factor a target > composite D, where I used Pell's Equation. It was brought to my attention by Penny Hassett in a comment on my > math blog that Fermat primes might be a good area to bring this new > solution to bear, as factoring D-1 is then trivial. The possibility here is in finding the next Fermat prime. Here is the > factoring algorithm: Given an odd composite D, to be factored, you factor it by taking its > gcd with a function I call r c(v), where: r c(v) = 2((D+1)v^2 - 2f 1*v + f 1^2) and f 1 is a factor of D-1, so with Fermat numbers, it is always just > 2 raised to some natural number power, where you find rational v, such > that v is in the following range: (f 1 - sqrt(f 1^2 - [f 1^2 - D/2](D+1)))/(D+1) < v < (f 1 + sqrt(f 1^2 > - [f 1^2 - D/2](D+1)))/(D+1) and r c(v) is an integer, where if that range gives an integer v, then > you're done, as you just plug that into r c(v), and you're guaranteed > have a factorization of D, from the gcd. If no integers are available for v, not to worry! Turns out a > rational solution MUST exist if there is rational range at all, and > it's denominator is, 2. Yup. 2. So like 1/2 or -1/2 will probably pop up a lot. Ok, so one of you code jockeys can script that up and give it a whirl > against Fermat numbers. When you see that it works, break some records. It will be screamingly fast. Like nothing you've ever seen. The > records should be easily within reach, within minutes. James Harris Well, silly me. I thought that a thread with a title like Factoring solution, test run would actually present the results of a test run of your factoring solution. No such luck, eh? Marcus. === Subject: Re: Factoring solution test run, Fermat primes [curious george, to JSH] > now that the factoring problem is solved, you may want to tackle the > Riemann hypothesis [David C. Ullrich] > He's already done that. I forget whether his prime counting function > shows that RH is almost certainly false or almost certainly true > but it's one or the other. He strengthed his claim to it's false, period. Why is it false? He never gave a reason, not even one based on completeing the square one or more times ;-) The /real/ reason he concluded RH is false appears to be that he /believes/ mathematicians believe RH is true -- and since academics are all lying scum, QED. > The rest of us were boggled how this could follow from an old > _algorithm_ for _computing_ pi(n). Shows how much we know. It supposedly follows from his partial difference equation gibberish. In hindsight, at least that was a refreshing break from the current endless gibberish about Pell's equation ;-) === Subject: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) and hey, share the wealth, versus going after the next Fermat prime-- > if it exists--on my own. As for pseudo-code, the algorithm is trivially easy. Given D = 2^k + 1, you have that D-1 = 2^k, so f 1 = 1, or f 1 = 2^c, > where c is a natural number up to k potentially, but you will not have > rational solutions that far up. Then you just check the range of possible rational v's with: (f 1 - sqrt(f 1^2 - [f 1^2 - D/2](D+1)))/(D+1) < v < (f 1 + sqrt(f 1^2 > - [f 1^2 - D/2](D+1)))/(D+1) > There's an asymptotic limit in these formulas as D->oo, which gives -1/sqrt(2) < v < 1/sqrt(2) at most. What do you think of that? See below for my investigation into using the algorithm to factor numbers, and code. > where you loop through every f 1 for which you have rational > solutions. Notice that once f 1 > sqrt(D/2) you have no more rational > solutions. For each range of possible solutions you look for integer v's within > that range, and for EACH of them, you will have a non-trivial > factorization of D, from r c(v), where: r c(v) = 2((D+1)v^2 - 2f 1*v + f 1^2) (you can actually leave off that factor of 2 of course) as the gcd of r c(v) and D will give you a non-trivial factor! Easy > as pie. If no integer solutions for v are available, then you use the > fractional one that must be available where the denominator of v is > 2. So, for instance, -1/2 could be a solution. Only fractions with 2 > itself as the denominator need be checked. The algorithm will give you each non-trivial factorization available > as you loop through possible f's. > I gave it a try. With the asymptotic limit, and this requirement that v need to be a integer or half integer, there are at most THREE possibilities for v: -1/2, 0, and 1/2. I tried D = 9. No joy. Other D seem to work, such as D = 65. However, NO actual Fermat number (i.e. k = power of two) seems to take, e.g. D = 4294967297 does not seem to factor. > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of 65537. Which happens to be a Fermat number itself. It seems that when it does yield factors, the first one it spits out is always a Fermat number, so apparently the number must have a Fermat-number factor in order for the algorithm to crack it. It does not appear to be able to factor any actual Fermat composites. I can't, for example, get D = 4294967297 to budge with your algorithm. It also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor criterion does not appear to be sufficient, although it sure appears to be necessary. But if your algorithm really does work, then it would seem I have made a mistake somewhere, since I should therefore be able to factor 4294967297. If so, what is my mistake? (Code at the bottom) > As you loop through the 4049, the algorithm will spit out any non- > trivial factors of 2^4048+1. > Well it did, it spat out 65537 for one of the factors. But it doesn't seem to work for other D and it doesn't seem to work for Fermat-number D. It can even factor D = 2^65535 + 1 -- vomiting up quite a few factors, in fact (although not all of them are primes) -- but 2^65536 + 1 fails to fall to this algorithm... And it is those real live Fermat numbers that we want to factor. > If it gives you none then that is a prime number. > Seems false according to my tests. 4294967297 is not a prime number. I came up with the following PARI/GP code: -- rc(v, f1, f2, D) = 2*((D+1)*v^2 - 2*f1*v + f1^2); k = 32; D = 2^k + 1; for(c=1,k/2, f1 = 2^c; f2 = (D-1)/f1; for(vmult=0,2, v = -1/2 + (vmult/2); g = gcd(rc(v, f1, f2, D), D); if((g != 1) && (g != D), print(g); break(2);); ); ); -- rc is just your function r c(v), D is the number to be factored, k is the exponent raising 2, f1 and f2 are 2 factors of D-1, such that D-1 = f1*f2, and the innermost loop just loops through the 3 possible v-values of -1/2, 0, and 1/2 and checks if gcd(r c(v), D) is not 1 or D. If it isn't, it spits it out and stops looping. You can remove the break to allow it to find more factors. Not all of them are necessarily prime. Note that for this D-value -- a real live Fermat number -- namely 4294967297, the algorithm fails to find any factors. Because there's only at *most* 3 possibilities for v I don't bother trying to eliminate any using the range formula, as there's so few to try, you know... it just adds an extra complication that isn't necessary for a first test. But all integer/ half- integer v in that range surely will be tested. If I've made a mistake in any of the above, by all means tell me. Are there more values for v to test? If so, what are they? === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) [JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. So did you? It's the only way you can ever be convinced that you're wrong -- and something any sane person would have tried at the start. So one of two things will happen, after you find your code doesn't work and can't be repaired: (1) you'll pretend you never made this promise, and continue ranting like a lunatic hoping no one will notice; or, (2) you'll start deleting all your posts on this topic, and never mention it again. Class act either way ;-) === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) [JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself > later today, and end this nonsense. [Tim Peters] > So did you? It's the only way you can ever be convinced that you're > wrong -- and something any sane person would have tried at the > start. [JSH] > Just getting started. Uh huh. Seems to me you're actually spending your time now ranting more on Usenet. Or do you code and rant at the same time? > So one of two things will happen, after you find your code doesn't > work and can't be repaired: (1) you'll pretend you never made this > promise, and continue ranting like a lunatic hoping no one will > notice; or, (2) you'll start deleting all your posts on this topic, > and never mention it again. > I worked on the proof first. Next I focused on the algorithm. Now I'm working on test code. Methodical process. Uh huh. > Class act either way ;-) > And your mocking is adult behavior? Compared to your behavior, absolutely. I'm mocking you /now/, you see. In my original post, I was simply predicting what would happen next. And, unlike you, I won't delete my post no matter what happens next -- or pretend I never posted it. That's what adults do, Jimmy: they accept the consequences of their actions. Leaves you out, damn near every time. > More and more I'm fascinated by how many of you are obsessed now with > trying to psych me out. There's no need to psych you out: write your code! It's long overdue, and is all that's needed to end this endlessly imbecilic mountain of threads. > Story here is, about a month ago I finally focused on this dual > factorization with Pell's Equation. After all kinds of arguing over > equations, I've settled both theory and implementation, and am ready > to code. You, on the other hand, are mocking me. You call that a class act? spend your time coding instead. === Subject: Re: Test run results [JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. So did you? It's the only way you can ever be convinced that you're wrong >-- and something any sane person would have tried at the start. So one of two things will happen, after you find your code doesn't work and >can't be repaired: (1) you'll pretend you never made this promise, and >continue ranting like a lunatic hoping no one will notice; or, (2) you'll >start deleting all your posts on this topic, and never mention it again. Class act either way ;-) This is a simple program that compresses any file - even random data - at a 1000:1 ratio, using about 1K of pure assembly language. The code is almost complete; I just have to fix one last bug (for some reason the decompression module outputs all zeros instead of the input file) but I am confident that I will be able to fix that one last bug any time now, and put all the other compression algorithms out of business. It also (in the same 1K!) correctly identifies and deletes This module also has a minor bug (for some weird reason it on the brink of fixing that one last bug. I have been told that the above description is enough for anyone to duplicate my work up to the point where I have it, so someone else may very well have fixed those bugs already and emailed me the result. I hope it gets past my -- Guy Macon === Subject: Re: Test run results >[JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. >So did you? It's the only way you can ever be convinced that you're wrong >-- and something any sane person would have tried at the start. >So one of two things will happen, after you find your code doesn't work and >can't be repaired: (1) you'll pretend you never made this promise, and >continue ranting like a lunatic hoping no one will notice; or, (2) you'll >start deleting all your posts on this topic, and never mention it again. >Class act either way ;-) This is a simple program that compresses any file - even random > data - at a 1000:1 ratio, using about 1K of pure assembly language. The code is almost complete; I just have to fix one last bug > (for some reason the decompression module outputs all zeros > instead of the input file) but I am confident that I will be > able to fix that one last bug any time now, and put all the > other compression algorithms out of business. It also (in the same 1K!) correctly identifies and deletes > This module also has a minor bug (for some weird reason it > on the brink of fixing that one last bug. I have been told that the above description is enough for > anyone to duplicate my work up to the point where I have > it, so someone else may very well have fixed those bugs > already and emailed me the result. I hope it gets past my Compress this! /dev/zero. -- Michael Press === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009020407 Iceweasel/3.0.6 (Debian-3.0.6-1),gzip(gfe),gzip(gfe) I gave it a try. With the asymptotic limit, and this requirement that > v need to be a integer or half integer, there are at most THREE > possibilities > for v: -1/2, 0, and 1/2. That doesn't sound right. I'll need to look at that later. > Ah, so there ARE more choices for v. That must be why it won't factor 4294967297. What are they? How many are they? > I tried D = 9. No joy. Other D seem to work, such as D = 65. However, It won't factor a square. But that's not a true issue. > Fine, but what about... > NO actual Fermat number (i.e. k = power of two) seems to take, e.g. > D = 4294967297 does not seem to factor. That can't be right. > that? > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of > 65537. Which happens to be a Fermat number itself. It seems that when > it does yield factors, the first one it spits out is always a Fermat > number, > so apparently the number must have a Fermat-number factor in order for > the algorithm to crack it. You're probably throwing away needed values. Did you use f 1 = 1? > Yes. Did I miss a v? If it's supposed to be some v with other denominator then there are an *infinite* number of those. Which ones should I try? > It does not appear to be able to factor any actual Fermat composites. > I > can't, for example, get D = 4294967297 to budge with your algorithm. > It > also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor It can't handle squares. > So why can't it handle 4294967297s either? Or for that matter, any true Fermat composite (i.e. composite 2^k + 1 where k is a power of 2 )? > criterion does not appear to be sufficient, although it sure appears > to be > necessary. > But if your algorithm really does work, then it would seem I have made > a mistake somewhere, since I should therefore be able to factor > 4294967297. > If so, what is my mistake? (Code at the bottom) I'm less interested in checking your mistakes than in coding it > myself. > Let's see that code, okay? > You went on about squares as if it were a dream come true that the > algorithm can't factor 9. But that's stupid. Who cares if an algorithm can't factor a square? > You just take the square root. > Sure. But now you're focusing so much on 9 and not focusing on... 4294967297. > And your cohorts are running wild on the newsgroups making negative > postings. I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. > If there's something I've missed it's because you didn't make it clear. Like you didn't make the bit clear about factoring squares. Is there perhaps also something else you're not making clear that explains the trouble with 4294967297? === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) I gave it a try. With the asymptotic limit, and this requirement that > v need to be a integer or half integer, there are at most THREE > possibilities > for v: -1/2, 0, and 1/2. > That doesn't sound right. I'll need to look at that later. Ah, so there ARE more choices for v. That must be why it won't > factor 4294967297. What are they? How many are they? > I tried D = 9. No joy. Other D seem to work, such as D = 65. However, > It won't factor a square. But that's not a true issue. Fine, but what about... > NO actual Fermat number (i.e. k = power of two) seems to take, e.g. > D = 4294967297 does not seem to factor. > That can't be right. that? > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of > 65537. Which happens to be a Fermat number itself. It seems that when > it does yield factors, the first one it spits out is always a Fermat > number, > so apparently the number must have a Fermat-number factor in order for > the algorithm to crack it. > You're probably throwing away needed values. Did you use f 1 = 1? Yes. Did I miss a v? If it's supposed to be some v with other denominator > then there > are an *infinite* number of those. Which ones should I try? > It does not appear to be able to factor any actual Fermat composites. > I > can't, for example, get D = 4294967297 to budge with your algorithm. > It > also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor > It can't handle squares. So why can't it handle 4294967297s either? Or for that matter, any > true Fermat composite (i.e. composite 2^k + 1 where k is a power of > 2 )? > criterion does not appear to be sufficient, although it sure appears > to be > necessary. > But if your algorithm really does work, then it would seem I have made > a mistake somewhere, since I should therefore be able to factor > 4294967297. > If so, what is my mistake? (Code at the bottom) > I'm less interested in checking your mistakes than in coding it > myself. Let's see that code, okay? > You went on about squares as if it were a dream come true that the > algorithm can't factor 9. > But that's stupid. Who cares if an algorithm can't factor a square? > You just take the square root. Sure. But now you're focusing so much on 9 and not focusing on... > 4294967297. > And your cohorts are running wild on the newsgroups making negative > postings. > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. If there's something I've missed it's because you didn't > make it clear. Like you didn't make the bit clear about factoring > squares. > Is there perhaps also something else you're not making clear that > explains the trouble with 4294967297? Hmm. It seems that v = -1/5 will work, if we use the NUMERATOR of the resulting RATIONAL r for our gcd, but now it seems there could be an infinite number of choices possible for v... === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > I have it coded. It works fine. Post the code so that folks can try it. -- Science is a differential equation. Religion is a boundary condition. --Alan Turing === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. So how many operations (either on average or worst case) are required to factor numbers on the order of 2^29? You could count each arithmetic operation, and since the total number of operations is less than 2^29, these counters would fit conveniently into 32-bit integers. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) <49BF6F40.9FEBCB4F@tesco.net So how many operations (either on average or worst case) are > required to factor numbers on the order of 2^29? Using the most recent version he has put up on the web as of posting time: 2^29+1 takes only 429 checkGCD calls finding the factor 3, but fails to find the small prime factor 59. 2^21+1 is rather slower: it takes 31757 checkGCD operations but at least gets all factors 3^2, 43, and 5919. 2^16+1 is asserted to be prime after 3606 checkGCD operations. It looks quite a bit slower than trial division, and less reliable. - Tim === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > Using the most recent version he has put up on the web as of posting > time: 2^29+1 takes only 429 checkGCD calls finding the factor 3, but > fails to find the small prime factor 59. 2^21+1 is rather slower: it takes 31757 checkGCD operations but at > least gets all factors 3^2, 43, and 5919. 2^16+1 is asserted to be prime after 3606 checkGCD operations. > It looks quite a bit slower than trial division, and less reliable. > - Tim This could be chalked up to 1 of 3 things, the language used (this is a timing reference not a reference to checkGCD operations as different languages will process the data at varying levels of efficiency), poor algorithm design (my opinion from what you posted), and the fact that it's not a final release. Going by your post Tim, it seems that James has things a little backwards. It is the smaller numbers that should be taking less calls to the checkGCD, not the other way around. This is evident by the fact that 2^29+1 only takes 429 checkGCD calls, and 2^21+1 taking 31757. It should scale with the size of the number, the bigger the number the more calls to the checkGCD. If it can't find every factor of every prime in the test data it's broken. Simple as that. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > I posted it on comp.theory and sci.physics, where yes, I had code > posted last night, which was severely flawed, so I started a new > thread, with very much cleaned up code, which also, yup, has the > updated factoring algorithm. I talk about having solve the factoring problem and having a > mathematical proof, but also talk about implementation being a > different issue. > In this case, the underlying mathematical proof has not changed, but > in trying to get a working algorithm, I've been having to make a lot > of changes to the implementation aspect. Specifically the > mathematical proof uses: x = r(v)/t(v) where r(v) and t(v) are coprime integers with a rational v. But I had problems getting them coprime, and found out I couldn't, So there was an addendum to handle a factor of that target composite D > that attaches itself to the only r(v) and t(v) I could get. THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. Wow. What a rush. > James Harris Any coder who is worth anything (there are many here) will tell you that there is absolutely no such thing as code perfect. Just because you can't find a fault, doesn't mean they aren't there waiting for someone else to can't break it, does not mean someone else wont be able to either now or sometime in the future. Even proof of concept code for the factoring problem should be able to factor anything, although quite sloppily and with mediocre efficiency, because it's not a finished product. Save the polishing for something you are going to release publicly and intended for everyone, even the layman to use (the general populace don't care how a program is made or how it does what it does as long as it does so cleanly and efficiently). Since I rarely pay any attention to your threads (as most people here rarely pay any attention to mine) I can only guess at what kind of primes you are trying to factor, but it doesn't matter. Even proof of concept code should be able to factor every known prime within the subset of primes you are trying to factor. Here is a tip, start with the largest prime from the subset you are trying to factor. By subset I am referring to Mersenne primes, Fermat primes etc. When you have an agorithm that can factor that efficiently and cleanly, every lesser prime will be a literal cake walk because they are smaller and therefore, generally speaking, use less resources in the factoring. Of course, as new primes of your chosen subset are discovered, you may need to tweak your code a little. Here is a hint, use a language that was designed with intensive numerical computations in mind, FORTRAN is the first one that springs up, or use something similar. Better yet, write it as close to machine code as you can, this will give you maximum efficiency. At present, your task is not even half finished. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) ... I can only guess at what kind of primes you are > trying to factor, Even Harris can factor primes. -- Science is a differential equation. Religion is a boundary condition. --Alan Turing === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > Even Harris can factor primes. That may be so, but different primes have different equations, hence the not knowing what kind of prime, is it Mersenne, Fermat, or one a host of others. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) <33%vl.29297$cu.23346@news-server.bigpond.net.au> <49C0BFEB.3D40D4E1@tesco.net> posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > Even Harris can factor primes. That may be so, but different primes have different equations, hence the not > knowing what kind of prime, is it Mersenne, Fermat, or one a host of others. I'm a bit confused here. Do you mean Primes have equations, or Primes have factors ? Brian Chandler === Subject: Re: Test run results sha1:UpsU5XR5kx+SsGE+V7QHoXZs6uM= > THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. Did you purposely build this limit into the program, or did you implement the algorithm as written and discover that the program fails on larger numbers? Why does it fail? Is it something to do with the programming language or the algorithm? It just seems odd to me that your proof of concept has this explicit limitation. -- I don't want to wine and dine and date you once or twice. I want to hold you now. I just want to spend the night. You tell me a better plan. Baby, I'm not a patient man. -- Jimmy Lafave, the romantic troubadour. === Subject: Re: Test run results [...] > I have it coded. It works fine. I'm going to clean up the code some and figure out what to do next. People have been challenging you to factor particular numbers for a week or two, you now have a factoring program (or are presumably close to one---perhaps it's currently focused on Fermat numbers), and you don't know what to do next? === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat ... > It's a very easy algorithm to code. =A0It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > > Turns out that is one number it seems to work on, yielding a factor of > 65537. Ah, but 2^4048 + 1 is *not* a Fermat number. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Pythagorean Quadruples in a 3d grid x^2 + y^2 + z^2 = h^2 Where x,y,z,h are integers. A Pythagorean Quadruple I believe can best be represented as a 3d map of a cubical grid where x,y,z and -x,-y,-z are represented as integer distance points within the cubical grid and (h) the distance back to the origin at the end point of (z) or (-z). A simple example would be the value of a set x,y,z where x=3,y=4,z=12 and h=13 3^2+ 4^2+ 12^2 = 13^2 Now (h) would = distance back to x=0,y=0,z=0 (origin) from the end point of value (z)or (-z) in a Cartesian coordinate 3d grid. So (h) hypotenuse = 13 Now if you bring in the next set with there own discrete values -- -x,-y,-z with -x=-4,-y=-12,-z=4. Now the values for the 2 sets are -- (x=3,y=4,z=12),(-x=-4,-y=-12,-z=-8) and then summing = 3+-4 = -1 = -x 4+-12 = -8 = -y 12+-8 = 4 = -z x^2 = 1 y^2 = 64 z^2 = 16 h^2 = 81 so h = 9 from end point of -z back to origin of x=0,y=0,z=0. Here is one type of Pythagorean quadruples. ------------x------y-----z------h or z+1 3* 4= 12---3^2 + 4^2 + 12^2 = 13^2 5* 6= 30---5^2 + 6^2 + 30^2 = 31^2 7* 8= 56---7^2 + 8^2 + 56^2 = 57^2 9* 10= 90---9^2 +10^2 + 90^2 = 91^2 11*12=132---11^2 +12^2 +132^2 =133^2 13*14=182---13^2 +14^2 +182^2 =183^2 15*16=240---15^2 +16^2 +240^2 =241^2 17*18 etc... --->oo Where these (h) values put in a sequence becomes a monic polynomial of degree 2. 13,31,57,91,133,183,241,... -------------------------------------------------- Another interesting calc. of x^2 + y^2 + z^2 = h^2 Where h^2 becomes closer and closer to an integer. The Fibonacci sequence -- 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987 Take the first sets of the sequence starting with (3) and (h) will get closer and closer to an integer. Below (h) is rounded up on the first set and rounded down on second set rounded up on third and so on. x,y,z,h = error of sqrt(h^2) rounded to integer. ------------------- 3,5,8,10 = -0.100505063... 5,8,13,16 = 0.062378404... 8,13,21,26 = -0.038490028... 13,21,34,42 = 0.023802778... 21,34,55,70 = -0.014707472... 34,55,89,110 = 0.009090533... 55,89,144,178 = -0.005618066... 89,144,233,288 = 0.003472201... 144,233,377,466 = -0.002145927... 233,377,610,754 = 0.001326258... .. These will converge slowly to integer (h) Dan === Subject: Re: Pythagorean Quadruples in a 3d grid > x^2 + y^2 + z^2 = h^2 > Where x,y,z,h are integers. > ... > where x,y,z and -x,-y,-z >of course you can restrict to x,y,z > 0 Yes, but when working with 3d objects I find it more interesting to use both sets +- especially when you are applying new values for each set (x,y,z) and then alternating signs between sets. eg. A Collatz sequence, which I know can not apply to a Cartesian coordinate system, but as an interesting exercise to show my method in 3d using only (level length)==0(mod 3) sequences. 3n+1 = 14,7,22,11, 34,17,52,26,13,40, 20,10, 5,16, 8, 4, 2, 1 Level = 18 ------------------------------------------------------ 3d---- = 14,7,22, 3,-27, 5,55,-1,18,15,-21, 8,20,-5,16,16, -7,15 sqrt(530) =23.021728 triangulation to origin derived from x=16,y=-7,z=15.(last values of x,y,z) One of the observations that happen in some sequences -- Crossover points from 3d abs(-5) to 3n+1 = (16) and (16) in 3d to (8) in 3n+1. > A simple example ... x=3,y=4,z=12 and h=13 First of all, we can restrict to h odd, as >(2h)^2 = x^2 + y^2 + z^2 has only solutions with x,y,z >all even, >proof : modulo 4, squares are 0 or 1. >hence x^2 + y^2 + z^2 is 0 mod 4 only when all three >are 0 modulo 4. >Hence h^2 is also a sum of three squares : >h^2 = (x/2)^2 + (y/2)^2 + (z/2)^2. >A theorem from Gauss says that all numbers not of the >form >(4^n)(8k+7) are sum of three squares, hence all squares >are sum >of three squares. (Modulo 8, a square is either 0, 1 or >4) >But this is useless here as it includes null squares. >It seems that all h^2 not of the form 4^n or 25*4^n are >sum of >three _non_null_ squares. >example : h = 123 h^2 = 15129 = >121^2 + 22^2 + 2^2 >110^2 + 55^2 + 2^2 >122^2 + 14^2 + 7^2 >118^2 + 34^2 + 7^2 >106^2 + 62^2 + 7^2 >98^2 + 74^2 + 7^2 >117^2 + 36^2 + 12^2 >99^2 + 72^2 + 12^2 >... (27 solutions) > Here is one type of Pythagorean quadruples. > ------------x------y-----z------h or z+1 > 3* 4= 12---3^2 + 4^2 + 12^2 = 13^2 >n^2 + (n+1)^2 + (n(n+1))^2 = (n^2 + n + 1)^2 Ok! >and yes, n^2 + n + 1 = n(n+1) + 1 >But your set is widely incomplete as it depends on only >one parameter. Yes, as I stated it was one type. >According to Mathworld : x = 2mp >y = 2np >z = p^2 - (m^2 + n^2) >h = p^2 + (m^2 + n^2) >where m, n and p are any integers (Mordell 1969). >This does not, however, generate all solutions. >For instance, it excludes (36, 8, 3, 37). >Wikipedia claims : >The set of all primitive Pythagorean quadruples, i.e. >those for >which gcd(x,y,z,h) = 1, is parameterized by >x = m^2 + n^2 - p^2 - q^2 >y = 2(mp + nq) >z = 2(np - mq) >h = m^2 + n^2 + p^2 + q^2 >m,n,p,q integer (and gcd(m,n,p,q)=1 and some other >conditions about >parity of m,n,p,q to yield gcd(x,y,z,h) = 1) >[R.D. Carmichael, Diophantine Analysis, 1915] Yes, it appears this has many more interesting properties then the Pythagorean triples. >Strange that Mordell in 1969 gives only a partial set, >fifty years >AFTER Carmichael had given a full set ! > ... > Where h^2 becomes closer and closer to an integer. > 3,5,8,10 = -0.100505063... > ... > 233,377,610,754 = 0.001326258... > .. > These will converge slowly to integer (h) >An infinite number, if we even may define such an >horror, is >however not an integer. That's why I always use --->oo (approaching infinity) when referring to any Iterative process that can ---->oo. -- >Philippe Ch., mail : chephip+news@free.fr Dan === Subject: Re: Pythagorean Quadruples in a 3d grid > x^2 + y^2 + z^2 = h^2 > Where x,y,z,h are integers. > ... > where x,y,z and -x,-y,-z of course you can restrict to x,y,z > 0 A simple example ... x=3,y=4,z=12 and h=13 > First of all, we can restrict to h odd, as (2h)^2 = x^2 + y^2 + z^2 has only solutions with x,y,z all even, proof : modulo 4, squares are 0 or 1. hence x^2 + y^2 + z^2 is 0 mod 4 only when all three are 0 modulo 4. Hence h^2 is also a sum of three squares : h^2 = (x/2)^2 + (y/2)^2 + (z/2)^2. A theorem from Gauss says that all numbers not of the form (4^n)(8k+7) are sum of three squares, hence all squares are sum of three squares. (Modulo 8, a square is either 0, 1 or 4) But this is useless here as it includes null squares. It seems that all h^2 not of the form 4^n or 25*4^n are sum of three _non_null_ squares. example : h = 123 h^2 = 15129 = 121^2 + 22^2 + 2^2 110^2 + 55^2 + 2^2 122^2 + 14^2 + 7^2 118^2 + 34^2 + 7^2 106^2 + 62^2 + 7^2 98^2 + 74^2 + 7^2 117^2 + 36^2 + 12^2 99^2 + 72^2 + 12^2 ... (27 solutions) > Here is one type of Pythagorean quadruples. ------------x------y-----z------h or z+1 > 3* 4= 12---3^2 + 4^2 + 12^2 = 13^2 n^2 + (n+1)^2 + (n(n+1))^2 = (n^2 + n + 1)^2 and yes, n^2 + n + 1 = n(n+1) + 1 But your set is widely incomplete as it depends on only one parameter. According to Mathworld : A set of Pythagorean quadruples is given by x = 2mp y = 2np z = p^2 - (m^2 + n^2) h = p^2 + (m^2 + n^2) where m, n and p are any integers (Mordell 1969). This does not, however, generate all solutions. For instance, it excludes (36, 8, 3, 37). Wikipedia claims : The set of all primitive Pythagorean quadruples, i.e. those for which gcd(x,y,z,h) = 1, is parameterized by x = m^2 + n^2 - p^2 - q^2 y = 2(mp + nq) z = 2(np - mq) h = m^2 + n^2 + p^2 + q^2 m,n,p,q integer (and gcd(m,n,p,q)=1 and some other conditions about parity of m,n,p,q to yield gcd(x,y,z,h) = 1) [R.D. Carmichael, Diophantine Analysis, 1915] Strange that Mordell in 1969 gives only a partial set, fifty years AFTER Carmichael had given a full set ! > ... > Where h^2 becomes closer and closer to an integer. > 3,5,8,10 = -0.100505063... > ... > 233,377,610,754 = 0.001326258... > .. > These will converge slowly to integer (h) An infinite number, if we even may define such an horror, is however not an integer. -- Philippe Ch., mail : chephip+news@free.fr site : http://mathafou.free.fr/ (recreational mathematics) === Subject: Re: Pythagorean Quadruples in a 3d grid > According to Mathworld : > x = 2mp > y = 2np > z = p^2 - (m^2 + n^2) > h = p^2 + (m^2 + n^2) > where m, n and p are any integers (Mordell 1969). > This does not, however, generate all solutions. > For instance, it excludes (36, 8, 3, 37). Wikipedia claims : > The set of all primitive Pythagorean quadruples, i.e. those for > which gcd(x,y,z,h) = 1, is parameterized by > x = m^2 + n^2 - p^2 - q^2 > y = 2(mp + nq) > z = 2(np - mq) > h = m^2 + n^2 + p^2 + q^2 > m,n,p,q integer (and gcd(m,n,p,q)=1 and some other conditions about > parity of m,n,p,q to yield gcd(x,y,z,h) = 1) > [R.D. Carmichael, Diophantine Analysis, 1915] Strange that Mordell in 1969 gives only a partial set, fifty years > AFTER Carmichael had given a full set ! Mordell cites Carmichael and gives Carmichael's solution together with a derivation he prefers to Carmichael's. Mordell gives the partial set as follows: The general solution of x^2 + y^2 + z^2 = h^2, gcd(x, y, z) = 1, h > 0, is given by d x = 2 m p, d y = 2 n p, d z = p^2 - m^2 - n^2, d h = p^2 + m^2 + n^2, where gcd(m, n, p) = 1, and d > 0 is taken so that gcd(x, y, z) = 1. It seems Mathworld missed the d parameter. Your (36, 8, 3, 37) comes from d = 5, m = 9, n = 2, p = 10. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Pythagorean Quadruples in a 3d grid x^2 + y^2 + z^2 = h^2 Where x,y,z,h are integers. A Pythagorean Quadruple I believe can best be represented as a 3d map of a cubical grid where x,y,z and -x,-y,-z are represented as integer distance points within the cubical grid and (h) the distance back to the origin at the end point of (z) or (-z). A simple example would be the value of a set x,y,z where x=3,y=4,z=12 and h=13 3^2+ 4^2+ 12^2 = 13^2 Now (h) would = distance back to x=0,y=0,z=0 (origin) from the end point of value (z)or (-z) in a Cartesian coordinate 3d grid. So (h) hypotenuse = 13 Now if you bring in the next set with there own discrete values -- -x,-y,-z with -x=-4,-y=-12,-z=4. Now the values for the 2 sets are -- (x=3,y=4,z=12),(-x=-4,-y=-12,-z=-8) and then summing = 3+-4 = -1 = -x 4+-12 = -8 = -y 12+-8 = 4 = -z x^2 = 1 y^2 = 64 z^2 = 16 h^2 = 81 so h = 9 from end point of -z back to origin of x=0,y=0,z=0. Here is one type of Pythagorean quadruples. ------------x------y-----z------h or z+1 3* 4= 12---3^2 + 4^2 + 12^2 = 13^2 5* 6= 30---5^2 + 6^2 + 30^2 = 31^2 7* 8= 56---7^2 + 8^2 + 56^2 = 57^2 9* 10= 90---9^2 +10^2 + 90^2 = 91^2 11*12=132---11^2 +12^2 +132^2 =133^2 13*14=182---13^2 +14^2 +182^2 =183^2 15*16=240---15^2 +16^2 +240^2 =241^2 17*18 etc... --->oo Where these (h) values put in a sequence becomes a monic polynomial of degree 2. 13,31,57,91,133,183,241,... -------------------------------------------------- Another interesting calc. of x^2 + y^2 + z^2 = h^2 Where h^2 becomes closer and closer to an integer. The Fibonacci sequence -- 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987 Take the first sets of the sequence starting with (3) and (h) will get closer and closer to an integer. Below (h) is rounded up on the first set and rounded down on second set rounded up on third and so on. x,y,z,h = error of sqrt(h^2) rounded to integer. ------------------- 3,5,8,10 = -0.100505063... 5,8,13,16 = 0.062378404... 8,13,21,26 = -0.038490028... 13,21,34,42 = 0.023802778... 21,34,55,70 = -0.014707472... 34,55,89,110 = 0.009090533... 55,89,144,178 = -0.005618066... 89,144,233,288 = 0.003472201... 144,233,377,466 = -0.002145927... 233,377,610,754 = 0.001326258... .. These will converge slowly to integer (h) Dan === Subject: Re: 40% in remedial math posting-account=9tP_uwoAAAD1vfWhLdsNH4ImDfm7cP1K 4337.29; Windows NT 5.1; SV1; GTB5; .NET CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) spider-mtc-tc09.proxy.aol.com[400C7049] (Prism/1.2.1), HTTP/1.1 cache-mtc-ae12.proxy.aol.com[400C7510] (Traffic-Server/6.1.5 [uScM]) > http://www.courant.com/news/education/hc-higher-admission-standards-0... Connecticut State Universities Raising Admission Standards > By GRACE E. MERRITT, The Hartford Courant March 13, 2009 Concerned that many freshmen arrive on campus poorly prepared for > college classes, Connecticut State University System trustees voted > Thursday to raise academic admission standards for students starting > in 2015. Currently four in every 10 freshmen at Central, Eastern, Southern and > Western Connecticut state universities must take a remedial math class > and 25 percent must take remedial English once they arrive on campus > before they are ready for college-level work, university officials > said. If you've not been taught Algebra II, you are not going to be ready > for college-level math, explained trustee John A. Doyle, chairman of > the academic affairs committee. The new admissions standards are more specific and demanding. Freshmen > will be required to have taken four years of mathematics rather than > the current minimum of three. They also will have to have taken three > years of science, rather than the current two-course requirement, and > an English composition class, among other changes. The higher admissions standards won't kick in until 2015 at the > earliest, to give high schools enough time to make sure they are > providing the necessary preparatory courses. Essentially, the new standards will affect today's sixth-graders, who > will be freshmen in 2015, said Bernard Kavaler, CSU's assistant vice > chancellor for public affairs. The timing dovetails with a bill that would raise high school > graduation standards statewide. The bill is based on a plan developed > by the state Department of Education for middle and high school > students and adopted by the State Board of Education in October. This is really part of an ongoing effort across the state to work > with educators at every level to set new standards, Kavaler said. Western Connecticut State University has already started an innovative > program designed to better align area high schools with the college > curriculum. Since it started three years ago, the number of freshmen > in remedial classes has dropped dramatically, and retention rates have > improved, Kavaler said. The program is now being developed at the > other CSU campuses in collaboration with area school districts. By my experience and reading, if the figure is 40%, then the current college-level math courses in CT are at too low a level. A national study last year reported only 15% of 12-grade graduates able to enter a college-level math course. With about 60% going to higher education, that should result in about 75% remediation, which is close to the rate at the State university where I work. === Subject: Re: 40% in remedial math If you've not been taught Algebra II, you are not going to be ready > for college-level math, > In the State of Texas even if you HAVE been taught Algebra II you can still graduate from high school not knowing: (1) How to find the area of a rectangle (2) How to find the perimeter of a rectangle. (3) How to find the circumference of a circle. (4) How many inches are in a foot. (5) How many quarts in a gallon. (6) Not knowing basic multiplication/division. etc .. etc .. etc You see ... the students are given (MANDATED!) a formula chart and a calculator for the state mandated test .. the vast majority have a calculator in hand from the 9th grade forward. I've watched an Algebra II student use a calculator to multiply 9 x 0 ... when I inquired as to the reason he used a calculator ... I was just checking myself . This same student asked for a formula chart to find the area of a rectangle! Solving equations? Easy .. example ... (1/2)x=6, procedure. Convert the 1/2 to .5, using a calculator. Divide 6 by .5, using a calculator. When I asked why not just multiply both sides of the equation by 2 ... I don't know how to do that, we weren't taught that way. Oh, forgot to tell you ... this was A JUNIOR IN HIGH SCHOOL !!! Finally ... I was tutoring a student to pass the 11th grade TAKS test (a state mandated test in Texas) ... trying to give her some concept of volume I gave her a Stanley tape measure and asked her to calculate the approximate volume of a that could be used to ship a toaster that was on my cabinet ... she stood with tape measure in hand .. dumbfounded ... she couldn't read a tape measure! 40% ?? I don't doubt it at all. Oh, these examples were all middle to (very) upper socioeconomic class white students .. Jerry === Subject: Re: 40% in remedial math > If you've not been taught Algebra II, you are not going to be ready > for college-level math, >In the State of Texas even if you HAVE been taught Algebra II you can still >graduate from high school not knowing: >(1) How to find the area of a rectangle >(2) How to find the perimeter of a rectangle. >(3) How to find the circumference of a circle. >(4) How many inches are in a foot. >(5) How many quarts in a gallon. >(6) Not knowing basic multiplication/division. >etc .. etc .. etc >You see ... the students are given (MANDATED!) a formula chart and a >calculator for the state mandated test .. the vast majority have a >calculator in hand from the 9th grade forward. I've watched an Algebra II >student use a calculator to multiply 9 x 0 ... when I inquired as to the >reason he used a calculator ... I was just checking myself . On this one, I can agree. Understanding the properties of the number 0 is basic, as is 1. Not much more is. This >same student asked for a formula chart to find the area of a rectangle! If the student knows what variables mean, and what formulas mean, this is far more valuable than being able to do arithmetic. Facts and routines can be looked up; concepts cannot. >Solving equations? Easy .. example ... (1/2)x=6, procedure. >Convert the 1/2 to .5, using a calculator. >Divide 6 by .5, using a calculator. That there are simple or other methods of solution is not all that important. Being familiar with arithmetic, and being able to do it without aids, can be convenient, and can enable things to be done more quickly. But it is in no way basic for an understanding of mathematics. Nor does it lead to an understanding. The original new math, introduced in the schools about 50 years ago, started because a child of a mathematician showed a lack of understanding of numbers DESPITE being proficient in arithmetic. The new math failed because the teachers could not understand the concepts. I am rather proficient in arithmetic, well beyond what is expected, and I use it, possibly too often. Also, I understand mathematical concepts, and if you look in mathematical journals, you will see little use of arithmetic done by hand. I could have done all of the questions asked above in elementary school, but only had an intuitive idea of the methods; the facts were memorized. I did develop some intuitive ideas of the structure of the numbers, but did not really understand them until they were formally presented. They can, and should, be taught to young children; the ordinal approach is self-contained, and even the proofs are withing the abilities of a first grader. But I question the ability of the brainwashed teachers to do so. Do you understand the cardinal and ordinal structure of the integers? The important idea of proof by induction, which belongs very early, is often not taught to math majors, including prospective high school teachers. >When I asked why not just multiply both sides of the equation by 2 ... I >don't know how to do that, we weren't taught that way. Oh, forgot to tell >you ... this was A JUNIOR IN HIGH SCHOOL !!! Here is the essence of algebra in two sentences. A variable is a temporary name that can stand for anything. The same operation performed on equal entities yields equal results. Algebra, alas, is not taught that simple way. That junior in high school was taught that the way to solve ax=b was to compute b/a, and not to compute (1/a)*b, which is what you were pointing out. Especially on a test, do not expect a student to find the easy way to solve a problem. >Finally ... I was tutoring a student to pass the 11th grade TAKS test (a >state mandated test in Texas) ... trying to give her some concept of volume >I gave her a Stanley tape measure and asked her to calculate the approximate >volume of a that could be used to ship a toaster that was on my cabinet ... >she stood with tape measure in hand .. dumbfounded ... she couldn't read a >tape measure! Volume is a mathematical concept. Using a tape measure is not. >40% ?? I don't doubt it at all. >Oh, these examples were all middle to (very) upper socioeconomic class white >students .. >Jerry -- 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: 40% in remedial math >If you've not been taught Algebra II, you are not going to be ready >for college-level math, > >In the State of Texas even if you HAVE been taught Algebra II you can still >graduate from high school not knowing: >(1) How to find the area of a rectangle >(2) How to find the perimeter of a rectangle. >(3) How to find the circumference of a circle. >(4) How many inches are in a foot. >(5) How many quarts in a gallon. >(6) Not knowing basic multiplication/division. >etc .. etc .. etc >You see ... the students are given (MANDATED!) a formula chart and a >calculator for the state mandated test .. the vast majority have a >calculator in hand from the 9th grade forward. I've watched an Algebra II >student use a calculator to multiply 9 x 0 ... when I inquired as to the >reason he used a calculator ... I was just checking myself . > On this one, I can agree. Understanding the properties > of the number 0 is basic, as is 1. Not much more is. This > >same student asked for a formula chart to find the area of a rectangle! > If the student knows what variables mean, and what > formulas mean, this is far more valuable than being > able to do arithmetic. Facts and routines can be > looked up; concepts cannot. Hmmmm... what about times when a chart isn't readily available? I agree that complicated formulas should probably be looked up, but something as basic as the area of a rectangle? >Solving equations? Easy .. example ... (1/2)x=6, procedure. >Convert the 1/2 to .5, using a calculator. >Divide 6 by .5, using a calculator. > That there are simple or other methods of solution is > not all that important. Being familiar with arithmetic, > and being able to do it without aids, can be convenient, > and can enable things to be done more quickly. But it > is in no way basic for an understanding of mathematics. Nor does it lead to an understanding. The original new > math, introduced in the schools about 50 years ago, > started because a child of a mathematician showed a lack > of understanding of numbers DESPITE being proficient in > arithmetic. The new math failed because the teachers > could not understand the concepts. I am rather proficient in arithmetic, well beyond what > is expected, and I use it, possibly too often. Also, I > understand mathematical concepts, and if you look in > mathematical journals, you will see little use of > arithmetic done by hand. I could have done all of the questions asked above in > elementary school, but only had an intuitive idea of the > methods; the facts were memorized. I did develop some > intuitive ideas of the structure of the numbers, but did > not really understand them until they were formally > presented. They can, and should, be taught to young > children; the ordinal approach is self-contained, and > even the proofs are withing the abilities of a first > grader. But I question the ability of the brainwashed > teachers to do so. Do you understand the cardinal and ordinal structure of > the integers? The important idea of proof by induction, > which belongs very early, is often not taught to math > majors, including prospective high school teachers. >When I asked why not just multiply both sides of the equation by 2 ... I >don't know how to do that, we weren't taught that way. Oh, forgot to tell >you ... this was A JUNIOR IN HIGH SCHOOL !!! > Here is the essence of algebra in two sentences. A variable is a temporary name that can stand for anything. The same operation performed on equal entities > yields equal results. Algebra, alas, is not taught that simple way. That junior > in high school was taught that the way to solve ax=b was to > compute b/a, and not to compute (1/a)*b, which is what you > were pointing out. Especially on a test, do not expect a > student to find the easy way to solve a problem. >Finally ... I was tutoring a student to pass the 11th grade TAKS test (a >state mandated test in Texas) ... trying to give her some concept of volume >I gave her a Stanley tape measure and asked her to calculate the approximate >volume of a that could be used to ship a toaster that was on my cabinet ... >she stood with tape measure in hand .. dumbfounded ... she couldn't read a >tape measure! > Volume is a mathematical concept. Using a tape measure is not. Theory vs. practical application... I know a lot of people that have problems making measurements.... Martin >40% ?? I don't doubt it at all. >Oh, these examples were all middle to (very) upper socioeconomic class white >students .. >Jerry === Subject: Re: 40% in remedial math and the other 70% are even further behind. === Subject: Re: 40% in remedial math >and the other 70% are even further behind. There are three kinds of people in the world; those who can count, and those who can't. :-) -- 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: Neat way to save your money ? posting-account=ULT0ywkAAAASzIGeqF0RK092m5F5motI Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) It is to only get the certificates for the boy You play a part in it Are you still denying your role ? If there is a prize for the boy after your having torn his life into pieces Online Offline Then he already suggested your family use it on your own Instead of setting up a fake marriage that The boy has never been accepting If you can generate funds for people You certainly can generate one for your son/daughter You claimed to have wanted to learn best values But how many years have you been in this field ? How many values have you collected ? Did you ever find you improved on them ? You are not ignorant! Absolutely! You only ignored them! Thousands of words would never be able to compare with A single term! === Subject: Re: Remember the goal > My stated aim for years has been to end the academic system as it > currently exists worldwide, and I need your help in making my case. > And your failures in the face of mathematical proof represent that > help. spoof, not proof. I think our academic system is a medieval anachronism that is all > about feudalism, and it fails all the time now, so it has to be > revamped in a major way. still angry your HS Algebra teacher FLUNKED you ? And what I'm learning more and more is that money makes the > difference, so the simplest way to help the system is to remove the > money. Wrong, PRINT more money. Once academics know that being a professor provides no guarantees as > tenure is destroyed, and learn that failing to be a researcher means > you stop getting paid to do research, the non-functional ones among > you will leave. Why are you even thinking of this stuff?, there is no way you would ever be a professor, teacher, student, researcher or even connected to a College or University, period. It's that simple. simple math, for simpletons Before this story ends, quite a few tenured academics will find they > are no longer professors, as tenure is destroyed and I'll worry about > the legal battles later. But don't assume if you are tenured in any > academic field that you will remain in your position without results. Your stated threats on the internet will get you sued for sure now. The white collar welfare system of our modern academic world is about > to end. JSH = Blue collar ? YES ! Cleans the coolers at the Quickie Mart. THAT is one of my primary goals. THAT is moronic. A Fools Goal. > James Harris, minor troll === Subject: Re: JSH: another one bites the dust Considering negative f_1 values is useless, as you'd realize if you > were competent and thought about it for even five seconds. Then you're doing something wrong. Possibly even deliberately. Wow, you really are thick, aren't you? According to your latest posts, r_c(v) = 2(D v^2 + (v - f_1)^2). If you replace f_1 by -f_1, all you need to do is replace v by -v to get *exactly the same value*. So considering negative f_1 values is useless, because you get nothing that you didn't already get with positive values. Do you see now? - Tim === Subject: Re: JSH: another one bites the dust James Harris === Subject: Re: JSH: another one bites the dust >nincompoops Anybody below 60 use that word? nope, only Grandpa. Get off my lawn, you gol-durned whippersnappers! === Subject: Re: JSH: another one bites the dust sha1:8wPtIaZKX0j3w2RAVgMfxcb216c= nincompoops Anybody below 60 use that word? nope, only Grandpa. Your criticisms seem to have hit a low point. You don't have to respond to every JSH post, you know. If you can't think of anything to say, you could just let one or two slip by. -- It seems to me that in wartime Americans shouldn't be attacking each other in this way on a *worldwide* forum. Then again, I know I'm an American, but I have no way of knowing that you are, which would explain a lot. --James Harris, on why Yanks should accept his proof === Subject: Re: JSH: another one bites the dust > Moving on to the next phase where I've finished theory, worked out the > algorithm, so now I'm playing with code as I do implementation. Could you be so kind as to post the code when you've done? I've seen more than a few cases where someone's code does not match the algorithm they're trying to code... -- Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth === Subject: Re: JSH: another one bites the dust Has James finally cracked the case? Nope. d=119: > It works. r_c(v) = 84. t_c(v) = 35. > Note that James does not state v or f1. Let's find out why, working > backwards from r_c(v) = 84. > d-1 = 118 = 2 * 59, and 59 is prime, so the possible f1 are: > 1, 2, 59, 118 The variable f_1 can be negative. When I try -1, -2, -59 and -118 for f1 I get four more irrational solutions for r_c(v) = 84 (two of them not even real). -- Ben. === Subject: Re: JSH: another one bites the dust posting-account=uHBwhwoAAABsLfRIUf5ZY39ic50RzUuL Gecko/2009030422 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) > On Mar 16, 12:51pm, Tim Smith His method also works at d=21 (a number that gave his earlier methods > problems): > {21,1}{-0.613244,0.704153}{-(1/2),0,1/2}{15,2,11}{3,1,1} > {21,2}{-0.460198,0.642016}{0,1/2}{8,15}{1,3} > {21,4} non-real range > {21,5} non-real range > {21,10} non-real range > {21,20} non-real range > Has James finally cracked the case? Nope. d=119: > It works. r c(v) = 84. t c(v) = 35. > Note that James does not state v or f1. Let's find out why, working > backwards from r c(v) = 84. > d-1 = 118 = 2 * 59, and 59 is prime, so the possible f1 are: > 1, 2, 59, 118 The variable f 1 can be negative. I know there is a rational v because I have a mathematical proof that > for every rational solution of x and y, where x^2 - Dy^2 = 1 there are rational solutions for u and v. If you've eliminated the positive factor cases, then it must be a > negative one. Note that x = 12/5, y = 1/5 is a rational solution, so u and v must > exist as rationals that correspond to that solution, by mathematical > proof. James Harris I pointed out over a week ago that f 1 can be any non-zero rational as long as f 1*f 2 = D-1. Although in your outline of the proof you stated that f 1 had to be a positive integer factor of D-1 my reading of your proof never saw any reason why this should in fact be the case. Indeed by limiting f 1 in this way it was always possible that some D will not factor for the subset of f 1 available. Now you are asking for negative f 1. Great! Any reason why you cannot go the whole way and allow rationals as well as integers? === Subject: Re: JSH: another one bites the dust > His method also works at d=21 (a number that gave his earlier methods > problems): > {21,1}{-0.613244,0.704153}{-(1/2),0,1/2}{15,2,11}{3,1,1} > {21,2}{-0.460198,0.642016}{0,1/2}{8,15}{1,3} > {21,4} non-real range > {21,5} non-real range > {21,10} non-real range > {21,20} non-real range > Has James finally cracked the case? Nope. d=119: > It works. r_c(v) = 84. t_c(v) = 35. > Note that James does not state v or f1. Let's find out why, working > backwards from r_c(v) = 84. > d-1 = 118 = 2 * 59, and 59 is prime, so the possible f1 are: > 1, 2, 59, 118 The variable f_1 can be negative. Of course, but: f_1 = -1: No rational v solution. f_1 = -2: No rational solution. f_1 = -59: No real solution. f_1 = -118: No real solution. I know there is a rational v because I have a mathematical proof that > for every rational solution of x and y, where x^2 - Dy^2 = 1 there are rational solutions for u and v. If you've eliminated the positive factor cases, then it must be a > negative one. > Sure doesn't look that way, at least for your r_c(v). Rick === Subject: Re: JSH: another one bites the dust >There is a major campaign going on now to sway people against this >research which clearly is political, oh, and is about lying about the >result, Drama Queen. === Subject: Re: JSH: another one bites the dust Btw, get a newsreader and a decent Usenet service. Using Google Groups and solving all the Worlds security issues by Einsteinian levels of mathematics, well, I got to tell ya', it's pole opposite methodologies. And it makes you look like a moron. HTH -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust Btw, get a newsreader and a decent Usenet service. Using Google Groups and solving all the Worlds security issues by Einsteinian levels of mathematics, well, I got to tell ya', it's pole opposite methodologies. And it makes you look like a moron. HTH -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust Btw, get a newsreader and a decent Usenet service. Using Google Groups and solving all the Worlds security issues by Einsteinian levels of mathematics, well, I got to tell ya', it's pole opposite methodologies. And it makes you look like a moron. HTH -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust Btw, get a newsreader and a decent Usenet service. Using Google Groups and solving all the Worlds security issues by Einsteinian levels of mathematics, well, I got to tell ya', it's pole opposite methodologies. And it makes you look like a moron. HTH -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust > > Btw, get a newsreader and a decent Usenet service. Using Google Groups > and solving all the Worlds security issues by Einsteinian levels of > mathematics, well, I got to tell ya', it's pole opposite methodologies. And it makes you look like a moron. Posting the identical message 4 times in 10 minutes doesn't instill > confidence in your qualifications to lecture others on what newsreader > they should be using. Idiot. The glitch wasn't the newsreader. Idiot. -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust > And yes, you can be tracked down unless you're a pro who is bouncing > his posts off of multiple servers somehow, or other, but I suspect it > will just be a matter of contacting your ISP and asking for your home > address. James Harris lol You're an asshole but I feel in the Xmas mood so............. I have some helpful information for you. you post. The first group comprises those who know you're a liar, a plagiarist, a fraud and an idiot. The second includes only those who have never heard of you. Your lies and incoherent nonsense just give the first group an opportunity to laugh at you, and any of the second group who see that crap will immediately migrate to the first. If you want to maintain as good an image as possible, your best bet? Shut the up. -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust > The insanity of this behavior is in that hey, all I have to do is post > _my_ threads to death? Clue: You don't own Usenet. -- A fireside chat not with Ari! http://tr.im/holj Motto: Live To Spooge It! === Subject: Re: JSH: another one bites the dust > >There is a major campaign going on now to sway people against this >research which clearly is political, oh, and is about lying about the >result, >Drama Queen. > You know I notice that often when I post, one of you comes along with The insanity of this behavior is in that hey, all I have to do is post > my threads to death? Since your proof is nonsense, there is no working code. Later, I'll note, when I have the entire world's attention that people > hide the solution, and you will be tracked down so that someone can > interview you as I'm curious. Your solutions are wrong. Get over it. What in the hell were you thinking? Yes, we realized you were wrong. Why would anyone think that would work? It has never worked to tell you your mistakes. You are not rational enough to understand that. And yes, you can be tracked down unless you're a pro who is bouncing > his posts off of multiple servers somehow, or other, but I suspect it > will just be a matter of contacting your ISP and asking for your home > address. Paranoia is not a mathematical technique. > James Harris === Subject: Re: JSH: another one bites the dust >There is a major campaign going on now to sway people against this >research which clearly is political, oh, and is about lying about the >result, > Drama Queen. You know I notice that often when I post, one of you comes along with behavior. Claiming that there is some vast conspiracy among all of the many folks who have told you that you are wrong -- a vast conspiracy that nobody here is brave enough or just plain you- can't-push-me-around enough to go against is pure Drama Queenery. Imagining that this vast conspiracy has the immense power to force me and everyone else to tell lies about your research but somehow becomes totally impotent and powerless when it comes to keeping you from posting is is Drama Queenery squared. >The insanity of this behavior is in that hey, all I have to do >is post working code, Go ahead. Nobody is stopping you. A single post with code that factors all of the RSA challenges in a short amount of time would prove your theories to be correct with no possible doubt. But you haven't posted the code, have you? How long has it been? You can't post working code, because your theories are not correct. >my threads to death? I let 99% of your Drama Queen statements slide, only commenting on a few. >Later, I'll note, when I have the entire world's attention that people >hide the solution, and you will be tracked down so that someone can >interview you as I'm curious. Drama Queen. >What in the hell were you thinking? Why would anyone think that would work? And yes, you can be tracked down unless you're a pro who is bouncing >his posts off of multiple servers somehow, or other, but I suspect it >will just be a matter of contacting your ISP and asking for your home >address. Are you on crack? Anyone who wishes can contact me by email, telephone or snail-mail or just walk up to my front door and knock any time they wish. My contact info is right there on my website. It's talk like that that makes you such a Drama Queen. -- Guy Macon === Subject: Re: JSH: another one bites the dust posting-account=DkG3nAkAAAAVuxctYYjlIz6_Yb78PVNd rv:1.8.1.3) Gecko/20070309 Firefox/2.0.0.3,gzip(gfe),gzip(gfe) > (Skip now if you are tired of seeing JSH refuted by yet another > counterexample). > Here's JSH's latest claimed solution to the factoring problem, with all > the blathering about how great he is stripped away. > Number to be factored: d > Let f1, f2 be positive integers such that f1 f2 = d - 1 > Let r(v) = 2 ((d + 1) v^2 - 2 f1 v + f1^2) > Let L = (f1 - Sqrt[f1^2 - (f1^2 - d/2) (d + 1)])/(d + 1), and > H = (f1 + Sqrt[f1^2 - (f1^2 - d/2) (d + 1)])/(d + 1) > James claims that there exists a v where v is either an integer or half > an integer, such that > L <= v <= H > and and r(v) is an integer and gcd(r(v), d) is a non-trivial factor of > d, for some f1, f2. > For many d, this is true. Has James finally cracked the case? Nope. d=119: It works. r_c(v) = 84. t_c(v) = 35. > Oh? Pray tell, what _rational_ v will give r_c(v) = 2(120 v^2 - 2 v f + f_1^2) = 84? Remember, you've limited yourself to f_1 = 1, 2 for D = 119. Rick === Subject: Re: JSH: another one bites the dust posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009020407 Iceweasel/3.0.6 (Debian-3.0.6-1),gzip(gfe),gzip(gfe) Oh, so now you've also resurrected t, which you didn't mention in the latest post. See, that's what I mean about leaving out details! Now how do we find v, what r c(v) do we use (same as the latest post about the Fermat numbers?), and what t c(v) (which was conspicuously absent in that post)? === Subject: Re: JSH: another one bites the dust > Why try to fight a mathematical proof? Oh yeah, posters are also trying to get a lot of traction out a recent > mistake I made about factors of 2p+1. Hey, I make mistakes. But I > also care about what's mathematically true. Unfortunately others > clearly do not. There is a major campaign going on now to sway people against this > research which clearly is political, oh, and is about lying about the > result, like claiming it doesn't factor 119. I was told that you are a leading expert, as far as mathematical proof is concerned. I wanted to know your opinion regarding proof by contradiction types of proofs. (They are sometimes also called reductio ad absurdum.) === Subject: Re: JSH: another one bites the dust > Why try to fight a mathematical proof? Oh yeah, posters are also trying to get a lot of traction out a recent > mistake I made about factors of 2p+1. Hey, I make mistakes. But I > also care about what's mathematically true. Unfortunately others > clearly do not. There is a major campaign going on now to sway people against this > research which clearly is political, oh, and is about lying about the > result, like claiming it doesn't factor 119. I was told that you are a leading expert, as far as mathematical proof >is concerned. I wanted to know your opinion regarding proof by contradiction types >of proofs. (They are sometimes also called reductio ad absurdum.) James typically skips the reductio ad step and now starts with absurdum. It saves time. His other great techniques are argumentum eternus and reductio ad delirium. Alan -- Defendit numerus === Subject: Re: JSH: another one bites the dust > (Skip now if you are tired of seeing JSH refuted by yet another > counterexample). > Here's JSH's latest claimed solution to the factoring problem, with all > the blathering about how great he is stripped away. > Number to be factored: d > Let f1, f2 be positive integers such that f1 f2 = d - 1 > Let r(v) = 2 ((d + 1) v^2 - 2 f1 v + f1^2) > Let L = (f1 - Sqrt[f1^2 - (f1^2 - d/2) (d + 1)])/(d + 1), and > H = (f1 + Sqrt[f1^2 - (f1^2 - d/2) (d + 1)])/(d + 1) > James claims that there exists a v where v is either an integer or half > an integer, such that > L <= v <= H > and and r(v) is an integer and gcd(r(v), d) is a non-trivial factor of > d, for some f1, f2. > For many d, this is true. For example, for d=15, here are the > possibilities. The first pair of numbers is d and f1, the second pair > is L and H, the third group of numbers are the v values in [L,H] that > are integers or half integers. The fourth group is r(v) at those v > values, and the final group is the gcd of the r(v) values with d. > {15,1}{-0.577934,0.702934}{-(1/2),0,1/2}{12,2,8}{3,1,1} > {15,2}{-0.359123,0.609123}{0,1/2}{8,12}{1,3} > {15,7} non-real range > {15,14} non-real range > His method finds the factor 3 of 15, at both f1=1 and f1=2. At f1=7 or > f1=14, L and H are not real. > His method also works at d=21 (a number that gave his earlier methods > problems): > {21,1}{-0.613244,0.704153}{-(1/2),0,1/2}{15,2,11}{3,1,1} > {21,2}{-0.460198,0.642016}{0,1/2}{8,15}{1,3} > {21,4} non-real range > {21,5} non-real range > {21,10} non-real range > {21,20} non-real range > Has James finally cracked the case? Nope. d=119: It works. r_c(v) = 84. t_c(v) = 35. Why try to fight a mathematical proof? Oh yeah, posters are also trying to get a lot of traction out a recent > mistake I made about factors of 2p+1. Hey, I make mistakes. But did you have or not a *mathematical proof* of the fact that, for each prime _p_, 2p + 1 must have, at most, two prime factors? Jose Carlos Santos === Subject: Re: JSH: another one bites the dust > (Skip now if you are tired of seeing JSH refuted by yet another > counterexample). Here's JSH's latest claimed solution to the factoring problem, with all > the blathering about how great he is stripped away. Number to be factored: d ...etc. While *I* find this convincing, you haven't got into what counts as a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is incontrovertably correct, your derivation MUST (by definition) be incorrect. Google define mathematical proof. Etc. QED. How did I do? M -- === Subject: Re: JSH: another one bites the dust > (Skip now if you are tired of seeing JSH refuted by yet another > counterexample). > Here's JSH's latest claimed solution to the factoring problem, with > all the blathering about how great he is stripped away. > Number to be factored: d ...etc. While *I* find this convincing, you haven't got into what counts as > a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is > incontrovertably correct, your derivation MUST (by definition) > be incorrect. Google define mathematical proof. Etc. BTW, he also proved that that if _p_ is a prime number, then 2p+1 can have at most two prime factors: in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so on. Jose Carlos Santos === Subject: Re: JSH: another one bites the dust > BTW, he also proved that that if _p_ is a prime number, then 2p+1 can > have at most two prime factors: in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so > on. While *I* find this convincing, you haven't got into what counts as a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is incontrovertably correct, you MUST be making this up. Google define mathematical proof. Etc. I'm getting the hang of this. Soon I'll be running the world too. M === Subject: Re: JSH: another one bites the dust > BTW, he also proved that that if p is a prime number, then 2p+1 can > have at most two prime factors:. > in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so > on. While *I* find this convincing, you haven't got into what counts as > a head in JSH's case. > He has a proof. I repeat. He has a proof. As a proof is > incontrovertably correct, you MUST be making this up. Google define mathematical proof. Etc. I'm getting the hang of this. Soon I'll be running the world too. M Not bad, but here are a few pointers: 1) 1st, you have to capitalize words if you want to refute an argument a la James Harris. As in, BUT I have mathematical PROOF. 2) 2nd, don't be afraid to use the word freakin (I mean if you go so far to assert that you have a freakin mathematical proof, then it's obvious you must have one.) 3) Point out how everyone knows that the all of the counter-examples are not true and are really just pesky attempts to slow you down. 4) Insert at least one threat as to how the conspiracy of all the mathematical elite trying to keep the truly deserving (such as his truly) from the gates will result in the collapse of mankind. 5) Insert a last rhetorical question to yourself musing about whether you should save mankind. But you know, it would be fun to make a game called, JSH or not JSH, where people look at 2 posts side by side, one from JSH, one from a gifted amateur such as yourself, and have to decide which is written by the real JSH. Peter === Subject: Re: JSH: another one bites the dust > Not bad, but here are a few pointers: > 1) 1st, you have to capitalize words if you want to > refute an argument > a la James Harris. As in, BUT I have mathematical > PROOF. > 2) 2nd, don't be afraid to use the word freakin (I > mean if you go so > far to assert that you have a freakin mathematical > proof, then it's > obvious you must have one.) > 3) Point out how everyone knows that the all of the > counter-examples > are not true and are really just pesky attempts to > slow you down. > 4) Insert at least one threat as to how the > conspiracy of all the > mathematical elite trying to keep the truly deserving > (such as his > truly) from the gates will result in the collapse of > mankind. > 5) Insert a last rhetorical question to yourself > musing about whether > you should save mankind. But you know, it would be fun to make a game called, > JSH or not JSH, > where people look at 2 posts side by side, one from > JSH, one from a > gifted amateur such as yourself, and have to decide > which is written > by the real JSH. Peter I am highly interested in this game. Steve === Subject: Re: JSH: another one bites the dust > Not bad, but here are a few pointers: > 1) 1st, you have to capitalize words if you want to > refute an argument > a la James Harris. As in, BUT I have mathematical > PROOF. > 2) 2nd, don't be afraid to use the word freakin (I > mean if you go so > far to assert that you have a freakin mathematical > proof, then it's > obvious you must have one.) > 3) Point out how everyone knows that the all of the > counter-examples > are not true and are really just pesky attempts to > slow you down. > 4) Insert at least one threat as to how the > conspiracy of all the > mathematical elite trying to keep the truly deserving > (such as his > truly) from the gates will result in the collapse of > mankind. > 5) Insert a last rhetorical question to yourself > musing about whether > you should save mankind. > But you know, it would be fun to make a game called, > JSH or not JSH, > where people look at 2 posts side by side, one from > JSH, one from a > gifted amateur such as yourself, and have to decide > which is written > by the real JSH. > Peter I am highly interested in this game. Steve was around 3 years ago. === Subject: Re: JSH: another one bites the dust > BTW, he also proved that that if _p_ is a prime number, then 2p+1 can > have at most two prime factors: > in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so > on. While *I* find this convincing, you haven't got into what counts as > a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is > incontrovertably correct, you MUST be making this up. JSH has a spoof, no proof. Since just has no assumptions, it is called justa spoof. Google define mathematical proof. Etc. I'm getting the hang of this. Soon I'll be running the world too. M === Subject: Re: Proof that roots of integers are either integers or irrational - how original? > > Here is my proof that roots of integers have to be either whole or > irrational. I worked it out many years ago (pi day yesterday reminded > me of this exercise.) I figure someone thought of this or similar before > but I haven't seen it elsewhere, simple as it is. It's a reductio like > the very old, other proof you see around. It's interesting in any case, > due to its great power but simplicity. If not an integer, assume that m^(1/n) is a fraction a/b. Consider that > all integers can be represented as a unique product series of powers of > primes (e.g., 637197957 = 3^2*11*23^5, etc.) We can represent a/b as > maximally reduced, so the fraction would have to be representable in the > form (5^3*13*29^7*...)/(7*17^4*61^2*...) That is, no prime on the top > can also be on the bottom. Then, consider squaring a/b (or cubing etc.) to attempt to result in 2, > or 11, etc. We'd have by exponent laws the same product series above as > before, but with each exponent times two (or three, etc.) Below we have > the same series as before with each exponent times two (or three, etc.) > Yet again, we can't divide them out to get an integer because there are > representation in product series of powers of primes, of any given > integer. Therefore you can't say, Suppose the series on top can *also* > be represented as the series below multiplied by the number we want to > any a/b that could be the square root of two, or the fifth root of 77, > etc. (This is a more powerful proof than simply for one integer or > exponent.) Has anyone seen this before? Well, yes, this is the basic idea of the standard proof that an > algebraic integer that is rational is an (ordinary) integer. Really? Precisely what do you think is that basic idea? --Bill Dubuque === Subject: Re: Proof that roots of integers are either integers or irrational - how original? roots of integers have to be either whole or irrational. > Assume r in N, r^(1/n) in Q. Thus some a,b in N with r^(1/n) = a/b. I really wish you'd either write in complete sentences or > stop complaining to others about their grammar. > I'm not giving proofs, only outlines or sketches of proofs with details left to the reader. Details like the reasons. I strive to be complete and detailed. Complex logic is better expressed in pseudo-symbolic logic than English. You have no complaint about my writing. > Anyway: > rb^n = a^n; b^n | a^n; b | a (by simple theorem) Do you know a complete proof of this simple theorem? > No. As I've said before, only an outline or sketch. Will you be able to fill in the details? BTW, simple is not trivial. For example dx^2 / dx = 2x is simple and not trivial. The theorem depends upon the equally not trivial simple theorem (a^n,b^n) = (a,b)^n which depends upon (r^n,s^n) = 1 where r = a/(a,b), s = b/(a,b) and (ku,kv) = k(u,v) which of course isn't scalar vector multiplication but multiplication of a positive integer by a gcf. > some k in N with a = kb; r = k^n, QED. === Subject: Re: Proof that roots of integers are either integers or irrational - how original? posting-account=AdyLXQoAAABgRay99CKv1O8Y_7jjivwq InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) > Did someone, like Gauss, think of this proof about the > irrationality of roots soon after discovery of the FTOA? > Who, when, etc. - note Wikipedia says can be ... not who > actually first said so. (I suppose someone needs to say so > and get credit thereby, however obvious of an implication > follows from something?) That leads into my second question, > why doesn't this (apparently, to me anyway) get around > more in discussions of the history of math? They talk a lot > about the old proof, but not IIRC the better one referred > in Wikipedia. For what it's worth, I've got several folders at home full of several hundred publications (this includes letters to the editor, short notes, book reviews, etc. in addition to actual papers) relating to irrationality proofs of n'th roots of integers, going back to the early 1800s, so this is a topic that's been mined quite extensively in the various elementary journals (the 3 MAA journals, Mathematical Gazette, Mathematics Teacher, Nouvelles Annales de Mathematiques, Journal de Mathematiques Elementaires, Mathematical Intelligencer, Elemente der Mathematik, Mathesis Recueil Mathematique, etc. to name just a few). However, these types of publications seem to have a life-span/memory in the mathematical community of no more than a decade or two (and this pertains to the small subset of the mathematical community that reads/read any of these journals), so the same ideas keep coming up over and over again (not just your idea, which is one of the more elegant and mathematically interesting proofs and thus well known to most mathematicians). Incidentally, Theodoros (ancient Greece) proved that each of the non-square integers from 2 to 17 were irrational. I don't recall if his method has come down to us, but I do remember reading that he supposedly treated each of these one-by-one (this being, I think, from others living during Theodoros time whose writings have come down to us), and I've got several papers (at home, so I can't cite reference information right now) that offer possible explanations, the most common of which is (I believe) is that the Greeks didn't have the concept of unique factorization (or if they did, they didn't have what they considered an air-tight proof -- remember, Greek mathematics was almost entirely geometrical; they didn't view numbers like sqrt(2) the same way that we do, but rather as something akin to lengths (and their ratios) in geometrical figures). In fact, now that I think about it, I believe there is a discussion of Theodoros and unique factorization somewhere in Hardy/Wright's The Theory of Numbers. Dave L. Renfro === Subject: Re: Proof that roots of integers are either integers or irrational - how original? I suspect the reason is that for most people in the intended audience > the distinction is going to be boring - we've shown sqrt(2) is > irrational, great, now what's the big deal about the cube root > of 17? > http://everything2.com/index.pl?node=The%20square%20root%20of%20any%20prime% 20number%20is%20irrational I think it is interesting that the square root of any prime has been proven to be irrational because it provides a means of generating an infinity of different initial finite segments. === Subject: Re: Proof that roots of integers are either integers or irrational - how original? Anyway: >rb^n = a^n; b^n | a^n; b | a (by simple theorem) Do you know a complete proof of this simple > theorem? > What do you mean? I though these are well known facts: If factorization into prime factors EXIST and is UNIQUE, then matching the prime factors of b^n with those in a^n immediately give b | a. AND factorization is unique over Z because of the existence of Euclid algorithm. === Subject: Re: Proof that roots of integers are either integers or irrational - how original? > A _question_ doesn't mean anything. If so, what are we to make of it when people ask them? -- Science is a differential equation. Religion is a boundary condition. --Alan Turing === Subject: Re: Proof that roots of integers are either integers or irrational - how original? > > A _question_ doesn't mean anything. If so, what are we to make of it when people ask them? Now you're just taking his comment out of context. To put it back in context, you should ask If so, what are we to make of it when David C. Ullrich asks them? which apparently has a whole 'nother answer. -- Patrick Hamlyn posting from Perth, Western Australia Windsurfing capital of the Southern Hemisphere Moderator: polyforms group (polyforms-subscribe@egroups.com) === Subject: Re: Proof that roots of integers are either integers or irrational - how original? <20090315183124.T93688@agora.rdrop.com> <024sr4lqfhcb0clhpg8jmqsnc1qb77iiv8@4ax.com> <619sr4ph32i5snneeashtpdquhemioasjt@4ax.com> posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Anyway: >rb^n = a^n; b^n | a^n; b | a (by simple theorem) > Do you know a complete proof of this simple > theorem? >What do you mean? A question doesn't mean anything. I was curious > whether William knew how to prove the result he > called a simple theorem. (Because he seemed to be > saying the result was entirely trivial; I suspect it's > less trivial than he thought, because it depends on > unique factorization...) >I though these are well known facts: I wasn't curious whether you knew how to prove it... > If factorization into prime factors EXIST and is UNIQUE, > then matching the prime factors of b^n with those in a^n > immediately give b | a. >AND factorization is unique over Z because of the > existence of Euclid algorithm. David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) Okay, sorry to alienate you, Dave. === Subject: Re: Proof that roots of integers are either integers or irrational - how original? > On Mar 16, 6:08pm, David C. Ullrich >On Mar 16, 4:40pm, David C. Ullrich > Elliot > Anyway: >rb^n = a^n; b^n | a^n; b | a (by simple > theorem) > Do you know a complete proof of this simple > theorem? >What do you mean? > A _question_ doesn't mean anything. I was curious > whether William knew how to prove the result he > called a simple theorem. (Because he seemed to be > saying the result was entirely trivial; I suspect > it's > less trivial than he thought, because it depends on > unique factorization...) >I though these are well known facts: > I _wasn't_ curious whether _you_ knew how to prove > it... > If factorization into prime factors EXIST and > is UNIQUE, > then matching the prime factors of b^n with > those in a^n > immediately give b | a. >AND factorization is unique over Z because of the > existence of Euclid algorithm. > David C. Ullrich > Understanding Godel isn't about following his > formal proof. > That would make a mockery of everything Godel was > up to. > (John Jones, My talk about Godel to the > post-grads. > in sci.logic.) Okay, sorry to alienate you, Dave. Oh, you haven't. He's like that to everyone! ;) === Subject: The concept of the aether posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) I believe as time it is the sustainer of all things. The aether is sustainer of the universe. The aether concept is one of sustainer of all immutable physical elements. When aether changes so does energy. Mitch Raemsch === Subject: Re: The concept of the aether posting-account=vpv29woAAAAjASPtep1bSfPEIqZVH03h 4334.5003; Windows NT 5.0; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-mtc-td04.proxy.aol.com[400C7064] (Prism/1.2.1), HTTP/1.1 cache-mtc-aa06.proxy.aol.com[400C740A] (Traffic-Server/6.1.5 [uScM]) > I believe as time it is the sustainer of all things. The aether is > sustainer of the universe. The aether concept is one of sustainer of > all immutable physical elements. If there was no universe, would aether still hang around? Anything immutable would not require a sustainer. Doug Chandler === Subject: Re: The concept of the aether posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > I believe as time it is the sustainer of all things. The aether is > sustainer of the universe. The aether concept is one of sustainer of > all immutable physical elements. If there was no universe, would aether still hang around? Anything immutable would not require a sustainer. Doug Chandler I disagree. Do you spend your time sustaining nothing doug? === Subject: Re: The concept of the aether > I believe as time it is the sustainer of all things. The aether is > sustainer of the universe. The aether concept is one of sustainer of > all immutable physical elements. > Anything immutable would not require a sustainer. Doug Chandler That is where I disagree. The universal immutable elements are maintained by aether. There are 14. Mitch Raemsch === Subject: Re: Values of d in AP 11+210*d*i, i=0..10, with 11 primes. > http://zak08.livejournal.com/6400.html > %S A158256 > 7315048,23389398,368453046,397698469, > 476527246,716025940,1428738103, 1517391167, > 1761057635,1796879220,2436613965,2762038441, > 3041254151,3340639523,3551566265,3698215410 > %N A158256 Values of d in AP 11+210*d*i, i=0..10, > with 11 primes. > %C A158256 No more terms < 4 10^9. > %Y A158256 Cf. A088430, A113834. > %A A158256 Zak Seidov (zakseidov(AT)yahoo.com), Mar > 15 2009 More terms? Six more terms: 4207031185 4407805122 4556491589 5072158298 5626167378 5986324571 === Subject: Re: infinite sum >how does one go about sum {k=0..inf} k!/(k+m)! if m>=2? Any hints >would be appreciated. >Thinking of 0 < x < 1, we have sum {k=0..inf} x^k = 1/(1 - x). >Integrate from 0 to y to get sum {k=0..inf} y^(k+1)/(k+1) = int [0,y] >dx/(1-x) = -log(1-y). Integrate again to get sum {k=0..inf} >z^(k+2)/[(k+2)(k+1)] = int [0,z] -log(1-y) dy. Now let z -> 1- to get > sum {k=0..inf} 1/[(k+2)(k+1)] = int [0,1] -log(1-y) dy, >which is easily done. That's the case m = 2. Rinse, lather, repeat for >higher m. >The case for m = 2 is sum(k=1..infty, 1/[(k+1) (k+2)]), which is the >collapsingsumsum(k=1..infty, 1/(k+1) - 1/(k+2)). I wonder if one can >generalize this collapsing by induction. I don't know about by induction, but there certainly is an > argument that generalizes the collapsing (see my second > post here). David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) the collapsing argument is really good to start with, but quickly looks intractable with so many initial terms surviving. One needs to be really good with combinatorics... === Subject: Basis rep. of symmetric ,bilinear map after tensoring. How? Say A is a torsion-free Abelian group, with basis {v_1,..,v_n} ; AFAIK , a torsion-free modules over a PID are free (after $9.99 S&H .) and we have a symmetric quadratic bilinear form Q(a,b) : AxA-->Z , with a matrix representation Q_ij = Q(v_i,v_j); i,j=1,..,n. Now, we tensor A with R over Z , i.e., A(X)IR , tensor over Z -integers. (not clear in the book, but I assume it is tensoring of Z-modules, which would seem obvious) Question: How does the matrix rep. of Q(a,b) change after the tensoring above (given that the map on A(x)R is now (Z-)linear and not bilinear anymore.)? Do we just use the basis rep. of A(x)R for the matrix, using basis {v_i(x)1; i=1,..,n} ?. Is the matrix rep. still diagonalizable? ( the original matrix is symmetric, so diagonalizable) === Subject: Re: Basis rep. of symmetric ,bilinear map after tensoring. How? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009030503 Fedora/3.0.7-1.fc10 Firefox/3.0.7,gzip(gfe),gzip(gfe) Say A is a torsion-free Abelian group, with basis {v 1,..,v n} ; AFAIK , a torsion-free modules over > a PID are free (after $9.99 S&H .) and we have a symmetric quadratic bilinear form Q(a,b) : AxA-->Z , with a matrix representation Q ij = Q(v i,v j); i,j=1,..,n. Now, we tensor A with R over Z , i.e., A(X)IR , tensor over Z -integers. (not clear in the book, but I assume it is tensoring of Z-modules, which would seem obvious) Question: How does the matrix rep. of Q(a,b) change after > the tensoring above (given that the map on A(x)R is > now (Z-)linear and not bilinear anymore.)? Write (x) for tensor product over Z and A' = A (x) R. Q' : A' x A' --> R defined by Q'( (a (x) r) x (b (x) s) = Q(a, b) r s If you pick a basis B for A, tensoring it with R gives you basis B' of A'. The matrix M' of the R-bilineal form Q' with respect to B' is the same as the matrix M of Q with respect to B, upto the following: you have to change every entry in the matrix M by its image under the unique ring homomorphism Z --> R. -- m === Subject: Re: Basis rep. of symmetric ,bilinear map after tensoring. How? Say A is a torsion-free Abelian group, with basis > sis {v_1,..,v_n} ; AFAIK , a torsion-free modules > over > a PID are free (after $9.99 S&H .) and we have a symmetric quadratic bilinear form Q(a,b) : AxA-->Z , with a matrix representation Q_ij = Q(v_i,v_j); i,j=1,..,n. Now, we tensor A with R over Z , i.e., A(X)IR , > R , tensor over Z -integers. (just to specify that both mentions, R, IR , stand for the real numbers --I know, a mistake to use diffe- rent symbols for the same thing. And the tensoring, I think --cannot think of any other possibility-- is a Z-module tensoring. (not clear in the book, but I assume it is > is tensoring of Z-modules, which would seem obvious) Question: How does the matrix rep. of Q(a,b) change > change after > the tensoring above (given that the map on A(x)R > (x)R is > now (Z-)linear and not bilinear anymore.)? Do we just use the basis rep. of A(x)R for the > matrix, using basis {v_i(x)1; i=1,..,n} ?. > Is the matrix rep. still diagonalizable? ( the > original matrix is symmetric, so diagonalizable) > === Subject: Re: Hammer is not working (was Re: JSH: So what's your explanation?) <18794924.1237071452401.JavaMail.jakarta@nitrogen.mathforum.org I have a mathematical proof. If you have, then you've never posted it. If you have a mathematical proof that you've solved the factoring problem, then I have a trillion dollars. There is equal evidence for both. - Tim === Subject: example of a covering space posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009030423 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) I am searching for an example of a covering projection E-->X of which I can draw a picture, such that E is not the universal cover, but one is able to draw a picture of the universal cover E'-->E-->X also. At first, I have looked at X=S1vS1 which is covered by something which looks like ooo. However, the universal cover of X is not drawable. The other standard examples R-->S1, RxR-->S1xS1 are already universal. Can anybody help me? S. === Subject: Re: example of a covering space posting-account=hhC2JwoAAAAQt9ZcdRPKAFNCTwZjbe1M 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I am searching for an example of a covering projection E-->X of which > I can draw a picture, such that E is not the universal cover, but one > is able to draw a picture of the universal cover E'-->E-->X also. At first, I have looked at X=S1vS1 which is covered by something which > looks like ooo. However, the universal cover of X is not drawable. The > other standard examples R-->S1, RxR-->S1xS1 are already universal. Can > anybody help me? What's wrong with R-->S1-->S1? === Subject: Re: example of a covering space posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009030503 Fedora/3.0.7-1.fc10 Firefox/3.0.7,gzip(gfe),gzip(gfe) > I am searching for an example of a covering projection E-->X of which > I can draw a picture, such that E is not the universal cover, but one > is able to draw a picture of the universal cover E'-->E-->X also. > At first, I have looked at X=S1vS1 which is covered by something which > looks like ooo. However, the universal cover of X is not drawable. The > other standard examples R-->S1, RxR-->S1xS1 are already universal. Can > anybody help me? What's wrong with R-->S1-->S1? What does that notation mean? A covering of S1 by S1 with fiber R? There are very few of those ;-) -- m === Subject: Re: example of a covering space posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009030423 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) On 17 Mrz., 15:43, Mariano Su.87rez-Alvarez > I am searching for an example of a covering projection E-->X of which > I can draw a picture, such that E is not the universal cover, but one > is able to draw a picture of the universal cover E'-->E-->X also. > At first, I have looked at X=S1vS1 which is covered by something which > looks like ooo. However, the universal cover of X is not drawable. The > other standard examples R-->S1, RxR-->S1xS1 are already universal. Can > anybody help me? > What's wrong with R-->S1-->S1? What does that notation mean? A covering of S1 by S1 > with fiber R? There are very few of those ;-) -- m Since you've mentioned the notation F x --> E --p--> X there is something unclear to me, too: Let X be connected. If p is a fibration, the Fiber F x at a point *-x->X is defined as the pullback F x --> E | |p v v * -x-> X If p is a covering map, the fibers of points of x are all isomorphic. Is this true for fiber bundles or general fibrations, too? Moreover, if p is a covering map, the map F x --> E of the diagram is the inclucion of a (closed?) subspace. Is this true for fiber bundles or fibrations in general? Prehaps one has the following: If a pullback A --> B | | v v C --> D is given, the above map is the inclusion of a subspace (and closed/ open) if the bottom map is the inclusion of a subspace (and closed open). This is true forpushout diagrams. S. === Subject: Re: example of a covering space posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009030423 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) > If p is a covering map, the fibers of points of x are all isomorphic. > Is this true for fiber bundles or general fibrations, too? Sorry, this is true for fiber bundles. But for fibrations...? === Subject: Re: example of a covering space > > If p is a covering map, the fibers of points of x are all isomorphic. > Is this true for fiber bundles or general fibrations, too? Sorry, this is true for fiber bundles. But for fibrations...? For Hurewicz fibrations, the fibres are homotopy equivalent. They do not need to be homeomorphic. Here's an example: Take the (solid) triangle mapped vertically to the interval, as the following suggests: . ... ..... ....... ......... ........... ............. ............... ................. ................... ..................... ....................... ......................... | | |/ v ......................... Here you have a Hurewicz fibration in which the fibres over the interior points of the interval are intervals, while the fibres over the ends are single points. I'm not sure of the invariance properties of Serre fibrations, however. Dale === Subject: Re: example of a covering space posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > I am searching for an example of a covering projection E-->X of which > I can draw a picture, such that E is not the universal cover, but one > is able to draw a picture of the universal cover E'-->E-->X also. > At first, I have looked at X=S1vS1 which is covered by something which > looks like ooo. However, the universal cover of X is not drawable. The > other standard examples R-->S1, RxR-->S1xS1 are already universal. Can > anybody help me? What's wrong with R-->S1-->S1? Other examples: double cover of S1 over itself ( z -> z^2 for the unit circle in C ) cylinder R1xS1 over torus S1xS1. BTW, the universal cover of S1vS1 is the Cayley graph for the free group with 2 generators: http://en.wikipedia.org/wiki/File:Cayley graph of F2.svg === Subject: Re: JSH: So what happened? posting-account=lj-kRgoAAADbp-o6laOVCIWXjFF53GYz Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) > Factoring problem is solved. No more room for confusion about the > result. All issues are resolved. > James Harris > For some strange reason I'm reminded of that scene where Bush is standing behind the banner that had Mission Accomplished on it. Peter === Subject: Re: JSH: So what happened? > For r_c(v) and t_c(v) to both be integers, b = 2. Rubbish. You already yourself posted one with b = 5 (for D=119). - Tim === Subject: Re: JSH: So what happened? > Factoring problem is solved. No more room for confusion about the > result. All issues are resolved. Except that you still haven't given any method for finding suitable v. All you have said is that one exists. - Tim === Subject: Re: JSH: So what happened? Nntp-Posting-Host: hera.cwi.nl > Factoring problem is solved. No more room for confusion about the > result. All issues are resolved. > > Except that you still haven't given any method for finding suitable v. > All you have said is that one exists. In the example for 21 he has given how it works. He finds some r(v) and multiplies it by a factor of 21. An excellent way to find something that works in factoring. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: So what happened? > >Factoring problem is solved. No more room for confusion about the >result. All issues are resolved. >Except that you still haven't given any method for finding suitable v. >All you have said is that one exists. > No. I've proven mathematically that v exists. And it was a simple > proof which I posted and there was no disagreement with it. I'm seeing now posts where people claim that v doesn't exist for some > value or other, but it's a waste of time to worry about every time > some poster claims to have refuted mathematical proof! Translation: just because your proof does not work means you think it is still correct. That is pretty sad that you could be so deluded. So I'm focusing on test code, though I am a bit distracted, or I > wouldn't be making this post now! Oh well. Enough silly arguing. With test code there is no debate any > more and people arguing against proof just get to be crackpots. So enough posting. Time to work. > James Harris > === Subject: Re: JSH: So what happened? > I've coded it to tackle numbers of the form 2^n + 1, in a range where > n < 30. Not bad, but code is still not following theory in a puzzling way. So > I'm not ready to celebrate. I'm still missing something, so... Oh well, it is implementation phase. First comes theory, then comes > algorithm development, then comes implementation. Just to give you something to compare against... $ cat foo.bc define aux(n,k) { m = sqrt(n) for (i = k; i <= m; i += 2) if (n%i == 0) { print i, ; return aux(n/i,i) } return n } for (j = 1; j <= 40; ++j) { n = 2^j+1 print 2^,j,+1 = ; aux(n,3) } $ time bc < foo.bc 2^1+1 = 3 2^2+1 = 5 2^3+1 = 3 3 2^4+1 = 17 2^5+1 = 3 11 2^6+1 = 5 13 2^7+1 = 3 43 2^8+1 = 257 2^9+1 = 3 3 3 19 2^10+1 = 5 5 41 2^11+1 = 3 683 2^12+1 = 17 241 2^13+1 = 3 2731 2^14+1 = 5 29 113 2^15+1 = 3 3 11 331 2^16+1 = 65537 2^17+1 = 3 43691 2^18+1 = 5 13 37 109 2^19+1 = 3 174763 2^20+1 = 17 61681 2^21+1 = 3 3 43 5419 2^22+1 = 5 397 2113 2^23+1 = 3 2796203 2^24+1 = 97 257 673 2^25+1 = 3 11 251 4051 2^26+1 = 5 53 157 1613 2^27+1 = 3 3 3 3 19 87211 2^28+1 = 17 15790321 2^29+1 = 3 59 3033169 2^30+1 = 5 5 13 41 61 1321 2^31+1 = 3 715827883 2^32+1 = 641 6700417 2^33+1 = 3 3 67 683 20857 2^34+1 = 5 137 953 26317 2^35+1 = 3 11 43 281 86171 2^36+1 = 17 241 433 38737 2^37+1 = 3 1777 25781083 2^38+1 = 5 229 457 525313 2^39+1 = 3 3 2731 22366891 2^40+1 = 257 4278255361 real 0m0.500s user 0m0.499s sys 0m0.015s === Subject: Re: JSH: So what happened? > I've coded it to tackle numbers of the form 2^n + 1, in a range where > n < 30. Not bad, but code is still not following theory in a puzzling way. So > I'm not ready to celebrate. I'm still missing something, so... Oh well, it is implementation phase. First comes theory, then comes > algorithm development, then comes implementation. Just to give you something to compare against... [snip factorizations up to 2^40+1] Yeah, but does your program use an ACTUAL mathematical PROOF, fancy boy? Didn't think so. James' program is based on MATHEMATICS. Unlike yours, which is probably based on architecture or interpretive dance or something. Alan -- Defendit numerus === Subject: Re: JSH: So what happened? > >Factoring problem is solved. No more room for confusion about the >result. All issues are resolved. >Except that you still haven't given any method for finding suitable v. >All you have said is that one exists. >No. I've proven mathematically that v exists. And it was a simple >proof which I posted and there was no disagreement with it. >I'm seeing now posts where people claim that v doesn't exist for some >value or other, but it's a waste of time to worry about every time >some poster claims to have refuted mathematical proof! >Translation: just because your proof does not work means you think >it is still correct. That is pretty sad that you could be so deluded. > I've coded it to tackle numbers of the form 2^n + 1, in a range where > n<30. Not bad, but code is still not following theory in a puzzling way. So > I'm not ready to celebrate. I'm still missing something, so... Oh well, it is implementation phase. First comes theory, then comes > algorithm development, then comes implementation. Codes up on comp.theory where I've posted it. I'm still fiddling with > it, so to get the latest version I'm posting, go to my math group. > Code is Java. To find my math group, Google: mymathgroup I should be in the top 10. That is about where crank.net rates you. > James Harris > === Subject: Re: JSH: So what happened? n<30. You do realise that testing of new Fermat numbers requires n >= 8589934592, right? - Tim === Subject: Re: JSH: So what happened? Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) > I've coded it to tackle numbers of the form 2^n + 1, in a range where > n<30. You do realise that testing of new Fermat numbers requires >n >= 8589934592, right? Actually n = 2^14 = 16384 would already be interesting. 2^2^14 + 1 is known to be composite but no factors are known. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: JSH: So what happened? posting-account=DkG3nAkAAAAVuxctYYjlIz6_Yb78PVNd rv:1.8.1.3) Gecko/20070309 Firefox/2.0.0.3,gzip(gfe),gzip(gfe) > I've coded it to tackle numbers of the form 2^n + 1, in a range where > n<30. You do realise that testing of new Fermat numbers requires > n >= 8589934592, right? - Tim His algorithm fails far earlier than that. It can't find the factors of 2^32 + 1. Rick === Subject: Re: JSH: So what happened? His algorithm fails far earlier than that. It can't > find the factors of 2^32 + 1. I am not at all surprised. I was just trying to give him an inkling of an idea of just how spectacularly far he is from reaching his goal. Even if by some miracle it worked, it would still be useless for Fermat testing. - Tim === Subject: Re: JSH: So what happened? Nntp-Posting-Host: hera.cwi.nl ... > My current program actually fails first at D = 513. That is not a Fermat number. The first five are: 3, 5, 17, 257, 65537. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: So what happened? > His algorithm fails far earlier than that. It can't > find the factors of 2^32 + 1. > I am not at all surprised. I was just trying to give him an inkling > of an idea of just how spectacularly far he is from reaching his goal. > Even if by some miracle it worked, it would still be useless for > Fermat testing. > - Tim My current program actually fails first at D=513. But that's why I talk about implementation versus theory. You get the proof first. Then you go after implementation. As otherwise you get lost. I know why it fails, so I can fix it! Oh yeah, I don't doubt now the failure for D=119. Ok. Time to fix some things. All answers await. The factoring problem has been solved. And the demonstration of that is just around the corner. What's your timetable for factoring an RSA number, James? James Harris === Subject: Re: JSH: So what happened? posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > His algorithm fails far earlier than that. It can't > find the factors of 2^32 + 1. > I am not at all surprised. I was just trying to give him an inkling > of an idea of just how spectacularly far he is from reaching his goal. > Even if by some miracle it worked, it would still be useless for > Fermat testing. > - Tim My current program actually fails first at D=513. But that's why I talk about implementation versus theory. You get the proof first. Then you go after implementation. As otherwise you get lost. I know why it fails, so I can fix it! Oh yeah, I don't doubt now the failure for D=119. Ok. Time to fix some things. All answers await. The factoring problem has been solved. And the demonstration of that is just around the corner. James Harris Great - I've been wondering the factors of those RSA numbers for quite some time. Can you start with the smallest one and provide the factors - I await that like you can't imagine! === Subject: Re: JSH: So what happened? posting-account=lj-kRgoAAADbp-o6laOVCIWXjFF53GYz Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) My current program actually fails first at D=513. But that's why I talk about implementation versus theory. > You get the proof first. Then you go after implementation. > As otherwise you get lost. I know why it fails, so I can fix it! > Who was it who said , Proofs can't fail. That's the point of proof. If you have a proof, it is perfect. If your argument fails, it's not a proof!!! Where, in your *definition* of mathematical proof, was the part dealing with implementation, getting lost, and how to fix a proof How do you know when a proof is beyond fixing? What is the difference between a proof and its implementation? Maybe in addition to actually writing up a coherent algorithm, one of these days you'll have to get around to writing up your complete definition of mathematical proof, so we can all admire your cleverness and genius. TIA, Peter === Subject: Re: JSH: So what happened? value or other, but it's a waste of time to worry about every time > some poster claims to have refuted mathematical proof! They're saying that a suitable v doesn't always exist *given your extra conditions*, such as having to be a multiple of 1/2. > So I'm focusing on test code, though I am a bit distracted, or I > wouldn't be making this post now! Sorry to distract you, keep working on that code. - Tim === Subject: Re: JSH: So what happened? > you were challanged for monhs to factor 15, now try 21. The solution has only been around for about a month. And I DID factor 15 after posters repeatedly claimed it couldn't. For 21, r_c(v) = 15, which I guess is kind of ironic. *** 15 is not a factor of 21 ! There was some confusion in the early goings but all issues are worked out now, and yes, the method can factor ANY non-square composite. I just realized it won't factor a square. James Harris *** try to factor 33 with it and see what happens... === Subject: Re: JSH: So what happened? > [...] >Factoring problem is solved. No more room for confusion about the >result. All issues are resolved. > Except you can't factor a large number. Or, apparently, a small one. >James Harris === Subject: Re: JSH: So what happened? > Some of you may have noticed a very big discussion over the last few > weeks where I've claimed to have solved the factoring problem and > various posters have said I haven't and put up issues with my claims. So here's a quick synopsis to get you up to speed on what happened: 1. I noticed that you can use Pell's Equation to do dual > factorizations to attack factoring a composite target D by factoring > D-1 instead: In rationals, x^2 - Dy^2 = 1 requires that (D-1)j^2 + (j+/-1)^2 = (x+y)^2 where j = ((x+Dy) -/+1)/D. Ok, so I know you've seen that but the issue was how to actually get a > key variable called v, where j=uv, and I had an explicit solution for > x that looked like: x = +/-(f_1 + f_2*v^2)/(f_1 - f_2*v^2 - 2v) - [+/-2Dv/(f_1 - f_2*v^2 - > 2v) +/- 1 -/+(f_1 + f_2*v^2)/(f_1 - f_2*v^2 - 2v)]/(D-1) where f_1*f_2 = D-1, and the f's are integers, while v is a free > variable, which is a mess I didn't want to deal with, so I didn't try > to simplify it, and just hoped others with math software would do so, > but I talked about factoring D non-trivially with its numerator and > denominator, as with functions I call r(v) and t(v), and x=r(v)/t(v) it is trivial that if they are integers and abs(r(v) - t(v)) < D, and > abs(r(v) + t(v)) < D, then you non-trivially factor D. And I'd proven the existence of integer solutions so I thought I was > done. But posters started claiming they couldn't work, and some put up: r(v) + t(v) = 2Dv^2 which to me implied that v had to have a non-trivial factor in common > with D before you could use it, but hey, that couldn't work as v is > squared, so you'd always have a fraction! So I figured they were > lying, and said so repeatedly as I didn't want to bother with that > monster expression I had for x, and kept thinking that all those plus > or minuses meant a lot of variations. But I was wrong. I finally simplified things further and found a > simple equation for x: x = [(D+1)v^2 - 2f_1*v + f_1^2]/[f1(f_1 - f_2*v^2 - 2v)] And lo and behold if adding the numerator to the denominator didn't > give what I'd claimed had to be wrong!!! Turned out the math was more subtle than I'd imagined and was slapping > a freaking non-trivial factor of D on the numerator and denominator. > That divides off easily enough--if you know what it is--but when you > add them, you get 2Dv^2. But NOT a big deal as instead of taking the gcd of r(v) + t(v) with D > as I'd originally said, you take it with r(v). No worries, I thought. But then I noticed that I could NOT get r(v) = (D+1)v^2 - 2f_1*v + f_1^2 and t(v) = f_1*(f_1 - f_2*v^2 - 2v) to both be integers with a rational v. It was a what the f-moment. Turns out the algebra had one more trick up its sleeve as both have > been divided by 2. They have to both be integers to force a non-trivial solution with abs > (r(v)) < D--oh yeah, I found that as a primary condition--so I ended > up needing to multiply both by 2, and that's it. However, a month of me working through these issues, especially weeks > of me refusing to simplify x left the door open to posters who spread > confusion about the result! One funny part though was when they > specifically claimed it couldn't factor 15. But I had an example of a > factorization of 15, so I knew they were wrong. And that's the story, of how there can have been so much debate about > a solution to the factoring problem for weeks. Synopsis: I didn't feel like simplifying a key equation. The algebra > had some subtleties that opened the door to confusion if you DID > simplify the damn thing. And even after that point you needed to > figure out one more wacky thing as in the functions had been divided > by 2, and then everything works just fine. Factoring problem is solved. No more room for confusion about the > result. All issues are resolved. Except that it does not work. You have been given counterexamples which show your proof is wrong. Don't you believe in basic math? > James Harris === Subject: Re: JSH: So what happened? Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >Factoring problem is solved. Could you give a precise statement of the factoring problem, and tell us whether it was already solved? -- Richard -- Please remember to mention me / in tapes you leave behind. === Subject: Re: JSH: So what happened? I have read parts of the discussion and must say. I am still a bit confused about your algorithm. I can't say I have fully understood how it works and why. As far as I can see, the ammount of work to factor a number N with your algorithm grows with sqrt(N). That is also true for simply trying to divide by all numbers from 2 to sqrt(N). If my observation is true, the complexity has not improved with your algorithm. > Factoring problem is solved. Exactly that is not the case, if I have understood the complexity of your algorithm. I don't say, you can not factor a Number with your algorithm. Theoretically any number can be factored by test divisions. Runtime for really large numbers is the problem, not factoring at all. Christof === === Subject: centroids of a finite set in a normed space can anybody of you help me with the following problem: Let V be a real, normed vector space of finite dimension. A centroid z of the finite set {v1,...,vr} is a solution of the optimization problem min ( |v-v1|+...+|v-vr| ) . It is known that a centroid exists. It is unique if the unit ball in V is strictly convex. In the case of the euclidean norm the centroid is given by z = 1/r * (v1+...+vr). Question: is there a closed-form-solution for other normed spaces too? H === Subject: Limit question Hi! I need some hint for this: if a_n is a non-negative sequence converging to a finite constant c >= 0 then (a_n)^p/sum_i=1^n (a_i)^p = O(1/n), n -> infinity with p > 0. My goal is to remove the assumption: a_n is decreasing. RSimmons === Subject: Re: Limit question <9332390.1237281351709.JavaMail.jakarta@nitrogen.mathforum.org>, > Hi! I need some hint for this: if a_n is a non-negative sequence converging > to a finite constant c >= 0 then (a_n)^p/sum_i=1^n (a_i)^p = O(1/n), n -> infinity You have a tendency to allow 0 denominators in your problems. Let's assume at least some a_n > 0. > with p > 0. My goal is to remove the assumption: a_n is decreasing. The power p is immaterial, so take p = 1. If a_n -> c > 0, then (a_1 + ... + a_n)/n -> c. This implies a_n/[(a_1 + ... + a_n)/n] -> 1, so a_n/(a_1 + ... + a_n) is asymptotic to 1/n, which is a better result than O(1/n). If a_n -> 0, O(1/n) can fail. For example, let a_n = 1/sqrt(n) if n is a perfect square, a_n = 1/2^n otherwise. Then a_(m^2)/(a_1 + ... + a_(m^2)) > (1/m)/[1 + 1/2 + ... + 1/m + 2], > (1/m)/[log(m) + 3] > 1/m^2. === Subject: Re: Limit question <9332390.1237281351709.JavaMail.jakarta@nitrogen.mathforum.org>, > Hi! I need some hint for this: if a_n is a non-negative sequence converging > to a finite constant c >= 0 then (a_n)^p/sum_i=1^n (a_i)^p = O(1/n), n -> infinity with p > 0. My goal is to remove the assumption: a_n is decreasing. As stated it's not true (for example maybe a_n = 0 for all n). If you assume c > 0 then what Torsten said. > RSimmons -- David C. Ullrich === Subject: Re: Limit question > Hi! I need some hint for this: if a_n is a > non-negative sequence converging to a finite constant > c >= 0 then (a_n)^p/sum_i=1^n (a_i)^p = O(1/n), n -> infinity with p > 0. My goal is to remove the assumption: a_n > is decreasing. RSimmons a_n -> c Ç -> (a_n)^p -> c^p -> 1/n*sum_{i=1}^{n} (a_i)^p -> c^p Now use |(a_n)^p-c^p|/(1/n*sum_{i=1}^{n} (a_i)^p) -> 0 and c^p/(1/n*sum_{i=1}^{n} (a_i)^p) = O(1) to show that (a_n)^p/(1/n*sum_{i=1}^{n} (a_i)^p) = O(1). Best wishes Torsten. === Subject: Re: Limit question > Hi! I need some hint for this: if a_n is a > non-negative sequence converging to a finite > constant > c >= 0 then (a_n)^p/sum_i=1^n (a_i)^p = O(1/n), n -> infinity with p > 0. My goal is to remove the assumption: > a_n > is decreasing. RSimmons > a_n -> c Ç > -> (a_n)^p -> c^p > -> 1/n*sum_{i=1}^{n} (a_i)^p -> c^p Now use |(a_n)^p-c^p|/(1/n*sum_{i=1}^{n} (a_i)^p) - 0 > and c^p/(1/n*sum_{i=1}^{n} (a_i)^p) = O(1) to show > that (a_n)^p/(1/n*sum_{i=1}^{n} (a_i)^p) = O(1). Best wishes > Torsten. As others have pointed out, the assertion may fail in the case c=0 for arbitrary sequences (a_n). Maybe that's where you need the assumption that (a_n) is decreasing because for this case you get (a_n)^p / (1/n * sum_{i=1}^{n} (a_i)^p) <= 1. Best wishes Torsten. === Subject: Self-proclaimed genius discovers division by zero WAS:Small numbers for small Denialist brains posting-account=32kyHQoAAABCJbXmMdnX-j-O3VdI5K3F Gecko/20071126 Fedora/1.5.0.12-7.fc6 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) Apologies to readers of sci.math for cross-posting this, but I thought you just might enjoy a laugh > I have been viciously attacked by small fractions several times. > Do we have to be scared of all small numbers, or just the AGW ones. > It is important to compare apples with apples. > Don't compare CO2 with Polonium. > Normal amount of Polonium = 0.00000g > Lethal dose of Polonium = 0.00005g > Percentage increase = 0.00005 * 100 / 0.00000 = infinity % > Alas no. Had you ever taken a mathematics course during your > education, you would have learned that division by zero is > expressly excluded from arithmetic. I can see now that all those > claims about having A's in everything you studied are just so > much mendacity. JohnM, you are obviously limited to elementary (school) mathematics. Those of us who have graduated to higher mathematics, have no problem > understanding this concept. Wow. Graduated to higher mathematics he has. Wow! > When you get out of short britches, you > may be able to appreciate the following information. As you read the following, consider these points: > 1) I am a computer programmer, with about 25 years of practical > programming experience (see the section on computer arithmetic) > 2) The extended non-negative real number line is appropriate when > dealing with physical matter (like Polonium), since you can not have > a negative amount of Polonium. > 3) The symbol for infinity did not copy and paste properly. I have > inserted the word infinity where I noticed this. Gosh. Considering those three things explains everything. Isn't higher mathematics a wonderful thing. Ask Dr. Math http://mathforum.org/library/drmath/view/55795.html Zero and Infinity Some people say that 1/0 is infinity as a kind of short hand for what > happens to 1/x as x approaches 0. Note that if x approaches 0 from the > right, 1/x becomes larger and larger; often we say that 1/x approaches > infinity. Note also that 1/x becomes smaller and smaller as x > approaches 0 from the left, so that 1/x approaches negative infinity. ---------- In mathematics, a division is called a division by zero if the divisor > is zero. Such a division can be formally expressed as a/0 where a is > the dividend. Whether this expression can be assigned a well-defined > value depends upon the mathematical setting. In ordinary (real number) > arithmetic, the expression has no meaning. > ---------- > This connection of division by zero to infinity takes us beyond > elementary arithmetic (see below). > ---------- > Formal operations > A formal calculation is one which is carried out using rules of > arithmetic, without consideration of whether the result of the > calculation is well-defined. Thus, as a rule of thumb, it is sometimes > useful to think of a/0 as being infinity, provided a is not zero. This > infinity can be either positive, negative or unsigned, depending on > context. > ---------- >Extended non-negative real number line. > The negative real numbers can be discarded, and infinity introduced, > leading to the set [0, infinity], where division by zero can be > naturally defined as a/0 = infinity, for positive a. While this makes > division defined in more cases than usual, subtraction is instead left > undefined in many cases, because there are no negative numbers. > ---------- > In computer arithmetic > The IEEE floating-point standard, supported by almost all modern > processors, specifies that every floating point arithmetic operation, > including division by zero, has a well-defined result. In IEEE 754 > arithmetic, a .85 0 is positive infinity when a is positive, negative > infinity when a is negative, and NaN (not a number) when a = 0. The > infinity signs change when dividing by -0 instead. This is possible > because in IEEE 754 there are two zero values, plus zero and minus > zero, and thus no ambiguity. So. Just as I said. In normal, real-number arithmetic there is no way you can write a result for a division by zero. Defining it as positive infinity leads to the impossibility of correctly defining subtraction. All the lengthy references you have just given tell you that had you bothered to read them. === Subject: Re: Self-proclaimed genius discovers division by zero WAS:Small numbers for small Denialist brains I, JohnM, am a blithering douche-nozzle. === Subject: JohnM-proclaimed genius, teaches JohnM about division by zero (was: Small numbers for small Denialist brains) posting-account=kYCflQoAAABc0Os-abVEiyZDkuVglBKp 2.0.50727),gzip(gfe),gzip(gfe) > Apologies to readers of sci.math for cross-posting this, but I thought > you just might enjoy a laugh > I have been viciously attacked by small fractions several times. > Do we have to be scared of all small numbers, or just the AGW ones. > It is important to compare apples with apples. > Don't compare CO2 with Polonium. > Normal amount of Polonium = 0.00000g > Lethal dose of Polonium = 0.00005g > Percentage increase = 0.00005 * 100 / 0.00000 = infinity % > Alas no. Had you ever taken a mathematics course during your > education, you would have learned that division by zero is > expressly excluded from arithmetic. I can see now that all those > claims about having A's in everything you studied are just so > much mendacity. > JohnM, you are obviously limited to elementary (school) mathematics. > Those of us who have graduated to higher mathematics, have no problem > understanding this concept. Wow. Graduated to higher mathematics he has. Wow! > When you get out of short britches, you > may be able to appreciate the following information. > As you read the following, consider these points: > 1) I am a computer programmer, with about 25 years of practical > programming experience (see the section on computer arithmetic) > 2) The extended non-negative real number line is appropriate when > dealing with physical matter (like Polonium), since you can not have > a negative amount of Polonium. > 3) The symbol for infinity did not copy and paste properly. I have > inserted the word infinity where I noticed this. Gosh. Considering those three things explains everything. Isn't higher > mathematics a wonderful thing. ---------- > Ask Dr. Math http://mathforum.org/library/drmath/view/55795.html > Zero and Infinity > Some people say that 1/0 is infinity as a kind of short hand for what > happens to 1/x as x approaches 0. Note that if x approaches 0 from the > right, 1/x becomes larger and larger; often we say that 1/x approaches > infinity. Note also that 1/x becomes smaller and smaller as x > approaches 0 from the left, so that 1/x approaches negative infinity. > ---------- > In mathematics, a division is called a division by zero if the divisor > is zero. Such a division can be formally expressed as a/0 where a is > the dividend. Whether this expression can be assigned a well-defined > value depends upon the mathematical setting. In ordinary (real number) > arithmetic, the expression has no meaning. > ---------- > This connection of division by zero to infinity takes us beyond > elementary arithmetic (see below). > ---------- > Formal operations > A formal calculation is one which is carried out using rules of > arithmetic, without consideration of whether the result of the > calculation is well-defined. Thus, as a rule of thumb, it is sometimes > useful to think of a/0 as being infinity, provided a is not zero. This > infinity can be either positive, negative or unsigned, depending on > context. > ---------- >Extended non-negative real number line. > The negative real numbers can be discarded, and infinity introduced, > leading to the set [0, infinity], where division by zero can be > naturally defined as a/0 = infinity, for positive a. While this makes > division defined in more cases than usual, subtraction is instead left > undefined in many cases, because there are no negative numbers. > ---------- > In computer arithmetic > The IEEE floating-point standard, supported by almost all modern > processors, specifies that every floating point arithmetic operation, > including division by zero, has a well-defined result. In IEEE 754 > arithmetic, a .85 0 is positive infinity when a is positive, negative > infinity when a is negative, and NaN (not a number) when a = 0. The > infinity signs change when dividing by -0 instead. This is possible > because in IEEE 754 there are two zero values, plus zero and minus > zero, and thus no ambiguity. So. Just as I said. In normal, real-number arithmetic there is no way > you can write a result for a division by zero. Defining it as positive > infinity leads to the impossibility of correctly defining subtraction. > All the lengthy references you have just given tell you that had you > bothered to read them. JohnM, I never proclaimed myself a genius. You did (presumably trying to turn people against me). So I have changed the title to the factual JohnM-proclaimed genius, teaches JohnM about division by zero (was: Small numbers for small Denialist brains). Anybody wishing to see the desperate lengths that JohnM is going to, in order to try and prove his superiority, should read the other posts in alt.global-warming (from him and me). They are worth a laugh. Mr Right, self-proclaimed scientific genius, runs for cover. Sorry, Mr Right... Mr Right, stands his ground Mr Right waves his hands a bit more... I have left out two other threads that JohnM posted the same stuff to. ---------- Anybody interested in seeing how this started (on Feb 6th), should read the first two posts of this thread: What does the south australian heatwave tell us about AGW? I posted some simple facts (mostly temperatures and dates), with links so that people could check that they were true. They were mostly from the official Australian Government's Bureau of Meteorology website. JohnM obviously didn't like my facts. He compared me to a holocaust denying pope. This was the first time I had ever heard from him. It has been downhill ever since. :) === Subject: Prime Numbers of form 10^n+27 posting-account=em7BlwoAAADOhRXv8AilqN49TjuokE7m Trident/4.0; .NET CLR 2.0.50727; FDM; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) Prove/Disprove: 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} === Subject: Re: Prime Numbers of form 10^n+27 posting-account=-Z3yxwoAAAC8hrDdnCbK2tYGsCLKT7qj CLR 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} How exactly is 10 to the power of a set defined? ;) === Subject: Re: Prime Numbers of form 10^n+27 posting-account=em7BlwoAAADOhRXv8AilqN49TjuokE7m Trident/4.0; InfoPath.2; FDM; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} How exactly is 10 to the power of a set defined? ;) Well there in no great logic behind it but it seems these are the only possible numbers Have a look at: http://www.research.att.com/~njas/sequences/A108312 === Subject: Re: Prime Numbers of form 10^n+27 > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 I would suspect that (i) The statement is false (and, in fact, that 10^n+27 is prime infinitely often) and (ii) Nobody is likely to prove (or disprove) this anytime soon. Statement (i) follows from standard density heuristics. de Pumpster === Subject: Re: Prime Numbers of form 10^n+27 > > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) > Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 I would suspect that (i) The statement is false (and, in fact, that 10^n+27 is prime > infinitely often) and (ii) Nobody is likely to prove (or disprove) this anytime soon. Statement (i) follows from standard density heuristics. The same applies to a^n + b, n = 1, 2, 3, ..., for any fixed a and b, provided there isn't some simple reason for the number of primes in the sequence to be finite (such as gcd(a, b) > 1). So the question is, why should anyone care about 10^n + 27? What makes it more interesting than 10^n + 7, or 43^n + 10, or any of the other infinity of similar formulas a person could write down? -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Prime Numbers of form 10^n+27 posting-account=em7BlwoAAADOhRXv8AilqN49TjuokE7m Trident/4.0; .NET CLR 2.0.50727; FDM; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) On Mar 18, 2:48am, Gerry Myerson Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) > Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 > I would suspect that > (i) The statement is false (and, in fact, that 10^n+27 is prime > infinitely often) > and > (ii) Nobody is likely to prove (or disprove) this anytime soon. > Statement (i) follows from standard density heuristics. The same applies to a^n + b, n = 1, 2, 3, ..., for any fixed a and b, > provided there isn't some simple reason for the number of primes in > the sequence to be finite (such as gcd(a, b) > 1). So the question is, why should anyone care about 10^n + 27? > What makes it more interesting than 10^n + 7, or 43^n + 10, > or any of the other infinity of similar formulas a person could > write down? -- > Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)- Hide quoted text - - Show quoted text - I asked this question because 10^n + 27 is of form a^n + p^p (p denotes prime & a is base of our decimal number system) so I thought there may be some kind of proof for that which I am not aware of. But Other interestig (similar) question goes here: === Subject: Re: Prime Numbers of form 10^n+27 posting-account=DLD3MQkAAACJxulKt9xouw3DPpXKssCI GTB5; SLCC1; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On Mar 17, 2:48pm, Gerry Myerson Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) > Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 > I would suspect that > (i) The statement is false (and, in fact, that 10^n+27 is prime > infinitely often) > and > (ii) Nobody is likely to prove (or disprove) this anytime soon. > Statement (i) follows from standard density heuristics. The same applies to a^n + b, n = 1, 2, 3, ..., for any fixed a and b, > provided there isn't some simple reason for the number of primes in > the sequence to be finite (such as gcd(a, b) > 1). So the question is, why should anyone care about 10^n + 27? > What makes it more interesting than 10^n + 7, or 43^n + 10, > or any of the other infinity of similar formulas a person could > write down? If there are only 5 of that format it would be interesting. For instance, these are all prime: 17, 107, 10007, 100000007, 1000000007, 1000000000000000000000007, 1000000000000000000000000000000000000000000000000000000000007, 1000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000007, 1000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000007, 1000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000 0 0000000000000000000000000000000000000000000000000000000000000000000007 ... so they appear to be more plentiful. Similarly for 10^k + 3: 13, 103, 100003, 1000003, 100000000003, 100000000000000003, 1000000000000000003, 1000000000000000000000000000000000000003, 100000000000000000000000000000000000000000000000000000003, 1000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000003, 1000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000003, 1000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000003, 1000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000003 ... When strings of the digit 1 are prime, that seems interesting to me. 10^k + 1 appears to be prime only for 11 and 101. {just conjecture, I have no proof of this} I think that it is fun to look for patterns. If the case for 10^k + 27 is a small, exhaustive set then that is interesting too. === Subject: Re: Prime Numbers of form 10^n+27 > On Mar 17, 2:48pm, Gerry Myerson Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) > Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 > I would suspect that > (i) The statement is false (and, in fact, that 10^n+27 is prime > infinitely often) > and > (ii) Nobody is likely to prove (or disprove) this anytime soon. > Statement (i) follows from standard density heuristics. > The same applies to a^n + b, n = 1, 2, 3, ..., for any fixed a and b, > provided there isn't some simple reason for the number of primes in > the sequence to be finite (such as gcd(a, b) > 1). > So the question is, why should anyone care about 10^n + 27? > What makes it more interesting than 10^n + 7, or 43^n + 10, > or any of the other infinity of similar formulas a person could > write down? If there are only 5 of that format it would be interesting. It would be a lot more than interesting, it would be downright sensational. But as a previous poster mentioned, there's no good reason to believe it. > 10^k + 1 appears to be prime only for 11 and 101. {just conjecture, I > have no proof of this} Note that it's composite unless k is a power of 2. Cf Fermat primes. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: Prime Numbers of form 10^n+27 posting-account=T7Gd-QoAAACeQajv7mi_Za6uPu3TpBXy AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.48 Safari/525.19,gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) > Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 I would suspect that (i) The statement is false (and, in fact, that 10^n+27 is prime > infinitely often) and (ii) Nobody is likely to prove (or disprove) this anytime soon. Statement (i) follows from standard density heuristics. de Pumpster Standard density heuristics: For large n, the density of primes around n is 1/log(n). So around 10^n it is 1/(n log 10). But we know 10^n + 27 is not divisible by 2, 3, or 5, so we can multiply this by (2/1)(3/2)(5/4) = 15/4. Thus in general we would expect 10^n + 27 to be prime with probability 15/(4n log 10). So for large n, the expected number of primes in the sequence is about sum(r=1 to n) 15/(4r log 10) = 15/(4 log 10) sum(r=1 to n) 1/r which is about 15 log n / (4 log 10). This tends to infinity with n, so we would expect an infinite number of such primes. But as far as I know, nobody knows how to prove this rigorously. Incidentally, if n is 10000, then log n / log 10 = 4, so according to this formula, we should expect 15 primes instead of the five that we find. This (I presume) is down to statistical fluctuation, and the fact that I left Euler's gamma constant out of the harmonic sum. === Subject: Re: Prime Numbers of form 10^n+27 posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp SV1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-dtc-td02.proxy.aol.com[CDBC7062] (Prism/1.2.1) > Standard density heuristics: > For large n, the density of primes around n is 1/log(n). So around > 10^n it is 1/(n log 10). But we know 10^n + 27 is not divisible by 2, > 3, or 5, so we can multiply this by (2/1)(3/2)(5/4) = 15/4. Thus in > general we would expect 10^n + 27 to be prime with probability 15/(4n > log 10). So for large n, the expected number of primes in the sequence > is about You left out a major consideration. n itself can not be a multiple of 3; 10^(3k) + 27 is the sum of two cubes....... === Subject: Re: Prime Numbers of form 10^n+27 > > Standard density heuristics: > For large n, the density of primes around n is 1/log(n). So around > 10^n it is 1/(n log 10). But we know 10^n + 27 is not divisible by 2, > 3, or 5, so we can multiply this by (2/1)(3/2)(5/4) =3D 15/4. Thus in > general we would expect 10^n + 27 to be prime with probability 15/(4n > log 10). So for large n, the expected number of primes in the sequence > is about You left out a major consideration. n itself can not > be a multiple of 3; 10^(3k) + 27 is the sum of two cubes....... And n can't be congruent to 1 mod 3, as 10^(3k+1) + 27 is divisible by 37. So n must be congruent to 2 mod 3. -- === Subject: Re: Prime Numbers of form 10^n+27 posting-account=XzESVgkAAAASMMQZpglhqosZg-ouN3uW AppleWebKit/523.12 (KHTML, like Gecko) Version/3.0.4 Safari/523.12,gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > How exactly is 10 to the power of a set defined? ;) > Well there in no great logic behind it but it seems these are the only > possible numbers > Have a look at:http://www.research.att.com/~njas/sequences/A108312 > I would suspect that > (i) The statement is false (and, in fact, that 10^n+27 is prime > infinitely often) > and > (ii) Nobody is likely to prove (or disprove) this anytime soon. > Statement (i) follows from standard density heuristics. > de Pumpster Standard density heuristics: > For large n, the density of primes around n is 1/log(n). So around > 10^n it is 1/(n log 10). But we know 10^n + 27 is not divisible by 2, > 3, or 5, so we can multiply this by (2/1)(3/2)(5/4) = 15/4. Thus in > general we would expect 10^n + 27 to be prime with probability 15/(4n > log 10). So for large n, the expected number of primes in the sequence > is about sum(r=1 to n) 15/(4r log 10) = 15/(4 log 10) sum(r=1 to n) 1/r which is about 15 log n / (4 log 10). This tends to infinity with n, > so we would expect an infinite number of such primes. But as far as I > know, nobody knows how to prove this rigorously. > Incidentally, if n is 10000, then log n / log 10 = 4, so according to > this formula, we should expect 15 primes instead of the five that we > find. This (I presume) is down to statistical fluctuation, and the > fact that I left Euler's gamma constant out of the harmonic sum. We also can factor in some local conditions for n (e.g. that n <> 0 mod 3, etc) which would reduce our expected number somewhat.... In any case, we'd probably be predicting a few more than 4 up to 10000.... === Subject: Re: Prime Numbers of form 10^n+27 posting-account=em7BlwoAAADOhRXv8AilqN49TjuokE7m Trident/4.0; InfoPath.2; FDM; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} How exactly is 10 to the power of a set defined? ;) Well there is not logic behind it but I seems these are the only possible ones :) Have a look at http://www.research.att.com/~njas/sequences/A108312 === Subject: Re: Prime Numbers of form 10^n+27 posting-account=DLD3MQkAAACJxulKt9xouw3DPpXKssCI GTB5; SLCC1; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} n=1 c:tmp>factor 127 this number is prime! n=2 c:tmp>factor 1027 first trying brute force division by small primes PRIME FACTOR 13 PRIME FACTOR 79 check: 13*79=1027 disprove by counterexample. === Subject: Re: Prime Numbers of form 10^n+27 > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} n=1 > c:tmp>factor 127 > this number is prime! For n = 1, 10^1 + 27 = 10 + 27 = 37, which is prime. n=2 > c:tmp>factor 1027 > first trying brute force division by small primes > PRIME FACTOR 13 > PRIME FACTOR 79 check: > 13*79=1027 disprove by counterexample. How does factoring 10^3 + 27 disprove the claim? === Subject: Re: Prime Numbers of form 10^n+27 posting-account=DLD3MQkAAACJxulKt9xouw3DPpXKssCI GTB5; SLCC1; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} > n=1 > c:tmp>factor 127 > this number is prime! For n = 1, 10^1 + 27 = 10 + 27 = 37, which is prime. > n=2 > c:tmp>factor 1027 > first trying brute force division by small primes > PRIME FACTOR 13 > PRIME FACTOR 79 > check: > 13*79=1027 > disprove by counterexample. How does factoring 10^3 + 27 disprove the claim? It doesn't. Hence my nevermind follow-up post. === Subject: Re: Prime Numbers of form 10^n+27 posting-account=DLD3MQkAAACJxulKt9xouw3DPpXKssCI GTB5; SLCC1; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > Prove/Disprove: > 10^n + 27 will be prime only when n = {1, 2, 83, 167, 242} n=1 > c:tmp>factor 127 > this number is prime! n=2 > c:tmp>factor 1027 > first trying brute force division by small primes > PRIME FACTOR 13 > PRIME FACTOR 79 check: > 13*79=1027 disprove by counterexample. Oops, that was 10^3. Never mind. === Subject: Interesting but Rare numbers posting-account=em7BlwoAAADOhRXv8AilqN49TjuokE7m Trident/4.0; .NET CLR 2.0.50727; FDM; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) Have a look at following sequence submitted by me on OEIS http://www.research.att.com/~njas/sequences/A153874 Can you prove that those are the only possible numbers having such properties? Following is the related question which I had asked: http://answers.yahoo.com/question/index?qid=20090102093449AAwlM3m === Subject: Re: Interesting but Rare numbers posting-account=Cbgh4AoAAAAr0dt1RqLOClWCyUWii2fU Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Have a look at following sequence submitted by me on OEIShttp://www.research.att.com/~njas/sequences/A153874 Can you prove that those are the only possible numbers having such > properties? Following is the related question which I had asked:http://answers.yahoo.com/question/index?qid=20090102093449AAwlM3m > A few trivialties: LEMMA: At least one digit is even. Proof: If all a_i are odd, then (a_1*...*a_n)^2 = 1 mod 8, hence a_n even -- contradiction. COROLLARY: The number is 3 mod 4. Proof: It is one less than an even square. LEMMA: If any of the digits is 5, then a_{n-1} = a_n = 9 Proof: The product of the digits is 0 mod 5, hence their square -1 is 4 mod 5 and hence a_n in {4,9}. But it is already known that a_n in {3,9} and that a_n = 9 implies a_{n-1} = 9. LEMMA: If no digit is 5, then a_n = 3 and a_{n-1} in {2,4,6,8}. Proof: The product of the digits is non-zero mod 5, hence their square is +/- 1 mod 5 and hence a_n = 4 +/- 1 mod 5. Again, use a_n in {3,9}. Since the complete number must be 3 mod 4, it follows that a_{n-1} is even. Do you have any other numbers abc...d such that a^2*b^2*c^2*...*d^2 - 1 - abc...d is divisible by a high power of ten? === Subject: JohnM makes an embarrassing mistake posting-account=kYCflQoAAABc0Os-abVEiyZDkuVglBKp 2.0.50727),gzip(gfe),gzip(gfe) JohnM makes an embarrassing mistake. < I challenged you to prove your credentials by performing a simple < piece of stats. You ignored that in your latest rant, so here's the < ten years of data, again. Your task is to identify the distribution- < free test I used to discover if any grounds existed for attempting a < regression of temperature on date. < < 2009 14.41 < 2008 14.15 < 2007 14.61 < 2006 14.59 < 2005 14.56 < ++++++++ < 2002 14.70 < 2001 14.41 < 2000 14.51 < < The null hypothesis is that temperature data for the two groups is < identical. Name the test that gives a derived statistic of 15.5 and < calculate the probability of getting this value or smaller under the < null hypothesis. ---------- JohnM, If you want somebody to jump through your hoop, then I suggest that you buy a dog. I know that you have only one purpose in mind, when asking this question, and it is not an honourable one. Your recent behaviour means that you do not have the right to demand anything. I seem to remember that you once claimed to be a scientist. I find that hard to believe, given that your behaviour is not acceptable for a scientist. I still don't believe that you have posted the answer to this problem on alt.global-warming, even though you said you did. The message-id that you gave, did not show it. Please post a normal link to it, to prove that you are not lying. Other people can manage this, what about you? ---------- I know that you will immediately claim that I am not able to answer your question. So I have devised a way to prove that I know the answer to the question, without actually telling you the answer. The thing is, you have not calculated the statistic correctly. If you swap sample 1 and sample 2, and recalculate the statistic, you will find that the correct answer is 9.5 (not 15.5). Note the relationship (with sample sizes of 5): 9.5 + 15.5 = 25 = 5 * 5 Nice, isn't it. The smaller value (in this case 9.5) is the one used when consulting significance tables. It looks like it is back to the significance tables, for you. === Subject: Re: JohnM makes an embarrassing mistake posting-account=32kyHQoAAABCJbXmMdnX-j-O3VdI5K3F Gecko/20071126 Fedora/1.5.0.12-7.fc6 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > JohnM makes an embarrassing mistake. > < I challenged you to prove your credentials by performing a simple > < piece of stats. You ignored that in your latest rant, so here's the > < ten years of data, again. Your task is to identify the distribution- > < free test I used to discover if any grounds existed for attempting a > < regression of temperature on date. > < > < 2009 14.41 > < 2008 14.15 > < 2007 14.61 > < 2006 14.59 > < 2005 14.56 > < ++++++++ > < 2002 14.70 > < 2001 14.41 > < 2000 14.51 > < > < The null hypothesis is that temperature data for the two groups is > < identical. Name the test that gives a derived statistic of 15.5 and > < calculate the probability of getting this value or smaller under the > < null hypothesis. ---------- JohnM, If you want somebody to jump through your hoop, then I suggest that > you buy a dog. I know that you have only one purpose in mind, when asking this > question, and it is not an honourable one. Your recent behaviour means that you do not have the right to demand > anything. I seem to remember that you once claimed to be a scientist. I find > that hard to believe, given that your behaviour is not acceptable for > a scientist. I still don't believe that you have posted the answer to this problem > on alt.global-warming, even though you said you did. The message-id > that you gave, did not show it. Please post a normal link to it, to > prove that you are not lying. Other people can manage this, what about > you? The answer couldn't be clearer than stated in the post - the result is not significant. > ---------- I know that you will immediately claim that I am not able to answer > your question. So I have devised a way to prove that I know the answer to the > question, without actually telling you the answer. The thing is, you have not calculated the statistic correctly. If you > swap sample 1 and sample 2, and recalculate the statistic, you > will find that the correct answer is 9.5 (not 15.5). Aha. You found the test I used was M-W-W and ,as it is very simple to apply, you were able to do it even in your educationally-challenged condition. Pity you didn't read the instructions in the book more carefully. *The* correct answer I have outlined below, in case you may have confused readers by your incorrect statement.. > Note the relationship (with sample sizes of 5): 9.5 + 15.5 = 25 = 5 * 5 Nice, isn't it. In fact, due to the symmetry n1 = n2, both values do give the same result as one another if applied using a method I've mentioned below. Application of all forms of the test require one to use the larger of 'n1*n2 - C' and 'C' for the value of 'U' if the statistic is tabulated in that way. My tables are, but I see various free tables on the internet are indeed tabulated in the forward and reverse sense. Some even give pairs of values. > The smaller value (in this case 9.5) is the one used when consulting > significance tables. If one doesn't have tabulated values for this test one can do an approximate test. Anyway, there is no exact test because of tied values across the groups. Simply convert the correct value (15.5 or 9.5, because n1 = n2 ) into a 't.81.87' value using published formula, ignoring the negative sign if you improperly use 9.5. As the value is nowhere near significance, accept the null hypothesis. > It looks like it is back to the significance tables, for you. Why bother: http://elegans.swmed.edu/~leon/core_2002/stats/formulas.htm#utest Putting the data through this site shows nicely the equivalence when n1 = n2 as it gives an identical result for [5,5,9.5] and for [5,5,15.5] Also the size of error made when using the calculation of 't.81.87' as an approximate test of U can be judged. === Subject: JohnM successfully proves that there has been NO global warming in the last 10 years posting-account=kYCflQoAAABc0Os-abVEiyZDkuVglBKp 2.0.50727),gzip(gfe),gzip(gfe) JohnM successfully proves that there has been NO global warming in the last 10 years. ---------- I challenged you to prove your credentials by performing a simple piece of stats. You ignored that in your latest rant, so here's the ten years of data, again. Your task is to identify the distribution- free test I used to discover if any grounds existed for attempting a regression of temperature on date. 2009 14.41 2008 14.15 2007 14.61 2006 14.59 2005 14.56 ++++++++ 2002 14.70 2001 14.41 2000 14.51 The null hypothesis is that temperature data for the two groups is identical. Name the test that gives a derived statistic of 15.5 and calculate the probability of getting this value or smaller under the null hypothesis. ---------- The answer couldn't be clearer than stated in the post - the result is not significant. Aha. You found the test I used was M-W-W and ,as it is very simple to apply, you were able to do it even in your educationally-challenged condition. As the value is nowhere near significance, accept the null hypothesis. ---------- JohnM, congratulations. You are the second AGW Alarmist (that I know of), to accidently statistically prove that global warming is not happening. I am afraid that Roger Coppock has done this several times before you, but he is too scared to look at the last 10 years, which you have done. You were so busy trying to discredit me, by setting me this difficult problem, that you didn't consider what the result actually means. Not only did I successfully answer your question, but you have successfully proved that there has been NO global warming in the last 10 years. Analysis: JohnM said: The null hypothesis is that temperature data for the two groups is identical. Name the test that gives a derived statistic of 15.5 and calculate the probability of getting this value or smaller under the null hypothesis. JohnM said: As the value is nowhere near significance, accept the null hypothesis. Conclusion: We accept the null hypothesis, that temperature data for the two groups is identical. That means that there is no evidence of warming, or cooling, between the 2 groups. The temperature had been stable for the last 10 years. ---------- JohnM, I give you full credit for finding this statistical test. Knowing your views on AGW, I suspect that you did not realise the meaning of the result. Without your help, we would not have this proof. It would be VERY interesting to apply this test to other year ranges, even over the entire 130 year range of Hansens data. I will allow you the honour of doing this test on other date ranges, since YOU came up with the test. If you do not want to do it, then I think that you have provided enough information in your posts, for somebody else to do the work. I eagerly await the results. === Subject: Re: JohnM successfully proves that there has been NO global warming in the last 10 years > JohnM successfully proves that there has been NO global warming in the > last 10 years. ---------- > I challenged you to prove your credentials by performing a simple > piece of stats. You ignored that in your latest rant, so here's the > ten years of data, again. Your task is to identify the distribution- > free test I used to discover if any grounds existed for attempting a > regression of temperature on date. 2009 14.41 > 2008 14.15 > 2007 14.61 > 2006 14.59 > 2005 14.56 > ++++++++ > 2002 14.70 > 2001 14.41 > 2000 14.51 The null hypothesis is that temperature data for the two groups is > identical. Name the test that gives a derived statistic of 15.5 and > calculate the probability of getting this value or smaller under the > null hypothesis. ---------- > The answer couldn't be clearer than stated in the post - the result is > not significant. Aha. You found the test I used was M-W-W and ,as it is very simple to > apply, you were able to do it even in your educationally-challenged > condition. As the value is nowhere near significance, accept the null hypothesis. ---------- > JohnM, congratulations. You are the second AGW Alarmist (that I know > of), to accidently statistically prove that global warming is not > happening. I am afraid that Roger Coppock has done this several times > before you, but he is too scared to look at the last 10 years, which > you have done. You were so busy trying to discredit me, by setting me this difficult > problem, that you didn't consider what the result actually means. Not > only did I successfully answer your question, but you have > successfully proved that there has been NO global warming in the last > 10 years. Analysis: JohnM said: The null hypothesis is that temperature data for the two > groups is identical. Name the test that gives a derived statistic of > 15.5 and calculate the probability of getting this value or smaller > under the null hypothesis. JohnM said: As the value is nowhere near significance, accept the > null hypothesis. Conclusion: We accept the null hypothesis, that temperature data for the two > groups is identical. That means that there is no evidence of warming, or cooling, between > the 2 groups. The temperature had been stable for the last 10 years. HAW HAW HAW HAW HAW HAW HAW k00k-a-d00dle-d0000! === Subject: Re: JohnM makes an embarrassing mistake posting-account=110qqwkAAABKPssNm5skLt7zXJ8irOne AppleWebKit/312.9 (KHTML, like Gecko) Safari/312.6,gzip(gfe),gzip(gfe) Mr. Right, you are both wrong and a total moron. === Subject: Re: JohnM makes an embarrassing mistake < Mr. Right, you are both wrong and a total moron. Roger Coppock (Mr Post and Run, himself) , are you staking your reputation on this as well? All that you need to do is post the proof. Why don't you join JohnM, frantically trying to find another distribution-free test that gives a statistic of 15.5 Two birds with one stone. Think of the CO2 that I've saved. :) === Subject: Re: JohnM makes an embarrassing mistake > Why don't you join JohnM, frantically trying to find another > distribution-free test that gives a statistic of 15.5 ROTFLMSAO! === Subject: Re: JohnM makes an embarrassing mistake posting-account=kYCflQoAAABc0Os-abVEiyZDkuVglBKp 2.0.50727),gzip(gfe),gzip(gfe) < [ . . . ] < < > Why don't you join JohnM, frantically trying to find another < > distribution-free test that gives a statistic of 15.5 < < ROTFLMSAO! Roger, I know that ROTFLMSAO! is a proof in AGW Alarmist circles, but you are going to have to better than that here (in skeptics territory). === Subject: Re: JohnM makes an embarrassing mistake posting-account=110qqwkAAABKPssNm5skLt7zXJ8irOne AppleWebKit/312.9 (KHTML, like Gecko) Safari/312.6,gzip(gfe),gzip(gfe) > < [ . . . ] > < > < > Why don't you join JohnM, frantically trying to find another > < > distribution-free test that gives a statistic of 15.5 > < > < ROTFLMSAO! Roger, I know that ROTFLMSAO! is a proof in AGW Alarmist circles, but you > are going to have to better than that here (in skeptics territory). LOL! === Subject: Re: JohnM makes an embarrassing mistake > < [ . . . ] > < > < > Why don't you join JohnM, frantically trying to find another > < > distribution-free test that gives a statistic of 15.5 > < > < ROTFLMSAO! Roger, I know that ROTFLMSAO! is a proof in AGW Alarmist circles, but you > are going to have to better than that here (in skeptics territory). Poor Mr. Right - he lies, and lies, and lies, and lies... lol === Subject: apparent blowup of Euler equations (fluid mechanics) << Many numerical computations appear to exhibit blowup for solutions of the Euler equations, but the extreme numerical instability of the equations makes it very hard to draw reliable conclusions. > The Euler equations result from the Navier-Stokes Equations by setting the viscosity to zero. I'd be interested in animations or graphics showing what appears to be blowup of the 3D Euler equations. David Bernier === Subject: Convergence of Infinite Product [1 sin (1/1)][2 sin (2/2)][3 sin (3/3)] ... posting-account=BMywQAoAAABW1Fwx_p4f0WYtQAeVs4vI 1.1.4322),gzip(gfe),gzip(gfe) Does the infinite product Prod(1,inf) n sin(1/n) go to zero? (The correct terminology may be diverges to zero.) Reference? L === Subject: =?windows-1252?Q?ECCOMAS_VipIMAGE_2009_=96_Abstract_SUBMISSION_DEADLI?= =?windows-1252?Q?NE_EXTENDED?= posting-account=N5wzPwoAAACfM7xTOME2HKP_WjJviHXd Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) ---------------------------------------------------------------------------- ----------------------------------------------------------------- (Apologies for cross-posting) International ECCOMAS Thematic Conference VipIMAGE 2009 - II ECCOMAS THEMATIC CONFERENCE ON COMPUTATIONAL VISION AND MEDICAL IMAGE PROCESSING 14-16th October 2009, FEUP, Porto, Portugal www.fe.up.pt/~vipimage Abstract submission deadline extended to 4th April We would appreciate if you could distribute this information by your colleagues and co-workers. ---------------------------------------------------------------------------- ----------------------------------------------------------------- We are pleased to announce an extension of the deadline for abstract submission to the II ECCOMAS THEMATIC CONFERENCE ON COMPUTATIONAL VISION AND MEDICAL IMAGE PROCESSING (VipIMAGE 2009) to April 6 (www.fe.up.pt/~vipimage). Possible Topics (not limited to) ´ Image Processing and Analysis ´ Segmentation, Tracking and Analyze of Objects in Images ´ 3D Vision ´ Signal Processing ´ Data Interpolation, Registration, Acquisition and Compression ´ Objects Simulation ´ Virtual Reality ´ Software Development for Image Processing and Analysis ´ Computer Aided Diagnosis, Surgery, Therapy and Treatment ´ Computational Bioimaging and Visualization ´ Telemedicine Systems and their Applications Invited Lecturers ´ Alejandro Frangi - Pompeu Fabra University, Spain ´ Christos E. Constantinou - Stanford University School of Medicine, USA ´ Demetri Terzopoulos - University of California, USA ´ Joaquim A. Jorge - Instituto Superior T.8ecnico, Portugal ´ Jos.8e Carlos Pr.92ncipe - University of Florida, USA ´ Lionel Moisan - Universit.8e Paris V, France ´ Tony Chan - University of California, USA Thematic Sessions Proposals to organize Thematic Session within VipIMAGE 2009 are mostly welcome. The organizers of the selected thematic sessions will be included in the conference scientific committee and will have a reduced registration fee. They will be responsible for the dissemination of their thematic session, may invite expertise researches to have invited keynotes during their session and will participate in the review process of the submitted contributions. Proposals for Thematic Sessions should be submitted by email to the conference co-chairs (tavares@fe.up.pt, rnatal@fe.up.pt). Confirmed Thematic Sessions (not yet closed) - Computer Vision in Robotics - Texture Image Analysis: Methods and Applications - Processing and Classification of Satellite Imagery - Small Animal Imaging: Trends and Techniques - Imaging of Biological Flows: Trends and Challenges Publications The proceedings book is going to be published by the Taylor & Francis Group, as happened with VipIMAGE 2007 (ISBN: 9780415457774). The organizers will encourage the submission of extended versions of the accepted papers to related International Journals; in particular for special issues dedicated to the conference. One possibility already confirmed is the International Journal for Computational Vision and Biomechanics (IJCV&B). As what happened with VipIMAGE 2007, the organizers are going to edit a book to be published by SPRINGER (ISBN: 978-1-4020-9085-1), under the Computational Methods in Applied Sciences series, with invited works from the most important ones presented in the conference. Awards best paper award and best student paper award are going to be given to the author(s) of two papers presented at the conference, selected by the Organizing Committee based on the best combined marks from the Scientific Committee and Session Chairs. Important dates ´ Submission of extended abstracts: April 6, 2009 (extended) ´ Lectures and Final Papers: June 15, 2009 We are looking forward to see you in Porto next October. Jo.8bo Manuel R. S. Tavares Renato Natal Jorge (conference co-chairs) PS. For further details, please see the conference website at: www.fe.up.pt/~vipimage === Subject: Re: Convergence of Infinite Product [1 sin (1/1)][2 sin (1/2)][3 sin (1/3)] ... posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > Does the infinite product Prod(1,inf) n sin(1/n) go to zero? (The > correct terminology may be diverges to zero.) Reference? n sin(1/n) = 1 - 1/6n^2 + O(n^{-4}) = 1 + O(n^[-2}). As sum_n 1/n^2 converges, so does product_n [n sin(1/n)] [title corrected] === Subject: Re: The modern mathematical concept of infinity is ... Nntp-Posting-Host: hera.cwi.nl > If you could think without prejudice then you would recognize: > Every finite maximal number of symbols (per number) is used to > distinguish a finite number of numbers. There is no place in > mathematics (that uses only distinguishable natural numbers) for a > number of numbers that is larger than every finite number. > > No, I do not see it. I agree that every finite maximal number of symbols > per number can be used to distinguish a finite number of numbers. > > It is your there is no place in mathematics which boggles the mind. Why > not? Just because that is your opinion? > > If you recognize that every finite maximal number of symbols per > number can be used to distinguish a finite number of numbers. What > would you use to distinguish aleph_0 numbers? Obviously a finite > number of symbols per number is not sufficient. No, a finite maximal number of symbols per number is insufficient. That is not the same, because a maximal number is assumed. But when I state a finite number of symbols per number there is no maximum on the number of symbols per number. > As at no time you have properly defined your paths and path-bunches. > > Every infinite sequence of edges of the binary tree is a path-bunch. > Every path is a path-bunch containing only one path. > > Eh, is the last statement a definition? And if it is, is it not a little > bit circular? Can you not give proper definitions of paths and > path-bunches? > > A path is but the geometrical representation of the infinite binary > representation of a real number. I assume that the latter is known. A > path bunch is the union of one or more paths in the binary tree. I still do not see a good definition, how do you define the union of two infinite binary representations of real numbers? So let me attempt two definitions: (1) a path is an infinite sequence of elements from the set {0,1}. (2) a path bunch is a finite or infinite sequence of elements from the set {0,1}. Is that correct? (Because I have never seen a definition of the union of sequences.) -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The modern mathematical concept of infinity is ... A path is but the geometrical representation of the infinite binary > representation of a real number. I assume that the latter is known. > A path bunch is the union of one or more paths in the binary tree. > I guess he meant (a certain) _set_ (or collection, etc.) of paths. (WM is not used to correct/precise set theoretic terminology, you know.) Btw.: I once defined the notion of a /path bunch/ (Pfadb.9fndel) for this mathematical illiterate, since he was not able to to state it himself. For a while he used my definition, but now he obviously has forgotten about it (again)... Herb === Subject: Re: The modern mathematical concept of infinity is ... Nntp-Posting-Host: hera.cwi.nl [about the definition of path bunch] ... > Btw.: I once defined the notion of a /path bunch/ (Pfadb.9fndel) for this > mathematical illiterate, since he was not able to to state it himself. For > a while he used my definition, but now he obviously has forgotten about it > (again)... In his book he even gives two definitions. Apparently he had not seen that they conflict with each other. And in his proof he switched from one definition to the other there. That is, he proved something for path bunches according to one definition and assumed that it would be valid for path bunches according to the other definition. That is one of the reasons I asked for a definition. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The modern mathematical concept of infinity is ... ... > A path is but the geometrical representation of the infinite binary > representation of a real number. I assume that the latter is known. A > path bunch is the union of one or more paths in the binary tree. I still do not see a good definition, how do you define the union of two > infinite binary representations of real numbers? So let me attempt two > definitions: > (1) a path is an infinite sequence of elements from the set {0,1}. > (2) a path bunch is a finite or infinite sequence of elements from > the set {0,1}. > Is that correct? (Because I have never seen a definition of the union of > sequences.) Presumably by taking something like [0,0,1,1,0] as a path bunch, we are supposed to think of all (potentially?) infinite sequences with [0,0,1,1,0] as the initial segment. The terminology of union is not enlightening ... > -- > dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, > home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ -- Alan Smaill === Subject: Re: The modern mathematical concept of infinity is ... Nntp-Posting-Host: hera.cwi.nl ... > Well, you would get many surprises if you did *not* distinguish a and {a}. > But consider a set as a box containing things. Would you think that a > box that contains a collection of apples is the same as the collection of > apples themselves? That is how I, and I think many other mathematicians, > think about when they talk about sets. > > You are funny. That sets are a kind of boxes nonsense is exactly what > Mueckenheim is applying (although he will not admit it). After all, one can > put things in and out of boxes; the contents of a box is not fixed. O, well, perhaps. But Mueckenheim is strongly opposed to that view. He even thinks that the empty set is nonsense. But I should have said: firmly closed boxes... -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The modern mathematical concept of infinity is ... Nntp-Posting-Host: hera.cwi.nl ... > This definition is contradicted by the fact that there is no set of X > FISONs with each FISON having less than X elements. > > X being a natural number again. Why do you always omit that from your > considerations? You need that assertion for infinitely many FISONs, but > you can not prove it for that. > > As I have proved that *all* natural numbers are used to distinguish > the elements of FISONs, there is no X remaining to distinguish an > actually infinite set of naturals. This statement makes no sense. Either you mean that there is no X remaining to distinguish an actually infinite set of naturals from the FISONs. That would be right, but irrelevant. Or you mean that there is no X remaining to distinguish the elements of an actually set from each other, but that is nonsense, because you can not distinguish the elements of a set using a single X. Moreover, *each* natural number is used in the distinguishingg of elements from infinitely many FISONs, so *each* natural number can also be used to distinguish the naturals in the actually infinite set of naturals, and that is what happens. The first is irrelevant because what you must distinguish is all (infinitely many) FISONs from each other, not some actually infinite set from them using the natural numbers. > Indeed the statement is false for every *natural* number n, for this > I do not need to insists that it is not proven for n + 1, because it > is proven for every *natural* number n. > > So there is nothing remaining for X > n. > > What nonsense. There are aleph_0 natural numbers > > That is just in question. And it is disproved by the fact that there > is no number with aleph_0 symbols. But that is not *needed*. > Or do you disagree that aleph_0 natural numbers can not distinguish > aleph_0 objects? > > I have proved that at least aleph_0 symbols per at least one number > would be required to distinguish aleph_0 numbers. But there is no > number with aleph_0 symbols. No, you have not proven that. Of the aleph_0 natural numbers, 1 gets one stroke, 2 two, and so on. Look, all aleph_0 numbers are distinguished from each other and none of them has aleph_0 strokes. Or do you think that there is a natural number that requires aleph_0 strokes? If so, why? > Or do you disagree that there are not aleph_0 natural numbers that are all > finite? > > I think it is the latter. In that case you ought to clearly state *that* > Not all that rigmarole about FISONs. And in that case you also have to > show how that is valid when we assume the axiom of infinity and the > definitions of set theory. Otherwise you will be unable to prove > inconsistency of set theory. > > I have proved that at least aleph_0 symbols per at least one number > would be required to distinguish aleph_0 numbers. See above, where I show the opposite. Note: per has three different meanings: 1. by means of 2. for each 3. according to adding at least makes no sense when meaning two is meant. > But there is no > number with aleph_0 symbols. Because any smaller maximal number of > symbols per number is insufficient. Eh? How is the logic here? > But aleph_0 is *not* a natural number, nor > is there a natural number n such that aleph_0 = n + 1. So it is not > proven for aleph_0. > > The proof is valid, because there is no natural number X of symbols > per number remaining. > > That is irrelevant, see above. > > No. See above. It is irrelevant, see above. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The modern mathematical concept of infinity is ... Nntp-Posting-Host: hera.cwi.nl ... > How lucky we are that Cantor introduced curly brackets! But it was no > he who introduced the silly distinction between a and {a} that enables > so called mathematicians to build card houses on nothing. > > Well, you would get many surprises if you did *not* distinguish a and {a}. > > Cantor would not have been surprised! Nor would Bolzano. Surprised are > only those who interprete the curly brackets as some holy grail. This > development is a typical degeneration (in German called > Entartung) as it can be observed often, but mainly in non-exact > sciences and cultural branches. Hrm. Yes, I know the word entarted, especially when applied to art. > But consider a set as a box containing things. Would you think that a > box that contains a collection of apples is the same as the collection of > apples themselves? That is how I, and I think many other mathematicians, > think about when they talk about sets. > > But N is not a box! N is nothing but all natural numbers considered > together, at once - with no further ingredients. As if in a box. > The distinction becomes crucial when there are nested sets involved, the > set > {a, {b, c}} > has two elements, not three. When you try to show inconsistency, use the > language of the theory for which you want to show inconsistency. Otherwise > the only thing you show is that the language of the theory is not > compatible with the language you use yourself. > > I show that the number of natural numbers cannot be larger than every > natural number. All additional boxes that you may consider are of no > interest to me - only the numbers. You do not show that. > No. All natural numbers is not a natural nunber and does not > increase the number of natural numbers. > > Eh? N is the set of all natural numbers. N has as element all > natural numbers. You equate all natural numbers with N, so N has as > element N. > > See above. What is wrong with my logic when I use your statement that all natural numbers equals N? > You continuously fail to distinguish a set from its elements, and > also being an element of and being a subset of. Those distinctions > are crucial in understanding set theory. > > They do not help to increase the number of natural numbers that exist > in mathematics. > > No, of course not. That number of elements is aleph_0, due to the axiom > of infinity and the definition of aleph_0. The distinctions is crucial to > understand how set theory works. As you do not make the distinctions you > apparently do not know how set theory works. > > With or without set theory: The number of all natural numbers is not a > number that is larger than every natural number. This is provable > fact. Every opponent is wrong. You have not proven it. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The modern mathematical concept of infinity is ... posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Clocks are not things that don't change that change. > like infinite sets. Not outside of Wolkenmuekenheim. > Only in Wolkenmuekenhiem do we have things that don't change > that change You need to find a contradiction without assuming that > N changes. > This is the contradiction: Every maximal If N does not change, then N does not > have a maximal number. Then it does neither have a fixed number aleph_0 of numbers that is larger than every natural number. A set of X natural numbers in unary representation cannot exist unless there is at least one natural number represented by X symbols. As every natural number X of symbols is used to distinguish a finite set of numbers, there is no natural number X of symbols capable of distinguishing a larger number of numbers, i.e., an actually infinite set of aleph_0 numbers. === Subject: Re: The modern mathematical concept of infinity is ... > Clocks are not things that don't change that change. > like infinite sets. > Not outside of Wolkenmuekenheim. > Only in Wolkenmuekenhiem do we have things that don't change > that change > You need to find a contradiction without assuming that > N changes. > This is the contradiction: Every maximal > If N does not change, then N does not > have a maximal number. Then it does neither have a fixed number aleph_0 of numbers that is > larger than every natural number. It does by any standard definition of N. But since WM has no definition of N, he cannot establish any of its properties. A set of X natural numbers in unary representation cannot exist unless > there is at least one natural number represented by X symbols. Nowhere outside of WM's mathUnrealism is any natural required to be represented in unary notation. And in the von Neumann model, it would be quite unnecessary and artificial, as each natural already has a non-unary representation as a set. === Subject: Re: The modern mathematical concept of infinity is ... posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > Clocks are not things that don't change that change. > like infinite sets. > Not outside of Wolkenmuekenheim. > Only in Wolkenmuekenhiem do we have things that don't change > that change > I am glad to see that you have given up your futile quest to find something that doesn't change that changes outside of Wolkenmuekenheim. > You need to find a contradiction without assuming that > N changes. > This is the contradiction: Every maximal > If N does not change, then N does not > have a maximal number. Then it does neither have a fixed number aleph_0 of numbers that is > larger than every natural number. Nope, this does not follow. If N is fixed then the number of elements in N is the supremum of N and this supremum is fixed. By definition, the supremum is larger than every element of N. Nope. A set of X natural numbers in unary representation cannot exist unless > there is at least one natural number represented by X symbols. You have only shown this for X a natural number. Note that aleph_0 is not a natural number. A set of aleph_0 natural numbers in unary representation can exist even though there is no natural number represented by aleph_0 symbols. This is because the number of natural numbers in the set is the supremum of the number of symbols used per number. If the set has a largest element then this supremum is also a maximum. If the set does not have a largest element (e.g. N) then the supremum is not a maximum. Thus aleph_0 is a supremum, but not a maximum, so there is no natural number represented by aleph_0 symbols. As every natural number X of symbols is used to distinguish a finite > set of numbers, there is no natural number X of symbols capable of > distinguishing a larger number of numbers, i.e., an actually infinite > set of aleph_0 numbers. Correct, no *one* natural number can distinguish aleph_0 numbers. However, a set of natural numbers without largest element can do what no *one* natural number can do. In particular, aleph_0 natural numbers can distinguish aleph_0 numbers. - William Hughes === Subject: Re: The modern mathematical concept of infinity is ... <49bd7a08$0$15799$426a74cc@news.free.fr> posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > This is the contradiction: Every maximal number of symbols per number > limits the number of different elements in a set of unary > representations of natural numbers to this maximal number. As long as > there are only natural numbers of symbols per number allowed for, the > number of different elements in a set of unary representations of > natural numbers is limited to a natural number. > If N is assumed to have aleph_0 > n (forall n in N) elements, then > there must be at least one element with X > n (forall n in N) symbols. > Contradiction. > It is not difficult to see. Every student not yet spoilt by the > worshippers of the empty set and finished infinity does understand > that. Do you mean that you have used your academic authority to teach these > idocies to students? There is no authority required to teach and to learn the obvious. Regars, WM === Subject: Re: The modern mathematical concept of infinity is ... This is the contradiction: Every maximal number of symbols per number > limits the number of different elements in a set of unary > representations of natural numbers to this maximal number. As long as > there are only natural numbers of symbols per number allowed for, the > number of different elements in a set of unary representations of > natural numbers is limited to a natural number. > If N is assumed to have aleph_0 > n (forall n in N) elements, then > there must be at least one element with X > n (forall n in N) symbols. > Contradiction. > It is not difficult to see. Every student not yet spoilt by the > worshippers of the empty set and finished infinity does understand > that. > Do you mean that you have used your academic authority to teach these > idocies to students? There is no authority required to teach and to learn the obvious. unworkabble. === Subject: Re: The modern mathematical concept of infinity is ... WM a .8ecrit : > > This is the contradiction: Every maximal number of symbols per number > limits the number of different elements in a set of unary > representations of natural numbers to this maximal number. As long as > there are only natural numbers of symbols per number allowed for, the > number of different elements in a set of unary representations of > natural numbers is limited to a natural number. > If N is assumed to have aleph_0 > n (forall n in N) elements, then > there must be at least one element with X > n (forall n in N) symbols. > Contradiction. > It is not difficult to see. Every student not yet spoilt by the > worshippers of the empty set and finished infinity does understand > that. > Do you mean that you have used your academic authority to teach these > idocies to students? There is no authority required to teach and to learn the obvious. So, you confirm that you have actually taught your theory to students in your University ? === Subject: Re: The modern mathematical concept of infinity is ... posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Well, you would get many surprises if you did *not* distinguish a and {a}. My interest is the number of natural numbers. The number of numbers in {4} is the same as the number of numbers in {{{4}}} or the number of numbers in the next line: 4 It is always one number. And { } does not contain any number. Therefore we do not need it (although it is useful on some occasions). > The distinction becomes crucial when there are nested sets involved, the set > {a, {b, c}} > has two elements, not three. That may be true, but I am not at all intersted in that hierarchical structure. With respect to numbers, or letters in the present case, there is but one single answer, namely there are three letters. >When you try to show inconsistency, use the > language of the theory for which you want to show inconsistency. Otherwise > the only thing you show is that the language of the theory is not compatible > with the language you use yourself. Some people play Chess others play Go others play set theory. I do not object. But all that has no authority with respect to the *mathematical* question: What do we know about the number of natural numbers? I have proved my answer based on the fact that it is impossible to distinguish X numbers in unary representation by less than X symbols per number. One could add as a second condition that natural numbers that cannot be distinguished do not belong to mathematics. But it should not be necessssary to emphasize such a self evident truth. === Subject: Re: The modern mathematical concept of infinity is ... Nntp-Posting-Host: hera.cwi.nl > > Well, you would get many surprises if you did *not* distinguish a and {a}. > > My interest is the number of natural numbers. The number of numbers in > {4} is the same as the number of numbers in {{{4}}} or the number of > numbers in the next line: > 4 > > It is always one number. And { } does not contain any number. > Therefore we do not need it (although it is useful on some occasions). You are using in in a way that is not common in set theory. Normally when it is stated that something is in a set A, that means that that something is an element of the set A. In that sense, there is no numbre in {{{4}}}. > > The distinction becomes crucial when there are nested sets involved, the > set > {a, {b, c}} > has two elements, not three. > > That may be true, but I am not at all intersted in that hierarchical > structure. With respect to numbers, or letters in the present case, > there is but one single answer, namely there are three letters. Yes, but they play a crucially different role. > When you try to show inconsistency, use the > language of the theory for which you want to show inconsistency. > Otherwise the only thing you show is that the language of the theory > is not compatible with the language you use yourself. > > Some people play Chess others play Go others play set theory. I do not > object. But all that has no authority with respect to the > *mathematical* question: What do we know about the number of natural > numbers? Without the definition of st theory, nothing. > I have proved my answer based on the fact that it is impossible to > distinguish X numbers in unary representation by less than X symbols > per number. No, you have proven that only when X is a natural number. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The modern mathematical concept of infinity is ... Well, you would get many surprises if you did *not* distinguish a and {a}. My interest is the number of natural numbers. The number of numbers in > {4} is the same as the number of numbers in {{{4}}} or the number of > numbers in the next line: > 4 Actually, the number of numbers in {{4}} can be zero if in is interpreted to mean is a member of as is quite common. It is always one number. And { } does not contain any number. > Therefore we do not need it (although it is useful on some occasions). What WM needs or does not need is irrelevant outside his weird weird world of MathUnrealsm. The needs of mathematics are quite different and include any number of things which do not exist in that MathUnrealism The distinction becomes crucial when there are nested sets involved, the set > {a, {b, c}} > has two elements, not three. That may be true, but I am not at all intersted in that hierarchical > structure. Then do not pontificate on set theories, as they are specifically intersted in the membership relation. >When you try to show inconsistency, use the > language of the theory for which you want to show inconsistency. Otherwise > the only thing you show is that the language of the theory is not compatible > with the language you use yourself. Some people play Chess others play Go others play set theory. I do not > object. But all that has no authority with respect to the > *mathematical* question: What do we know about the number of natural > numbers? Much of what WM claims to know about them is wrong. I have proved my answer based on the fact that it is impossible to > distinguish X numbers in unary representation by less than X symbols > per number. And that is one of the things that is wrong, unless X is required to be a natural number, as there are numbers, X, which are not natural for which it is false. > One could add as a second condition that natural numbers > that cannot be distinguished do not belong to mathematics. Since WM's standard of distinguishability for naturals requires a unary representation for each such natural, most of the naturals that mathematics require are simply not available to him. That WM insists on conditions that make his pseudomath unusable in actual mathematics is, fortunately for most of us, a problem only for those poor students of his whom he indoctrinates in his false faith. But it should not be necessssary to emphasize such a self evident truth. === Subject: Re: The modern mathematical concept of infinity is ... > [...] The number of numbers in {4} is the same as the number > of numbers in {{{4}}} or the number of numbers in the next line: > 4 > Actually, the number of numbers in {{4}} can be zero if in is > interpreted to mean is a member of as is quite common. > Right. Especially when we treat the natural numbers 0, 1, 2, 3, ... as urelements (i.e. non-sets). Then the number of numbers in {4} would be 1 and the number of numbers in {{{4}}} would be 0 (since {{4}} is a set). > [...] And { } does not contain any number. > Well, that's true!!! :-) > Therefore we do not need it (although it is useful on some occasions). >What WM needs or does not need is irrelevant outside his weird, weird > world of MathUnrealsm. The needs of mathematics are quite different and > include any number of things which do not exist in that MathUnrealism > Right. When defining the natural numbers following von Neumann, we would have: 0 := {} 1 := {0} = {{}} 2 := {0, 1} = {{},{{}}} : So {} is rather useful in _real math_. > The distinction becomes crucial when there are nested sets involved, > the set > {a, {b, c}} > has two elements, not three. > That may be true, but I am not at all interested in that hierarchical > structure. > *sigh* With other words, WM does not consider _sets_; and hence he does not consider _set theory_. Good to know. Then do not pontificate on set theories, as they are specifically > interested in the membership relation. > Right. > What do we know about the number of natural numbers? > Much of what WM claims to know about them is wrong. > Right. In standard set theory, say ZFC, we call the number of natural numbers (i.e. the cardinality of the set of natural numbers) aleph_0. And we know that there we (then) have: An e N: n < aleph_0. Herb === Subject: convergence in measure, show cf_n ---> cf Show that is f_n ---> f, convergence in measure, then cf_n--->cf Proof: If f_n ---> f then we have lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = 0. For cf_n--->cf we would have: lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = lim(n->oo) mu{x in X:|cf_n(x) - cf| >= d} = lim(n->oo) mu{x in X:|c(f_n(x) - f)| >= d} = and by the properties of limits: c * lim(n->oo) mu{x in X:|(f_n(x) - f)| >= d} = c * 0 . Q.E.D. Is this correct? === Subject: Re: convergence in measure, show if fn-->f and gn-->g then fn+gn-->f+g I think this can be done similarly using the properties of limits: Show that if f_n ---> f and g_n ---> g, convergence in measure, then f_n + g_n --->f + g Proof: For f_n ---> f then we have L_0=lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = 0. For g_n ---> g then we have L_1=lim(n->oo) mu{x in X:|g_n(x) - g| >= d} = 0. Now, for g_n + f+n, lim(n->oo) mu{x in X: |f_n(x) - f| + |g_n(x) - g| >= d} = which by the properties of limits is: lim(n->oo) mu{x in X:|f_n(x) - f| >= d} + lim(n->oo) mu{x in X:|f_n(x) - f| >= d} =L_0 + L_1 = 0 + 0. Q.E.D. Is this also correct? === Subject: Re: convergence in measure, show cf_n ---> cf > Show that is f_n ---> f, convergence in measure, then cf_n--->cf > Proof: > If f_n ---> f then we have lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = 0. > For cf_n--->cf we would have: > lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = > lim(n->oo) mu{x in X:|cf_n(x) - cf| >= d} = > lim(n->oo) mu{x in X:|c(f_n(x) - f)| >= d} = > and by the properties of limits: > c * lim(n->oo) mu{x in X:|(f_n(x) - f)| >= d} = > c * 0 . Q.E.D. Is this correct? Actually, this step lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = lim(n->oo) mu{x in X:|cf_n(x) - cf| >= d} is no good. You should say: lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = lim(n->oo) mu{x in X:|cf_n(x) - cf| >= |c|d} (unless c=0) === Subject: Re: convergence in measure, show cf_n ---> cf > > Show that is f_n ---> f, convergence in measure, then cf_n--->cf > Proof: > If f_n ---> f then we have lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = 0. > For cf_n--->cf we would have: > lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = > lim(n->oo) mu{x in X:|cf_n(x) - cf| >= d} = > lim(n->oo) mu{x in X:|c(f_n(x) - f)| >= d} = > and by the properties of limits: > c * lim(n->oo) mu{x in X:|(f_n(x) - f)| >= d} = > c * 0 . Q.E.D. > Is this correct? Actually, this step lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = > lim(n->oo) mu{x in X:|cf_n(x) - cf| >= d} is no good. You should say: lim(n->oo) mu{x in X:|f_n(x) - f| >= d} = > lim(n->oo) mu{x in X:|cf_n(x) - cf| >= |c|d} (unless c=0) === === Subject: Re: wavelets > I am trying to learn a bit about wavelets, but never studied > the subject academically. A semester length textbook would be overload. I am looking > for maybe a chapter of a book, or a tutorial paper in one of the > academic journals. Suggestions? -- > Mark this concept is just Dumb; I already got bored with Fourier's superposition Principles and Linearity Concepts Any counters..? You are mostly welcome. === Subject: Re: wavelets posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.13~pre080614i-0etch1),gzip(gfe),gzip(gfe) > On Mar 13, 11:12 am, Jon Slaughter I am trying to learn a bit about wavelets, but never studied > the subject academically. > A semester length textbook would be overload. I am looking > for maybe a chapter of a book, or a tutorial paper in one of the > academic journals. > Suggestions? > Wavelets are like any other functional approximation scheme except that they > work on a local basis. > Instead of approximating functions with other functions that have infinite > support they use functions that have finite support. > One starts with a class of scaling function that are orthogonal to each > other. Generally the haar scaling function is introduced at this point > because it is the easiest. > The haar scaling function is simply the rectangular function. It has a > certain width and height. Note that any other haar scaling function that > doesn't overlap will be orthogonal to it. (since there product will be 0) I highly reccomend this post by Jon Slaughter as a document of the > introduction to wavelet theory. Who says you need a book when such a > small amount of information will do? At the kernel the wavelet theory > must be simple, or else it isn't a theory at all. I studied wavelets as an independent study while getting my undergrad > degree. At the time (the early nineties) this stuff was all the buzz > at UNH in Durham NH USA. A man from MIT named Gilbert Strang came to > UNH on a lunch time presentation and the room was packed with > physicists, EE's, and mathematicians. This is how important the theory > was thought to be at that time and I have not followed it closeley > since. But I did write a little bit of C code that would perform the > wavelet transform on a one dimensional signal of finite length. This > is what I feel comfortable sharing here is just the simple computation > of a discrete sampled signal and it need only be ten units long to get > the idea. Again, the simplicity is easily embodied, yet the extensions > seem to run astray into the modern challenges of the many branches of > science. I suppose this comes about because the wavelet can be posed > as a new basis. By altering the basis that we work from a new view of > the subject matter; an altered context comes about. So for the Haar coding on a ten unit integer stream let's maintain the > signal within the computation by building the signal as a ramp: > s = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Sorry, this was supposed to be s = 0, 1, 2, 3, 4, 5, 6, 7 . > and let's not do any compression while performing the mathematics of > the wavelet transform so that we may always traverse bidirectionally > forward through the math and back out of it any place along the way. h = + 0 + 1 + 2 + 3 - 4 - 5 - 6 - 7, (forgot a comma) + 0 + 1 - 2 - 3, + 4 + 5 - 6 - 7, ( and a boo boo) + 0 - 1, + 2 - 3, + 4 - 5, + 6 - 7 . (that's the end but you can see it would grow out like a tree if it kept going) = - 16, - 4, - 4, -1, -1, -1, -1 ; unboobood this is a structured form but in this stream equivalent no structure has been graphically presented. I didn't do the reverse transform here but that should follow. > Above is the result but I do wish that Jon would confirm that I got > this correct since I botched it once and to botch it twice would be even sadder. > This is a fine practical instance in that if we were to construct > binary hardware we could detect this particular ramp pulse via a > simplistic counter on the value -1 coming down a pipe, resetting > otherwise, thus flagging a potential operation down the pipe based on > the signal feed. This description is not an exact ramp detector. >I suppose to keep things simple we'd have to > packetize the signal source but that is fine for physicists, and these > days signal processors too. The mathematician can attempt to keep some > general features going but the wavelet was regarded as a practical > thing. Upon seeing the simplest transform painted in a clean binary > hardware implementation when we go back to the generality it seems > easy to break a lot of the construction. I had a hard time with the > orthogonal requirement and maybe still do. What cannot be overlooked > is that we see structured data on the exit of the Haar transform > whereas there was nothing but a nondescript stream flowing in until we > packetized. This structured form I am now taking interest in and it > may not be so cleanly information theoretic as was the istream of a > fourier analysis. This is its beauty as well since we should allow for > the idea of the local packet if we accept atomic theory, photons, and > so forth. Here is even a simple argument on how an atom might absorb a > given photon packet or not just from receiving the packet out of synch > so that its own detection mechanism fails its own desire to gain > energy. Then too could be a false detection which could lead to atomic > loss of energy by misdetecting a nonreceivable packet, thus allowing > stimulated emission of stowed energy. Oy, there's a double negative in > there. It does hold the tatrix structure (triangular matrix) so I guess I'll Close to the tatrix structure but not quite exact, so the question arises whether a tatrix style equivalent can be formed. - Tim > have to play even more with it sometime. Sorry, got to go. > - Tim > You actually have used haar scaling functions many times before such as in > reimann integration(the rectangles used to approximate the area) or in > lebesque measure theory when talking about simple functions. > In this case we have two parameters to deal with. One is the shifting of > the function and the other is the Scaling. > Let > f(x) = 1 if 0 <= x < 1, else 0 > now if we shift f(x) left or right by k such as f(x + k) then f(x+k) is > orthogonal to f(x+m) if k!=m. > If we scale so that instead of using [0,1], we use [0,1/2] or in general > [0,1/2^j] then we can get better resolution. > Then in general we have > f(2^j*x + k) as a haar scaling function. > Then we can write any function g(x) as a linear combination of those haar > scaling functions > g(x) = sum(a_k*f(2^j*x + k)) > (this is almost like the dirac delta function. Note that a_k is just some > value of g(x) on the interval of the specific haar) > You could use this for riemann sums... and infact this is exactly what we do > except that we don't scale in halfs but making the scaling arbitrary(i.e., > any partition size) and we want the area of each rectangle instead of the > height. > So if you understood that, then the the next step is the wavelet function. > Essentially if you look at one part of g(x) and then the next when it > transitions from one haar scaling function to another, you can think of the > difference between the two as what is important. (in a since it is like > differentiation) > note that the difference will always look like >http://en.wikipedia.org/wiki/Haar_wavelet > (look at the picture that says haar wavelet) > What this allows us to do is write the scaling function in terms of the > wavelets and vice versa. > Since wavelets represent change(and local change at that), we can use them > to describe the local change. This is impossible with global approximation > methods. With fourier analysis it is about writing functions in terms of > harmonics which have infinite support(it would be really nice if we could > do it with harmonics that have finite support but then there are > orthogonality problems... wavelets come close to this). > So, if you realize that j is the resolution level then we can use it to > determine local behavior at a certain resolution. > Most of the theory about it is simply making much of what I have said > rigorous and developing some of the techniques and properties of wavelets. >http://en.wikipedia.org/wiki/Daubechies_wavelet > you can see some of the more advanced wavelets. > Notice how the daubechies 4 tap wavelet looks sorta like the haar but > spikier. The others also are haar like but it is much less obvious. > The thing is that a wavelet has the properties of orthogonality and we can > use them just as we used haar. If the function we are trying to approximate > has certain features then it might be better to use wavelets that express > those features more exactly. This means we need a lower resolution to see > them than with others. > Hopefully that will get you started. If you can understand them conceptually > then that is the main thing. There should be plenty of books and online > tutorials to get you further. === Subject: Re: iteration equation On Mar 15, 7:19.8cpm, amy666 On Mar 15, 7:01.8cpm, amy666 > f(f(x)) + a(x)*f(x) + b(x) = 0 > a(x) and b(x) given. > find f(f(x)). > the operator half iterate at fixed point ... > is > allowed. > And what does that operator possibly do? > -- m > it takes the regular half iterate of a taylor > series at one of its fixed points. > which fixed point is free to define. How do you know that such a thing even exists? -- m i dont. in fact in some cases , it WONT EXIST. becuase e.g. no fixpoint , no radius of convergeance > 0 etc You may actually have something here that could be useful under some circumstances. If you write the equation as f(f(x)) = -a(x) f(x) - b(x) then you could imagine an iterative process where at some stage you have an approximate solution f_n(x), and for the next iteration you find f_{n+1}(x) satisfying (at least approximately) f_{n+1}(f_{n+1}(x)) = - a(x) f_n(x) - b(x) and you could imagine that this process might converge under appropriate conditions. Of course the hard part will be to determine what those appropriate conditions are. -- === Subject: Re: iteration equation <442713.1237155602662.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=AphEFQoAAADpN_uxZavuHwV48pQ6OAwv Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 16, 7:11am, What Happened, indeed which fixed point is free to define. >How do you know that such a thing even exists? Please do not respond to this blithering mathforum imbecile. > mathforum is a vast sewer of idiocy. An uncountable Sorry, I am newbie here, but what's wrong with amy666's problem? Of course, vi did not mentioned limitations, but, as far as I remember, if function f(x) has a static point and it is analytic in that point (i.e. it can be represented as Taylor series), then Taylor series for half-iterated function can be obtained in a unique way. Though there is no guaranty that series for half-iteration are converging at all, AFAIR. Besides of that, I doubt that amy666's problem can be solved. === Subject: Re: iteration equation <442713.1237155602662.JavaMail.jakarta@nitrogen.mathforum.orgOn Mar 16, 7:11=A0am, What Happened, indeed which fixed point is free to define. >How do you know that such a thing even exists? > Please do not respond to this blithering mathforum imbecile. > mathforum is a vast sewer of idiocy. =A0An uncountable Sorry, I am newbie here, but what's wrong with amy666's problem? Of > course, vi did not mentioned limitations, but, as far as I remember, > if function f(x) has a static point and it is analytic in that point > (i.e. it can be represented as Taylor series), then Taylor series for > half-iterated function can be obtained in a unique way. Not quite. If, say, g(0) = 0, g is analytic at 0 and the first nonzero term in the Taylor series of g(x) is a x^m, then the first nonzero term in the Taylor series of g(g(x)) is a^(m+1) x^(m^2). So f with a fixed point at 0 can only have an analytic functional square root g with fixed point at 0 if the multiplicity of the zero of f at 0 is a square. -- === Subject: Re: iteration equation > which fixed point is free to define. >How do you know that such a thing even exists? > Please do not respond to this blithering mathforum imbecile. > mathforum is a vast sewer of idiocy. An uncountable Sorry, I am newbie here, but what's wrong with amy666's problem? Of > course, vi did not mentioned limitations, but, as far as I remember, > if function f(x) has a static point and it is analytic in that point > (i.e. it can be represented as Taylor series), then Taylor series for > half-iterated function can be obtained in a unique way. > Though there is no guaranty that series for half-iteration are > converging at all, AFAIR. Besides of that, I doubt that amy666's problem can be solved. Bonsoir, If we want to play with iterates instead of f(f(x)) + a(x)*f(x) + b(x) = 0 We might see : f(f(x)) + a(f(x)) + b*x = 0 or f^2 + a o f + b*f^[0] Alain === Subject: Book on Analysis. posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Category : Numerical Analysis Is there any book 'Especially' to deal with the errors in Numerical procedures. I mean Totally dedicated to Error Analysis in Numerical Process so much for the help { if possible, please give the reference to it; else no problem I'll Google myself } === Subject: Re: Book on Analysis. Category : Numerical Analysis >Is there any book 'Especially' to deal >with the errors in Numerical procedures. >I mean Totally dedicated to >Error Analysis in Numerical Process J. H. Wilkinson, /Rounding Errors in Algebraic Processes/ (1963) > was reprinted as a Dover paperback (1994). It is now once again > out of print, but you might be able to find a second-hand copy. -- > Angus Rodgers > Also Nicholas J. Higham: Accuracy and Stability of Numerical Algorithms ISBN 0-89871-355-2 ZVK(Slavek) === Subject: Student Doctor (Getting Solutions) posting-account=QNiqfAoAAACEafcXkDwdHRuYo6O0iSI2 Gecko/20090305 Firefox/3.1b3,gzip(gfe),gzip(gfe) Hi. We created a platform that students can challange with their problems about finding books. We have a large book database and you can access them with just a few steps. We are aware of the problems that studentsÍ obstacles. And we are here for resolve them. www.studentdoctor.wordpress.com We have got hundreds of solution manual books. We guarantee to send them in a few hours. Some examples from our solution manuals list: Advanced Accounting 9th Edition - Hoyle, Schaefer, Doupnik ( Solution Manual ) Basic Engineering Circuit Analysis, 9th Edition Irwin, Nelms Calculus, Early Transcendentals, 7E by C. Henry Edwards ,David E. 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We are aware of the obstacles to students' problems. ?? We are aware of the problems with students' obstacles. ?? We are aware of the problems and obstacles that students have. ?? We are aware that students have problems and obstacles. Dave L. Renfro === Subject: Sigmoidal Function from [0, 1] to [0,1]? I'm looking for a sigmoidal function from reals in [0,1] to [0,1] such that f(0)=0, f(1)=1, and the turning point and slope can be adjusted with parameters. Much to my dismay, I have no clue how to find such a function. :/ Any help would be appreciated! Best, John === Subject: Re: Sigmoidal Function from [0, 1] to [0,1]? I'm looking for a sigmoidal function from reals in [0,1] to [0,1] such > that f(0)=0, f(1)=1, and the turning point and slope can be adjusted with > parameters. Much to my dismay, I have no clue how to find such a > function. :/ Any help would be appreciated! > concept. http://www.4shared.com/file/88779418/7314652a/CurveFitting.html http://www.mediafire.com/download.php?1awmnmzzm2l Go to the examples section on polynomials. All you have to do is solve a matrix equation(or system of linear equations). You can fit points, tangents, inflections, etc... I was trying to do what you were doing but wanted to generalize it and the paper is what I came up with. Not only did I want to fit to points but fit tangents and other things. It turns out that you just end up solving a system of linear equations for such cases. === Subject: Re: Sigmoidal Function from [0, 1] to [0,1]? work fine for my purposes. === Subject: Re: Sigmoidal Function from [0, 1] to [0,1]? I'm looking for a sigmoidal function from reals in [0,1] to [0,1] such > that f(0)=0, f(1)=1, and the turning point and slope can be adjusted with > parameters. Much to my dismay, I have no clue how to find such a > function. :/ Any help would be appreciated! Incomplete Beta function: Beta(x; m, n) = K(n, m) int_0^x t^{m+1} (1-t)^{n+1} dt Gamma(m + n) K(m, n) = ------------------- Gamma(m) Gamma(n) -- Michael Press === Subject: Re: Sigmoidal Function from [0, 1] to [0,1]? posting-account=hpt42QoAAABDnno5zhbo6rttOvGGwEhX Gecko/2009011913 Firefox/3.0.6,gzip(gfe),gzip(gfe) Hi John, you will find many functional forms that will be of interest. See for example, http://www.systat.co.kr/products/TableCurve2D/help/1077.html which allows you to adjust the center, width and height of the curve by adjusting some parameters. This could be rescaled to map [0,1] to [0,1]. Wilf. I'm looking for a sigmoidal function from reals in [0,1] to [0,1] such > that f(0)=0, f(1)=1, and the turning point and slope can be adjusted with > parameters. Much to my dismay, I have no clue how to find such a > function. :/ Any help would be appreciated! Best, John === Subject: Re: Sigmoidal Function from [0, 1] to [0,1]? > I'm looking for a sigmoidal function from reals in [0,1] to [0,1] > such that f(0)=0, f(1)=1, and the turning point and slope can be > adjusted with parameters. Much to my dismay, I have no clue how to > find such a function. :/ There are many such functions. It sounds like you want: f(0) = 0, f'(0) = 0, f(1) = 1, f'(1) = 0, f(a) = b, f'(a) = c, f''(a) = 0, for parameters a, b, c. There is a degree-6 polynomial that does what you want: f(x) = x^2 (a4 x^4 + a3 x^3 + a2 x^2 + a1 x + a0), for some choice of coefficients. The conditions imply linear equations on the coefficients. I already accounted for the first two with the product x^2. The rest correspond to: a4 + a3 + a2 + a1 + a0 = 1 6 a4 + 5 a3 + 4 a2 + 3 a1 + 2 a0 = 0 a^6 a4 + a^5 a3 + a^4 a2 + a^3 a1 + a^2 a0 = b 6 a^5 a4 + 5 a^4 a3 + 4 a^3 a2 + 3 a^2 a1 + 2 a a0 = c 30 a^4 a4 + 20 a^3 a3 + 12 a^2 a2 + 6 a a1 + 2 a0 = 0 These equations should normally have exactly one solution for given (a,b,c), easily found with a standard computer linear algebra library. There are alternative methods to coming up with suitable functions, perhaps with more direct parameters, depending upon what other considerations you might have for the situation. - Tim === Subject: Re: Sigmoidal Function from [0, 1] to [0,1]? posting-account=HR1dqAkAAAA9E7mXiqvduHAelsrIxH3e Gecko/2008102920 Firefox/3.0.4,gzip(gfe),gzip(gfe) I'm looking for a sigmoidal function from reals in [0,1] to [0,1] such > that f(0)=0, f(1)=1, and the turning point and slope can be adjusted with > parameters. Much to my dismay, I have no clue how to find such a > function. :/ Any help would be appreciated! Best, John If you look up cubic spline interpolation it will do what you want. http://en.wikipedia.org/wiki/Spline interpolation If you pick a point (a,b) and a slope at (a,b) it will give you two cubics, one for x in [0,a] and one for x in [a,1] such that the values of both at a are b and the slopes of both at a are what you chose. You will still have to specify the slope at (0,0) and (1,1), or you can use the natural spline which has zero second derivative at the endpoints. === Subject: Re: Convergence of Infinite Product [1 sin (1/1)][2 sin (2/2)][3 sin (3/3)] ... >Does the infinite product Prod(1,inf) n sin(1/n) go to zero? (The >correct terminology may be diverges to zero.) Reference? The infinite product converges to a non-zero value. The quantity n*sin(1/n) = 1 - c_{1/n}*/n^2, 0 < c_n < 1/6. However the product of sqrt(n)*sin(1/sqrt(n)) does diverge to 0, as c_x is increasing with decreasing x. -- 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: Convergence of Infinite Product [1 sin (1/1)][2 sin (2/2)][3 sin (3/3)] ... posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Does the infinite product Prod(1,inf) n sin(1/n) go to zero? (The > correct terminology may be diverges to zero.) Reference? > L Nope, it converges. You can use the inequality: 1 - x^2/6 < sin(x)/x for x in (0,1], to derive a non-zero lower bound of Prod(1,inf) n sin(1/n). === Subject: Re: 64-bit KISS RNGs posting-account=1wPXHwkAAACFV0NiGWX7tZb1o0HYkMjT GTB5; .NET CLR 2.0.50727; PeoplePal 6.6; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) RNGs> Consistent with the Keep It Simple Stupid (KISS) principle,> I have previously suggested 32-bit KISS Random Number> Generators (RNGs) that seem to have been frequently adopted.> Having had requests for 64-bit KISSes, and now that> 64-bit integers are becoming more available, I will> describe here a 64-bit KISS RNG, with comments on> implementation for various languages, speed, periods> and performance after extensive tests of randomness.> This 64-bit KISS RNG has three components, each nearly> good enough to serve alone. The components are:> Multiply-With-Carry (MWC), period (2^121+2^63-1)> Xorshift (XSH), period 2^64-1> Congruential (CNG), period 2^64> Compact C and Fortran listings are given below. They> can be cut, pasted, compiled and run to see if, after> 100 million calls, results agree with that provided> by theory, assuming the default seeds.> Users may want to put the content in other forms, and,> for general use, provide means to set the 250 seed bits> required in the variables x,y,z (64 bits) and c (58 bits)> that have been given default values in the test versions.> The C version uses #define macros to enumerate the few> instructions that MWC, XSH and CNG require. The KISS> macro adds MWC +XSH+CNG mod 2^64, so that KISS can be> inserted at any place in a C program where a random 64-bit> integer is required.> Fortran's requirement that integers be signed makes the> necessary code more complicated, hence a function KISS().> C version; test by invoking macro KISS 100 million times> -----------------------------------------------------------------> #include static unsigned long long> x=1234567890987654321ULL,c=123456123456123456ULL,> y=362436362436362436ULL,z=1066149217761810ULL,t;> #define MWC (t= (x<<58)+c, c=(x>6), x+=t, c+=(x #define XSH ( y^=(y<<13), y^= (y>17), y^=(y<<43) )> #define CNG ( z=6906969069LL*z+1234567 )> #define KISS (MWC+XSH+CNG)> int main(void)> {int i;> for (i=0;i<100000000;i++) t=KISS;> (t==1666297717051644203ULL) ?> printf(100 million uses of KISS OK):> printf(Fail);> }> ---------------------------------------------------------------> Fortran version; test by calling KISS() 100 million times> ---------------------------------------------------------------> program testkiss> implicit integer*8(a-z)> do i=1,100000000; t=KISS (); end do> if(t.eq.1666297717051644203 8) then> print*,100 million calls to KISS() OK> else; print*,Fail> end if; end> function KISS()> implicit integer*8(a-z)> data x,y,z,c / 1234567890987654321 8, 362436362436362436 8,&> 1066149217761810 8, 123456123456123456 8/> save x,y,z,c> m(x,k)=ieor(x,ishft(x,k)) ! statement function> s(x)=ishft(x,-63) !statement function> t=ishft(x,58)+c> if(s(x).eq.s(t)) then; c=ishft(x,-6)+s(x) > else; c=ishft(x,-6)+1-s(x+t); endif> x=t+x> y=m(m(m(y, 13 8),-17 8),43 8)> z=6906969069 8*z+1234567> KISS=x+y+z> return; end> --------------------------------------------------------------- Output from using the macro KISS or the function KISS() is> MWC+XSH +CNG mod 2^64.> CNG is easily implemented on machines with 64-bit integers,> as arithmetic is automatically mod 2^64, whether integers> are considered signed or unsigned. The CNG statement is> z=6906969069*z+1234567.> When I established the lattice structure of congruential> generators in the 60's, a search produced 69069 as an easy-> to-remember multiplier with nearly cubic lattices in 2,3,4,5-> space, so I tried concatenating, using 6906969069 as> my first test multiplier. Remarkably---a seemingly one in many> hundreds chance---it turned out to also have excellent lattice> structure in 2,3,4,5-space, so that's the one chosen.> (I doubt if lattice structure of CNG has much influence on the> composite 64-bit KISS produced via MWC+XSH+CNG mod 2^64.)> XSH, the Xorshift component, described in> www.jstatsoft.org/v08/i14/paper> uses three invocations of an integer xored with a shifted> version of itself.> The XSH component used for this KISS is, in C notation:> y^=(y<<13); y^=(y>17); y^=(y<<43)> with Fortran equivalents y=ieor(y,ishft(y,13)), etc., although> this can be effected by a Fortran statement function:> f(y,k)=ieor (y,ishft(y,k))> y=f(f(f(y,13),-17),43)> As with lattice structure, choice of the triple 13,-17,43 is> probably of no particular importance; any one of the 275 full-> period triples listed XSH for the composite MWC+XSH+CNG.> The choice of multiplier 'a' for the multiply-with-carry (MWC)> component of KISS is not so easily made. In effect, a multiply-> with-carry sequence has a current value x and current carry c,> and from each given x,c a new x,c pair is constructed by forming> t=a*x+c, then x=t mod b=2^64 and c=floor(t/ b).> This is easily implemented for 32-bit computers that permit> forming a*t+c in 64 bits, from which the new x is the bottom and> the new c the top 32-bits.> When a,x and c are 64-bits, not many computers seem to have an easy> way to form t=a*x+c in 128 bits, then extract the top and bottom> 64-bit segments. For that reason, special choices for 'a' are> needed among those that satisfy the general requirement that> p=a*b-1 is a prime for which b=2^64 has order (p-1)/ 2.> My choice---and the only one of this form---is a=2^58+1. Then the> top 64 bits of an imagined 128-bit t=a*x+c may be obtained as> (using C notation) (x>6)+ 1 or 0, depending> on whether the 64-bit parts of (x<<58)+c+x cause an overflow.> Since (x<<58)+c cannot itself cause overflow (c will always be we get the carry as c=(x>6) plus overflow from (x<<58)+x.> This is easily done in C with unsigned integers, using a different> kind of 't': t=(x<<58)+c; c= (x>6); x=t+x; c=c+(x For Fortran and others that permit only signed integers, more work> is needed.> Equivalent mod 2^64 versions of t=(x<<58)+c and c=(x>6) are easy,> and if s(x) represents (x>63) in C or ishft(x,-66) in Fortran,> then for signed integers, the new carry c comes from the rule> if s(x) equals s(t) then c=(x>6)+s(x) else c=(x>6)+1-s(x+t)> Speed:> A C version of this KISS RNG takes 18 nanosecs for each> 64-bit random number on my desktop (Vista) PC, thus> producing KISSes at a rate exceeding 55 million per second.> Fortran or other integers-must-be-signed compilers might get> only around 40 million per second.> Setting seeds:> Use of KISS or KISS() as a general 64-bit RNG requires specifying> 3*64+58=250 bits for seeds, 64 bits each for x,y,z and 58 for c,> resulting in a composite sequence with period around 2^250.> The actual period is> (2^250+2^192+2^64-2^186-2^129)/6 ~= 2^(247.42) or 10^(74.48).> We lose 1+1.58=2.58 bits from maximum possible period, one bit> because b=2^64, a square, cannot be a primitive root of p=ab-1,> so the best possible order for b is (p-1)/2.> The periods of MWC and XSH have gcd 3=2^1.58, so another 1.58> bits are lost from the best possible period we could expect> from 250 seed bits.> Some users may think 250 seed bits are an unreasonable requirement.> A good seeding procedure might be to assume the default seed> values then let the user choose none, one, two,..., or all> of x,y,z, and c to be reseeded.> Tests:> Latest tests in The Diehard Battery, available at> http://i.cs.hku.hk/~diehard/> were applied extensively. Those tests that specifically required> 32-bit integers were applied to the leftmost 32 bits> (e,g, KISS>32;), then to the middle 32-bits ((KISS<<16)>32;)> then to the rightmost 32 bits, ( (KISS<<32)>32).> There were no extremes in the more than 700 p-values returned> by the tests, nor indeed for similar tests applied to just two of the> KISS components: MWC+XSH, then MWC+CNG, then XSH+CNG.> The simplicity, speed, period around 2^250 and performance on> tests of randomness--- as well as ability to produce exactly> the same 64-bit patterns, whether considered signed or unsigned> integers---make this 64-bit KISS well worth considering for> adoption or adaption to languages other than C or Fortran,> as has been done for 32-bit KISSes.> George MarsagliaAssembling a as an equality function is a fairly appliable algorithm method.It appears stalworth. The seed appears indivisible in code. Memory overuns cause inability to address memory.z= f(z) is in there. Please consider taking it out. Running through all random numbers by using f(z) is possible.It is a simple function that can map seed to series.Z= F(seed) WAS NOT TO BE NOT USED.Is it critical to the whole series? === Subject: Re: 64-bit KISS RNGs > In my view Pierre L'Ecuyer is the leading expert on this area active > today[*]. I would do so were I still active in this area myself; it > would unquestionably pass most of them, as I have tried. I have some > other tests, one of which is harsh enough that it is one of very few > that will fail most of Marsaglia's; >You are only guessing. >Until you have actually run all such tests, your post is just hype. > Back under your bridge with you! And take your nonsense about imagined results possibly differing from > actual ones with you. Good programmers don't even need to profile/test > their code; they just know! There's no substitute for rigorous testing. Nor is there any excuse for denigrating an expert's work -- as Maclaren has done -- without having done a single test. === Subject: Re: 64-bit KISS RNGs > In my view Pierre L'Ecuyer is the leading expert on this area active > today[*]. I would do so were I still active in this area myself; it > would unquestionably pass most of them, as I have tried. I have some > other tests, one of which is harsh enough that it is one of very few > that will fail most of Marsaglia's; >You are only guessing. >Until you have actually run all such tests, your post is just hype. > Back under your bridge with you! > And take your nonsense about imagined results possibly differing from > actual ones with you. Good programmers don't even need to profile/test > their code; they just know! There's no substitute for rigorous testing. Nor is there any excuse for denigrating an expert's work >-- as Maclaren has done -- >without having done a single test. Oh dear, not much into irony and sarcasm are we? Richard Harter, cri@tiac.net http://home.tiac.net/~cri, http://www.varinoma.com If I do not see as far as others, it is because I stand in the footprints of giants. === Subject: Re: 64-bit KISS RNGs > Absolutely. Analyse first. Design second. Code and debug third. > Every good engineer knows that rule! You need to run a couple of simple tests to check that your code > matches your analysis, and there isn't a major flaw in the analysis > itself, but you don't need to do more than that. The main testing > comes where you can't analyse the problem, or where you suspect the > analysis may be unreliable. Which, in practice, is all the time. I mean, have _you_ ever spoken to a customer who knew what he wanted, completely, correctly, and up front? I know I haven't. Richard === Subject: Re: 64-bit KISS RNGs <49be607d.12561515@news.xs4all.nl> posting-account=G1KGwgkAAAAyw4z0LxHH0fja6wAbo7Cz Gecko/2008112309 Iceweasel/3.0.4 (Debian-3.0.4-1),gzip(gfe),gzip(gfe) > Absolutely. Analyse first. Design second. Code and debug third. > Every good engineer knows that rule! > You need to run a couple of simple tests to check that your code > matches your analysis, and there isn't a major flaw in the analysis > itself, but you don't need to do more than that. The main testing > comes where you can't analyse the problem, or where you suspect the > analysis may be unreliable. Which, in practice, is all the time. I mean, have you ever spoken to a > customer who knew what he wanted, completely, correctly, and up front? > I know I haven't. Richard I did. It was wonderful. The University Registrar's Office. My boss had grown up with punchcards and chewed JCL and MARKIV (now called, I think, Vision:Builder) in her sleep. My job was to run database queries to make Lovely. First I made a WinBatch front-end to automate the TN3270 emulator (hit TAB once instead of 7 times, etc.), then I made a Macro-processor to translate a more sensible query language to MARKIV, then I made a compiler to MARKIV. As long as the labels kept flowing, I basically optimized my job away (but I got to stay, just with massive amounts of paid time). lxt === Subject: Re: 64-bit KISS RNGs > Absolutely. Analyse first. Design second. Code and debug third. > Every good engineer knows that rule! You need to run a couple of simple tests to check that your code > matches your analysis, and there isn't a major flaw in the analysis > itself, but you don't need to do more than that. The main testing > comes where you can't analyse the problem, or where you suspect the > analysis may be unreliable. Which, in practice, is all the time. I mean, have _you_ ever spoken to a >customer who knew what he wanted, completely, correctly, and up front? >I know I haven't. Oh, yes, but you had better deliver the solution within a couple of days - if not, the requirement will have started drifting .... Nick Maclaren. === Subject: tetration: another family of powerseries for fractional iteration Recently I discussed the tetration of the pascalmatrix here and compiled This was then only an exercise, but now spinned off a new access to a family of tetration-powerseries for different height and may be it shows up useful for the fractional iteration as well. Maybe this is all known; I didn't see it so far. The idea was triggered by the comments of V Jovovic in the OEIS concerning the below generating functions. Consider the sequence of functions T0(x) = 1, T1(x) = exp(x*1), T2(x) = exp(x*exp(x)), T_h(x) = exp(x*T_{h-1}(x)),... They are also the generation-functions for the following sequence of powerseries: T0: 1 + 0 + 0 + .... T1: 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 ... T2: 1 + x + 3/2*x^2 + 10/6*x^3 + 41/24*x^4 + 196/120*x^5 + 1057/720*x^6 + 6322/5040*x^7 +... T3: 1 + x + 3/2*x^2 + 16/6*x^3 + 101/24*x^4 + 756/120*x^5 + 6607/720*x^6 + 160504/5040*x^7 + ... T4: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1176/120*x^5 + 12847/720*x^6 + 229384/5040*x^7 + ... T5: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16087/720*x^6 + 257104/5040*x^7 + ... T6: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... T7: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... T8: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... T9: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... ... Too: 1 + x + 3/2*x^2 + 4^2/3!*x^3 + 5^3/4!*x^4 + 6^4/5!*x^5 + 7^5/6!*x^6 + 8^6/7!*x^7 + ... //limit h->inf That means, if x = log(b), we have by this T0(x) = 1 T1(x) = b = b^^1 T2(x) = b^b = b^^2 T3(x) = b^b^b = b^^3 ... Too(x) = ...^b^b = b^^oo and for the limit h->inf we have with Too(x) the series for the h-function of b: Too(x) = h(b) which is convergent for |x|h, so any T_h(x) can possibly more easily be expressed as difference from Too(x): T_h(x) = Too(x) - x^h*D_h(x) where D_h might have an even simpler expression than T_h(x) itself... Besides that surprising regularity: what does this mean for the interpolation to fractional heights? It's suggestive to assume, that for the half-iterates the coefficients are very near the neighboured integer-iterates. I've tried the binomial-formula for fractional iterates, but this needs a lot of terms, and I've only done an attempt using the 64x64-matrices. Maybe someone else has a hand to get the b^^0.5 or b^^1.5 - iterate for some b; for b^^3.5, b^^4.5 and higher the coefficients are pretty near at the coefficients of the nearest integer heights. Otherwise I'll try to get usable approximates tomorrow. Next: this representation should also give a drastical reduction for the expression of the alternating sum of powertowers of increasing height (iteration-series). Because if we subtract neighboured rows in the list above, we seem to get a leading triangle of zeros. Hmmm... Gottfried (*1) http://go.helms-net.de/math/tetdocs/PascalMatrixTetrated.pdf ,updated === Subject: Re: tetration: another family of powerseries for fractional iteration > Recently I discussed the tetration of the pascalmatrix here and compiled > This was then only an exercise, but now spinned off a new access to a family > of > tetration-powerseries for different height and may be it shows up useful > for the fractional iteration as well. Maybe this is all known; I didn't see it so far. The idea was triggered by > the comments of V Jovovic in the OEIS concerning the below generating > functions. Consider the sequence of functions T0(x) = 1, T1(x) = exp(x*1), T2(x) = exp(x*exp(x)), T_h(x) = > exp(x*T_{h-1}(x)),... They are also the generation-functions for the following sequence of > powerseries: T0: 1 + 0 + 0 + .... > T1: 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + > 1/5040*x^7 ... > T2: 1 + x + 3/2*x^2 + 10/6*x^3 + 41/24*x^4 + 196/120*x^5 + 1057/720*x^6 + > 6322/5040*x^7 +... > T3: 1 + x + 3/2*x^2 + 16/6*x^3 + 101/24*x^4 + 756/120*x^5 + 6607/720*x^6 + > 160504/5040*x^7 + ... > T4: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1176/120*x^5 + 12847/720*x^6 + > 229384/5040*x^7 + ... > T5: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16087/720*x^6 + > 257104/5040*x^7 + ... > T6: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + > 262144/5040*x^7 + ... > T7: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + > 262144/5040*x^7 + ... > T8: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + > 262144/5040*x^7 + ... > T9: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + > 262144/5040*x^7 + ... ... > Too: 1 + x + 3/2*x^2 + 4^2/3!*x^3 + 5^3/4!*x^4 + 6^4/5!*x^5 + 7^5/6!*x^6 + > 8^6/7!*x^7 + ... //limit h->inf That means, if x = log(b), we have by this T0(x) = 1 > T1(x) = b = b^^1 > T2(x) = b^b = b^^2 > T3(x) = b^b^b = b^^3 > ... > Too(x) = ...^b^b = b^^oo > and for the limit h->inf we have with Too(x) the series for the h-function of > b: Too(x) = h(b) > which is convergent for |x| especially the > series-representation where the base-parameter is explicit and isolated were > complicated; > but now this is a stunning regularity and simpliness: the leading terms > from k=0..h are the same for all heights h1>h, so any T_h(x) can possibly > more easily > be expressed as difference from Too(x): T_h(x) = Too(x) - x^h*D_h(x) where D_h might have an even simpler expression than T_h(x) itself... > Besides that surprising regularity: what does this mean for the interpolation > to > fractional heights? It's suggestive to assume, that for the half-iterates the > coefficients > are very near the neighboured integer-iterates. I've tried the > binomial-formula for fractional > iterates, but this needs a lot of terms, and I've only done an attempt using > the 64x64-matrices. Maybe someone else has a hand to get the b^^0.5 or b^^1.5 > - iterate for > some b; for b^^3.5, b^^4.5 and higher the coefficients are pretty near at the > coefficients > of the nearest integer heights. Otherwise I'll try to get usable approximates > tomorrow. Next: this representation should also give a drastical reduction for the > expression > of the alternating sum of powertowers of increasing height (iteration-series). > Because if we subtract neighboured rows in the list above, we seem to get a > leading > triangle of zeros. Hmmm... Gottfried (*1) http://go.helms-net.de/math/tetdocs/PascalMatrixTetrated.pdf ,updated Gottfried, I think I mentioned in a prior post, that these are exactly the series (7) and (8) in the Wolfram page: http://mathworld.wolfram.com/PowerTower.html Yes, the limiting series is related to the expansion of Lambert's W function, since the coefficients eventually stabilize. They are, in fact, the coefficients of the expansion of -W(-x)/x. The question of finding a continuation for min R^+N remains open and looks non-trivial. I was in fact hoping that *you* would be able to continue the series for such m, using your matrix method. However, the recursive expression for the coefficients given in (6) does not seem to allow that. If you can find a way to interpolate between those coefficients for non-natural heights using your matrix method AND at the same time you manage to preserve the functional equation F(x + 1) = e^{x*F(x)}, then, by Jove, you've got a nice analytic solution to tetration :-) -- Ioannis --- There's _always_ a mistake, somewhere. Chaos --- === Subject: Re: tetration: another family of powerseries for fractional iteration Hi Ioannis - Am 17.03.2009 22:48 schrieb Ioannis: > Gottfried, I think I mentioned in a prior post, that these are exactly the series (7) and > (8) in the Wolfram page: http://mathworld.wolfram.com/PowerTower.html Ah, I see. I've many times read this page, but without explicite numerical examples I often pass sequences of formulas just glancing over The question of finding a continuation for min R^+N remains open and looks > non-trivial. There you say what... ;-) I was in fact hoping that *you* would be able to continue the series for such m, > using your matrix method. given in (6) does not seem to allow that. If you can find a way to interpolate between those coefficients for non-natural > heights using your matrix method AND at the same time you manage to preserve the > functional equation F(x + 1) = e^{x*F(x)}, then, by Jove, you've got a nice > analytic solution to tetration :-) Ok, let's give a start. Recall: T0: 1 + 0 + 0 + .... T1: 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 ... T2: 1 + x + 3/2*x^2 + 10/6*x^3 + 41/24*x^4 + 196/120*x^5 + 1057/720*x^6 + 6322/5040*x^7 +... T3: 1 + x + 3/2*x^2 + 16/6*x^3 + 101/24*x^4 + 756/120*x^5 + 6607/720*x^6 + 160504/5040*x^7 + ... T4: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1176/120*x^5 + 12847/720*x^6 + 229384/5040*x^7 + ... T5: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16087/720*x^6 + 257104/5040*x^7 + ... T6: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... T7: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... T8: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... T9: 1 + x + 3/2*x^2 + 16/6*x^3 + 125/24*x^4 + 1296/120*x^5 + 16807/720*x^6 + 262144/5040*x^7 + ... ... Too: 1 + x + 3/2*x^2 + 4^2/3!*x^3 + 5^3/4!*x^4 + 6^4/5!*x^5 + 7^5/6!*x^6 + 8^6/7!*x^7 + ... //limit h->inf We want to interpolate for coefficients of T0.5, means between rows T0 and T1. I'll rewrite the powerseries without the powers of x. And since we do the binomial composition of coefficients at like powers of x, we compose the coefficients down a column; so the common denominator(the factorial) of a column can be omitted for the scheme. Thus I get for the original coefficients, only rescaled T0: 1 0 0 0 0 0 0 0 ... T1: 1 1 1 1 1 1 1 1 ... T2: 1 1 3 10 41 196 1057 6322 T3: 1 1 3 16 101 756 6607 65794 T4: 1 1 3 16 125 1176 12847 160504 T5: 1 1 3 16 125 1296 16087 229384 T6: 1 1 3 16 125 1296 16807 257104 T7: 1 1 3 16 125 1296 16807 262144 T8: 1 1 3 16 125 1296 16807 262144 T9: 1 1 3 16 125 1296 16807 262144 ... The first binomial-composition along the columns gives X0: 1 0 0 0 0 0 0 0 ... X1: 0 1 1 1 1 1 1 1 ... X2: 0 -1 1 8 39 194 1055 6320 X3: 0 1 -3 -11 -19 171 3439 46831 X4: 0 -1 5 8 -37 -676 -7243 -64744 X5: 0 1 -7 1 105 1021 7357 21589 X6: 0 -1 9 -16 -161 -1026 -3301 67304 X7: 0 1 -11 37 181 631 -3605 -168125 X8: 0 -1 13 -64 -141 104 10961 246224 X9: 0 1 -15 97 17 -999 -16007 -278711 ... ... The second binomial-composition (using h=0.5) Y0: 1 0 0 0 0 0 0 ... Y1: 0 1/2 1/2 1/2 1/2 1/2 1/2 ... Y2: 0 1/8 -1/8 -1 -39/8 -97/4 -1055/8 Y3: 0 1/16 -3/16 -11/16 -19/16 171/16 3439/16 Y4: 0 5/128 -25/128 -5/16 185/128 845/32 36215/128 Y5: 0 7/256 -49/256 7/256 735/256 7147/256 51499/256 Y6: 0 21/1024 -189/1024 21/64 3381/1024 10773/512 69321/1024 Y7: 0 33/2048 -363/2048 1221/2048 5973/2048 20823/2048 -118965/2048 Y8: 0 429/32768 -5577/32768 429/512 60489/32768 -5577/4096 -4702269/32768 Y9: 0 715/65536 -10725/65536 69355/65536 12155/65536 -714285/65536 -11445005/65536 ... ... ... ... the interpolated coefficients c0,c1,c2,... for h=0.5 should then be computed by the column-sums (and finally the rescaling by the omitted factorials). The partial sums in the columns converge only badly if at all, so let's look, whether we can find some analytic solution. The denominators in the rows can be majorized by powers of 4, and all can then be divided by 2, so let's rewrite this common scaling Y0: 1/2 0 0 0 0 0 0 0 0 0 *2 /4^0 Y1: 0 1 1 1 1 1 1 1 1 1 *2 /4^1 Y2: 0 1 -1 -8 -39 -194 -1055 -6320 -41391 -293606 *2 /4^2 Y3: 0 2 -6 -22 -38 342 6878 93662 1219314 16331654 *2 /4^3 Y4: 0 5 -25 -40 185 3380 36215 323720 2128445 -5199340 *2 /4^4 Y5: 0 14 -98 14 1470 14294 102998 302246 -9722034 -332756410 ... Y6: 0 42 -378 672 6762 43092 138642 -2826768 -93176118 -1954258068 Y7: 0 132 -1452 4884 23892 83292 -475860 -22192500 -463551132 -7659247332 Y8: 0 429 -5577 27456 60489 -44616 -4702269 -105630096 -1778712507 -23047084632 Y9: 0 1430 -21450 138710 24310 -1428570 -22890010 -398556730 -5760084330 -51266562490 ... ... ---------------------------------------------------------------------------- ------------------------ sum. s0 s1 s2 s3 ... T0.5: c0 c1 c2 c3 ... and T0.5(x) = c0 + c1*x + c2*x^2/2! + c3*x^/3! + ... Let's look at the columnsums of the table; that sums, divided by the factorial, give the coefficients c_k for the T0.5(x)-powerseries. First, s0 = 1, (remember the scaling extracted to the rhs) , so c0 = 1 Next, s1. Here we recognize, that the numbers are the catalan-numbers, and, with the current scaling have the generation-function 1- sqrt(1-x). Since we want to know simply the sum, we set x=1 and get for the sum s1 = 1- sqrt(1-1) = 1 so c1 =1 Next, s2. It becomes more difficult. We can add columns s2 and s1 to get a sequence, which can formally be expressed as the derivative of the sqrt(1 - x)-function, where possibly we need also a scaling at x, so likely something like 1 - sqrt(1 - a x)' It looks, as if the series is divergent, too, so we'll have to see, whether this operation (and the following, which surely are similar) can be justified/make sense at all. ----------------- But it's late and it's just a task of creative fiddling until possibly a common structure becomes visible. So far just for a start... ;-) Gottfried === Subject: Re: tetration: another family of powerseries for fractional iteration Am 18.03.2009 01:16 schrieb Gottfried Helms: The second binomial-composition (using h=0.5) > Y0: 1 0 0 0 0 0 0 ... > Y1: 0 1/2 1/2 1/2 1/2 1/2 1/2 ... > Y2: 0 1/8 -1/8 -1 -39/8 -97/4 -1055/8 > Y3: 0 1/16 -3/16 -11/16 -19/16 171/16 3439/16 > Y4: 0 5/128 -25/128 -5/16 185/128 845/32 36215/128 > Y5: 0 7/256 -49/256 7/256 735/256 7147/256 51499/256 > Y6: 0 21/1024 -189/1024 21/64 3381/1024 10773/512 69321/1024 > Y7: 0 33/2048 -363/2048 1221/2048 5973/2048 20823/2048 -118965/2048 > Y8: 0 429/32768 -5577/32768 429/512 60489/32768 -5577/4096 -4702269/32768 > Y9: 0 715/65536 -10725/65536 69355/65536 12155/65536 -714285/65536 -11445005/65536 ... > ... ... ... the interpolated coefficients c0,c1,c2,... for h=0.5 should then be computed by the > column-sums (and finally the rescaling by the omitted factorials). ---------------------------------------------------------------------------- - ----------------------- > sum. s0 s1 s2 s3 ... > T0.5: c0 c1 c2 c3 ... and T0.5(x) = c0 + c1*x + c2*x^2/2! + c3*x^/3! + ... Then the first two coefficients are: First, s0 = 1, (remember the scaling extracted to the rhs) , > so c0 = 1 Next, s1. Here we recognize, that the numbers are the catalan-numbers, and, with the > current scaling have the generation-function 1- sqrt(1-z). Since we want to know > simply the sum, we set z=1 and get for the sum > s1 = 1- sqrt(1-1) = 1 > so c1 =1 > T0.5(x) = 1 + 1 *x + c2*x^2/2! + c3*x^/3! + ... > Next, s2. It becomes more difficult. We can add columns s2 and s1 to get a sequence, > which can formally be expressed as the derivative of the sqrt(1 - z)-function, where > possibly we need also a scaling at z, so likely something like 1 - sqrt(1 - a z)' > Let's change the notion of variables to avoid confusion. I'll use z for the formal variable in the generation-function (and changed this in the cited snippets) I get indeed a composition of sqrt(1 - z) and its derivative. It comes out that f(z) = ( 2*z - 3)/sqrt(1 - z) + 3 is a generation-function for the coefficients of s2 . This gives a singularity at z=1 and then T0.5(x) = 1 + 1 *x + ??? * x^2/2! + c3*x^/3! + ... No idea, how to proceed... Gottfried === Subject: Re: tetration: another family of powerseries for fractional iteration Am 18.03.2009 08:47 schrieb Gottfried Helms: > Am 18.03.2009 01:16 schrieb Gottfried Helms: > The second binomial-composition (using h=0.5) > Y0: 1 0 0 0 0 0 0 ... > Y1: 0 1/2 1/2 1/2 1/2 1/2 1/2 ... > Y2: 0 1/8 -1/8 -1 -39/8 -97/4 -1055/8 > Y3: 0 1/16 -3/16 -11/16 -19/16 171/16 3439/16 > Y4: 0 5/128 -25/128 -5/16 185/128 845/32 36215/128 > Y5: 0 7/256 -49/256 7/256 735/256 7147/256 51499/256 > Y6: 0 21/1024 -189/1024 21/64 3381/1024 10773/512 69321/1024 > Y7: 0 33/2048 -363/2048 1221/2048 5973/2048 20823/2048 -118965/2048 > Y8: 0 429/32768 -5577/32768 429/512 60489/32768 -5577/4096 -4702269/32768 > Y9: 0 715/65536 -10725/65536 69355/65536 12155/65536 -714285/65536 -11445005/65536 ... > ... ... ... > the interpolated coefficients c0,c1,c2,... for h=0.5 should then be computed by the > column-sums (and finally the rescaling by the omitted factorials). > ---------------------------------------------------------------------------- - ----------------------- > sum. s0 s1 s2 s3 ... > T0.5: c0 c1 c2 c3 ... > and T0.5(x) = c0 + c1*x + c2*x^2/2! + c3*x^/3! + ... Then the first two coefficients are: > > First, s0 = 1, (remember the scaling extracted to the rhs) , > so c0 = 1 > Next, s1. Here we recognize, that the numbers are the catalan-numbers, and, with the > current scaling have the generation-function 1- sqrt(1-z). Since we want to know > simply the sum, we set z=1 and get for the sum > s1 = 1- sqrt(1-1) = 1 > so c1 =1 T0.5(x) = 1 + 1 *x + c2*x^2/2! + c3*x^/3! + ... > Next, s2. It becomes more difficult. We can add columns s2 and s1 to get a sequence, > which can formally be expressed as the derivative of the sqrt(1 - z)-function, where > possibly we need also a scaling at z, so likely something like > 1 - sqrt(1 - a z)' > Let's change the notion of variables to avoid confusion. I'll use z for the > formal variable in the generation-function (and changed this in the cited > snippets) > I get indeed a composition of sqrt(1 - z) and its derivative. It comes out that f(z) = ( 2*z - 3)/sqrt(1 - z) + 3 is a generation-function for the coefficients of s2 . This gives a singularity at z=1 > and then T0.5(x) = 1 + 1 *x + ??? * x^2/2! + c3*x^/3! + ... No idea, how to proceed... Gottfried Formally composed by derivatives of sqrt(1-z) I get for the series s1,s2,s3,... the following generating functions s0: 1 s1: 1 - 1*sqrt(1-z) s2: 3 - 3*sqrt(1-z) + 2*z*(sqrt(1-z)') s3: 16 - 16*sqrt(1-z) + 15*z*(sqrt(1-z)') - 3*z^2*(sqrt(1-z)'') s4: 125 - 125*sqrt(1-z) + 124*z*(sqrt(1-z)') - 42*z^2*(sqrt(1-z)'') + 4*z^3*(sqrt(1-z)''') s5: 1296 - 1296*sqrt(1-z) + 1295*z*(sqrt(1-z)') - 550*z^2*(sqrt(1-z)'') + 90*z^3*(sqrt(1-z)''') - 5*z^4*(sqrt(1-z)'''') ... which have to be evaluated at z=1 to give the value for the sums. Now the derivatives have a vertical asymptote at z=1, so here are infinities everywhere... Even more obvious, if I expand the derivatives into terms of sqrt(1-z) I get the following explicite generating functions for the series of s0,s1,s2,...: s0: 1 s1: 1 - sqrt(1-z) * ( 1 ) s2: 3 - sqrt(1-z)/(1-z)^1* ( 3 - 4/2*z) s3: 16 - sqrt(1-z)/(1-z)^2* ( 16 - 49/2*z + 31/4*z^2 ) s4: 125 - sqrt(1-z)/(1-z)^3* ( 125 - 626/2*z + 962/4*z^2 - 408/8*z^3 ) s5: 1296 - sqrt(1-z)/(1-z)^4* (1296 - 9073/2*z + 22784/4*z^2 - 23462/8*z^3 + 7561/16*z^4) where all except the first two grow unboundedly, if z->1 So for that approach: it looks as if we cannot express a half-iterate based on this type of powerseries. Pity.... Maybe we can find a workaround - change order of summation or something else, don't have an idea. Gottfried === Subject: LambertW posting-account=F_LoEAoAAABiCLd8O-wEJP4C3lkbvptm Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) Is there any branch of the LambertW function for which the imaginary part of LambertW(x) is 0 when x < -1/e ? === Subject: Re: LambertW Is there any branch of the LambertW function for which the imaginary > part of LambertW(x) is 0 when x < -1/e ? Please don't post the same question more than once. If memory serves right, W(z)in R, iff: 1) zin [-1/e, +oo) for branch 0 (the principal branch) of W, 2) zin [-1/e, 0) for branch -1 of W. So the answer is no. > -- Ioannis --- There's _always_ a mistake, somewhere. Chaos --- === Subject: Re: LambertW <1237327343.136481@athprx03> posting-account=F_LoEAoAAABiCLd8O-wEJP4C3lkbvptm Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > If memory serves right, W(z)in R, iff: 1) zin [-1/e, +oo) for branch 0 (the principal branch) of W, > 2) zin [-1/e, 0) for branch -1 of W. > have a reference for that? ps: i removed the other posts. sorry. > So the answer is no. -- > Ioannis --- There's _always_ a mistake, somewhere. > Chaos --- === Subject: Re: LambertW > If memory serves right, W(z)in R, iff: > 1) zin [-1/e, +oo) for branch 0 (the principal branch) of W, > 2) zin [-1/e, 0) for branch -1 of W. i was wondering if the implication goes in both ways. I would think so. > have a reference for that? http://ioannis.virtualcomposer2000.com/math/ExponentialsPaper.html Lemma 2.10 on page 762. Also look at references [16] and [17] mentioned in that paper. ps: i removed the other posts. sorry. -- Ioannis --- There's _always_ a mistake, somewhere. Chaos --- === Subject: LambertW imaginary / real posting-account=F_LoEAoAAABiCLd8O-wEJP4C3lkbvptm Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) Is there any branch of the Lambert function for which LambertW(x) has zero imaginary part for any x < -1/e ? === Subject: LambertW imaginary / real posting-account=F_LoEAoAAABiCLd8O-wEJP4C3lkbvptm Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) Is there any branch of the Lambert function for which the imaginary part of LambertW( x ) is non zero for any x < -1/e ? === Subject: principal value posting-account=AqhfagoAAADXici1E9pNfoNWFql4em6j 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Hello all' I would like to know where do we use pricipal value integrals? And what is the importance of them Sun === Subject: Re: not for the squeamish: question and answer from Yahoo! Sports <498C79FA.D80625CB@bestweb.net> <7r7o66-1he.ln1@news.ducksburg.com> Not quite: there's no _gematria_ because Leo uses his own system. > What if we call it isopsephy? > That's OK with me, but what does Dr Matrix think? > Who is Dr. Matrix? > I like it. He was The World's Greatest Numerologist. http://www.amazon.com/Incredible-Dr-Matrix-Martin-Gardner/dp/068414669X -- A: Because it messes up the order in which people normally read text. Q: Why is top-posting such a bad thing? A: Top-posting. Q: What is the most annoying thing on usenet and in e-mail? === Subject: Re: not for the squeamish: question and answer from Yahoo! Sports <498C79FA.D80625CB@bestweb.net> <7r7o66-1he.ln1@news.ducksburg.com> posting-account=IUHPBAkAAAAdE4H5DjXDwApEgTTGsxiq Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Not quite: there's no gematria because Leo uses his own system. > What if we call it isopsephy? > That's OK with me, but what does Dr Matrix think? > Who is Dr. Matrix? > I like it. He was The World's Greatest Numerologist. > I he's dead, then HAW HAW, Dr Matrix is decomposing himself. === Subject: index of a subgroup posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009030423 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) does the index of a subgroup H in a group G equals the number of conjugacy classes of H in G? S. === Subject: Re: index of a subgroup posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) does the index of a subgroup H in a group G equals the number of > conjugacy classes of H in G? What would this mean, if true, when H is normal in G? Arturo Magidin === Subject: Re: index of a subgroup posting-account=R7AgUAoAAADVFAtIe36IBmgohoHjZsKW Gecko/2009030422 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) > does the index of a subgroup H in a group G equals the number of > conjugacy classes of H in G? What would this mean, if true, when H is normal in G? Arturo Magidin If G is a finite group, can one say that the number of conjugacy classes of H in G is less or equal than the index of H in G? S. === Subject: Re: index of a subgroup posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009030422 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) > does the index of a subgroup H in a group G equals the number of > conjugacy classes of H in G? > What would this mean, if true, when H is normal in G? If G is a finite group, can one say that the number of conjugacy > classes of H in G is less or equal than the index of H in G? Yes: as Jack pointed out, the number of conjugates of H in G is equal to the index of the normalizer of H in G, [G:N G(H)]. Recall that N G(H) = { g in G : gHg^{-1} = H}. Now, if xHx^{-1} = yHy^{-1}, then y^{-1}xHx^{-1}y = H, so y^{-1}x is in N G(H). Thus, of x is congruent to y on the left modulo N G(H), then x and y determine the same conjugate of H. And if x and y are congruent on the left modulo N G(H), so that y^{-1}x = n with n in N G (H), then H = nHn^{-1} = (y^{-1}x)H(y^{-1}x)^{-1}, from which you get xHx^{-1} = yHy^{-1}. So the conjugates of H are in 1-to-1 correspondence with the left cosets of N G(H). Since H is contained in N G(H), you get # Conjugates of H = [G:N G(H)] <= [G:N G(H)][N G(H):H)] = [G:H], the inequality you asked for. Arturo Magidin === Subject: Re: index of a subgroup > does the index of a subgroup H in a group G equals > the number of conjugacy classes of H in G? Sometimes, but not usually. If a group G acts on some set X (like the set of G-conjugates of H), then the index of the stabilizer of a point x (like H) is equal to the size of the orbit of x under G. The number of G-conjugates of H is the index of the normalizer of H in G. If H happens to be self- normalizing, then this is the index of H. When asking these sorts of questions, you should check a few examples first. Does it work for any pair (G,H) where H is a proper subgroup of G and G is abelian? === Subject: the imaginary part of LambertW posting-account=F_LoEAoAAABiCLd8O-wEJP4C3lkbvptm Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) Is there a branch of the Lambert function for which the imaginary part of LambertW(x) is different than zero for x < -1/e ? === Subject: Re: Hyperbolic Only for (x^3 + Px + Q = 0) posting-account=0JR5swoAAADYQEG_z3avrNrWsn0bztdN Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 16, 5:10am, Gerry Myerson <49b39b9d$1_2@news.bluewin.ch> <1236590474_3930@sicinfo3.epfl.ch> posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) >Of course he was. How often must the argument be rehashed until it is >finally understood? We all know that quantum mechanics is 100% >correct and the tests that prove it can be repeated again and again >with the same results. Sadly, the same cannot be said for relativity. >Except, of course, for the century of experiments that have tested >it and the daily testing in the gps system. >The problem it seems is one of intellect. >Strich does have that problem. > The majority of physicists >are too intellectually inferior to grasp the underlying principles of >quantum mechanics. The human mind has yet to evolve for the majority >of humanity to understand the very advanced concepts being espoused by >QM. Most people can only grasp the cute geometries of relativity, and >would prefer the latter for the simple reason of comprehension, not >veracity. >The conflict between relativity and QM has long been resolved in favor >of QM. Here is the summary: >1) QM and SR/GR are mutually inconsistent >2) Thus Einstein formulated the EPR paradox as the counterargument >against QM >3) Bell showed the EPR paradox does not falsify QM; hence it falsifies >SR/GR >4) End of story >Again, QM is counter-intuitive. SR/GR is counter-logical. >It counter to strich's prejudice and ignorance but that is >not a scientific argument. > It is >easier for people to suspend logic than intuition (as seen in the >prevalence of supernatural explanations worldwide) thus the favor of >SR/GR over QM. It would take another millenia of human evolution >before people can grasp the structure of QM.- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - > age and dwelled in caves. Your mindset suggests that you still prefer > cave dwelling, because such places are such well proven habitats. .84 > NoEinstein .84 Being correct got us out of the caves. Your nonsense would put us > back in. Why should science retreat hundreds of years into ignorance > just to make you happy?- Hide quoted text - - Show quoted text - preferring to live in caves. The world is... flat. Remember? Ha, ha, HA, HA, HA! .84 NoEinstein .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... > >Of course he was. How often must the argument be rehashed until it is >finally understood? We all know that quantum mechanics is 100% >correct and the tests that prove it can be repeated again and again >with the same results. Sadly, the same cannot be said for relativity. >Except, of course, for the century of experiments that have tested >it and the daily testing in the gps system. >The problem it seems is one of intellect. >Strich does have that problem. > The majority of physicists >are too intellectually inferior to grasp the underlying principles of >quantum mechanics. The human mind has yet to evolve for the majority >of humanity to understand the very advanced concepts being espoused by >QM. Most people can only grasp the cute geometries of relativity, and >would prefer the latter for the simple reason of comprehension, not >veracity. >The conflict between relativity and QM has long been resolved in favor >of QM. Here is the summary: >1) QM and SR/GR are mutually inconsistent >2) Thus Einstein formulated the EPR paradox as the counterargument >against QM >3) Bell showed the EPR paradox does not falsify QM; hence it falsifies >SR/GR >4) End of story >Again, QM is counter-intuitive. SR/GR is counter-logical. >It counter to strich's prejudice and ignorance but that is >not a scientific argument. > It is >easier for people to suspend logic than intuition (as seen in the >prevalence of supernatural explanations worldwide) thus the favor of >SR/GR over QM. It would take another millenia of human evolution >before people can grasp the structure of QM.- Hide quoted text - >- Show quoted text -- Hide quoted text - >- Show quoted text - >age and dwelled in caves. Your mindset suggests that you still prefer >cave dwelling, because such places are such well proven habitats. .84 >NoEinstein .84 >Being correct got us out of the caves. Your nonsense would put us >back in. Why should science retreat hundreds of years into ignorance >just to make you happy?- Hide quoted text - >- Show quoted text - > preferring to live in caves. The world is... flat. Remember? Ha, > ha, HA, HA, HA! .84 NoEinstein .84 And john is wrong. Lets come back in ten years and see any of physics has changed to follow john's delusions. There is no chance of that since john does not know any science. === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... <1236246052_3731@sicinfo3.epfl.ch> <49b39b9d$1_2@news.bluewin.ch> <1236590474_3930@sicinfo3.epfl.ch> posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > There are no paradoxes in physics. There are many things that are > counter to our *intuitions*, but those intuitions are based on > extrapolations of what we are accustomed to from our senses. Many of > those extrapolations objectively fail. That is not a contradiction. > That is just a surprise. > such people being too willing to disregard logic, common sense and > intuition. I completely sympathize with your profound desire that the universe be > sensible by conforming to common sense and intuition. However, common > sense and intuition are products of gray meat between the ears and do > not spring from an innate grasp of the universe. Humans make mistakes > about the rules that nature works by. Whenever that happens, and a > mistake is realized, this conflicts with our common sense and > intuition, which is the assemblage of rules we *thought* that nature > worked by. Removing those mistakes is necessary to make further > progress, even though that means tell our own intuition and common > sense that they are mistaken. For some people, this is an easier task than for other people. Other > people, particularly retired workers in architectural firms, this is > completely uncomfortable, and so they rebel against it. PD offended, there is a probable mistake in the garbage that was just postulated! .84 NoEinstein .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > IOTAs, the smallest energy units in the ether. Light doesn't require > a 'medium' for its propagation; so light never is a wave. Light is > quanta. The 'bending' of light off of the line of sight at slits and > pin holes is due to light being polar. When light passes any mass, > the polar ether in such acts like magnets to cause the course of the > IOTAs to bend. But the light itself remains quanta, NOT waves! .84 > NoEinstein .84 Ah, good, then you should be able to calculate where the third > maximum > in an interference pattern from a $15 laser pointer shining through a > slit in a black-painted sheet of glass will be, BEFORE you turn on > the > laser -- by using your theory of iotas and polarity. I can. That's what makes my theory useful. Is yours as useful? Demonstrate, please. PD they can't be used for interferometer experiments. Please explain what useful information you gathered from a non-existent experiment? .84 NoEinstein .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... > >IOTAs, the smallest energy units in the ether. Light doesn't require >a 'medium' for its propagation; so light never is a wave. Light is >quanta. The 'bending' of light off of the line of sight at slits and >pin holes is due to light being polar. When light passes any mass, >the polar ether in such acts like magnets to cause the course of the >IOTAs to bend. But the light itself remains quanta, NOT waves! .84 >NoEinstein .84 >Ah, good, then you should be able to calculate where the third >maximum >in an interference pattern from a $15 laser pointer shining through a >slit in a black-painted sheet of glass will be, BEFORE you turn on >the >laser -- by using your theory of iotas and polarity. >I can. That's what makes my theory useful. >Is yours as useful? Demonstrate, please. >PD > they can't be used for interferometer experiments. Please explain > what useful information you gathered from a non-existent > experiment? .84 NoEinstein .84 It is good to see that you are keeping your record of being wrong on everything intact. It is very easy to see interference with a $15 laser. For the double slit experiment, the coherence length does not need to be very large, but a diode laser will have plenty of coherence length for even a standard interferometer. I am using some of them on my interferometer setups at home. === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... <8-qdnamB2p8qiCDUnZ2dnUVZ_tLinZ2d@posted.docknet> posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > IOTAs, the smallest energy units in the ether. Oh good, now you claim that light does not go at the speed of > light. I suppose next you will claim that sound does not go > at the speed of sound. Light doesn't require> a 'medium' for its propagation; so light never is a wave. Light is > quanta. The 'bending' of light off of the line of sight at slits and > pin holes is due to light being polar. When light passes any mass, > the polar ether in such acts like magnets to cause the course of the > IOTAs to bend. But the light itself remains quanta, NOT waves! .84 > NoEinstein .84 This is even stupider than your other postings. > Study some actual physics. >Let me clarify some basic truths about QM. >1) QM is non-relativistic. >2) QM does not treat time on the same footing as space. >3) This is important. In QM time is a paramter, >whereas spatial coordinates are operators. >4) A space-time continuum fantasy does not exist in QM. >5) QM deals with the fine structure of matter. >In comparison, SR/GR is clueless as to what is going on at this >level. >6) QM is the most fundamental theory. >In comparison, SR/GR is a superfluous theory about this childish >fetish >with retarded clocks, shrunken rulers and crooked space. >7) There are no hidden variables in QM. >8) The fanatics of SR/GR adapted QM to a relativistic formulation >called QFT. >9) Guess what, the logical inconsistencies of SR/GR was dragged into >QFT. >10) The theory is now plagued by infinities. >11) This is corrected by renormalization. >12) Renormalization is possible because >QM provides the correct underlying foundation. >13) A type of QFT for gravity has been attempted. >14) It is also beset by infinities. >15) These cannot be corrected by the usual renormalization. >16) Why? Because there is no underlying Quantum Mechanical treatment >of >gravity that can be used as a template for the correction. >(Ha ha ha, the underlying treatment for gravity by >GR is useless as a template to obtain correct answers!) >In summary, if QFT adds nothing new, then why was it introduced? Why >dress the perfect QM with the cross-dressing SR/GR blouse only to come >up with the mutant QFT that can only be kept alive by renormalization >life support? The answer is all too human. Relativist vanity wanted >to legitimize SR/GR by incorporating it into QM. And look at them >now. Still with their thumbs in their mouths. >----------------------- >Again we expect the usual ad hominems, though my points are based on >fact. After a while, the comical ad hominems become increasingly >transparent as the anemic attempts at rebuttal by feeble minds. Note >how relativists cannot engage one single quantum mechanical idea. >They can only go as far as the simple algebra of SR and the simple >pictures of GR (the equations are mere window dressing to transmute >the normally Euclidean equations to a Riemannian fantasy--talk about >the diametric opposite of Occam's principle). It is a shame. Tons >and tons of relativists, and not a single one with a useful brain. >6) debatable >7) correct >8) NO, QFT exists or not has nothing to do with SR/GR. >9) N/A because (8) >10) yes, >11) sort of, on 3+1 dim we basically only know how to get rid >of the infinities in presence of some local symmetries. >infinities and allow us to absorb the remaining few as a >renormalization of parameters in the theory. >12) Nope, it just works. nothing to do whether QM is fundamental' >or not. In fact, people simply view 'renormalization' as a >hint our current theory is a low-energy effective theory of >the true theory. >13-14) yes. >regular QFT, the problem of gravity has nothing to do with GR. >to describe the quanta of GR. A side effect is the infinities >becomes much worst than usual and we don't have an alternate >16) All the QM/QFT are only approximate. In fact, we only know how >to compute concrete number using divergence series expansion :-( >BTW, QM/QFT works very well with SR. >Idiotic BULL. >*plonk* >Do not reply to this generic message, it was automatically generated; >you have been kill-filed, either for being boringly stupid, repetitive, >unfunny, repeatedly posting politics or religion to a sci. newsgroup, >attempting free advertising or because you are a troll; any reply will >go unread. There is no appeal, I have despotic power over whom I will >admit into my home and you do not qualify. >This should not trouble you, many of those plonked find it a blessing >that they are not required to think and can persist in their bigotry >or crackpot theories without challenge. You have the right to free >speech, I have the right not to listen. The kill-file will be cleared >annually with spring cleaning or whenever I purchase a new computer or >hard drive. I hope this explanation is satisfactory. >Have a nice day. >you say >Change your name again, I have plenty of space. >*plonk* >Do not reply to this generic message, it was automatically generated; >you have been kill-filed, either for being boringly stupid, repetitive, >unfunny, repeatedly posting politics or religion to a sci. newsgroup, >attempting free advertising or because you are a troll; any reply will >go unread. There is no appeal, I have despotic power over whom I will >admit into my home and you do not qualify. >This should not trouble you, many of those plonked find it a blessing >that they are not required to think and can persist in their bigotry >or crackpot theories without challenge. You have the right to free >speech, I have the right not to listen. The kill-file will be cleared >annually with spring cleaning or whenever I purchase a new computer or >hard drive. I hope this explanation is satisfactory. >Have a nice day. >you say >I thought the physics cranks are bad. This guy is telling us to just >dive deep into dispair and hopelessness. When he starts of going on >about the contradictions in relativity, you know he knows nothing >about >it. His comments on QM are similarly ignorant. He tries to take the >comic book overview and make something deeper out of it that is not >there. It reads like a comedy sketch parodying philosophers spouting >when people attack the person and not the arguments you know they cant >attack the arguments >It is not even well enough done to be wrong. It needs a lot of >cleaning up to get to that point. >how about telling us what wrong with dean cliams rather than tell us >whats wrong with dean >you have wick telling you QM is full of paradox and contradiction >And you have the rest of the world telling you it is not. Your inability >to understand it is not a scientific argument. For instance, you seem >upset about the dual nature of light. You think that is a problem with >QM. What it means is you are asking the wrong question. Nature has told >not that there is any problem with qm, but that you have asked the wrong >question. The categories you have chosen for light are wrong. It has >properties that do not neatly fit your preconceived notions. The >real problem with the philosphers is that there is always a it >is obvious type statement in the process. This is where the >scientist would stop but the philosopher barges right along. The whole >paper was full of nonsense taken from out of context quotes. This >comes from the ignorance of what the scientific theories actually >are. If you want to make some sense, study what the theories >actually are. This takes years to understand and does not come >out of a comic book. Your whole paper comes from the comic >book level and is thus pretty silly. >you say > You think that is a problem with >QM. What it means is you are asking the wrong question. Nature has >told- Hide quoted text - - Show quoted text -... read more é are a pseudo expert on the postings of others. Status quo physics is all screwed up, and you are just an attack the messenger junkie. State YOUR notions about physics or buzz off! .84 NoEinstein .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... > >IOTAs, the smallest energy units in the ether. >Oh good, now you claim that light does not go at the speed of >light. I suppose next you will claim that sound does not go >at the speed of sound. > Light doesn't require> a 'medium' for its propagation; so light never is a wave. Light is >quanta. The 'bending' of light off of the line of sight at slits and >pin holes is due to light being polar. When light passes any mass, >the polar ether in such acts like magnets to cause the course of the >IOTAs to bend. But the light itself remains quanta, NOT waves! .84 >NoEinstein .84 >This is even stupider than your other postings. >Study some actual physics. >Let me clarify some basic truths about QM. >1) QM is non-relativistic. >2) QM does not treat time on the same footing as space. >3) This is important. In QM time is a paramter, >whereas spatial coordinates are operators. >4) A space-time continuum fantasy does not exist in QM. >5) QM deals with the fine structure of matter. >In comparison, SR/GR is clueless as to what is going on at this >level. >6) QM is the most fundamental theory. >In comparison, SR/GR is a superfluous theory about this childish >fetish >with retarded clocks, shrunken rulers and crooked space. >7) There are no hidden variables in QM. >8) The fanatics of SR/GR adapted QM to a relativistic formulation >called QFT. >9) Guess what, the logical inconsistencies of SR/GR was dragged into >QFT. >10) The theory is now plagued by infinities. >11) This is corrected by renormalization. >12) Renormalization is possible because >QM provides the correct underlying foundation. >13) A type of QFT for gravity has been attempted. >14) It is also beset by infinities. >15) These cannot be corrected by the usual renormalization. >16) Why? Because there is no underlying Quantum Mechanical treatment >of >gravity that can be used as a template for the correction. >(Ha ha ha, the underlying treatment for gravity by >GR is useless as a template to obtain correct answers!) >In summary, if QFT adds nothing new, then why was it introduced? Why >dress the perfect QM with the cross-dressing SR/GR blouse only to come >up with the mutant QFT that can only be kept alive by renormalization >life support? The answer is all too human. Relativist vanity wanted >to legitimize SR/GR by incorporating it into QM. And look at them >now. Still with their thumbs in their mouths. >----------------------- >Again we expect the usual ad hominems, though my points are based on >fact. After a while, the comical ad hominems become increasingly >transparent as the anemic attempts at rebuttal by feeble minds. Note >how relativists cannot engage one single quantum mechanical idea. >They can only go as far as the simple algebra of SR and the simple >pictures of GR (the equations are mere window dressing to transmute >the normally Euclidean equations to a Riemannian fantasy--talk about >the diametric opposite of Occam's principle). It is a shame. Tons >and tons of relativists, and not a single one with a useful brain. >6) debatable >7) correct >8) NO, QFT exists or not has nothing to do with SR/GR. >9) N/A because (8) >10) yes, >11) sort of, on 3+1 dim we basically only know how to get rid >of the infinities in presence of some local symmetries. >infinities and allow us to absorb the remaining few as a >renormalization of parameters in the theory. >12) Nope, it just works. nothing to do whether QM is fundamental' >or not. In fact, people simply view 'renormalization' as a >hint our current theory is a low-energy effective theory of >the true theory. >13-14) yes. >regular QFT, the problem of gravity has nothing to do with GR. >to describe the quanta of GR. A side effect is the infinities >becomes much worst than usual and we don't have an alternate >16) All the QM/QFT are only approximate. In fact, we only know how >to compute concrete number using divergence series expansion :-( >BTW, QM/QFT works very well with SR. >Idiotic BULL. >*plonk* >Do not reply to this generic message, it was automatically generated; >you have been kill-filed, either for being boringly stupid, repetitive, >unfunny, repeatedly posting politics or religion to a sci. newsgroup, >attempting free advertising or because you are a troll; any reply will >go unread. There is no appeal, I have despotic power over whom I will >admit into my home and you do not qualify. >This should not trouble you, many of those plonked find it a blessing >that they are not required to think and can persist in their bigotry >or crackpot theories without challenge. You have the right to free >speech, I have the right not to listen. The kill-file will be cleared >annually with spring cleaning or whenever I purchase a new computer or >hard drive. I hope this explanation is satisfactory. >Have a nice day. >you say >Change your name again, I have plenty of space. >*plonk* >Do not reply to this generic message, it was automatically generated; >you have been kill-filed, either for being boringly stupid, repetitive, >unfunny, repeatedly posting politics or religion to a sci. newsgroup, >attempting free advertising or because you are a troll; any reply will >go unread. There is no appeal, I have despotic power over whom I will >admit into my home and you do not qualify. >This should not trouble you, many of those plonked find it a blessing >that they are not required to think and can persist in their bigotry >or crackpot theories without challenge. You have the right to free >speech, I have the right not to listen. The kill-file will be cleared >annually with spring cleaning or whenever I purchase a new computer or >hard drive. I hope this explanation is satisfactory. >Have a nice day. >you say >I thought the physics cranks are bad. This guy is telling us to just >dive deep into dispair and hopelessness. When he starts of going on >about the contradictions in relativity, you know he knows nothing >about >it. His comments on QM are similarly ignorant. He tries to take the >comic book overview and make something deeper out of it that is not >there. It reads like a comedy sketch parodying philosophers spouting >when people attack the person and not the arguments you know they cant >attack the arguments >It is not even well enough done to be wrong. It needs a lot of >cleaning up to get to that point. >how about telling us what wrong with dean cliams rather than tell us >whats wrong with dean >you have wick telling you QM is full of paradox and contradiction >And you have the rest of the world telling you it is not. Your inability >to understand it is not a scientific argument. For instance, you seem >upset about the dual nature of light. You think that is a problem with >QM. What it means is you are asking the wrong question. Nature has told >not that there is any problem with qm, but that you have asked the wrong >question. The categories you have chosen for light are wrong. It has >properties that do not neatly fit your preconceived notions. The >real problem with the philosphers is that there is always a it >is obvious type statement in the process. This is where the >scientist would stop but the philosopher barges right along. The whole >paper was full of nonsense taken from out of context quotes. This >comes from the ignorance of what the scientific theories actually >are. If you want to make some sense, study what the theories >actually are. This takes years to understand and does not come >out of a comic book. Your whole paper comes from the comic >book level and is thus pretty silly. >you say >You think that is a problem with >QM. What it means is you are asking the wrong question. Nature has >told- Hide quoted text - >- Show quoted text -... >read more é > are a pseudo expert on the postings of others. Status quo physics is > all screwed up, and you are just an attack the messenger junkie. > State YOUR notions about physics or buzz off! .84 NoEinstein .84 You make claims that physics is all screwed up. What do you think is screwed up? You have never shown anything that even remotely brings any science into question. You have demonstrated that you are incapable of learning but that has no effect on science. === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > IOTAs, the smallest energy units in the ether. > Do you even know the *definition* of 'c' speed? Yes. > In agreement with experience we further assume the quantity > 2AB/(t'A-tA) = c > to be a universal constant--the velocity of light in empty space. -- Albert > wit Einstein. the velocity of light in our theory plays the part, physically, of an > infinitely great velocity. -- Albert wit Einstein. Just how far is it from A to A anyway? Was Einstein a stupid cunt? Of course he was... :) !! .84 NE .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > 2) Is quantum tunnelling faster-than-light travel? Yes/No. > No. > There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum_tunnelling > tunneling is faster-than-light travel? > That's merely a tutorial to bring you up to speed. > Ah, good, so you decide it's not there after all, and dig a little > further and you find an abstract from a poster session from a regional > clean-up meeting, where the cranks and goofballs are allowed to speak... So any data that contradicts your Einstein pet peeve with its intuitive but illogical framework comes from cranks? Don't worry, pretty soon, more data will come in and slowly you will find yourself on the other side of the fence, as the prime goofball... technology, as the tech becomes more widely available, this experiment will be repeated with increasing accuracy routinely. And you will still be screaming 'crank' at the top of your lungs, not realizing your relativistic world has been turned on its head... http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 I am wondering. What do you have against the progress of science? Why do you cling to the old theories? Is it just easier for you to understand Einstein's geometrically simple Riemannian world than the superposed non-geometric Hilbert world of quantum mechanics? Perhaps Einstein's world is for humans and the quantum world is for super humans? http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 I am wondering. What do you have against the progress of science? Why do you cling to the old theories? Is it just easier for you to understand Einstein's geometrically simple Riemannian world than the superposed non-geometric Hilbert world of quantum mechanics? Perhaps Einstein's world is for proto-humans and the quantum world is for super-humans? === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) > 2) Is quantum tunnelling faster-than-light travel? Yes/No. > No. > There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum tunnelling > tunneling is faster-than-light travel? > That's merely a tutorial to bring you up to speed. > Ah, good, so you decide it's not there after all, and dig a little > further and you find an abstract from a poster session from a regional > clean-up meeting, where the cranks and goofballs are allowed to speak... So any data that contradicts your Einstein pet peeve with its > intuitive but illogical framework comes from cranks? Don't worry, > pretty soon, more data will come in and slowly you will find yourself > on the other side of the fence, as the prime goofball... technology, as the tech becomes more widely available, this experiment > will be repeated with increasing accuracy routinely. And you will > still be screaming 'crank' at the top of your lungs, not realizing > your relativistic world has been turned on its head... http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 I am wondering. What do you have against the progress of science? Why > do you cling to the old theories? Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for humans and the quantum world is for super > humans? http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 I am wondering. What do you have against the progress of science? > Why do you cling to the old theories? Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for proto-humans and the quantum world is for > super-humans? :) !!! .84 NoEinstein .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > 2) Is quantum tunnelling faster-than-light travel? Yes/No. > No. > There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum tunnelling > tunneling is faster-than-light travel? > That's merely a tutorial to bring you up to speed. Ah, good, so you decide it's not there after all, and dig a little > further and you find an abstract from a poster session from a regional > clean-up meeting, where the cranks and goofballs are allowed to speak... So any data that contradicts your Einstein pet peeve with its intuitive but illogical framework comes from cranks? Don't worry, pretty soon, more data will come in and slowly you will find yourself on the other side of the fence, as the prime goofball... technology, as the tech becomes more widely available, this experiment will be repeated with increasing accuracy routinely. And you will still be screaming 'crank' at the top of your lungs, not realizing your relativistic world has been turned on its head... http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 I am wondering. What do you have against the progress of science? Why do you cling to the old theories? Is it just easier for you to understand Einstein's geometrically simple Riemannian world than the superposed non-geometric Hilbert world of quantum mechanics? Perhaps Einstein's world is for humans and the quantum world is for super humans? http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 I am wondering. What do you have against the progress of science? Why do you cling to the old theories? Is it just easier for you to understand Einstein's geometrically simple Riemannian world than the superposed non-geometric Hilbert world of quantum mechanics? Perhaps Einstein's world is for proto-humans and the quantum world is for super-humans? === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... > >2) Is quantum tunnelling faster-than-light travel? Yes/No. >No. >There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum_tunnelling >tunneling is faster-than-light travel? >That's merely a tutorial to bring you up to speed. >Ah, good, so you decide it's not there after all, and dig a little >further and you find an abstract from a poster session from a regional >clean-up meeting, where the cranks and goofballs are allowed to speak... > So any data that contradicts your Einstein pet peeve with its > intuitive but illogical framework comes from cranks? Don't worry, > pretty soon, more data will come in and slowly you will find yourself > on the other side of the fence, as the prime goofball... technology, as the tech becomes more widely available, this experiment > will be repeated with increasing accuracy routinely. And you will > still be screaming 'crank' at the top of your lungs, not realizing > your relativistic world has been turned on its head... http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 There is nothing here that poses any problem with relativity. What do you have against learning science? > I am wondering. What do you have against the progress of science? > Why do you cling to the old theories? Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for humans and the quantum world is for super > humans? http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Same experiment. Same agrement with relativity. What do you have against learning science? I am wondering. What do you have against the progress of science? > Why do you cling to the old theories? Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for proto-humans and the quantum world is for > super-humans? === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... <7JKdndzs05YBhyLUnZ2dnUVZ_sfinZ2d@posted.docknet> posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) >2) Is quantum tunnelling faster-than-light travel? Yes/No. >No. >There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum tunnelling >tunneling is faster-than-light travel? >That's merely a tutorial to bring you up to speed. >Ah, good, so you decide it's not there after all, and dig a little >further and you find an abstract from a poster session from a regional >clean-up meeting, where the cranks and goofballs are allowed to speak... > So any data that contradicts your Einstein pet peeve with its > intuitive but illogical framework comes from cranks? Don't worry, > pretty soon, more data will come in and slowly you will find yourself > on the other side of the fence, as the prime goofball... > technology, as the tech becomes more widely available, this experiment > will be repeated with increasing accuracy routinely. And you will > still be screaming 'crank' at the top of your lungs, not realizing > your relativistic world has been turned on its head... >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 There is nothing here that poses any problem with relativity. > What do you have against learning science? > I am wondering. What do you have against the progress of science? > Why do you cling to the old theories? Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for humans and the quantum world is for super > humans? >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Same experiment. Same agrement with relativity. > What do you have against learning science? > I am wondering. What do you have against the progress of science? > Why do you cling to the old theories? Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for proto-humans and the quantum world is for > super-humans?- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - Science needed to judge Einstein as wrong. He was not. And I am here to validate it. Mitch Raemsch === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729; MS-RTC EA 2),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > 2) Is quantum tunnelling faster-than-light travel? Yes/No. > No. > There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum tunnelling > tunneling is faster-than-light travel? > That's merely a tutorial to bring you up to speed. > Ah, good, so you decide it's not there after all, and dig a little > further and you find an abstract from a poster session from a regional > clean-up meeting, where the cranks and goofballs are allowed to speak... > So any data that contradicts your Einstein pet peeve with its > intuitive but illogical framework comes from cranks? Don't worry, > pretty soon, more data will come in and slowly you will find yourself > on the other side of the fence, as the prime goofball... That will be very exciting. Are you holding your breath? I hope so. Just have your wife let me know where it is. > technology, as the tech becomes more widely available, this experiment > will be repeated with increasing accuracy routinely. And you will > still be screaming 'crank' at the top of your lungs, not realizing > your relativistic world has been turned on its head... >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 anything about tunneling being faster than light. > Ah, you have to use your head. That is why they have the attoclock. You can perform the calculations. Apparently simply stating in black and white that the speed of light has been violated can have negative repercussions on publication chances, and the authors deferred on that option. > I am wondering. What do you have against the progress of science? > Why do you cling to the old theories? I don't. I'm actually quite eager to find experimental evidence that > is inconsistent with relativity. But there hasn't been any yet. > Really? How eager were you to embrace the negative results of LIGO and GPB? > Nor does disparaging a theory just for the sake of being contrary > serve any useful purpose. Some people have lots of time to waste on > things like that. > So why are you disparaging quantum mechanics? > Is it just easier for you to > understand Einstein's geometrically simple Riemannian world than the > superposed non-geometric Hilbert world of quantum mechanics? Perhaps > Einstein's world is for humans and the quantum world is for super > humans? This would be worth discussing further if you knew what 50% of the > words on those two sentences meant. > You must be speaking for yourself. It is obvious that you have a harder time with QM than SR/GR. === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... > >2) Is quantum tunnelling faster-than-light travel? Yes/No. >No. >There you go. Delusion confirmed.http://en.wikipedia.org/wiki/Quantum_tunnelling >tunneling is faster-than-light travel? >That's merely a tutorial to bring you up to speed. >Ah, good, so you decide it's not there after all, and dig a little >further and you find an abstract from a poster session from a regional >clean-up meeting, where the cranks and goofballs are allowed to speak... >So any data that contradicts your Einstein pet peeve with its >intuitive but illogical framework comes from cranks? Don't worry, >pretty soon, more data will come in and slowly you will find yourself >on the other side of the fence, as the prime goofball... >That will be very exciting. Are you holding your breath? I hope so. > Just have your wife let me know where it is. >technology, as the tech becomes more widely available, this experiment >will be repeated with increasing accuracy routinely. And you will >still be screaming 'crank' at the top of your lungs, not realizing >your relativistic world has been turned on its head... >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >anything about tunneling being faster than light. > Ah, you have to use your head. That is why they have the attoclock. > You can perform the calculations. Yes, we can. Apparently strich cannot. Apparently simply stating in black > and white that the speed of light has been violated can have negative > repercussions on publication chances, and the authors deferred on that > option. It would also be a lie. Strich does not know any physics or logic so now he is showing that he does not know any math either. This is grade school stuff here. But, since strich is not capable of math, lets do the multiplication. 12 x10^-18 (12 attoseconds) times 3x10^8 meters/second gives a distance of 36 x 10^-10 meters. Thus, at the speed of light, the electron could travel 360 picometers. Since atoms are on the order of 10 picometers, there is no issue with an electron going away in the time scales quoted. No greater than c, no problem with relativity. Strich fails again (and again and again...). >I am wondering. What do you have against the progress of science? >Why do you cling to the old theories? >I don't. I'm actually quite eager to find experimental evidence that >is inconsistent with relativity. But there hasn't been any yet. > Really? How eager were you to embrace the negative results of LIGO > and GPB? Since they were not negative, we are happy with them. Strich does not read well either. >Nor does disparaging a theory just for the sake of being contrary >serve any useful purpose. Some people have lots of time to waste on >things like that. > So why are you disparaging quantum mechanics? > Is it just easier for you to >understand Einstein's geometrically simple Riemannian world than the >superposed non-geometric Hilbert world of quantum mechanics? Perhaps >Einstein's world is for humans and the quantum world is for super >humans? >This would be worth discussing further if you knew what 50% of the >words on those two sentences meant. > You must be speaking for yourself. It is obvious that you have a > harder time with QM than SR/GR. === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) [...] Since they were not negative, we are happy with them. Strich does not > read well either. > Something happened while he was out on his dignity recovery break... http://einstein.stanford.edu/highlights/status1.html [...] === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) [...] > Since they were not negative, we are happy with them. Strich does not > read well either. Something happened while he was out on his dignity recovery break... http://einstein.stanford.edu/highlights/status1.html [...] Eric Gisse majored in physics to achieve status. But he couldn't graduate. Now, he pops in to take pot shots at those independent thinkers willing to separate the wheat from the chaff in science. Is there status in that, Eric? .84 NoEinstein .84 === Subject: Re: Was Einstein Wrong ? Article discussion... Of course he was... [...] >Since they were not negative, we are happy with them. Strich does not >read well either. > Something happened while he was out on his dignity recovery break... http://einstein.stanford.edu/highlights/status1.html > Yes but strich was not out on an intelligence recovery break. He still looks as stupid as ever. > [...] === Subject: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=LxihSQoAAABzdzEeG7JudGr6Yl-Mh-CT InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > Really? How eager were you to embrace the negative results of LIGO > and GPB? They aren't negative. Show us the positive resultS then... (Watch PD lie once more. As for Eric the Crook's link, that simply provided us three 'official' results for the GPB, he is still desperately trying to manufacture proof to support his fumbles. This is 21st century physics. No physicist has enough brains anymore to come up with a new and better theory, so experimental data is merely curve-fitted to the existing theory. I wonder how long this Ponzi-ish scheme will last... [*As for the thread title, this refers to Relativity Physicists, who try to infect all branches of physics with their faulty relativistic interpretations.) And here is the solid evidence against relativity that PD has ignored and continue to willingly ignore: http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) [snip crap] > And here is the solid evidence against relativity that PD has ignored > and continue to willingly ignore: >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 The technique relies on establishing an absolute reference point in > the laboratory frame > AL-zheimer, what is your point? Next time, take your medications first before replying so you can generate a coherent reply. And Please go beyond the abstract, if that is possible in your infinite state of stupidity. As for PD, notice how he still has not shown us the positive result for LIGO or GPB. He continues to weasel, true to his nature. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=LxihSQoAAABzdzEeG7JudGr6Yl-Mh-CT InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) Strich gave the following link as evidence against relativity: http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Specifically, it concerns faster than light tunneling. With no specific rebuttal, the relativists are at a loss and uses various means to divert the topic. Their replies are both amusing and pathetic... Here is professional liar PD (note how his reply is totally unrelated to the topic at hand): trillions of dollars being squirreled away by scientists for their eventual domination of the world. Here is demented AL (note how he merely quotes a line in the abstract, 'The technique relies on establishing an absolute reference point in the laboratory frame'. Did you study to be stooopid? Tell us the differece between a yardstick and a reference frame. Here is Doug the troll (note how he imagines (or lies) that a mathematical counter-argument was ever given): No, it is not. You were shown the math. Do you not understand math either? Strich continues to argue from ignorance as usual. Here is Doug the troll again (Note how he is begging us to explain the With strich's usual stupidity about physics, he does not seem to problem for relativity. If strich thinks there is, he should probably try to point it out so we can show him his mistake. tunneling of electrons. It spits on the special relativity speed limit of light. Note that none of the relativists who have replied ignorance, and hope that sheer noise and innuendo can drown the === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* > Strich gave the following link as evidence against relativity: > http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 Specifically, it concerns faster than light tunneling. With no > specific rebuttal, the relativists are at a loss and uses various > means to divert the topic. Their replies are both amusing and > pathetic... Here is professional liar PD (note how his reply is totally unrelated > to the topic at hand): > trillions of dollars being squirreled away by scientists for their > eventual domination of the world. Here is demented AL (note how he merely quotes a line in the abstract, > 'The technique relies on establishing an absolute reference point in > the laboratory frame'. Did you study to be stooopid? Tell us the > differece between a yardstick and a reference frame. Here is Doug the troll (note how he imagines (or lies) that a > mathematical counter-argument was ever given): > No, it is not. You were shown the math. Do you not understand math > either? Strich continues to argue from ignorance as usual. Here is Doug the troll again (Note how he is begging us to explain the > With strich's usual stupidity about physics, he does not seem to > problem for relativity. If strich thinks there is, he should probably > try to point it out so we can show him his mistake. > tunneling of electrons. It spits on the special relativity speed > limit of light. Note that none of the relativists who have replied > ignorance, and hope that sheer noise and innuendo can drown the Given that the speeds calculated from the times given are below that of light, there is no issue with problems with the speed of light. Strich was shown the math in an earlier post but apparently he cannot multiply two numbers. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > Given that the speeds calculated from the times given are below > that of light, there is no issue with problems with the speed of > light. Strich was shown the math in an earlier post but apparently > he cannot multiply two numbers. You mean you showed me a math*, not the math. You cannot bluster your way through this one. You have to read the understand, or too crazy to make sense. Get a brain transplant, and not from a monkey :-) *Here is your grade school calcs: ... lets do the multiplication. 12 x10^-18 (12 attoseconds) times 3x10^8 meters/second gives a distance of 36 x 10^-10 meters. Thus, at the speed of light, the electron could travel 360 picometers. Since atoms are on the order of 10 picometers... === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* > >Given that the speeds calculated from the times given are below >that of light, there is no issue with problems with the speed of >light. Strich was shown the math in an earlier post but apparently >he cannot multiply two numbers. > You mean you showed me a math*, not the math. You cannot bluster your way through this one. No bluster on my part since the facts are as I said. You have to read the No, because they did not even consider that there might be a problem with relativity. You just made it up. Either you are too lazy to read, too dumb to > understand, or too crazy to make sense. Get a brain transplant, and > not from a monkey :-) You would be better off either increasing your meds or studying. _________________________________ > *Here is your grade school calcs: ... lets do the multiplication. 12 > x10^-18 (12 attoseconds) times 3x10^8 meters/second gives a distance > of 36 x 10^-10 meters. Thus, at the speed of light, the electron could > travel 360 picometers. Since atoms are on the order of 10 > picometers... === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) >Given that the speeds calculated from the times given are below >that of light, there is no issue with problems with the speed of >light. Strich was shown the math in an earlier post but apparently >he cannot multiply two numbers. > You mean you showed me a math*, not the math. > You cannot bluster your way through this one. No bluster on my part since the facts are as I said. You have to read the > No, because they did not even consider that there might be a problem > with relativity. You just made it up. Either you are too lazy to read, too dumb to > understand, or too crazy to make sense. Get a brain transplant, and > not from a monkey :-) You would be better off either increasing your meds or studying. > > *Here is your grade school calcs: ... lets do the multiplication. 12 > x10^-18 (12 attoseconds) times 3x10^8 meters/second gives a distance > of 36 x 10^-10 meters. Thus, at the speed of light, the electron could > travel 360 picometers. Since atoms are on the order of 10 > picometers...- Hide quoted text - - Show quoted text - NOT! === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) [...] NOT! against relativity? === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) [...] > NOT! against relativity? relativity. It simply disproves relativity. Second, I also read the ...which is what started this thread. Please review the thread Eric the Crook before you open your crooked mouth. Of course 'review' is what you are clueless about, hence your flunkie status in a weak university. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > [...] > NOT! > against relativity? > Good morning Dave, looks like you are back to your wake up and start posting schedule. You were keeping it to one post a day for awhile after you got back from your two week dignity recovery break. You are rebounding nicely with the 9am start time of posting. I imagine you'll be back to your 9am - 5pm [with 1 hour off for lunch] schedule within a week. You never did tell us what you did on your dignity recovery break! We saw that you came back relatively angry, with all that labeling of complicated and obscure psychological terms against Paul. Was your treatment rough? > relativity. It simply disproves relativity. Since special relativity has a limited region of application, that isn't abundantly surprising. We've known for a century that SR doesn't apply everywhere. Why do you feel this is an insight worth shouting from the rooftops? >Second, I also read the You read but do you comprehend? Since you have read it, perhaps you'd be able to explain - in your own words - why (or why not) entanglement isn't a challenge to special relativity. ...which is what started this thread. Please review the thread Eric > the Crook before you open your crooked mouth. Of course 'review' is > what you are clueless about, hence your flunkie status in a weak > university. Is that jealousy I detect, Dave? Does it bother you that someone as unstudious and lazy as me can amass such knowledge and wield it with such relative ease? === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > [...] > NOT! > against relativity? Good morning Dave... Top of the morning to you. It looks like your antisocial personality disorder* is in full swing. Are you failing to comply with your treatment regimen? > Since you have read it, perhaps you'd be able to explain - in your own > words - why (or why not) entanglement isn't a challenge to special > relativity. > you in my usual clear and layman translation, as opposed to you doing the hard work of reading and understanding it? That sounds like criteria #2 below is not under control as well :-) ______________________________________ *Three or more of the following: (at least 3,4,6 applies to Eric) 1) Failure to conform to social norms with respect to lawful behaviors as indicated by repeatedly performing acts that are grounds for arrest; 2) Deceitfulness, as indicated by repeatedly lying, use of aliases, or conning others for personal profit or pleasure; 3) Impulsivity or failure to plan ahead; 4) Irritability and aggressiveness, as indicated by repeated physical fights or assaults; 5) Reckless disregard for safety of self or others; 6) Consistent irresponsibility, as indicated by repeated failure to sustain consistent work behavior or honor financial obligations; 7) Lack of remorse, as indicated by being indifferent to or rationalizing having hurt, mistreated, or stolen from another. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > [...] > NOT! > against relativity? > Good morning Dave... Top of the morning to you. It looks like your antisocial personality > disorder* is in full swing. Are you failing to comply with your > treatment regimen? My friends suggest bars. I don't like bars. Guilty. But I have friends. I'm confused. Not guilty? > Since you have read it, perhaps you'd be able to explain - in your own > words - why (or why not) entanglement isn't a challenge to special > relativity. Again your laziness is evident. Your command of the obvious is top notch. I said I was lazy - what genius does it require to make THAT intuitive leap? > you in my usual clear and layman translation, as opposed to you doing > the hard work of reading and understanding it? That sounds like > criteria #2 below is not under control as well :-) Naw, I just want a one sentence display of understanding. > *Three or more of the following: (at least 3,4,6 applies to Eric) > 1) Failure to conform to social norms with respect to lawful behaviors > as indicated by repeatedly performing acts that are grounds for > arrest; I'm /rarely/ ever arrested, and I probably don't have any felony convictions. That Canada wouldn't let me in that /one time/ was a fluke. > 2) Deceitfulness, as indicated by repeatedly lying, use of aliases, or > conning others for personal profit or pleasure; I post under my real name. You post under a pseudonym that rotates weekly. > 3) Impulsivity or failure to plan ahead; Hey, I managed to make it from Portland to San Francisco then mid-way to the top of British Columbia before I had to look at a map. It only took me two tries to make it across San Fracisco at 3 in the morning when the entire bay area was covered in fog when I had never been there before. Beat that! > 4) Irritability and aggressiveness, as indicated by repeated physical > fights or assaults; The last time I was involved in a fight involved an angry french guy. I can't take an angry french guy seriously. Its' a funny story, actually. It involves piss soaked jeans (not even mine!) and the weakest headbutt I have ever felt. If you guess how many months it has been since he last acknowledged the sound of my voice, you win a prize. My roommate doesn't think he would play me pool for the right for me to talk to him [or never talk to him again if he wins] but I'm itching for the chance. > 5) Reckless disregard for safety of self or others; Since I haven't seriously hurt myself or anyone else in a very long time, how reckless is it really? Reckless is the way people drive here. C'mon! Don't pass a guy and cut him off when there's still ice on the street. That's just dumb! , now that you mention it there was that one time I burnt my thumbprint off with hot glue... > 6) Consistent irresponsibility, as indicated by repeated failure to > sustain consistent work behavior or honor financial obligations; When I work I'm pretty consistent, and I almost always pay my bills on time. Do you worry about this much, Dave? You strike me as a more ward of the state type of guy. > 7) Lack of remorse, as indicated by being indifferent to or > rationalizing having hurt, mistreated, or stolen from another. Want to see this funny video of a whale exploding? I will say that your understanding of the DSM-IV is pretty interesting. You seem to reference it frequently. Do you have a copy of it on your bookshelf? === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > [...] > NOT! > against relativity? > Good morning Dave... > Top of the morning to you. It looks like your antisocial personality > disorder* is in full swing. Are you failing to comply with your > treatment regimen? My friends suggest bars. I don't like bars. Guilty. But I have friends. I'm confused. Not guilty? > Since you have read it, perhaps you'd be able to explain - in your own > words - why (or why not) entanglement isn't a challenge to special > relativity. > Again your laziness is evident. Your command of the obvious is top notch. I said I was lazy - what > genius does it require to make THAT intuitive leap? > you in my usual clear and layman translation, as opposed to you doing > the hard work of reading and understanding it? That sounds like > criteria #2 below is not under control as well :-) Naw, I just want a one sentence display of understanding. > > *Three or more of the following: (at least 3,4,6 applies to Eric) > 1) Failure to conform to social norms with respect to lawful behaviors > as indicated by repeatedly performing acts that are grounds for > arrest; I'm /rarely/ ever arrested, and I probably don't have any felony > convictions. That Canada wouldn't let me in that /one time/ was a fluke. > 2) Deceitfulness, as indicated by repeatedly lying, use of aliases, or > conning others for personal profit or pleasure; I post under my real name. You post under a pseudonym that rotates > weekly. > 3) Impulsivity or failure to plan ahead; Hey, I managed to make it from Portland to San Francisco then mid-way > to the top of British Columbia before I had to look at a map. It only took me two tries to make it across San Fracisco at 3 in the > morning when the entire bay area was covered in fog when I had never > been there before. Beat that! > 4) Irritability and aggressiveness, as indicated by repeated physical > fights or assaults; The last time I was involved in a fight involved an angry french guy. > I can't take an angry french guy seriously. Its' a funny story, actually. It involves piss soaked jeans (not even > mine!) and the weakest headbutt I have ever felt. If you guess how > many months it has been since he last acknowledged the sound of my > voice, you win a prize. My roommate doesn't think he would play me pool for the right for me > to talk to him [or never talk to him again if he wins] but I'm itching > for the chance. > 5) Reckless disregard for safety of self or others; Since I haven't seriously hurt myself or anyone else in a very long > time, how reckless is it really? Reckless is the way people drive here. C'mon! Don't pass a guy and cut > him off when there's still ice on the street. That's just dumb! , now that you mention it there was that one time I burnt my > thumbprint off with hot glue... > 6) Consistent irresponsibility, as indicated by repeated failure to > sustain consistent work behavior or honor financial obligations; When I work I'm pretty consistent, and I almost always pay my bills on > time. Do you worry about this much, Dave? You strike me as a more ward of > the state type of guy. > 7) Lack of remorse, as indicated by being indifferent to or > rationalizing having hurt, mistreated, or stolen from another. Want to see this funny video of a whale exploding? I will say that your understanding of the DSM-IV is pretty > interesting. You seem to reference it frequently. Do you have a copy > of it on your bookshelf?- Hide quoted text - - Show quoted text - There is nothing like an accurate diagnosis for someone to start spilling their guts over. Unfortunately, your condition is not easily treatable. There are medical opinions that you cannot be rehabilitated. But you should continue the psychotherapy. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=8k9z_QoAAABfJ6zct3wDB2k3FKfRerU2 2.0.50727),gzip(gfe),gzip(gfe) [...] > NOT! against relativity? ground, no weapons are needed to counter its past demise. .84 NoEinstein .84 === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009022621 Gentoo Firefox/3.0.6,gzip(gfe),gzip(gfe) > [...] > NOT! > against relativity? ground, no weapons are needed to counter its past demise. .84 > NoEinstein .84 Why are you assaulting something you do not understand? You spend lots of time arguing about things you know nothing about, John. You are now currently arguing about how 15$ lasers somehow 'can't' make coherent light. I bet you can not even accurately explain Newton's three laws of motion. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* > >[...] >NOT! >against relativity? > ground, no weapons are needed to counter its past demise. .84 > NoEinstein .84 Except, of course, that there is no evidence against it. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729; MS-RTC EA 2),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > Strich gave the following link as evidence against relativity:http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 > Specifically, it concerns faster than light tunneling. Actually, it has as much to do with faster-than-light tunneling as it > has to do with radio signals being received by implants in Strich9's > head. But you have to read between the lines, of course. > With no > specific rebuttal, the relativists are at a loss and uses various > means to divert the topic. Their replies are both amusing and > pathetic... I'm sure you'd like folks to spend their time rebutting a claim that > closets down the hall, plotting to tackle you as you are wheeled by. After all, while folks are making specific rebuttals about one wild, > goofball claim, they might as well be making specific rebuttals about > another. Anything to keep relativists busy, eh, Strich9? > Here is professional liar PD (note how his reply is totally unrelated > to the topic at hand): > trillions of dollars being squirreled away by scientists for their > eventual domination of the world. > Here is demented AL (note how he merely quotes a line in the abstract, > 'The technique relies on establishing an absolute reference point in > the laboratory frame'. Did you study to be stooopid? Tell us the > differece between a yardstick and a reference frame. > Here is Doug the troll (note how he imagines (or lies) that a > mathematical counter-argument was ever given): > No, it is not. You were shown the math. Do you not understand math > either? Strich continues to argue from ignorance as usual. > Here is Doug the troll again (Note how he is begging us to explain the > With strich's usual stupidity about physics, he does not seem to > problem for relativity. If strich thinks there is, he should probably > try to point it out so we can show him his mistake. > tunneling of electrons. It spits on the special relativity speed > limit of light. Note that none of the relativists who have replied > ignorance, and hope that sheer noise and innuendo can drown the This is known as the Zick Blossom, a device whereby a previous poster > named Lester Zick would follow-up one goofball statement (to which he > was baiting for a rebuttal) with multiple goofball statements (to > which he was also baiting for a rebuttal), in an attempt to increase > his footprint on the newsgroup, the end objective being attention, > even if it was paid to himself by himself. PD- Hide quoted text - - Show quoted text - PD's psychosis assumes a malignant turn for the worse as he confronts the dreaded evidence against relativity. Note the pathognomonic clang associations* and word salad with his use of Lester Zick and Zick Blossom. [*Thought disorder wherein words are chosen or repeated based on similar sounds, instead of semantic meaning. The train rain brained me. He ate the skate, inflated yesterdays gate toward the cheese grater.] === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* > >[snip crap] >And here is the solid evidence against relativity that PD has ignored >and continue to willingly ignore: >http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 >The technique relies on establishing an absolute reference point in >the laboratory frame > AL-zheimer, what is your point? Next time, take your medications > first before replying so you can generate a coherent reply. And No, it is not. You were shown the math. Do you not understand math either? > Please go beyond the abstract, if that is possible in your infinite > state of stupidity. As for PD, notice how he still has not shown us the positive result > for LIGO or GPB. He continues to weasel, true to his nature. Strich continues to argue from ignorance as usual. === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* > >Really? How eager were you to embrace the negative results of LIGO >and GPB? >They aren't negative. > Show us the positive resultS then... (Watch PD lie once more. As for Eric the Crook's link, that simply > provided us three 'official' results for the GPB, he is still > desperately trying to manufacture proof to support his fumbles. This > is 21st century physics. No physicist has enough brains anymore to > come up with a new and better theory, so experimental data is merely > curve-fitted to the existing theory. I wonder how long this Ponzi-ish > scheme will last... [*As for the thread title, this refers to > Relativity Physicists, who try to infect all branches of physics with > their faulty relativistic interpretations.) And here is the solid evidence against relativity that PD has ignored > and continue to willingly ignore: > http://www.sciencemag.org/cgi/content/abstract/322/5907/1525 With strich's usual stupidity about physics, he does not seem to makes a problem for relativity. If strich thinks there is, he should probably try to point it out so we can show him his mistake. > === Subject: Re: Physicists are too dumb to make a better theory; Data is curve-fitted to the old theories* posting-account=-Yr6sAoAAAArJwgdHLA4MBxm4oIdzdtZ InfoPath.1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; MS-RTC LM 8; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) (NetCache NetApp/6.0.2P1) > Really? How eager were you to embrace the negative results of LIGO > and GPB? > They aren't negative. > Show us the positive resultS then... Say I go looking for mushrooms in the woods, testing the hypothesis > that mushrooms can be found in the woods. But I look in the tops of > bushes and at the ends of hanging vines, and I find no mushrooms. Is this a negative result? Have I conducted an experiment that shows > that mushrooms cannot be found in the woods? No. Is it then a positive result? Have I found mushrooms in the woods? No. Your feeble attempt to cast the lack of a positive result as being > indicative of a negative result, which in turn disproves a hypothesis, > is just another piss-poor boondoggle on your part which you will > nevertheless stick to your guns on, because you'd rather insist that > you meant to do that when you've crapped your pants. > (Watch PD lie once more. As for Eric the Crook's link, that simply > provided us three 'official' results for the GPB, he is still > desperately trying to manufacture proof to support his fumbles. This > is 21st century physics. No physicist has enough brains anymore to > come up with a new and better theory, so experimental data is merely > curve-fitted to the existing theory. I wonder how long this Ponzi-ish > scheme will last... [*As for the thread title, this refers to > Relativity Physicists, who try to infect all branches of physics with > their faulty relativistic interpretations.) > And here is the solid evidence against relativity that PD has ignored > and continue to willingly ignore:http://www.sciencemag.org/cgi/content/abstract/322/5907/1525- Hide quoted text - - Show quoted text - I am tempted to snip the excuses. But I'll leave it as a humiliating testament to PD's pathetic attempt at deception. Again, show us the positive result of the LIGO and GPB? Do not LIE this time. === Subject: Question about parameter estimation by using RLS with quantization error I have a question about parameters estimation by using recursive least square algorithm with quantization error. For example, there is a linear discrete system: y(k)=a*u(k)+v(k)+q(k); (1) Here, y(k) is the measured system output,u(k) is the system input, they are all known. v(k) is the gaussian white noise, and we know the variance of v(k). q(k) is the quantization error, we know it is distributed between -6.25 to +6.25. q(k) is produced by the equation below. q(k)=6.25*fix[(a*u(k)+v(k))/6.25]-(a*u(k)+v(k)); (2) Here, fix() is a Matlab command, it means rounding toward 0. So fix(1.2)=1, fix(2.9)=2, fix(-4.3)=-4, ... So from (1) and (2), we know the actual system is y(k)= 6.25*fix[(a*u(k)+v(k))/6.25]; (3) The problem is, if the system is a simple linear system with no quantization error. Like equation below, y1(k)=a1*u1(k)+v1(k); (4) I can use recursive least square algorithm to analyse it. I can get the covariance matrix of estimated parameters. By using this covariance, I can determine the distribution of the estimated parameter around the real parameters. But, when the quantization error is introduced, I found recursive least square algorithem cannot work. The covariance of the estimation residual is always very small. It seems the simple least square fit cannot solve this system. I hope someone can give me some idea about this quantization error problem. What I care about is the distribution of the estimated parameters. I need to know when I run the algorithm 1000 times recursively, the estimated parameter should be around the real parameter, what is the bound of their distance, or at least in statistical concept, what is the 95% probability interval for parameter estimated? === Subject: Convergence Is the following statement true or false: The sequence (s_n) converges to s iff lim(s_n) = s. I think this is a false statement, since we call s the lim of the sequence; however, convergence is based on the epsilon definition. Is this correct? === Subject: Re: Convergence > Is the following statement true or false: > The sequence (s_n) converges to s iff lim(s_n) = s. As usually defined, the sides of the iff are mathematically identical. Not just provably equivalent, but have identical definitions. Therefore true in a most trivial sense. - Tim === Subject: Re: iteration equation ( avoid half iterate !!! ) <27838577.1237325694209.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009011913 Firefox/3.0.6,gzip(gfe),gzip(gfe) > On Mar 15, 7:19.8cpm, amy666 > On Mar 15, 7:01.8cpm, amy666 > f(f(x)) + a(x)*f(x) + b(x) = 0 > a(x) and b(x) given. > find f(f(x)). > the operator half iterate at fixed > point > ... > is > allowed. > And what does that operator possibly do? > -- m > it takes the regular half iterate of a > taylor > series at one of its fixed points. > which fixed point is free to define. > How do you know that such a thing even exists? > -- m > i dont. > in fact in some cases , it WONT EXIST. > becuase e.g. no fixpoint , no radius of > convergeance > 0 etc > You may actually have something here that could be > useful under > some circumstances. If you write the equation as > f(f(x)) = -a(x) f(x) - b(x) > then you could imagine an iterative process where > at > some stage you > have an approximate solution f n(x), and for the > next > iteration you > find f {n+1}(x) satisfying (at least > approximately) > f {n+1}(f {n+1}(x)) = - a(x) f n(x) - b(x) however , maybe we can avoid the neccessity of taking half iterates in some cases : f {n+1}(f {n+1}(x)) = - a(x) f n(x) - b(x) => f {n+1}(f {n+1}(x)) / - a(x) + b(x) = f n(x) => f (n)(f (n)(x)) / - a(x) + b(x) = f (n+1)(x) And this last implication holds why exactly? -- m === Subject: Re: iteration equation ( avoid half iterate !!! ) <15051252.1237392274061.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009011913 Firefox/3.0.6,gzip(gfe),gzip(gfe) > On Mar 17, 6:34pm, amy666 On Mar 15, 7:19.8cpm, amy666 > On Mar 15, 7:01.8cpm, amy666 > f(f(x)) + a(x)*f(x) + b(x) = 0 > a(x) and b(x) given. > find f(f(x)). > the operator half iterate at fixed > point > ... > is > allowed. > And what does that operator possibly > do? > -- m > it takes the regular half iterate of a > taylor > series at one of its fixed points. > which fixed point is free to define. > How do you know that such a thing even > exists? > -- m > i dont. > in fact in some cases , it WONT EXIST. > becuase e.g. no fixpoint , no radius of > convergeance > 0 etc > You may actually have something here that could > be > useful under > some circumstances. If you write the equation > as > f(f(x)) = -a(x) f(x) - b(x) > then you could imagine an iterative process > where > at > some stage you > have an approximate solution f n(x), and for > the > next > iteration you > find f {n+1}(x) satisfying (at least > approximately) > f {n+1}(f {n+1}(x)) = - a(x) f n(x) - b(x) > however , maybe we can avoid the neccessity of > taking half iterates in some cases : > f {n+1}(f {n+1}(x)) = - a(x) f n(x) - b(x) > => f {n+1}(f {n+1}(x)) / - a(x) + b(x) = f n(x) > => f (n)(f (n)(x)) / - a(x) + b(x) = f (n+1)(x) > And this last implication holds why exactly? lim = fixed point in some cases. But neither f n nor f {n+1} is the limit, so your explanation explains nothing... There are (at least) two ways to turn the equation f(f(x)) + a(x)*f(x) + b(x) = 0 into an iteration: either you put f {n+1}(x) = T(- a(x)*f n(x) - b(x)) where T is your formal half-iterate operator, or you put f {n+1}(x) = - (f n(f n(x)) + b(x)) / a(x) But those two iterations are in principle quite unrelated. In particular, your implication simply makes no sense. -- m === Subject: a cute proposition posting-account=B_ql5woAAABEePt1fDMNH7lHfjEScu4Z Gecko/2008102920 Firefox/3.0.4,gzip(gfe),gzip(gfe) Consider a sequence of 3 coin tosses. There are 8 such: HHT, HTH, etc. And each is equiprobable, right? Let's play a game, betting $1, even money. You select one of those sequences, then I select one of the remaining 7. Toss a coin repeatedly, whoever's sequence occurs first, wins. Do you feel lucky? Step right up... To be precise: the coin is not tossed in separate sets of 3, resetting each time neither player wins. Rather, a 'sliding window' is employed; if neither sequence occurs in the first 3 tosses, check the 2nd... 4th, then 3rd.. 5th, etc. Left as an exercise for the student. -- Mark === Subject: Re: a cute proposition posting-account=YUVDEAoAAADy0b0DWFp7F-O3S06gZA3W Gecko/2009030423 Ubuntu/8.10 (intrepid) Firefox/3.0.7,gzip(gfe),gzip(gfe) > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? Let's play a game, betting $1, even money. > You select one of those sequences, then I select > one of the remaining 7. Toss a coin repeatedly, > whoever's sequence occurs first, wins. > Do you feel lucky? Step right up... To be precise: the coin is not tossed in separate > sets of 3, resetting each time neither player > wins. Rather, a 'sliding window' is employed; > if neither sequence occurs in the first 3 tosses, > check the 2nd... 4th, then 3rd.. 5th, etc. Left as an exercise for the student. -- > Mark Here's the full table for the probability that row beats column: HHH HHT HTH HTT THH THT TTH TTT HHH --- 1/2 2/5 2/5 1/8 5/12 3/10 1/2 HHT 1/2 --- 2/3 2/3 1/4 5/8 1/2 7/10 HTH 3/5 1/3 --- 1/2 1/2 1/2 3/8 7/12 HTT 3/5 1/3 1/2 --- 1/2 1/2 3/4 7/8 THH 7/8 3/4 1/2 1/2 --- 1/2 1/3 3/5 THT 7/12 3/8 1/2 1/2 1/2 --- 1/3 3/5 TTH 7/10 1/2 5/8 1/4 2/3 2/3 --- 1/2 TTT 1/2 3/10 5/12 1/8 2/5 2/5 1/2 --- For example, HHT beats HTH 2/3 of the time. Done by hand, verified by computer. === Subject: Re: a cute proposition posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? > Let's play a game, betting $1, even money. > You select one of those sequences, then I select > one of the remaining 7. ?Toss a coin repeatedly, > whoever's sequence occurs first, wins. > Do you feel lucky? ?Step right up... > To be precise: the coin is not tossed in separate > sets of 3, resetting each time neither player > wins. ?Rather, a 'sliding window' is employed; > if neither sequence occurs in the first 3 tosses, > check the 2nd... 4th, then 3rd.. 5th, etc. > Left as an exercise for the student. > -- > Mark Here's the full table for the probability that row beats column: ? ? ? ? HHH ? ? HHT ? ? HTH ? ? HTT ? ? THH ? ? THT ? ? TTH ? ? TTT > HHH ? ? --- ? ? 1/2 ? ? 2/5 ? ? 2/5 ? ? 1/8 ? ? 5/12 ? ?3/10 ? ?1/2 > HHT ? ? 1/2 ? ? --- ? ? 2/3 ? ? 2/3 ? ? 1/4 ? ? 5/8 ? ? 1/2 ? ? 7/10 > HTH ? ? 3/5 ? ? 1/3 ? ? --- ? ? 1/2 ? ? 1/2 ? ? 1/2 ? ? 3/8 ? ? 7/12 > HTT ? ? 3/5 ? ? 1/3 ? ? 1/2 ? ? --- ? ? 1/2 ? ? 1/2 ? ? 3/4 ? ? 7/8 > THH ? ? 7/8 ? ? 3/4 ? ? 1/2 ? ? 1/2 ? ? --- ? ? 1/2 ? ? 1/3 ? ? 3/5 > THT ? ? 7/12 ? ?3/8 ? ? 1/2 ? ? 1/2 ? ? 1/2 ? ? --- ? ? 1/3 ? ? 3/5 > TTH ? ? 7/10 ? ?1/2 ? ? 5/8 ? ? 1/4 ? ? 2/3 ? ? 2/3 ? ? --- ? ? 1/2 > TTT ? ? 1/2 ? ? 3/10 ? ?5/12 ? ?1/8 ? ? 2/5 ? ? 2/5 ? ? 1/2 ? ? --- For example, HHT beats HTH 2/3 of the time. Done by hand, verified by > computer. It turns out this game has been studied by Penney in 1969: http://en.wikipedia.org/wiki/Penney%27s game === Subject: Re: a cute proposition | Consider a sequence of 3 coin tosses. | There are 8 such: HHT, HTH, etc. | And each is equiprobable, right? | | Let's play a game, betting $1, even money. | You select one of those sequences, then I select | one of the remaining 7. Toss a coin repeatedly, | whoever's sequence occurs first, wins. | Do you feel lucky? Step right up... | | To be precise: the coin is not tossed in separate | sets of 3, resetting each time neither player | wins. Rather, a 'sliding window' is employed; | if neither sequence occurs in the first 3 tosses, | check the 2nd... 4th, then 3rd.. 5th, etc. | | | Left as an exercise for the student. | | -- | Mark It is a scam. Upon hearing the first players choice, the second player merely prepends an H or a T. At the third flip the first player has a 1/8 chance of winning and zero(0) on subsequent flips. The second player will win 7/8 times ................... certainly NOT an even money wager!! e.g. Player 1 = HHH Player 2 = THH -- --- David J. Snook === Subject: Re: a cute proposition posting-account=msV4aQkAAACFdekrjeDyuMHhzZGN7wbC 3.14; GTB5; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; InfoPath.2; IEMB3),gzip(gfe),gzip(gfe) | Consider a sequence of 3 coin tosses. > | There are 8 such: HHT, HTH, etc. > | And each is equiprobable, right? > | > | Let's play a game, betting $1, even money. > | You select one of those sequences, then I select > | one of the remaining 7. Toss a coin repeatedly, > | whoever's sequence occurs first, wins. > | Do you feel lucky? Step right up... > | > | To be precise: the coin is not tossed in separate > | sets of 3, resetting each time neither player > | wins. Rather, a 'sliding window' is employed; > | if neither sequence occurs in the first 3 tosses, > | check the 2nd... 4th, then 3rd.. 5th, etc. > | > | > | Left as an exercise for the student. > | > | -- > | Mark It is a scam. Upon hearing the first players choice, the second player > merely prepends an H or a T. At the third flip the first player has a 1/8 > chance of winning and zero(0) on subsequent flips. The second player > will win 7/8 times ................... certainly NOT an even money wager!! e.g. Player 1 = HHH Player 2 = THH -- > --- > David J. Snook Umm, without thinking this through too much (which is probably a warning to myself to stop right now...), if Player 1 chooses HHT, then Player 2 would choose THT, right? But if the first two rolls are HH.. (a 1 in 4 chance), then player 1 has a 100% chance of winning. How do you get 1/8 for player 1 for overall odds? Am I understanding your description correctly? --riverman === Subject: Re: a cute proposition sha1:PE6BqT3V1dKwt+i+YtW6oRav1YQ= > It is a scam. Upon hearing the first players choice, the second player > merely prepends an H or a T. At the third flip the first player has a 1/8 > chance of winning and zero(0) on subsequent flips. The second player > will win 7/8 times ................... certainly NOT an even money wager!! > e.g. Player 1 = HHH Player 2 = THH > -- > --- > David J. Snook Umm, without thinking this through too much (which is probably a > warning to myself to stop right now...), if Player 1 chooses HHT, then > Player 2 would choose THT, right? No, Player 2 would choose THH. (Or maybe HHH?) If player 1 choose (X1)(X2)(X3), then player 2 chooses (X0)(X1)(X2), where X0 is chosen so that player 2's sequence differs from player 1's (in the case that player 1 chose HHH or TTT). At least, I *think* that's the idea. -- Jesse F. Hughes So, what kind of stuff do you like to do and junk? Well, I really enjoy some of the music black people have been coming up with lately. -- Family Guy, first dates. === Subject: Re: a cute proposition <87vdq63ooc.fsf@phiwumbda.org> posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) No, Player 2 would choose THH. (Or maybe HHH?) > This is also what I get, if Player 1 choose HHT, Player 2 should choose THH with Player 1 has 1/4 chance to win. If both Player 1 & Player 2 are rational, there are 4 possible outcomes and Player 1 has 1/3 chance to win Player 1 Player 2 THH TTH HTH HHT THT TTH HTT HHT > If player 1 choose (X1)(X2)(X3), then player 2 chooses (X0)(X1)(X2), > where X0 is chosen so that player 2's sequence differs from player 1's > (in the case that player 1 chose HHH or TTT). At least, I *think* that's the idea. === Subject: Re: a cute proposition posting-account=xLsqvAoAAADY4BMAqIw3ROq0faU4tvyS 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... And each is equiprobable, right? > Do you feel lucky? Step right up... The probability the *first* roll in a craps session is 7 is 1/6. What is the probability the last roll is 7? The probability the second roll in a backgammon game is double-6 is 1/36. What is the probability the last roll is double-6? > Left as an exercise for the student. James Dow Allen === Subject: Re: a cute proposition Originator: msb@shell.vex.net (Mark Brader) James Allen: > The probability the *first* roll in a craps session is 7 is 1/6. > What is the probability the last roll is 7? Interesting question. If the first roll is 2, 3, 11, or 12 (possible 6 ways out of the 36), it is the last roll, so the probability P that the last roll is 7 is 0. If the first roll is 7 (6 ways), it is the last roll but P = 1. If the first roll is 4 or 10 (6 ways), the last roll must be that number or 7, so P = 6/(3+6). If the first roll is 5 or 9 (8 ways), the last roll must be that number or 7, so P = 6/(4+6). If the first roll is 6 or 8 (10 ways), the last roll must be that number or 7, so P = 6/(5+6). So overall we have P = (6*1 + 6*6/(3+6) + 8*6/(4+6) + 10*6/(5+6))/36 = 557/990 if I compute correctly. > The probability the second roll in a backgammon game is double-6 > is 1/36. What is the probability the last roll is double-6? Hmm, that's tougher and I think it's got to depend on one's endgame strategy. Even if you ignore strategy, I think you have to enumerate all the positions of stones from which a double-6 would win the game, then for each one work out the chance that any game-winning numbers would be rolled. Oh, and the possibility of being blocked by points made by the opponent has to be figured in too. Pretty much intractable without some significant computer assistance, I'd think. Oh, and not only endgame strategy, but doubling and acceptance. You're less likely to double and end the game if your opponent just rolled a double 6, right? David Ullrich: > You may be missing the point. In those games the events are > independent. The end of the game is not independent of the die roll. The original problem I'll leave to others. -- Mark Brader | Of course, if you only see one movie this year, msb@vex.net | you're in the wrong newsgroup. Toronto | --Chris Pierson, rec.arts.movies.past-films === Subject: Re: a cute proposition > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? > No, you can't conclude equal probabilities. That's an assumption equivalent to assuming a fair coin. === Subject: Re: a cute proposition > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? >No, you can't conclude equal probabilities. >That's an assumption equivalent to assuming a fair coin. By default, a fair coin is assumed. However the rules of the game, which you snipped, yield a strong advantage to player 2. quasi === Subject: Re: a cute proposition > Let's play a game, betting $1, even money. You select one of those > sequences, then I select one of the remaining 7. Toss a coin > repeatedly, whoever's sequence occurs first, wins. Do you feel > lucky? Step right up... That is cute. Minimum of 2:1 odds unless I miscalculated, better if the first player chooses poorly. - Tim === === Subject: Re: happy pi day !!! <30463087.1237061673424.JavaMail.jakarta@nitrogen.mathforum.org>, > happy pi day everyone !!! > may god continue to bless pi. Why isn't e day (February 7th I suppose) even more famous? === Subject: Re: JSH: Remember the goal > My stated aim for years has been to end the academic system as it > currently exists worldwide Undergrads the world over will be grateful. === Subject: Re: #294 Chapter 10; Lwal, can the standard Reals have a FrontView > So, Lwal, can your Standard Reals make room for FrontView along with > BackView They don't. Standard reals between zero and one have only a FrontView, with no BackView possible. > So, Lwal, instead of wasting your time trying to get the AP-Reals > axiomatized, for which they are already > axiomatized as All Possible Digit Arrangements. But Winter, Tribble, and most standard analysts don't accept that as a rigorous axiomatization. I'm trying to find a way to characterize the AP-reals that is acceptable to both AP himself and the standard analysts. I did try to convince the standard analysts that AP wants geometry , not set theory or arithmetic, to be the foundation of his theory, but the standard analysts so far have not budged on this issue. === Subject: Re: #294 Chapter 10; Lwal, can the standard Reals have a FrontView plus BackView?; new book 2nd edition: New True Mathematics sha1:ewGzUYzzFyVgm8aSyO+yiFxAheU= > I did try to convince the standard analysts that AP wants > _geometry_, not set theory or arithmetic, to be the > foundation of his theory, but the standard analysts so far > have not budged on this issue. LWalker, are you saying that you *agree* that AP has axiomatized the AP-reals by using geometry? I've never seen anyone claim that a geometric axiomatization is inadmissible, so as far as I can tell, you are lying about the standard analysts. But if you're as competent as an undergraduate, you should see clearly that AP has axiomatized *nothing at all* by uttering the magic phrase All Possible Digit Arrangements and slipping in references to geometry and probability. If he wants to give a fundamentally geometric theory, let him give it. But neither he nor you have given one so far. -- Jesse F. Hughes Really, I'm not out to destroy Microsoft. That will just be a completely unintentional side effect. -- Linus Torvalds === Subject: Discount Lacoste Shoes and Crocs Shoes posting-account=Q4U-cwoAAABQkzl0ZrlUWbwGi0KpkY5H Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; Embedded Web Browser from: http://bsalsa.com/),gzip(gfe),gzip(gfe) Our Lacoste Shoes and Crocs Shoes are the fine quality. You can check them: http://www.luxury-fashion.org/static/Shoes/Lacoste-Shoes.html http://www.luxury-fashion.org/static/Shoes/Crocs-Shoes.html If you need find more kinds of fashionable apparels and shoes,please view: http://www.luxury-fashion.org Welcome check our other pages or feel free contact us. You can find what do you want here! === Subject: does anybody recognize this number? posting-account=i6LhmwkAAAA3KqiGA282c1QpgBTwJ-V0 Gecko/20070725 Firefox/2.0.0.6,gzip(gfe),gzip(gfe) A question to the regulars of sci.math: 1 = 1/1x2 + 1/2x3 + 1/3x4 ... or simply '1x2 '2x3 '3x4 ... Developed as a stairway: 1 = '1 1 = '1x2 '2 1 = 1x2 '2x3 '3 1 = 1x2 '2x3 '3x4 '4 1 = '1x2 '2x3 '3x4 '4x5 '5 1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6x7 '7x8 '8x9 ... '1x2 '3x4 '4x5 '6x7 '8x9 ... = ln2 The following stairways approximate the natural logarithm of 2: '1x2 '5 '1x2 '3x4 '9 '1x2 '3x4 '5x6 '13 1 minus '3x4 '7 1 minus '3x4 '5x6 '11 1 minus '3x4 '5x6 '7x8 '15 Converting 1/2 or '2 into an infinite series: '2 = '1x3 '3x5 '5x7 '7x9 '9x11 '11x13 '13x15 '15x17 ... '1x3 '5x7 '9x11 '13x15 '17x19 ... = '8 of pi The following stairways approximate one eighth of pi: '1x3 '16 '1x3 '5x7 '32 '1x3 '5x7 '9x11 '48 '2 minus '3x5 '24 '2 minus '3x5 '7x9 '40 '2 minus '3x5 '7x9 '11x13 '56 Converting '3 into an infinite series: '3 = '1x4 '4x7 '7x10 '10x13 '13x16 '16x19 ... '1x4 '7x10 '13x16 '19x22 '25x28 '31x34 ... = ??? What number do the following stairways approximate? '1x4 '35 '1x4 '7x10 '71 '1x4 '7x10 '13x16 '107 '1x4 '7x10 '13x16 '19x27 '143 '3 minus '4x7 '51 '3 minus '4x7 '10x13 '87 '3 minus '4x7 '10x13 '16x19 '123 '3 minus '4x7 '10x13 '16x19 '22x25 '159 Line twelve of the first pattern yields 0.2785398, line twelve of the second pattern 0.2785487, average 0.27854..., and 16 times the average 4.4567... Does anyone reconize this number? or another multiple of the average? Franz Gnaedinger (More on the background of my question in the math-history-list, thread: Who discovered irrational numbers?) === Subject: Re: does anybody recognize this number? posting-account=Jz4DtgkAAAAZkdWvJAd__jMF7l1N5_1V CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > A question to the regulars of sci.math: 1 = 1/1x2 + 1/2x3 + 1/3x4 ... or simply '1x2 '2x3 '3x4 ... > Developed as a stairway: 1 = '1 > 1 = '1x2 '2 > 1 = 1x2 '2x3 '3 > 1 = 1x2 '2x3 '3x4 '4 > 1 = '1x2 '2x3 '3x4 '4x5 '5 1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6x7 '7x8 '8x9 ... '1x2 '3x4 '4x5 '6x7 '8x9 ... = ln2 The following stairways approximate the natural logarithm of 2: '1x2 '5 > '1x2 '3x4 '9 > '1x2 '3x4 '5x6 '13 1 minus '3x4 '7 > 1 minus '3x4 '5x6 '11 > 1 minus '3x4 '5x6 '7x8 '15 Converting 1/2 or '2 into an infinite series: '2 = '1x3 '3x5 '5x7 '7x9 '9x11 '11x13 '13x15 '15x17 ... '1x3 '5x7 '9x11 '13x15 '17x19 ... = '8 of pi The following stairways approximate one eighth of pi: '1x3 '16 > '1x3 '5x7 '32 > '1x3 '5x7 '9x11 '48 '2 minus '3x5 '24 > '2 minus '3x5 '7x9 '40 > '2 minus '3x5 '7x9 '11x13 '56 Converting '3 into an infinite series: '3 = '1x4 '4x7 '7x10 '10x13 '13x16 '16x19 ... '1x4 '7x10 '13x16 '19x22 '25x28 '31x34 ... = ??? What number do the following stairways approximate? '1x4 '35 > '1x4 '7x10 '71 > '1x4 '7x10 '13x16 '107 > '1x4 '7x10 '13x16 '19x27 '143 '3 minus '4x7 '51 > '3 minus '4x7 '10x13 '87 > '3 minus '4x7 '10x13 '16x19 '123 > '3 minus '4x7 '10x13 '16x19 '22x25 '159 Line twelve of the first pattern yields 0.2785398, > line twelve of the second pattern 0.2785487, > average 0.27854..., and 16 times the average > 4.4567... Does anyone reconize this number? > or another multiple of the average? > Franz Gnaedinger (More on the background of my question in the > math-history-list, thread: Who discovered irrational > numbers?) It could be close to (pi/sqrt(3) + ln(2)) / 9 === Subject: Re: does anybody recognize this number? posting-account=i6LhmwkAAAA3KqiGA282c1QpgBTwJ-V0 Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > It could be close to (pi/sqrt(3) + ln(2)) / 9 0.27854961... Using the corrected stairways '1x4 '33 '1x4 '7x10 '69 '1x4 '7x10 '13x16 '105 '3 minus '4x7 '51 '3 minus '4x7 '10x13 '87 '3 minus '4x7 '10x13 '16x19 '123 and calculating the average of lines hundred I got the same value 0.27854961... I hoped for a simple term, and perhaps another constant, but if you are right, all these stairways may concern ln2 and pi. === Subject: Saint Patrick's Day Puns > > found > these unused words floating about: > was sent this: > A farmer had a cow, Bessie. She was difficult, kicking over the > milk > pail and refusing to come in at night. Well, Bessie got pregnant. > After > she gave birth, she changed. Bessie's really mellowed out, the > farmer told his wife. What do you think happened? That's > easy, she > replied. Don't you know, Bessie's been decalf-inated! > How cheesy. >Udder nonsense. > Bulling for you ... > Bull Lee: A pushy Korean male bovine. Don't you mean a bossy Korean male bovine. You should be using Latin derivatives more now. As in the derivative of X Squared is 2X, and the derivative of X Cubed is 3X Squared? IIRC correctly, the derivative of Sine X is Cosine X, and the derivative of Cosine X is minus Sine X. === Subject: Re: JSH: Closing moments on first part of saga posting-account=T_1GRgoAAAByqBeLzvfvxYLZaG5_a0HC Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > With Fermat numbers though--suggested to me by Penny Hassett in a > comment to my math blog--it's easier, as if you have D = 2^k + 1, then > there are k+1 iterations, which is, um, yeah, polynomial time as in > LINEAR. Since the arithmetic operations for big numbers can't be computed in constant time I suggest to compute the bit complexity that takes this into account. I presume you use at least one of the following operations during each iteration: +, -, *, /. The complexity class of plus and minus is O(k). Multiplication can be done in O(k * log k * log log k) time (Sch.9anhage- Strassen algorithm) or O(n^1.585) time (Karatsuba algorithm). If I recall correctly java.math.BigInteger uses the Karatsuba algorithm for multiplication. SG === Subject: Re: JSH: Closing moments on first part of saga > The battle over the solution to the factoring problem is drawing to a > close as I finally have the full algorithm and correct method, but I > find it interesting that certain posters who have warred for so long > against my research are still fighting the fight. But the war is over on the example of D=15, where I see one attempt > already at moving to obscure the result, which I answered. > You factored 15? Well that's a start. Have you published yet? Wait don't do that, you'll put another math journal out of business :-) === Subject: Re: Enjoy your home. You are part of it, posting-account=WhTfrQoAAAA1j4LTeJDN70zmipFDHvPZ iCafeMedia),gzip(gfe),gzip(gfe) > http://belizephotographs.com/art/Astronaut Sunita Williams Pics of Ea... (may take a few min to download) hanson Hmm...it's beautiful. And it reminds me a lot,can we still see our planet clearly years later? I'm not sure. === Subject: Which is your favorite Integral Transform ? posting-account=LChCFQoAAACR0FoxHzVn6GGERsr9zp8c Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Honestly, I like all types of transforms, especially transforms which doesn't deal with 'COMPLEX VARIABLES' 1) Laplace Transform 2) Fourier Transform 3) Hartley Transform 4) Mellin Transform 5) Hankel Transform 6) Y-transform 7) Meijer Transform 8) Bochner Transform 9) Weber transform 10) Kontorovich-Lebedev Transform 11) Meler-Fock Transform 12) Hilbert Transform These are the main Integral transorms {to my knowledge} Google is your friend; don't forget that. 1) which is your Favorite Transform? If you know any other transforms,please do share that. so long nimo by the by; can you recommend a couple of books on Non- Linear I.E & Non- Linear D.E {if PDE's too included that would be double bonus for me } for the reference. === Subject: Re: Which is your favorite Integral Transform ? > If you know any other transforms,please > do share that. === === Subject: Question on matrix analysis Let A_n and B_n be two sequences of symmetric positive define matrices such that A_n x_n = B_n x_n for some vector x_n with non-collinear components for all n. Can be conclude that A_n is asymptotically equivalent to B_n as n goes to infinity? That is, each entry of A_n is asymptotically equivalent to the respectively one of B_n? Andreas U. Kelmer === Subject: Yet another Euclidean geometry problem Hi all, I was unable to solve a problem and I would appreciate some help. The problem is this: given two points A ad B on a plane and given a distance _d_, to find two points C and D such that: 1) A, B, and C are collinear; 2) D belongs to the straight line perpendicular to AB passing through A; 3) the distance from C to D is _d_; 4) the angle BDC is a right angle. Any ideas? Jose Carlos Santos === Subject: Re: Yet another Euclidean geometry problem > Hi all, I was unable to solve a problem and I would appreciate some help. The > problem is this: given two points A ad B on a plane and given a > distance _d_, to find two points C and D such that: 1) A, B, and C are collinear; 2) D belongs to the straight line perpendicular to AB passing through A; 3) the distance from C to D is _d_; 4) the angle BDC is a right angle. Any ideas? > Jose Carlos Santos The angle BDC is supposed to be a right angle in: D /| / | d/ | / | / | / | C-----A-----B So we have: (AC + AB)^2 = CD^2 + BD^2 AB^2 + AD^2 = BD^2 AC^2 + AD^2 = CD^2 Where CD = d and AB are _given_. Right? AC^2 + 2.AC.AB + AB^2 = (AC^2 + AD^2) + (AB^2 + AD^2) ==> 2.AC.AB = 2.AD^2 ==> AC.AB = d^2 - AC^2 ==> AC = sqrt((AB/2)^2 + d^2) - AB/2 ; AD = sqrt(d^2 - AC^2) . Han de Bruijn === Subject: Re: Yet another Euclidean geometry problem > I was unable to solve a problem and I would appreciate some help. The > problem is this: given two points A ad B on a plane and given a > distance _d_, to find two points C and D such that: > 1) A, B, and C are collinear; > 2) D belongs to the straight line perpendicular to AB passing through A; > 3) the distance from C to D is _d_; > 4) the angle BDC is a right angle. > Any ideas? The angle BDC is supposed to be a right angle in: D > /| > / | > d/ | > / | > / | > / | > C-----A-----B Nice picture. > So we have: (AC + AB)^2 = CD^2 + BD^2 > AB^2 + AD^2 = BD^2 > AC^2 + AD^2 = CD^2 Where CD = d and AB are _given_. Right? Right. > AC^2 + 2.AC.AB + AB^2 = (AC^2 + AD^2) + (AB^2 + AD^2) == 2.AC.AB = 2.AD^2 ==> AC.AB = d^2 - AC^2 == AC = sqrt((AB/2)^2 + d^2) - AB/2 ; AD = sqrt(d^2 - AC^2) . Jose Carlos Santos === Subject: Re: Yet another Euclidean geometry problem posting-account=cvz5-QoAAABVNzogw177Plx_25TguPUZ 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.2; MS-RTC LM 8),gzip(gfe),gzip(gfe) > Hi all, I was unable to solve a problem and I would appreciate some help. The > problem is this: given two points A ad B on a plane and given a > distance d , to find two points C and D such that: 1) A, B, and C are collinear; 2) D belongs to the straight line perpendicular to AB passing through A; 3) the distance from C to D is d ; 4) the angle BDC is a right angle. Any ideas? > Jose Carlos Santos Triangles ACD, DCB, and ADB are similar. Angles /ACD and /ADB are the could be found. - MO === === Subject: Re: Factoring problem solution, proof of concept code ...> private boolean checkForSquare(long D){ > long temp_long = (long)Math.sqrt(D); > if (temp_long*temp_long == D) return true; > else return false; > } ... This method of checking whether a long is a square is only reliable if > the long is guaranteed to have no more than 53 significant bits, so that > it is exactly representable as a double. I hope to inspire real researchers who'd like to go after a Fermat number with an algorithm that will scream through it. Those who run the code will notice I just let it run through a complete factorization versus ending when it FIRST factors, as I'm demonstrating. This demonstration is a lot more impressive than quantum computing factoring 15. Even the most rabid among you will have a hard time explaining how over 20 numbers are factored or determined to be prime in a methodical fashion by a program that is clearly just pulling out factors in freaking order by size, using a mathematical proof, which shows how to factor D, by factoring D-1, where an underlying equation is Pell's Equation. It's gut check time. Yeah, lots of social crap says I'm a crackpot just mouthing off, but you have a program that says otherwise and now you can get motivated to read the proof and understand the easy algebra, and then you can start worrying about your planet for once, and help me inform the world about this factoring result. It's not about your feelings. It is about your duty. Mathematics doesn't play favorites. You may hate me. You can despise me. But anyone can use this result, and they may hate you. They may despise you. Do you really want to just wait and see, hope, that they don't hurt you because you sit on your hands and cry about a mathematical result you hate? Irony is a strong suit of our reality. You do not want to think about what I'd think would be ironic if it happened to some of you over this result and your refusal to accept it as you continue class wars. Class wars should have died with feudalism, but some of you still wish to believe you can be special human above others you see as beneath you. So yeah, you think you're better than me. I believe all men and women are created equal. Your way should have died centuries ago, but here you are. You think you can DECIDE what human can make a major discovery? I think some of you will hold on to your class beliefs no matter what, even if it kills you, and your countries. And that would be ironic, don't you think? James Harris **** what is so cool about being 25 times slower than trial division ? **** === Subject: Re: .9 repeating posting-account=PalVlwoAAAA1TKsKLVCsNe7APQhpWkGd 1.5); .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > On Mar 10, 10:36am, Frederick Williams > It is the closest thing > to one. > True. > -- > Science is a differential equation. > Religion is a boundary condition. > --Alan Turing Among the real numbers there is no number which is the closest to one. > Any one you choose, I can find one closer. 0.999... means the limit as the 9's are extended, and that limit is > EXACTLY 1. Look up the definition of a limit. Uncle Ben I wonder whether people are not applying the law of the excluded middle. Either the number IS one, or the number is NOT one. Correctly acknowledging that there are two different representations; . 9 repeating, and 1. It seems amazing that these two things could be the same number. In support that they are two different numbers, you have that they have two different decimal representations. This seems to convince many people that they are really two different numbers, but there seems to be a much more rigorous argument to the contrary: In support that they are the same number, you need only consider that both numbers are precisely equal to 9*(1/9), because 1/9 = .1 repeating. Unless you somehow mystify the multiplication of fractions, so that you think that multiplying a number by its reciprocal does not *quite* give 1, I think this is pretty convincing. The fact that the two numbers HAVE two different decimal representations, is unique to all nonrepeating rational numbers. For instance, .15 = .14999999999999999999999999999999... But on the other hand, (unless I've overlooked something) repeating decimals and irrational numbers have only one decimal representation. Also, the appearance of this phenomenon would always appear with 1. But the other fractions with which the double-representation phenomenon occured would be different depending on what base you chose. === Subject: Re: .9 repeating > On Mar 10, 10:36 am, Frederick Williams > It is the closest thing > to one. > True. > -- > Science is a differential equation. > Religion is a boundary condition. > --Alan Turing Among the real numbers there is no number which is the closest to one. > Any one you choose, I can find one closer. 0.999... means the limit as the 9's are extended, and that limit is > EXACTLY 1. Look up the definition of a limit. Uncle Ben I wonder whether people are not applying the law of the excluded middle. Either the number IS one, or the number is NOT one. Correctly acknowledging that there are two different representations; . 9 repeating, and 1. It seems amazing that these two things could be the same number. In support that they are two different numbers, you have that they have two different decimal representations. This seems to convince many people that they are really two different numbers, but there seems to be a much more rigorous argument to the contrary: In support that they are the same number, you need only consider that both numbers are precisely equal to 9*(1/9), because 1/9 = .1 repeating. Unless you somehow mystify the multiplication of fractions, so that you think that multiplying a number by its reciprocal does not *quite* give 1, I think this is pretty convincing. The fact that the two numbers HAVE two different decimal representations, is unique to all nonrepeating rational numbers. For instance, .15 = .14999999999999999999999999999999... But on the other hand, (unless I've overlooked something) repeating decimals and irrational numbers have only one decimal representation. Also, the appearance of this phenomenon would always appear with 1. But the other fractions with which the double-representation phenomenon occured would be different depending on what base you chose. SANITY WARNING (Droolin' Doolin) Scruffy Rat's postulate: light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body bears no resemblance whatsoever to Doolin's: Scruffy Rat's 2nd postulate of S.cruffy R.at says that the speed of light is c in every inertial frame. Scruffy Rat himself says But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v, so that t = x'/(c-v). Doolin makes no apology for misrepresenting Scruffy Rat by echoing the popular prayer, instead he chants the mantra spoken unto him by the insane Bonehead Green. Chanting mantras is like saying prayers, a form of witchcraft known as uttering spells. Doolin cannot distinguish c-v in the stationary frame from c in the moving frame. This form of insanity is known professionally among scientists as bigotry and lying. Guilty by reason of insanity is still guilty. The asylum inmates assert that it is the doctors treating them that are lying, even those untrained in psychiatry. Physician, heal thyself. - Jesus H. Christ, self-proclaimed son of Gawd, superman and god-on-a-stick, professional holy man and sky pilot, Captain of the starship Cloud, litterbug of the Holy Grail (now lost) and diner of Last Suppers. Other characteristics - walked on water, turned water into whine, preferred the male company of twelve rent boys and advocated love to them all and their neighbours. Was not popular among the establishment, having upset their banco and causing widespread economic disruption. (Banco is an Italian word for bench from which the English word Bank is derived. He upset the money benches or tables outside the temple to Gawd.) Favourite quote: Eloi, eloi, lama sabathani. (Translation: Oh, it! I screwed up. You were supposed to help Doolin wants to play hardball http://tinyurl.com/bw55 === Subject: Re: .9 repeating > I wonder whether people are not applying the law of the excluded > middle. Nope. There are many subtle points regarding decimal expansions of reals in intuitionistic mathematics -- and here we might recall Brouwer's celebrated proof that not all reals have a decimal expansion! However, 0.9999.... = 1 is not one of them. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: .9 repeating posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > 0.999...9998. > So, since you seem to be good at reading his mind, perhaps you can > eplain whether he thinks these 9s go on endlessly before ending with > an 8, and perhaps you can explain the obvious problems in identifying > the end of something that doesn't end. Just because there are infinitely many 9's there, it doesn't mean that > the 9's don't end. Despite the fact that infinite comes from a Latin > word meaning something like unending, there are infinite sets that end. >. > The set [0,1] is infinite. It has an end (i.e., a maximal element > under the standard ordering), namely 1. Do the infinite number of elements in set [0,1] have an end? If you started counting all the elements, would you ever reach the last one? > The set Z- is infinite. It has an end (i.e., a maximal element under > the standard ordering), namely -1. But no first element at the other end. You knew that, right? > The set ({0}xZ+)u({1}xZ-) is infinite. It has an end (i.e., a maximal > element under the lexicographic ordering), namely (1,-1). But no minimal element under the same ordering. You knew that, right? > In each case, the ordering of the set is not isomorphic to omega, or > any wellordered set for that matter. Thus, when Chandler refers to > identifying the end of something that doesn't end, I point out that > infinite sets can end, [...] Except when they don't. Oh, look, here's an infinite set: {0,1,2,3,...}. Obviously it's infinite, and obviously it has an end (the digit 0). Therefore infinite sets can have an end. You're kind of missing Brian's entire point, here, aren't you? === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > In each case, the ordering of the set is not isomorphic to omega, or > any wellordered set for that matter. Thus, when Chandler refers to > identifying the end of something that doesn't end, I point out that > infinite sets can end, [...] > Except when they don't. I never denied that some infinite sets have no end! The problem was that that Chandler assumed that in the number .999...9998, since there were infinitely many nines, the nines didn't end, so that therefore one was placing the eight at the end of something that has no end. I wasn't talking about whether infinite sets can have ends or not, but whether a particular infinite set, namely a set of digits, can have an end or not. Chandler, like most standard analysts, apparently believed that all digits must be indexed by finite numbers, so that .999...9998 would be impossible. But Katz, via Ralf Bader's link, has shown otherwise. Katz has shown that it's possible to have digits that are indexed by hypernaturals. So .999...9998 can represent a number with nines indexed by the numbers from 1 to H-1, and then the eight indexed by H, a particular hypernatural number. This is not the same, as Chandler implied, as putting the eight at the end of something with no end. > Oh, look, here's an infinite set: {0,1,2,3,...}. > Obviously it's infinite, and obviously it has an end (the digit 0). > Therefore infinite sets can have an end. But I was thinking about a particular set -- the set {1,2,3,4,...,H-3,H-2,H-1,H}, which is a set with both a beginning and an end. The main point I'm making is that 0.999...9998 is not , as the standard analysts would have us believe, finding the end of something with no end. === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) >Just because there are infinitely many 9's there, it doesn't mean that >the 9's don't end. > The implication of a sequence of digits followed by ... is that the > digits are indexed by natural numbers. Presumably you don't mean that > when you write 0.999...9998, because which natural numbers are those > last 3 9s and the 8 meant to go with? They aren't indexed by standard natural numbers, but by something called hypernatural numbers. Please see the link given by Ralf Bader for more information. === Subject: Re: .9 repeating called hypernatural numbers. Please see the link given by Ralf Bader > for more information. If you actually read the link, you'd notice that there is no last hypernatural number either. Hence that cannot be a model for Mitch's assertions. - Tim === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > They aren't indexed by standard natural numbers, but by something > called hypernatural numbers. Please see the link given by Ralf Bader > for more information. > If you actually read the link, you'd notice that there is no last > hypernatural number either. I already know that there is no last hypernatural number. The problem here is that the set of numbers that MR wants to accept is a proper subset of the set of hyperreals, but contains, for every standard real, a hyperreal whose standard part is that real. Perhaps the distinction that must be made is that MR is thinking in terms of points , thinking about the next point after 0 or the last point before 1. To every point we assign a hyperreal, but we don't assign to every hyperreal a point. Thus, if H is a hypernatural following Katz, then we might say that the next point after 0 is 10^-H. This does not mean that 10^-H is the smallest hyperreal, or that (10^-H)/2 is not a hyperreal. It does mean that there is no point corresponding to (10^-H)/2, in the same way that there's no integer corresponding to 1/2, so that 1 is the next integer after 0. So we see that the standard analysts/geometers don't accept the concept of adjacent points, especially if we tried to assign hyperreal coordinates to those points. The problem, as mentioned earlier, is that the standard analysts consider the number system first, then make the geometry fit the numbers -- so that if we take as coordinates the set R of standard reals, or the full set of hyperreals, then they conclude that adjacent points are impossible. MR would rather consider the geometry first, declare that adjacent points are possible, then make the numbers fit the geometry -- and conclude that there must exist a hypernatural H such that 10^-H is adjacent to 0, with no infinitesimal hyperreals strictly between 0 and 10^-H a coordinate of a point . This sentiment is similar to AP's. But at this point I will no longer compare AP to MR, since AP has already specifically rejected the hyperreals. === Subject: Re: .9 repeating to accept is a _proper_ subset of the set of hyperreals, I very much doubt that you have the faintest idea what MR wants. Or indeed any of the other people whose wants you repeatedly claim to know - occasionally even in contradiction of what they actually state. It's an exceedingly poor habit you have, and definitely at least skirting the border of intellectual dishonesty. > Perhaps the distinction that must be made is that MR is thinking in > terms of _points_, thinking about the next point after 0 or the > last point before 1. To every point we assign a hyperreal, but we > _don't_ assign to every hyperreal a point. Again, here you're claiming knowledge of what MR is *thinking*: in terms of points assigned to hyperreals. MR has never mentioned hyperreals, as far back as I can remember. > MR would rather consider the geometry first, declare that adjacent > points are possible, then make the numbers fit the geometry -- and > conclude that there must exist a hypernatural H I will not accept any pronouncement from you as to what MR would rather consider. Using other people's names to serve as mouthpieces for your own views and arguments is frankly unethical. - Tim === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > They aren't indexed by standard natural numbers, but by something > called hypernatural numbers. Please see the link given by Ralf Bader > for more information. If you actually read the link, you'd notice that there is no last > hypernatural number either. Hence that cannot be a model for Mitch's > assertions. - Tim The infinitely small nonzero or next to zero is what I assert exists in math. Mitch Raemsch === Subject: Re: .9 repeating posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > The infinitely small nonzero or next to zero is what I assert exists > in math. We look forward to your proof of that assertion. === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > The infinitely small nonzero or next to zero is what I assert exists > in math. We look forward to your proof of that assertion. Maybe you can find a proof yourself. It is too simple to require one. === Subject: Re: .9 repeating posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > The infinitely small nonzero or next to zero is what I assert exists > in math. Wonderful. And someone else asserts the triangulary medium size and next to the squart root of -1 in math. A stand-alone declaration no less persuasive than yours. MoeBlee === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > The infinitely small nonzero or next to zero is what I assert exists > in math. Wonderful. And someone else asserts the triangulary medium size and > next to the squart root of -1 in math. A stand-alone declaration no > less persuasive than yours. MoeBlee One divided by infinity is nonzero. Mitch Raemsch === Subject: Re: .9 repeating posting-account=FH_Q0goAAAAJ5KtCX_meKSiqoRvUgwne Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > The infinitely small nonzero or next to zero is what I assert exists > in math. > Wonderful. And someone else asserts the triangulary medium size and > next to the squart root of -1 in math. A stand-alone declaration no > less persuasive than yours. > MoeBlee One divided by infinity is nonzero. Mitch Raemsch Burt, you are forcing yourself to be dismissed as a crank in an actually quite reputable forum. It's frustrating that you're not putting significant and rigorous mathematical thought into many of the responses. The idea that there is a number not equal to 1 but is infinitessimally close to 1 has been proven false, assuming you are using the real numbers and standard representations of decimals, etc. The problem has been explained to you in many different ways, but they are all saying essentially the same thing. Funny things happen in the world of infinity. The number 0.999... does not end in a 9 because it does not end at all. Numbers have infinitely many ways to be represented. For example, 0.5 can be represented as 0.5, 1/2, 0.50000..., or sqrt(1/4). Different symbols, same quantity. 0.49999... is in fact another way to represent this but you never see it used in part because of how clumsy it is to work with. Similarly, 1, 9/9, 1.0000..., and 3-2 are all different symbols that represent the same quantity. 0.999... is another string of symbols that, surprisingly, also equals 1. It's surprising because it seems like it should be slightly less, but the infinite number of 9s is what makes it just another representation of 1. You're welcome to continue debating, but it's somewhat akin to debating that 4 actually equals 5. Defending the notion may lead to greater understanding, but ultimately, everyone here is trying to help you understand why your idea is misguided. === Subject: Re: .9 repeating sha1:9QwpLWHRcZsRy9znkor/pN2D7DU= > One divided by infinity is nonzero. > Mitch Raemsch Burt, you are forcing yourself to be dismissed as a crank in an > actually quite reputable forum. Which forum would that be? -- Just be aware that anti-Cantorians are sick of being called crackpots, and the day will soon come when the crankiest Cantorians will eat their words, and this rot will be extricated from mathematics. -- Tony Orlow, an anti-Cantorian ready to rumble === Subject: Re: .9 repeating <87r60u3n2j.fsf@phiwumbda.org> posting-account=FH_Q0goAAAAJ5KtCX_meKSiqoRvUgwne Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > One divided by infinity is nonzero. > Mitch Raemsch > Burt, you are forcing yourself to be dismissed as a crank in an > actually quite reputable forum. Which forum would that be? -- > Just be aware that anti-Cantorians are sick of being called crackpots, > and the day will soon come when the crankiest Cantorians will eat > their words, and this rot will be extricated from mathematics. > -- Tony Orlow, an anti-Cantorian ready to rumble lol. Fair enough. I guess the crank-to-legitimate poster ratio is not exactly infinitessimally close to zero. === Subject: Re: .9 repeating sha1:Ezqe4FLLrQnfbrw6oQEogjGk0dY= > The infinitely small nonzero or next to zero is what I assert exists > in math. Wonderful. And someone else asserts the triangulary medium size and > next to the squart root of -1 in math. A stand-alone declaration no > less persuasive than yours. He also asserts that the aether either sustains or maintains all immutable elements. There are fourteen immutable elements. But lwalker claims that there is no principled distinction between Mitch's theories and the standard theories. That's even less plausible. -- At some point in the future history of humanity, AP will eclipse even Jesus. -- Archimedes Plutonium, 10/21/07 very humble and down to earth. -- Archimedes Plutonium, 10/22/07 === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) >Just because there are infinitely many 9's there, it doesn't mean that >the 9's don't end. > The implication of a sequence of digits followed by ... is that the > digits are indexed by natural numbers. Presumably you don't mean that > when you write 0.999...9998, because which natural numbers are those > last 3 9s and the 8 meant to go with? They aren't indexed by standard natural numbers, but by > something called hypernatural numbers. Please see the > link given by Ralf Bader for more information. By the infinitely small a quantity can be distinguished that is different. . === Subject: Re: .9 repeating sha1:2zv8fOR/q3RL1G/JZQhnENKo6BQ= >Just because there are infinitely many 9's there, it doesn't mean that >the 9's don't end. > The implication of a sequence of digits followed by ... is that the > digits are indexed by natural numbers. Presumably you don't mean that > when you write 0.999...9998, because which natural numbers are those > last 3 9s and the 8 meant to go with? > They aren't indexed by standard natural numbers, but by > something called hypernatural numbers. Please see the > link given by Ralf Bader for more information. By the infinitely small a quantity can be distinguished that is > different. > . Wow. The quality of your mathematical reasoning is utterly indistinguishable from that of LWalker's reference! Did you publish under a pseudonym? -- Jesse F. Hughes The people who made up the words could have said 'newspaper' is 'trees'. -- Quincy P. Hughes, five-year-old Wittgensteinian (This comment came out of the blue at breakfast.) === Subject: Re: .9 repeating sha1:hCksDFwLJReRcYnvNmXmdJx7Ol0= >Just because there are infinitely many 9's there, it doesn't mean that >the 9's don't end. > The implication of a sequence of digits followed by ... is that the > digits are indexed by natural numbers. Presumably you don't mean that > when you write 0.999...9998, because which natural numbers are those > last 3 9s and the 8 meant to go with? They aren't indexed by standard natural numbers, but by > something called hypernatural numbers. Please see the > link given by Ralf Bader for more information. Are you suggesting that this paper is related to Mitch's claim? You really are good at reading between the lines. You make up a number that Mitch has in fact never mentioned, 0.999...998. As far as I know, Mitch has never claimed that infinite strings of digits have a last number. Then, you decide that this paper is a good representation of Mitch's ideas. All because Mitch said that 0.999... is smaller than 1? And that it is the largest number smaller than 1? If I recall correctly, the paper does *not* support the claim that there is a number x such that x is the largest number < 1. Thus, this paper does *nothing* to show that Mitch's ideas really are a somewhat incomplete expression of a consistent mathematical theory, as you suggest. -- Jesse F. Hughes Of course, I don't need any more education. -- Quincy P. Hughes (age 7) === Subject: Re: .9 repeating <87sklb6bu1.fsf@phiwumbda.org> posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU CLR 1.1.4322),gzip(gfe),gzip(gfe) > They aren't indexed by standard natural numbers, but by > something called hypernatural numbers. Please see the > link given by Ralf Bader for more information. > You really are good at reading between the lines. You make up a > number that Mitch has in fact never mentioned, > 0.999...998. Actually, MR does mention this number, but indirectly. We all agree that MR considers .999... to be the last number before 1. Then, back on March 11th, Chandler asked of MR: I wonder -- what is the closest thing less than .9 repeating? i.e., he asked what the penultimate number before 1 must be. And MR's response, which was early am, East Coast US timezone on March 12th: It would be .9 repeating with an ending 8 So what else could MR have possibly meant in the wee hours of March 12th by this, if not 0.999...9998? Now Chandler responded to MR, about an hour and a half after MR posted, by: I suppose a naive person might wonder if the answer is a string that never ends at 8, but the only one of those I know is .888... (recurring), and I know for a fact that this can't be the closest, since .934 is in between. In other words, Chandler interpreted MR's comment about .9 repeating with an ending 8 (which I'll abbreviate as .9r8) to be .888... or 8/9. But no one, not even an infinitesimalist crank, would believe that 8/9 is the penultimate number before 1 -- since an infinitesimalist believes in the existence of more -- not fewer -- numbers than standard analysts do. Given that MR believes that .999... is the last number before 1, what would MR consider the penultimate number before 1 to be? If we define iota to be what MR considers as the infinitesimal difference between 1 and .999..., so that the last number before 1 is 1-iota, there are really only two sensible possibilities: 1. The penultimate number before 1 is 1-2iota. 2. There is no penultimate number before 1. The latter possibility is analogous to the lexicographic ordering of P(omega) -- the last set before {1} is {0,2,3,4,...} (i.e., it's omega{1}), but there's no penultimate element before {1}. Indeed, if we let S be the set of surreals (Conway's numbers, not Robinson's hyperreals) with birthday on or before the first infinite birthday, then the last surreal before 1 is 1-1/omega, but there is no penultimate surreal before 1. > As far as I know, Mitch has never claimed that infinite strings of > digits have a last number. If Hughes's claim is true here -- the post on March 12th notwithstanding -- then the last number before 1 would be .999..., but then there would be no penultimate number before 1, he said, It would be .9 repeating with an ending 8 which sounds as if there is a penultimate number before 1. But who knows? Maybe MR no longer believes that there's a penultimate number before 1. === Subject: Re: .9 repeating posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > We all agree that MR considers .999... to be the last > number before 1. Then, back on March 11th, Chandler > asked of MR: I wonder -- what is the closest thing less than .9 > repeating? i.e., he asked what the penultimate number before 1 > must be. And MR's response, which was early am, > East Coast US timezone on March 12th: It would be .9 repeating with an ending 8 So what else could MR have possibly meant in the wee > hours of March 12th by this, if not 0.999...9998? Now Chandler responded to MR, about an hour and a > half after MR posted, by: I suppose a > naive person might wonder if the answer is a string that never ends > at > 8, but the only one of those I know is .888... (recurring), ... Oh dear. It's a joke, see? At least we mean by .999,.. or . 9recurring, is the decimal representation that starts with 9, followed by another 9, and another, without ever ending. Because it never ends, it never ends in 9, and in logic it never ends in 5 either. But in the curious variant of reason used by those in the legal trade for example, I expect they would claim that the answer to what number does it not end in? is definitely 9. On this basis, the first number I thought of that doesn't end in 8 is .888... (yes, of course, actually I know lots of such numbers, but this is a Usenet post, OK?) I suppose this is all rather familiar from the days of Orlovia. Tony got quite worked up about his misunderstanding of limits, wanting a limit essentially to preserve every property of the sequence of which it is the limit. But in the end this means that there _are_ no limits: no two different sequences can have the same limit, and we end up just referring to the sequences themselves. So here there's a sequence of decimal representations not ending in 8: 0.8... 0.98... 0.998... 0.9998... 0.99998... 0.999998... whose limit in the normal sense is 1, but whose Orlovian limit might be 0.999...998. Now this is a representation that _does_ end in 8, rather violating the obvious application of the Rule of Limit Property Preservation, which says that any property of all members of a sequence is a property of the Limit, except for the handy Except when Tony says so clause which presumably one would invoke. Well, Brian Chandler === Subject: Re: .9 repeating <87sklb6bu1.fsf@phiwumbda.org It would be .9 repeating with an ending 8 So what else could MR have possibly meant in the wee > hours of March 12th by this, if not 0.999...9998? It could have been 0.999...8, where the digits are indexed by w+1 so that the 8 digit has no predecessor. Or any number of other possibilities. > But who knows? Maybe MR no longer believes that there's a > penultimate number before 1. Indeed. And that's rather a large problem with trying to axiomatize a system based on a crank's utterances. - Tim === Subject: Re: .9 repeating posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > It could have been 0.999...8, where the digits are indexed by w+1 so > that the 8 digit has no predecessor. Or any number of other > possibilities. But if the digit 8 has no predecessor, that would probably contradict what Mitch says about 1.000... having a predecessor (0.999...). Surely every number has a predecessor under his scheme. === Subject: Re: .9 repeating <87sklb6bu1.fsf@phiwumbda.org> contradict what Mitch says about 1.000... having a predecessor > (0.999...). I meant that 0.999...8 could have an infinite prefix with positions labelled by the usual natural-numbers, all of those filled with 9's, and a digit 8 stuck on the end corresponding to position omega. > Surely every number has a predecessor under his scheme. Could be! He isn't exactly disposed toward attempting to clarify anything - which is sort of my point. Assuming that the sequence ends ...9998 is more than the evidence supports, was all I was arguing. - Tim === Subject: Re: .9 repeating sha1:NZ96I9ZrQaMFuKq6XrGheREtp3w= > They aren't indexed by standard natural numbers, but by > something called hypernatural numbers. Please see the > link given by Ralf Bader for more information. > You really are good at reading between the lines. You make up a > number that Mitch has in fact never mentioned, > 0.999...998. Actually, MR does mention this number, but indirectly. > [...] > So what else could MR have possibly meant in the wee > hours of March 12th by this, if not 0.999...9998? Quite right. I had forgotten that post. -- Jesse F. Hughes Of course, my ability to admit my mistakes and correct them is a trait that many of you seem to never have properly appreciated. -- JSH, discussing his 1463rd proof of Fermat's Last Theorem. === Subject: Re: .9 repeating posting-account=gpERugkAAAB5_qKVhbO9UpGpOXFNrIYf 5.1),gzip(gfe),gzip(gfe) > Is below one by the infinitely nonzero small. It is the closest thing > to one. Add the infinitely small and you get one. Mitch Raemsch You really are the limit. Socks === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > Is below one by the infinitely nonzero small. It is the closest thing > to one. > Add the infinitely small and you get one. > Mitch Raemsch You really are the limit. > Socks It can be seen what the infinitely small nonzero must be through .9 repeating. === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > But unfortunately, there are some axioms that one can't deny without > being labeled a crank. Infinity is one of them. And the unwritten > rule that only standard reals may be assigned digits is another. > And you can assign digits to non-standard reals. But you have to state > how you do that. If you do not state that you are a crank when you try > to prove things about it. So the only questions remaining are what > does that notation actually mean. And there is no reply forecoming. The problem is that there is no one-sentence, nor even a one- paragraph, definition of the digits of nonstandard reals, that Winter, Tribble, or the other standard analysts would accept as valid. Let's go back to Suppes, the mathematician whose book I bought due to the recommendation of several sci.math posters. I notice that the concept of a real number isn't defined until page 181. That's right -- page 181 of a 267-page book! The reason is that Suppes derives the real numbers from the axioms of ZFC, and it takes much effort to derive the real numbers from the axioms. The numbers proposed by AP and MR don't work in ZFC. So we need to start from scratch with new axioms. If it took 181 pages for Suppes to get from the axioms to real numbers, imagine how long it will take us to get from the new axioms to the new reals! But that's the only way to give a formal definition of the new reals that will satisfy the standard analysts. Moreover, long before we reach the new reals, most standard analysts will have stopped reading the axiomatization. And admittedly I don't blame them -- why would they want to read a long description of how to derive the new reals from the new axioms, when they already have standard reals and standard axioms? They've already invested a great deal of effort to learn standard set theory and analysis, and so they have no need to spend time learning another theory! Once would think that AP, who's been posting to sci.math for over a decade and a half, would have finished the rigorous axiomatization of his AP-adics and AP-reals by now, but apparently he hasn't. And if AP, after many thousands of posts over the years, can't convince the standard analysts of accept his theory, what chance have I? Notice that MR's comments seem to support AP's theory. Indeed, MR made yet another comment that sounds a lot like AP: Zero and one are the beginning of math. That is their meaning. We recall that AP has recently criticized Peano's Axioms, noting that the first axiom is 0 is a natural number (or possibly 1 is a natural number), while AP prefers that the axiom state that both 0 and 1 are natural numbers, not one or the other. And apparently MR agrees. To see why AP and MR want both 0 and 1 to be primitive concepts, we need to think geometrically. The Birkhoff Ruler Postulate, often the first postulate in a high school geometry text, is often stated as follows: Given points A and B, the points on line AB can be paired with the real numbers such that A is paired with 0, B is paired with 1, and if P and Q are two points on line AB, P is paired with p, and Q is paired with q, then the distance between P and Q is given by abs(p-q). Now suppose we were to pair A with 0, but leave out the part about pairing B with 1. Then B could be paired with any arbitrary real, so that the distance between P and Q is no longer unique, but would differ by a constant multiple depending on the coordinate of B. It takes two pairings -- A with 0, and B with 1 -- to guarantee that the distance between P and Q is unique. Of course, the reason that PA only needs to have one primitive, 0 or 1 and not both, is that PA is a theory of arithmetic, not geometry -- PA has nothing to do with assigning coordinates to points. But still, this does show how both AP and MR would prefer that geometry , not arithmetic or set theory, be the foundation of mathematics. Of all the so-called crank theories, I believe that those of AP and tommy1729 are the closest to being axiomatized. Therefore, I focus my axiomatizations on this two theories. But since MR's intuitions so far appear to agree with AP's, by axiomatizating AP, I will have formalized numbers that MR will accept as well. Making numbers such as 0.999...999 rigorous will require a great deal of effort. Standard analysis has been around for over a century, so it already has a head start on our new theory. I'd rather start with ZFC and make more modest changes to the theory to come up with the AP-reals, but this appears impossible. So I'll have to start from scratch, and start with axioms that at first seem to have nothing to do with 0.999...999. So 0.999...999 is a long way off. Indeed, when I first come up with the AP-reals, I'll be using binary notation, not decimal, so that I'll have 0.111...111 well before I reach anything like 0.999...999. This is because I want to take advantage of Boolean logic, where I'll use xey to denote the digit 1 and ~xey to denote the digit 0. Attempting to use decimal would therefore require me to use ten-valued logic, representing an even more radical departure from standard set theory and logic, since standard reals can be written in decimal without needing ten-valued logic at all. I want to see whether my axiomatization will work with Boolean logic and binary notation before attempting decimal. I've already posted snippets of this theory in other threads, but maybe it's time to continue this axiomatization once more. === Subject: Re: .9 repeating Distribution: world > And you can assign digits to non-standard reals. But you have to state > how you do that. If you do not state that you are a crank when you try > to prove things about it. So the only questions remaining are what > does that notation actually mean. And there is no reply forecoming. >Let's go back to Suppes, the mathematician whose book I bought due >to the recommendation of several sci.math posters. I notice that the >concept of a real number isn't defined until page 181. That's right -- >page 181 of a 267-page book! The reason is that Suppes derives the >real numbers from the axioms of ZFC, and it takes much effort to >derive the real numbers from the axioms. The other reason is that _Axiomatic Set Theory_ isn't solely a book about how to define the reals. It's a book about set theory. Suppes covers a lot of material that has exactly nothing to do with development of the reals. To claim that it takes 181 pages to define the reals is deceitful. Once you have the definitions of sets (first half of Chapter 2), equivalence relations (Sections 3.1 and 3.3), and cardinals (Chapter 4), you have enough to define the naturals. >The numbers proposed by AP and MR don't work in ZFC. So we need >to start from scratch with new axioms. If it took 181 pages for Suppes >to get from the axioms to real numbers, imagine how long it will take >us to get from the new axioms to the new reals! But that's the only >way to give a formal definition of the new reals that will satisfy the >standard analysts. Once you have the naturals, any of the following can be built in the equivalent of a few pages: - The integers as equivalence classes of pairs of naturals - The rationals as equivalence classes of pairs of integers - The reals as equivalence classes of Cauchy sequences of rationals (Note that this is not the approach that Suppes takes.) But, to provide a definition of non-standard reals would not necessarily take even this much. If the point of divergence from the standard approach is only at the reals, then such a definition could start by stipulating the rationals as its basis. There would be no need to redefine them, as long as the new definition of reals is based on the same rationals. Conversely, if the new non-standard reals aren't based on the standard rationals, or standard integers, or standard naturals, then it shouldn't be surprising that it would take a lot of work to rebuild this from the ground up. Either way, without a clear definition of what they are, it's going to be rather difficult to see if their definition is consistent and what its consequences are. >Moreover, long before we reach the new reals, most standard analysts >will have stopped reading the axiomatization. There appears to be some projecting happening here. I'm not a mathematician myself, but I'd guess that a new method of defining numbers would be electrifying -- if it was coherent, consistent, and truly new. > And admittedly I don't >blame them -- why would they want to read a long description of how >to derive the new reals from the new axioms, when they already have >standard reals and standard axioms? Because it would be a new field of mathematical study. >Once would think that AP, who's been posting to sci.math for over a >decade and a half, would have finished the rigorous axiomatization of >his AP-adics and AP-reals by now, Only if you assume that he ever started such an axiomatization. And assume that he listened to corrections offered when flaws were found. > And if >AP, after many thousands of posts over the years, can't convince the >standard analysts of accept his theory, what chance have I? If you never start, none whatsoever. >Notice that MR's comments seem to support AP's theory. Indeed, MR >made yet another comment that sounds a lot like AP: Zero and one are the beginning of math. That is their meaning. Yes, this does sound like something that AP would say, along with the universe is contained in a plutonium atom. Both statements have equal meaningful content. >Making numbers such as 0.999...999 rigorous will require a great >deal of effort. Standard analysis has been around for over a century, >so it already has a head start on our new theory. I'd rather start >with >ZFC and make more modest changes to the theory to come up with >the AP-reals, but this appears impossible. So I'll have to start from >scratch, and start with axioms that at first seem to have nothing to >do with 0.999...999. So 0.999...999 is a long way off. Just out of curiousity, have you already done a literature search on non-standard analysis? You might want to start with Robinson's book on the topic. If you don't feel like shelling out fifty bucks, topic. -- Michael F. Stemper #include Economists have correctly predicted seven of the last three recessions. === Subject: Re: .9 repeating Distribution: world >The numbers proposed by AP and MR don't work in ZFC. So we need >to start from scratch with new axioms. If it took 181 pages for Suppes >to get from the axioms to real numbers, imagine how long it will take >us to get from the new axioms to the new reals! But that's the only >way to give a formal definition of the new reals that will satisfy the >standard analysts. Once you have the naturals, any of the following can be built in >the equivalent of a few pages: >- The integers as equivalence classes of pairs of naturals >- The rationals as equivalence classes of pairs of integers >- The reals as equivalence classes of Cauchy sequences of rationals >(Note that this is not the approach that Suppes takes.) But, to provide a definition of non-standard reals would not necessarily >take even this much. If the point of divergence from the standard approach >is only at the reals, then such a definition could start by stipulating >the rationals as its basis. There would be no need to redefine them, as >long as the new definition of reals is based on the same rationals. For more information on this topic, and to see that sci.math is not, as <20060416132837.484$Pd@newsreader.com>, which was posted by David W. Cantrell about three years back. Interestingly, his presentation doesn't need to spend 180 pages developing all of set theory, either. He explicitly starts his exposition with the statement: We shall assume that the system Q of rationals, together with appropriate relations and operations, has already been developed. -- Michael F. Stemper #include Twenty-four hours in a day; twenty-four beers in a case. Coincidence? === Subject: Re: .9 repeating Nntp-Posting-Host: hera.cwi.nl > And you can assign digits to non-standard reals. But you have to state > how you do that. If you do not state that you are a crank when you try > to prove things about it. So the only questions remaining are what > does that notation actually mean. And there is no reply forecoming. > > The problem is that there is no one-sentence, nor even a one- > paragraph, > definition of the digits of nonstandard reals, that Winter, Tribble, > or the > other standard analysts would accept as valid. Why not? I have not yet seen such a definition, so come up with one... > Let's go back to Suppes, the mathematician whose book I bought due > to the recommendation of several sci.math posters. I notice that the > concept of a real number isn't defined until page 181. That's right -- > page 181 of a 267-page book! The reason is that Suppes derives the > real numbers from the axioms of ZFC, and it takes much effort to > derive the real numbers from the axioms. Possibly because first a lot of things have to be defined before even the naturals plus their arithmetic is properly defined. > The numbers proposed by AP and MR don't work in ZFC. So we need > to start from scratch with new axioms. If it took 181 pages for Suppes > to get from the axioms to real numbers, imagine how long it will take > us to get from the new axioms to the new reals! But that's the only > way to give a formal definition of the new reals that will satisfy the > standard analysts. Well, I think it is unsatisfactory when some notation is used for which no meaning is given. But apparently you do not mind. Moreover, how do you *know* that the numbers proposed by AP do not work in ZFC? (I do not consider what MR does do even a proposal for numbers.) What part of ZFC would it not work with? > Once would think that AP, who's been posting to sci.math for over a > decade and a half, would have finished the rigorous axiomatization of > his AP-adics and AP-reals by now, but apparently he hasn't. And if > AP, after many thousands of posts over the years, can't convince the > standard analysts of accept his theory, what chance have I? AP has not convinced the mathematicians because he makes to many errors, uses to many undefined terms and so on. He is not convincing for exactly the same reason JSH is not convincing. > Notice that MR's comments seem to support AP's theory. Indeed, MR > made yet another comment that sounds a lot like AP: > > Zero and one are the beginning of math. That is their meaning. Yeah, well, whatever that may mean. > We recall that AP has recently criticized Peano's Axioms, noting that > the first axiom is 0 is a natural number (or possibly 1 is a > natural > number), while AP prefers that the axiom state that _both_ 0 and 1 > are natural numbers, not one or the other. And apparently MR agrees. AP does not understand the Peano axioms. When in the Peano axioms 0 is given as a natural number, automatically 1 is also a natural number, because it is the successor of 0, there is no reason to mention it specially. The distinction between 0 is a natural number and 1 is a natural number is only in what you consider natural numbers. In the first case 0 is also considered a natural number, in the second case not. There is no further significant distinction. With the former you do not have to introduce 0 separately when you are developping the numbers, with the latter you need that, but that is also not much of a problem. > To see why AP and MR want both 0 and 1 to be primitive concepts, > we need to think geometrically. The Birkhoff Ruler Postulate, often > the > first postulate in a high school geometry text, is often stated as > follows: > > Given points A and B, the points on line AB can be paired with the > real > numbers such that A is paired with 0, B is paired with 1, and if P and > Q are two points on line AB, P is paired with p, and Q is paired with > q, > then the distance between P and Q is given by abs(p-q). And that is a reason to mention them *both* in the Peano axioms? Makes no sense. However, during my courses at school and university I have never seen that axiom. I have found a reference on the web and it states: if k is a line and R denotes the set of real numbers, there exists a one-to-one correspondence (X <-> x) between the points X c k and the real numbers x c R such that |AB| = |a - b| where A <-> a and B <-> b. which makes much more sense. That is, in your formulation you define the distance between two points based on an arbitrary mapping of the line to the real numbers, while Birkhoff's axiom actually assumes that a distance is given and that there can be a mapping of a line on R such that the distances remain invariant. > Now suppose we were to pair A with 0, but leave out the part about > pairing B with 1. Then B could be paired with _any_ arbitrary real, so > that the distance between P and Q is no longer unique, but would > differ by a constant multiple depending on the coordinate of B. It > takes > two pairings -- A with 0, and B with 1 -- to guarantee that the > distance > between P and Q is unique. Also with your formulation the distance is not unique. It depends on the reference points A and B. > Indeed, when I first come up with the AP-reals, I'll be using binary > notation, not decimal, so that I'll have 0.111...111 well before I > reach anything like 0.999...999. In that case you will not come up with the AP-reals, because they are tightly connected with the decimal notation. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: .9 repeating Suppes derives the real numbers from the axioms of ZFC, and it takes > much effort to derive the real numbers from the axioms. It takes quite a lot to derive much of anything from simple set-theory axioms. It's a rather short process from rationals with their usual arithmetic properties to reals, though. All you need to do is define Dedekind cuts, then call each nontrivial Dedekind cut a real number with a few simple rules for arithmetic. Then all you need to do is show that each rational is represented by a rather obvious Dedekind cut and has exactly the same properties. > The numbers proposed by AP and MR don't work in ZFC. What makes you think they have any coherent proposals at all? MR shows no sign of having any idea about mathematical systems, and AP keeps changing what he wants. In either case, and making the somewhat counterfactual assumption that a system exists that models what either wants, what makes you so sure that it cannot exist within ZFC? > Once would think that AP, who's been posting to sci.math for over a > decade and a half, would have finished the rigorous axiomatization of > his AP-adics and AP-reals by now, but apparently he hasn't. He hasn't even started on such a project, and from prior engagements it doesn't appear he would even know how to work with axiomatic systems. Have you actually *read* the mathematical work in posts, or just skimmed for judging his apparent intent? It may be surprising to you that he hasn't finished such a task, but certainly not to me. > Of all the so-called crank theories, I believe that those of AP > and tommy1729 are the closest to being axiomatized. Therefore, I > focus my axiomatizations on this two theories. But since MR's > intuitions so far appear to agree with AP's, by axiomatizating AP, I > will have formalized numbers that MR will accept as well. I strongly doubt that there is any axiomatization that either AP or MR will accept, since I doubt they would be capable of understanding it. > Making numbers such as 0.999...999 rigorous will require a great > deal of effort. There are already models of numbers whose decimal representations can go beyond infinity. The trouble is that AP wants more, much more, and what he wants keeps changing as he posts. Perhaps if you have ever designed computer applications you'll be familiar with what a mess continually changing customer requirements can make. > I've already posted snippets of this theory in other threads, but > maybe it's time to continue this axiomatization once more. Sure, give it a go. I doubt you'll get AP or MR to sign off on it, but don't let my pessimism stop you. - Tim === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > But unfortunately, there are some axioms that one can't deny without > being labeled a crank. Infinity is one of them. > I've NEVER seen anyone define or use the word 'crank' in such a way > that a person is a crank merely for rejecting the axiom of infinity. As Platonists, most mathematicians accept certain statements as being absolutely true. Therefore perhaps it would be more accurate to state that a mathematician considers a crank to be someone who contradicts what he or she considers to be absolutely true. Both standard set theorists and I accept 2 + 2 = 4 as absolutely true. Both standard geometers and I accept the existence of exactly five Platonic solids as absolutely true. Standard set theorists accept Infinity as absolutely true, but I don't. Standard analysts accept 0.999... = 1 as absolutely true, but I don't. Therefore, we will continue be labeled cranks by those Platonists who do accept Infinity and 0.999... = 1 as absolutely true. === Subject: Re: .9 repeating posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > But unfortunately, there are some axioms that one can't deny without > being labeled a crank. Infinity is one of them. > I've NEVER seen anyone define or use the word 'crank' in such a way > that a person is a crank merely for rejecting the axiom of infinity. As Platonists, most mathematicians accept certain statements as > being absolutely true. Therefore perhaps it would be more accurate > to state that a mathematician considers a crank to be someone who > contradicts what he or she considers to be absolutely true. I've never seen anyone define 'crank' that way. > Both standard set theorists and I accept 2 + 2 = 4 as absolutely true. > Both standard geometers and I accept the existence of exactly five > Platonic solids as absolutely true. > Standard set theorists accept Infinity as absolutely true, At what International Conference of Standard Set Theorists was there given a definition of 'infinity' along with a proclamation that infinity is absolutely true (whatever that means). > but I > don't. > Standard analysts accept 0.999... = 1 as absolutely true, but I don't. I'm not familiar with this series of papers issued by standard analysts in which it is determined that '0.999... = 1' is absolutely true, whatever that even means. > Therefore, we will continue be labeled cranks by those Platonists > who do accept Infinity and 0.999... = 1 as absolutely true. You've not shown a SINGLE ACTUAL person who has defined 'crank' in such a way that one is a crank merely for not accepting that Infinity and the the statement 0.999... = 1' are absolutely true. I mean, I DO think you have an idea for pretty good, though recondite, science fiction movie about wars and tribunals involving an evil interplanetary junta of Standard Analysts and a rebel force of space rocket flying rebels fighting for the right to speak the unspeakable 0.999... = 1. But other than that, I don't see your remarks has having much to do with any discussion actually taking place here. Meanwhile, please take a look at Hilbert's notion of the contentual and the ideal. There you may find some actual sensible handling of some ideas that seem to making their way to you. MoeBlee === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Both standard set theorists and I accept 2 + 2 = 4 as absolutely true. > Both standard geometers and I accept the existence of exactly five > Platonic solids as absolutely true. > Standard set theorists accept Infinity as absolutely true, > At what International Conference of Standard Set Theorists was there > given a definition of 'infinity' When I say Infinity, with a capital I, I usually mean the three-word phrase Axiom of Infinity. I've noticed, and apparently absorbed, a habit among some sci.math posters to refer to an axiom of ZFC by a single word name, so they would say Extensionality when they mean Axiom of Extensionality, Choice when they mean Axiom of Choice, Replacement when they mean Schema of Replacement, and so on. Therefore, I've done If this turns out to be confusing, I guess I have to include the words Axiom of every single time I write the name of an axiom, no matter how cumbersome it may become. At least for Choice there is the handy abbreviation AC, but the Axiom of Infinity has no convenient abbreviation for me to use. Therefore, my statement becomes: Standard set theorists accept the Axiom of Infinity as absolutely true, but I don't. > Standard analysts accept 0.999... = 1 as absolutely true, but I don't. > I'm not familiar with this series of papers issued by standard > analysts in which it is determined that '0.999... = 1' is absolutely > true, whatever that even means. Here's what I mean by absolutely true: and small values of 5. And they did so rigorously, by giving axioms and definitions of large value, small value, and so on -- definitions that satisfy eliminability and anticreativity -- and prove using only those axioms, definitions, and first order logic with identity that 2 + 2 = 5, a proof that would be just as rigorous as any proof of ZFC is. Would that proof be taken seriously, or would the poster be considered a crank? Of course the poster would be a crank -- the definitions, however rigorous, are nonsensical, and the poster would be accused of taking words with standard definitions (such as two, five, and value) and giving them nonstandard definitions. In other words, the statement 2 + 2 = 4 would be considered absolutely true, and no theory, no matter how rigorous, would ever be considered if it were to contradict that basic fact of arithmetic. Notice that even MoeBlee himself mentioned a similar concept, earlier in this thread: Or because the mathematician finds the axiom of choice fits his conception of sets, or even that the axiom of choice is true to that conception, or simply true. I'm using the words absolutely true the same way that MoeBlee used the words simply true -- 2 + 2 = 4 fits the mathematician's conception of numbers, the Axiom of Infinity fits the standard set theorist's conception of sets, and 0.999... = 1 fits the standard analyst's conception of analysis. Perhaps, from now on, I'll replace my phrase absolutely true with MoeBlee's simply true, in order to emphasize that I'm using the phrase to mean the exact same thing. Therefore, my statement becomes: Standard analysts accept 0.999... = 1 as simply true, but I don't. The point of all this discussion is that many posters believe that I'd defend any crazy theory, even ones which argue that 2 + 2 = 5, since the theories that I do defend are, in their opinion, just as crazy as those which prove that 2 + 2 = 5. So I was trying to explain the difference between 2 + 2 = 5 and 0.999... < 1 such that I'd defend theories which argue the latter, but not those which argue the former. Still, I wonder whether my explanation would convince anyone, since in the eyes of most, there's no real difference between the former and the latter. > Therefore, we will continue be labeled cranks by those Platonists > who do accept [the Axiom of] Infinity and 0.999... = 1 as [simply] true. > You've not shown a SINGLE ACTUAL person who has defined 'crank' in > such a way that one is a crank merely for not accepting that [the Axiom > of] Infinity and the the statement 0.999... = 1' are [simply] true. Do I actually have to go back and count the number of times that MR was called a crank? I used to associate crankdom with opposition to ZFC. I now concede the point and weaken my claim to say that it's not opposition to ZFC per se, but lack of acceptance of certain facts as simply true that serves to distinguish the cranks from their opponents. But many are still in denial that they call those who argue in favor of theories that do not satisfy the conceptions of most mathematicians cranks. Anyone who argues that 2 + 2 = 5 is considered a crank, no matter how rigorous their argument is. Anyone who argues that 0.999... < 1 is considered a crank, no matter how rigorous their argument is. === Subject: Re: .9 repeating sha1:p0MeCAnvAHXX2Wo4p7GlPe3TmaE= > Anyone who argues that 0.999... < 1 is considered a crank, no matter > how rigorous their argument is. http://arxiv.org/pdf/0811.0164.pdf in which the authors argue So long as the number system has not been specified, the students' hunch that .999 . . . can fall infinitesimally short of 1, can be justified in a mathematically rigorous fashion. The conclude, in part (4) in a particular larger system called the hyperreal numbers, there is a generalized notion of decimal expansion for such numbers, starting in each case with an unbounded number of digits 9; (5) all such numbers therefore have an arguable claim to the no- tation .999 . . . which is patently ambiguous (the meaning of the ellipsis . . . requires disambiguation); seem the slightest bit crankish to me, and no one else has claimed that they are cranks, near as I can tell. How is this consistent with your claim? -- Jesse F. Hughes Ultimately, I can bring the entire mathematical establishment to its knees... Live in a fantasy world if you wish, but to me that's just an expression of your intellectual inferiority. --James Harris === Subject: Re: .9 repeating posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Standard set theorists accept the Axiom of Infinity as absolutely > true, but I don't. And you determined this how? And what do you mean by 'standard set theorist'? You do know that a researcher in set theory may work in a wide variety of systems and that among researchers even in just ZFC, there is a wide range of philosophical views, right? > Here's what I mean by absolutely true: and small values of 5. And they did so rigorously, by giving axioms > and > definitions of large value, small value, and so on -- definitions > that > satisfy eliminability and anticreativity -- and prove using only those > axioms, definitions, and first order logic with identity that 2 + 2 = > 5, a > proof that would be just as rigorous as any proof of ZFC is. Would that proof be taken seriously, or would the poster be considered > a crank? Of course the poster would be a crank -- the definitions, > however rigorous, are nonsensical, and the poster would be accused > of taking words with standard definitions (such as two, five, and > value) and giving them nonstandard definitions. How do you know? How do you know that if it were clear enough that the poster was setting forth a rigorous system that people would still call the poster a 'crank'? Moreover, the point about redefining standard terminology might not be about crankism but rather simply the problems in communication that such WIDESPREAD re-defining causes. > In other words, the > statement 2 + 2 = 4 would be considered absolutely true, and no > theory, no matter how rigorous, would ever be considered if it were to > contradict that basic fact of arithmetic. You've confused REDEFINING terms such as '2' with such finitistic facts as that two strokes concatenated with two strokes is four strokes. Yes, I would imagine that many mathematicians regard the later as in some sense or another basic, fundamental, perhaps even absolute. But that doesn't entail that one would call someone a 'crank' merely for choosing to use a diffrent definition for the symbol '2', et. al, though one might comment that such redefinitions don't help communication. > Notice that even MoeBlee himself mentioned a similar concept, > earlier in this thread: Or because the mathematician finds the axiom of choice fits his > conception of sets, or even that the axiom of choice is true to that > conception, or simply true. (1) I didn't say 'absolutely'. Though, of course there may be SOME people who also take the axiom of choice as 'absolutely true' in some sense or another of 'absolute'. But my notion is NOT the same as yours. > I'm using the words absolutely true the same way that MoeBlee > used the words simply true -- 2 + 2 = 4 fits the mathematician's > conception of numbers, the Axiom of Infinity fits the standard set > theorist's conception of sets, and 0.999... = 1 fits the standard > analyst's conception of analysis. Then, you're going fuzzy all over now with your definitions. Your first explanation does not match the one above. Moreover, you STILL have given no evidence that this, or any other view, is the uniform view of the standard set theorist. Your fuzzy broadstrokes are not informational. You contribute only to silly oversimplification of a wide range of thought among mathematicians. You would do so much better if instead you were to speak of SPECIFIC views of SPECIFIC mathematicians and philosophers. > Perhaps, from now on, I'll replace my phrase absolutely true > with MoeBlee's simply true, in order to emphasize that I'm > using the phrase to mean the exact same thing. But YOUR notion is NOT the same as my notion. In fact, I didn't even DEFINE 'simply true'. I would leave that to various individuals who might use the term to describe their views. I don't necessarily expect that they would agree that YOUR definition of 'absolute' is the same as their definition of 'simply'; and I can tell you that any notion I have of 'simple truth' is NOT the same as your notion of 'absolute truth'. So, please, don't tangle YOUR views with mine. You already have a horrible record of mischaracterizing and even egregiously mispresenting the views of others. Please don't set this conversation up on the VERY BASIS of another such mischaracterization and blurring of who believes what. > Therefore, my statement becomes: Standard analysts accept 0.999... = 1 as simply true, but I don't. The point of all this discussion is that many posters believe that > I'd defend any crazy theory, even ones which argue that 2 + 2 = 5, > since the theories that I do defend are, in their opinion, just as > crazy as those which prove that 2 + 2 = 5. So I was trying to > explain the difference between 2 + 2 = 5 and 0.999... < 1 such > that I'd defend theories which argue the latter, but not those which > argue the former. Still, I wonder whether my explanation would > convince anyone, since in the eyes of most, there's no real > difference between the former and the latter. > Therefore, we will continue be labeled cranks by those Platonists > who do accept [the Axiom of] Infinity and 0.999... = 1 as [simply] true. > You've not shown a SINGLE ACTUAL person who has defined 'crank' in > such a way that one is a crank merely for not accepting that [the Axiom > of] Infinity and the the statement 0.999... = 1' are [simply] true. Do I actually have to go back and count the number of times that MR > was called a crank? Not JUST for not accepting the axiom of infinity or convergence as simply true. This has been explained to you over and over and over. > I used to associate crankdom with opposition to ZFC. I now concede > the point and weaken my claim to say that it's not opposition to ZFC > per > se, but lack of acceptance of certain facts as simply true that serves > to > distinguish the cranks from their opponents. But many are still in > denial that they call those who argue in favor of theories that do not > satisfy the conceptions of most mathematicians cranks. I don't take the axiom of choice as simply true (given some reasonable definition of 'simply true') (nor do I take the axiom of choice as simply false). No one has ever called me a 'crank' for that. I don't take infinitistic statements as true except PER the method of models. That is, by a reasonable definition of 'simply true', I don't take infinitistic statements to be SIMPLY true. No one has called me a 'crank' for that. You are just plain wrong; and you have not a SINGLE ACTUAL instance to point to of someone being called a crank JUST for not taking the axiom of infinity (or some other such mathematical principle) as simply true or even true AT ALL! > Anyone who argues that 2 + 2 = 5 is considered a crank, no matter > how rigorous their argument is. Anyone who argues that 0.999... < 1 is considered a crank, no matter > how rigorous their argument is. No one in this thread has given a rigorous treatment of .999... < 1. AGAIN, for about the thousandth time in such discussions, you claim that people are being called 'crank' unjustifiably, but you just keep bypassing that what is called 'crank' is indeed the LACK of a rigorous argument, among other behaviors. And, again, you didn't answer my repeated question in my post: On what basis did you arrive at your sweeping generalization that there is some notion of 'absolute truth' regarding such things as the axiom of infinity held uniformly among standard set theorists? MoeBlee === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > And, again, you didn't answer my repeated question in my post: On what > basis did you arrive at your sweeping generalization that there is > some notion of 'absolute truth' regarding such things as the axiom of > infinity held uniformly among standard set theorists? Well, most standard set theories contain an Axiom of Infinity, don't they? I've yet to see any set theory lack this axiom and still be labeled standard. Similarly, I consider standard analysts to accept as simply true many, if not most, of the theorems of standard analysis. My labels standard set theorist, standard analyst, etc., is my effort to avoid the label standard mathematician, which previously led to an argument on how nonstandard analysis is still standard mathematics. So a standard analyst explicitly accepts standard analysis, as opposed to nonstandard analysis. And let's add another concept to the list -- the idea of adjacent points in geometry. Standard analysts -- or should I say, standard geometers -- continue to frown upon coming up with a system in which points can be adjacent, no matter how rigorous the theory may be. === Subject: Re: .9 repeating posting-account=PalVlwoAAAA1TKsKLVCsNe7APQhpWkGd 1.5); .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > And, again, you didn't answer my repeated question in my post: On what > basis did you arrive at your sweeping generalization that there is > some notion of 'absolute truth' regarding such things as the axiom of > infinity held uniformly among standard set theorists? Well, most standard set theories contain an Axiom of Infinity, > don't they? I've yet to see any set theory lack this axiom and > still be labeled standard. Similarly, I consider standard > analysts to accept as simply true many, if not most, of the > theorems of standard analysis. My labels standard set theorist, standard analyst, etc., > is my effort to avoid the label standard mathematician, > which previously led to an argument on how nonstandard > analysis is still standard mathematics. So a standard > analyst explicitly accepts standard analysis, as opposed to > nonstandard analysis. And let's add another concept to the list -- the idea of > adjacent points in geometry. Standard analysts -- or should > I say, standard geometers -- continue to frown upon coming > up with a system in which points can be adjacent, no matter > how rigorous the theory may be. When they frown upon such a system, it supports the idea that such an idea is merely an opinion. But no matter how ironclad the argument, of course, if someone's opinion is there *should* be an infinitesimal space between the numbers; or if they are not equal; only touching, can I argue by frowning? Except that if two numbers on a continuous number line are touching I cannot see how they could be unequal. But even my inability to see this only shows that perhaps I should be frowned on. Perhaps they develop a new field of mathematics where real numbers can be both touching and unequal. Perhaps, if it exists at all, it would surprise us all just how useless this system would be, or perhaps not! === Subject: Re: .9 repeating > And, again, you didn't answer my repeated question in my post: On what > basis did you arrive at your sweeping generalization that there is > some notion of 'absolute truth' regarding such things as the axiom of > infinity held uniformly among standard set theorists? Well, most standard set theories contain an Axiom of Infinity, > don't they? I've yet to see any set theory lack this axiom and > still be labeled standard. Similarly, I consider standard > analysts to accept as simply true many, if not most, of the > theorems of standard analysis. My labels standard set theorist, standard analyst, etc., > is my effort to avoid the label standard mathematician, > which previously led to an argument on how nonstandard > analysis is still standard mathematics. So a standard > analyst explicitly accepts standard analysis, as opposed to > nonstandard analysis. And let's add another concept to the list -- the idea of > adjacent points in geometry. Standard analysts -- or should > I say, standard _geometers_ -- continue to frown upon coming > up with a system in which points can be adjacent, no matter > how rigorous the theory may be. When they frown upon such a system, it supports the idea that such an idea is merely an opinion. But no matter how ironclad the argument, of course, if someone's opinion is there *should* be an infinitesimal space between the numbers; or if they are not equal; only touching, can I argue by frowning? Except that if two numbers on a continuous number line are touching I cannot see how they could be unequal. But even my inability to see this only shows that perhaps I should be frowned on. Perhaps they develop a new field of mathematics where real numbers can be both touching and unequal. Perhaps, if it exists at all, it would surprise us all just how useless this system would be, or perhaps not! SANITY WARNING (Droolin' Doolin) Scruffy Rat's postulate: light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body bears no resemblance whatsoever to Doolin's: Scruffy Rat's 2nd postulate of S.cruffy R.at says that the speed of light is c in every inertial frame. Scruffy Rat himself says But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v, so that t = x'/(c-v). Doolin makes no apology for misrepresenting Scruffy Rat by echoing the popular prayer, instead he chants the mantra spoken unto him by the insane Bonehead Green. Chanting mantras is like saying prayers, a form of witchcraft known as uttering spells. Doolin cannot distinguish c-v in the stationary frame from c in the moving frame. This form of insanity is known professionally among scientists as bigotry and lying. Guilty by reason of insanity is still guilty. The asylum inmates assert that it is the doctors treating them that are lying, even those untrained in psychiatry. Physician, heal thyself. - Jesus H. Christ, self-proclaimed son of Gawd, superman and god-on-a-stick, professional holy man and sky pilot, Captain of the starship Cloud, litterbug of the Holy Grail (now lost) and diner of Last Suppers. Other characteristics - walked on water, turned water into whine, preferred the male company of twelve rent boys and advocated love to them all and their neighbours. Was not popular among the establishment, having upset their banco and causing widespread economic disruption. (Banco is an Italian word for bench from which the English word Bank is derived. He upset the money benches or tables outside the temple to Gawd.) Favourite quote: Eloi, eloi, lama sabathani. (Translation: Oh, it! I screwed up. You were supposed to help Doolin wants to play hardball http://tinyurl.com/bw55 === Subject: Re: .9 repeating > My labels standard set theorist, standard analyst, etc., > is my effort to avoid the label standard mathematician, > which previously led to an argument on how nonstandard > analysis is still standard mathematics. So a standard > analyst explicitly accepts standard analysis, as opposed to > nonstandard analysis. What sort of acceptance is this? You'd be hard pressed to find any standard analyst who forcefully proclaims I hereby reject non-standard analysis except perhaps in the sense of finding it didactically unsound or mathematically barren. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: .9 repeating sha1:lX1CUAIa/UWE2EU6CzKZI7Ag/BE= > And let's add another concept to the list -- the idea of > adjacent points in geometry. Standard analysts -- or should > I say, standard _geometers_ -- continue to frown upon coming > up with a system in which points can be adjacent, no matter > how rigorous the theory may be. Once again, bull. How can you not see the difference between coming up with a system and making pronouncements that there is a smallest positive non-zero number and this fact is so obvious that it requires no proof? There may well be interesting geometries in which adjacency plays a role. It simply doesn't follow that Mitch is therefore intellectually respectable. -- Jesse F. Hughes It is not as satisfying to disagree with a book. -- Russell Easterly, on why he argues against set theory without reading a book on set theory. === Subject: Re: .9 repeating sha1:3a3JsFCXqfhhq7tlabsD8BXtcps= > My labels standard set theorist, standard analyst, etc., > is my effort to avoid the label standard mathematician, > which previously led to an argument on how nonstandard > analysis is still standard mathematics. So a standard > analyst explicitly accepts standard analysis, as opposed to > nonstandard analysis. Seems to me that you still lean too heavily on accepts. I've done some work in non-well-founded set theory (a long time ago), as well as ZFC. Which theory do you think I accept? Because I need to know if I'm standard or not. It's for a loan application. (please be standard! please be standard! ... ) -- Jesse F. Hughes It's easy folks. Just talk about my approach to your favorite mathematician. If they can't be interested in it, they've demonstrated a lack of mathematical skill. -- James Harris === Subject: Re: .9 repeating sha1:lYRoVvrKh5HNldR2EEayOR8CTXM= > Well, most standard set theories contain an Axiom of Infinity, > don't they? I've yet to see any set theory lack this axiom and > still be labeled standard. I have honestly *never* seen the term standard applied to a set theory outside of your threads. -- Even if [...] a communistic regime should come [to China], the old tradition [...] will break Communism and change it beyond recognition, rather than Communism [...] break the old tradition. It must be so. -- Lin Yutang on Socialism with Chinese characteristics in 1935 === Subject: Re: .9 repeating > I have honestly *never* seen the term standard applied to a set > theory outside of your threads. Well, I have. See for example http://plato.stanford.edu/entries/nonwellfounded-set-theory/ -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: .9 repeating sha1:Y8uEWlyTTkbrax5Bacxtd2bCU1o= > I have honestly *never* seen the term standard applied to a set > theory outside of your threads. Well, I have. See for example http://plato.stanford.edu/entries/nonwellfounded-set-theory/ Very good. Here's the quote: Discussion of such sets is very old in the history of set theory, but non-wellfounded sets are ruled out of Zermelo-Fraenkel set theory (the standard theory) due to the Foundation Axiom (FA). Of course, there is no suggestion that standard set theorists reject a non-standard theory such as ZFA, just because the accept a (the) standard theory. Nonetheless, your point is taken: there is at least one description of a specific set theory as the standard theory. -- But you people are scum of the earth who pretend to be something that is clearly beyond you--real mathematicians. I wouldn't be having these problems with Gauss or Euler. I wouldn't be having these problems with Fermat or Archimedes. -- James S. Harris on pretending === Subject: Re: .9 repeating > Of course, there is no suggestion that standard set theorists reject > a non-standard theory such as ZFA, just because the accept a (the) > standard theory. Indeed there is no such suggestion. I am completely baffled by lwalke's talk about acceptance and rejection of this or that. After all, it's not as if those whose main preoccupation is standard set theory go about saying things like I reject this foul circular non-sense! Away with you johnny-come-latelys and your repugnant crank notions!. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon man nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: .9 repeating Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >Anyone who argues that 0.999... < 1 is considered a crank, no matter >how rigorous their argument is. Example please. Show us a case of someone having a rigorous argument that 0.999... < 1 and being considered a crank. -- Richard -- Please remember to mention me / in tapes you leave behind. === Subject: Re: .9 repeating a crank? Of course the poster would be a crank No, that could be interesting. I'd certainly at least explore the system a bit to see what other stuff it could prove. I just wouldn't use it as a model for ordinary arithmetic. Now if the poster *also* claimed that it must be the one and only model for arithmetic (as most cranks insist for similar propositions), then yes - that would make them a crank. > -- the definitions, however rigorous, are nonsensical, and the > poster would be accused of taking words with standard definitions > (such as two, five, and value) and giving them nonstandard > definitions. Of course they'd be nonstandard definitions. So what? At least they'd be well-defined which would make it 100x better than the stuff most cranks come out with. After all, plenty of mathematicians accept 1 + 1 = 0. It's what this discussion medium is fundamentally built on. - Tim === Subject: Re: .9 repeating sha1:NFd8r0eBQ2ZHSRCrelpGPt05C3I= > Anyone who argues that 2 + 2 = 5 is considered a crank, no matter > how rigorous their argument is. Anyone who argues that 0.999... < 1 is considered a crank, no matter > how rigorous their argument is. Well, you may think so. The rest of us have told you time and again it just isn't so. I don't personally know of any interesting theories in which that inequality holds, but that means little. But let's ask another question. Suppose someone repeatedly claims that 0.999... < 1, but offers *nothing at all like* a rigorous argument. Would you call such a person a crank? Or is the mere repetition of claims that contradict basic mathematics a sure sign of intellectual prowess? -- For some reason mathematicians are pushing some weird mind-control crap which works quite well from what I've seen over the last two years, but I'm asking you to snap out of it!!!! -- James S. Harris learns the truth about the Mind Control Lasers === Subject: Re: .9 repeating > Do I actually have to go back and count the number of times that MR > was called a crank? I used to associate crankdom with opposition to ZFC. I now concede > the point and weaken my claim to say that it's not opposition to ZFC > per > se, but lack of acceptance of certain facts as simply true that serves > to > distinguish the cranks from their opponents. But many are still in > denial that they call those who argue in favor of theories that do not > satisfy the conceptions of most mathematicians cranks. Anyone who argues that 2 + 2 = 5 is considered a crank, no matter > how rigorous their argument is. Anyone who argues that 0.999... < 1 is considered a crank, no matter > how rigorous their argument is. The distinctive feature of a crank is that he doesn't have anything that might reasonably be called a theory. Mueckenheim, for example, is just babbling idiotic nonsense, and that his nonsense of today resembles the nonsense of yesterday doesn't make it a theory. Van Bendegem (->wikipedia) is a strict finitist who presents this point of view in a serious way, and is far from crankdom. In which class a person arguing that 2 + 2 = 5 will fall depends on the arguments of that person. If someone argues that 0.999... < 1 by appealing to undefined notions of infinitely smaller and endless repetition then that is garbage. A serious explanation how one can get to 0.999... < 1, and what this inequality then actually means can be found in the paper http://arxiv.org/pdf/0811.0164.pdf === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) > Both standard set theorists and I accept 2 + 2 = 4 as absolutely true. > Both standard geometers and I accept the existence of exactly five > Platonic solids as absolutely true. > Standard set theorists accept Infinity as absolutely true, > At what International Conference of Standard Set Theorists was there > given a definition of 'infinity' When I say Infinity, with a capital I, I usually mean the three-word > phrase Axiom of Infinity. I've noticed, and apparently absorbed, a habit among some sci.math > posters to refer to an axiom of ZFC by a single word name, so they > would say Extensionality when they mean Axiom of Extensionality, > Choice when they mean Axiom of Choice, Replacement when > they mean Schema of Replacement, and so on. Therefore, I've done If this turns out to be confusing, I guess I have to include the words > Axiom of every single time I write the name of an axiom, no matter > how cumbersome it may become. At least for Choice there is the > handy abbreviation AC, but the Axiom of Infinity has no convenient > abbreviation for me to use. Therefore, my statement becomes: Standard set theorists accept the Axiom of Infinity as absolutely > true, but I don't. > Standard analysts accept 0.999... = 1 as absolutely true, but I don't. > I'm not familiar with this series of papers issued by standard > analysts in which it is determined that '0.999... = 1' is absolutely > true, whatever that even means. Here's what I mean by absolutely true: and small values of 5. And they did so rigorously, by giving axioms > and > definitions of large value, small value, and so on -- definitions > that > satisfy eliminability and anticreativity -- and prove using only those > axioms, definitions, and first order logic with identity that 2 + 2 = > 5, a > proof that would be just as rigorous as any proof of ZFC is. Would that proof be taken seriously, or would the poster be considered > a crank? Of course the poster would be a crank -- the definitions, > however rigorous, are nonsensical, and the poster would be accused > of taking words with standard definitions (such as two, five, and > value) and giving them nonstandard definitions. In other words, the > statement 2 + 2 = 4 would be considered absolutely true, and no > theory, no matter how rigorous, would ever be considered if it were to > contradict that basic fact of arithmetic. Notice that even MoeBlee himself mentioned a similar concept, > earlier in this thread: Or because the mathematician finds the axiom of choice fits his > conception of sets, or even that the axiom of choice is true to that > conception, or simply true. I'm using the words absolutely true the same way that MoeBlee > used the words simply true -- 2 + 2 = 4 fits the mathematician's > conception of numbers, the Axiom of Infinity fits the standard set > theorist's conception of sets, and 0.999... = 1 fits the standard > analyst's conception of analysis. Perhaps, from now on, I'll replace my phrase absolutely true > with MoeBlee's simply true, in order to emphasize that I'm > using the phrase to mean the exact same thing. Therefore, my statement becomes: Standard analysts accept 0.999... = 1 as simply true, but I don't. The point of all this discussion is that many posters believe that > I'd defend any crazy theory, even ones which argue that 2 + 2 = 5, > since the theories that I do defend are, in their opinion, just as > crazy as those which prove that 2 + 2 = 5. So I was trying to > explain the difference between 2 + 2 = 5 and 0.999... < 1 such > that I'd defend theories which argue the latter, but not those which > argue the former. Still, I wonder whether my explanation would > convince anyone, since in the eyes of most, there's no real > difference between the former and the latter. > Therefore, we will continue be labeled cranks by those Platonists > who do accept [the Axiom of] Infinity and 0.999... = 1 as [simply] true. > You've not shown a SINGLE ACTUAL person who has defined 'crank' in > such a way that one is a crank merely for not accepting that [the Axiom > of] Infinity and the the statement 0.999... = 1' are [simply] true. Do I actually have to go back and count the number of times that MR > was called a crank? I used to associate crankdom with opposition to ZFC. I now concede > the point and weaken my claim to say that it's not opposition to ZFC > per > se, but lack of acceptance of certain facts as simply true that serves > to > distinguish the cranks from their opponents. But many are still in > denial that they call those who argue in favor of theories that do not > satisfy the conceptions of most mathematicians cranks. Anyone who argues that 2 + 2 = 5 is considered a crank, no matter > how rigorous their argument is. Anyone who argues that 0.999... < 1 is considered a crank, no matter > how rigorous their argument is. Its less by the nonzero infinitely small. It is the closest thing. Mitch Raemsch === Subject: Re: .9 repeating posting-account=euF15goAAACbw3KIqEWxZHCIPUc2KPmU .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > Notice there are some objects in ZFC, such as cardinals, which > are not divisible (aleph 0/2 is an awkward concept at best, and > aleph 0/aleph 0 is impossible to define), while there are others, > such as the real numbers, which are certainly divisible. > Absolutely. Divisibility isn't defined for platonic solids -- that > doesn't mean they are not part of mathematics. The problem with > Mitch's pronouncements, is that they are just that -- statements with > no mathematical content. What he (and perhaps you) can't see is that I > can just as well define chocolate sundae as the next platonic solid > in Extended Geometry, with comments that the polygons forming its > faces have a number of sides called strawberry (not a conventional > number, but part of the Extended Numbers I'm using),... and so on and > so on. I've noticed how Chandler seems to have some sort of obsession with ice cream -- first in the WM threads, where he uses vanilla to mean finite and strawberry to mean countably infinite, and now here he is with the ice cream again in this thread. > Why don't you take up some other causes? What about people who think > there ought to be more Platonic solids? In a 21st-century economy, > five is just not enough! > That one's easy! We simply switch from three-dimensional up to > four-dimensional geometry. > No. Solid means three-dimensional. What about non-Euclidean geometry? I've rarely seen any discussion of three-dimensional non-Euclidean geometry. I wonder whether there can be anywhere from zero Platonic solids to six or more in such a geometry, or whether it is fixed at five for all such geometries. But now let's go back to the main point that Chandler is most likely trying to make with this mental exercise. Let's start by considering the following three statements: 1) 2 + 2 = 4 (mentioned by Ullrich in another thread). 2) There are exactly five Platonic solids (Chandler). 3) 0.999... cannot equal any number other than 1. Obviously, all three statements are true in standard mathematics. But MR claims that 3) is false. And so I've tried to find some nonstandard analysis in which 3) can be true. But now we see the problem. If I can attempt to find a nonstandard analysis in which 3) is true, then what's stopping me from attempting to find nonstandard math in which 1) or 2) are true? And if I were to say that theories in which 1) or 2) are true aren't worth considering, then why can't I go one step further and say that a theory in which 3) is true isn't worth considering? I believe that there are some statements are absolutely true in a sense that I'll only consider theories in which their negations aren't known to be provable. Clearly 1) is one of them. There's an old joke about how 2 + 2 = 5 for large values of 2 or small values of 5, but they're just jokes. I have yet to be convinced by any argument that 2 + 2 is anything other than 4. Therefore, to me, 2 + 2 = 4 -- the arithmetic of small finite numbers -- is absolutely true. If a so- called crank posted that 2 + 2 is anything other than 4, I wouldn't even bother to post in the thread. Barring any forthcoming argument about the Platonic solids in non-Euclidean geometry, I accept 2) as absolutely true. If a so-called crank posted that there are six Platonic three-dimensional solids, I wouldn't even bother to post in the thread (once again, barring any counterexample in non-Euclidean geometry). This is essentially what mathematical Platonism is. Now, here's the debate. To the standard analysts, 3) is absolutely true in exactly the same way that 1) and 2) are absolutely true. To them, anyone who argues against 1) is a crank, anyone who argues against 2) is a crank, and anyone who argues against 3) is a crank. So we see that the standard analysts accept more statements as absolutely true than I do -- and this is the essential difference between the standard analysts and myself. They are as unswayed by attempts to come up with a theory in which 3) is false in the same way that I am unswayed by attempts to come up with a theory in which either 1) or 2) is false. In the eyes of the standard analyst, there is no essential difference between 3) vs. 1) and 2). And so, one asks, what is the difference between 3) vs. 1) and 2), such that I won't accept 3) as absolutely true but will accept 1) and 2)? I admit that it's tough for me to answer, but here are some factors: 1. The physical universe. I can verify that 2 + 2 = 4 in the physical universe, but not 0.999... = 1. Now I know that mathematics is not physics, and so there's no need for anyone to repeat that standard theory proves many theorems that are not verifiable in the physical universe. But I still look to the physical universe to determine what statements I want to consider as absolutely true. I admit from first order logic applied to the axioms of ZFC, we can prove that 0.999... = 1. But I don't accept 0.999... = 1 as absolutely true in the same way that 2 + 2 = 4 is true. To me, there's a difference between saying first-order logic applied to ZFC proves phi and the statement phi is absolutely true. In particular, I accept many fewer statements about infinity as true than the standard set theorists. 2. The frequency and and strength of the arguments. If posts on sci.math appeared every couple of months or so arguing that there were six Platonic solids, and I found some of those arguments to be compelling, then I might not consider 2) as absolutely true. But since I haven't seen such posts, I consider 2) as absolutely true. On the other hand, arguments that 0.999... < 1 appear regularly. They make arguments about infinitesimals that are interesting, at least from my perspective. Therefore, I don't accept 3) as absolutely true, and so I entertain theories in which they aren't true. Of course, these arguments aren't compelling to standard analysts. So they don't entertain theories in which 0.999... < 1, and therefore they consider those who make such arguments to be cranks. Notice that many so-called cranks, most likely including MR, consider the negation of 3) to be absolutely true. MR appears convinced that 0.999... is strictly less than 1, and therefore doesn't accept arguments that 0.999... really does equal 1. I myself accept neither 3) not its negation as absolutely true. So I don't reject ZFC in which 3) is provable, not do I reject MR's potential theory in which its negation would be provable. Therefore I accept as absolutely true fewer statements than both the standard analysts and most cranks. I know that the standard analysts won't be convinced by this post, and they will continue to compare my failure to accept 3) as absolutely true to someone who doesn't accept 1) or 2) as absolutely true. === Subject: Re: .9 repeating posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) I've noticed how Chandler seems to have some sort of obsession with > ice cream -- first in the WM threads, where he uses vanilla to mean > finite and strawberry to mean countably infinite, and now here > he > is with the ice cream again in this thread. Well spotted. 2) There are exactly five Platonic solids (Chandler). > 3) 0.999... cannot equal any number other than 1. Excellent! > Obviously, all three statements are true in standard mathematics. No. All three statements are true if we mean by them the usual thing. Nothing to do with standard mathematics, within which all three statements can also be false, if we are talking about unusual things: arithmetic modulo 3, 4D space, some properly formalised system that hasn't been presented yet, respectively. > But MR claims that 3) is false. And so I've tried to find some nonstandard > analysis in which 3) can be true. [I think you have true and false slightly confused by the negation in 3)... but no matter] > But now we see the problem. If I can attempt to find a nonstandard > analysis in which 3) is true, then what's stopping me from attempting > to find nonstandard math in which 1) or 2) are true? Only you see the problem. Of course it's easy to construct _some_ system or other in which any of 1) 2) 3) is false, but in all cases the constituents of the statement mean something other than their usual meaning. Brian Chandler === Subject: Re: .9 repeating true in exactly the same way that 1) and 2) are absolutely true. To > them, anyone who argues against 1) is a crank, anyone who argues > against 2) is a crank, and anyone who argues against 3) is a > crank. That's actually completely false. Mere assertion of a statement false in standard mathematics is not enough to label someone as a crank. At that point they may merely be unclear about what system they're working with, mistaken about what the terms mean, or how mathematical reasoning works. The hallmark of a crank is to persistently reject or ignore efforts to clarify and/or correct any of those possibilities. Especially how mathematical reasoning works. Some are borderline, accepting some clarifications and corrections but persistently rejecting or ignoring others. In the case of 0.9(repeating) =/= 1, the terms have a well-defined standard meaning, and solid mathematical reasoning that requires that 0.9(repeating) with that meaning is equal to 1. Exploring alternative definitions is fine - but MR isn't doing that, and has rejected previous attempts to do that. Now such attempts are simply ignored by MR, as you are seeing. Making up some other system and asserting that MR could be using that system is disingenuous. Explore some systems if you like, in which 0.9(repeating) =/= 1, but it won't have anything to do with MR. Most of us already know from previous experience that MR wouldn't even recognize a mathematical system, let alone be capable of reasoning in one. - Tim === Subject: Re: .9 repeating posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > To the standard analysts, 3) is absolutely > true in exactly the same way that 1) and 2) are absolutely true. To > them, anyone who argues against 1) is a crank, anyone who argues > against 2) is a crank, and anyone who argues against 3) is a > crank. And this was a resolution adopted at exactly which International Conference of the Standard Analysts? MoeBlee === Subject: Re: .9 repeating posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > .9r is short of one mathematically by a defined infinitesimal. In ordinary notation '.999...' stands for a certain limit, which is 1. If you have some other system and notation by which you construe '. 999...' as defined, then you are welcome to state your primitives, formation rules, axioms, and definitions. MoeBlee === Subject: Re: .9 repeating Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >Right below it. The closest thing to 1 but <1. What's the mean of it and 1? -- Richard -- Please remember to mention me / in tapes you leave behind. === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) >Right below it. The closest thing to 1 but <1. What's the mean of it and 1? -- Richard > -- > Please remember to mention me / in tapes you leave behind. Zero and one are the beginning of math. That is their meaning. === Subject: Re: .9 repeating Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >Right below it. The closest thing to 1 but <1. > What's the mean of it and 1? >Zero and one are the beginning of math. That is their meaning. Ha ha. You seem to be unable to deal with these questions. -- Richard -- Please remember to mention me / in tapes you leave behind. === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) >Right below it. The closest thing to 1 but <1. > What's the mean of it and 1? >Zero and one are the beginning of math. That is their meaning. Ha ha. You seem to be unable to deal with these question How are you going to argue if I don't define 0 and 1? Mitch Raemsch === Subject: Re: .9 repeating Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >How are you going to argue if I don't define 0 and 1? We won't argue, we'll just make fun of you. -- Richard -- Please remember to mention me / in tapes you leave behind. === Subject: Re: .9 repeating posting-account=DLD3MQkAAACJxulKt9xouw3DPpXKssCI GTB5; SLCC1; .NET CLR 2.0.50727; .NET CLR 1.1.4322; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) >Right below it. The closest thing to 1 but <1. > What's the mean of it and 1? >Zero and one are the beginning of math. That is their meaning. > Ha ha. > You seem to be unable to deal with these question How are you going to argue if I don't define 0 and 1? You seem to be using a different definition than everyone else. The standard definition for 1 is that .9r and 1 are synonyms. You can easily prove that you are right by showing us the error in this simple proof: http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/ If you cannot find an error then we have a clear proof that .9r==1. If you can find an error in the proof then you are right. It seems very simple to me. === Subject: Re: .9 repeating posting-account=5ApcPgoAAABKcgEyKsQmJVb3Rz63IGGL .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; WWTClient2),gzip(gfe),gzip(gfe) >Right below it. The closest thing to 1 but <1. > What's the mean of it and 1? >Zero and one are the beginning of math. That is their meaning. > Ha ha. > You seem to be unable to deal with these question > How are you going to argue if I don't define 0 and 1? You seem to be using a different definition than everyone else. The > standard definition for 1 is that .9r and 1 are synonyms. One is wrong. It is short by the infinitely small. Mitch Raemsch You can easily prove that you are right by showing us the error in > this simple proof: http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0.999eq1/ If you cannot find an error then we have a clear proof that .9r==1. If you can find an error in the proof then you are right. It seems > very simple to me. === === Subject: How to take 200th order derivative, and then evaluate it numerically? We need to take the 200th order derivative of a complicated formula, and then evaluate it numerically. What's the best way to handle this? More specifically, we figured that it's impossible to do this via finite difference, i.e. do everything completely in the numerical domain, because the noise will be huge and error will dominate. So a plan was to first obtain the 200th order derivative thru symbolic calculation in Maple, Matlab, Mathematica, and then copy the huge result and somehow make it into a form that is numerically evaluable either in Matlab or C++. Then evaluate that huge expression numerically. Still, that sounds daunting, the symbolic result of 200th order derivative will be huge and we are not sure if Maple or Mathematica can handle it. Another possibility is to do some sort of Automatic Differentiation. But we are new to AD. Is it possible that with the help from an AD package, we just need to give inputs of the parameter values, and the package will crank out the numerical result of the 200th order derivative with almost no error? We see that lots of free packages are in C/C++ or Fortune, which are not convenient for fast prototyping(we are at evaluating stage, if this idea doesn't work, we don't want to spend too much time on it). So are there free AD packages that can go with Matlab or Mathematica or Maple that can take 200th order differentiation and are convenient for prototyping? Which one is the best AD package that we could try on? If it doesn't work, then we would discard this crazy idea of taking 200th order derivative completely. Please shed some lights on us! === Subject: Re: How to take 200th order derivative, and then evaluate it numerically? posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Hi all, We need to take the 200th order derivative of a complicated formula, > and then evaluate it numerically. What's the best way to handle this? More specifically, we figured that it's impossible to do this via > finite difference, i.e. do everything completely in the numerical > domain, because the noise will be huge and error will dominate. So a plan was to first obtain the 200th order derivative thru symbolic > calculation in Maple, Matlab, Mathematica, and then copy the huge > result and somehow make it into a form that is numerically evaluable > either in Matlab or C++. Then evaluate that huge expression > numerically. Still, that sounds daunting, the symbolic result of 200th > order derivative will be huge and we are not sure if Maple or > Mathematica can handle it. Another possibility is to do some sort of Automatic Differentiation. > But we are new to AD. Is it possible that with the help from an AD > package, we just need to give inputs of the parameter values, and the > package will crank out the numerical result of the 200th order > derivative with almost no error? We see that lots of free packages are in C/C++ or Fortune, which are > not convenient for fast prototyping(we are at evaluating stage, if > this idea doesn't work, we don't want to spend too much time on it). > So are there free AD packages that can go with Matlab or Mathematica > or Maple that can take 200th order differentiation and are convenient > for prototyping? Which one is the best AD package that we could try > on? If it doesn't work, then we would discard this crazy idea of > taking 200th order derivative completely. Please shed some lights on us! > The first question is what the heck are you doing? If you have a formula, you can use a CAS like Mathematica and ask it for the 200th derivative and see if it converges on returning a formula. of course, that in itself might be suspect. If you are strictly using numerical methods - toss this statement out the window and re-evaluate what you are asking for because on the surface it sounds nonsensical. ~A === Subject: Re: How to take 200th order derivative, and then evaluate it numerically? > Hi all, We need to take the 200th order derivative of a complicated formula, > and then evaluate it numerically. My first question: why? I can see why you might want to take the 1st derivative, or the 2nd derivative, or maybe even the 3rd or 4th derivative of a function. The 200th? How are you planning to use the value you receive from this procedure? *snip* -- Steve Lord slord@mathworks.com === Subject: Re: How to take 200th order derivative, and then evaluate it numerically? >Hi all, We need to take the 200th order derivative of a complicated formula, >and then evaluate it numerically. What's the best way to handle this? Firs, you should think 10 times whether you need this. Seems to be a nonsense for me. A.L. === Subject: Re: average = ??? posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2009011913 Firefox/3.0.6,gzip(gfe),gzip(gfe) > consider a Coo function of z : f(z) consider a sequence starting somewhere at some z0. f(z0),f(f(z0)),f(f(f(z0))),... what is the average of this ? sure if the iterations go to oo , oo is the average. also if the iterations converge to number A , A is the average. but what if the iterations dont converge , what is the average then ? in many cases - i guess - a fixed point of f(z). but its not always a fixed point is it ?? or am i too pessimistic here ? limit cycles and saddle points for example lead me to believe its not always a fixed point ... further if a function has more than one fixed point ? on the other hand , chaos does not occur in 2 dimensions , so maybe the average is a fixed point afterall ? Of course not. Take the function f which rotates the plane around the origin by any fixed rational-multiple-of-pi angle around the origin. Then the limit of the average of the iterates of the point (1,0) is the origin. Now pick a diffeomorphism h of the plane which is the identity outside of the disk or radius 1/2 centered at the origin, and such that the h(0,0) != (0,0). Consider g = h^{-1} . f . h. Then the orbit of (1,0) under g is the same thing as the orbit under f, so in particular, the limit of its averages is still the origin. But the origin is not a fixed point of g. -- m === Subject: Re: average = ??? > consider a Coo function of z : f(z) consider a sequence starting somewhere at some z0. f(z0),f(f(z0)),f(f(f(z0))),... what is the average of this ? sure if the iterations go to oo , oo is the average. Just out of curiosity, can you prove this? For example, what if the iterations go to oo VERY, VERY slowly, so that maybe we don't leave the unit disk until after a Graham's number of iterations? Dave L. Renfro P.S. To others, yes, I can prove or disprove this, as the case may be. === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light <49b91708$0$5481$bbae4d71@news.suddenlink.net> <49b93f6a$0$5498$bbae4d71@news.suddenlink.net> posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > does light have an absolute minimum speed under which it ceases to be > light? > There isn't one. All speeds are relative. The red tail light from my car > will never catch up to the front of the car, it's going the wrong way. you can see it in rear view mirror, right, or if you were to do > rubbernecking? any way, that's not how i meant it. both the light travel > path and the observer have to have same reference. Yes it does--liht reaches the plasmonic band of the material and -Aut === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light <49ba1ffc$0$4046$afc38c87@news.optusnet.com.au> posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > The above is conjectural, but what is not conjectural is that the Sun does > have a very long radius of matter around it, above the surface, similar to > Earth's atmosphere. So rays from the stars *must* bend as they go through > it. They just have to. The Sun *must* act like any optical lens. To > pretend it does not, to justify the light bending via absurd theories of > general relativity making the Sun act like a gravitational lens, is simply > wrong. However, it is on this one experiment (comparing positions of stars > at night - without sun - and their positions when the sun is eclipsed by the > moon) that the whole experimental basis of GR rests. They would already know if it were the solar wind adrag makun the lens. But the sun is a body, so it keeps everywhere in the univers. No known el.8fctric body (el.8fctr.98n, quark) is insubject to mass, so el.8fctric potentials must be tyen intom gravital potentials--so a gravital lens is inevitabil. -Aut === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) >so, i am speculating that light speed is > amenable to manipulation from its fastest speed to down to blackhole speed > of zero. which raises the question then, is it possbile that some forces > might actually aid the light travel faster than what its normal speed is. Fastness has nothing to do with speed. By the way, look up Alternate View Column for such diael.8fctrics. > Well yes, the speed of light does vary with the speed of the object > casting the light, just like any thing else. If you throw a ball at > speed v from a train moving with the velocity V, in the direction of > travel, the speed of the ball with respect to the ground is V+v. Or v > - V, if you throw it against the direction of travel. So if you are > flying in a spacecraft at 2c, where c is the speed of light, then a > beam of light thrown in the direction of travel with be 2c+c=3c, and > in the other direction 2c-c = c > This speed is with respect to the ether, or the all-pervading medium > through which the electromagnetic waves travel. The aither is epifainomenaic of a body or bodies; your transforms don't exist. === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > Friends, Eppur si muove or Nonetheless, it moves, said Galileo about the Earth > under his breath at his inquisition where he had to formally state the > supremacy of the Aristotlian model over the Copernican. That is, when he > was forced to state that the Earth is still. Check out www.users.bigpond.com/adda1234/MMInt.htm which is essentiallly a restatement of the works of Galileo and Newton, and > debunking the modern snake oil Aristotlians like Einstein and Hawking (who > now rule, ugh). Earth has to be still. You may need aspirin. I think you forgot masses. (I didn't read your essay.) === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light >The area around the sun has matter (extended solar atmosphere) and it >*has* to be denser than vacuum. So the sun is acting like any normal >optical lens. > Actualy, there would be an energy gradient that gets less dense as you > get > away from the sun. Whether it be particulate or electromagnetic (same > thing > realy I think) energy it would exist. > And, that would bend light as you suggest I believe. I'd never thought > about that before. > Whether you're actualy right or otherwise, I thank you.. > Vince Amazing what a little thinking can do. One thing you can be certain > of. Einstein was a dork, whether he was otherstupid or actually wrong Hear, hear. May all the world think so, and more importantly, so so. AB: Oops, I meant say so. Sorry! It it values it sanity, health and also wealth. Bengal Tiger Arindam Banerjee. .- Hide quoted text - - Show quoted text - === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Do you assume that the ether is at rest? >Most certainly. To quote from Pages 112-113 about the nature of ether from the book Physics of the Atom by Wehr and Richards: begin quotation Every wave motion has something that 'waves'. Sound waves have air and water waves have water. Surely, it was argued, light waves must involve the waving of something even in free space. No one knew what it was, but it was given the name luminiferous ether'. Light passes through many kinds of materials. It passes through relatively heavy materials like glass and it passes through the nearly perfect vacuum that must lie between the stars and the earth. Thus ether must permeate all of space. Light is a transverse wave motion. Here is the error. . In nature no seperate transverse waves or longitudinal waves. There are only the play of the strain and stress in a medium. Always are the two components. But we have only seperate math equations for ideal simplified media. No equations for real waves. Here is the same situation like with EM. We have the equations for the hydraulic analogy and we have not such for REAL gas analogy. >This comes out of Maxwell's theory and from many experimental observations, particularly those on polarized light. This implies that the ether is a solid. Transverse waves involve shear forces and can occur only in solids which can support shear. Sound waves in air must be longitudinal because of this fact. Furthermore, the ether must be a rigid solid. Now we know more about waves. Always are the both components. But the fundamental assumption is that the ether is a huge sold, which *must* be at rest as a consequence. What is obligatory: assumption or experiments? S* === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Do you assume that the ether is at rest? >Most certainly. >To quote from Pages 112-113 about the nature of ether from the book > Physics of the Atom by Wehr and Richards: > begin quotation > Every wave motion has something that 'waves'. Sound waves have air > and water waves have water. Surely, it was argued, light waves must > involve the waving of something even in free space. No one knew what > it was, but it was given the name luminiferous ether'. > Light passes through many kinds of materials. It passes through > relatively heavy materials like glass and it passes through the nearly > perfect vacuum that must lie between the stars and the earth. Thus > ether must permeate all of space. Light is a transverse wave motion. Here is the error. . In nature no seperate transverse waves or > longitudinal waves. There are only the play > of the strain and stress in a medium. Always are the two components. But > we > have only seperate math equations for ideal simplified media. No equations > for real waves. only oscillating around their mean position. Just like a Mexican wave in any stadium. The spectators do not move, they only jump up and down as the next person jumps up and down. The faster they jump up and down, the faster the wave (or disturbance) travels. Now jumping up and down is *transverse* wave motion, for the movement is perpendicular to the direction of the wave. If they moved *sideways and back*, that would be *longitudinal* wave motion. So of course there are two components of wave motion - in some media there would be more of one than other. So light is a transverse wave motion, while sound in air is longitudinal. In any case, whether the movement of light is transverse or longitudinal through ether, is just not the point. The point is that you cannot fix your equipment in ether, which is the solid permeating the universe. That is simply impossible. So the Michelson-Morley experiment could *never* have found the velocity of the earth with respect to the fixed ether. > Here is the same situation like with EM. We have the equations for the > hydraulic analogy and we have not such for REAL gas analogy. You are not making any sense, so far as the context is concerned. The real point is that ether is a solid which pervades the whole universe. Light is carried by it, as is other electromagnetic waves. >This comes out of Maxwell's theory and from many experimental > observations, particularly those on polarized light. This implies > that the ether is a solid. Transverse waves involve shear forces and > can occur only in solids which can support shear. Sound waves in air > must be longitudinal because of this fact. Furthermore, the ether must > be a rigid solid. Now we know more about waves. Always are the both components. No. Do study the motion of waves in hollow waveguides. There are always TE and TM modes of propagation, depending upon the geometry of the waveguide. They come from Maxwell's boundary conditions. Read some basic textbook in microwave engineering. >But the fundamental assumption is that the ether is a huge sold, which > *must* be at rest as a consequence. What is obligatory: assumption or experiments? Experiments based upon false assumptions have to be wrong. No matter how many times they are repeated, they will always give wrong results when there are false assumptions make. It was falsely assumed in the MMI expt. that the equipment would not move in ether, like it was stuck as the floats were stuck in the river bed in the analogy that gave us the famously wrong Lorentz transformation. But you just cannot do that. The equipment moves with the movement of the earth in ether - we just cannot say that it is stuck like the floats were stuck in the river bed. That the ether pervades the universe is more like an *axiom*, which works as the fundamental assumption like any axiom. It is justified by the fact that light, high frequencey gamma rays, low frequency radio all can go through vacuum and solids. Wave nature is shown by all these radiations, and we cannot have a wave motion without a media with minute elements that oscillate. This media is called ether, through which all electromagnetic rays travel. Since experiment shows that 1. em radiation is a wave motion 2. wave motion needs media (like humans in human Mexican wave in stadia , sound in air/solid, water waves in water) we can with logic say that it is a very likely assumption that em radiation needs a medium and that medium is called *ether*. So ultimately I leave to the world to decide what is more right - the assumption that ether exists as a solid throughout the whole universe, or that the assumption is right that the equipment of the MMI were actually stuck in the rigid ether when the Earth was moving. Arindam Banerjee > S* > === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Do you assume that the ether is at rest? >Most certainly. >To quote from Pages 112-113 about the nature of ether from the book > Physics of the Atom by Wehr and Richards: There no word about Sagnac (1913) and Michelson-Gale (1925). > Here is the same situation like with EM. We have the equations for the > hydraulic analogy and we have not such for REAL gas analogy. You are not making any sense, so far as the context is concerned. The > real point is that ether is a solid which pervades the whole universe. > Light is carried by it, as is other electromagnetic waves. In the book by Wehr and Richards no information that Maxwell used for electricity the hydraulic analogy. Now we know that in conductors is electron gas. >This comes out of Maxwell's theory and from many experimental > observations, particularly those on polarized light. Maxwell's theory was checked by Helmholtz and Hertz. It was dipol with the plates or the balls on the ends. Hydraulic analogy radiate from dipol. Gas analogy radiate from the ends (there appear and disappear the electric charges). Which one do you prefer? >This implies > that the ether is a solid. Transverse waves involve shear forces and > can occur only in solids which can support shear. Sound waves in air > must be longitudinal because of this fact. Furthermore, the ether must > be a rigid solid. > Now we know more about waves. Always are the both components. No. Do study the motion of waves in hollow waveguides. There are always > TE and TM modes of propagation, depending upon the geometry of the > waveguide. They come from Maxwell's boundary conditions. Read some basic > textbook in microwave engineering. Maxwell's (Heaveside) hydraulic analogy is a history. >But the fundamental assumption is that the ether is a huge sold, which > *must* be at rest as a consequence. > What is obligatory: assumption or experiments? Experiments based upon false assumptions have to be wrong. No matter how > many times they are repeated, they will always give wrong results when > there are false assumptions make. It was falsely assumed in the MMI expt. > that the equipment would not move in ether, like it was stuck as the > floats were stuck in the river bed in the analogy that gave us the > famously wrong Lorentz transformation. But you just cannot do that. The > equipment moves with the movement of the earth in ether - we just cannot > say that it is stuck like the floats were stuck in the river bed. That the ether pervades the universe is more like an *axiom*, which works > as the fundamental assumption like any axiom. It is justified by the fact > that light, high frequencey gamma rays, low frequency radio all can go > through vacuum and solids. Wave nature is shown by all these radiations, > and we cannot have a wave motion without a media with minute elements that > oscillate. This media is called ether, through which all electromagnetic > rays travel. Since experiment shows that 1. em radiation is a wave motion 2. wave > motion needs media (like humans in human Mexican wave in stadia , sound in > air/solid, water waves in water) we can with logic say that it is a very > likely assumption that em radiation needs a medium and that medium is > called *ether*. So ultimately I leave to the world to decide what is more right - the > assumption that ether exists as a solid throughout the whole universe, or > that the assumption is right that the equipment of the MMI were actually > stuck in the rigid ether when the Earth was moving. Some solids can flow (metals). So the ether may be elastic and can flow. S* === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Do you assume that the ether is at rest? >Most certainly. >To quote from Pages 112-113 about the nature of ether from the book > Physics of the Atom by Wehr and Richards: There no word about Sagnac (1913) and Michelson-Gale (1925). > Here is the same situation like with EM. We have the equations for the > hydraulic analogy and we have not such for REAL gas analogy. > You are not making any sense, so far as the context is concerned. The > real point is that ether is a solid which pervades the whole universe. > Light is carried by it, as is other electromagnetic waves. In the book by Wehr and Richards no information that Maxwell used for > electricity the hydraulic analogy. Now we know that in conductors is > electron gas. >This comes out of Maxwell's theory and from many experimental > observations, particularly those on polarized light. Maxwell's theory was checked by Helmholtz and Hertz. It was dipol with the > plates or the balls on the ends. Hydraulic analogy radiate from dipol. Gas > analogy radiate from the ends (there appear and disappear the electric > charges). > Which one do you prefer? >This implies > that the ether is a solid. Transverse waves involve shear forces and > can occur only in solids which can support shear. Sound waves in air > must be longitudinal because of this fact. Furthermore, the ether must > be a rigid solid. > Now we know more about waves. Always are the both components. > No. Do study the motion of waves in hollow waveguides. There are always > TE and TM modes of propagation, depending upon the geometry of the > waveguide. They come from Maxwell's boundary conditions. Read some basic > textbook in microwave engineering. Maxwell's (Heaveside) hydraulic analogy is a history. Analogies are dangerous, as I have just pointed out. If you want to say that light or em waves have a longitudinal component, then you have to do better than analogies. If you read the following textbook, Electromagnetic Waves and Radiating Systems (Chapter 8.01) by Edward C Jordan and Keith G Balmain, you will find that the Ez or Hz component has to be zero for the rectangular waveguide. For the TM mode, Hz = 0, and the electric field does have a component in the direction of propagation. This is the nearest one may get to longitudinal-like propagation of em waves. In free space, the excitation of the electric field is always transverse to the direction of propagation, whether or not the wave be polarised. >But the fundamental assumption is that the ether is a huge sold, which > *must* be at rest as a consequence. > What is obligatory: assumption or experiments? > Experiments based upon false assumptions have to be wrong. No matter how > many times they are repeated, they will always give wrong results when > there are false assumptions make. It was falsely assumed in the MMI expt. > that the equipment would not move in ether, like it was stuck as the > floats were stuck in the river bed in the analogy that gave us the > famously wrong Lorentz transformation. But you just cannot do that. The > equipment moves with the movement of the earth in ether - we just cannot > say that it is stuck like the floats were stuck in the river bed. > That the ether pervades the universe is more like an *axiom*, which works > as the fundamental assumption like any axiom. It is justified by the > fact that light, high frequencey gamma rays, low frequency radio all can > go through vacuum and solids. Wave nature is shown by all these > radiations, and we cannot have a wave motion without a media with minute > elements that oscillate. This media is called ether, through which all > electromagnetic rays travel. > Since experiment shows that 1. em radiation is a wave motion 2. wave > motion needs media (like humans in human Mexican wave in stadia , sound > in air/solid, water waves in water) we can with logic say that it is a > very likely assumption that em radiation needs a medium and that medium > is called *ether*. > So ultimately I leave to the world to decide what is more right - the > assumption that ether exists as a solid throughout the whole universe, or > that the assumption is right that the equipment of the MMI were actually > stuck in the rigid ether when the Earth was moving. Some solids can flow (metals). So the ether may be elastic and can flow. Matter exists normally in three states - gas, liquid and solid. It is the temperature to which it is subjected, that determines the state. Under normal temperature (where we humans live) changes of state do not normally take place for matter. Unless we are talking about boiling water from ice cubes! The very definition of a solid comes from its lack of flow - thus in all the spectators taking part in a Mexican wave in a football or (alas) cricket stadium. But there are amorphous solids like chalk, and viscous liquids like glass. In any case, ether is held to be a highly elastic solid permeating the whole universe. > S* === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Some solids can flow (metals). So the ether may be elastic and can flow. Matter exists normally in three states - gas, liquid and solid. It is the > temperature to which it is subjected, that determines the state. Under > normal temperature (where we humans live) changes of state do not normally > take place for matter. Unless we are talking about boiling water from ice > cubes! The very definition of a solid comes from its lack of flow Metals are solids and can flow. other, Only in ionic crystals. > like all the spectators taking part in a Mexican wave in a football or > (alas) cricket stadium. But there are amorphous solids like chalk, and > viscous liquids like glass. In any case, ether is held to be a highly > elastic solid Which can flow > permeating the whole universe. S* > === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Some solids can flow (metals). So the ether may be elastic and can flow. > Matter exists normally in three states - gas, liquid and solid. It is > the temperature to which it is subjected, that determines the state. > Under normal temperature (where we humans live) changes of state do not > normally take place for matter. Unless we are talking about boiling > water from ice cubes! The very definition of a solid comes from its lack > of flow Metals are solids and can flow. Mercury is a metal, it flows, and it is not a solid at room temperatures. each other, Only in ionic crystals. > like all the spectators taking part in a Mexican wave in a football or > (alas) cricket stadium. But there are amorphous solids like chalk, and > viscous liquids like glass. In any case, ether is held to be a highly > elastic solid Which can flow As per the axiom, the whole universe is filled with ether, and we all move in it. The ether stays put, and we can never know our velocity with respect to the ether. We have currently no way of knowing whether the ether can move or not. What with the speed of light being the same whichever way we measure it on earth, it seems very likely that ether does not move at all. > permeating the whole universe. > S* > === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light <5KCul.28453$cu.6486@news-server.bigpond.net.au> <%Crvl.28974$cu.8727@news-server.bigpond.net.au> posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > Some solids can flow (metals). So the ether may be elastic and can flow. > Matter exists normally in three states - gas, liquid and solid. It is > the temperature to which it is subjected, that determines the state. > Under normal temperature (where we humans live) changes of state do not > normally take place for matter. Unless we are talking about boiling > water from ice cubes! The very definition of a solid comes from its lack > of flow > Metals are solids and can flow. Mercury is a metal, it flows, and it is not a solid at room temperatures. > each other, > Only in ionic crystals. > like all the spectators taking part in a Mexican wave in a football or > (alas) cricket stadium. But there are amorphous solids like chalk, and > viscous liquids like glass. In any case, ether is held to be a highly > elastic solid > Which can flow As per the axiom, the whole universe is filled with ether, and we all move > in it. The ether stays put, and we can never know our velocity with respect > to the ether. We have currently no way of knowing whether the ether can > move or not. What with the speed of light being the same whichever way we > measure it on earth, it seems very likely that ether does not move at all. The aither takes on whichever state or speed is within, as it needs a body. Celerity, horizons, and alfa are all time-variant, so the aither too. === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Some solids can flow (metals). So the ether may be elastic and can > flow. > Matter exists normally in three states - gas, liquid and solid. It is > the temperature to which it is subjected, that determines the state. > Under normal temperature (where we humans live) changes of state do not > normally take place for matter. Unless we are talking about boiling > water from ice cubes! The very definition of a solid comes from its > lack of flow > Metals are solids and can flow. Mercury is a metal, it flows, and it is not a solid at room temperatures. > each other, > Only in ionic crystals. > like all the spectators taking part in a Mexican wave in a football or > (alas) cricket stadium. But there are amorphous solids like chalk, and > viscous liquids like glass. In any case, ether is held to be a highly > elastic solid > Which can flow As per the axiom, the whole universe is filled with ether, and we all move > in it. The ether stays put, and we can never know our velocity with > respect to the ether. We have currently no way of knowing whether the > ether can move or not. What with the speed of light being the same > whichever way we measure it on earth, it seems very likely that ether does > not move at all. > To clarify what I mean by the important word axiom - an axiom is a construction of thought that is a fundamental for further development, and as such beyond the scope of dispute. When axioms are upset, one upsets an entire thought structure. So in geometry it is axiomatic that a line has no width. In practice, in drawing a line, it must have some width - but in theory it does not have any width. > permeating the whole universe. > S* === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light <5KCul.28453$cu.6486@news-server.bigpond.net.au> <%Crvl.28974$cu.8727@news-server.bigpond.net.au> posting-account=rYPZmwoAAAAw0Rr6v7tFHSxiDUs0Dzew AppleWebKit/525.27.1 (KHTML, like Gecko) Version/3.2.1 Safari/525.27.1,gzip(gfe),gzip(gfe) > Some solids can flow (metals). So the ether may be elastic and can > flow. > Matter exists normally in three states - gas, liquid and solid. It is > the temperature to which it is subjected, that determines the state. > Under normal temperature (where we humans live) changes of state do not > normally take place for matter. Unless we are talking about boiling > water from ice cubes! The very definition of a solid comes from its > lack of flow > Metals are solids and can flow. > Mercury is a metal, it flows, and it is not a solid at room temperatures. > each other, > Only in ionic crystals. > like all the spectators taking part in a Mexican wave in a football or > (alas) cricket stadium. But there are amorphous solids like chalk, and > viscous liquids like glass. In any case, ether is held to be a highly > elastic solid > Which can flow > As per the axiom, the whole universe is filled with ether, and we all move > in it. The ether stays put, and we can never know our velocity with > respect to the ether. We have currently no way of knowing whether the > ether can move or not. What with the speed of light being the same > whichever way we measure it on earth, it seems very likely that ether does > not move at all. To clarify what I mean by the important word axiom - an axiom is a > construction of thought that is a fundamental for further development, and > as such beyond the scope of dispute. When axioms are upset, one upsets an > entire thought structure. So in geometry it is axiomatic that a line has no > width. In practice, in drawing a line, it must have some width - but in > theory it does not have any width. Uh, the first dimension is width, so the line has all width. Length is in the time dimension. === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > As per the axiom, the whole universe is filled with ether, and we all > move in it. The ether stays put, and we can never know our velocity with > respect to the ether. We have currently no way of knowing whether the > ether can move or not. What with the speed of light being the same > whichever way we measure it on earth, it seems very likely that ether > does not move at all. You write like Einstein in 1905 the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,''. But in 1913 and 1925 the succesful attempts take place. Now mainstream science measure anomalies in rotations of the Earth. See: http://www.ringlaser.org.nz/content/about_us.php To clarify what I mean by the important word axiom - an axiom is a > construction of thought that is a fundamental for further development, and > as such beyond the scope of dispute. When axioms are upset, one upsets an > entire thought structure. So in geometry it is axiomatic that a line has > no width. In practice, in drawing a line, it must have some width - but > in theory it does not have any width. The full citation Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest The idea of absolute rest was not an axiom. After 1913 and 1925 is a history. S* > === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light <49ba1ffc$0$4046$afc38c87@news.optusnet.com.au> posting-account=WtWlpwoAAABtMc3YhLOw2GNjBkWJwBh5 SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > Einstein was a dork Hear, hear. Anyone who could look at such a human being as Albert Einstein and not be delighted, is decidedly looking at him through space distorted by something really scary or absurdly infantile. In any case, the argument from lensing is refuted by the fact that Einstein was totally taking that variable into account (what else?), such that the degree of deflection he predicted of fully 1.75 arc seconds was far more than could be accounted for by such a puny little phenomenon as that alone. Add to that his result for the perihelion advance of Mercury's orbit, and the many experiments that have confirmed time dilation--and these two birds haven't got scaly, skinny leg to stand on. They simply can't stand for having their sci-fi fantasies for superluminal space travel laughed to scorn by the Theory of Relativity--and that's all there is to it. Add in a dash of swinish anti-semitism and you've got the whole toxic, stinking dish. JM -- http://whosenose.blogspot.com/2008/06/by-force-of-historical-necessity.html http://whosenose.blogspot.com/2008/04/new-crusade.html === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Einstein was a dork Hear, hear. Anyone who could look at such a human being as Albert Einstein and not be delighted, is decidedly looking at him through space distorted by something really scary or absurdly infantile. In any case, the argument from lensing is refuted by the fact that Einstein was totally taking that variable into account (what else?), AB: Rubbish. I was the first person in the world who said that the bending of light was due to the Sun being an actual and very powerful optical lens, and not in any sense a gravitational lens. such that the degree of deflection he predicted of fully 1.75 arc seconds was far more than could be accounted for by such a puny little phenomenon as that alone. Add to that his result for the perihelion advance of Mercury's orbit, and the many experiments that have confirmed time dilation--and these two birds haven't got scaly, skinny leg to stand on. AB: Actually, the scoundrel relativists have no leg to stand upon, after my debunking of the ridiculous Lorentz transformation. They simply can't stand for having their sci-fi fantasies for superluminal space travel laughed to scorn by the Theory of Relativity--and that's all there is to it. Add in a dash of swinish anti-semitism and you've got the whole toxic, stinking dish. JM -- http://whosenose.blogspot.com/2008/06/by-force-of-historical-necessity.html http://whosenose.blogspot.com/2008/04/new-crusade.html === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light <49ba1ffc$0$4046$afc38c87@news.optusnet.com.au> posting-account=WtWlpwoAAABtMc3YhLOw2GNjBkWJwBh5 SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > AB: Rubbish. I was the first person in the world who said that the bending > of light was due to the Sun being an actual and very powerful optical lens, > and not in any sense a gravitational lens. You are certainly not the first person in the world to think he was the first person in the world to think he was thinking something, like, 'first'. But what is the nature of that which you presume to think you are thinking? For one, quite incredibly, you actually think you are smarter than Einstein--but while he was being squired round the world on strength of what other men and women of science were finding in his thought to be valid and firmly based in solid scientific method and principle--you? Where are you? Where are those beloved photos of Mr. Arindam Banerjee posing with Indian Chiefs, the greatest men and women of science, AND Charlie Chaplin? You think you are so smart? Show me a picture of you with Jim Carey, Richard Feynman and Chief Dan George--then I'll be willing to consider it. Otherwise, I am moved to suppose that the only thing that can possibly inspire a person to think himself smarter than Albert Einstein is a Supreme Ignorance of Einstein as to what he was in fact thinking. You think you know something concerning the phenomenon of light deflection about the limbs of the sun? You think you've got what it takes to second guess the first man who on this planet had the quality of mind to anticipate that such a thing would be the case--whatever might be the cause? That was not you, Mr. Banerjee, it was Einstein. Not you. It was not you who won the Nobel Prize for discovery of the photoelectric effect, that was Einstein. Will you try to demean that? Do so! Reveal yourself for precisely the sort that would! Demean the photoelectric effect, Mr. Banerjee. Refer to it as the work of a bungler. Come on! Show us who you really are, so we can really know, and describe you in terms far less uncertain and shy of forcefulness than these, if you please. But just on the way outside chance that the world of science is utterly without excuse in failing till now to have noticed, the Man who is Smarter than Einstein, Mr. Arindam Banerjee--well, let's just see. Here, from Google Books and the Princeton University Press is a theory of gravitational light deflection, in a book by none other than Ignazio Ciufolini and John Archibald Wheeler. Let us see you take no more than just the ONE PAGE, namely page 120 and explain, by means of your wiser than Einstein genius, from top to bottom, exactly what is being said in those terms, so that at least a mathematician can understand what you would have to say about how WRONG all this is . . . http://tinyurl.com/cacdcv -- JM http://jpdavid.blogspot.com/ http://bobbisoxsnatchers.blogspot.com http://vignettes-mackie.blogspot.com/ === Subject: Re: Eppur si muove - Debunking Einstein's postulate about the invariance of the speed of light > Einstein was a dork > Hear, hear. Anyone who could look at such a human being as Albert Einstein and not > be delighted, is decidedly looking at him through space distorted by > something really scary or absurdly infantile. Nonsense. At best, he was just a huge and overrated bungler, who has completely corrupted the whole field of physics; by equating appearance with reality he did even worse, he made morality a matter of inconsequence. He was horribly wrong. He discovered through pure bungling a wrong formula to equate mass and energy. That at least I have corrected. > In any case, the argument from lensing is refuted by the fact that > Einstein was totally taking that variable into account (what else?), AB: Rubbish. I was the first person in the world who said that the bending > of light was due to the Sun being an actual and very powerful optical > lens, and not in any sense a gravitational lens. such that the degree of deflection he predicted of fully 1.75 arc > seconds was far more than could be accounted for by such a puny little > phenomenon as that alone. Add to that his result for the perihelion > advance of Mercury's orbit, and the many experiments that have > confirmed time dilation--and these two birds haven't got scaly, skinny > leg to stand on. AB: Actually, the scoundrel relativists have no leg to stand upon, after > my debunking of the ridiculous Lorentz transformation. > They simply can't stand for having their sci-fi fantasies for > superluminal space travel laughed to scorn by the Theory of > Relativity--and that's all there is to it. Space travel well beyond the speed of light may well take place within my lifetime. The machines for same are described in www.users.bigpond.com/adda1234/index.htm It is amazing how well that work has stood up. It only needs minor corrections. That action and reaction do not balance, for em forces, has been *proved* in the US by the rail gun experiment (the reaction has been found to be less than 1/70 the action, by a team in the University of Texas, in one Schroeder's M.Tech thesis. Now that boy certainly deserves the Nobel Prize!). So that experiment proves that antigravity is possible, and with that, the Internal Force Engine is as good as done. My designs are uncannily correct - surely I was being blessed by the Divine for such work. In the meantime, the outing of the law of conservation of energy bodes very well for the human race and all other life forms. We can thus get not just unlimited energy, but pure water as well, in every corner of the earth. Just see www.users.bigpond.com/adda1234/HP.htm Arindam Banerjee. === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem posting-account=mOPVswkAAACQ29cN7EDDKOuqToMebV9C Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) On Mar 15, 9:50 am, mikeP...@TOGROUPmacconsult.com (Mike Rosenberg) > why not just take the cable with you? it's not very big. Or put it away in a drawer instead of leaving it out in the open. i think i can put it away or take it with me every day. just that it is too troublesome and our office is a startup and has no drawer... just a desk. also, i can't always take it with me during lunch or dinner time, during which the cable can be gone too. === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem If you want to use it please also use this Authorline. > i think i can put it away or take it with me every day. just that it > is too troublesome and our office is a startup and has no drawer... > just a desk. Are you saying that they can't afford drawers? -- Mac and geek T-shirts & gifts Prius shirts/bumper stickers Ballroom dance shirts & gifts === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem <1iwoie9.wtsnye53oha8N%mikePOST@TOGROUPmacconsult.com> posting-account=mOPVswkAAACQ29cN7EDDKOuqToMebV9C Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On Mar 16, 1:13pm, mikeP...@TOGROUPmacconsult.com (Mike Rosenberg) > i think i can put it away or take it with me every day. just that it > is too troublesome and our office is a startup and has no drawer... > just a desk. Are you saying that they can't afford drawers? they can certainly afford drawers. but the desk as of right now is just a simple flat surface desk, with no drawers and that's the way it is. they can certain invest $100 to add some drawers for each person and spend $8000, but certainly it is not a high priority. and that's the way it is. Please be aware that someone in the world indeed have no drawers. === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem > On Mar 16, 1:13 pm, mikeP...@TOGROUPmacconsult.com (Mike Rosenberg) > i think i can put it away or take it with me every day. just that it > is too troublesome and our office is a startup and has no drawer... > just a desk. > Are you saying that they can't afford drawers? they can certainly afford drawers. but the desk as of right now is > just a simple flat surface desk, with no drawers and that's the way it > is. they can certain invest $100 to add some drawers for each person > and spend $8000, but certainly it is not a high priority. and that's > the way it is. Please be aware that someone in the world indeed have > no drawers. Well, we can only hope they all have knickers, though. -- john mcwilliams === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem > On Mar 15, 9:50 am, mikeP...@TOGROUPmacconsult.com (Mike Rosenberg) > why not just take the cable with you? it's not very big. > Or put it away in a drawer instead of leaving it out in the open. i think i can put it away or take it with me every day. just that it > is too troublesome and our office is a startup and has no drawer... > just a desk. also, i can't always take it with me during lunch or > dinner time, during which the cable can be gone too. You could attach a tag to the cable asking that it not be borrowed. Would that be likely to work in your office? If not, would it be acceptable to make a permanent attachment to the computer? Go to Radio Shack or someplace and get a suitable wire and clamp. Attach one end of the wire to the USB cable and then epoxy the other end of the wire to the computer or to the desk. This is an iMac, right? If you could fabricate a loop on the end of the wire you could run the wire through the hole in the iMac's pedestal and then padlock it. This arrangement would not deter a thief, but then at least he would clearly be a thief and not a borrower. -- John Varela Trade NEWlamps for OLDlamps for email === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem &BCN}w}|9b>uS&>g5Uy4e.@-b@J;!~^'av>N$!vGo.[zo9[0gkA!|e/.W76 i think i can put it away or take it with me every day. just that it > is too troublesome and our office is a startup and has no drawer... > just a desk. also, i can't always take it with me during lunch or > dinner time, during which the cable can be gone too. Has this actually ever happened in your office? To you or to anyone else? -- It's now time for healing, and for fixing the damage the GOP did to America. === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem posting-account=mOPVswkAAACQ29cN7EDDKOuqToMebV9C Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Has this actually ever happened in your office? To you or to anyone > else? something similar happened to me before... and out of 3 cases of somebody hitting my car's front bumper, scratching the tail of the rear bumper, and scratching and denting the side door, only 1 person left a note saying that she will be responsible for the damage. and i have had my shoes stolen at a skiing resort. the shoes was at the top of the lockers. so somebody stole shoes that someone else wore... and he left his pair of shoes that looked like having been worn for 5 years. and yet in america, everybody appears so righteous. === Subject: Re: possible to lock the iphone or ipod USB cable to the mac or pc - as a topology problem posting-account=mOPVswkAAACQ29cN7EDDKOuqToMebV9C Gecko/20081217 Firefox/2.0.0.20,gzip(gfe),gzip(gfe) and then i thought of this solution: just pass through the iPod / iPhone cable through the loop part of the lock first, and then also put another cable, such as the monitor's VGA cable and / or keyboard and mouse cable. now lock the small lock... now any one who needs to take the iPod / iPhone cable also has unscrew both sides of the VGA cable, the keyboard, the mouse, and usually they will decide that it is not worth it to do so much work... of course, this only deters the causal taker -- if the person is determined, he or she can still take it when nobody is at the office at all. but then, he or she can also easily take several mouse away and sell it on ebay... probably locking the cable and use a CD-R marker to write property of [name] at both sides of the cable plugs. === Subject: Chaos Engine http://giannoni.homestead.com/sa18.html === Subject: Re: new list of solutions manual posting-account=P6qJwQoAAADMUKw1yDRfa7ojhB-pYpv0 rv:1.9.0.7) Gecko/2009021906 Firefox/3.0.7,gzip(gfe),gzip(gfe) > ello here I leave my list of solutions manual that I have ,his list > is more extensive. please contact: > mbfix8...@gmail.com or luisqu...@hotmail.com CIVIL AND ENVIROMENTAL ENGINEERING Structural Steel Design, 4/E > Jack C. McCormac Fluid Mechanics With Engineering Applications, 10th Edition > E.John Finnemore,Joseph B Franzini Steel Structures: Behavior and LRFD > Ramulu S. Vinnakota Introduction to Engineering and the Environment > Edward S. Rubin Urban Transportation Planning, 2E > Michael Meyer,Eric J. Miller Open Channel Hydraulics > Terry W. Sturm Water Chemistry > Mark M. Benjamin Environmental Biotechnology: Principles and Applications > Bruce E. Rittmann, Perry L. McCarty Construction Management Fundamentals, 1st Edition > Clifford J. Schexnayder,Richard Mayo Dynamics of Structures, 3/E > Anil K. Chopra Introduction to Transportation Engineering, 2E > James H. Banks Design of Concrete Structures, 13th Edition > Arthur H Nilson, David Darwin,Charles W. Dolan Water-Resources Engineering, 2/E > David A. Chin Traffic & Highway Engineering, 4th Edition > Nicholas J. Garber | Lester A. Hoel Traffic and Highway Engineering, 3rd, 3rd Edition > Nicholas J. Garber | Lester A. Hoel Principles of Environmental Engineering and Science, 2/e > Mackenzie L Davis, Susan J Masten Geotechnical Engineering > Richard L. Handy, Merlin G. Spangler Concrete Structures > Mehdi Setareh,Mehdi Setareh,Robert M. Darvas, Steel Design, 4th Edition > William T. Segui Engineering Fundamentals: An Introduction to Engineering, 3rd Edition > Saeed Moaveni Water and Wastewater Technology, 6/E > Mark J. Hammer Introduction to Environmental Engineering, 2nd Edition > P. Aarne Vesilind Susan M. Morgan Chemistry for Environmental Engineering and Science, 5th Edition > Clair N Sawyer,Perry L. McCarty, Gene F. Parkin, Unit Operations and Processes in Environmental Engineering, 2nd > Edition > Tom D. Reynolds , Paul Richards Structural Analysis , 3rd Edition > Aslam Kassimali The Engineering of Foundations, 1st Edition > Rodrigo Salgado Fundamentals of Structural Analysis, 3rd Edition > Kenneth M. Leet, Chia-Ming Uang, Anne Gilbert Design of Wood Structures > Donald E. Breyer, Kenneth J. Fridley, David G Pollock, Kelly Cobeen Construction Planning, Equipment, and Methods, 7th Edition > Robert L Peurifoy, Clifford J. Schexnayder, Aviad Shapira, Technion Introduction to Environmental Engineering and Science, 3/E > Gilbert M. Masters,Wendell P. Ela Hazardous Waste Management, 2nd Edition > Michael D LaGrega, Phillip L Buckingham, Retired Jeffrey C Evans Introduction to Environmental Engineering, 4th Edition > Mackenzie L Davis,David A Cornwell Principles of Foundation Engineering, 6th Edition > Braja M. Das Reinforced Concrete: Mechanics and Design, 5/E > James K. Wight,James G. MacGregor Statics and Strength of Materials for Architecture and Building > Construction, 3/E > Barry S. Onouye, Kevin Kane Hydrology and Floodplain Analysis, 4/E > Philip B. Bedient, Wayne C. Huber,Baxter E. Vieux Water-Resources Engineering, 2/E > David A. Chin Structural Analysis, 7/E > Russell C. Hibbeler Water and Wastewater Technology, 6/E > Mark J. Hammer Water Supply and Pollution Control, 8/E > Warren Viessman,Mark J. Hammer,Elizabeth M. Perez,Paul A. Chadik The Science and Design of Engineering Materials, 2nd Edition > James P Schaffer,Ashok Saxena, Stephen D. Antolovich,Thomas H. > Sanders, Steven B Warner ELECTRICAL ENGINEERING > Advanced Digital Logic Design Using Verilog, State Machines, and > Synthesis for FPGA's, 1st Edition > Sunggu Lee Embedded Systems: Architechture, Programming and Design > D. P. Kothari,I. J. Nagrath Modern Wireless Communications > Simon Haykin, Michael Mohe Semiconductor Heterojunctions and Nanostructures > Omar Manasreh Analysis and Design of Digital Integrated Circuits, 3E > David A. Hodges,Horace G. Jackson,Resve Saleh Design of Analog CMOS Integrated Circuits > Behzad Razavi An Introduction to the Finite Element Method, 3rd Edition > J. N. Reddy Modern Power System Analysis > Kothari Fundamentals of Electric Circuits, 4th Edition > Charles Alexander, Matthew Sadiku Embedded Systems > Kamal Fundamentals of Signals and Systems Using the Web and MATLAB¬, 3/E > Edward W. Kamen, Bonnie S Heck Digital Signal Processing, 4/E > John G. Proakis,Dimitris K Manolakis Microprocessor Design: Principles and Practices (with VHDL), 1st > Edition > Enoch O. Hwang Error Control Coding, 2/E > Shu Lin,Daniel J. Costello Introduction to Signal and System Analysis, 1st Edition > Kaliappan Gopalan Fundamentals of Digital Logic with Verilog Design, 2nd Edition > Stephen Brown, Zvonko Vranesic Modern Digital Signal Processing, 1st Edition > Roberto Cristi Digital Signal Processing Using MATLAB¬, 2nd Edition > Vinay K. Ingle ,John G. Proakis Digital Signal Processing - A Modern Introduction, 1st Edition > Ashok Ambardar Chip Design for Submicron VLSI: CMOS Layout and Simulation, 1st > Edition > John P. Uyemura Advanced Digital Logic: State Machine Design using VHDL, Verilog, and > Synthesis for FPGAs, 1st Edition > Sunggu Lee Power Systems Analysis and Design, 4th Edition > J. Duncan Glover , Mulukutla S. Sarma , Thomas Overbye Embedded Microcomputer Systems: Real Time Interfacing > Valvano Fundamentals of Logic Design > Charles H. Roth, Jr Fundamentals of Applied Electromagnetics, 5/E > Fawwaz T. Ulaby Circuits and Networks > Sudhakar Silicon VLSI Technology: Fundamentals, Practice, and Modeling > James D. Plummer,Michael D. Deal,Peter B. Griffin An Introduction to Signals and Systems, 1st Edition > John Alan Stuller Microwave Engineering > Annapurna Das Modern Digital Electronics > R.P. Jain Verilog Digital System Design > Zainalabedin Navabi CMOS Digital Integrated Circuits: Analysis and Design, 3/e > Sung-Mo Kang,Yusuf Leblebici Verilog Digital System Design : Register Transfer Level Synthesis, > Testbench, and Verification, 2nd Edition > Zainalabedin Navabi Spectral Analysis of Signals > Petre Stoica,Randolph L. Moses Data Communications and Networking, 4/e > Behrouz A. Forouzan Cryptography and Network Security > Behrouz A. Forouzan Embedded System Design with C805, 1st Edition > Han-Way Huang Chip Design for Submicron VLSI: CMOS Layout and Simulation, 1st > Edition > John P. Uyemura Digital Communications, 5th Edition > John Proakis,Massoud Salehi Programmable Logic Controllers, 3rd Edition > Frank D. Petruzella An Introduction to Signals and Systems, 1st Edition > John Alan Stuller Elements of Engineering Electromagnetics, 6/E > Nannapaneni Narayana Rao Introduction to Microelectronic Fabrication: Volume 5 of Modular > Series on Solid State Devices, 2/E > Richard C. Jaeger Electric Circuits, 8/E > James W. Nilsson,Susan Riedel Introductory Circuits for Electrical and Computer Engineering > James W. Nilsson,Susan A. Riedel Fundamentals of Applied Electromagnetics, 5/E > Fawwaz T. Ulaby Introduction to Signal and System Analysis, 1st Edition > Kaliappan Gopalan Signals, Systems, and Transforms, 4/E > Charles L Phillips , Parr > Eve Riskin Probability, Statistics, and Random Processes for Engineers, 1st > Edition > Richard H. Williams Probability, Statistics, and Random Processes For Electrical > Engineering, 3/E > Alberto Leon-Garcia Electrical Engineering: Principles and Applications, 4/E > Allan R. Hambley Introduction to Logic Design, 2nd Edition > Alan B Marcovitz Digital Principles and Design, 1st Edition > Donald D. Givone Control Systems > Madan Gopal Probabilistic Systems and Random Signals > Abraham H Haddad Modern Power System Analysis > D. P. Kothari,I. J. Nagrath Introduction to Computing Systems: > Yale N. Patt,Sanjay J. Patel System Dynamics > William J. Palm III CMOS Digital Integrated Circuits > Analysis & Design, 3E > Sung-Mo (Steve) Kang,Yusuf Leblebici Embedded Microcomputer Systems: Real Time Interfacing, 2nd Edition > Jonathan W. Valvano Introduction to Embedded Microcomputer Systems: Motorola 6811/6812 > Simulations, 1st Edition > Jonathan W. Valvano Introduction to Wireless and Mobile Systems, 2nd Edition > Dharma P. Agrawal , Qing-An Zeng Power Systems Analysis and Design, 4th Edition > J. Duncan Glover , Mulukutla S. Sarma , Thomas Overbye Microwave Engineering > Das Engineering Electromagnetics with CD, 7th Edition > William H. Hayt,John A. Buck Control Systems > Gopal Digital & Analog Communication Systems, 7/E > Leon W. Couch Introduction to Wireless and Mobile Systems, 2nd Edition > Dharma P. Agrawal,Qing-An Zeng Programmable Logic Controllers, 3rd Edition > Frank D. Petruzella Electrical Engineering: Principles and Applications, 4/E > Allan R. Hambley Digital & Analog Communication Systems, 7/E > Leon W. Couch Cryptography and Network Security, 4/E > William Stallings Design with Operational Amplifiers and Analog Integrated Circuits, 3E > Sergio Franco Semiconductor Physics and Devices, 3E > Donald Neamen An Introduction to Semiconductor Devices > Donald Neamen Principles of Electronic Materials and Devices, 3rd Edition > Safa O. Kasap MECHANICAL ENGINEERING > Engineering Mechanics: Statics-Computational Edition, 1st Edition > Robert W. Soutas-Little | Daniel J. Inman | Daniel S. Balint Modern Compressible Flow: > With Historical Perspective, 3E > John D. Anderson Design of Fluid Thermal Systems, 2nd Edition > William S. Janna Principles of Heat Transfer, 6th Edition > Frank Kreith Foundations of Materials Science and Engineering, 4th Edition > William F. Smith, Javad Hashemi An Introduction to Mechanical Engineering, 2nd Edition > Jonathan Wickert Mechanics of Materials , 7th Edition > James M. Gere Design of Fluid Thermal Systems, 2nd Edition > William S. Janna Electrical Machines, Drives and Power Systems, 6/E > Theodore Wildi Engineering Mechanics: Dynamics, 5/E > Anthony M. Bedford,Wallace Fowler Principles of Statics and Dynamics, 10/E > Russell C. Hibbeler Mechanics of Materials, 7/E > Russell C. Hibbeler Engineering Mechanics: Statics, 5/E > Anthony M. Bedford,Wallace Fowler system Dynamics and Response - SI Version, 1st Edition > S. Graham Kelly Viscous Fluid Flow, 3/e > White Essentials of Materials ... l.8as mer é Foundations of materials science and engineering solution manual?? === Subject: Re: SVD -> QR Decomposition posting-account=9MUq6goAAADgjsPh96c7CaIVgaYLzn3V 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-dtc-tg10.proxy.aol.com[CDBC70CA] (Prism/1.2.1), HTTP/1.1 cache-dtc-aa03.proxy.aol.com[CDBC7407] (Traffic-Server/6.1.5 [uScM]) On Mar 15, 11:21?am, spellu...@fb04814.mathematik.tu-darmstadt.de >A is m x n of rank n. ?Smallest singular value of A is s n with >corresponding singular vectors Av=(s n )u where || v || 2 = || u || 2 >= 1. ?I want to choose a permutation P so that >w=P' v , >and >| w n |=|| w || inf , >and then let AP=Q (R 0)' be a QR decomposition of AP. >I need to ultimately show | r nn | <= sqrt(n) * s n. >My question is should i begin doing what and then what is next? >defeat this problem. >Edward homework! > hint > insert anything you know about the form of A ?and w in terms of > Q,R,w,s n. > isolate R*w what do yuo know about the realtion between ||.|| inf and ||.|| 2? done hth > peter- Hide quoted text - - Show quoted text - AP=USV'P=Q(R 0)' || x || 2 <= sqrt(n)*|| x || inf APw=US=Q(R 0)'w (R 0)'w=Q'US TRY TO ISOLATE R*w R*w =Q'US (economy?) and i know |w n| = || w || inf so w n is the largest entry of vector w || R*w || 2 = || S || 2 but i think || S || 2 = s 1 not s n. Is that what the P is doing and i lost track? anyway this is the list about what i know for the problem. i ahve no more stupid (extra-thoughts) today. its because i am sober like a door knob. === Subject: Re: SVD -> QR Decomposition >On Mar 15, 11:21=EF=BF=BDam, spellu...@fb04814.mathematik.tu-darmstadt.de >.com>, >A is m x n of rank n. =EF=BF=BDSmallest singular value of A is s_n with >corresponding singular vectors Av=3D(s_n )u where || v ||_2 =3D || u ||_= >2 >=3D 1. =EF=BF=BDI want to choose a permutation P so that >w=3DP' v , >and >| w_n |=3D|| w ||_inf , >and then let AP=3DQ (R 0)' be a QR decomposition of AP. >I need to ultimately show | r_nn | <=3D sqrt(n) * s_n. >My question is should i begin doing what and then what is next? >defeat this problem. >Edward > homework! > hint > insert anything you know about the form of A =EF=BF=BDand w in terms of > Q,R,w,s_n. > isolate R*w > what do yuo know about the realtion between ||.||_inf and ||.||_2? > done > hth > peter- Hide quoted text - > - Show quoted text - AP=3DUSV'P=3DQ(R 0)' || x ||_2 <=3D sqrt(n)*|| x ||_inf APw=3DUS=3DQ(R 0)'w (R 0)'w=3DQ'US TRY TO ISOLATE R*w >R*w =3DQ'US (economy?) and i know |w_n| =3D || w ||_inf so w_n is the largest entry of vector w || R*w ||_2 =3D || S ||_2 but i think || S ||_2 =3D s_1 not s_n. Is that what the P is doing and >i lost track? anyway this is the list about what i know for the problem. i ahve no >more stupid (extra-thoughts) today. its because i am sober like a >door knob. A=USV' S of the same shape as A assume the diagonal of S monotonically nonincreasing hence s(n,n) is the smallest singular value let v(n) be the associated right singular vector and u(n) the corresponding left on USV'v(n) = s(n,n)u(n) AP = QR R upper triangular but of the same shape as A USV'PP'v(n) = AP (P'v(n)) = s(n,n)u(n) = QR (P'v(n)) = s(n,n)u(n) hence R(P'v(n)) = s(n,n)Q'u(n) (**) |(P'v(n))(n)| (last component) = ||(P'v(n))||_inf by assumption on P and ||x||_2 >= ||x||_inf >= 1/sqrt(n) ||x||_2 for all x now consider equation number n in (**): |R(n,n)| = s(n,n)|(Q'u(n))(n)|/|(P'v(n))(n)| <= s(n,n)sqrt(n) done peter (getting 2 honors points) === Subject: Re: SVD -> QR Decomposition posting-account=9MUq6goAAADgjsPh96c7CaIVgaYLzn3V 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-mtc-tc06.proxy.aol.com[400C7046] (Prism/1.2.1), HTTP/1.1 cache-mtc-aa10.proxy.aol.com[400C740E] (Traffic-Server/6.1.5 [uScM]) On Mar 17, 9:22?am, spellu...@fb04814.mathematik.tu-darmstadt.de >On Mar 15, 11:21=EF=BF=BDam, spellu...@fb04814.mathematik.tu-darmstadt.de >.com>, >A is m x n of rank n. =EF=BF=BDSmallest singular value of A is s n with >corresponding singular vectors Av=3D(s n )u where || v || 2 =3D || u || = >2 >=3D 1. =EF=BF=BDI want to choose a permutation P so that >w=3DP' v , >and >| w n |=3D|| w || inf , >and then let AP=3DQ (R 0)' be a QR decomposition of AP. >I need to ultimately show | r nn | <=3D sqrt(n) * s n. >My question is should i begin doing what and then what is next? >defeat this problem. >Edward > homework! > hint > insert anything you know about the form of A =EF=BF=BDand w in terms of > Q,R,w,s n. > isolate R*w > what do yuo know about the realtion between ||.|| inf and ||.|| 2? > done > hth > peter- Hide quoted text - > - Show quoted text - >AP=3DUSV'P=3DQ(R 0)' >|| x || 2 <=3D sqrt(n)*|| x || inf >APw=3DUS=3DQ(R 0)'w >(R 0)'w=3DQ'US >TRY TO ISOLATE R*w >R*w =3DQ'US ?(economy?) >and i know |w n| =3D || w || inf so w n is the largest entry of vector w >|| R*w || 2 =3D || S || 2 >but i think || S || 2 =3D s 1 not s n. ?Is that what the P is doing and >i lost track? >anyway this is the list about what i know for the problem. ?i ahve no >more stupid (extra-thoughts) today. ?its because i am sober like a >door knob. ? A=USV' ?S of the same shape as A > ? assume the diagonal of S monotonically nonincreasing ? hence s(n,n) is the smallest singular value > ? let v(n) be the associated right singular vector > ? and u(n) the corresponding left on ? USV'v(n) = s(n,n)u(n) ? AP = QR ?R upper triangular but of the same shape as A ? USV'PP'v(n) = AP (P'v(n)) = s(n,n)u(n) = QR (P'v(n)) = s(n,n)u(n) ? hence ? R(P'v(n)) = s(n,n)Q'u(n) ?(**) ? ? |(P'v(n))(n)| (last component) ?= ||(P'v(n))|| inf by assumption on P ? and ? ||x|| 2 >= ||x|| inf >= 1/sqrt(n) ||x|| 2 ?for all x ? now consider equation number n in (**): ? |R(n,n)| = s(n,n)|(Q'u(n))(n)|/|(P'v(n))(n)| <= s(n,n)sqrt(n) ? done > ? peter > ? (getting 2 honors points)- Hide quoted text - - Show quoted text - know very little. i had no idea how to use the P and w information. I was looking at R=Q'USV'P and crying. edward === Subject: Re: 40% in remedial math posting-account=9tP_uwoAAAD1vfWhLdsNH4ImDfm7cP1K 4337.29; Windows NT 5.1; SV1; GTB5; .NET CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) spider-mtc-tc09.proxy.aol.com[400C7049] (Prism/1.2.1), HTTP/1.1 cache-mtc-ae12.proxy.aol.com[400C7510] (Traffic-Server/6.1.5 [uScM]) > http://www.courant.com/news/education/hc-higher-admission-standards-0... Connecticut State Universities Raising Admission Standards > By GRACE E. MERRITT, The Hartford Courant March 13, 2009 Concerned that many freshmen arrive on campus poorly prepared for > college classes, Connecticut State University System trustees voted > Thursday to raise academic admission standards for students starting > in 2015. Currently four in every 10 freshmen at Central, Eastern, Southern and > Western Connecticut state universities must take a remedial math class > and 25 percent must take remedial English once they arrive on campus > before they are ready for college-level work, university officials > said. If you've not been taught Algebra II, you are not going to be ready > for college-level math, explained trustee John A. Doyle, chairman of > the academic affairs committee. The new admissions standards are more specific and demanding. Freshmen > will be required to have taken four years of mathematics rather than > the current minimum of three. They also will have to have taken three > years of science, rather than the current two-course requirement, and > an English composition class, among other changes. The higher admissions standards won't kick in until 2015 at the > earliest, to give high schools enough time to make sure they are > providing the necessary preparatory courses. Essentially, the new standards will affect today's sixth-graders, who > will be freshmen in 2015, said Bernard Kavaler, CSU's assistant vice > chancellor for public affairs. The timing dovetails with a bill that would raise high school > graduation standards statewide. The bill is based on a plan developed > by the state Department of Education for middle and high school > students and adopted by the State Board of Education in October. This is really part of an ongoing effort across the state to work > with educators at every level to set new standards, Kavaler said. Western Connecticut State University has already started an innovative > program designed to better align area high schools with the college > curriculum. Since it started three years ago, the number of freshmen > in remedial classes has dropped dramatically, and retention rates have > improved, Kavaler said. The program is now being developed at the > other CSU campuses in collaboration with area school districts. By my experience and reading, if the figure is 40%, then the current college-level math courses in CT are at too low a level. A national study last year reported only 15% of 12-grade graduates able to enter a college-level math course. With about 60% going to higher education, that should result in about 75% remediation, which is close to the rate at the State university where I work. === Subject: Re: 40% in remedial math If you've not been taught Algebra II, you are not going to be ready > for college-level math, > In the State of Texas even if you HAVE been taught Algebra II you can still graduate from high school not knowing: (1) How to find the area of a rectangle (2) How to find the perimeter of a rectangle. (3) How to find the circumference of a circle. (4) How many inches are in a foot. (5) How many quarts in a gallon. (6) Not knowing basic multiplication/division. etc .. etc .. etc You see ... the students are given (MANDATED!) a formula chart and a calculator for the state mandated test .. the vast majority have a calculator in hand from the 9th grade forward. I've watched an Algebra II student use a calculator to multiply 9 x 0 ... when I inquired as to the reason he used a calculator ... I was just checking myself . This same student asked for a formula chart to find the area of a rectangle! Solving equations? Easy .. example ... (1/2)x=6, procedure. Convert the 1/2 to .5, using a calculator. Divide 6 by .5, using a calculator. When I asked why not just multiply both sides of the equation by 2 ... I don't know how to do that, we weren't taught that way. Oh, forgot to tell you ... this was A JUNIOR IN HIGH SCHOOL !!! Finally ... I was tutoring a student to pass the 11th grade TAKS test (a state mandated test in Texas) ... trying to give her some concept of volume I gave her a Stanley tape measure and asked her to calculate the approximate volume of a that could be used to ship a toaster that was on my cabinet ... she stood with tape measure in hand .. dumbfounded ... she couldn't read a tape measure! 40% ?? I don't doubt it at all. Oh, these examples were all middle to (very) upper socioeconomic class white students .. Jerry === Subject: Re: 40% in remedial math > If you've not been taught Algebra II, you are not going to be ready > for college-level math, >In the State of Texas even if you HAVE been taught Algebra II you can still >graduate from high school not knowing: >(1) How to find the area of a rectangle >(2) How to find the perimeter of a rectangle. >(3) How to find the circumference of a circle. >(4) How many inches are in a foot. >(5) How many quarts in a gallon. >(6) Not knowing basic multiplication/division. >etc .. etc .. etc >You see ... the students are given (MANDATED!) a formula chart and a >calculator for the state mandated test .. the vast majority have a >calculator in hand from the 9th grade forward. I've watched an Algebra II >student use a calculator to multiply 9 x 0 ... when I inquired as to the >reason he used a calculator ... I was just checking myself . On this one, I can agree. Understanding the properties of the number 0 is basic, as is 1. Not much more is. This >same student asked for a formula chart to find the area of a rectangle! If the student knows what variables mean, and what formulas mean, this is far more valuable than being able to do arithmetic. Facts and routines can be looked up; concepts cannot. >Solving equations? Easy .. example ... (1/2)x=6, procedure. >Convert the 1/2 to .5, using a calculator. >Divide 6 by .5, using a calculator. That there are simple or other methods of solution is not all that important. Being familiar with arithmetic, and being able to do it without aids, can be convenient, and can enable things to be done more quickly. But it is in no way basic for an understanding of mathematics. Nor does it lead to an understanding. The original new math, introduced in the schools about 50 years ago, started because a child of a mathematician showed a lack of understanding of numbers DESPITE being proficient in arithmetic. The new math failed because the teachers could not understand the concepts. I am rather proficient in arithmetic, well beyond what is expected, and I use it, possibly too often. Also, I understand mathematical concepts, and if you look in mathematical journals, you will see little use of arithmetic done by hand. I could have done all of the questions asked above in elementary school, but only had an intuitive idea of the methods; the facts were memorized. I did develop some intuitive ideas of the structure of the numbers, but did not really understand them until they were formally presented. They can, and should, be taught to young children; the ordinal approach is self-contained, and even the proofs are withing the abilities of a first grader. But I question the ability of the brainwashed teachers to do so. Do you understand the cardinal and ordinal structure of the integers? The important idea of proof by induction, which belongs very early, is often not taught to math majors, including prospective high school teachers. >When I asked why not just multiply both sides of the equation by 2 ... I >don't know how to do that, we weren't taught that way. Oh, forgot to tell >you ... this was A JUNIOR IN HIGH SCHOOL !!! Here is the essence of algebra in two sentences. A variable is a temporary name that can stand for anything. The same operation performed on equal entities yields equal results. Algebra, alas, is not taught that simple way. That junior in high school was taught that the way to solve ax=b was to compute b/a, and not to compute (1/a)*b, which is what you were pointing out. Especially on a test, do not expect a student to find the easy way to solve a problem. >Finally ... I was tutoring a student to pass the 11th grade TAKS test (a >state mandated test in Texas) ... trying to give her some concept of volume >I gave her a Stanley tape measure and asked her to calculate the approximate >volume of a that could be used to ship a toaster that was on my cabinet ... >she stood with tape measure in hand .. dumbfounded ... she couldn't read a >tape measure! Volume is a mathematical concept. Using a tape measure is not. >40% ?? I don't doubt it at all. >Oh, these examples were all middle to (very) upper socioeconomic class white >students .. >Jerry -- 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: 40% in remedial math >If you've not been taught Algebra II, you are not going to be ready >for college-level math, > >In the State of Texas even if you HAVE been taught Algebra II you can still >graduate from high school not knowing: >(1) How to find the area of a rectangle >(2) How to find the perimeter of a rectangle. >(3) How to find the circumference of a circle. >(4) How many inches are in a foot. >(5) How many quarts in a gallon. >(6) Not knowing basic multiplication/division. >etc .. etc .. etc >You see ... the students are given (MANDATED!) a formula chart and a >calculator for the state mandated test .. the vast majority have a >calculator in hand from the 9th grade forward. I've watched an Algebra II >student use a calculator to multiply 9 x 0 ... when I inquired as to the >reason he used a calculator ... I was just checking myself . > On this one, I can agree. Understanding the properties > of the number 0 is basic, as is 1. Not much more is. This > >same student asked for a formula chart to find the area of a rectangle! > If the student knows what variables mean, and what > formulas mean, this is far more valuable than being > able to do arithmetic. Facts and routines can be > looked up; concepts cannot. Hmmmm... what about times when a chart isn't readily available? I agree that complicated formulas should probably be looked up, but something as basic as the area of a rectangle? >Solving equations? Easy .. example ... (1/2)x=6, procedure. >Convert the 1/2 to .5, using a calculator. >Divide 6 by .5, using a calculator. > That there are simple or other methods of solution is > not all that important. Being familiar with arithmetic, > and being able to do it without aids, can be convenient, > and can enable things to be done more quickly. But it > is in no way basic for an understanding of mathematics. Nor does it lead to an understanding. The original new > math, introduced in the schools about 50 years ago, > started because a child of a mathematician showed a lack > of understanding of numbers DESPITE being proficient in > arithmetic. The new math failed because the teachers > could not understand the concepts. I am rather proficient in arithmetic, well beyond what > is expected, and I use it, possibly too often. Also, I > understand mathematical concepts, and if you look in > mathematical journals, you will see little use of > arithmetic done by hand. I could have done all of the questions asked above in > elementary school, but only had an intuitive idea of the > methods; the facts were memorized. I did develop some > intuitive ideas of the structure of the numbers, but did > not really understand them until they were formally > presented. They can, and should, be taught to young > children; the ordinal approach is self-contained, and > even the proofs are withing the abilities of a first > grader. But I question the ability of the brainwashed > teachers to do so. Do you understand the cardinal and ordinal structure of > the integers? The important idea of proof by induction, > which belongs very early, is often not taught to math > majors, including prospective high school teachers. >When I asked why not just multiply both sides of the equation by 2 ... I >don't know how to do that, we weren't taught that way. Oh, forgot to tell >you ... this was A JUNIOR IN HIGH SCHOOL !!! > Here is the essence of algebra in two sentences. A variable is a temporary name that can stand for anything. The same operation performed on equal entities > yields equal results. Algebra, alas, is not taught that simple way. That junior > in high school was taught that the way to solve ax=b was to > compute b/a, and not to compute (1/a)*b, which is what you > were pointing out. Especially on a test, do not expect a > student to find the easy way to solve a problem. >Finally ... I was tutoring a student to pass the 11th grade TAKS test (a >state mandated test in Texas) ... trying to give her some concept of volume >I gave her a Stanley tape measure and asked her to calculate the approximate >volume of a that could be used to ship a toaster that was on my cabinet ... >she stood with tape measure in hand .. dumbfounded ... she couldn't read a >tape measure! > Volume is a mathematical concept. Using a tape measure is not. Theory vs. practical application... I know a lot of people that have problems making measurements.... Martin >40% ?? I don't doubt it at all. >Oh, these examples were all middle to (very) upper socioeconomic class white >students .. >Jerry === Subject: Re: 40% in remedial math and the other 70% are even further behind. === Subject: Re: 40% in remedial math >and the other 70% are even further behind. There are three kinds of people in the world; those who can count, and those who can't. :-) -- 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: NMF problem posting-account=qfzVJQoAAADfy5TJING7HwgSJ6RCrIqv Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) Hi friends, I am making a project where I have to make use of NMF (non-negative matrix factorization). But there's a problem I'm facing. Its been quite some time since I studied any maths. I am getting to understand NMF slowly but it does not seem to be working. I have a few questions: 1. Kindly tell me some good resources to study NMF and LNMF from. I would prefer resources that start from scratch. 2. Whats the real intuitive/graphical meaning of the multiplicative update functions? O! I forget to mention. I only have to study NMF for minimizing Euclidean distance and KL Divergence. I understand well through graphs. I need conceptual information on how this stuff works. Vaibhav === Subject: Decide f(x) if Hello! Can somebody tell me how I do to find f(x) if I have f(x+2) = x*x + 4*x I assume there must be some trick! //Tony === Subject: Re: Decide f(x) if > .... > Can somebody tell me how I do to find f(x) if I have > f(x+2) = x*x + 4*x I assume there must be some trick! .... You want to replace the (x + 2) by a single letter, so just do that. Let x + 2 = w, so x = w - 2. Substitute (w - 2) for x in your formula and see what happens. Ken Pledger. === Subject: Re: Roman Numeral CIVD. : THERE could be 100 sextillion (or 100 billion trillion) Earthlike planets in Universe ?? posting-account=9fll0QoAAACXgjqfBK4ApzIcZd1A5wfO 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.1; student.vuw.ac.nz),gzip(gfe),gzip(gfe) > What does the Roman Numeral CIVD represent. > e.g. ( M ) > e.g. M vinculum ??? . > II XX. > 23,ooo,ooo. ?? encyc britannica. palindrome civic. > bcc; Roman Numeral CIVD. : THERE could be 100 sextillion (or 100 billion > trillion) Earthlik e planets in Universe ?? 63 5 readers digest/............. > VI TRIO LIC. VX CL IM D. cheers, 23/2/09. Don S. McDonald ... THANK YOU Don MacDonald from PHILLIP O'SULLIVAN === Subject: Re: Prime counting function posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > Can pi(x), where pi(x) is the prime counting conjecture be transformed > into something like: > x/logx + r , where r could possibly be a function, variable and but > not likely a constant > thank you. Jon Look up the Meisel-Lehmer function. The existence of such a function is, of course, trivial. Computing it, however, is a different matter. === Subject: Probability question I recently saw a Probability question which has me beat - it relates to the relative probabilities of throwing a two heads after throwing a head and a tail - with the probability of throwing two tails after throwing a head and a tail - I may have muddled it somehow but the answer was 3:1 . I am sure the question is known to listers I would love an explanation === Subject: This Week's Finds in Mathematical Physics (Week 270) Originator: baez@math.UUCP (John Baez) October 11, 2008 This Week's Finds in Mathematical Physics (Week 270) John Baez Greg Egan has a new novel out, called Incandescence - so I want to talk about that. Then I'll talk about three of my favorite numbers: 5, 8, and 24. I'll show you how each regular polytope with 5-fold rotational symmetry has a secret link to a lattice living in twice as many dimensions. For example, the pentagon is a 2d projection of a beautiful shape that lives in 4 dimensions. Finally, I'll wrap up with a simple but surprising property of the number 12. But first: another picture of Jupiter's moon Io! Now we'll zoom in much closer. This was taken in 2000 by the Galileo probe: 1) A continuous eruption on Jupiter's moon Io, Astronomy Picture of the Day, http://apod.nasa.gov/apod/ap000606.html Here we see a vast plain of sulfur and silicate rock, 250 kilometers across - and on the left, glowing hot lava! The white dots are spots so hot that their infrared radiation oversaturated the detection equipment. This was the first photo of an active lava flow on another world. If you like pictures like this, maybe you like science fiction. And if you like hard science fiction - diamond-scratching hard, as one reviewer put it - Greg Egan is your man. His latest novel is one of the most realistic evocations of the distant future I've ever read: 2) Greg Egan, Incandescence, Night Shade Books, 2008. Website at http://www.gregegan.net/INCANDESCENCE/Incandescence.html The story features two parallel plots. One is about a galaxy-spanning civilization called the Amalgam, and two of its members who go on a quest to our Galaxy's core, which is home to enigmatic beings that may be still more advanced: the Aloof. The other is about the inhabitants of a small world orbiting a black hole. This is where the serious physics comes in. I might as well quote Egan himself: Incandescence grew out of the notion that the theory of general relativity - widely regarded as one of the pinnacles of human intellectual achievement - could be discovered by a pre-industrial civilization with no steam engines, no electric lights, no radio transmitters, and absolutely no tradition of astronomy. At first glance, this premise might strike you as a little hard to believe. We humans came to a detailed understanding of gravity after centuries of painstaking astronomical observations, most crucially of the motions of the planets across the sky. Johannes Kepler found that these observations could be explained if the planets moved around the sun along elliptical orbits, with the square of the orbital period proportional to the cube of the length of the longest axis of the ellipse. Newton showed that just such a motion would arise from a universal attraction between bodies that was inversely proportional to the square of the distance between them. That hypothesis was a close enough approximation to the truth to survive for more than three centuries. When Newton was finally overthrown by Einstein, the birth of the new theory owed much less to the astronomical facts it could explain - such as a puzzling drift in the point where Mercury made its closest approach to the sun - than to an elegant theory of electromagnetism that had arisen more or less independently of ideas about gravity. Electrostatic and magnetic effects had been unified by James Clerk Maxwell, but Maxwell's equations only offered one value for the speed of light, however you happened to be moving when you measured it. Making sense of this fact led Einstein first to special relativity, in which the geometry of space-time had the unvarying speed of light built into it, then general relativity, in which the curvature of the same geometry accounted for the motion of objects free-falling through space. So for us, astronomy was crucial even to reach as far as Newton, and postulating Einstein's theory - let alone validating it to high precision, with atomic clocks on satellites and observations of pulsar orbits - depended on a wealth of other ideas and technologies. How, then, could my alien civilization possibly reach the same conceptual heights, when they were armed with none of these apparent prerequisites? The short answer is that they would need to be living in just the right environment: the accretion disk of a large black hole. When SF readers think of the experience of being close to a black hole, the phenomena that most easily come to mind are those that are most exotic from our own perspective: time dilation, gravitational blue-shifts, and massive distortions of the view of the sky. But those are all a matter of making astronomical observations, or at least arranging some kind of comparison between the near-black-hole experience and the experience of other beings who have kept their distance. My aliens would probably need to be sheltering deep inside some rocky structure to protect them from the radiation of the accretion disk - and the glow of the disk itself would also render astronomy immensely difficult. Blind to the heavens, how could they come to learn anything at all about gravity, let alone the subtleties of general relativity? After all, didn?t Einstein tell us that if we?re free-falling, weightless, in a windowless elevator, gravity itself becomes impossible to detect? Not quite! To render its passenger completely oblivious to gravity, not only does the elevator need to be small, but the passenger's observations need to be curtailed in time just as surely as they're limited in space. Given time, gravity makes its mark. Forget about black holes for a moment: even inside a windowless space station orbiting the Earth, you could easily prove that you were not just drifting through interstellar space, light-years from the nearest planet. How? Put on your space suit, and pump out all the station's air. Then fill the station with small objects - paper clips, pens, whatever - being careful to place them initially at rest with respect to the walls. Wait, and see what happens. Most objects will eventually hit the walls; the exact proportion will depend on the station's spin. But however the station is or isn't spinning, some objects will undergo a cyclic motion, moving back and forth, all with the same period. That period is the orbital period of the space station around the Earth. The paper clips and pens that are moving back and forth inside the station are following orbits that are inclined at a very small angle to the orbit of the station's center of mass. Twice in every orbit, the two paths cross, and the paper clip passes through the center of the space station. Then it moves away, reaches the point of greatest separation of the orbits, then turns around and comes back. This minuscule difference in orbits is enough to reveal the fact that you're not drifting in interstellar space. A sufficiently delicate spring balance could reveal the tiny tidal gravitational force that is another way of thinking about exactly the same thing, but unless the orbital period was very long, you could stick with the technology-free approach and just watch and wait. A range of simple experiments like this - none of them much harder than those conducted by Galileo and his contemporaries - were the solution to my aliens' need to catch up with Newton. But catching up with Einstein? Surely that was beyond hope? I thought it might be, until I sat down and did some detailed calculations. It turned out that, close to a black hole, the differences between Newton's and Einstein's predictions would easily be big enough for anyone to spot without sophisticated instrumentation. What about sophisticated mathematics? The geometry of general relativity isn't trivial, but much of its difficulty, for us, revolves around the need to dispose of our preconceptions. By putting my aliens in a world of curved and twisted tunnels, rather than the flat, almost Euclidean landscape of a patch of planetary surface, they came better prepared for the need to cope with a space-time geometry that also twisted and curved. The result was an alternative, low-tech path into some of the most beautiful truths we've yet discovered about the universe. To add to the drama, though, there needed to be a sense of urgency; the intellectual progress of the aliens had to be a matter of life and death. But having already put them beside a black hole, danger was never going to be far behind. As you can tell, this is a novel of ideas. You have to be willing to work through these ideas to enjoy it. It's also not what I'd call a feel-good novel. As with Diaspora and Schild's Ladder, the main characters seem to become more and more isolated and focused on their work as they delve deeper into the mysteries they are pursuing. By the time the mysteries are unraveled, there's almost nobody to talk to. It's a problem many mathematicians will recognize. Indeed, near the end of Diaspora we read: In the end, there was only mathematics. In fact, I was carrying Incandescence with me when in mid-September I left the scorched and smoggy sprawl of southern California for the cool, wet, beautiful old city of Glasgow. I spent a lovely week there talking math with Tom Leinster, Eugenia Cheng, Bruce Bartlett and Simon Willerton. I'd been invited to the University of Glasgow to give a series of talks called the 2008 Rankin Lectures. I spoke about my three favorite numbers, and you can see the slides here: 3) John Baez, My favorite numbers, available at http://math.ucr.edu/home/baez/numbers/ I wanted to explain how different numbers have different personalities that radiate like force fields through diverse areas of mathematics and interact with each other in surprising ways. I've been exploring this theme for many years here. So, it was nice to polish some things I've written and present them in a more organized way. These lectures were sponsored by the trust that runs the Glasgow Mathematical Journal, so I'll eventually publish them there. I plan to add a lot of detail that didn't fit in the talks. I began with the number 5, since the golden ratio and the five-fold symmetry of the dodecahedron lead quickly to a wealth of easily enjoyed phenomena: from Penrose tilings and quasicrystals, to Hurwitz's theorem on approximating numbers by fractions, to the 120-cell and the Poincare homology sphere. After giving the first talk I discovered the head of the math department, Peter Kropholler, is a big fan of Rubik's cubes. I'd never been attracted to them myself. But his enthusiasm was contagious, especially when he started pulling out the unusual variants that he collects, eagerly explaining their subtleties. My favorite was the Rubik's dodecahedron, or Megaminx: 4) Wikipedia, Megaminx, http://en.wikipedia.org/wiki/Megaminx Then I got to thinking: it would be even better to have a Rubik's icosahedron, since its symmetries would then include M12, the smallest Mathieu group. And it turns out that such a gadget exists! It's called Dogic: 5) Wikipedia, Dogic, http://en.wikipedia.org/wiki/Dogic The Mathieu group M12 is the smallest of the sporadic finite simple groups. Someday I'd like to understand the Monster, which is the biggest of the lot. But if the Monster is the Mount Everest of finite group theory, M12 is like a small foothill. A good place to start. Way back in week20, I gave a cute description of M12 lifted from Conway and Sloane's classic book. If you get 12 equal-sized balls to touch a central one of the same size, and arrange them to lie at the corners of a regular icosahedron, they don't touch their neighbors. There's even room to roll them around in interesting ways! For example, you can twist 5 of them around clockwise so that this arrangement: 1 5 2 6 4 3 becomes this: 5 4 1 6 3 2 We can generate lots of permutations of the 12 outer balls using twists of this sort - in fact, all even permutations. But suppose we only use moves where we first twist 5 balls around clockwise and then twist 5 others counterclockwise. These generate a smaller group: the Mathieu group M12. Since we can do twists like this in the Dogic puzzle, I believe M12 sits inside the symmetry group of this puzzle! In a way it's not surprising: the Dogic puzzle has a vast group of symmetries, while M12 has a measly 8 x 9 x 10 x 11 x 12 = 95040 elements. But it'd still be cool to have a toy where you can explore the Mathieu group M12 with your own hands! The math department lounge at the University of Glasgow has some old books in the shelves waiting for someone to pick them up and read them and love them. They're sort of like dogs at the pound, sadly waiting for somebody to take them home. I took one that explains how Mathieu groups arise as symmetries of Steiner systems: 6) Thomas Beth, Dieter Jungnickel, and Hanfried Lenz, Design Theory, Cambridge U. Press, Cambridge, 1986. Here's how they get M12. Take a 12-point set and think of it as the projective line over F11 - in other words, the integers mod 11 together with a point called infinity. Among the integers mod 11, six are perfect squares: {0,1,3,4,5,9} by applying fractional linear transformations: z |-> (az + b)/(cz + d) where the matrix (a b) (c d) has determinant 1. These blocks then form a Steiner (5,6,12) system. In other words: there are 12 points, 6 points in each block, and any set of 5 points lies in a unique block. The group M12 is then the group of all transformations of the projective line that map points to points and blocks to blocks! If I make more progress on understanding this stuff I'll let you know. It would be fun to find deep mathematics lurking in mutant Rubik's cubes. Anyway, in my second talk I turned to the number 8. This gave me a great excuse to tell the story of how Graves discovered the octonions, and then talk about sphere packings and the marvelous E8 lattice, whose points can also be seen as integer octonions. I also sketched the basic ideas behind Bott periodicity, triality, and the role of division algebras in superstring theory. If you look at my slides you'll also see an appendix that describes two ways to get the E8 lattice starting from the dodecahedron. This is a nice interaction between the magic powers of the number 5 and those of the number 8. After my talk, Christian Korff from the University of Glasgow showed me a paper that fits this relation into a bigger pattern: 7) Andreas Fring and Christian Korff, Non-crystallographic reduction of Calogero-Moser models, Jour. Phys. A 39 (2006), 1115-1131. Also available as hep-th/0509152. They set up a nice correspondence between some non-crystallographic Coxeter groups and some crystallographic ones: the H2 Coxeter group and the A4 Coxeter group, the H3 Coxeter group and the D6 Coxeter group, the H4 Coxeter group and the E8 Coxeter group. A Coxeter group is a finite group of linear transformations of R^n that's generated by reflections. We say such a group is non-crystallographic if it's not the symmetries of any lattice. The ones listed above are closely tied to the number 5: H2 is the symmetry group of a regular pentagon. H3 is the symmetry group of a regular dodecahedron. H4 is the symmetry group of a regular 120-cell. Note these live in 2d, 3d and 4d space. Only in these dimensions are there regular polytopes with 5-fold rotational symmetry! Their symmetry groups are non-crystallographic, because no lattice can have 5-fold rotational symmetry. A Coxeter group is crystallographic, or a Weyl group, if it *is* symmetries of a lattice. In particular: A4 is the symmetry group of a 4-dimensional lattice also called A4. D6 is the symmetry group of a 6-dimensional lattice also called D6. E8 is the symmetry group of an 8-dimensional lattice also called E8. You can see precise descriptions of these lattices in week65 - they're pretty simple. Both crystallographic and noncrystallographic Coxeter groups are described by Coxeter diagrams, as explained back in week62. The H2, H3 and H4 Coxeter diagrams look like this: 5 o---o 5 o---o---o 5 o---o---o---o The A4, A6 and E8 Coxeter diagrams (usually called Dynkin diagrams) have twice as many dots as their smaller partners H2, H3 and H4: o---o---o---o o | o---o---o---o---o o | o | o---o---o---o---o---o I've drawn these in a slightly unorthodox way to show how they grow. In every case, each dot in the diagram corresponds to one of the reflections that generates the Coxeter group. The edges in the diagram describe relations - you can read how in week62. All this is well-known stuff. But Fring and Korff investigate something more esoteric. Each dot in the big diagram corresponds to 2 dots in its smaller partner: 5 o---o o---o---o---o A B B' A B A' o C 5 | o---o---o o---o---o---o---o A B C C' B' A B A' o D | o C 5 | o---o---o---o o---o---o---o---o---o A B C D D' C' B' A B A' If we map each generator of the smaller group (say, the generator D in H5) to the product of the two corresponding generators in the bigger one (say, D'D in E8), we get a group homomorphism. In fact, we get an *inclusion* of the smaller group in the bigger one! This is just the starting point of Fring and Korff's work. Their real goal is to show how certain exactly solvable physics problems associated to crystallographic Coxeter groups can be generalized to these three noncrystallographic ones. For this, they must develop more detailed connections than those I've described. But I'm already happy just pondering this small piece of their paper. For example, what does the inclusion of H2 in A4 really look like? It's actually quite beautiful. H2 is the symmetry group of a regular pentagon, including rotations and reflections. A4 happens to be the symmetry group of a 4-simplex. If you draw a 4-simplex in the plane, it looks like a pentagram! So, any symmetry of the pentagon gives a symmetry of the 4-simplex. So, we get an inclusion of H2 in A4. People often say that Penrose tilings arise from lattices in 4d space. Maybe I'm finally starting to understand how! The A4 lattice has a bunch of 4-simplices in it - but when we project these onto the plane correctly, they give pentagrams. I'd be very happy if this were the key. What about the inclusion of H3 in D6? Here James Dolan helped me make a guess. H3 is the symmetry group of a regular dodecahedron, including rotations and reflections. D6 consists of all linear transformations of R^6 generated by permuting the 6 coordinate axes and switching the signs of an even number of coordinates. But a dodecahedron has 6 axes going between opposite pentagons! If we arbitrarily orient all these axes, I believe any rotation or reflection of the dodecahedron gives an element of D6. So, we get an inclusion of H3 in D6. And finally, what about the inclusion of H4 in E8? H4 is the symmetry group of the 120-cell, including rotations and reflections. In 8 dimensions, you can get 240 equal-sized balls to touch a central ball of the same size. E8 acts as symmetries of this arrangement. There's a clever trick for grouping the 240 balls into 120 ordered pairs, which is explained by Fring and Korff and also by Conway's icosian construction of E8 described at the end of my talk on the number 8. Each element of H4 gives a permutation of the a permutation of the 240 balls. This permutation actually comes from an element of E8. So, we get an inclusion of H4 in E8. My last talk was on the number 24. Here I explained Euler's crazy proof that 1 + 2 + 3 + ... = -1/12 and how this makes bosonic strings happy when they have 24 transverse directions to wiggle around in. I also touched on the 24-dimensional Leech lattice and how this gives a version of bosonic string theory whose symmetry group is the Monster: the largest sporadic finite simple group. A lot of the special properties of the number 24 are really properties of the number 12 - and most of these come from the period-12 behavior of modular forms. I explained this back in week125. I recently ran into these papers describing yet another curious property of the number 12, also related to modular forms, but very easy to state: 8) Bjorn Poonen and Fernando Rodriguez-Villegas, Lattice polygons and the number 12. Available at http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.2555 9) John M. Burns and David O'Keeffe, Lattice polygons in the plane and the number 12, Irish Math. Soc. Bulletin 57 (2006), 65-68. Also available at http://www.maths.tcd.ie/pub/ims/bull57/M5700.pdf Consider the lattice in the plane consisting of points with integer coordinates. Draw a convex polygon whose vertices lie on this lattice. Obviously, the *differences* of successive vertices also lie on the lattice. We can create a new convex polygon with these differences as vertices. This is called the dual polygon. Say our original polygon is so small that the only lattice point in its interior is (0,0). Then the same is true of its dual! Furthermore, the dual of the dual is the original polygon! But now for the cool part. Take a polygon of this sort, and add up the number of lattice points on its boundary and the number of lattice points on the boundary of its dual. The total is 12. You can see an example in Figure 1 of the paper by Poonen and Rodriguez-Villegas. I like how their paper uses this theorem as a springboard for discussing a big question: what does it mean to explain the appearance of the number 12 here? They write: Our reason for selecting this particular statement, besides the intriguing appearance of the number 12, is that its proofs display a surprisingly rich variety of methods, and at least some of them are symptomatic of connections between branches of mathematics that on the surface appear to have little to do with one another. The theorem (implicitly) and proofs 2 and 3 sketched below appear in Fulton's book on toric varieties. We will give our new proof 4, which uses modular forms instead, in full. ----------------------------------------------------------------------- Quote of the Week: When the blind beetle crawls over the surface of a globe, he doesn't realize that the track he has covered is curved. I was lucky enough to have spotted it. - Albert Einstein ----------------------------------------------------------------------- Addenda: I thank Adam Glesser and David Speyer for catching mistakes. The only noncrystallographic Coxeter groups are the symmetry groups of the 120-cell (H4), the dodecahedron (H3), and the regular n-gons where n = 5,7,8,9,... The last list of groups is usually called I_n - or better, I_2(n), so that the subscript denotes the number of dots in the Dynkin diagram, as usual. But Fring and Korff use H2 as a special name for I_2(5), and that's nice if you're focused on 5-fold symmetry, because then H2 forms a little series together with H3 and H4. If you examine Poonen and Rodriguez-Villegas' picture carefully, you'll see a subtlety concerning the claim that the dual of the dual is the original polygon. Apparently you need to count every boundary point as a vertex! Read the papers for more precise details. For more discussion visit the n-Category Cafe: http://golem.ph.utexas.edu/category/2008/10/this_weeks_finds_in_mathematic_3 1.html ----------------------------------------------------------------------- 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/twfcontents.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: This Week's Finds in Mathematical Physics (Week 274) Originator: baez@math.UUCP (John Baez) Also available at http://math.ucr.edu/home/baez/week274.html March 12, 2009 This Week's Finds in Mathematical Physics (Week 274) John Baez I've been too busy. But luckily, I've been too busy writing papers about math and physics. So, let me talk about one of those. First, the astronomy picture of the week: 1) NASA Photojournal, 'Victoria Crater' at Meridiani Planum, http://photojournal.jpl.nasa.gov/catalog/PIA08813 This is the crater that NASA's rover called Opportunity has been exploring. It's 800 meters across. I like this picture just because it's beautiful. It was taken by the High Resolution Imaging Science Experiment on NASA's Mars Reconnaissance Orbiter. Now, on to business! I want to talk about this paper, which took over 2 years to write: 1) John Baez, Aristide Baratin, Laurent Freidel and Derek Wise, Representations of 2-groups on infinite-dimensional 2-vector spaces, available as arXiv:0812.4969. We can dream up the notion of 2-vector space by pondering this analogy chart: numbers vector spaces addition direct sum multiplication tensor product 0 the 0-dimensional vector space 1 the 1-dimensional vector space Just as you can add and multiply numbers, you can add and multiply vector spaces - but people call these operations direct sum and tensor product, to make them sound more intimidating. These new operations satisfy axioms similar to the old ones. However, what used to be equations like this: x + y = y + x now become isomorphisms like this: X + Y is isomorphic to Y + X. This means we're categorifying the concepts of plus and times. The unit for addition of vector spaces is the 0-dimensional vector space, and the unit for multiplication of vector spaces is the 1-dimensional vector space. But here's the coolest part. Our chart is like a snake eating its own tail. The first entry of the first column matches the last entry of the second column! The set of all numbers is the same as the 1-dimensional vector space. If by numbers we mean complex numbers, these are both just C. This suggests continuing the chart with a third column, like this: numbers (C) vector spaces (Vect) 2-vector spaces (2Vect) addition direct sum direct sum multiplication tensor product tensor product 0 C^0 Vect^0 1 C^1 Vect^1 Here C^0 is short for the 0-dimensional vector space, while C^1 is short for the 1-dimensional vector space - in other words the complex numbers, C. Vect is the category of all vector spaces. So, whatever a 2-vector space is, to make the chart nice we'd better have Vect be the 1-dimensional 2-vector space. We can emphasize this by calling it Vect^1. In fact, about 15 years ago Kapranov and Voevodsky invented a theory of 2-vector spaces that makes all this stuff work: 2) Mikhail Kapranov and Vladimir Voevodsky, 2-categories and Zamolodchikov tetrahedra equations, in Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods, RI, 1994, pp. 177-259. They mainly considered *finite-dimensional* 2-vector spaces. Every finite-dimensional vector space is secretly just C^n, or at least something isomorphic to that. Similarly, every finite-dimensional 2-vector space is secretly just Vect^n, or at least something equivalent to that. (You see, when we categorify once, equality becomes isomorphism. When we do it again, isomorphism becomes equivalence.) What's Vect^n, you ask? Well, what's C^n? It's the set where an element is an n-tuple of numbers: (x_1, ..., x_n) So, Vect^n is the category where an object is an n-tuple of vector spaces: (X_1, ..., X_n) It's all pathetically straightforward. Of course we also need to know what's a morphism in Vect^n. What's a morphism from (X_1, ..., X_n) to (Y_1, ..., Y_n)? It's just the obvious thing: an n-tuple of linear operators (f_1: X_1 -> Y_1, ..., f_n: X_n -> Y_n) And we compose these in the obvious way, namely componentwise. This may seem like an exercise in abstract nonsense, extending formal patterns just for the fun of it. But in fact, 2-vector spaces are all over the place once you start looking. For example, take the category of representations of a finite group, or the category of vector bundles over a finite set. These are finite-dimensional 2-vector spaces! Here I can't resist a more sophisticated digression, just to impress you. The whole theory of Fourier transforms for finite abelian groups categorifies nicely, using these examples. Any finite abelian group G has Pontryagin dual G* which is again a finite abelian group. I explained how this works back in week273. The Fourier transform is a map from functions on G to functions on G*. So, it's a map between vector spaces. But, lurking behind this is a map between 2-vector spaces! It's a map from representations of G to vector bundles over G*. You can safely ignore that last paragraph if you like. But if you want more details, try section 6.1 of this old paper: 3) John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125--189. Also available as arXiv:q-alg/9609018. As you can see from the title, I was trying to go beyond 2-vector spaces and think about 2-Hilbert spaces. That's because in quantum physics, we use Hilbert spaces to describe physical systems. Recent work on physics suggests that we categorify this idea and study 2-Hilbert spaces, 3-Hilbert spaces and so on - see week58 for details. In the above paper I defined and studied finite-dimensional 2-Hilbert spaces. But a lot of the gnarly fun details of Hilbert space theory show up only for infinite-dimensional Hilbert spaces - and we should expect the same for 2-Hilbert spaces. After these old papers on 2-vector spaces and 2-Hilbert spaces, various people came along and improved the whole story. For example: 4) Martin Neuchl, Representation Theory of Hopf Categories, Ph.D. dissertation, University of Munich, 1997. Chapter 2: 2-dimensional linear algebra. Available at http://math.ucr.edu/home/baez/neuchl.ps 5) Josep Elgueta, A strict totally coordinatized version of Kapranov and Voevodsky 2-vector spaces, to appear in Math. Proc. Cambridge Phil. Soc. Also available as arXiv:math/0406475. 6) Bruce Bartlett, The geometry of unitary 2-representations of finite groups and their 2-characters, available as arXiv:math/0807.1329. In the last of these, Bruce worked out how finite-dimensional 2-Hilbert spaces arise naturally in certain topological quantum field theories! Just as we can study representations of groups on vector spaces, we can study representations of 2-groups on 2-vector spaces: 7) Magnus Forrester-Barker, Representations of crossed modules and cat^1-groups, Ph.D. thesis, Department of Mathematics, University of http://www.informatics.bangor.ac.uk/public/mathematics/research/ftp/theses/f orrester-barker.pdf 8) John W. Barrett and Marco Mackaay, Categorical representations of categorical groups, Th. Appl. Cat. 16 (2006), 529-557. Also available as arXiv:math/0407463. 9) Josep Elgueta, Representation theory of 2-groups on finite dimensional 2-vector spaces, available as math.CT/0408120. A group is a category with one object, all of whose morphisms are invertible. Similarly, a 2-group is a 2-category with one object, all of whose morphisms and 2-morphisms are invertible. Just as we can define Lie groups to be groups where the group operations are smooth, we can define Lie 2-groups to be 2-groups where all the 2-group operations are smooth. Lie groups are wonderful things, so we can hope Lie 2-groups will be interesting too. There are already lots of examples known. You can see a bunch here: 10) John Baez and Aaron Lauda, Higher-dimensional algebra V: 2-groups, at http://www.tac.mta.ca/tac/volumes/12/14/12-14abs.html and also as arXiv:math/0307200. However, Barrett and Mackaay discovered something rather upsetting. While Lie groups have lots of interesting representations on finite-dimensional vector spaces, Lie 2-groups don't have many representations on finite-dimensional 2-vector spaces! In fact, the problem already shows up for representations of plain old Lie *groups* on 2-vector spaces. A Lie group can be seen as a special sort of Lie 2-group, where the only 2-morphisms are identity morphisms. The problem is that unlike a vector space, a 2-vector space has a unique basis - at least up to isomorphism. In C^n there's an obvious basis consisting of vectors like (1,0,0,...) (0,1,0,...) (0,0,1,...) and so on, but there are lots of other bases too. But in Vect^n the only basis goes like this: (C^1,C^0,C^0,...) (C^0,C^1,C^0,...) (C^0,C^0,C^1,...) Well, I'm exaggerating slightly: we could replace C^1 here by any other 1-dimensional vector space, and C^0 by any other 0-dimensional vector space. That would give other bases - but they'd still be *isomorphic* to the basis shown above. So, if we have a group acting on a finite-dimensional 2-vector space, it can't do much more than permute the basis elements. So, any representation of a group on a finite-dimensional 2-vector space gives an action of this group as permutations of a finite set! That's okay for finite groups, since these can act in interesting ways as permutations of finite sets. But it's no good for Lie groups. Lie groups are usually infinite: they're manifolds. So, they have lots of actions on *manifolds*, but not many actions on finite sets. This suggests that to study representations of Lie groups (or more general Lie 2-groups) on 2-vector spaces, we should invent some notion of infinite-dimensional 2-vector space, where the basis can be not a finite set but an infinite set - indeed, something more like a manifold. Luckily, such a concept was already lurking in the mathematical literature! In the categorification game, it's always good when the concepts you invent shed light on existing issues in mathematics. And it's especially fun when you categorify a concept and get a concept that turns out to have been known - or at least partially known - under some other name. Then you're not just making up new stuff: you're seeing that existing math already had categorification built into it! This happens surprisingly often. That's why I take categorification so seriously. The concept I'm talking about here is called a field of Hilbert spaces. Roughly speaking, the idea is that you pick a set X, possibly infinite. X could be the real line, for example. Then a field of Hilbert spaces assigns to each point x in X a Hilbert space H_x. As I've just described it, a measurable field of Hilbert spaces is an object in what we might call Hilb^X - a hairier, scarier relative of the tame little Vect^n that I've been talking about. Let's think about how Hilb^X differs from Vect^n. First, the the finite number n has been replaced by an infinite set X. That's why Hilb^X deserves to be thought of as an *infinite-dimensional* 2-vector space. Second, Vect has been replaced by Hilb - the category of Hilbert spaces. This suggests that Hilb^X is something more than a mere infinite-dimensional 2-vector space. It's closer to an infinite-dimensional *2-Hilbert* space! So, we've departed somewhat from our original goal of inventing a notion of infinite- dimensional vector space. But that's okay, especially if we're interested in applications to quantum physics that involve analysis. And here I must admit that I've left out some important details. When studying fields of Hilbert spaces, people usually bring in some analysis to keep the Hilbert space H_x from jumping around too wildly as x varies. They restrict attention to measurable fields of Hilbert spaces. To do this, they assume X is a measurable space: a space with a sigma-algebra of subsets, like the Borel sets of the real line. Then they assume H_x depends in a measurable way on x. The last assumption must be made precise. I won't do that here - you can see the details in our paper. But, here's an example of what I mean. Take X and partition it into countably many disjoint measurable subsets. For each one of these subsets, pick some Hilbert space H and let H_x = H for points x in that subset. So, the dimension of the Hilbert space H_x can change as x moves around, but only in a measurable way. In fact, every measurable field of Hilbert spaces is isomorphic to one of this form. So, a measurable field of Hilbert spaces on X is like a vector bundle over X, except the fibers are Hilbert spaces and there's no smoothness or continuity - the dimension of the fiber can jump in a measurable way. If you've studied algebraic geometry, this should remind you of a coherent sheaf. That's another generalization of a vector bundle that allows the dimension of the fiber to jump - but in an algebraic way, rather than a measurable way. One reason algebraic geometers like categories of coherent sheaves is because they need a notion of infinite-dimensional 2-vector space. Similarly, one reason analysts like measurable fields of Hilbert spaces is because they want *their own* notion of infinite-dimensional 2-vector space. Of course, they don't know this - if you ask, they'll strenuously deny it. We learned most of what we know about measurable fields of Hilbert spaces from this classic book: 11) Jacques Dixmier, Von Neumann Algebras, North-Holland, Amsterdam, 1981. This book was also helpful: 12) William Arveson, An Invitation to C*-Algebra, Chapter 2.2, Springer, Berlin, 1976. As you might guess from the titles of these books, measurable fields of Hilbert spaces show up when we study representations of operator algebras that arise in quantum theory. For example, any commutative von Neumann algebra A is isomorphic to the algebra L^infinity(X) for some measure space X, and every representation of A comes from a measurable field of Hilbert spaces on X. The following treatment is less detailed, but it explains how measurable fields of Hilbert spaces show up in group representation theory: 13) George W. Mackey, Unitary Group Representations in Physics, Probability and Number Theory, Benjamin-Cummings, New York, 1978. I'll say a lot more about this at the very end of this post, but here's a quick, rough summary. Any sufficiently nice topological group G has a dual: a measure space G* whose points are irreducible representations of G. You can build any representation of G from a measurable field of Hilbert spaces on G* together with a measure on G*. You build the representation by taking a direct integral of Hilbert spaces over G*. This is a generalization of writing a representation as a direct sum of irreducible representation. Direct integrals generalize direct sums - just as integrals generalize sums! By the way, Mackey calls measurable fields of Hilbert spaces measurable Hilbert space bundles. Those who like vector bundles will enjoy his outlook. But let's get back to our main theme: representations of 2-groups on infinite-dimensional 2-vector spaces. We don't know the general definition of an infinite-dimensional 2-vector space. However, for any measurable space X, we can define measurable fields of Hilbert spaces on X. We can also define maps between them, so we get a category, called Meas(X). Crane and Yetter call these measurable categories. I believe someday we'll see that measurable categories are a halfway house between infinite-dimensional 2-vector spaces and infinite-dimensional 2-Hilbert spaces. In fact, when we move up to n-vector spaces, it seems there could be n+1 different levels of Hilbertness. The conclusions of our paper include a proposed definition of 2-Hilbert space that can handle the infinite-dimensional case. So, why work with measurable categories? One reason is that they're 14) David Yetter, Measurable categories, Appl. Cat. Str. 13 (2005), 469-500. Also available as arXiv:math/0309185. 15) Louis Crane and David N. Yetter, Measurable categories and 2-groups, Appl. Cat. Str. 13 (2005), 501-516. Also available as arXiv:math/0305176. The paper by Crane and Yetter studies representations of discrete 2-groups on measurable categories. Our paper pushes forward by studying representations of *topological* 2-groups, including Lie 2-groups. Topology really matters for infinite-dimensional representations. For example, it's a hopeless task to classify the infinite-dimensional unitary representations of even a little group like the circle, U(1). But it's easy to classify the *continuous* unitary representations. A group has a category of representations, but a 2-group has a 2-category of representations! So, as usual, we have representations and maps between these , which physicists call intertwining operators or intertwiners for short. But we also have maps between intertwining operators, called 2-intertwiners. This is what's really exciting about 2-group representation theory. Indeed, intertwiners between 2-group representations resemble group representations in many ways - a fact noticed by Elgueta. It turns out one can define direct sums and tensor products not only for 2-group representations, but also for intertwiners! One can also define irreducibility and indecomposability, not just for representations, but also for intertwiners. Our paper gives nice geometrical descriptions of these notions. Some of these can be seen as generalizing the following paper of Crane and Sheppeard: 16) Louis Crane and Marnie D. Sheppeard, 2-categorical Poincare representations and state sum applications, available as arXiv:math/0306440. Crane and Sheppeard studied the 2-category of representations of the Poincare 2-group. It turns out that we can get representations of the Poincare 2-group from discrete subgroups of the Lorentz group. Since the Lorentz group acts as symmetries of the hyperbolic plane, these discrete subgroups act as symmetries of patterns like these: 17) Don Hatch, Hyperbolic planar tesselations, http://www.plunk.org/~hatch/HyperbolicTesselations/ But Crane and Sheppeard weren't just interested in beautiful geometry. They developed their example as part of an attempt to build new spin foam models in 4 dimensions. I've talked about such models on and off for many years here. The models I've discussed were usually based on representations of groups or quantum groups. Now we can build models using 2-groups, taking advantage of the fact that we have not just representations and intertwiners, but also 2-intertwiners. You can think of these models as discretized path integrals for gauge theories with a gauge 2-group. To compute the path integral you take a 4-manifold, triangulate it, and label the edges by representations, the triangles by intertwiners, and the tetrahedra by 2-intertwiners. Then you compute a number for each 4-simplex, multiply all these numbers together, and sum the result over labellings. Baratin and Freidel have done a lot of interesting computations in the Crane-Sheppeard model. I hope they publish their results sometime soon. To wrap up, I'd like to make a few technical remarks about group representation theory and measurable fields of Hilbert spaces. In week272 I talked about a class of measurable spaces called standard Borel spaces. Their definition was frighteningly general: any measurable space X whose measurable subsets are the Borel sets for some complete separable metric on X is called a standard Borel space. But then I described a theorem saying these are all either countable or isomorphic to the real line! They are, in short, the nice measurable spaces - the ones we should content ourselves with studying. In our work on 2-group representations, we always assume our measurable spaces are standard Borel spaces. We need this to get things done. But standard Borel spaces also show up ordinary group representation theory. Let me explain how! To keep your eyes from glazing over, I'll write rep to mean a strongly continuous unitary representation of a topological group on a separable Hilbert space. And, I'll call an irreducible one of these guys an irrep. Mackey wanted to build all the reps of a topological group G starting from irreps. This will only work if G is nice. Since Haar measure is a crucial tool, he assumed G was locally compact and Hausdorff. Since he wanted L^2(G) to be separable, he also assumed G was second countable. For a group with all these properties - called an lcsc group by specialists wearing white lab coats and big horn-rimmed glasses - Mackey was able to construct a measure space G* called the unitary dual of G. The idea is simple: the points of G* are isomorphism classes of irreps of G. But let's think about some special cases.... When G is a finite group, G* is a finite set. When G is abelian group, not necessarily finite, G* is again an abelian group, called the Pontryagin dual of G. I talked about this a lot in week273. When G is both finite and abelian, so of course is G*. But the tricky case is the general case, where G can be infinite and nonabelian! Here Mackey described a procedure which is a grand generalization of writing a rep as a direct sum of irreps. If we choose a sigma-finite measure dm(x) on G* and a measurable field H_x of Hilbert spaces on G*, we can build a rep of G. Here's how. Each point x of G* gives an irrep of G, say R_x. These form another measurable field of Hilbert space on G*. So, we can tensor H_x and R_x, and then form the direct integral integral_x (H_x tensor R_x) dm(x) As I already mentioned, a direct integral is a generalization of a direct sum. The result of doing this direct integral is a Hilbert space, and in this case it's a rep of G. The Hilbert spaces H_x specify the multiplicity of each irrep R_x in the representation we are building. The big question is whether we get *all* the reps of G this way. And the amazing answer, due to James Glimm, is: yes, IF G* IS A STANDARD BOREL SPACE! In this case we say G is type I. People know lots of examples. For example, an lcsc group will be type I if it's compact, or abelian, or a connected real algebraic group, or a connected nilpotent Lie group. That covers a lot of ground. However, there are plenty of groups, even Lie groups, that aren't type I. The representation theory of these is more tricky! If you want to know more, either read Mackey's book listed above, or this summary: 18) George W. Mackey, Infinite-dimensional group representations, Bull. Amer. Math. Soc. 69 (1963), 628-686. Available from Project Euclid at http://projecteuclid.org/euclid.bams/1183525453 ----------------------------------------------------------------------- Quote of the Week: The most fascinating thing about algebra and geometry is the way they struggle to help each other to emerge from the chaos of non-being, from those dark depths of subconscious where all roots of intellectual creativity reside. - Yuri Manin ----------------------------------------------------------------------- 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/twfcontents.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: torsion bounds for homology of finite simplicial complexes posting-account=RYxI8QoAAAD9JUyAC1FNssc5HDaOULXQ Suppose that K is a simplicial complex on n vertices, and fix a prime p. I'm looking for a statement like if p>n-3, then the homology of K has no p-torsion. Has anyone seen anything like that? I've seen a result like this (due to Gabber) about torsion in the homology of a chain complex of free abelian groups, but I think one should be able to do much better in a simplicial complex. === Subject: convergence of Hill determinant? Originator: bergv@math.uiuc.edu (Maarten Bergvelt) can you, please, help me to find a simple proof that truncating the Hill determinant is reasonable? In particular: given the equation y'' + y * (a + 2b*cos(2t))=0 to find a periodic solution y(t) with period 2pi y(t) = sum_{n in Z} c_n exp(i n t) I substitute this series into the equation. Now, the terms exp(i n t) are independent, so the corresponding coefficients must vanish: (a-n^2) c_n + b c_{n-2} + b c_{n+2} = 0. This resembles the equation matrix.vector=0 which has nontrivial solution iff det(matrix)=0. Truncating the infinite matrix above and writing its determinant=0 gives an equation for a and b allowing to find a=a(b) as an implicit function and its series up to order, say 30. Now I am missing a simple proof that the omitted terms are of order, say O(b^29). Pavel Pokorny === Subject: Conjecture about quotients of the modular group. Originator: bergv@math.uiuc.edu (Maarten Bergvelt) I wonder if this could be true: All finite simple groups are quotients of the modular group. Perhaps someone can point to a simple counter-example. The reason I thought it could be true is built up of a number of steps, each of which might well contain an elementary error, since I am no expert: -All finite simple groups can be generated by 2 generators. Call the periods of these generators p and q. -The free group on these generators corresponds to a (p,q) tiling of the hyperbolic plane -The finite simple group in question is a quotient of the automorphism group of the (p,q) tiling. -The (p,q) tiling is a quotient of the (inf,inf) tiling, which is in turn a quotient of the modular tiling. Gerard === Subject: Re: Conjecture about quotients of the modular group. Originator: bergv@math.uiuc.edu (Maarten Bergvelt) > I wonder if this could be true: All finite simple groups are quotients of the modular group. Well C_p usually isn't :-) If the modular group is PSL(2,Z) then it is a free product of a group of order 2 and a group of order 3. Thus G is a quotient of PSL(2,Z) iff it is generated by an elements of order 2 and an element of order 3 (or if it has order <= 3). Surely simple group theorists must know this ? If the modular group is just SL(2,Z) then we have the same answer. The matrix -I must be mapped to an element of the centre of the quotient, whichmust be the identity if the quotient is non-abelian simple. === Subject: Re: Conjecture about quotients of the modular group. Originator: bergv@math.uiuc.edu (Maarten Bergvelt) I wonder if this could be true: All finite simple groups are quotients of the modular group. Perhaps someone can point to a simple counter-example. The reason I thought it could be true is built up of a number of steps, > each of which might well contain an elementary error, since I am no expert: -All finite simple groups can be generated by 2 generators. > Call the periods of these generators p and q. > -The free group on these generators corresponds to a (p,q) tiling of the > hyperbolic plane > -The finite simple group in question is a quotient of the automorphism > group of the (p,q) tiling. > -The (p,q) tiling is a quotient of the (inf,inf) tiling, which is in > turn a quotient of the modular tiling. Gerard [Urgh, I thought I had copied this into the previous message :( ] References for this are: Liebeck, Martin W.; Shalev, Aner. Classical groups, probabilistic methods, and the $(2,3)$-generation problem. Ann. of Math. (2) 144 (1996), no. 1, 77--125. MR1405944 (97e:20106a) Liebeck, Martin W.; Shalev, Aner. Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky. J. Algebra 184 (1996), no. 1, 31--57. MR1402569 (97e:20106b) -- m === Subject: Re: Conjecture about quotients of the modular group. Originator: bergv@math.uiuc.edu (Maarten Bergvelt) I wonder if this could be true: All finite simple groups are quotients of the modular group. Perhaps someone can point to a simple counter-example. The Suzuki groups Sz(2^{2n+1}) (with n>=1) are simple and do not have elements of order 3, so they are not images of the modular group, which is isomorphic to the free product Z_2 * Z_2. -- m === Subject: Re: Conjecture about quotients of the modular group. Originator: bergv@math.uiuc.edu (Maarten Bergvelt) > I wonder if this could be true: All finite simple groups are quotients of the modular group. The modular group PSL_2(Z) is isomorphic to the free product Z/2 * Z/ 3. Thus its quotients are precisely the groups which are generated by an element of order 2 together with an element of order 3. One often speaks of these groups as being (2,3)- generated. It is known that PSL_2(F_9) is not (2,3)-generated. This is exceptional: for any other prime power q, PSL_2(F_q) is (2,3)-generated. See Macbeath's paper Generators of the linear fractional groups. > The reason I thought it could be true is built up of a number of steps, > each of which might well contain an elementary error, since I am no expert: -All finite simple groups can be generated by 2 generators. This is true. It relies on the classification of finite simple groups. Moreover, I believe it is known exactly which finite simple groups are not (2,3)-generated, and the exceptions form a short list. At the moment I am not able to track this down, but I found the following on wikipedia: ---- 2B2(22n+1) Suzuki groups Simplicity: Simple for n.9c1. The group 2B2(2) is solvable. Order: q^2 (q^2+1) (q-1) where q = 2^(2n+1). ---- Note that these orders are not divisible by 3, so certainly the groups cannot be (2,3)-generated. > Call the periods of these generators p and q. > -The free group on these generators corresponds to a (p,q) tiling of the > hyperbolic plane > -The finite simple group in question is a quotient of the automorphism > group of the (p,q) tiling. > -The (p,q) tiling is a quotient of the (inf,inf) tiling, which is in > turn a quotient of the modular tiling. This last part is not true: the free group on two generators is not a quotient of PSL(2,Z). However, the congruence subgroup Gamma(2) of PSL(2,Z) is free on two generators, so every finite simple group is a quotient of Gamma(2), so a subquotient of PSL(2,Z). This is closely related to Belyi's theorem. P.L. Clark === Subject: Re: JSH: another one bites the dust > (Skip now if you are tired of seeing JSH refuted by yet another > counterexample). Here's JSH's latest claimed solution to the factoring problem, with all > the blathering about how great he is stripped away. Number to be factored: d ...etc. While *I* find this convincing, you haven't got into what counts as a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is incontrovertably correct, your derivation MUST (by definition) be incorrect. Google define mathematical proof. Etc. QED. How did I do? M -- === Subject: Re: JSH: another one bites the dust > (Skip now if you are tired of seeing JSH refuted by yet another > counterexample). > Here's JSH's latest claimed solution to the factoring problem, with > all the blathering about how great he is stripped away. > Number to be factored: d ...etc. While *I* find this convincing, you haven't got into what counts as > a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is > incontrovertably correct, your derivation MUST (by definition) > be incorrect. Google define mathematical proof. Etc. BTW, he also proved that that if _p_ is a prime number, then 2p+1 can have at most two prime factors: in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so on. Jose Carlos Santos === Subject: Re: JSH: another one bites the dust > BTW, he also proved that that if _p_ is a prime number, then 2p+1 can > have at most two prime factors: in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so > on. While *I* find this convincing, you haven't got into what counts as a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is incontrovertably correct, you MUST be making this up. Google define mathematical proof. Etc. I'm getting the hang of this. Soon I'll be running the world too. M === Subject: Re: JSH: another one bites the dust <49be3df5$0$2527$da0feed9@news.zen.co.uk> <726tjgFo8qf1U1@mid.individual.net> <49be4352$0$2530$da0feed9@news.zen.co.uk> posting-account=lj-kRgoAAADbp-o6laOVCIWXjFF53GYz Gecko/2008092417 Firefox/3.0.3,gzip(gfe),gzip(gfe) > BTW, he also proved that that if p is a prime number, then 2p+1 can > have at most two prime factors:. > in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so > on. While *I* find this convincing, you haven't got into what counts as > a head in JSH's case. > He has a proof. I repeat. He has a proof. As a proof is > incontrovertably correct, you MUST be making this up. Google define mathematical proof. Etc. I'm getting the hang of this. Soon I'll be running the world too. M Not bad, but here are a few pointers: 1) 1st, you have to capitalize words if you want to refute an argument a la James Harris. As in, BUT I have mathematical PROOF. 2) 2nd, don't be afraid to use the word freakin (I mean if you go so far to assert that you have a freakin mathematical proof, then it's obvious you must have one.) 3) Point out how everyone knows that the all of the counter-examples are not true and are really just pesky attempts to slow you down. 4) Insert at least one threat as to how the conspiracy of all the mathematical elite trying to keep the truly deserving (such as his truly) from the gates will result in the collapse of mankind. 5) Insert a last rhetorical question to yourself musing about whether you should save mankind. But you know, it would be fun to make a game called, JSH or not JSH, where people look at 2 posts side by side, one from JSH, one from a gifted amateur such as yourself, and have to decide which is written by the real JSH. Peter === Subject: Re: JSH: another one bites the dust > BTW, he also proved that that if _p_ is a prime number, then 2p+1 can > have at most two prime factors: > in spite of the fact that 2*97 + 1 = 3*5*13, 2*127 + 1 = 3*5*17, and so > on. While *I* find this convincing, you haven't got into what counts as > a head in JSH's case. He has a proof. I repeat. He has a proof. As a proof is > incontrovertably correct, you MUST be making this up. JSH has a spoof, no proof. Since just has no assumptions, it is called justa spoof. Google define mathematical proof. Etc. I'm getting the hang of this. Soon I'll be running the world too. 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Roberts === Subject: Re: JSH: Factoring solution test run, Fermat primes posting-account=DkG3nAkAAAAVuxctYYjlIz6_Yb78PVNd rv:1.8.1.3) Gecko/20070309 Firefox/2.0.0.3,gzip(gfe),gzip(gfe) > In case you missed it, I've found what I claim is a solution to the > factoring problem involving factor D-1 in order to factor a target > composite D, where I used Pell's Equation. > It was brought to my attention by Penny Hassett in a comment on my > math blog that Fermat primes might be a good area to bring this new > solution to bear, as factoring D-1 is then trivial. > The possibility here is in finding the next Fermat prime. Here is the > factoring algorithm: > Given an odd composite D, to be factored, you factor it by taking its > gcd with a function I call r_c(v), where: > r_c(v) = 2((D+1)v^2 - 2f_1*v + f_1^2) > and f_1 is a factor of D-1, so with Fermat numbers, it is always just > 2 raised to some natural number power, where you find rational v, such > that v is in the following range: > (f_1 - sqrt(f_1^2 - [f_1^2 - D/2](D+1)))/(D+1) < v < (f_1 + sqrt(f_1^2 > - [f_1^2 - D/2](D+1)))/(D+1) You're restricting yourself in two bad ways. First, by requiring |r (v)| < D you have essentially limited your range for v to v = -1/2, 0, 1/2, as mike3 has already pointed out (plug in some actual values for D and f_1 above and you'll see that). > and r_c(v) is an integer, where if that range gives an integer v, then > you're done, as you just plug that into r_c(v), and you're guaranteed > have a factorization of D, from the gcd. Here's your second bad choice. Requiring r_c(v) to be an integer will almost never yield a useful factor, especially for a Fermat prime. Observe that gcd(r_c(v), D) = gcd(2((D+1)v^2 - 2 v f_1 + f_1^2) = gcd(2((v - f_1)^2 + D v^2, D) = gcd(2(v - f_1)^2, D) = gcd((v - f_1)^2, D) since we may assume D is odd. But now even without your restriction on the range of v, we are basically looking at nothing but trial division to find a suitable v. If we relax the restriction that v be an integer or half an integer, we can indeed get nontrivial divisors for D. Suppose, for example, we wanted to test the primality of F_5 = 2^32 + 1. By Lucas' result we need only use f_1 = 128 (since g will be a factor of F_n only if g = 1 mod (2^{n+2})) and we find that v = -1/5 will yield r_c(-1/5) = 2((-1/10 - 128) + (2^32 + 1)/100) and the numerator of that fraction has a factor of 641, which we know divides 2^32 + 1. > If no integers are available for v, not to worry! Turns out a > rational solution MUST exist if there is rational range at all, and > it's denominator is, 2. Actually, no. There will be a rational solution (where the numerator has a factor dividing D), but its denominator won't in general be 2. Rick === Subject: Re: JSH: Factoring solution test run, Fermat primes Nntp-Posting-Host: hera.cwi.nl ... > Given D = 2^k + 1, you have that D-1 = 2^k, so f_1 = 1, or f_1 = 2^= > c, > where c is a natural number up to k potentially, but you will not have > rational solutions that far up. The smallest k for which it is unknown whether it is prime or not is 2^33, or 8589934592. > Then you just check the range of possible rational v's with: > > (f_1 - sqrt(f_1^2 - [f_1^2 - D/2](D+1)))/(D+1) < v < (f_1 + sqrt(f_1^2 > - [f_1^2 - D/2](D+1)))/(D+1) > > where you loop through every f_1 for which you have rational > solutions. Notice that once f_1 > sqrt(D/2) you have no more rational > solutions. Aha, so we have to loop only to f_1 = 2^4294967296. Helps a lot! I think it will take a bit of time to do all those calculations. Good luck. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: JSH: Factoring solution test run, Fermat primes posting-account=wVv_VwoAAAAVTfUuyxLzug5SzYWCgHj1 Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > In case you missed it, I've found what I claim is a solution to the > factoring problem involving factor D-1 in order to factor a target > composite D, where I used Pell's Equation. It was brought to my attention by Penny Hassett in a comment on my > math blog that Fermat primes might be a good area to bring this new > solution to bear, as factoring D-1 is then trivial. The possibility here is in finding the next Fermat prime. Here is the > factoring algorithm: Given an odd composite D, to be factored, you factor it by taking its > gcd with a function I call r c(v), where: r c(v) = 2((D+1)v^2 - 2f 1*v + f 1^2) and f 1 is a factor of D-1, so with Fermat numbers, it is always just > 2 raised to some natural number power, where you find rational v, such > that v is in the following range: (f 1 - sqrt(f 1^2 - [f 1^2 - D/2](D+1)))/(D+1) < v < (f 1 + sqrt(f 1^2 > - [f 1^2 - D/2](D+1)))/(D+1) and r c(v) is an integer, where if that range gives an integer v, then > you're done, as you just plug that into r c(v), and you're guaranteed > have a factorization of D, from the gcd. If no integers are available for v, not to worry! Turns out a > rational solution MUST exist if there is rational range at all, and > it's denominator is, 2. Yup. 2. So like 1/2 or -1/2 will probably pop up a lot. Ok, so one of you code jockeys can script that up and give it a whirl > against Fermat numbers. When you see that it works, break some records. It will be screamingly fast. Like nothing you've ever seen. The > records should be easily within reach, within minutes. James Harris Well, silly me. I thought that a thread with a title like Factoring solution, test run would actually present the results of a test run of your factoring solution. No such luck, eh? Marcus. === Subject: Re: Factoring solution test run, Fermat primes > In case you missed it, I've found what I claim is a solution to the > factoring problem involving factor D-1 in order to factor a target > composite D, where I used Pell's Equation. now that the factoring problem is solved, you may want to tackle the Riemann >hypothesis He's already done that. I forget whether his prime counting function shows that RH is almost certainly false or almost certainly true but it's one or the other. The rest of us were boggled how this could follow from an old _algorithm_ for _computing_ pi(n). Shows how much we know. >to show those corny mathematicians what you can do when you put >your mind to something. > David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: Factoring solution test run, Fermat primes [curious george, to JSH] > now that the factoring problem is solved, you may want to tackle the > Riemann hypothesis [David C. Ullrich] > He's already done that. I forget whether his prime counting function > shows that RH is almost certainly false or almost certainly true > but it's one or the other. He strengthed his claim to it's false, period. Why is it false? He never gave a reason, not even one based on completeing the square one or more times ;-) The /real/ reason he concluded RH is false appears to be that he /believes/ mathematicians believe RH is true -- and since academics are all lying scum, QED. > The rest of us were boggled how this could follow from an old > _algorithm_ for _computing_ pi(n). Shows how much we know. It supposedly follows from his partial difference equation gibberish. In hindsight, at least that was a refreshing break from the current endless gibberish about Pell's equation ;-) === Subject: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) and hey, share the wealth, versus going after the next Fermat prime-- > if it exists--on my own. As for pseudo-code, the algorithm is trivially easy. Given D = 2^k + 1, you have that D-1 = 2^k, so f 1 = 1, or f 1 = 2^c, > where c is a natural number up to k potentially, but you will not have > rational solutions that far up. Then you just check the range of possible rational v's with: (f 1 - sqrt(f 1^2 - [f 1^2 - D/2](D+1)))/(D+1) < v < (f 1 + sqrt(f 1^2 > - [f 1^2 - D/2](D+1)))/(D+1) > There's an asymptotic limit in these formulas as D->oo, which gives -1/sqrt(2) < v < 1/sqrt(2) at most. What do you think of that? See below for my investigation into using the algorithm to factor numbers, and code. > where you loop through every f 1 for which you have rational > solutions. Notice that once f 1 > sqrt(D/2) you have no more rational > solutions. For each range of possible solutions you look for integer v's within > that range, and for EACH of them, you will have a non-trivial > factorization of D, from r c(v), where: r c(v) = 2((D+1)v^2 - 2f 1*v + f 1^2) (you can actually leave off that factor of 2 of course) as the gcd of r c(v) and D will give you a non-trivial factor! Easy > as pie. If no integer solutions for v are available, then you use the > fractional one that must be available where the denominator of v is > 2. So, for instance, -1/2 could be a solution. Only fractions with 2 > itself as the denominator need be checked. The algorithm will give you each non-trivial factorization available > as you loop through possible f's. > I gave it a try. With the asymptotic limit, and this requirement that v need to be a integer or half integer, there are at most THREE possibilities for v: -1/2, 0, and 1/2. I tried D = 9. No joy. Other D seem to work, such as D = 65. However, NO actual Fermat number (i.e. k = power of two) seems to take, e.g. D = 4294967297 does not seem to factor. > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of 65537. Which happens to be a Fermat number itself. It seems that when it does yield factors, the first one it spits out is always a Fermat number, so apparently the number must have a Fermat-number factor in order for the algorithm to crack it. It does not appear to be able to factor any actual Fermat composites. I can't, for example, get D = 4294967297 to budge with your algorithm. It also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor criterion does not appear to be sufficient, although it sure appears to be necessary. But if your algorithm really does work, then it would seem I have made a mistake somewhere, since I should therefore be able to factor 4294967297. If so, what is my mistake? (Code at the bottom) > As you loop through the 4049, the algorithm will spit out any non- > trivial factors of 2^4048+1. > Well it did, it spat out 65537 for one of the factors. But it doesn't seem to work for other D and it doesn't seem to work for Fermat-number D. It can even factor D = 2^65535 + 1 -- vomiting up quite a few factors, in fact (although not all of them are primes) -- but 2^65536 + 1 fails to fall to this algorithm... And it is those real live Fermat numbers that we want to factor. > If it gives you none then that is a prime number. > Seems false according to my tests. 4294967297 is not a prime number. I came up with the following PARI/GP code: -- rc(v, f1, f2, D) = 2*((D+1)*v^2 - 2*f1*v + f1^2); k = 32; D = 2^k + 1; for(c=1,k/2, f1 = 2^c; f2 = (D-1)/f1; for(vmult=0,2, v = -1/2 + (vmult/2); g = gcd(rc(v, f1, f2, D), D); if((g != 1) && (g != D), print(g); break(2);); ); ); -- rc is just your function r c(v), D is the number to be factored, k is the exponent raising 2, f1 and f2 are 2 factors of D-1, such that D-1 = f1*f2, and the innermost loop just loops through the 3 possible v-values of -1/2, 0, and 1/2 and checks if gcd(r c(v), D) is not 1 or D. If it isn't, it spits it out and stops looping. You can remove the break to allow it to find more factors. Not all of them are necessarily prime. Note that for this D-value -- a real live Fermat number -- namely 4294967297, the algorithm fails to find any factors. Because there's only at *most* 3 possibilities for v I don't bother trying to eliminate any using the range formula, as there's so few to try, you know... it just adds an extra complication that isn't necessary for a first test. But all integer/ half- integer v in that range surely will be tested. If I've made a mistake in any of the above, by all means tell me. Are there more values for v to test? If so, what are they? === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat ... > It's a very easy algorithm to code. =A0It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > > Turns out that is one number it seems to work on, yielding a factor of > 65537. Ah, but 2^4048 + 1 is *not* a Fermat number. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.48 Safari/525.19,gzip(gfe),gzip(gfe) > I thought it might be faster to let someone else out there code it, > and hey, share the wealth, versus going after the next Fermat prime-- > if it exists--on my own. > As for pseudo-code, the algorithm is trivially easy. > Given D = 2^k + 1, you have that D-1 = 2^k, so f 1 = 1, or f 1 = 2^c, > where c is a natural number up to k potentially, but you will not have > rational solutions that far up. > Then you just check the range of possible rational v's with: > (f 1 - sqrt(f 1^2 - [f 1^2 - D/2](D+1)))/(D+1) < v < (f 1 + sqrt(f 1^2 > - [f 1^2 - D/2](D+1)))/(D+1) There's an asymptotic limit in these formulas as D->oo, which > gives -1/sqrt(2) < v < 1/sqrt(2) at most. What do you think of that? See below for my investigation into using the algorithm to factor > numbers, > and code. > where you loop through every f 1 for which you have rational > solutions. Notice that once f 1 > sqrt(D/2) you have no more rational > solutions. > For each range of possible solutions you look for integer v's within > that range, and for EACH of them, you will have a non-trivial > factorization of D, from r c(v), where: > r c(v) = 2((D+1)v^2 - 2f 1*v + f 1^2) > (you can actually leave off that factor of 2 of course) > as the gcd of r c(v) and D will give you a non-trivial factor! Easy > as pie. > If no integer solutions for v are available, then you use the > fractional one that must be available where the denominator of v is > 2. So, for instance, -1/2 could be a solution. Only fractions with 2 > itself as the denominator need be checked. > The algorithm will give you each non-trivial factorization available > as you loop through possible f's. I gave it a try. With the asymptotic limit, and this requirement that > v need to be a integer or half integer, there are at most THREE > possibilities > for v: -1/2, 0, and 1/2. That doesn't sound right. I'll need to look at that later. > I tried D = 9. No joy. Other D seem to work, such as D = 65. However, It won't factor a square. But that's not a true issue. > NO actual Fermat number (i.e. k = power of two) seems to take, e.g. > D = 4294967297 does not seem to factor. That can't be right. > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. Turns out that is one number it seems to work on, yielding a factor of > 65537. Which happens to be a Fermat number itself. It seems that when > it does yield factors, the first one it spits out is always a Fermat > number, > so apparently the number must have a Fermat-number factor in order for > the algorithm to crack it. You're probably throwing away needed values. Did you use f 1 = 1? > It does not appear to be able to factor any actual Fermat composites. > I > can't, for example, get D = 4294967297 to budge with your algorithm. > It > also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor It can't handle squares. > criterion does not appear to be sufficient, although it sure appears > to be > necessary. But if your algorithm really does work, then it would seem I have made > a mistake somewhere, since I should therefore be able to factor > 4294967297. > If so, what is my mistake? (Code at the bottom) I'm less interested in checking your mistakes than in coding it myself. You went on about squares as if it were a dream come true that the algorithm can't factor 9. But that's stupid. Who cares if an algorithm can't factor a square? You just take the square root. And your cohorts are running wild on the newsgroups making negative postings. I think it quite possible you are lying, so I'll code it myself later today, and end this nonsense. James Harris === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) [JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. So did you? It's the only way you can ever be convinced that you're wrong -- and something any sane person would have tried at the start. So one of two things will happen, after you find your code doesn't work and can't be repaired: (1) you'll pretend you never made this promise, and continue ranting like a lunatic hoping no one will notice; or, (2) you'll start deleting all your posts on this topic, and never mention it again. Class act either way ;-) === Subject: Re: Test run results [JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. So did you? It's the only way you can ever be convinced that you're wrong >-- and something any sane person would have tried at the start. So one of two things will happen, after you find your code doesn't work and >can't be repaired: (1) you'll pretend you never made this promise, and >continue ranting like a lunatic hoping no one will notice; or, (2) you'll >start deleting all your posts on this topic, and never mention it again. Class act either way ;-) This is a simple program that compresses any file - even random data - at a 1000:1 ratio, using about 1K of pure assembly language. The code is almost complete; I just have to fix one last bug (for some reason the decompression module outputs all zeros instead of the input file) but I am confident that I will be able to fix that one last bug any time now, and put all the other compression algorithms out of business. It also (in the same 1K!) correctly identifies and deletes This module also has a minor bug (for some weird reason it on the brink of fixing that one last bug. I have been told that the above description is enough for anyone to duplicate my work up to the point where I have it, so someone else may very well have fixed those bugs already and emailed me the result. I hope it gets past my -- Guy Macon === Subject: Re: Test run results >[JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. >So did you? It's the only way you can ever be convinced that you're wrong >-- and something any sane person would have tried at the start. >So one of two things will happen, after you find your code doesn't work and >can't be repaired: (1) you'll pretend you never made this promise, and >continue ranting like a lunatic hoping no one will notice; or, (2) you'll >start deleting all your posts on this topic, and never mention it again. >Class act either way ;-) This is a simple program that compresses any file - even random > data - at a 1000:1 ratio, using about 1K of pure assembly language. The code is almost complete; I just have to fix one last bug > (for some reason the decompression module outputs all zeros > instead of the input file) but I am confident that I will be > able to fix that one last bug any time now, and put all the > other compression algorithms out of business. It also (in the same 1K!) correctly identifies and deletes > This module also has a minor bug (for some weird reason it > on the brink of fixing that one last bug. I have been told that the above description is enough for > anyone to duplicate my work up to the point where I have > it, so someone else may very well have fixed those bugs > already and emailed me the result. I hope it gets past my Compress this! /dev/zero. -- Michael Press === Subject: Re: Test run results >[JSH, thrashing like a fish in desert sand] > ... > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. >So did you? It's the only way you can ever be convinced that you're wrong >-- and something any sane person would have tried at the start. >So one of two things will happen, after you find your code doesn't work and >can't be repaired: (1) you'll pretend you never made this promise, and >continue ranting like a lunatic hoping no one will notice; or, (2) you'll >start deleting all your posts on this topic, and never mention it again. >Class act either way ;-) This is a simple program that compresses any file - even random >data - at a 1000:1 ratio, using about 1K of pure assembly language. The code is almost complete; I just have to fix one last bug >(for some reason the decompression module outputs all zeros >instead of the input file) but I am confident that I will be >able to fix that one last bug any time now, and put all the >other compression algorithms out of business. Sounds interesting. In case it helps, I've read about programs that can compress any file to less than 1 KB. It seems the decompression works better if the original file has not been deleted. >It also (in the same 1K!) correctly identifies and deletes >This module also has a minor bug (for some weird reason it >on the brink of fixing that one last bug. I have been told that the above description is enough for >anyone to duplicate my work up to the point where I have >it, so someone else may very well have fixed those bugs >already and emailed me the result. I think I could help you with the compression algorithm, but I don't know anything about how email works, sorry. >I hope it gets past my David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009020407 Iceweasel/3.0.6 (Debian-3.0.6-1),gzip(gfe),gzip(gfe) I gave it a try. With the asymptotic limit, and this requirement that > v need to be a integer or half integer, there are at most THREE > possibilities > for v: -1/2, 0, and 1/2. That doesn't sound right. I'll need to look at that later. > Ah, so there ARE more choices for v. That must be why it won't factor 4294967297. What are they? How many are they? > I tried D = 9. No joy. Other D seem to work, such as D = 65. However, It won't factor a square. But that's not a true issue. > Fine, but what about... > NO actual Fermat number (i.e. k = power of two) seems to take, e.g. > D = 4294967297 does not seem to factor. That can't be right. > that? > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of > 65537. Which happens to be a Fermat number itself. It seems that when > it does yield factors, the first one it spits out is always a Fermat > number, > so apparently the number must have a Fermat-number factor in order for > the algorithm to crack it. You're probably throwing away needed values. Did you use f 1 = 1? > Yes. Did I miss a v? If it's supposed to be some v with other denominator then there are an *infinite* number of those. Which ones should I try? > It does not appear to be able to factor any actual Fermat composites. > I > can't, for example, get D = 4294967297 to budge with your algorithm. > It > also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor It can't handle squares. > So why can't it handle 4294967297s either? Or for that matter, any true Fermat composite (i.e. composite 2^k + 1 where k is a power of 2 )? > criterion does not appear to be sufficient, although it sure appears > to be > necessary. > But if your algorithm really does work, then it would seem I have made > a mistake somewhere, since I should therefore be able to factor > 4294967297. > If so, what is my mistake? (Code at the bottom) I'm less interested in checking your mistakes than in coding it > myself. > Let's see that code, okay? > You went on about squares as if it were a dream come true that the > algorithm can't factor 9. But that's stupid. Who cares if an algorithm can't factor a square? > You just take the square root. > Sure. But now you're focusing so much on 9 and not focusing on... 4294967297. > And your cohorts are running wild on the newsgroups making negative > postings. I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. > If there's something I've missed it's because you didn't make it clear. Like you didn't make the bit clear about factoring squares. Is there perhaps also something else you're not making clear that explains the trouble with 4294967297? === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) I gave it a try. With the asymptotic limit, and this requirement that > v need to be a integer or half integer, there are at most THREE > possibilities > for v: -1/2, 0, and 1/2. > That doesn't sound right. I'll need to look at that later. Ah, so there ARE more choices for v. That must be why it won't > factor 4294967297. What are they? How many are they? > I tried D = 9. No joy. Other D seem to work, such as D = 65. However, > It won't factor a square. But that's not a true issue. Fine, but what about... > NO actual Fermat number (i.e. k = power of two) seems to take, e.g. > D = 4294967297 does not seem to factor. > That can't be right. that? > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of > 65537. Which happens to be a Fermat number itself. It seems that when > it does yield factors, the first one it spits out is always a Fermat > number, > so apparently the number must have a Fermat-number factor in order for > the algorithm to crack it. > You're probably throwing away needed values. Did you use f 1 = 1? Yes. Did I miss a v? If it's supposed to be some v with other denominator > then there > are an *infinite* number of those. Which ones should I try? > It does not appear to be able to factor any actual Fermat composites. > I > can't, for example, get D = 4294967297 to budge with your algorithm. > It > also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor > It can't handle squares. So why can't it handle 4294967297s either? Or for that matter, any > true Fermat composite (i.e. composite 2^k + 1 where k is a power of > 2 )? > criterion does not appear to be sufficient, although it sure appears > to be > necessary. > But if your algorithm really does work, then it would seem I have made > a mistake somewhere, since I should therefore be able to factor > 4294967297. > If so, what is my mistake? (Code at the bottom) > I'm less interested in checking your mistakes than in coding it > myself. Let's see that code, okay? > You went on about squares as if it were a dream come true that the > algorithm can't factor 9. > But that's stupid. Who cares if an algorithm can't factor a square? > You just take the square root. Sure. But now you're focusing so much on 9 and not focusing on... > 4294967297. > And your cohorts are running wild on the newsgroups making negative > postings. > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. If there's something I've missed it's because you didn't > make it clear. Like you didn't make the bit clear about factoring > squares. > Is there perhaps also something else you're not making clear that > explains the trouble with 4294967297? Hmm. It seems that v = -1/5 will work, if we use the NUMERATOR of the resulting RATIONAL r for our gcd, but now it seems there could be an infinite number of choices possible for v... === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.48 Safari/525.19,gzip(gfe),gzip(gfe) > I gave it a try. With the asymptotic limit, and this requirement that > v need to be a integer or half integer, there are at most THREE > possibilities > for v: -1/2, 0, and 1/2. > That doesn't sound right. I'll need to look at that later. > Ah, so there ARE more choices for v. That must be why it won't > factor 4294967297. What are they? How many are they? > I tried D = 9. No joy. Other D seem to work, such as D = 65. However, > It won't factor a square. But that's not a true issue. > Fine, but what about... > NO actual Fermat number (i.e. k = power of two) seems to take, e.g. > D = 4294967297 does not seem to factor. > That can't be right. > that? > It's a very easy algorithm to code. It will scream through Fermat > numbers because for say 2^4048 + 1, you have only 4049 checks to do. > Turns out that is one number it seems to work on, yielding a factor of > 65537. Which happens to be a Fermat number itself. It seems that when > it does yield factors, the first one it spits out is always a Fermat > number, > so apparently the number must have a Fermat-number factor in order for > the algorithm to crack it. > You're probably throwing away needed values. Did you use f 1 = 1? > Yes. > Did I miss a v? If it's supposed to be some v with other denominator > then there > are an *infinite* number of those. Which ones should I try? > It does not appear to be able to factor any actual Fermat composites. > I > can't, for example, get D = 4294967297 to budge with your algorithm. > It > also doesn't seem to work for D = 9. Hmm. So the Fermat-number-factor > It can't handle squares. > So why can't it handle 4294967297s either? Or for that matter, any > true Fermat composite (i.e. composite 2^k + 1 where k is a power of > 2 )? > criterion does not appear to be sufficient, although it sure appears > to be > necessary. > But if your algorithm really does work, then it would seem I have made > a mistake somewhere, since I should therefore be able to factor > 4294967297. > If so, what is my mistake? (Code at the bottom) > I'm less interested in checking your mistakes than in coding it > myself. > Let's see that code, okay? > You went on about squares as if it were a dream come true that the > algorithm can't factor 9. > But that's stupid. Who cares if an algorithm can't factor a square? > You just take the square root. > Sure. But now you're focusing so much on 9 and not focusing on... > 4294967297. > And your cohorts are running wild on the newsgroups making negative > postings. > I think it quite possible you are lying, so I'll code it myself later > today, and end this nonsense. > If there's something I've missed it's because you didn't > make it clear. Like you didn't make the bit clear about factoring > squares. > Is there perhaps also something else you're not making clear that > explains the trouble with 4294967297? Hmm. It seems that v = -1/5 will work, if we use the NUMERATOR of the > resulting RATIONAL r for our gcd, but now it seems there could be an > infinite > number of choices possible for v... I have it coded. It works fine. I'm going to clean up the code some and figure out what to do next. JSH === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > I have it coded. It works fine. Post the code so that folks can try it. -- Science is a differential equation. Religion is a boundary condition. --Alan Turing === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) <49BF6F40.9FEBCB4F@tesco.net> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.48 Safari/525.19,gzip(gfe),gzip(gfe) On Mar 17, 2:37am, Frederick Williams I have it coded. It works fine. Post the code so that folks can try it. I posted it on comp.theory and sci.physics, where yes, I had code posted last night, which was severely flawed, so I started a new thread, with very much cleaned up code, which also, yup, has the updated factoring algorithm. I talk about having solve the factoring problem and having a mathematical proof, but also talk about implementation being a different issue. In this case, the underlying mathematical proof has not changed, but in trying to get a working algorithm, I've been having to make a lot of changes to the implementation aspect. Specifically the mathematical proof uses: x = r(v)/t(v) where r(v) and t(v) are coprime integers with a rational v. But I had problems getting them coprime, and found out I couldn't, So there was an addendum to handle a factor of that target composite D that attaches itself to the only r(v) and t(v) I could get. THEN I had more coprimeness issues between them, which I just resolved today, completing the algorithm, so I could update the code with the demonstrate it as a proof of concept will only factor up to 2^29+1, as it's a proof of concept program that only factors numbers of the form 2^n+1, with n a positive integer less than 30. Wow. What a rush. James Harris === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=yxbZkgkAAABQBvyYeebYQ-PAvi0uT3tG Gecko/20080829 Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. So how many operations (either on average or worst case) are required to factor numbers on the order of 2^29? You could count each arithmetic operation, and since the total number of operations is less than 2^29, these counters would fit conveniently into 32-bit integers. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > I posted it on comp.theory and sci.physics, where yes, I had code > posted last night, which was severely flawed, so I started a new > thread, with very much cleaned up code, which also, yup, has the > updated factoring algorithm. I talk about having solve the factoring problem and having a > mathematical proof, but also talk about implementation being a > different issue. > In this case, the underlying mathematical proof has not changed, but > in trying to get a working algorithm, I've been having to make a lot > of changes to the implementation aspect. Specifically the > mathematical proof uses: x = r(v)/t(v) where r(v) and t(v) are coprime integers with a rational v. But I had problems getting them coprime, and found out I couldn't, So there was an addendum to handle a factor of that target composite D > that attaches itself to the only r(v) and t(v) I could get. THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. Wow. What a rush. > James Harris Any coder who is worth anything (there are many here) will tell you that there is absolutely no such thing as code perfect. Just because you can't find a fault, doesn't mean they aren't there waiting for someone else to can't break it, does not mean someone else wont be able to either now or sometime in the future. Even proof of concept code for the factoring problem should be able to factor anything, although quite sloppily and with mediocre efficiency, because it's not a finished product. Save the polishing for something you are going to release publicly and intended for everyone, even the layman to use (the general populace don't care how a program is made or how it does what it does as long as it does so cleanly and efficiently). Since I rarely pay any attention to your threads (as most people here rarely pay any attention to mine) I can only guess at what kind of primes you are trying to factor, but it doesn't matter. Even proof of concept code should be able to factor every known prime within the subset of primes you are trying to factor. Here is a tip, start with the largest prime from the subset you are trying to factor. By subset I am referring to Mersenne primes, Fermat primes etc. When you have an agorithm that can factor that efficiently and cleanly, every lesser prime will be a literal cake walk because they are smaller and therefore, generally speaking, use less resources in the factoring. Of course, as new primes of your chosen subset are discovered, you may need to tweak your code a little. Here is a hint, use a language that was designed with intensive numerical computations in mind, FORTRAN is the first one that springs up, or use something similar. Better yet, write it as close to machine code as you can, this will give you maximum efficiency. At present, your task is not even half finished. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) ... I can only guess at what kind of primes you are > trying to factor, Even Harris can factor primes. -- Science is a differential equation. Religion is a boundary condition. --Alan Turing === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > Even Harris can factor primes. That may be so, but different primes have different equations, hence the not knowing what kind of prime, is it Mersenne, Fermat, or one a host of others. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) <33%vl.29297$cu.23346@news-server.bigpond.net.au> <49C0BFEB.3D40D4E1@tesco.net> posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080922 Ubuntu/7.10 (gutsy) Firefox/2.0.0.17,gzip(gfe),gzip(gfe) > Even Harris can factor primes. That may be so, but different primes have different equations, hence the not > knowing what kind of prime, is it Mersenne, Fermat, or one a host of others. I'm a bit confused here. Do you mean Primes have equations, or Primes have factors ? Brian Chandler === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > > I have it coded. It works fine. Post the code so that folks can try it. He posted it to comp.theory. It contains an off by one error: to compute 2^n he uses 2< QR Decomposition posting-account=9MUq6goAAADgjsPh96c7CaIVgaYLzn3V 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-dtc-tg10.proxy.aol.com[CDBC70CA] (Prism/1.2.1), HTTP/1.1 cache-dtc-aa03.proxy.aol.com[CDBC7407] (Traffic-Server/6.1.5 [uScM]) On Mar 15, 11:21?am, spellu...@fb04814.mathematik.tu-darmstadt.de >A is m x n of rank n. ?Smallest singular value of A is s n with >corresponding singular vectors Av=(s n )u where || v || 2 = || u || 2 >= 1. ?I want to choose a permutation P so that >w=P' v , >and >| w n |=|| w || inf , >and then let AP=Q (R 0)' be a QR decomposition of AP. >I need to ultimately show | r nn | <= sqrt(n) * s n. >My question is should i begin doing what and then what is next? >defeat this problem. >Edward homework! > hint > insert anything you know about the form of A ?and w in terms of > Q,R,w,s n. > isolate R*w what do yuo know about the realtion between ||.|| inf and ||.|| 2? done hth > peter- Hide quoted text - - Show quoted text - AP=USV'P=Q(R 0)' || x || 2 <= sqrt(n)*|| x || inf APw=US=Q(R 0)'w (R 0)'w=Q'US TRY TO ISOLATE R*w R*w =Q'US (economy?) and i know |w n| = || w || inf so w n is the largest entry of vector w || R*w || 2 = || S || 2 but i think || S || 2 = s 1 not s n. Is that what the P is doing and i lost track? anyway this is the list about what i know for the problem. i ahve no more stupid (extra-thoughts) today. its because i am sober like a door knob. === Subject: Re: SVD -> QR Decomposition >On Mar 15, 11:21=EF=BF=BDam, spellu...@fb04814.mathematik.tu-darmstadt.de >.com>, >A is m x n of rank n. =EF=BF=BDSmallest singular value of A is s_n with >corresponding singular vectors Av=3D(s_n )u where || v ||_2 =3D || u ||_= >2 >=3D 1. =EF=BF=BDI want to choose a permutation P so that >w=3DP' v , >and >| w_n |=3D|| w ||_inf , >and then let AP=3DQ (R 0)' be a QR decomposition of AP. >I need to ultimately show | r_nn | <=3D sqrt(n) * s_n. >My question is should i begin doing what and then what is next? >defeat this problem. >Edward > homework! > hint > insert anything you know about the form of A =EF=BF=BDand w in terms of > Q,R,w,s_n. > isolate R*w > what do yuo know about the realtion between ||.||_inf and ||.||_2? > done > hth > peter- Hide quoted text - > - Show quoted text - AP=3DUSV'P=3DQ(R 0)' || x ||_2 <=3D sqrt(n)*|| x ||_inf APw=3DUS=3DQ(R 0)'w (R 0)'w=3DQ'US TRY TO ISOLATE R*w >R*w =3DQ'US (economy?) and i know |w_n| =3D || w ||_inf so w_n is the largest entry of vector w || R*w ||_2 =3D || S ||_2 but i think || S ||_2 =3D s_1 not s_n. Is that what the P is doing and >i lost track? anyway this is the list about what i know for the problem. i ahve no >more stupid (extra-thoughts) today. its because i am sober like a >door knob. A=USV' S of the same shape as A assume the diagonal of S monotonically nonincreasing hence s(n,n) is the smallest singular value let v(n) be the associated right singular vector and u(n) the corresponding left on USV'v(n) = s(n,n)u(n) AP = QR R upper triangular but of the same shape as A USV'PP'v(n) = AP (P'v(n)) = s(n,n)u(n) = QR (P'v(n)) = s(n,n)u(n) hence R(P'v(n)) = s(n,n)Q'u(n) (**) |(P'v(n))(n)| (last component) = ||(P'v(n))||_inf by assumption on P and ||x||_2 >= ||x||_inf >= 1/sqrt(n) ||x||_2 for all x now consider equation number n in (**): |R(n,n)| = s(n,n)|(Q'u(n))(n)|/|(P'v(n))(n)| <= s(n,n)sqrt(n) done peter (getting 2 honors points) === Subject: Re: SVD -> QR Decomposition posting-account=9MUq6goAAADgjsPh96c7CaIVgaYLzn3V 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-mtc-tc06.proxy.aol.com[400C7046] (Prism/1.2.1), HTTP/1.1 cache-mtc-aa10.proxy.aol.com[400C740E] (Traffic-Server/6.1.5 [uScM]) On Mar 17, 9:22?am, spellu...@fb04814.mathematik.tu-darmstadt.de >On Mar 15, 11:21=EF=BF=BDam, spellu...@fb04814.mathematik.tu-darmstadt.de >.com>, >A is m x n of rank n. =EF=BF=BDSmallest singular value of A is s n with >corresponding singular vectors Av=3D(s n )u where || v || 2 =3D || u || = >2 >=3D 1. =EF=BF=BDI want to choose a permutation P so that >w=3DP' v , >and >| w n |=3D|| w || inf , >and then let AP=3DQ (R 0)' be a QR decomposition of AP. >I need to ultimately show | r nn | <=3D sqrt(n) * s n. >My question is should i begin doing what and then what is next? >defeat this problem. >Edward > homework! > hint > insert anything you know about the form of A =EF=BF=BDand w in terms of > Q,R,w,s n. > isolate R*w > what do yuo know about the realtion between ||.|| inf and ||.|| 2? > done > hth > peter- Hide quoted text - > - Show quoted text - >AP=3DUSV'P=3DQ(R 0)' >|| x || 2 <=3D sqrt(n)*|| x || inf >APw=3DUS=3DQ(R 0)'w >(R 0)'w=3DQ'US >TRY TO ISOLATE R*w >R*w =3DQ'US ?(economy?) >and i know |w n| =3D || w || inf so w n is the largest entry of vector w >|| R*w || 2 =3D || S || 2 >but i think || S || 2 =3D s 1 not s n. ?Is that what the P is doing and >i lost track? >anyway this is the list about what i know for the problem. ?i ahve no >more stupid (extra-thoughts) today. ?its because i am sober like a >door knob. ? A=USV' ?S of the same shape as A > ? assume the diagonal of S monotonically nonincreasing ? hence s(n,n) is the smallest singular value > ? let v(n) be the associated right singular vector > ? and u(n) the corresponding left on ? USV'v(n) = s(n,n)u(n) ? AP = QR ?R upper triangular but of the same shape as A ? USV'PP'v(n) = AP (P'v(n)) = s(n,n)u(n) = QR (P'v(n)) = s(n,n)u(n) ? hence ? R(P'v(n)) = s(n,n)Q'u(n) ?(**) ? ? |(P'v(n))(n)| (last component) ?= ||(P'v(n))|| inf by assumption on P ? and ? ||x|| 2 >= ||x|| inf >= 1/sqrt(n) ||x|| 2 ?for all x ? now consider equation number n in (**): ? |R(n,n)| = s(n,n)|(Q'u(n))(n)|/|(P'v(n))(n)| <= s(n,n)sqrt(n) ? done > ? peter > ? (getting 2 honors points)- Hide quoted text - - Show quoted text - know very little. i had no idea how to use the P and w information. I was looking at R=Q'USV'P and crying. edward === Subject: Re: Creating sub-groups Distribution: world > Let A and B be sub-groups of G. > Define: AB = { ab | a in A, b in B } > I was trying to prove that AB is a sub-group of G, but might have hit a > brick wall. > Probably because it is not always the case that AB is a subgroup... >Exercise. >If B is a normal subgroup, then AB is a subgroup. What I came up with was: If B is normal, than for any b_1 in B, and any a in A, (a^-1)(b_1)(a) = b_2, where b_2 in B. But, then (a)(a^-1)(b_1)(a) = (a)(b_2) and hence (b_1)(a) = (a)(b_2). Since (a)(b_2) is in AB, (b_1)(a) is in AB. Since b_1 and a were allowed to be any elements of B and A respectively, this shows that BA is a subset of AB. Similarly, for any b_3 in B, and any a in A, (a^-1)(b_3)(a) = b_4, where b_4 in B. This leads to (a^-1)(b_3)(a)(a^-1) = (b_4)(a^-1) and then to (a^-1)(b_3) = (b_4)(a^-1) is in BA, and therefore AB is a subset of BA. Since BA is a subset of AB and AB is a subset of BA, AB = BA. Show that if A, B are normal sub-groups of G, then AB is normal. >If A and B are normal subgroups, then AB is a normal subgroup. (subgroups of G) Let a_1, b_1, and g be elements of A, B, G, respectively. Then, by the definition of normal, (g^-1)(a_1)(g) = a_2 is in A, and (g^-1)(b_1)(g) = b_2 is in B. Therefore: (g^-1)(a_1)(g)(g^-1)(b_1)(g) = (g^-1)(a_1)(b_1)(g) = (a_2)(b_2), which is in AB. Therefore, AB is normal. -- Michael F. Stemper #include A preposition is something that you should never end a sentence with. === Subject: Re: Creating sub-groups Distribution: world <20090310212910.I76189@agora.rdrop.com> posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009030422 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 17, 7:24am, mstem...@walkabout.empros.com (Michael Stemper) > Let A and B be sub-groups of G. > Define: AB = { ab | a in A, b in B } > I was trying to prove that AB is a sub-group of G, but might have hit a > brick wall. > Probably because it is not always the case that AB is a subgroup... >Exercise. >If B is a normal subgroup, then AB is a subgroup. What I came up with was: If B is normal, than for any b 1 in B, and any a in A, > (a^-1)(b 1)(a) = b 2, where b 2 in B. But, then > (a)(a^-1)(b 1)(a) = (a)(b 2) and hence (b 1)(a) = (a)(b 2). > Since (a)(b 2) is in AB, (b 1)(a) is in AB. Since b 1 and a > were allowed to be any elements of B and A respectively, this > shows that BA is a subset of AB. Similarly, for any b 3 in B, and any a in A, (a^-1)(b 3)(a) = b 4, > where b 4 in B. This leads to (a^-1)(b 3)(a)(a^-1) = (b 4)(a^-1) > and then to (a^-1)(b 3) = (b 4)(a^-1) is in BA, and therefore > AB is a subset of BA. Since BA is a subset of AB and AB is a subset of BA, AB = BA. Correct; it's a little easier to work with the entire set, though. B is normal if and only if for every x in G, x^{-1}Bx =B (as sets). Equivalently, if and only if for every x in G, Bx = xB as sets. In particular, aB = Ba for every a in A, so AB=BA. Show that if A, B are normal sub-groups of G, then AB is normal. >If A and B are normal subgroups, then AB is a normal subgroup. (subgroups of G) Let a 1, b 1, and g be elements of A, B, G, respectively. > Then, by the definition of normal, (g^-1)(a 1)(g) = a 2 is in A, and > (g^-1)(b 1)(g) = b 2 is in B. Therefore: > (g^-1)(a 1)(g)(g^-1)(b 1)(g) = (g^-1)(a 1)(b 1)(g) = (a 2)(b 2), which > is in AB. Therefore, AB is normal. Again, much easier if you work with the entire set rather than the elements: you know that g^{-1}Ag = A, that g^{-1}Bg = B, and you want to show that g^{-1}(AB)g = AB. But g^{-1}(AB)g = (g^{-1}Ag)(g^{-1}Bg) = AB, so you are done. -- Arturo Magidin === Subject: Re: Creating sub-groups Distribution: world > Since BA is a subset of AB and AB is a subset of BA, AB = BA. Correct; it's a little easier to work with the entire set, though. B >is normal if and only if for every x in G, x^{-1}Bx = B (as sets). Equal? The definition that I have [1] says subset of. Wikipedia agrees with that, although I see that Mathworld uses equal. Does the subset definition imply the equal definition? (Obviously, it works the other way around.) >Equivalently, if and only if for every x in G, Bx = xB as sets. Okay, I can see how this immediately follows from the equal definition; it's basically what I proved below. > is in AB. Therefore, AB is normal. Again, much easier if you work with the entire set rather than the >elements: answering it even though I forgot to ask it! >elements: you know that g^{-1}Ag = A, that g^{-1}Bg = B, and you want >to show that g^{-1}(AB)g = AB. But g^{-1}(AB)g = (g^{-1}Ag)(g^{-1}Bg) >= AB, so you are done. To be honest, that doesn't seem any easier than my approach of working with individual elements. The simplicity seems to be from the use of the equal definition rather than the subset definition. [1] from McCarty. -- Michael F. Stemper #include Writing about jazz is like dancing about architecture - Thelonious Monk === Subject: Re: Creating sub-groups Distribution: world <20090310212910.I76189@agora.rdrop.com> posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009030422 Ubuntu/8.04 (hardy) Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 17, 12:20pm, mstem...@walkabout.empros.com (Michael Stemper) > Since BA is a subset of AB and AB is a subset of BA, AB = BA. >Correct; it's a little easier to work with the entire set, though. B >is normal if and only if for every x in G, x^{-1}Bx = B (as sets). Equal? The definition that I have [1] says subset of. Wikipedia agrees > with that, although I see that Mathworld uses equal. Does the subset > definition imply the equal definition? (Obviously, it works the other > way around.) Yes; If x^{-1}Bx is a subset of B for all x, then B=x(x^{-1}Bx)x^{-1} is a subset of xBx^{-1} for all x. The two together give you equality. But even if you do it at the subset level: if you know that x^{-1}Bx is a subset of B for every x, then aB = aB(a^{-1}a) = (aBa^{-1})a subset of Ba subset of BA, so AB subset of BA. Etc. >Equivalently, if and only if for every x in G, Bx = xB as sets. Okay, I can see how this immediately follows from the equal definition; > it's basically what I proved below. > is in AB. Therefore, AB is normal. >Again, much easier if you work with the entire set rather than the >elements: answering it even though I forgot to ask it! > you know that g^{-1}Ag = A, that g^{-1}Bg = B, and you want >to show that g^{-1}(AB)g = AB. But g^{-1}(AB)g = (g^{-1}Ag)(g^{-1}Bg) >= AB, so you are done. To be honest, that doesn't seem any easier than my approach of working > with individual elements. It is more in line with what you will want to be doing once you study quotients of groups. Trying to think about quotients at the element level gets really confusing really quickly. > The simplicity seems to be from the use of > the equal definition rather than the subset definition. At the subset level you get the the same thing as you do at the element level: g^{-1}ABg = g^{-1}A(gg^{-1})Bg = (g^{-1}Ag)(g^{-1}Bg subset of AB. Arturo Magidin === Subject: Gabriel's Hypothesis on TIME and SPACE posting-account=GtP9JAoAAAA60JU7XaHraX2zLqE7ckMu Gecko/2008121300 SUSE/3.0.5-1.1 Firefox/3.0.5,gzip(gfe),gzip(gfe) My name is Gabriel Agbasi and I am a Physicist (BS SUNY ALBANY 1995) doing private research in various areas of Physics and have understood there is an anomaly in the nature of TIME ans Space that you may direct your attention. The following is my hypothesis on TIME and SPACE: Gabriel's Hypothesis on TIME and SPACE [ PHYSICS ] TIME and SPACE are like electricity and magnetism. You can use TIME to create SPACE and use SPACE to create TIME. How tightly you twist SPACE will determine the perception of the movement of TIME. How tightly you twist TIME will determine the perception of SPACE. Dimensions or 'SPACES' could be understood as twists of TIME, which creates 'SPACES' / Dimensions. 'Knots' or 'corners of these 'twists' in TIME / SPACE create 'special effects' in TIME / SPACE. These 'knots' or 'corners' are doorways or 'gateways' into other SPACES / TIME and they occur in special places. These special places ( SPACES ), where TIME 'twists' or SPACE 'twists'; the land / area has special properties; that is: the invisible above the land, has special properties. The fabric of SPACE / TIME could be understood to be like a shawl, knitted from the yarn strings of SPACE and TIME; Where: in the shawl, the fabric after it is knitted, is 'full of knots'; that keeps the fabric together. These knots or twists in SPACE / TIME could be understood as intersections or planetary bodies Further, one of the constants in the universe is the idea of a 'spherical planet' or planets that occur or generated in SPACE exist in the form of a 'sphere'. So planets / suns / moons are just 'knots' in SPACE / TIME and there are all spherical. What defines SPACE? OR What is the border of SPACE? THOUGHT. Look at this equation: TIME THOUGHT MOTION SPACE PI All are ONE or Equal to '1'. Therefore: HYPOTHESIS (1) Since knots of TIME and SPACE occur (because they exist) gravity is not constant on every point of the planet (2) TIME is not 'linear' and its flow is not 'constant' or in a sequential order like seen on a clock. To prove this, follow this link and try this simple clock experiment. Further, TIME can be quantified by the THOUGHT going on (occurring) in a SPACE. (3) SPACE is not 'linear'. It is not constant. It does not stretch in a 'straight line' in any direction. It is more like two mirrors facing each other, reflecting into infinity. Each SPACE / TIME affects SPACE / TIME. To prove this, I also refer to the simple clock experiment. Where, TIME and SPACE could be understood to be in perfect balance. Any shift in one, will affect the other. The simple clock experiment is showing 'shifts' or 'anomalies' in TIME; therefore effects in SPACE are hypothesized to also occur. I have configured a quick experiment that can easily be repeated to confirm the results that I myself generated. Title of this work is: Time and Space, An Ongoing Experiment. How to set up the experiment can be found here (SEE BELOW): Time and Space An Ongoing Experiment [ Physics ] In my investigation into the nature of TIME and SPACE in Dimensions (third and fourth), I have discovered some interesting properties that you can investigate also for yourself. One being that TIME and Space are not linear. What you will need to conduct your own experiment (1) Sleep Program (2) An Alarm Clock (3) Pen and Paper OPTIONAL: STOP WATCH This chart will help arrange your findings: DATE: TIME BEGIN SLEEP: TIME ALARM IS SET: TIME WOKE UP: HOW MUCH TIME SLEPT: CONDITION OF ALARM CLOCK WHEN YOU WAKE UP: ( ON OR OFF ) STOP WATCH COUNT: ( If you used one ) ANSWER TO SLEEP Say OUTLOUD: I WISH TO KNOW THE TRUTH: ARE WE ALONE IN THE UNIVERSE? Then go to sleep, you get the truth in a dream tonight. NOTE: You can substitute this question with any question you have and get the answer tonight via sleep. Note: This paper will expand in future. TO BEGIN YOUR EXPERIMENT: 2. SET YOUR ALARM CLOCK FOR ONE HOUR INTO THE FUTURE. 3. GO TO SLEEP. When you wake up, please take note of the following: (1) Write down the answer to your question (2) Is your alarm clock ON or OFF, when you awake? (3) How much time elapsed while asleep and did it match up with your alarm clock time, your begin sleep time, wake up time, AND stop watch count? Please reset your alarm clock for 1 hour into the future when you awake and are ready to go back to sleep. Gather data when you wake up. Do this the whole night to the best of your ability. Carefully write down your experience. You can do this for several nights to get an average. Gabriel Agbasi, Physicist === Subject: Re: NEW AND SIMPLE METHOD OF SOLVING POLYNOMIAL EQUATION'(When all roots of the THANKS FOR YOUR WISHES. Sorry for delay.I am having a trouble in my right hand.So i can't use my right hand.Doctor said it needs an operation to cure it. I have a lot to say.I am trying to post it as soon as possible. Please give an example non integer equation.So i will see it comes under my method.Actually coefficient or constant need not an integer to solve in my method. === Subject: Solution Manual posting-account=QNiqfAoAAACEafcXkDwdHRuYo6O0iSI2 .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Hi. We created a platform that students can challange with their problems about finding books. We have a large book database and you can access them with just a few steps. We are aware of the problems that studentsÍ obstacles. And we are here for resolve them. www.studentdoctor.wordpress.com We have got hundreds of solution manual books. We guarantee to send them in a few hours. Some examples from our solution manuals list: Advanced Accounting 9th Edition - Hoyle, Schaefer, Doupnik ( Solution Manual ) Basic Engineering Circuit Analysis, 9th Edition Irwin, Nelms Calculus, Early Transcendentals, 7E by C. Henry Edwards ,David E. Penney Chemical, Biochemical, and Engineering Thermodynamics, 4th Edition Sandler Collins Mechanical Design of Machine Elements and Machines A Failure Prevention Perspective Design and Analysis of Experiments, 6th Edition Montgomery Elements of Electromagnetics, 3rd Ed., Matthew N.O. Sadiku Engineering Circuit Analysis 7Ed William Hart Hayt Jack E. Kemmerly Solutions Manual Engineering Mechanics Statics 11th Edition By R.C.Hibbeler Engineering Problem Solving with C, 3E Delores M. Etter and hundreds of other books. Visit our web address http://www.studentdoctor.wordpress.com or mail to studentdoctor@hotmail.com and solve your all problems. Fast service, Low price. Sincerly, Student Doctor Team... === Subject: a cute proposition posting-account=B_ql5woAAABEePt1fDMNH7lHfjEScu4Z Gecko/2008102920 Firefox/3.0.4,gzip(gfe),gzip(gfe) Consider a sequence of 3 coin tosses. There are 8 such: HHT, HTH, etc. And each is equiprobable, right? Let's play a game, betting $1, even money. You select one of those sequences, then I select one of the remaining 7. Toss a coin repeatedly, whoever's sequence occurs first, wins. Do you feel lucky? Step right up... To be precise: the coin is not tossed in separate sets of 3, resetting each time neither player wins. Rather, a 'sliding window' is employed; if neither sequence occurs in the first 3 tosses, check the 2nd... 4th, then 3rd.. 5th, etc. Left as an exercise for the student. -- Mark === Subject: Re: a cute proposition posting-account=YUVDEAoAAADy0b0DWFp7F-O3S06gZA3W Gecko/2009030423 Ubuntu/8.10 (intrepid) Firefox/3.0.7,gzip(gfe),gzip(gfe) > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? Let's play a game, betting $1, even money. > You select one of those sequences, then I select > one of the remaining 7. Toss a coin repeatedly, > whoever's sequence occurs first, wins. > Do you feel lucky? Step right up... To be precise: the coin is not tossed in separate > sets of 3, resetting each time neither player > wins. Rather, a 'sliding window' is employed; > if neither sequence occurs in the first 3 tosses, > check the 2nd... 4th, then 3rd.. 5th, etc. Left as an exercise for the student. -- > Mark Here's the full table for the probability that row beats column: HHH HHT HTH HTT THH THT TTH TTT HHH --- 1/2 2/5 2/5 1/8 5/12 3/10 1/2 HHT 1/2 --- 2/3 2/3 1/4 5/8 1/2 7/10 HTH 3/5 1/3 --- 1/2 1/2 1/2 3/8 7/12 HTT 3/5 1/3 1/2 --- 1/2 1/2 3/4 7/8 THH 7/8 3/4 1/2 1/2 --- 1/2 1/3 3/5 THT 7/12 3/8 1/2 1/2 1/2 --- 1/3 3/5 TTH 7/10 1/2 5/8 1/4 2/3 2/3 --- 1/2 TTT 1/2 3/10 5/12 1/8 2/5 2/5 1/2 --- For example, HHT beats HTH 2/3 of the time. Done by hand, verified by computer. === Subject: Re: a cute proposition posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? > Let's play a game, betting $1, even money. > You select one of those sequences, then I select > one of the remaining 7. ?Toss a coin repeatedly, > whoever's sequence occurs first, wins. > Do you feel lucky? ?Step right up... > To be precise: the coin is not tossed in separate > sets of 3, resetting each time neither player > wins. ?Rather, a 'sliding window' is employed; > if neither sequence occurs in the first 3 tosses, > check the 2nd... 4th, then 3rd.. 5th, etc. > Left as an exercise for the student. > -- > Mark Here's the full table for the probability that row beats column: ? ? ? ? HHH ? ? HHT ? ? HTH ? ? HTT ? ? THH ? ? THT ? ? TTH ? ? TTT > HHH ? ? --- ? ? 1/2 ? ? 2/5 ? ? 2/5 ? ? 1/8 ? ? 5/12 ? ?3/10 ? ?1/2 > HHT ? ? 1/2 ? ? --- ? ? 2/3 ? ? 2/3 ? ? 1/4 ? ? 5/8 ? ? 1/2 ? ? 7/10 > HTH ? ? 3/5 ? ? 1/3 ? ? --- ? ? 1/2 ? ? 1/2 ? ? 1/2 ? ? 3/8 ? ? 7/12 > HTT ? ? 3/5 ? ? 1/3 ? ? 1/2 ? ? --- ? ? 1/2 ? ? 1/2 ? ? 3/4 ? ? 7/8 > THH ? ? 7/8 ? ? 3/4 ? ? 1/2 ? ? 1/2 ? ? --- ? ? 1/2 ? ? 1/3 ? ? 3/5 > THT ? ? 7/12 ? ?3/8 ? ? 1/2 ? ? 1/2 ? ? 1/2 ? ? --- ? ? 1/3 ? ? 3/5 > TTH ? ? 7/10 ? ?1/2 ? ? 5/8 ? ? 1/4 ? ? 2/3 ? ? 2/3 ? ? --- ? ? 1/2 > TTT ? ? 1/2 ? ? 3/10 ? ?5/12 ? ?1/8 ? ? 2/5 ? ? 2/5 ? ? 1/2 ? ? --- For example, HHT beats HTH 2/3 of the time. Done by hand, verified by > computer. It turns out this game has been studied by Penney in 1969: http://en.wikipedia.org/wiki/Penney%27s game === Subject: Re: a cute proposition | Consider a sequence of 3 coin tosses. | There are 8 such: HHT, HTH, etc. | And each is equiprobable, right? | | Let's play a game, betting $1, even money. | You select one of those sequences, then I select | one of the remaining 7. Toss a coin repeatedly, | whoever's sequence occurs first, wins. | Do you feel lucky? Step right up... | | To be precise: the coin is not tossed in separate | sets of 3, resetting each time neither player | wins. Rather, a 'sliding window' is employed; | if neither sequence occurs in the first 3 tosses, | check the 2nd... 4th, then 3rd.. 5th, etc. | | | Left as an exercise for the student. | | -- | Mark It is a scam. Upon hearing the first players choice, the second player merely prepends an H or a T. At the third flip the first player has a 1/8 chance of winning and zero(0) on subsequent flips. The second player will win 7/8 times ................... certainly NOT an even money wager!! e.g. Player 1 = HHH Player 2 = THH -- --- David J. Snook === Subject: Re: a cute proposition posting-account=msV4aQkAAACFdekrjeDyuMHhzZGN7wbC 3.14; GTB5; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; InfoPath.2; IEMB3),gzip(gfe),gzip(gfe) | Consider a sequence of 3 coin tosses. > | There are 8 such: HHT, HTH, etc. > | And each is equiprobable, right? > | > | Let's play a game, betting $1, even money. > | You select one of those sequences, then I select > | one of the remaining 7. Toss a coin repeatedly, > | whoever's sequence occurs first, wins. > | Do you feel lucky? Step right up... > | > | To be precise: the coin is not tossed in separate > | sets of 3, resetting each time neither player > | wins. Rather, a 'sliding window' is employed; > | if neither sequence occurs in the first 3 tosses, > | check the 2nd... 4th, then 3rd.. 5th, etc. > | > | > | Left as an exercise for the student. > | > | -- > | Mark It is a scam. Upon hearing the first players choice, the second player > merely prepends an H or a T. At the third flip the first player has a 1/8 > chance of winning and zero(0) on subsequent flips. The second player > will win 7/8 times ................... certainly NOT an even money wager!! e.g. Player 1 = HHH Player 2 = THH -- > --- > David J. Snook Umm, without thinking this through too much (which is probably a warning to myself to stop right now...), if Player 1 chooses HHT, then Player 2 would choose THT, right? But if the first two rolls are HH.. (a 1 in 4 chance), then player 1 has a 100% chance of winning. How do you get 1/8 for player 1 for overall odds? Am I understanding your description correctly? --riverman === Subject: Re: a cute proposition sha1:PE6BqT3V1dKwt+i+YtW6oRav1YQ= > It is a scam. Upon hearing the first players choice, the second player > merely prepends an H or a T. At the third flip the first player has a 1/8 > chance of winning and zero(0) on subsequent flips. The second player > will win 7/8 times ................... certainly NOT an even money wager!! > e.g. Player 1 = HHH Player 2 = THH > -- > --- > David J. Snook Umm, without thinking this through too much (which is probably a > warning to myself to stop right now...), if Player 1 chooses HHT, then > Player 2 would choose THT, right? No, Player 2 would choose THH. (Or maybe HHH?) If player 1 choose (X1)(X2)(X3), then player 2 chooses (X0)(X1)(X2), where X0 is chosen so that player 2's sequence differs from player 1's (in the case that player 1 chose HHH or TTT). At least, I *think* that's the idea. -- Jesse F. Hughes So, what kind of stuff do you like to do and junk? Well, I really enjoy some of the music black people have been coming up with lately. -- Family Guy, first dates. === Subject: Re: a cute proposition <87vdq63ooc.fsf@phiwumbda.org> posting-account=SvltewoAAAAi7TTYrD3mAaLUHzDiF2d1 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) No, Player 2 would choose THH. (Or maybe HHH?) > This is also what I get, if Player 1 choose HHT, Player 2 should choose THH with Player 1 has 1/4 chance to win. If both Player 1 & Player 2 are rational, there are 4 possible outcomes and Player 1 has 1/3 chance to win Player 1 Player 2 THH TTH HTH HHT THT TTH HTT HHT > If player 1 choose (X1)(X2)(X3), then player 2 chooses (X0)(X1)(X2), > where X0 is chosen so that player 2's sequence differs from player 1's > (in the case that player 1 chose HHH or TTT). At least, I *think* that's the idea. === Subject: Re: a cute proposition posting-account=xLsqvAoAAADY4BMAqIw3ROq0faU4tvyS 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... And each is equiprobable, right? > Do you feel lucky? Step right up... The probability the *first* roll in a craps session is 7 is 1/6. What is the probability the last roll is 7? The probability the second roll in a backgammon game is double-6 is 1/36. What is the probability the last roll is double-6? > Left as an exercise for the student. James Dow Allen === Subject: Re: a cute proposition > ... And each is equiprobable, right? > Do you feel lucky? Step right up... The probability the *first* roll in a craps session is 7 is 1/6. >What is the probability the last roll is 7? The probability the second roll in a backgammon game is >double-6 is 1/36. What is the probability the last roll is double-6? You may be missing the point. In those games the events are independent. The relevant events here are _not_ independent! (Say T_n is the n-th coin toss. The first triple is (T_1, T_2, T_3). The second triple is (T_2, T_3, T_4); this is not independent of the first triple.) > Left as an exercise for the student. James Dow Allen David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: a cute proposition Originator: msb@shell.vex.net (Mark Brader) James Allen: > The probability the *first* roll in a craps session is 7 is 1/6. > What is the probability the last roll is 7? Interesting question. If the first roll is 2, 3, 11, or 12 (possible 6 ways out of the 36), it is the last roll, so the probability P that the last roll is 7 is 0. If the first roll is 7 (6 ways), it is the last roll but P = 1. If the first roll is 4 or 10 (6 ways), the last roll must be that number or 7, so P = 6/(3+6). If the first roll is 5 or 9 (8 ways), the last roll must be that number or 7, so P = 6/(4+6). If the first roll is 6 or 8 (10 ways), the last roll must be that number or 7, so P = 6/(5+6). So overall we have P = (6*1 + 6*6/(3+6) + 8*6/(4+6) + 10*6/(5+6))/36 = 557/990 if I compute correctly. > The probability the second roll in a backgammon game is double-6 > is 1/36. What is the probability the last roll is double-6? Hmm, that's tougher and I think it's got to depend on one's endgame strategy. Even if you ignore strategy, I think you have to enumerate all the positions of stones from which a double-6 would win the game, then for each one work out the chance that any game-winning numbers would be rolled. Oh, and the possibility of being blocked by points made by the opponent has to be figured in too. Pretty much intractable without some significant computer assistance, I'd think. Oh, and not only endgame strategy, but doubling and acceptance. You're less likely to double and end the game if your opponent just rolled a double 6, right? David Ullrich: > You may be missing the point. In those games the events are > independent. The end of the game is not independent of the die roll. The original problem I'll leave to others. -- Mark Brader | Of course, if you only see one movie this year, msb@vex.net | you're in the wrong newsgroup. Toronto | --Chris Pierson, rec.arts.movies.past-films === Subject: Re: a cute proposition > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? > No, you can't conclude equal probabilities. That's an assumption equivalent to assuming a fair coin. === Subject: Re: a cute proposition > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? >No, you can't conclude equal probabilities. >That's an assumption equivalent to assuming a fair coin. By default, a fair coin is assumed. However the rules of the game, which you snipped, yield a strong advantage to player 2. quasi === Subject: Re: a cute proposition > Let's play a game, betting $1, even money. You select one of those > sequences, then I select one of the remaining 7. Toss a coin > repeatedly, whoever's sequence occurs first, wins. Do you feel > lucky? Step right up... That is cute. Minimum of 2:1 odds unless I miscalculated, better if the first player chooses poorly. - Tim === Subject: 2-norm of orthogonal or permutation matrix posting-account=Qq_GEwoAAAD0Kc2k70q6xwuZdqx8sCzT 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-mtc-td01.proxy.aol.com[400C7061] (Prism/1.2.1), HTTP/1.1 cache-mtc-ab12.proxy.aol.com[400C744C] (Traffic-Server/6.1.5 [uScM]) is it ever shown that if A is orthogonal (or a permutation matrix as a special case) that ||A||_2 = 1? if so, would you be willing to do it? or is the invariance to the 2-norm when multiplying it on a matrix or vector property all that ever needs to be known. if so, i am a type of computer with no creativity. edward === Subject: Re: 2-norm of orthogonal or permutation matrix >is it ever shown that if A is orthogonal (or a permutation matrix as a >special case) that ||A||_2 = 1? if so, would you be willing to do it? or is the invariance to the 2-norm when multiplying it on a matrix >or vector property all that ever needs to be known. if so, i am a type of computer with no creativity. no, you seem to be a bit lazy: in homework you normally are assumed to use the lecture notes/books chapters just dealt with. here the job is only inserting edward take the definition of a subordinate matrix norm use ||.||_2 and its definition take the square use the definition of orthogonality done hth peter === Subject: Re: 2-norm of orthogonal or permutation matrix >is it ever shown that if A is orthogonal (or a permutation matrix as a >special case) that ||A||_2 = 1? Yes. >if so, would you be willing to do it? No, because this is very easy. You can do it yourself. First, what's the _definition_ of the norm of a matrix A? And second, what does it mean to say that A is orthogonal? >or is the invariance to the 2-norm when multiplying it on a matrix >or vector property all that ever needs to be known. Yes. >if so, i am a type of computer with no creativity. No creativity required here, just two definitions. >edward David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.48 Safari/525.19,gzip(gfe),gzip(gfe) > THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. So how many operations (either on average or worst case) are > required to factor numbers on the order of 2^29? It can take 1. > You could count each arithmetic operation, and since the > total number of operations is less than 2^29, these counters > would fit conveniently into 32-bit integers. I focused first on proof. Next I worked on the algorithm. Now I've worked a bit on implementation. With the test code, open minded people can see it do some rather amazing things. It MAY usually factor with one iteration using f 1 = 1. I suggest readers do their own experiments with the code. Posters who post a lot in my threads have their own agenda. James Harris === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) >Posters who post a lot in my threads have their own agenda. Drama Queen. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > I'm a bit confused here. Do you mean Primes have equations, or > Primes have factors ? Brian Chandler The equation for a Mersenne prime is 2n-1, this is an equation of one particular subset of prime number, within this subset there are prime factors. This statement is also true for the equation of Fermat primes of 2^2n+1. A very very short list of some of the different types of prime numbers is: Weiferich primes Wilsone primes Wall-Sun-Sun primes Wolstenholme primes Unique primes Newman-Shanks-Williams primes Smarandache-Wellin primes Wagstaff primes Supersingular primes And the list goes on and on and on. === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) <33%vl.29297$cu.23346@news-server.bigpond.net.au> <49C0BFEB.3D40D4E1@tesco.net> posting-account=mgs1FwoAAABD3j5T_RLZ06yrgt2dghDu Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) On Mar 18, 4:22pm, Antony Clements Is that an equation or an expression? Equations are made up of one or more expressions, if you want to go by what wikipedia says, then Mn = 2n - 1. Is that more satisfactory for you? === Subject: Re: Test run results (was Re: JSH: Factoring solution test run, Fermat primes) > Is that an equation or an expression? Equations are made up of one or more expressions, if you want to go by > what wikipedia says, then Mn = 2n - 1. Is that more satisfactory for you? Looking over the thread we are in fact talking about 2n + 1 which is not a Mersenne prime, so disregard most of my posts. === Subject: close form I know how to solve the recurrence relation of T(n) - 2T(n-1) = 3 * 2^n T(0) = 1 (boundary condition) homogenous solution = T_h(n) = A * 2^n particular solution = T_p(n) = 3n (2)^n T(n) = T_h(n) + T_p(n) = 3n (2)^n + (2)^n = 2^n (3n + 1) but if it is in this form n*T(n) + n*T(n-1) - T(n-1) = 2^n T(0) = 273 (boundary condition) how do I solve it? === Subject: Re: close form sci.math,alt.math,alt.math.undergrad: > I know how to solve the recurrence relation of > T(n) - 2T(n-1) = 3 * 2^n > T(0) = 1 (boundary condition) > homogenous solution = > T_h(n) = A * 2^n > particular solution = > T_p(n) = 3n (2)^n > T(n) = T_h(n) + T_p(n) > = 3n (2)^n + (2)^n > = 2^n (3n + 1) > but if it is in this form > n*T(n) + n*T(n-1) - T(n-1) = 2^n > T(0) = 273 (boundary condition) > how do I solve it? Let S(n) = n * T(n), get a recurrence for S(n), and solve that. Brian === Subject: the 1 by n chess board Is that true the following problem will lead to the Fibonacci sequence? T(n) = T(n-1) + T(n-2) ############################### Consider a 1 by n chessboard. suppose that we color each square of the chessboard in either red or blue. Let T(n) represent the number of possible colored chessboards in which no 2 squares that are colored red are adjacent. Find the recurrence relation for T(n). T(n) = T(n-1) + T(n-2) ############################### Question is why it lead to fibonacci squence recurrence relation? === Subject: Re: the 1 by n chess board > Is that true the following problem will lead to the Fibonacci > sequence? T(n) = T(n-1) + T(n-2) If you mean the usual Fibonacci sequence (1,1,2,3,5,8,13,...) then you also need to properly specify the initial boundary conditions. > ############################### > Consider a 1 by n chessboard. suppose that we color each square of > the chessboard in either red or blue. Let T(n) represent the number of possible colored chessboards in which > no 2 squares that are colored red are adjacent. Find the recurrence relation for T(n). T(n) = T(n-1) + T(n-2) > ############################### Question is why it lead to fibonacci squence recurrence relation? That's a cute problem, which I presume is homework. Here's a hint: * Every legal sequence (of length N) of R and B must begin with B or RB (since it cannot begin with RR). * How many sequences (of length N) begin with B ? * How many begin with RB ? If you get stuck, show us what you have done and where you got stuck. -- --------------------------- | BBB b Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- === Subject: tree relationship Why the follow tree recurrence relations T(h,k) = max number of leaves of a tree of height h, where each node has outdegree (number of children) k or less. Been told T(h,k) = T(h/2) + k How is this answer be reach? Is there any way to show this? === Subject: Re: tree relationship >Why the follow tree recurrence relations T(h,k) = max number of leaves of a tree of height h, where each node >has outdegree (number of children) k or less. Been told T(h,k) = T(h/2) + k That's not right, unless I'm misunderstanding something. >How is this answer be reach? Is there any way to show this? It's easy to find the correct recurrence. Say you have a tree of hieght h. Then T(h-1,k) is the maximum number of nodes at depth h-1. Given that number, what's the maximum number of nodes at depth h? David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: a cute proposition >James Allen: > The probability the *first* roll in a craps session is 7 is 1/6. > What is the probability the last roll is 7? Interesting question. If the first roll is 2, 3, 11, or 12 (possible 6 ways out of the 36), > it is the last roll, so the probability P that the last roll > is 7 is 0. > If the first roll is 7 (6 ways), it is the last roll but P = 1. > If the first roll is 4 or 10 (6 ways), the last roll must be that > number or 7, so P = 6/(3+6). > If the first roll is 5 or 9 (8 ways), the last roll must be that > number or 7, so P = 6/(4+6). > If the first roll is 6 or 8 (10 ways), the last roll must be that > number or 7, so P = 6/(5+6). So overall we have P = (6*1 + 6*6/(3+6) + 8*6/(4+6) + 10*6/(5+6))/36 >= 557/990 if I compute correctly. > The probability the second roll in a backgammon game is double-6 > is 1/36. What is the probability the last roll is double-6? Hmm, that's tougher and I think it's got to depend on one's endgame >strategy. Even if you ignore strategy, I think you have to enumerate >all the positions of stones from which a double-6 would win the game, >then for each one work out the chance that any game-winning numbers >would be rolled. Oh, and the possibility of being blocked by points >made by the opponent has to be figured in too. Pretty much intractable >without some significant computer assistance, I'd think. Oh, and not only endgame strategy, but doubling and acceptance. You're >less likely to double and end the game if your opponent just rolled a >double 6, right? David Ullrich: > You may be missing the point. In those games the events are > independent. > >The end of the game is not independent of the die roll. For a minute I thought this was ridiculous - the probability that any given roll is 66 is 1/36, period. Then I realized you have a point - a roll has to be the _last_ roll to count. _Then_ I was about to say that if we're at a point where there exists a game-ending roll then 66 will do. But that's wrong as well - could be you have two men outside, so maybe 55 or 44 will bring them both in and bear them off, but 66 is blocked. So you're right, this is much more complicated than I realized. >The original problem I'll leave to others. David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: a cute proposition > The probability the second roll in a backgammon game is double-6 > is 1/36. What is the probability the last roll is double-6? Hmm, that's tougher and I think it's got to depend on one's endgame >strategy. Even if you ignore strategy, I think you have to enumerate >all the positions of stones from which a double-6 would win the game, >then for each one work out the chance that any game-winning numbers >would be rolled. Oh, and the possibility of being blocked by points >made by the opponent has to be figured in too. Pretty much intractable >without some significant computer assistance, I'd think. Oh, and not only endgame strategy, but doubling and acceptance. You're >less likely to double and end the game if your opponent just rolled a >double 6, right? If we eliminate the doubling rule (since I've never played for money or played with that rule), I wonder if that makes it easier. My intuition is that under those conditions, double-6 is about twice as likely as a last roll (compared to its probability as a first roll). I'm picturing that the guy who's about to win has all of his pieces in safely in his, um, whatever-it's-called -- those last 6 spots before you can, um, is it called bearing off? (Dang, I could use some terminology.) Anyway, he's got all his pieces in the last 6 squares there, and he's getting them off the board roughly two at a time. And now it's the roll that might be his last roll. If he has 1 or 2 pieces left, he can win on the spot without doubles. If he has 3 or 4 pieces left, he will only win on the spot with doubles. And, actually, the fact that it's double SIXES makes it even more likely he'll win on the spot. It seems to me that the average pair of non-doubled dice has a 50%-or-less chance of clearing off two randomly placed pieces. For example, a 4-3 won't clear off a 5-2, and vice versa. So now, I'm thinking that the odds of double sixes being the final roll is closer to four times as likely. In any case, somewhere between 2/36 and 4/36. Can someone just program their backgammon computer to play 10,000 consecutive games, so we can get some brute force numbers? === Subject: Re: a cute proposition >Consider a sequence of 3 coin tosses. >There are 8 such: HHT, HTH, etc. >And each is equiprobable, right? Let's play a game, betting $1, even money. >You select one of those sequences, then I select >one of the remaining 7. Toss a coin repeatedly, >whoever's sequence occurs first, wins. >Do you feel lucky? Step right up... To be precise: the coin is not tossed in separate >sets of 3, resetting each time neither player >wins. Rather, a 'sliding window' is employed; >if neither sequence occurs in the first 3 tosses, >check the 2nd... 4th, then 3rd.. 5th, etc. >Left as an exercise for the student. If I bet on HHH, I assume you'll bet on THH. Then, the only chance I'd have of winning (1/8) is if the first three flips are all heads. Otherwise you'll eventually win. I wouldn't be surprised to find that you can intercept any bet I might lay down. I wonder what you'd play if I took HTH. My guess is HHT, since, even if mine were about to come up, you'd still have a 50-50 chance of intercepting it (if an H rather than a T came up before mine). === Subject: Re: a cute proposition posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > For example, HHT beats HTH 2/3 of the time. Done by hand, verified by > computer. It turns out this game has been studied by Penney in 1969: http://en.wikipedia.org/wiki/Penney%27s game Book of Mathematics, pp 302-309, available on Google Books at http://tinyurl.com/dmluv5 where Gardner describes Conway's algorithm (damn you Conway! why must you be so clever!?!) to determine in general which of two n-length sequences of coin flips, A or B, are more likely to occur first. === Subject: Re: a cute proposition <87vdq63ooc.fsf@phiwumbda.org> if Player 1 chooses HHT, then > Player 2 would choose THT, right? No, Player 2 would choose THH. (Or maybe HHH?) Definitely THH. If you draw a little diagram with vertices corresponding to 2-flip sequences and links to the next, a game consists of randomly hopping along the links, ending when a link corresponding to a player's sequence is taken. In that form it is clear that THH cuts off access to HH and therefore to HHT. Thus player 1 wins iff the flips start HH. - Tim === Subject: Re: a cute proposition <87vdq63ooc.fsf@phiwumbda.org> posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) > if Player 1 chooses HHT, then > Player 2 would choose THT, right? > No, Player 2 would choose THH. (Or maybe HHH?) Definitely THH. If you draw a little diagram with vertices > corresponding to 2-flip sequences and links to the next, a game > consists of randomly hopping along the links, ending when a link > corresponding to a player's sequence is taken. In that form it is clear that THH cuts off access to HH and therefore > to HHT. Thus player 1 wins iff the flips start HH. > In this form, it is known as a De Bruijn graph; see interesting analysis at: http://research.cs.queensu.ca/~dawes/coins.html === Subject: Re: a cute proposition > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? > Let's play a game, betting $1, even money. > You select one of those sequences, then I select > one of the remaining 7. Toss a coin repeatedly, > whoever's sequence occurs first, wins. > Do you feel lucky? Step right up... > To be precise: the coin is not tossed in separate > sets of 3, resetting each time neither player > wins. Rather, a 'sliding window' is employed; > if neither sequence occurs in the first 3 tosses, > check the 2nd... 4th, then 3rd.. 5th, etc. > Left as an exercise for the student. > -- > Mark Here's the full table for the probability that row beats column: HHH HHT HTH HTT THH THT TTH TTT >HHH --- 1/2 2/5 2/5 1/8 5/12 3/10 1/2 >HHT 1/2 --- 2/3 2/3 1/4 5/8 1/2 7/10 >HTH 3/5 1/3 --- 1/2 1/2 1/2 3/8 7/12 >HTT 3/5 1/3 1/2 --- 1/2 1/2 3/4 7/8 >THH 7/8 3/4 1/2 1/2 --- 1/2 1/3 3/5 >THT 7/12 3/8 1/2 1/2 1/2 --- 1/3 3/5 >TTH 7/10 1/2 5/8 1/4 2/3 2/3 --- 1/2 >TTT 1/2 3/10 5/12 1/8 2/5 2/5 1/2 --- For example, HHT beats HTH 2/3 of the time. Done by hand, verified by >computer. Interesting. Here's a variant ... Suppose the 2 players select their sequences simultaneously. What's an optimal mixed strategy? quasi === Subject: Re: a cute proposition posting-account=YUVDEAoAAADy0b0DWFp7F-O3S06gZA3W Gecko/2009030423 Ubuntu/8.10 (intrepid) Firefox/3.0.7,gzip(gfe),gzip(gfe) > Consider a sequence of 3 coin tosses. > There are 8 such: HHT, HTH, etc. > And each is equiprobable, right? > Let's play a game, betting $1, even money. > You select one of those sequences, then I select > one of the remaining 7. Toss a coin repeatedly, > whoever's sequence occurs first, wins. > Do you feel lucky? Step right up... > To be precise: the coin is not tossed in separate > sets of 3, resetting each time neither player > wins. Rather, a 'sliding window' is employed; > if neither sequence occurs in the first 3 tosses, > check the 2nd... 4th, then 3rd.. 5th, etc. > Left as an exercise for the student. > -- > Mark >Here's the full table for the probability that row beats column: > HHH HHT HTH HTT THH THT TTH TTT >HHH --- 1/2 2/5 2/5 1/8 5/12 3/10 1/2 >HHT 1/2 --- 2/3 2/3 1/4 5/8 1/2 7/10 >HTH 3/5 1/3 --- 1/2 1/2 1/2 3/8 7/12 >HTT 3/5 1/3 1/2 --- 1/2 1/2 3/4 7/8 >THH 7/8 3/4 1/2 1/2 --- 1/2 1/3 3/5 >THT 7/12 3/8 1/2 1/2 1/2 --- 1/3 3/5 >TTH 7/10 1/2 5/8 1/4 2/3 2/3 --- 1/2 >TTT 1/2 3/10 5/12 1/8 2/5 2/5 1/2 --- >For example, HHT beats HTH 2/3 of the time. Done by hand, verified by >computer. Interesting. Here's a variant ... Suppose the 2 players select their sequences simultaneously. What's an > optimal mixed strategy? quasi It's helpful to convert the matrix into payoffs (subtract 1/2 and multiply by 120): --- HHH HHT HTH HTT THH THT TTH TTT HHH 0 0 -12 -12 -45 -10 -24 0 HHT 0 0 20 20 -30 15 0 24 HTH 12 -20 0 0 0 0 -15 10 HTT 12 -20 0 0 0 0 30 45 THH 45 30 0 0 0 0 -20 12 THT 10 -15 0 0 0 0 -20 12 TTH 24 0 15 -30 20 20 0 0 TTT 0 -24 -10 -45 -12 -12 0 0 So it seems the optimal strategy would be to take either HTT or THH, with equal probability. HHH and TTT are losers (meaning win chances are at most one-half) from the beginning. After removing them (for both players), HTH and THT are losers. After removing them, HHT and TTH are losers, since any strategy would be symmetric and have to average the two. That leaves HTT and THH. === Subject: Connected implies path connected? Originator: bergv@math.uiuc.edu (Maarten Bergvelt) Is it true that a connected projective variety is path-connected? I think it is, but I am not sure. Of course for manifolds, this is true (because they are locally path-connected), but a projective variety may have singularities. === Subject: Re: Connected implies path connected? Originator: bergv@math.uiuc.edu (Maarten Bergvelt) > Is it true that a connected projective variety is path-connected? I > think it is, but I am not sure. Of course for manifolds, this is true > (because they are locally path-connected), but a projective variety > may have singularities. Yes. A connected projective variety over C (as I presume you intend) can also be seen as (the real points) a compact variety over R (of double the dimension). Every compact real algebraic set can be triangulated --- this is even true for compact semi-algebraic sets (defined by polynomial inequalities). See texts on semi-algebraic geometry, e.g. that of Michel Coste perso.univ-rennes1.fr/michel.coste/polyens/SAG.pdf . 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Comprehensive Volume, 31st Edition, Willis, Hoffman, Maloney, Raabe, Test Bank West Federal Taxation 2008; Corporations, Partnerships, Estates, and Trusts, 31st Edition, Hoffman, Raabe, Smith, Maloney, Instructor's Guide West Federal Taxation 2008; Corporations, Partnerships, Estates, and Trusts, 31st Edition, Hoffman, Raabe, Smith, Maloney, Solutions Manual West Federal Taxation 2008; Corporations, Partnerships, Estates, and Trusts, 31st Edition, Hoffman, Raabe, Smith, Maloney, Test Bank West Federal Taxation 2008; Individual Income Taxes, 31st Edition, Hoffman, Smith, Willis, Instructor's Guide West Federal Taxation 2008; Individual Income Taxes, 31st Edition, Hoffman, Smith, Willis, Test Bank West Federal Taxation 2008; Taxation of Business Entities, 11th Edition, Raabe, Smith, Maloney, Instructor's Guide West Federal Taxation 2008; Taxation of Business Entities, 11th Edition, Raabe, Smith, Maloney, Solutions Manual West Federal Taxation 2008; Taxation of Business Entities, 11th Edition, Raabe, Smith, Maloney, Test Bank West's Business Law, 10th Edition, Clarkson, Miller, Jentz, Cross, Test Bank Wireless Communications, 2nd Edition, Theodore Rappaport, Solution Manual Student.plus(At)Hotmail(Dot)Com === Subject: Re: a cute proposition posting-account=xLsqvAoAAADY4BMAqIw3ROq0faU4tvyS 2.0.50727),gzip(gfe),gzip(gfe) > James Allen: > The probability the *first* roll in a craps session is 7 is 1/6. > What is the probability the last roll is 7? ... So ... we have P = (6*1 + 6*6/(3+6) + 8*6/(4+6) + 10*6/(5+6))/36 > = 557/990 if I compute correctly. In Las Vegas, shooter keeps the dice after a craps roll, which makes the probability of last roll 7 to be 1. In fact, since Nevada does't levy personal income tax, some Nevadans rewrite a well known motto to be Nothing in life is certain but Death and Seven Out. > The probability the second roll in a backgammon game is double-6 > is 1/36. What is the probability the last roll is double-6? Hmm, that's tougher ... Yes, I wasn't expecting an exact answer, just much greater than 1/36. > David Ullrich: > You may be missing the point. In those games the events are > independent. Sorry if I implied the scenarios were exactly equivalent, though a subsequent comment by David suggests that he sees that in each case, a temporal relationship destroys independence. Whether I missed the point of OP, I'll leave to my own conscience! James Dow Allen === Subject: Re: a cute proposition > James Allen: > The probability the second roll in a backgammon game is double-6 > is 1/36. What is the probability the last roll is double-6? > Hmm, that's tougher ... Yes, I wasn't expecting an exact answer, just much greater >than 1/36. What do you think of my ballpark that it's 4 times greater. I doubled it, simply because rolling doubles bears off twice as many men, and doubled it again because a 6 will bear off a man on any spot, making it about twice as likely to clear a man than a random roll. I'd still be interested in someone running a simulation of 10,000 games between two decent players who don't use a doubling cube and don't resign. === Subject: Re: a cute proposition > If I bet on HHH, I assume you'll bet on THH. Then, the only chance > I'd have of winning (1/8) is if the first three flips are all heads. > Otherwise you'll eventually win. Yes. > I wouldn't be surprised to find that you can intercept any bet I might > lay down. Yes. > I wonder what you'd play if I took HTH. My guess is HHT, since, even > if mine were about to come up, you'd still have a 50-50 chance of > intercepting it (if an H rather than a T came up before mine). Yes, HHT beats HTH with probability 2/3. THH beats HHT with probability 3/4, and HHT beats HTT with probability 2/3. Interchange H and T for the rest of the optimal strategy. -- === Subject: Borel sets of the extended real line Define a real valued function f on a measurable space (X,S) to be *measurable* if, for any Borel set M, intersection({x:f(x) != 0}, {x:f(x) in M}) in S It is my understanding that this definition can be generalized to an extended real valued function g on a measurable space (X,S) by regarding the two subsets {+oo} and {-oo} of the extended real line R_ to be Borel sets. 1. Does that mean that unions and differences of sets such as, say, {-oo} union M, or such as {-oo} M, where M is a Borel set of the real line R, are also Borel sets? In other words, are the Borel sets of the extended real line, including {+oo} and {-oo}, still a ring? 2. Is it the case that the extended real line R_ = {-oo} union R union{+oo} is itself a Borel set of the extended real line and therefore, given a measurable extended real valued function g on (X,S), that intersection({x:g(x) != 0},{x, g(x) in R_}) = intersection({x:g(x) != 0}, X) = {x:g(x) != 0} in S in which case {x:g(x) != 0} is a measurable set? 3. Going further, if h is an extended real valued Borel measurable function on the extended real line, then is it the case that for any Borel set M of the extended real line intersection({t:h(t) != 0},{t:h(t) in M}) will be a Borel set of the extended real line (as opposed to a Borel set of the regular real line, which set does not contain the elements +oo or -oo)? -sto === Subject: Re: Borel sets of the extended real line posting-account=AdyLXQoAAABgRay99CKv1O8Y_7jjivwq InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) > It is my understanding that this definition can be generalized > to an extended real valued function g on a measurable space > (X,S) by regarding the two subsets {+oo} and {-oo} of the > extended real line R_ to be Borel sets. It seems to me that your questions can be simply answered by observing {+oo} and {-oo} are closed sets (of a very simple type, in fact, being singletons), which are about as simple as you can be for a Borel set. Note also that the real line is an open subset of the extended real line. In fact, without looking back to be sure, I think all the sets you mentioned are not just Borel, but in fact belong to the lowest non-trivial ambiguous class in the Borel hierarchy (kind of like saying 0 or 1, except it's even more extreme than this). Dave L. Renfro === Subject: Re: Borel sets of the extended real line > > It is my understanding that this definition can be generalized > to an extended real valued function g on a measurable space > (X,S) by regarding the two subsets {+oo} and {-oo} of the > extended real line R_ to be Borel sets. It seems to me that your questions can be simply answered by > observing {+oo} and {-oo} are closed sets (of a very simple > type, in fact, being singletons), which are about as simple > as you can be for a Borel set. Note also that the real line > is an open subset of the extended real line. Perhaps the problem is how the term Borel set is defined for subsets sets of the extended real line one takes the Borel sets of the real line and simply tacks on two elements: +oo and -oo. What I don't understand is how one can take a sigma-ring and simply add two sets to it and still have a sigma ring. For example, the class {0,X} of subsets of a set X is a sigma-ring. If I then decide to add two arbitrary sets, a and b, to it I get the class of sets {0,a,b,X}, which is no longer necessarily a sigma-ring (I think the set difference ab, for example, is not member of the class if a and b are distinct and nonempty). If {+oo} and {-oo} are declared to be Borel sets, then how do I know that the class of Borel sets is still a sigma-ring? In fact, how do I know whether any other statements about the Borel sets of the real line are true for the Borel sets of the extended real line? (for example, it does not seem to be the case that the Borel sets of the extended real line are the sigma ring generated by the semiring of sets of the form {x: -oo <= c < d < oo}, for c and d real). -sto === Subject: Re: Borel sets of the extended real line > It is my understanding that this definition can be generalized > to an extended real valued function g on a measurable space > (X,S) by regarding the two subsets {+oo} and {-oo} of the > extended real line R_ to be Borel sets. It seems to me that your questions can be simply answered by > observing {+oo} and {-oo} are closed sets (of a very simple > type, in fact, being singletons), which are about as simple > as you can be for a Borel set. Note also that the real line > is an open subset of the extended real line. Perhaps the problem is how the term Borel set is defined for subsets >sets of the extended real line one takes the Borel sets of the real line >and simply tacks on two elements: +oo and -oo. What I don't understand >is how one can take a sigma-ring and simply add two sets to it and still >have a sigma ring. That's not what was meant when someone said tack on those two elements. The truth is this: A is a Borel subset of [-oo,oo] if and only if there exists B, a Borel subset of R, such that A is equal to one of the four sets B, B union {oo}, B union {-oo} and B union {oo, -oo}. >For example, the class {0,X} of subsets of a set X >is a sigma-ring. If I then decide to add two arbitrary sets, a and b, >to it I get the class of sets {0,a,b,X}, which is no longer necessarily >a sigma-ring (I think the set difference ab, for example, is not member >of the class if a and b are distinct and nonempty). If {+oo} and {-oo} are declared to be Borel sets, then how do I know >that the class of Borel sets is still a sigma-ring? In fact, how do I >know whether any other statements about the Borel sets of the real line >are true for the Borel sets of the extended real line? This should be clear, with the revised notion of tack on oo and -oo. >(for example, it >does not seem to be the case that the Borel sets of the extended real >line are the sigma ring generated by the semiring of sets of the form >{x: -oo <= c < d < oo}, for c and d real). The notation is scrambled - you meant sets of the form {x : c < x < d} for -oo < c < d < oo. (Leaving out one x was a minor typo, but it's _important_ that the restrictions on c and d are _not_ included inside those braces...) Anway: That's not what's required. What's required is that the Borel algebra on [-oo, oo] should be generated by the _open_ _subsets_ of [-oo, oo]. That turns out to be the algebra generated by the open intervals, _except_ you need to note that now (a, oo], [-oo, b) and [-oo, oo] count as open intervals. (Well, they're intervals, and they're open...) >-sto David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: Borel sets of the extended real line posting-account=AdyLXQoAAABgRay99CKv1O8Y_7jjivwq InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) > In fact, without looking back to be sure, I think all > the sets you mentioned are not just Borel, but in fact > belong to the lowest non-trivial ambiguous class in the > Borel hierarchy [...] O-K, I re-read your post and I see mention of measurable functions and sets obtained from them, so in these cases you could be arbitrarily high in the Borel hierarchy, or even beyond it (unless by measurable you mean Borel measurable). My earlier comment was based on some statements you made, such as the following: Is it the case that the extended real line R_ = {-oo} union R union{+oo} is itself a Borel set of the extended real line Any topological space is an open subset of itself, as well as a closed subset of itself. Dave L. Renfro === Subject: If intersect( {x:f(x)+g(x) space (X,S). Here X is an arbitrary set, and S is a sigma-ring of subsets of X. In particular, the class of sets S does not necessarily contain X as one of its elements. Then it is possible to show that, for any real number c, > the set {x:f(x) measurable set. (You can do that by writing the set {x:f(x) in the form union_{q in Q} intersection( {x:f(x) valued measurable function h, measurable set E, and Borel set M, the > set intersection( E, {x:h(x) in M} ) is measurable. Because (-oo,q) and (q-c,oo) are open, and therefore > Borel, sets it follows that {x:f(x) measurable intersection with every measurable set and consequently > that {x:f(x) measurable set.) The fact that the set {x:f(x) with every measurable set is somehow supposed to imply that the sum of > real valued measurable functions is measurable. I don't see how. Clearly if, for any real number c, the set intersection( {x:f(x)+g(x) != 0}, {x:f(x)+g(x) measurable. Furthermore, since f and g are finite, the set > {x:f(x)+g(x) has a measurable intersection with every measurable set. However, how > does the fact that {x:f(x)+g(x) that f+g is a measurable function? Can anybody prove that? -sto === Subject: Re: If intersect( {x:f(x)+g(x) space (X,S). Then it is possible to show that, for any real number c, > the set {x:f(x) measurable set. has a measurable intersection with every measurable set is the same thing as is measurable. After all, X itself is measurable. > (You can do that by writing the set {x:f(x) in the form union_{q in Q} intersection( {x:f(x) valued measurable function h, measurable set E, and Borel set M, the > set intersection( E, {x:h(x) in M} ) is measurable. Because (-oo,q) and (q-c,oo) are open, and therefore > Borel, sets it follows that {x:f(x) measurable intersection with every measurable set and consequently > that {x:f(x) measurable set.) The fact that the set {x:f(x) with every measurable set is somehow supposed to imply that the sum of > real valued measurable functions is measurable. I don't see how. f(x) < g(x) + c is equivalent to f(x) - g(x) < c. The statement that this is measurable for all c says that f - g is a measurable function. So the difference of two measurable functions is a measurable function. Now, do you see how to write the sum of two functions as the difference of two functions? -- === Subject: Re: If intersect( {x:f(x)+g(x) > Let f and g be finite real valued measurable functions on a measurable > space (X,S). Then it is possible to show that, for any real number c, > the set {x:f(x) measurable set. has a measurable intersection with every measurable set is the same thing as > is measurable. After all, X itself is measurable. > Why is X measurable? Certainly not by assumption: I should have stated that X is an arbitrary set and S is a sigma-ring of subsets of X, in which case the class of sets S does not necessarily have to contain X as one of its elements. > The fact that the set {x:f(x) with every measurable set is somehow supposed to imply that the sum of > real valued measurable functions is measurable. I don't see how. f(x) < g(x) + c is equivalent to f(x) - g(x) < c. The statement that > this is measurable for all c says that f - g is a measurable function. So the > difference of two measurable functions is a measurable function. > Now, do you see how to write the sum of two functions as the difference > of two functions? If -h is a measurable function, then {x:-h(x)c}, in which case h is also a measurable function. So I'm not worried about f+g vs. f-g. However, in order for f+g to be measurable, it is necessary for the set intersection( {x:f(x)+g(x) !=0} , {x:f(x)+g(x) THEN I had more coprimeness issues between them, which I just resolved > today, completing the algorithm, so I could update the code with the > demonstrate it as a proof of concept will only factor up to 2^29+1, as > it's a proof of concept program that only factors numbers of the form > 2^n+1, with n a positive integer less than 30. > So how many operations (either on average or worst case) are > required to factor numbers on the order of 2^29? It can take 1. > You could count each arithmetic operation, and since the > total number of operations is less than 2^29, these counters > would fit conveniently into 32-bit integers. I focused first on proof. Next I worked on the algorithm. Now I've > worked a bit on implementation. With the test code, open minded people can see it do some rather > amazing things. It MAY usually factor with one iteration using f 1 = 1. I suggest readers do their own experiments with the code. Posters who > post a lot in my threads have their own agenda. It turns out, you're not the ONLY ONE who can SOLVE THE FACTORING PROBLEM!!! #include #include using namespace std; // With profound apologies to George Marsaglia for using his PRNG, // I give you... // Drumroll please... // BOGOFACTOR!!!! The true-blue and new solution to the factoring problem. class Kiss { private: unsigned long long x, c, y, z, t; public: // constructor: Kiss() { x = 1234567890987654321ULL; c = 123456123456123456ULL; y = 362436362436362436ULL; z = 1066149217761810ULL; } ~Kiss() { } // public method to collect random number: unsigned long long Rand() { t = ((t = (x << 58) + c, c = (x > 6), x += t, c += (x < t), x) + (y ^= (y << 13), y ^= (y > 17), y ^= (y << 43)) + (z = 6906969069ULL * z + 1234567ULL)); return t; } }; // // The mighty factoring main() routine for BOGOFACTOR!!! // We are not even afraid of perfect squares! // int main(void) { unsigned long long t, n; cout << Enter a number to factor << endl; cin > n; // Here we collect the inscrutible value! // How romantic! If only I had a class Hug, // I could make an instance named 'o'. class Kiss x; // This loop will find factors to titanic primes up to 18 digits, // which will really put a scare into MI5 and the CIA. // Someday, we may go as high as 50, but I really don't know // what that will do to you So let's just see what we have here (for now): for (;;) { // In order to be extra-hyper-efficient, we will only try factors up to // the square root of the input. Of course, the math isn't as lovely as // if we had tried them all. It's cheating, I know, but remember -- // we are going for the world's record here! do { t = x.Rand(); } while (t > floor(sqrt((long double)n))); // to perform the mighty deed! if (n % t == 0) { cout << factor: << t << endl; // We are so clever that we even reduce the size of our input. // The whole world kneels in wonder. Shall I take a bow? n /= t; } } return 0; } === Subject: (40 choose 7) / ((15 choose 6) * 25) = 148.999481 ?? Cc: MCDONEwt@yahoo.co.nz posting-account=TV2szgkAAACrA1vyuh8IN_0zzgzcwogw .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) (40 choose 7) / ((15 choose 6) * 25) = 148.999481 (40 choose 7) / ((15 choose 6) * 25) = 148.999481 8-22 pix 6 out of (6+bonus.) nearly 1 / 149 ??? query not certain. unusual fraction. new zealand 14.3.09. birthdays lotteries.co.nz combo ? $509,105.00. === Subject: Re: Newbie question on definition of a subset posting-account=wzCFHwoAAACNjb4w9hAuIijU5lDzX9PN Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > So it's not that the elements outside of A and B somehow involved a > definition of subset, because there is no subset being defined. A is > a subset of B is equivalent to an assertion that a certain set is > empty (namely, A-B), as is the statement Everything is in B or in the > complement of A. Now, I'll go explain that to the students in my class! (yes, I'm ashamed) Alejo === Subject: Re: Newbie question on definition of a subset posting-account=wzCFHwoAAACNjb4w9hAuIijU5lDzX9PN Gecko/2009021910 Firefox/3.0.7 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > So it's not that the elements outside of A and B somehow involved a > definition of subset, because there is no subset being defined. A is > a subset of B is equivalent to an assertion that a certain set is > empty (namely, A-B), as is the statement Everything is in B or in the > complement of A. Now, I'll go explain that to the students in my class! (yes, I'm ashamed) Alejo === Subject: Re: 40% in remedial math posting-account=NgMGSwkAAABJni6NIYF05Yc4jNzXwHf- 1.1.4322),gzip(gfe),gzip(gfe) > If you've not been taught Algebra II, you are not going to be ready > for college-level math, In the State of Texas even if you HAVE been taught Algebra II you can still > graduate from high school not knowing: (1) How to find the area of a rectangle > (2) How to find the perimeter of a rectangle. > (3) How to find the circumference of a circle. > (4) How many inches are in a foot. > (5) How many quarts in a gallon. > (6) Not knowing basic multiplication/division. etc .. etc .. etc You see ... the students are given (MANDATED!) a formula chart and a > calculator for the state mandated test .. the vast majority have a > calculator in hand from the 9th grade forward. I've watched an Algebra II > student use a calculator to multiply 9 x 0 ... when I inquired as to the > reason he used a calculator ... I was just checking myself . This > same student asked for a formula chart to find the area of a rectangle! Solving equations? Easy .. example ... (1/2)x=6, procedure. Convert the 1/2 to .5, using a calculator. > Divide 6 by .5, using a calculator. When I asked why not just multiply both sides of the equation by 2 ... I > don't know how to do that, we weren't taught that way. Oh, forgot to tell > you ... this was A JUNIOR IN HIGH SCHOOL !!! Finally ... I was tutoring a student to pass the 11th grade TAKS test (a > state mandated test in Texas) ... trying to give her some concept of volume > I gave her a Stanley tape measure and asked her to calculate the approximate > volume of a that could be used to ship a toaster that was on my cabinet ... > she stood with tape measure in hand .. dumbfounded ... she couldn't read a > tape measure! 40% ?? I don't doubt it at all. Oh, these examples were all middle to (very) upper socioeconomic class white > students .. Jerry Some pundits would dismiss the above as meaningless anecdotal observations. In fact, you have described the grim reality that is so widespread in the U.S. === Subject: Prolate elongation equals...? Mail-To-News-Contact: abuse@dizum.com If an oblate spheroid flattens, f= (a-b)/a, with a squared eccentricity (e^2) of (a^2-b^2)/a^2, what does a prolate spheroid do and what is the equivalent equation for f, (b-a)/b, (b-a)/a, or something else (I know that e^2 equals (b^2-a^2)/b^2)? I can't find any websites that give much information for the prolate case! === Subject: Re: Prolate elongation equals...? > If an oblate spheroid flattens, f= (a-b)/a, with a squared > eccentricity (e^2) of (a^2-b^2)/a^2, what does a prolate > spheroid do and what is the equivalent equation for f, > (b-a)/b, (b-a)/a, or something else (I know that e^2 equals > (b^2-a^2)/b^2)? > I can't find any websites that give much information for the > prolate case! Eccentricity is a 2-dimensional concept. Each of your spheroids can be obtained by rotating an ellipse, and you're asking about the eccentricity of that ellipse. You probably know that an ellipse with major axis 2a and minor axis 2b has eccentricity sqrt(1 - (b/a)^2). For each spheroid you just need to be sure of labelling the ellipse's major and minor axes the right way round. Ken Pledger. === Subject: Proving a Series Convergence posting-account=VGgocAoAAABOrCjDMYTifqUxnXjU97x4 Gecko/2009021910 Firefox/3.0.7,gzip(gfe),gzip(gfe) How can I prove the sum of the series terms of 1/n^2 never passes 2? 1+ 1/2^2 + 1/3^2 + ... + 1/n^2 < 2 === Subject: Re: Proving a Series Convergence How can I prove the sum of the series terms of 1/n^2 never passes 2? 1+ 1/2^2 + 1/3^2 + ... + 1/n^2 < 2 > 1 + 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 + 1/(2*1) + 1/(3*2) + ... + 1/(n*(n-1)) = 1 + (1 - 1/2) + (1/2 - 1/3) + ... + (1/(n-1) - 1/n) = 2 - 1/n. === Subject: Re: Proving a Series Convergence How can I prove the sum of the series terms of 1/n^2 never passes 2? 1+ 1/2^2 + 1/3^2 + ... + 1/n^2 < 2 > Or 1/2^2 + 1/3^2 + ... + 1/n^2 < 1. Hint: Look at lower rectangular approximations for the integral: int[ 1..oo] (1 / x^2 ) dx --Lynn http://math.asu.edu/~kurtz === Subject: Finished a fresh install of WinDoze Magizia 2009 HyperTurbo 2.6c on 2000 viao laptop w/.5gb ram posting-account=ophFTAoAAABAHT8hcZ4WRuasht7jipgB CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) 17,179,869,180 precision rootshell level hooks, excessive hardware, network, and os debugging, programming/patching, & the best reverse engineering of 2009 by Hunter Reon Barnes TheMagizian@gmail.com (208)741-1569 Running in Cool Mode 283mb/s (no strain on cpu, hd, ram (.5gb), buses, or other hardware). If running in Hot Mode (cpu maxed, hd always spinning fast, 1.5gb ram + 1-4gb flashram, and 34,359,738,360 precision hooks).. ..then multiply available velocity times 4,032 ((283mb/s)*2 (3*6*4*28)) or 1,141,056mb/s (1.1gb/s) processing capability! ..I made a hybred OS better. faster, and more stable.. ...than any other OS on or off the market.. ... ..in a week. ..add it to the list, ~ HRB === Subject: Re: 2-norm of orthogonal or permutation matrix posting-account=Qq_GEwoAAAD0Kc2k70q6xwuZdqx8sCzT 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-mtc-te12.proxy.aol.com[400C708C] (Prism/1.2.1), HTTP/1.1 cache-mtc-ad07.proxy.aol.com[400C74C9] (Traffic-Server/6.1.5 [uScM]) >is it ever shown that if A is orthogonal (or a permutation matrix as a >special case) that ||A|| 2 = 1? Yes. >if so, would you be willing to do it? No, because this is very easy. You can do it yourself. First, what's the definition of the norm of a matrix A? > And second, what does it mean to say that A is orthogonal? >or is the invariance to ?the 2-norm when multiplying it on a matrix >or vector property all that ever needs to be known. Yes. >if so, i am a type of computer with no creativity. No creativity required here, just two definitions. >edward David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) there. bird === Subject: Re: 2-norm of orthogonal or permutation matrix >[...] there. No problem. Here's a hint for future reference: Any time you want to prove something about anything you really need to know the definition! Sometimes just knowing the definitions will make the problem trivial, as happened here. Even when the problem is not trivial from the definitions, you still need to know the definitions, otherwise you don't know what you're talking about. >bird David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: 2-norm of orthogonal or permutation matrix posting-account=Qq_GEwoAAAD0Kc2k70q6xwuZdqx8sCzT 4334.5003; Windows NT 5.1; SV1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-mtc-te12.proxy.aol.com[400C708C] (Prism/1.2.1), HTTP/1.1 cache-mtc-ad07.proxy.aol.com[400C74C9] (Traffic-Server/6.1.5 [uScM]) On Mar 19, 9:00?am, spellu...@fb04814.mathematik.tu-darmstadt.de >is it ever shown that if A is orthogonal (or a permutation matrix as a >special case) that ||A|| 2 = 1? >if so, would you be willing to do it? >or is the invariance to ?the 2-norm when multiplying it on a matrix >or vector property all that ever needs to be known. >if so, i am a type of computer with no creativity. no, you seem to be a bit lazy: in homework you normally are assumed to use > the lecture notes/books chapters just dealt with. > here the job is only inserting >edward take the definition of a subordinate matrix norm > use ||.|| 2 and its definition > take the square > use the definition of orthogonality > done hth > peter annihilated. scatterbrain === Subject: Udpated Pell's Equation general solution posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.19 (KHTML, like Gecko) Chrome/1.0.154.48 Safari/525.19,gzip(gfe),gzip(gfe) A previous posting of mine giving a general solution to Pell's Equation had a sign error. Here is a corrected, and much simpler general solution. In rationals, given x^2 - Dy^2 = 1 I have proven: y = 2[f_2*v - 1]/[(D-1) + 2f_2*v - f_2^2*v^2] and x = [f_2*v^2 - 2f_2*v + (D+1)]/[(D-1) + 2f_2*v - f_2^2*v^2] where f_1*f_2 = D-1, and the f's are non-zero integer factors, while v is nonzero but is otherwise a free variable. Note then Pell's Equation has a parametric solution with a hidden variable. As Pell's Equation is normally considered in integers as a Diophantine equation note that you find rational v such that x and y are integers, which gives the 'why' of Pell's Equation. For instance, for D=2, f_1*f_2 = 1, so I have: y = 2(v - 1)/(1 + 2v - v^2) and x = (v^2 - 2v + 3)/(1 + 2v - v^2) and v = 2, gives y = 2, x = 3, and, of course, 9 - 2(4) = 1. James Harris === Subject: Re: Udpated Pell's Equation general solution >A previous posting of mine giving a general solution to Pell's > Equation had a sign error. JSH, an error in every post. and, In what century was Pells Equation first solved ? === Subject: Re: Udpated Pell's Equation general solution posting-account=rIfu6QoAAAD5nXG3h9QEE0J3dZn1U45R Gecko/2009031504 Gentoo Firefox/3.0.7,gzip(gfe),gzip(gfe) > A previous posting of mine giving a general solution to Pell's > Equation had a sign error. Post it to your blog. [snip rest]