mm-4712 === Subject: Re: JSH: Iterative process, factoring > My experience is that posters deny any and all evidence or just keep > raising the bar until the request is to demonstrate factoring better > than anything else previously known. So, you claim to have a factoring method that is better than anything > else previously known, and people ask you to demonstrate it by > factoring better than anything else previously known? The bastards. No. I've solved the factoring problem, or the best assessment given > the result is that the factoring problem is solved. Look, it's quite simple: the factoring problem is not find some > equations which might somehow lead to an algorithm which can > efficiently factor large integers. The factoring problem is find an > algorithm which can efficiently factor large integers. If you have > solved the factoring problem, then you have found an algorithm to > efficiently factor large integers. If you have not found an algorithm > to efficiently factor large integers, then you haven't solved the > factoring problem. The only possible barrier between theory and > implementation of a solution to the factoring problem would be if you > didn't have a computer on which to run your algorithm, which you > evidently do. > I don't have to factor anything. Of one thing there is little doubt in my mind it's if I'm right then someone will do the grunt work. Now if you deny that then you're insane. Why argue? If I have solved the factoring problem and I say theory proves it, and I'm not implementing then if I am correct someone in the world will do the rest, so why bother arguing? It's just stupid. James Harris === Subject: Re: JSH: Iterative process, factoring posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I don't have to factor anything. Of one thing there is little doubt in my mind it's if I'm right then > someone will do the grunt work. Now if you deny that then you're insane. Why argue? If I have solved the factoring problem and I say theory proves it, and > I'm not implementing then if I am correct someone in the world will do > the rest, so why bother arguing? It's just stupid. Suit yourself. Just for the record, how long will it be with nobody implementing your solution before you realise you were wrong again? === Subject: Re: JSH: Iterative process, factoring posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I don't have to factor anything. Of one thing there is little doubt in my mind it's if I'm right then > someone will do the grunt work. Now if you deny that then you're insane. Why argue? If I have solved the factoring problem and I say theory proves it, and > I'm not implementing then if I am correct someone in the world will do > the rest, so why bother arguing? It's just stupid. Suit yourself. Just for the record, how long will it be with nobody > implementing your solution before you realise you were wrong again? I'm not wrong. The derivation is trivial. All your arguing is equivalent to claiming that given z^2 = y^2 + nT x^2 = y^2 mod p 2x = k and z = x + k that it's meaningless that z^2 = 8^{-1} (9nT) mod p which is a DERIVED result. If the derivation is useless then the algebra that gives it is nonsensical and lost, like a human being. Issues around finding p as an odd prime are separate from the mathematical reality that those 4 equations give that result, which is about loving mathematics for what it tells us, not denying it for human reasons. ___JSH === Subject: Re: JSH: Iterative process, factoring >The derivation is trivial. That tells us nothing. The derivation of trial factorisation is both trivial and correct. Trial factorisation is not fast enough to amke an impact on the factorisation problem. We do not need to know how trivial the derivation is, we need to know that your algorithm can factor numbers quickly. Show us. rossum === Subject: Re: JSH: Iterative process, factoring <0nvl44dsf7t42pja12ntibvkmpd43souno@4ax.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) >The derivation is trivial. That tells us nothing. The derivation of trial factorisation is both > trivial and correct. Trial factorisation is not fast enough to amke > an impact on the factorisation problem. But it does not give you z mod p when z^2 = y^2 + nT. Hiding information is useless here, besides being just wacky. > We do not need to know how trivial the derivation is, we need to know > that your algorithm can factor numbers quickly. Show us. > Theory and engineering a solution are DIFFERENT THINGS. No matter how many times people repeat like a mantra the request for an example to prove a proof, it will not change the fact that building a skyscraper is different from designing one. ___JSH === Subject: Re: JSH: Iterative process, factoring >The derivation is trivial. > That tells us nothing. The derivation of trial factorisation is both > trivial and correct. Trial factorisation is not fast enough to amke > an impact on the factorisation problem. But it does not give you z mod p when z^2 = y^2 + nT. Hiding information is useless here, besides being just wacky. > We do not need to know how trivial the derivation is, we need to know > that your algorithm can factor numbers quickly. Show us. Theory and engineering a solution are DIFFERENT THINGS. Look. For _this_ problem a correct solution _must_ be fast - if it's not fast then it's simply not a correct solution. By definition of the problem. >No matter how many times people repeat like a mantra the request for >an example to prove a proof, it will not change the fact that building >a skyscraper is different from designing one. And no matter how many times it's explained to you that a correct but slow factoring algorithm is of no interest whatever, and in particular is _not_ a solution to the factoring problem you don't seem to catch on. ___JSH David C. Ullrich === Subject: Re: JSH: Iterative process, factoring > Suit yourself. Just for the record, how long will it be with nobody > implementing your solution before you realise you were wrong again? I'm not wrong. The derivation is trivial. Right. Of course you're not wrong. So, we have the following situation: (1) If you're right, then someone will factor big numbers using your method soon. (2) You're right. Now, as crazy as this sounds, what if no one factors big numbers within one month? What if no one factors big numbers within one year? At some point, you'd have to admit that either (1) (which is insane to deny, you say) or (2) is false. At what point would you reconsider (1) and (2)? -- If you go to my blog you may notice that I have a link to a Princeton graduate student who seems to think I'm a great 'mathematican', and I do wonder why he has that word wrongly spelled. -- James S. Harris has mathematic supporters === Subject: Re: JSH: Iterative process, factoring <87y75h7yif.fsf@phiwumbda.org> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > Suit yourself. Just for the record, how long will it be with nobody > implementing your solution before you realise you were wrong again? I'm not wrong. The derivation is trivial. Right. Of course you're not wrong. So, we have the following > situation: (1) If you're right, then someone will factor big numbers using your > method soon. (2) You're right. Now, as crazy as this sounds, what if no one factors big numbers > within one month? What if no one factors big numbers within one year? > At some point, you'd have to admit that either (1) (which is insane to > deny, you say) or (2) is false. At what point would you reconsider (1) and (2)? Daily. Or better yet, several times a day. People, including myself, are notable for easily being complete fools, idiots and total morons for things they want to believe. And are quite capable of doing so to unseemly limits, like blowing themselves up. We as a species are remarkably bonkers in general. I fully believe that I am quite capable of being totally and completely wrong, and believing I'm right indefinitely, and have reached a point where I find I trust little if anything, especially myself. Sometimes I believe that our planet is best simply described as world of fools and I may be one of the greatest of all time. James Harris === Subject: Re: JSH: Iterative process, factoring posting-account=p_Xd1AoAAABf87DPZ9h5zXLGtOF7If8A 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Suit yourself. Just for the record, how long will it be with nobody > implementing your solution before you realise you were wrong again? I'm not wrong. æThe derivation is trivial. Right. æOf course you're not wrong. æSo, we have the following > situation: (1) If you're right, then someone will factor big numbers using your > method soon. (2) You're right. Now, as crazy as this sounds, what if no one factors big numbers > within one month? æWhat if no one factors big numbers within one year? > At some point, you'd have to admit that either (1) (which is insane to > deny, you say) or (2) is false. At what point would you reconsider (1) and (2)? Daily. æOr better yet, several times a day. People, including myself, are notable for easily being complete fools, > idiots and total morons for things they want to believe. æAnd are > quite capable of doing so to unseemly limits, like blowing themselves > up. We as a species are remarkably bonkers in general. I fully believe that I am quite capable of being totally and > completely wrong, and believing I'm right indefinitely, and have > reached a point where I find I trust little if anything, especially > myself. Sometimes I believe that our planet is best simply described as world > of fools and I may be one of the greatest of all time. James Harris- Hide quoted text - - Show quoted text - your sentences are too well strung together. can't be real. === Subject: Re: JSH: Iterative process, factoring > I fully believe that I am quite capable of being totally and > completely wrong, and believing I'm right indefinitely, and have > reached a point where I find I trust little if anything, especially > myself. So, when you write things like, I'm not wrong. The derivation is trivial, and Now if you deny that then you're insane, what you mean is, I might be wrong and no one should trust what I say? -- Jesse F. Hughes [I]t's the damndest thing. There's something wrong with every last one of you, and I *never* thought that was a possibility. But now I feel it's the only reasonable conclusion. --JSH sees some sorta light === Subject: Re: JSH: Iterative process, factoring <87od6c8y9j.fsf@phiwumbda.org> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > I fully believe that I am quite capable of being totally and > completely wrong, and believing I'm right indefinitely, and have > reached a point where I find I trust little if anything, especially > myself. So, when you write things like, I'm not wrong. The derivation is > trivial, and Now if you deny that then you're insane, what you mean > is, I might be wrong and no one should trust what I say? You should never just trust. I'm not saying anything new. ___JSH === Subject: Re: JSH: Iterative process, factoring > I fully believe that I am quite capable of being totally and > completely wrong, and believing I'm right indefinitely, and have > reached a point where I find I trust little if anything, especially > myself. > So, when you write things like, I'm not wrong. The derivation is > trivial, and Now if you deny that then you're insane, what you mean > is, I might be wrong and no one should trust what I say? You should never just trust. Trust, but Verify. Use a Proof. Then you have proved it. > I'm not saying anything new. that is true more in a global way. > ___JSH === Subject: Re: Solution Manual of Engineering Mechanics - Statics And Dynamics 11ed by Hibbeler in pdf form <13945622.1210606307967.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=pmAhdQoAAAC_zq8cQIM-jK9Xt3ScO21e SIMBAR={8B0CDDA0-61AF-4cce-AA2A-270D7D7AB089}; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; IEMB3; IEMB3),gzip(gfe),gzip(gfe) Could you send it to markadi2002@hotmail.com === Subject: Re: Labview 8 student edition solutions manual posting-account=14ou_goAAAA-hjz3u1vHKuyW-l3ZkYCI Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > Hi. I was wondering if I could get the Labview 8 student edition > solutions manual? How much is it and can I get it through email? I can sell you this FULL solution manual in PDF if you still need it. $19.99. I can also provide a single chapter as well, just to show I'm legit. === Subject: learn maths from 0 to infinity posting-account=LQuUVwoAAADdaDADDCh40lGAIEY_7C9Y Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) === Subject: Re: JSH: Some basics about factoring > But, you may then naturally wonder, if it's such a big deal to find z > mod p, then how can it be something argued out on newsgroups without > experts in the field caring? One note of warning: I doubt the foremost experts in this arena read newsgroups on a regular basis. So it can be easily done. > Short of it is that how the newsgroups react doesn't matter. No > matter what if the research is viable that will be known and probably > in a rather short amount of time as we have a world today that > consumes information. But what you cannot forget later, or I don't > want you to forget it, is if you couldn't resolve the issue on your > own despite the algebra being easy and the problem being hugely > significant. I've not been following closely, but the gist of what I've seen is that the controversy is that what you say and what the algebra says is, in fact, two non-equivalent sets. Also, this may just be the commaphile in me, but I think you're missing a few commas in your rant there... Run-on sentences don't improve your arguments. [Sorry if this is a duplicate, my NNTP server is complaining today] === Subject: Re: JSH: Some basics about factoring posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > It occurs to me that some of you may not understand how my research > changes the landscape with factoring so I want to explain simply and > give some factoring basics. First off, if you have z^2 = y^2 + nT where T is your target to factor, and you also have z mod p_1, z mod > p_2, and z mod p_3, where z is for a non-trivial factorization and > those are odd primes with a minimum value greater than 2sqrt(nT)/3, > then necessarily you can calculate z exactly and with z you can factor > nT from (z-y)(z+y) = nT. That is just an absolute in terms of basic algebra. So it IS a big deal for me to present equations that allow you to just > calculate z mod p. > Given an equation that gives z mod p, there are only two places to dispute it: 1. It's not correct. 2. It's impractical to find a prime p that will work in the size range necessary. Those are it. Otherwise, three primes will do it regardless of the size of the target composite T, as the equation under discussion requires primes less than 2sqrt(nT)/3 (but hopefully close to that value). My interest in discussions on this issue are to see if any serious error can be shown in the derivation of the key equation, despite its apparent simplicity to me. And to see if someone can show that it is too difficult to find primes in the necessary range. But also I think it fascinating to study group processes. There is nothing in the mathematical literature prior to this research that even gives a hint that you can find z mod p, but with an easy derivation of an equation that gives something never before done in human history I can check the limits of modern math society to reject anything and everything that doesn't suit a social agenda. That is, I'm kind of curious about how little most of you believe in mathematics. That helps me decide what things I can push forward later in good conscience. James Harris === Subject: Re: JSH: Some basics about factoring >There is nothing in the mathematical literature prior to this research >that even gives a hint that you can find z mod p, but with an easy >derivation of an equation that gives something never before done in >human history I can check the limits of modern math society to reject >anything and everything that doesn't suit a social agenda. James, I'm interested to know what mathematical literature you read on a regular basis? -- Chris. === Subject: Re: JSH: Some basics about factoring >There is nothing in the mathematical literature prior to this research >that even gives a hint that you can find z mod p, but with an easy >derivation of an equation that gives something never before done in >human history I can check the limits of modern math society to reject >anything and everything that doesn't suit a social agenda. James, I'm interested to know what mathematical literature you read on > a regular basis? -- > Chris. page 5 girl in the Midnight News === Subject: Re: JSH: Some basics about factoring posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1),gzip(gfe),gzip(gfe) > It occurs to me that some of you may not understand how my research > changes the landscape with factoring [.snip delusioal diatribe.] James Harris Great point and insight! It occurs to me that you don't have a clue of what you speak! You can't even factor the smallest RSA number (and you know the factors) with your nonsense. Your method is almost as bad as trial division (which I'd rather use over your jibberish). Get your head out of your ass you delusional narcissist with false notions of granduer! You have NOTHING! So yes - you don't understand and ALL of us KNOW it. === Subject: Re: JSH: Some basics about factoring anything except 6 Originator: gordon@hammy.burditt.org (Gordon Burditt) >It occurs to me that some of you may not understand how my research >changes the landscape with factoring so I want to explain simply and >give some factoring basics. You mean factoring anything but 6 basics. When JSH both proves that his method can factor 6 and demonstrates that it cannot, you can bet that the proof is what's wrong. >First off, if you have z^2 = y^2 + nT where T is your target to factor, You forgot the part about T != 6. And somewhere within this so-called proof, you should NEED to use the fact that T != 6. Since this problem is about factoring, I'll forgive you for not disallowing values of T that are non-integer, negative, 0, or 1 (but instructors would take off points for it on an exam). And if you want to restrict it to larger values, fine, but you need to SAY that (at which point you've only solved PART of the factoring problem, even if the part you haven't covered is trivial for elementary-school students to solve without pencil and paper). When your so-called proof proves falsehoods, you blow your credibility. You forgot to specify that n, and probably x and y are integers. >and you also have z mod p_1, z mod >p_2, and z mod p_3, where z is for a non-trivial factorization and >those are odd primes with a minimum value greater than 2sqrt(nT)/3, You haven't demonstrated that these values will exist that satisfy the conditions. >then necessarily you can calculate z exactly and with z you can factor >nT from (z-y)(z+y) = nT. That is just an absolute in terms of basic algebra. Are you sure you won't factor nT into n and T? Well, if n = 1, no problem, but how can you be sure of this otherwise? >So it IS a big deal for me to present equations that allow you to just >calculate z mod p. Do you have a proof that there *IS* a value of z mod p for every value of T under consideration? Solving the factoring problem is unusual in mathematics since it requires *efficiency* as well as just working properly. If you just want it to work properly, use trial division. It's slow but it's really easy to prove it works. And it even factors 6. >Most modern factoring methods in some way or another use an equation >like z^2 = y^2 + nT, or more familiarly you often have x^2 = y^2 mod >N, where N is the target composite, so it's just about variable names >and if you know any math at all you know that shifting letters is not >a big deal. Even the Number Field Sieve is a lot about using x^2 = y^2 mod N, as >in trying to find x and y (I think it uses two congruences of that >type), so the result I have has implications for the most advanced >factoring techniques known. But, you may then naturally wonder, if it's such a big deal to find z >mod p, then how can it be something argued out on newsgroups without >experts in the field caring? When your proof claims to factor 6, and it does not factor 6, and the author of the proof admits that it does not factor 6, then it's obviously crap, and deserves no further consideraton. When the author is confronted with this problem and sees nothing wrong, I wouldn't blame the experts for not reading anything else by the same author. >One simple possible answer to that question is that I must be wrong. Yes, when you prove you can factor something (6, among other choices) you can demonstrate it won't factor, you're wrong. >REMEMBER, if p_1, p_2 and p_3 can be found in the size range necessary >then it is an ABSOLUTE that you can factor non-trivially. Yes, but to solve the factoring problem you need to prove that it works for all composite values of T. Either that or restrict your claims to the portion of the problem it can actually solve. >I claim to have a method that gives z mod p, so if that claim is >correct and you can get z mod p in the necessary range for just three >prime numbers then ABSOLUTELY you will factor non-trivially. So theory says one thing, absolutely. Where notice I still haven't >answered the question of whether or not I must be wrong. Well, there's the derivation which you can look over, and there is >doing examples and you might wonder if maybe with a big target >composite T, maybe it IS really hard to find odd primes p that will >work, and you can muddle along with those questions believing there >must be something wrong somewhere or top people in the field would >acknowledge this result! Top people in the field are not required to read or acknowledge USENET postings or blogs, regardless of what the contents of the posts are. If they were, they'd never have any time to do any math. Or sleep. >I think this situation for some of you is a test of your trust in >people versus your trust in mathematics and it's probably not fair, >but I think some of you wrongly believe that you have mathematical >ability, when you do not. Is it possible to prove something true (JSH's method can factor 6) and demonstrate that it is false (JSH's method cannot factor 6), with no errors in the proof *OR* the demonstration? JSH seems to believe this. Does JSH have mathematical ability? His Usenet postings don't show it. >Short of it is that how the newsgroups react doesn't matter. No >matter what if the research is viable that will be known and probably >in a rather short amount of time as we have a world today that >consumes information. But what you cannot forget later, or I don't >want you to forget it, is if you couldn't resolve the issue on your >own despite the algebra being easy and the problem being hugely >significant. I am not really convinced that if SSL as used in web transaction for e-commerce disappeared overnight that anything would significantly change. >As if you cannot evaluate easy algebra and get the right answer when >it's handed to you because you're waiting on some other people or >trusting that someone else out there has the judgment you need, then >you are NOT a mathematician, no matter what you tell yourself when you >look in the mirror. === Subject: Re: JSH: Some basics about factoring anything except 6 posting-account=kxPkPAoAAACjJi8w0gL9bnyznPzdw9HW SV1),gzip(gfe),gzip(gfe) >It occurs to me that some of you may not understand how my research >changes the landscape with factoring so I want to explain simply and >give some factoring basics. You mean factoring anything but 6 basics. æWhen JSH both proves > that his method can factor 6 and demonstrates that it cannot, > you can bet that the proof is what's wrong. First off, if you have z^2 = y^2 + nT where T is your target to factor, You forgot the part about T != 6. æAnd somewhere within this so-called > proof, you should NEED to use the fact that T != 6. æSince this > problem is about factoring, I'll forgive you for not disallowing > values of T that are non-integer, negative, 0, or 1 (but instructors > would take off points for it on an exam). æAnd if you want to > restrict it to larger values, fine, but you need to SAY that (at > which point you've only solved PART of the factoring problem, even > if the part you haven't covered is trivial for elementary-school > students to solve without pencil and paper). æWhen your so-called > proof proves falsehoods, you blow your credibility. You forgot to specify that n, and probably x and y are integers. æ and you also have z mod p 1, z mod >p 2, and z mod p 3, where z is for a non-trivial factorization and >those are odd primes with a minimum value greater than 2sqrt(nT)/3, You haven't demonstrated that these values will exist that satisfy > the conditions. then necessarily you can calculate z exactly and with z you can factor >nT from (z-y)(z+y) = nT. That is just an absolute in terms of basic algebra. Are you sure you won't factor nT into n and T? æWell, if n = 1, no > problem, but how can you be sure of this otherwise? So it IS a big deal for me to present equations that allow you to just >calculate z mod p. Do you have a proof that there *IS* a value of z mod p for every value > of T under consideration? Solving the factoring problem is unusual in mathematics since it > requires *efficiency* as well as just working properly. æIf you > just want it to work properly, use trial division. æIt's slow but > it's really easy to prove it works. æAnd it even factors 6. Most modern factoring methods in some way or another use an equation >like z^2 = y^2 + nT, or more familiarly you often have x^2 = y^2 mod >N, where N is the target composite, so it's just about variable names >and if you know any math at all you know that shifting letters is not >a big deal. Even the Number Field Sieve is a lot about using x^2 = y^2 mod N, as >in trying to find x and y (I think it uses two congruences of that >type), so the result I have has implications for the most advanced >factoring techniques known. But, you may then naturally wonder, if it's such a big deal to find z >mod p, then how can it be something argued out on newsgroups without >experts in the field caring? When your proof claims to factor 6, and it does not factor 6, and > the author of the proof admits that it does not factor 6, then it's > obviously crap, and deserves no further consideraton. æWhen the author > is confronted with this problem and sees nothing wrong, I wouldn't > blame the experts for not reading anything else by the same author. One simple possible answer to that question is that I must be wrong. Yes, when you prove you can factor something (6, among other choices) > you can demonstrate it won't factor, you're wrong. REMEMBER, if p 1, p 2 and p 3 can be found in the size range necessary >then it is an ABSOLUTE that you can factor non-trivially. Yes, but to solve the factoring problem you need to prove that it > works for all composite values of T. æEither that or restrict your > claims to the portion of the problem it can actually solve. I claim to have a method that gives z mod p, so if that claim is >correct and you can get z mod p in the necessary range for just three >prime numbers then ABSOLUTELY you will factor non-trivially. So theory says one thing, absolutely. æWhere notice I still haven't >answered the question of whether or not I must be wrong. Well, there's the derivation which you can look over, and there is >doing examples and you might wonder if maybe with a big target >composite T, maybe it IS really hard to find odd primes p that will >work, and you can muddle along with those questions believing there >must be something wrong somewhere or top people in the field would >acknowledge this result! Top people in the field are not required to read or acknowledge > USENET postings or blogs, regardless of what the contents of the > posts are. æIf they were, they'd never have any time to do any > math. æOr sleep. I think this situation for some of you is a test of your trust in >people versus your trust in mathematics and it's probably not fair, >but I think some of you wrongly believe that you have mathematical >ability, when you do not. Is it possible to prove something true (JSH's method can factor 6) > and demonstrate that it is false (JSH's method cannot factor 6), > with no errors in the proof *OR* the demonstration? æJSH seems to > believe this. æDoes JSH have mathematical ability? æHis Usenet > postings don't show it. Short of it is that how the newsgroups react doesn't matter. æNo >matter what if the research is viable that will be known and probably >in a rather short amount of time as we have a world today that >consumes information. æBut what you cannot forget later, or I don't >want you to forget it, is if you couldn't resolve the issue on your >own despite the algebra being easy and the problem being hugely >significant. I am not really convinced that if SSL as used in web transaction > for e-commerce disappeared overnight that anything would significantly > change. As if you cannot evaluate easy algebra and get the right answer when >it's handed to you because you're waiting on some other people or >trusting that someone else out there has the judgment you need, then >you are NOT a mathematician, no matter what you tell yourself when you >look in the mirror.- D.9alj citerad text - - Visa citerad text - I only think JSH's formula factors composites made of primes. ... === Subject: Re: JSH: Some basics about factoring anything except 6 Originator: gordon@hammy.burditt.org (Gordon Burditt) I only think JSH's formula factors composites made of primes. > 2 and 3 aren't primes? It would probably be trivial for JSH to fix my complaints about his proof, but it's also too much work for him. He can limit it to factoring composites T > 100 or something, and say at some point in his proof that this restriction guarantees that there are prime values for some variable or other that satisfy whatever inequalities he sets up. Then he can get on to the important part where he asks you to hunt for a prime needle in a haystack, without any proof that the haystack has a needle in it. === Subject: Re: JSH: Some basics about factoring posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. Stated without proof. Bingo. Well no, as he's also incorrect. The iteration is mod 3p, not 3. ___JSH === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. Well no, as he's also incorrect. The iteration is mod 3p, not 3. > For some undetermined prime p. Since you don't know p, you have no alternative but to search by 3's. Here's a numerical example for you. Take T = 18089363 and pretend you don't know that z = 5778, y = 3911, x = z/3 = 1926. Now to have z^2 = 8^{-1} 9nT mod p (of course in this case n = 1) we'll have to have p dividing either of x+y or x-y, so the only candidate primes will be p = 3, 5, 13, 397, or 449. All other primes will either result in quadratic non-residues (which you can test) or will give invalid answers for z (which you can't check, since you don't know z). Now IF you knew these five candidate primes, you could indeed find z using the CRT. But you don't know what primes will work, so your method appears to be dead in the water. So let's try your latest fix. We'll find the z_0 divisible by 3 that minimizes |18089363 - 8(z_0 / 3)^2| It's not difficult to find z_0 = 4512. The difference between this and the correct answer for z (= 5778, recall) is 1266 = 3 * 422 so 422 steps of 3 will indeed give you the z you want. You can't speed this up by taking steps of p, since you don't know which p will work. (In fact, the only primes p that will work are p = 2 and p = 211.) In other words, you have no choice that I can see except to try z_0, z_0 + 3, z_0 + 6, and so on. As I said. Rick === Subject: Re: JSH: Some basics about factoring His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. The iteration is mod 3p, not 3. > For some undetermined prime p. Since you don't know p, you have no > alternative but to search by 3's. Here's a numerical example for you. Take T = 18089363 and pretend > you don't know that z = 5778, y = 3911, x = z/3 = 1926. Now to > have z^2 = 8^{-1} 9nT mod p (of course in this case n = 1) we'll have to have p dividing either of x+y or x-y, so the only > candidate primes will be p = 3, 5, 13, 397, or 449. All other > primes will either result in quadratic non-residues (which > you can test) or will give invalid answers for z (which you > can't check, since you don't know z). Now IF you knew these > five candidate primes, you could indeed find z using the CRT. > But you don't know what primes will work, so your method > appears to be dead in the water. So let's try your latest fix. We'll find the z_0 divisible > by 3 that minimizes |18089363 - 8(z_0 / 3)^2| It's not difficult to find z_0 = 4512. The difference between > this and the correct answer for z (= 5778, recall) is > 1266 = 3 * 422 so 422 steps of 3 will indeed give you the z > you want. You can't speed this up by taking steps of p, > since you don't know which p will work. (In fact, the only > primes p that will work are p = 2 and p = 211.) In other > words, you have no choice that I can see except to try > z_0, z_0 + 3, z_0 + 6, and so on. T = 18089363, I get the prime factorization: 1867* 9689 z+y = 9689 z- y = 1867 and of course (z+y)*(z-y) = T . Maybe there's one thing I'm not so clear about: how few of the possible 'p' candidates are needed to find x and y (roughly) ? David Bernier === Subject: Re: JSH: Some basics about factoring <1371b$484c8463$9999@news.teranews.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. The iteration is mod 3p, not 3. For some undetermined prime p. Since you don't know p, you have no > alternative but to search by 3's. Here's a numerical example for you. Take T = 18089363 and pretend > you don't know that z = 5778, y = 3911, x = z/3 = 1926. Now to > have z^2 = 8^{-1} 9nT mod p (of course in this case n = 1) we'll have to have p dividing either of x+y or x-y, so the only > candidate primes will be p = 3, 5, 13, 397, or 449. All other > primes will either result in quadratic non-residues (which > you can test) or will give invalid answers for z (which you > can't check, since you don't know z). Now IF you knew these > five candidate primes, you could indeed find z using the CRT. > But you don't know what primes will work, so your method > appears to be dead in the water. So let's try your latest fix. We'll find the z_0 divisible > by 3 that minimizes |18089363 - 8(z_0 / 3)^2| It's not difficult to find z_0 = 4512. The difference between > this and the correct answer for z (= 5778, recall) is > 1266 = 3 * 422 so 422 steps of 3 will indeed give you the z > you want. You can't speed this up by taking steps of p, > since you don't know which p will work. (In fact, the only > primes p that will work are p = 2 and p = 211.) In other > words, you have no choice that I can see except to try > z_0, z_0 + 3, z_0 + 6, and so on. T = 18089363, I get the prime factorization: > 1867* 9689 z+y = 9689 > z- y = 1867 and of course (z+y)*(z-y) = T . Maybe there's one thing I'm not so clear about: > how few of the possible 'p' candidates are needed to > find x and y (roughly) ? I abandoned this approach once I realized that for p to work it had to be true that 2f_1 - f_2 = 0 mod p where f_1*f_2 = nT, as it seems increasingly unlikely that you'd find enough primes that would work as T increases in size. As a sidenote though the z_0/(3p) steps result is just a remarkably neat result to me, though yes, you do need to know p to get it to work, but p=3 would work in this case to give you an upper limit on z. James Harris === Subject: Re: JSH: Some basics about factoring T = 18089363, I get the prime factorization: > 1867* 9689 > z+y = 9689 > z- y = 1867 > and of course (z+y)*(z-y) = T . > Maybe there's one thing I'm not so clear about: > how few of the possible 'p' candidates are needed to > find x and y (roughly) ? I abandoned this approach once I realized that for p to work it had to > be true that 2f_1 - f_2 = 0 mod p where f_1*f_2 = nT, as it seems increasingly unlikely that you'd find > enough primes that would work as T increases in size. As a sidenote though the z_0/(3p) steps result is just a remarkably > neat result to me, though yes, you do need to know p to get it to > work, but p=3 would work in this case to give you an upper limit on z. p = 3 always works. Rick === Subject: Re: JSH: Some basics about factoring posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-ntc-ta07.proxy.aol.com[CFC87007] (Prism/1.2.1), HTTP/1.1 cache-ntc-ac09.proxy.aol.com[CFC8748A] (Traffic-Server/6.1.5 [uScM]) > His latest add-on, minimizing |nT - 8(z 0 / 3)^2| and then > trying z 0 + 3, z 0 + 6, z 0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. Well no, as he's also incorrect. ?The iteration is mod 3p, not 3. For some undetermined prime p. Since you don't know p, you have no > alternative but to search by 3's. Here's a numerical example for you. Take T = 18089363 and pretend > you don't know that z = 5778, y = 3911, x = z/3 = 1926. Now to > have ? ? ?z^2 = 8^{-1} 9nT mod p ?(of course in this case n = 1) we'll have to have p dividing either of x+y or x-y, so the only > candidate primes will be p = 3, 5, 13, 397, or 449. All other > primes will either result in quadratic non-residues (which > you can test) or will give invalid answers for z (which you > can't check, since you don't know z). Now IF you knew these > five candidate primes, you could indeed find z using the CRT. > But you don't know what primes will work, so your method > appears to be dead in the water. So let's try your latest fix. We'll find the z 0 divisible > by 3 that minimizes ? ? ?|18089363 - 8(z 0 / 3)^2| It's not difficult to find z 0 = 4512. The difference between > this and the correct answer for z (= 5778, recall) is > 1266 = 3 * 422 so 422 steps of 3 will indeed give you the z > you want. You can't speed this up by taking steps of p, > since you don't know which p will work. (In fact, the only > primes p that will work are p = 2 and p = 211.) In other > words, you have no choice that I can see except to try > z 0, z 0 + 3, z 0 + 6, and so on. As I said. > Rick ----------------------------------------------------------------- he's thrown in the towel again. Enrico === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. ?The iteration is mod 3p, not 3. > For some undetermined prime p. Since you don't know p, you have no > alternative but to search by 3's. > Here's a numerical example for you. Take T = 18089363 and pretend > you don't know that z = 5778, y = 3911, x = z/3 = 1926. Now to > have > ? ? ?z^2 = 8^{-1} 9nT mod p ?(of course in this case n = 1) > we'll have to have p dividing either of x+y or x-y, so the only > candidate primes will be p = 3, 5, 13, 397, or 449. All other > primes will either result in quadratic non-residues (which > you can test) or will give invalid answers for z (which you > can't check, since you don't know z). Now IF you knew these > five candidate primes, you could indeed find z using the CRT. > But you don't know what primes will work, so your method > appears to be dead in the water. > So let's try your latest fix. We'll find the z_0 divisible > by 3 that minimizes > ? ? ?|18089363 - 8(z_0 / 3)^2| > It's not difficult to find z_0 = 4512. The difference between > this and the correct answer for z (= 5778, recall) is > 1266 = 3 * 422 so 422 steps of 3 will indeed give you the z > you want. You can't speed this up by taking steps of p, > since you don't know which p will work. (In fact, the only > primes p that will work are p = 2 and p = 211.) In other > words, you have no choice that I can see except to try > z_0, z_0 + 3, z_0 + 6, and so on. > As I said. > Rick ----------------------------------------------------------------- > he's thrown in the towel again. Enrico No matter. Give him a month and this will be added to his list of successes, thwarted by the Math Cabal. BTW, don't forget the June meeting of the Cabal. All the pork rinds you can eat, at the usual place and time. Rick === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. Well no, as he's also incorrect. The iteration is mod 3p, not 3. >___JSH I think that you missed the point of Rotwang's reply James. rossum P.S. Rotwang, we need to get together to talk about robots sometime. :) === Subject: Re: JSH: Some basics about factoring posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. Well no, as he's also incorrect. The iteration is mod 3p, not 3. ___JSH I think that you missed the point of Rotwang's reply James. rossum P.S. Rotwang, we need to get together to talk about robots sometime. > :) Decker had an error in his reply. Screwing up mathematics is just screwing up mathematics. People talking around the mistake do not change it. And he's an actual professor of something or other. I'm just a guy talking about his own amateur research that totally blows away anything and everything the professors ever imagined they could do. Because partly, I think, their imagination is too small. They can't find what they're not looking for. ___JSH === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. The iteration is mod 3p, not 3. > ___JSH > I think that you missed the point of Rotwang's reply James. > rossum > P.S. Rotwang, we need to get together to talk about robots sometime. > :) Decker had an error in his reply. Screwing up mathematics is just > screwing up mathematics. People talking around the mistake do not change it. And he's an actual professor of something or other. I'm just a guy talking about his own amateur research that totally > blows away anything and everything the professors ever imagined they > could do. Because partly, I think, their imagination is too small. They can't find what they're not looking for. And you couldn't find your arse with both hands. === Subject: Re: JSH: Some basics about factoring posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. The iteration is mod 3p, not 3. > ___JSH > I think that you missed the point of Rotwang's reply James. > rossum > P.S. Rotwang, we need to get together to talk about robots sometime. > :) Decker had an error in his reply. Screwing up mathematics is just > screwing up mathematics. People talking around the mistake do not change it. And he's an actual professor of something or other. I'm just a guy talking about his own amateur research that totally > blows away anything and everything the professors ever imagined they > could do. Because partly, I think, their imagination is too small. They can't find what they're not looking for. And you couldn't find your arse with both hands. Oh, that bit didn't it? God forbid I criticize your precious professors. Not my fault if they're not up to the task. Not my fault if they are more actors than real mathematicians. Not my fault if at the end of the day they NEED people like you to protect them, cherish them, and try to save them because they cannot save themselves. But the entire point of this exercise was that you can't save them at this point. The point was to find a result that could blow through all of you. Line up. All the math people around the world, line up and finally understand the true power of mathematical proof as it blows through every single one of you, and calls you to your destiny. You were born to lose here. It is your destiny. ___JSH === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. The iteration is mod 3p, not 3. > ___JSH > I think that you missed the point of Rotwang's reply James. > rossum > P.S. Rotwang, we need to get together to talk about robots sometime. > :) > Decker had an error in his reply. Screwing up mathematics is just > screwing up mathematics. > People talking around the mistake do not change it. > And he's an actual professor of something or other. > I'm just a guy talking about his own amateur research that totally > blows away anything and everything the professors ever imagined they > could do. > Because partly, I think, their imagination is too small. > They can't find what they're not looking for. > And you couldn't find your arse with both hands. Oh, that bit didn't it? God forbid I criticize your precious > professors. Not my fault if they're not up to the task. Not my fault if they are more actors than real mathematicians. Not my fault if at the end of the day they NEED people like you to > protect them, cherish them, and try to save them because they cannot > save themselves. But the entire point of this exercise was that you can't save them at > this point. The point was to find a result that could blow through all of you. [...] There is a minor mistake in the first 15 lines of Rick Decker's reply to my post, isn't there? David Bernier === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z_0 / 3)^2| and then > trying z_0 + 3, z_0 + 6, z_0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. The iteration is mod 3p, not 3. > ___JSH > I think that you missed the point of Rotwang's reply James. > rossum > P.S. Rotwang, we need to get together to talk about robots sometime. > :) > Decker had an error in his reply. Screwing up mathematics is just > screwing up mathematics. > People talking around the mistake do not change it. > And he's an actual professor of something or other. > I'm just a guy talking about his own amateur research that totally > blows away anything and everything the professors ever imagined they > could do. > Because partly, I think, their imagination is too small. > They can't find what they're not looking for. > And you couldn't find your arse with both hands. Oh, that bit didn't it? God forbid I criticize your precious > professors. Not my fault if they're not up to the task. Not my fault if they are more actors than real mathematicians. Not my fault if at the end of the day they NEED people like you to > protect them, cherish them, and try to save them because they cannot > save themselves. But the entire point of this exercise was that you can't save them at > this point. The point was to find a result that could blow through all of you. Line up. All the math people around the world, line up and finally > understand the true power of mathematical proof as it blows through > every single one of you, and calls you to your destiny. You were born to lose here. It is your destiny. That has a ring to it. Perhaps you could make it into a song. === Subject: Re: JSH: Some basics about factoring > His latest add-on, minimizing |nT - 8(z 0 / 3)^2| and then > trying z 0 + 3, z 0 + 6, z 0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. ?The iteration is mod 3p, not 3. > JSH > I think that you missed the point of Rotwang's reply James. > rossum > P.S. Rotwang, we need to get together to talk about robots sometime. > :) > Decker had an error in his reply. ?Screwing up mathematics is just > screwing up mathematics. > People talking around the mistake do not change it. > And he's an actual professor of something or other. > I'm just a guy talking about his own amateur research that totally > blows away anything and everything the professors ever imagined they > could do. > Because partly, I think, their imagination is too small. > They can't find what they're not looking for. > And you couldn't find your arse with both hands. Oh, that bit didn't it? ?God forbid I criticize your precious > professors. Not my fault if they're not up to the task. Not my fault if they are more actors than real mathematicians. Not my fault if at the end of the day they NEED people like you to > protect them, cherish them, and try to save them because they cannot > save themselves. But the entire point of this exercise was that you can't save them at > this point. The point was to find a result that could blow through all of you. Line up. ?All the math people around the world, line up and finally > understand the true power of mathematical proof as it blows through > every single one of you, and calls you to your destiny. You were born to lose here. It is your destiny. That has a ring to it. ?Perhaps you could make it into a song. Or perhaps a movie. With Jimmie's father siding with the Dark Side of mathematics. Hey, Jimmie, think your dad would agree to this? I'm sure you'll jump at the chance to get Hollywood babes, but what about your dad? Think he'll go for it? You still talk to him after moving away from Atlanta, don't you? === Subject: Re: JSH: Some basics about factoring >Or perhaps a movie. With Jimmie's father siding >with the Dark Side of mathematics. Come to the Dark Side - we have cookies! :) rossum === Subject: Re: JSH: Some basics about factoring posting-account=tCEoyAoAAAAkltU5zxOoI8uJ4lyz5-kv .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > It is your destiny. [ voice of James Earl Jones ] > That has a ring to it. ?Perhaps you could make it into a song. Or perhaps a movie. With Jimmie's father siding > with the Dark Side of mathematics. Hey, Jimmie, think your dad would agree to this? > I'm sure you'll jump at the chance to get Hollywood > babes, but what about your dad? Think he'll go > for it? You still talk to him after moving away > from Atlanta, don't you?- Hide quoted text - - Show quoted text - Might make an interesting video. Mathematicians Gone Wild. Young, unruly and undisciplined amateurs tease and torment, trying to draw people into their corrupted world of nonsense, and stripping themselves of their sensibilities piece by piece as if dancing the dance of the seven veils. Millions of dollars are made and then the producer goes to jail. === Subject: Re: JSH: Some basics about factoring posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.34; Windows NT 5.1; SV1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-dtc-td09.proxy.aol.com[CDBC7069] (Prism/1.2.1), HTTP/1.1 cache-dtc-ad05.proxy.aol.com[CDBC74C7] (Traffic-Server/6.1.5 [uScM]) On Jun 7, 8:50æpm, Tomoko Kanazawa dom arigato > It is your destiny. [ voice of James Earl Jones ] That has a ring to it. ?Perhaps you could make it into a song. Or perhaps a movie. With Jimmie's father siding > with the Dark Side of mathematics. Hey, Jimmie, think your dad would agree to this? > I'm sure you'll jump at the chance to get Hollywood > babes, but what about your dad? Think he'll go > for it? You still talk to him after moving away > from Atlanta, don't you?- Hide quoted text - - Show quoted text - Might make an interesting video. Mathematicians Gone Wild. Young, > unruly and undisciplined amateurs tease and torment, trying to draw > people into their corrupted world of nonsense, and stripping > themselves of their sensibilities piece by piece as if dancing the > dance of the seven veils. Millions of dollars are made and then the > producer goes to jail. Yeah, now that Max Hardcore is going to jail there's a void waiting for someone to step in. Maybe Jimmie could style himself as Max Factor! Wait, that's been used, hasn't it? === Subject: Re: JSH: Some basics about factoring posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > His latest add-on, minimizing |nT - 8(z 0 / 3)^2| and then > trying z 0 + 3, z 0 + 6, z 0 + 9, ... to find z, seems to > be little more than trial and error. > Stated without proof. > Bingo. > Well no, as he's also incorrect. ?The iteration is mod 3p, not 3. > JSH > I think that you missed the point of Rotwang's reply James. > rossum > P.S. Rotwang, we need to get together to talk about robots sometime. > :) > Decker had an error in his reply. ?Screwing up mathematics is just > screwing up mathematics. > People talking around the mistake do not change it. > And he's an actual professor of something or other. > I'm just a guy talking about his own amateur research that totally > blows away anything and everything the professors ever imagined they > could do. > Because partly, I think, their imagination is too small. > They can't find what they're not looking for. > And you couldn't find your arse with both hands. Oh, that bit didn't it? ?God forbid I criticize your precious > professors. Not my fault if they're not up to the task. Not my fault if they are more actors than real mathematicians. Not my fault if at the end of the day they NEED people like you to > protect them, cherish them, and try to save them because they cannot > save themselves. But the entire point of this exercise was that you can't save them at > this point. The point was to find a result that could blow through all of you. Line up. ?All the math people around the world, line up and finally > understand the true power of mathematical proof as it blows through > every single one of you, and calls you to your destiny. You were born to lose here. It is your destiny. That has a ring to it. ?Perhaps you could make it into a song. Or perhaps a movie. With Jimmie's father siding > with the Dark Side of mathematics. Hey, Jimmie, think your dad would agree to this? > I'm sure you'll jump at the chance to get Hollywood > babes, but what about your dad? Think he'll go > for it? You still talk to him after moving away > from Atlanta, don't you? Good catch. I was thinking it was very Empire Strikes Back. Never underestimate the true power of the Force. JSH === Subject: Re: JSH: Some basics about factoring > babes, but what about your dad? Think he'll go > for it? You still talk to him after moving away > from Atlanta, don't you? >Good catch. I was thinking it was very Empire Strikes Back. >Never underestimate the true power of the Force. Never underestimate the true power of the *FARCE* >___JSH === Subject: Re: Re-cap, why factoring is done posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-ntc-tc05.proxy.aol.com[CFC87045] (Prism/1.2.1), HTTP/1.1 cache-ntc-ac09.proxy.aol.com[CFC8748A] (Traffic-Server/6.1.5 [uScM]) > Assuming I have correctly understood your claim, here is a > counterexample: let N = 19*23 = 437 = 2 mod 3, so that c = 1. Then x = > (19 + 23)/2 = 21. Let p = 11, which is less than 2x/3; the inverse of > 8 mod 11 is 7. Therefore 8^{-1}*(9Nc) = 9 mod 11 and 9 = 3^2 is a quadratic residue mod 11. But x^2 = 1 mod 11. Hmmm...a false positive. ?3 & 5 work as expected. ?My assumption was > that 11 would not give a valid x in this situation, which is clearly > wrong. ?But why? See my reply to Rick in this thread, in which I point out what I > believe is a bogus step in your derivation. Long story short, you > assume the existence of an integer x which satisfies both 3x = z mod p and x^2 = y^2 mod p. The first of these equations can always be satisfied and gives a > unique value of x mod p, but that value will not satisfy the second > equation in general. As far as I have seen you have given no It's trivial algebra which is why I kept puzzling over what looked > like a counterexample until I figured it out. Human nature is to believe there is only one factorization of 19(23) > when there are two integer factorizations. justification as to why 8^{-1}*9nT will fail to be a quadratic residue > if the second equation above is not satisfied, and my counterexample > shows that it can be. Nope. ?I figured it out. ?There are TWO factorizations possible. You forgot about the trivial factorization. The equations do work perfectly. ?Just sometimes they won't give the > non-trivial factorization's residue for a particular p, but those > instances can be eliminated easily from consideration. Nope that's wrong. ?They still don't work for the trivial > factorization. ?Yuck.- Hide quoted text - - Show quoted text - -------------------------------------------------------- Didn't you run into something like this before? > It was just before you began your entries about > non-rationals and surrogate factoring, I think. æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ Enrico Nope. æI'm using a greatly simplified argument where I shifted from 2ax = k mod p to 2x = k, setting a=1, and turning that into an explicit equation. > Then I get z^2 = y^2 + nT with n chosen such that nT = 2 mod 3, means that z^2 = 8^{-1] (9nT) mod p where p is and odd prime and p < 2z/3, and posters found cases where > that wasn't sufficient to rule out primes that would not work. So you have false positive with just those rules. Does that mean factoring is not done? No, as it turns out I left off some things in my continuing urge to > simplify, so I just put them back. I think it remarkable how desperately posters reach for anything to > refute simple algebra which gives the derivation and the general > result which is applicable across any factoring system so it even > impacts the Number Field Sieve. Given z^2 = y^2 + nT with z a positive integer divisible by 3 it is just a mathematical > fact that æz^2 = 8^{-1] (9nT) mod p when an odd prime p can be found such that the quadratic residue > exists, that prime is less than 2z/3 and--the part I left off--that z > is within a certain number of steps by increments of 3p from a number > I call z 0, which is given by finding the largest integer divisible by > 3 such that abs(nT - 8z 0^2/9) is a minimum and then z is within z 0/(3p) steps of that value. (The last part may be the rigid mathematical rules that force a cut- > off in size of the prime p, as in that if z 0/(3p) does not allow any > steps then that prime is too large.) It's beautiful mathematics especially considering how much research > has been done in this area and how easy the derivation of æz^2 = 8^{-1] (9nT) mod p is. æI'm discussing the research as I normally do to flesh out any > areas where I might have screwed up, but it's not like there is much > room for mistakes to hide, so the effort is feeling more like a > formality. Still I am a process person so the process continues which means I'll > still be monitoring discussions for a while. James Harris- Hide quoted text - - Show quoted text - ------------------------------------------------------------------------ How do you use this when you don't know Z yet?: When you say that Z is within a certain number of steps by increments of 3p from Z 0, do you have to hit Z exactly or does it just have to be within the range? Given z^2 = y^2 + nT with z a positive integer divisible by 3 it is just a mathematical fact that z^2 = 8^{-1] (9nT) mod p when an odd prime p can be found such that the quadratic residue exists, that prime is less than 2z/3 and--the part I left off--that z is within a certain number of steps by increments of 3p from a number I call z 0, which is given by finding the largest integer divisible by 3 such that abs(nT - 8z 0^2/9) is a minimum and then z is within z 0/(3p) steps of that value. Enrico === Subject: Re: Re-cap, why factoring is done posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Assuming I have correctly understood your claim, here is a > counterexample: let N = 19*23 = 437 = 2 mod 3, so that c = 1. Then x = > (19 + 23)/2 = 21. Let p = 11, which is less than 2x/3; the inverse of > 8 mod 11 is 7. Therefore 8^{-1}*(9Nc) = 9 mod 11 and 9 = 3^2 is a quadratic residue mod 11. But x^2 = 1 mod 11. Hmmm...a false positive. ?3 & 5 work as expected. ?My assumption was > that 11 would not give a valid x in this situation, which is clearly > wrong. ?But why? See my reply to Rick in this thread, in which I point out what I > believe is a bogus step in your derivation. Long story short, you > assume the existence of an integer x which satisfies both 3x = z mod p and x^2 = y^2 mod p. The first of these equations can always be satisfied and gives a > unique value of x mod p, but that value will not satisfy the second > equation in general. As far as I have seen you have given no It's trivial algebra which is why I kept puzzling over what looked > like a counterexample until I figured it out. Human nature is to believe there is only one factorization of 19(23) > when there are two integer factorizations. justification as to why 8^{-1}*9nT will fail to be a quadratic residue > if the second equation above is not satisfied, and my counterexample > shows that it can be. Nope. ?I figured it out. ?There are TWO factorizations possible. You forgot about the trivial factorization. The equations do work perfectly. ?Just sometimes they won't give the > non-trivial factorization's residue for a particular p, but those > instances can be eliminated easily from consideration. Nope that's wrong. ?They still don't work for the trivial > factorization. ?Yuck.- Hide quoted text - - Show quoted text - -------------------------------------------------------- Didn't you run into something like this before? > It was just before you began your entries about > non-rationals and surrogate factoring, I think. Enrico Nope. I'm using a greatly simplified argument where I shifted from 2ax = k mod p to 2x = k, setting a=1, and turning that into an explicit equation. > Then I get z^2 = y^2 + nT with n chosen such that nT = 2 mod 3, means that z^2 = 8^{-1] (9nT) mod p where p is and odd prime and p < 2z/3, and posters found cases where > that wasn't sufficient to rule out primes that would not work. So you have false positive with just those rules. Does that mean factoring is not done? No, as it turns out I left off some things in my continuing urge to > simplify, so I just put them back. I think it remarkable how desperately posters reach for anything to > refute simple algebra which gives the derivation and the general > result which is applicable across any factoring system so it even > impacts the Number Field Sieve. Given z^2 = y^2 + nT with z a positive integer divisible by 3 it is just a mathematical > fact that z^2 = 8^{-1] (9nT) mod p when an odd prime p can be found such that the quadratic residue > exists, that prime is less than 2z/3 and--the part I left off--that z > is within a certain number of steps by increments of 3p from a number > I call z 0, which is given by finding the largest integer divisible by > 3 such that abs(nT - 8z 0^2/9) is a minimum and then z is within z 0/(3p) steps of that value. (The last part may be the rigid mathematical rules that force a cut- > off in size of the prime p, as in that if z 0/(3p) does not allow any > steps then that prime is too large.) It's beautiful mathematics especially considering how much research > has been done in this area and how easy the derivation of z^2 = 8^{-1] (9nT) mod p is. I'm discussing the research as I normally do to flesh out any > areas where I might have screwed up, but it's not like there is much > room for mistakes to hide, so the effort is feeling more like a > formality. Still I am a process person so the process continues which means I'll > still be monitoring discussions for a while. James Harris- Hide quoted text - - Show quoted text - ------------------------------------------------------------------------ How do you use this when you don't know Z yet?: > When you say that Z is within a certain number of steps > by increments of 3p from Z 0, do you have to hit Z exactly > or does it just have to be within the range? Given z^2 = y^2 + nT with z a positive integer divisible by 3 it is just a mathematical > fact that z^2 = 8^{-1] (9nT) mod p when an odd prime p can be found such that the quadratic residue > exists, that prime is less than 2z/3 and--the part I left off--that z > is within a certain number of steps by increments of 3p from a number > I call z 0, which is given by finding the largest integer divisible > by > 3 such that abs(nT - 8z 0^2/9) is a minimum and then z is within z 0/(3p) steps of that value. Enrico I have an elegant proof that show that z has to be within a certain range of z 0, which at the time I thought was really cool. Regardless I've backed off from this particular approach after I finally calculated that 2f 1 - f 2 = 0 mod p where f 1*f 2 = nT, so you'd have to get lucky with your guesses for the odd prime p. If you do get lucky, or just cheat and use small enough primes until you find one that works then you can get limits on the value of z as it will be within z 0/(3p) steps. James Harris === Subject: Re: Re-cap, why factoring is done > I think it remarkable how desperately posters reach for anything to > refute simple algebra which gives the derivation and the general > result which is applicable across any factoring system so it even > impacts the Number Field Sieve. > How dare them produce counter-examples to your claim? They should own up to what you really mean and prove it for you, and write the factoring programs and bring down the world-wide financial network. That would teach them. -- Michael Press === Subject: Re: Re-cap, why factoring is done posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I think it remarkable how desperately posters reach for anything to > refute simple algebra which gives the derivation and the general > result which is applicable across any factoring system so it even > impacts the Number Field Sieve. How dare them produce counter-examples to your claim? What counter examples? > They should own up to what you really mean and prove > it for you, and write the factoring programs and bring > down the world-wide financial network. That would teach > them. The proof is the easy part. An issue was made about the limit I had for primes p as it was insufficient. The derivation has not been successfully challenged. Or do you claim otherwise? I think that some of you really believe that if you talk down the research here it will make certain no one around the world bothers to check it, which is about as naive and childish a belief as there is. As I've noted, if this research is viable it does not matter what you say, if it is not, then of course, nothing will happen. Time is a harsh negative against this approach. Each day that passes without it being acknowledged is a serious indication that something must be wrong with the approach. James Harris === Subject: Re: Re-cap, why factoring is done posting-account=p_Xd1AoAAABf87DPZ9h5zXLGtOF7If8A 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > I think it remarkable how desperately posters reach for anything to > refute simple algebra which gives the derivation and the general > result which is applicable across any factoring system so it even > impacts the Number Field Sieve. How dare them produce counter-examples to your claim? What counter examples? They should own up to what you really mean and prove > it for you, and write the factoring programs and bring > down the world-wide financial network. That would teach > them. The proof is the easy part. An issue was made about the limit I had for primes p as it was > insufficient. The derivation has not been successfully challenged. Or do you claim otherwise? I think that some of you really believe that if you talk down the > research here it will make certain no one around the world bothers to > check it, which is about as naive and childish a belief as there is. As I've noted, if this research is viable it does not matter what you > say, if it is not, then of course, nothing will happen. Time is a harsh negative against this approach. Each day that passes without it being acknowledged is a serious > indication that something must be wrong with the approach. James Harris May I suggest that you learn some programming and be able to prove what you claim? I doubt if anyone will take the trouble of programming your extraordinarily vague algorithm. === Subject: Re: Re-cap, why factoring is done May I suggest that you [i.e. James Harris] learn some programming and be able to prove > what you claim? I think that Harris has worked as a computer programmer, but how he now fills his time I don't know. -- === Subject: Re: Re-cap, why factoring is done posting-account=p_Xd1AoAAABf87DPZ9h5zXLGtOF7If8A 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On Jun 8, 3:34æpm, Frederick Williams what you claim? I think that Harris has worked as a computer programmer, but how he now > fills his time I don't know. -- so who is this JSH anyway? seems he's been around for >8 years. === Subject: Re: Re-cap, why factoring is done > On Jun 8, 3:34 pm, Frederick Williams May I suggest that you [i.e. James Harris] learn some programming and be able to prove > what you claim? > I think that Harris has worked as a computer programmer, but how he now > fills his time I don't know. > -- so who is this JSH anyway? seems he's been around for >8 years. > He's been around quite a bit longer than that. He's the fellow who's found an elementary proof of Fermat's Last Theorem, a partial differential equation for the prime counting function and has shown a fundamental flaw in the algebraic integers. Some people find him amusing, some spend more time than is seemly insulting him, and I suspect most just ignore his posts or add him to their killfiles. Some few of us stick to critiques of his mathematics, being suckers for vituperation. Rick === Subject: Re: Re-cap, why factoring is done > I think it remarkable how desperately posters reach for anything to > refute simple algebra which gives the derivation and the general > result which is applicable across any factoring system so it even > impacts the Number Field Sieve. > How dare them produce counter-examples to your claim? > What counter examples? > They should own up to what you really mean and prove > it for you, and write the factoring programs and bring > down the world-wide financial network. That would teach > them. > The proof is the easy part. > An issue was made about the limit I had for primes p as it was > insufficient. > The derivation has not been successfully challenged. > Or do you claim otherwise? > I think that some of you really believe that if you talk down the > research here it will make certain no one around the world bothers to > check it, which is about as naive and childish a belief as there is. > As I've noted, if this research is viable it does not matter what you > say, if it is not, then of course, nothing will happen. > Time is a harsh negative against this approach. > Each day that passes without it being acknowledged is a serious > indication that something must be wrong with the approach. > James Harris May I suggest that you learn some programming and be able to prove >what you claim? James can program already. He has written a prime counting program in Java. He sometimes posts output from his own verision of his factoring algorithm. >I doubt if anyone will take the trouble of programming your >extraordinarily vague algorithm. He has to keep his algorithms vague, because he needs to be able to criticise any actual implementation that fails to factorise numbers quickly as not actually being his algorithm. A precise algorithm would not let him do this. rossum === Subject: 2500 Solutions manual posting-account=Tr_lEAoAAAADSBji3TkK41k7g4TuE_dn SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506; InfoPath.2; Media Center PC 5.0),gzip(gfe),gzip(gfe) My List of Solutions Manual (ALL THEY ARE FOR SALE) contact me to : mattosbw1@gmail.com mattosbw1(at)gmail.com ot to : newbergh123yahoo.com newbergh123(at)yahoo.com .... try with both emails . If your wanted solutions manual is not in this list, also can ask me if is available . These are some only. 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Ginsberg) Finite Element Analysis Theory and Application with ANSYS (2nd Ed., Moaveni) Finite Element Analysis Theory and Application with ANSYS (3rd Ed., Moaveni) The Finite Element Method in Engineering (4th Ed., Rao) The Finite Element Method and Applications in Engineering Using ANSYS (Madenci & Guven) + original Ebook Modeling and Analysis of Dynamic Systems (3rd Ed., Close) System Dynamics (1st Ed., William J Palm III) System Dynamics: Modeling and Simulation of Mechatronic Systems (4th Ed., Karnopp, Margolis & Rosenberg) Concepts and Applications of Finite Element Analysis (4th Ed., Cook, Malkus, Plesha & Witt) Finite Element Modeling for Stress Analysis (Robert Cook) Fracture Mechanics: An Introduction (2nd Ed., by E.E. Gdoutos) + original Ebook Fracture Mechanics (2nd Ed., Anderson) Mechanical Behavior of Materials (3rd Ed. Dowling) Mechanical Behavior of Materials (W.F. Hosford) + original Ebook Mechanical Behavior of Materials (Keith Bowman) Theory and Design for Mechanical Measurements (4th Ed, Figliola & Beasley) Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard) Measurement and Data Analysis for Engineering and Science (Patrick F Dunn) Design and Analysis of Lean Production Systems (Askin & Goldberg) Work Systems: The Methods, Measurement & Management of Work (Mikell P. Groover) Automation, Production Systems, and Computer-Integrated Manufacturing (2nd Ed., Groover) Automation, Production Systems, and Computer-Integrated Manufacturing (3rd Ed., Groover) Fundamentals of Modern Manufacturing: Materials, Processes, and Systems (3rd Ed., Mikell P. Groover) Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. T. Black, Ronald A. Kohser) DeGarmo's Materials and Processes in Manufacturing (10th Ed., E. Paul DeGarmo, J. T. Black, Ronald A. 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Bolton) Wind Energy Explained : Theory, Design and Application (Manwell, McGowan & Rogers) Fundamentals of Renewable Energy Processes (Aldo da Rosa) + original Ebook Renewable Energy (3rd Ed., SÀrensen or Sorensen) + original Ebook Energy Technology and Directions for the Future (Fanchi) Power Generation Technologies (Paul Breeze) + original Ebook Concepts in Engineering (Holtzapple & Reece) Foundations of Engineering (2nd Ed, Holtzapple & Dan Reece) Industrial Mechanics and Maintenance (3rd Ed., Larry Chastain) Mechanical & Electrical Systems in Buildings (4th Ed., Richard Janis & William Tao) Autodesk Inventor (James M. Leake) Energy and the Environment (2nd Ed, Robert A. Ristinen & Jack P. Kraushaar) Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems (Donald L. Bartel, Dwight T. Davy & Tony M. Keaveny) Science for Engineering (3rd Ed., John Bird) - Electrical, Electronics & Computer Engineering Design for Electrical and Computer Engineers (J. 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Jaeger) Fundamentals of Digital Logic with VHDL Design (1st Ed., Stephen Brown & Zvonko Vranesic) Fundamentals of Digital Logic with VHDL Design (2nd Ed., Stephen Brown & Zvonko Vranesic) Design of Analog CMOS Integrated Circuits (Behzad Razavi) Design of Integrated Circuits for Optical Communications (Behzad Razavi) Fundamentals of Microelectronics, Preliminary Edition (Behzad Razavi) Fundamentals of Microelectronics (1st Ed., Behzad Razavi) Design with Operational Amplifiers and Analog Integrated Circuits (3rd Ed., Sergio Franco) Microwave Engineering (Annapurna Das) Control Systems (Madan Gopal) Mechanical & Electrical Systems in Buildings (4th Ed., Richard Janis & William Tao) Silicon VLSI Technology: Fundamentals, Practice, and Modeling (Plummer, Deal & Griffin) Engineering Electromagnetics (Kenneth Demarest) Field and Wave Electromagnetics (2nd Ed., David Cheng) Probability, Statistics, and Random Processes For Electrical Engineering (3rd Ed., Alberto Leon-Garcia) Detection and Estimation Theory (Thomas Schonhoff & Arthur Giordano) The Intel Microprocessors (8th Ed., Barry B. Brey) Digital Signal Processing System Design: LabVIEW-Based Hybrid Programming (2nd Ed., Kehtarnavaz) Wireless Networking (Kumar, Manjunath & Kuri) Digital Electronics and Design with VHDL (Volnei A. Pedroni) System-on-Chip Test Architectures: Nanometer Design for Testability (Wang, Stroud & Touba) Digital Design (Verilog): An Embedded Systems Approach Using Verilog (Peter Ashenden) Digital Design (VHDL): An Embedded Systems Approach Using VHDL (Peter Ashenden) Computer Organization and Design: The Hardware/Software Interface (3rd Ed., Patterson & Hennessy) Wireless Communications & Networking (Vijay Garg) Network Analysis, Architecture, and Design (3rd Ed., James McCabe) Computer Networks: A Systems Approach (4th Ed., Peterson & Davie) Computer Networks ISE: A Systems Approach (4th Ed., Peterson & Davie) Digital Design and Computer Architecture (David Harris & Sarah Harris) Fault-Tolerant Systems (Israel Koren & C. Krishna) Computer Architecture: A Quantitative Approach (4th Ed., Hennessy & Patterson) High-Performance Embedded Computing: Architectures, Applications, and Methodologies (Wayne Wolf) Pattern Recognition (3rd Ed., Theodoridis & Koutroumbas) Data Mining: Concepts and Techniques (2nd Ed., Han & Kamber) Commonsense Reasoning (Erik Mueller) Introduction to Data Compression (3rd Ed., Khalid Sayood) Programming Language Pragmatics (2nd Ed., Michael Scott) Database Modeling and Design: Logical Design (4th Ed., Teorey, Lightstone & Nadeau) Computers As Components: Principles of Embedded Computing System Design (Wayne Wolf) Virtual Machines: Versatile Platforms for Systems and Processes (Jim Smith & Ravi Nair) Comprehensive Functional Verification: The Complete Industry Cycle (Wile, Goss & Roesner) User Interface Design and Evaluation (Stone, Jarrett, Woodroffe & Minocha) Network Algorithmics: An Interdisciplinary Approach to Designing Fast Networked Devices (George Varghese) Data Modeling Essentials (3rd Ed., Simsion & Witt) A Student Guide to Object-Oriented Development (Carol Britton & Jill Doake) Routing, Flow, and Capacity Design in Communication and Computer Networks (Pioro & Medhi) Knowledge Representation and Reasoning (Brachman & Levesque) Communication Networking: An Analytical Approach (Kumar, D. Manjunath & Joy Kuri) Principles and Practices of Interconnection Networks (Dally & Towles) Game Physics (David Eberly) Engineering a Compiler (Keith Cooper & Linda Torczon) Constraint Processing (Rina Dechter) Design Methods for Reactive Systems: Yourdon, Statemate, and the UML (R. J. Wieringa) Mining the Web: Discovering Knowledge from Hypertext Data (Soumen Chakrabarti) Essential Java for Scientists and Engineers (B. Hahn & K. Malan) Java Made Simple (2nd Ed., McBride) Optical Networks: A Practical Perspective (2nd Ed., Ramaswami & Sivarajan) Usability Engineering: Scenario-Based Development of Human-Computer Interaction (Rosson & Carroll) The Designer's Guide to VHDL (2nd Ed., Peter Ashenden) Transactional Information Systems: Theory, Algorithms, and the Practice of Concurrency Control and Recovery (Weikum & Vossen) Parallel Computer Architecture: A Hardware/Software Approach (Culler, Singh & Gupta) Advanced Compiler Design and Implementation (Steven Muchnick) Parallel Programming with MPI (Peter Pacheco) Distributed Algorithms (Nancy Lynch) Digital Signal Processing: Fundamentals and Applications (Li Tan) Electrical and Electronic Principles and Technology (3rd Ed., John Bird) Electrical Circuit Theory and Technology (3rd Ed., John Bird) Electronic Circuits: Fundamentals & Applications (3rd Ed., Mike Tooley) Multidimensional Signal, Image, and Video Processing and Coding (John Woods) Bioelectrical Signal Processing in Cardiac and Neurological Applications (Leif S.9arnmo & Pablo Laguna) Foundations of Analog and Digital Electronic Circuits (Anant Agarwal & Jeffrey Lang) (Luis Moura & Izzat Darwazeh) Embedded Systems Architecture: A Comprehensive Guide for Engineers and Programmers (Tammy Noergaard) Bioimpedance and Bioelectricity Basics (2nd Ed., Grimnes & Martinsen) Simulation Modeling and Analysis with ARENA (Tayfur Altiok & Benjamin Melamed) The Visual Story: Creating the Visual Structure of Film, TV and Digital Media (2nd Ed., Bruce Block) The Shut Up and Shoot Documentary Guide: A Down & Dirty DV Production (Anthony Artis) Portable Video: ENG & EFP (5th Ed., Medoff & Fink) Voice and Vision: A Creative Approach to Narrative Film and DV Production (Mick Hurbis-Cherrier) Writing for Multimedia and the Web: A Practical Guide to Content Development for Interactive Media (3rd Ed., Timothy Garrand) Developing and Maintaining a Design-Tech Portfolio: A Guide for Theatre, Film & TV (Rafael Jaen) Producing for TV and Video: A Real-World Approach (Cathrine Kellison) Placing Shadows: Lighting Techniques for Video Production (3rd Ed., Gloman & Tom LeTourneau) Film Directing Fundamentals: See Your Film Before Shooting (2nd Ed., Nicholas Proferes) Introduction to Media Production: The Path to Digital Media Production (3rd Ed., Musburger & Kindem) Directing the Documentary (4th Ed., Michael Rabiger) Breslin) Prepare to Board! 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Jackson) Mastering the Internet, XHTML and JavaScript (2nd Ed., Ibrahim Zeid) Weaving a Website: Programming in HTML, Java Script, Perl and Java (Susan Anderson-Freed) Simply C++: An Application-Driven Tutorial Approach (Harvey & Paul Deitel) Visual C# 2005 How to Program (2nd Ed., Harvey & Paul Deitel) Simply C#: An Application-Driven Tutorial Approach (Harvey & Paul Deitel, Hoey & Yaeger) Java: Introduction to Problem Solving and Programming (5th Ed., Savitch & Carrano) Introduction to Computing and Programming with Java: A Multimedia Approach (Guzdial & Ericson) Java How to Program (7th Ed., Harvey & Paul Deitel) Java For Students (5th Ed., Bell & Parr) Java, Java, Java, Object-Oriented Problem Solving (3rd Ed., Morelli & Walde) Java: An Eventful Approach (Bruce, Danyluk & Murtagh) Introduction to Java Programming with JBuilder (3rd Ed., Y. Daniel Liang) Starting Out with Visual Basic 2008 (4th Ed., Gaddis & Irvine) Starting Out with Python (Tony Gaddis) Object-Oriented Programming in Python (Goldwasser & Letscher) Introduction to MathCAD 11 (Ronald W. Larsen) Introduction to MathCAD 13 (2nd Ed., Ronald W. Larsen) MatLAB Programming (David Kuncicky) Introduction to Maple 8 (David Schwartz) Introduction to FORTRAN 90 (2nd Ed., Larry R. Nyhoff & Sanford Leestma) Introduction to Java (Stephen J. Chapman) Java Software Solutions for AP Computer Science A (2nd Ed., Lewis, Loftus & Cocking) Business Data Networks and Telecommunications (6th Ed., Raymond R. Panko) Business Data Networks and Telecommunications (7th Ed., Raymond R. Panko) Business Data Communications (Allen Dooley) Object-Oriented Programming in C++ (4th Ed., Robert Lafore) C++: Classes and Data Structures (Jeffrey Childs) Data Structures Outside-In with Java (Sesh Venugopal) Data Structures and Abstractions with Java (2nd Ed., Frank M. 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Tanenbaum) Assembly Language for Intel-Based Computers (5th Ed., Kip Irvine) Fundamentals of Multimedia (Ze-Nian Li & Mark Drew) Digital Media Primer (Yue-Ling Wong) Gray) Modern Database Management (8th Ed., Hoffer, Prescott & Topi) Modern Database Management (9th Ed., Hoffer, Prescott & Topi) Database Systems Using Oracle (2nd Ed., Nilesh Shah) An Advanced Course in Database Systems: Beyond Relational Databases (Dietrich & Urban) Data and Text Mining: A Business Applications Approach (Thomas Miller) Network Management: Concepts and Practice, A Hands-On Approach (J. Richard Burke) Computer and Communication Networks (Nader F. Mir) High Performance TCP/IP Networking (Mahbub Hassan & Raj Jain) Computer Security : Principles and Practice (William Stallings & Lawrie Brown) Computer Forensics: Principles and Practices (Volonino, Anzaldua & Godwin) Disaster Recovery: Principles and Practices (April Wells, Charlyne Walker & Timothy Walker) Firewalls and VPNs: Principles and Practices (Richard Tibbs & Edward Oakes) Network Defense and Countermeasures: Principles and Practices (Chuck Easttom) Corporate Computer and Network Security (Raymond Panko) IP Telephony Using CallManager Express Lab Portfolio (Cheryl Schmidt & Ernie Friend) High-Speed Networks and Internets: Performance and Quality of Service (2nd Ed., William Stallings) Object-Oriented Modeling and Design with UML (2nd Ed., Michael Blaha & James Rumbaugh) Operating Systems: Internals and Design Principles (5th Ed., William Stallings) Operating Systems: Internals and Design Principles (6th Ed., William Stallings) Distributed Systems: Principles and Paradigms (2nd Ed., Tanenbaum & Van Steen) Modern Operating Systems (3rd Ed., Andrew Tanenbaum) Operating Systems Design and Implementation (3rd Ed., Andrew Tanenbaum & Albert Woodhull) UNIX Unbounded: A Beginning Approach (5th Ed., Amir Afzal) Introduction to Operating Systems and Networks (Ruth Watson) Operating Systems (3rd Ed., Harvey Deitel, Paul Deitel & David Choffnes) Operating Systems Principles (Lubomir Bic & Alan Shaw) A Practical Guide to Linux: Commands, Editors, and Shell Programming (Mark Sobell) A Practical Guide to Red Hat Linux: Fedora Core and Red Hat Enterprise Linux (2nd Ed., Mark Sobell) A Practical Guide to Red Hat Linux: Fedora Core and Red Hat Enterprise Linux (3rd Ed., Mark Sobell) A Practical Guide to Fedora and Red Hat Enterprise Linux: College Edition (Mark Sobell) A Practical Guide to Ubuntu Linux (Mark Sobell) Automata, Computability and Complexity: Theory and Applications (Elaine Rich) Modern Digital Electronics (R.P. Jain) Introduction to Digital Systems (Milo D. Ercegovac, Lang & Moreno) Embedded Systems: Architechture, Programming and Design (Raj Kamal) Modern Power System Analysis (D. P. Kothari & I. J. Nagrath) Circuits and Networks (A. Sudhakar & S. Palli Shyammohan) Communication Systems (4th. Ed., A. Bruce Carlson et al.) Modern Processor Design: Fundamentals of Superscalar Processors (John P. Shen) Computer Networks : Principles, Technologies and Protocols for Network Design (N. Olifer & V. Olifer) Computer Networking: Internet Protocols in Action (Jeanna Matthews) Computer Organization (5th Ed., Hamacher et al.) CMOS Digital Integrated Circuits: Analysis and Design (3rd Ed., Sung- Mo Kang & Yusuf Leblebici) Introduction to Logic Design (2nd Ed., Alan B Marcovitz) Introduction to Logic and Computer Design (Alan B Marcovitz) Digital Principles and Design (Donald D. Givone) Programmable Logic Controllers (3rd Ed., Frank Petruzella) Digital Signal Processing : Signals, Systems, and Filters (Andreas Antoniou) Digital Signal Processing (Charles Schuler & Mahesh Chugani) Antenna Theory and Design (2nd Ed., Stutzman & Thiele) Antennas for All Applications (3rd Ed., John Kraus & Ronald Marhefka) Principles of Neurocomputing for Science and Engineering (Fredric M. Ham & Ivica Kostanic) Introduction to Algorithms and Java (2nd Ed., Cormen, et al.) Algorithms (Dasgupta, et al.) Applied Operating Systems Concepts (Silberschatz, Galvin & Gagne) Operating System Concepts (7th Ed., Silberschatz, Galvin & Gagne) Operating System Concepts with Java (7th Ed., Silberschatz, Galvin & Gagne) Operating System Concepts (6th Ed., Silberschatz, Galvin & Gagne) Operating Systems Concepts with Java (6th Ed., Silberschatz, Galvin & Gagne) C++ Program Design (3rd Ed., Cohoon & Davidson) Java: Program Design 5.0 (Cohoon & Davidson) Programming in C++: Lessons and Applications (Timothy B. D'Orazio) Applied C: An Introduction and More (Alice Fischer) Programming Languages: Principles and Paradigms (2nd Ed., Allen Tucker & Robert Noonan) Parallel Programming in C with MPI and Open MP (Michael J Quinn) Data Communications and Network Security (Houston H. Carr & Charles Snyder) Data Communications and Networks (David Miller) Database Design, Application, Development & Administration (2nd Ed., Michael V. Mannino) Database Design, Application, Development & Administration (3rd Ed., Michael V. Mannino) Management Information Systems (3rd Ed., Post & Anderson) Management Information Systems (4th Ed., Post & Anderson) Database Management Systems (3rd Ed. Post) Systems Analysis and Design Methods (6th Ed., Whitten et.al) Systems Analysis and Design Methods (7th Ed., Whitten et.al) Introduction to Systems Analysis and Design (Whitten & Bentley) Systems Analysis & Design: An Active Approach (2nd Ed., Marakas) An Introduction to Object-Oriented Programming with Java (4th Ed., C. Thomas Wu - Otani) A Comprehensive Introduction to Object-Oriented Programming With Java (C. Thomas Wu) Data Structures and the Java Collections Framework (1st Ed., William J. Collins) Data Structures and the Java Collections Framework (2nd Ed., William J. Collins) Data Structures and the Standard Template Library (William J. Collins) Database System Concepts (4th Ed. Silberschatz) Database System Concepts (5th Ed. Silberschatz) Database Management Systems (3rd Ed., Ramakrishnan & Gehrke) Fundamentals of Network Security (Eric Maiwald) Computing Concepts (1st Ed., Haag, et al.) Computing Concepts (2nd Ed., Haag et al.) Advanced Programming Using Visual Basic .NET (2nd Ed., Julia Case Bradley & Anita C. Millspaugh) Advanced Programming Using Visual Basic 2005 (3rd Ed., Julia Case Bradley & Anita C. Millspaugh) Programming with Java (Julia Case Bradley & Anita C. Millspaugh) Programming in C#.Net (1st Ed., Julia Case Bradley & Anita C. Millspaugh) Programming in Visual C# 2005 (2nd Ed., Julia Case Bradley & Anita C. Millspaugh) Learning Programming Using Visual Basic.Net (Bill Burrows & Joe Lanford) Programming in Visual Basic.NET: Visual Basic.NET 2005 (6th Ed., Julia Case Bradley & Anita C. Millspaugh) Case Bradley & Anita C. Millspaugh) Survey of Operating Systems (2nd Ed., Jane Holcombe & Charles Holcombe) Principles of Voice and Data Communications (Regis J. Bates & Marcus Bates) Mike Meyers' Network+ Guide To Managing and Troubleshooting Networks (Michael Meyers) Programming The Web: An Introduction (Barrie Sosinsky & Valda Hilley) Programming The Web Using XML (Ellen Pearlman & Eileen Mullin) Internet Marketing: Building Advantage in a Networked Economy (2nd Ed., Rafi Mohammed et al.) Internet Technologies at Work (Fred T. Hofstetter) Internet Literacy (4th Ed., Fred T. Hofstetter) Software Engineering: A Practitioner's Approach (5th Ed., Roger S. Pressman) Software Engineering: A Practitioner's Approach (6th Ed., Roger S. 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Bhadeshia & Honeycombe) Theory of Plasticity (3rd Ed. Jagabanduhu Chakrabarty) Engineering Materials Vol. 1 : An Introduction to Properties, Applications and Design (3rd Ed., Michael Ashby & David R H Jones) Engineering Materials Vol. 2 : An Introduction to Microstructures, Processing and Design (3rd Ed., Michael Ashby & David R H Jones) Plastics: Microstructure and Engineering Applications (3rd Ed., Nigel Mills) Laser Processing of Engineering Materials : Principles, Procedure and Industrial Application (John Ion) Sintering : Densification, Grain Growth and Microstructure (Suk-Joong Kang) Biomaterials Science : An Introduction to Materials in Medicine (2nd Ed., Buddy D. Ratner, Allan Hoffman, Frederick Schoen & Jack Lemons) Fundamentals of Solid State Engineering (2nd Ed., Manijeh Razeghi) Smart Electronic Materials: Fundamentals and Applications (Jasprit Singh) Laminar Composites (by George Staab) + original Ebook Physical Metallurgy and Advanced Materials (7th Ed., R E Smallman & A.H.W. Ngan) contact me to : newbergh123@yahoo.com or mattosbw1@gmail.com === Subject: Re: But how easy? Fundamental factoring congruence James Harris === Subject: JSH: Newest factoring algorithm posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) After my latest miss-steps I went back, looked everything over again and finally noticed something that was bizarrely, simply obvious and staring me in the face. Here's the factoring algorithm that results. Given an odd target composite T, for a test odd prime p, iterate through non-zero integers k until T - k^2 mod p is a quadratic residue. If no k will work, discard that prime p and try another. If one does work then get .87 from .87^2 = (T - k^2)(k^2)^{-1} mod p. Then you have residues of your factors modulo p from f 1 = .87k mod p and f 2 = .87^{-1}(1 + .87^2)k mod p where f 1*f 2 = T. Trivial factorizations if they are given can be discarded by noting that your residues is the same as T, though one caveat is that for a given prime p, one of your factors may equal the residue of the target composite T. Also if with r^2 = T - k^2 mod p, r^2 = k^2, then that result should be discarded, though it may indicate that one of your factors equals the residue of T for that particular prime. The sign of the correct k and .87 that work seems to correlate with the sign of the factors as long as neither factor is less than p. The simplification occurred to me after noticing a few obvious things. It should work well though I guess maybe I'm still missing something so out it goes to see if someone will test it. If it does work well then factoring a target composite T is just about getting enough primes that will work. For example, if 80 primes are found then a target at least as large as 80! would topple even if you took primes starting at 3 and working your way up, so assuming about 50% would work then using only primes under 1000, you could factor a number greater than 7.1569457046263802294811533723187e+118. James Harris === Subject: Re: JSH: Newest factoring algorithm posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-ntc-ta08.proxy.aol.com[CFC87008] (Prism/1.2.1), HTTP/1.1 cache-ntc-ac09.proxy.aol.com[CFC8748A] (Traffic-Server/6.1.5 [uScM]) > After my latest miss-steps I went back, looked everything over again > and finally noticed something that was bizarrely, simply obvious and > staring me in the face. Here's the factoring algorithm that results. Given an odd target composite T, for a test odd prime p, iterate > through non-zero integers k until T - k^2 mod p is a quadratic residue. If no k will work, discard that prime p and > try another. ?If one does work then get ? from ?2 = (T - k^2)(k^2)^{-1} mod p. Then you have residues of your factors modulo p from f 1 = ?k mod p and f 2 = ?^{-1}(1 + ?2)k mod p where f 1*f 2 = T. Trivial factorizations if they are given can be discarded by noting > that your residues is the same as T, though one caveat is that for a > given prime p, one of your factors may equal the residue of the target > composite T. Also if with r^2 = T - k^2 mod p, r^2 = k^2, then that result should > be discarded, though it may indicate that one of your factors equals > the residue of T for that particular prime. The sign of the correct k and ? that work seems to correlate with the > sign of the factors as long as neither factor is less than p. The simplification occurred to me after noticing a few obvious > things. ?It should work well though I guess maybe I'm still missing > something so out it goes to see if someone will test it. If it does work well then factoring a target composite T is just about > getting enough primes that will work. For example, if 80 primes are found then a target at least as large as > 80! would topple even if you took primes starting at 3 and working > your way up, so assuming about 50% would work then using only primes > under 1000, you could factor a number greater than > 7.1569457046263802294811533723187e+118. James Harris -------------------------------------------------- No good. Too many k's will work for each prime. Too many false positives will result from this. Enrico === Subject: Re: JSH: Newest factoring algorithm >After my latest miss-steps I went back, looked everything over again >and finally noticed something that was bizarrely, simply obvious and >staring me in the face. Here's the factoring algorithm that results. Given an odd target composite T, for a test odd prime p, There are an infinite number of odd primes p. What limits would you suggest for the search: 3 <= p <= ???. Searching an infinite number of primes can take an infinite amount of time. > iterate through non-zero integers k until T - k^2 mod p is a quadratic residue. If no k will work, discard that prime p and >try another. There are an infinite number of non-zero integers k. What are the positive, but what is your upper limit for k: 1 <= k <= ???. With no upper limit then the search for a k that works can take an infinite time. > If one does work then get .87 from .87^2 = (T - k^2)(k^2)^{-1} mod p. Then you have residues of your factors modulo p from f_1 = .87k mod p and f_2 = .87^{-1}(1 + .87^2)k mod p where f_1*f_2 = T. Trivial factorizations if they are given can be discarded by noting >that your residues is the same as T, though one caveat is that for a >given prime p, one of your factors may equal the residue of the target >composite T. Also if with r^2 = T - k^2 mod p, r^2 = k^2, then that result should >be discarded, though it may indicate that one of your factors equals >the residue of T for that particular prime. The sign of the correct k and .87 that work seems to correlate with the >sign of the factors as long as neither factor is less than p. You say seem to correlate. Please do more work here so you can say for certain either does correlate or does not correlate. The simplification occurred to me after noticing a few obvious >things. It should work well though I guess maybe I'm still missing >something so out it goes to see if someone will test it. You say It should work well. To me that indicates that you have not yet tested this iteration of you method. Test it on 15, 81, 121, 437 and 2261 to see how well it works. If it does work well then factoring a target composite T is just about >getting enough primes that will work. And if it does not work then we are all back to square one. You need to test your methods James, that way you will not have to retract what you say quite so often. All you previous claims to have solved the factoring problem have been incorrect. For example, if 80 primes are found then a target at least as large as >80! would topple even if you took primes starting at 3 and working >your way up, so assuming about 50% would work then using only primes >under 1000, you could factor a number greater than >7.1569457046263802294811533723187e+118. Start by factoring some smaller numbers for us, and show us worked examples. rossum >James Harris === Subject: Re: JSH: Newest factoring algorithm posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) >After my latest miss-steps I went back, looked everything over again >and finally noticed something that was bizarrely, simply obvious and >staring me in the face. Here's the factoring algorithm that results. Given an odd target composite T, for a test odd prime p, There are an infinite number of odd primes p. What limits would you > suggest for the search: 3 <= p <= ???. Searching an infinite number > of primes can take an infinite amount of time. You start with p=3 and work up from there until the product of your primes that work is greater than the square root of the target. > iterate through non-zero integers k until T - k^2 mod p is a quadratic residue. If no k will work, discard that prime p and >try another. There are an infinite number of non-zero integers k. What are the There are a finite number of residues modulo p. It'd be stupid to iterate through anything but residues, so I thought that was just obvious enough without me having to state it. So in more detail, yes, you iterate through p-1 residues for k, checking T - k^2 mod p for each to see if it is a quadratic residue, and if it is, then you have alpha from ¬¢^2 = (T - k^2)(k^2)^{-1} mod p. I've thought about this some more and it occurs to me that one thing that might happen as you use more and more primes is that you get a LOT of possible values for alpha by that method, but weirdly enough, my use of p as an odd prime is just because, well, it just seemed appropriate as you can use N, a composite. So if you get a lot of possible for a particular prime p 1, you can get another prime p 2 and get possible and then find k such that T - k^2 mod p 1*p 2 is a quadratic residue modulo p 1*p 2, and then find alpha from ¬¢^2 = (T - k^2)(k^2)^{-1} mod p 1*p 2 and find the factors from f 1 = .a6'k mod p 1*p 2 and f 2 = .a6'^{-1}(1 + .a6'^2)k mod p 1*p 2. Though I do want to go back over my derivation of those to be sure. Oh, I have them on my math blog under Factors mod N so I must have done the math before as that's dated January 27, 2008. Oh, so now you should have fewer possibles and can just correlate back to your first sets and just keep doing this prime by prime. Oddly enough, if this technique holds, you will probably be able to factor any RSA encryption type number with primes under 2000. That is, for primes that are no bigger than 2000. Definitely no bigger than 5000, which would be needed for an unimaginably HUGE number greater than 320!, so mega size. So checking residues is the least of the effort. Just figured this out yesterday so I'm looking to see if it holds or if anyone can shoot holes in it. James Harris === Subject: Re: JSH: Newest factoring algorithm posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-ntc-ta08.proxy.aol.com[CFC87008] (Prism/1.2.1), HTTP/1.1 cache-ntc-ac09.proxy.aol.com[CFC8748A] (Traffic-Server/6.1.5 [uScM]) After my latest miss-steps I went back, looked everything over again >and finally noticed something that was bizarrely, simply obvious and >staring me in the face. Here's the factoring algorithm that results. Given an odd target composite T, for a test odd prime p, There are an infinite number of odd primes p. What limits would you > suggest for the search: 3 <= p <= ???. Searching an infinite number > of primes can take an infinite amount of time. You start with p=3 and work up from there until the product of your > primes that work is greater than the square root of the target. iterate through non-zero integers k until T - k^2 mod p is a quadratic residue. If no k will work, discard that prime p and >try another. There are an infinite number of non-zero integers k. What are the There are a finite number of residues modulo p. It'd be stupid to iterate through anything but residues, so I thought > that was just obvious enough without me having to state it. So in more detail, yes, you iterate through p-1 residues for k, > checking T - k^2 mod p for each to see if it is a quadratic residue, and if it is, then you > have alpha from ¬¢^2 = (T - k^2)(k^2)^{-1} mod p. I've thought about this some more and it occurs to me that one thing > that might happen as you use more and more primes is that you get a > LOT of possible values for alpha by that method, but weirdly enough, > my use of p as an odd prime is just because, well, it just seemed > appropriate as you can use N, a composite. So if you get a lot of possible for a particular prime p 1, you can > get another prime p 2 and get possible and then find k such that T - k^2 mod p 1*p 2 is a quadratic residue modulo p 1*p 2, and then find alpha from ¬¢^2 = (T - k^2)(k^2)^{-1} mod p 1*p 2 and find the factors from f 1 = .a6'k mod p 1*p 2 and f 2 = .a6'^{-1}(1 + .a6'^2)k mod p 1*p 2. Though I do want to go back over my derivation of those to be sure. > Oh, I have them on my math blog under Factors mod N so I must have > done the math before as that's dated January 27, 2008. Oh, so now you should have fewer possibles and can just correlate back > to your first sets and just keep doing this prime by prime. Oddly enough, if this technique holds, you will probably be able to > factor any RSA encryption type number with primes under 2000. That > is, for primes that are no bigger than 2000. Definitely no bigger > than 5000, which would be needed for an unimaginably HUGE number > greater than 320!, so mega size. So checking residues is the least of the effort. Just figured this out yesterday so I'm looking to see if it holds or > if anyone can shoot holes in it. James Harris ------------------------------------------------------- Nice try. The number of possibles for each prime multiply together when the modulus is the product of those primes. For certain values of T mod p, the number of possibles can be reduced by using a modulus of p^i. Enrico === Subject: Re: JSH: Newest factoring algorithm After my latest miss-steps I went back, looked everything over again >and finally noticed something that was bizarrely, simply obvious and >staring me in the face. Here's the factoring algorithm that results. Given an odd target composite T, for a test odd prime p, There are an infinite number of odd primes p. What limits would you > suggest for the search: 3 <= p <= ???. Searching an infinite number > of primes can take an infinite amount of time. You start with p=3 and work up from there until the product of your > primes that work is greater than the square root of the target. iterate through non-zero integers k until T - k^2 mod p is a quadratic residue. If no k will work, discard that prime p and >try another. There are an infinite number of non-zero integers k. What are the There are a finite number of residues modulo p. It'd be stupid to iterate through anything but residues, so I thought > that was just obvious enough without me having to state it. So in more detail, yes, you iterate through p-1 residues for k, > checking T - k^2 mod p for each to see if it is a quadratic residue, and if it is, then you > have alpha from ¢^2 = (T - k^2)(k^2)^{-1} mod p. I've thought about this some more and it occurs to me that one thing > that might happen as you use more and more primes is that you get a > LOT of possible values for alpha by that method, but weirdly enough, > my use of p as an odd prime is just because, well, it just seemed > appropriate as you can use N, a composite. So if you get a lot of possible for a particular prime p_1, you can > get another prime p_2 and get possible and then find k such that T - k^2 mod p_1*p_2 is a quadratic residue modulo p_1*p_2, and then find alpha from ¢^2 = (T - k^2)(k^2)^{-1} mod p_1*p_2 and find the factors from f_1 = ì.8dk mod p_1*p_2 and f_2 = ì.8d^{-1}(1 + ì.8d^2)k mod p_1*p_2. Though I do want to go back over my derivation of those to be sure. > Oh, I have them on my math blog under Factors mod N so I must have > done the math before as that's dated January 27, 2008. Oh, so now you should have fewer possibles and can just correlate back > to your first sets and just keep doing this prime by prime. Oddly enough, if this technique holds, you will probably be able to > factor any RSA encryption type number with primes under 2000. That > is, for primes that are no bigger than 2000. Definitely no bigger > than 5000, which would be needed for an unimaginably HUGE number > greater than 320!, so mega size. So checking residues is the least of the effort. Just figured this out yesterday so I'm looking to see if it holds or > if anyone can shoot holes in it. James Harris ------------------------------------------------------- Nice try. The number of possibles for each prime multiply together when the modulus is the product of those primes. For certain values of T mod p, the number of possibles can be reduced by using a modulus of p^i. Enrico ******************************* obvious, and trivial. === Subject: Re: JSH: Newest factoring algorithm > After my latest miss-steps I went back, looked everything over again > and finally noticed something that was bizarrely, simply obvious and > staring me in the face. Interesting concept of what's bizarre. === Subject: Re: JSH: Newest factoring algorithm > For example, if 80 primes are found then a target at least as large as > 80! would topple even if you took primes starting at 3 and working your > way up, so assuming about 50% would work then using only primes under > 1000, you could factor a number greater than > 7.1569457046263802294811533723187e+118. OK, for the nth time, factorize 5E7153F9EA8C67E08660CE08001D42715D6008A1718CDAD2F67D79844FD0013ACBDD05 081A1A26AF8AD662EFF37E47FB1FB33D8F7E66207FEEB439B2665EBD87745DC4BF4332 038A55E5F3C110E2CA6CB96689C2EF15C40C40AE6D2F3128B2423A11BFAB030F8D1386 9BF4B4AB367D26DDB90A47FC0ECCEB2BA7D0C6EC21B7A7 I bet your pathetic method can't tackle this before the end of the universe. Come on, you nitwit, prove me wrong. === Subject: Re: JSH: Newest factoring algorithm > > For example, if 80 primes are found then a target at least as large as > 80! would topple even if you took primes starting at 3 and working your > way up, so assuming about 50% would work then using only primes under > 1000, you could factor a number greater than > 7.1569457046263802294811533723187e+118. OK, for the nth time, factorize 5E7153F9EA8C67E08660CE08001D42715D6008A1718CDAD2F67D79844FD0013ACBDD05 > 081A1A26AF8AD662EFF37E47FB1FB33D8F7E66207FEEB439B2665EBD87745DC4BF4332 > 038A55E5F3C110E2CA6CB96689C2EF15C40C40AE6D2F3128B2423A11BFAB030F8D1386 > 9BF4B4AB367D26DDB90A47FC0ECCEB2BA7D0C6EC21B7A7 I bet your pathetic method can't tackle this before the end of > the universe. Come on, you nitwit, prove me wrong. > Maybe he can solve it in almost-infinite time. === Subject: solution manual for heating ventilating and air conditioning 6th posting-account=5_aWUwoAAAAywtwHlnjic0X4KATz2jr1 CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) hi there I'm looking for the solution manual for heating ventilating and air conditioning 6th edition but I don't know how to contact you. plz send me an email at xxabodexx(at)hotmail.com === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > As already noted, this was before the development of formal systems as > a study. And before the invention of aeroplanes. What have these things to do > with mathematics??? Answer A) Should you continue to lose good manners I will cease this discussion with you. I am not willing to talk to uncivilized individuals. Answer B) The entire topic of this conversation is the consistency of > a formal system. No, the entire topic of this discussion is the question whether there are infinitely many natural numbers and uncountably many reals. What you understand by a formal system is not of interest for me. > If you bring in someone's opinions who was much later > in life a theorist about formal systems, but at the time of the > quotation had no inkling of formal systems, why would we bother with > that person's opinions? Cantor was never in his life a theorist about formal systems. The questuion for him as for me is simply whether there are infinite sets or not. No reason for any objections as long as those games do not interfere > with mathematics. But if a little group of gamblers gets to the > conclusion that numbers must cease to exist as individuals in order to > comply with their (the gamblers') silly ideas, then a limit is > crossed, then they go beyond what is permissible. Oh, we all say that the numbers exist as individuals. However, we > can't name them all. You can't name them, you don't know where these numbers exist, you know nothing about these questions. With respect to that question, you are on the same intellectual level as superstitious savages. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 CLR 1.1.4322; InfoPath.1),gzip(gfe),gzip(gfe) > Should you continue to lose good manners I will cease this discussion > with you. I am not willing to talk to uncivilized individuals. Bah, you continue to talk to lots of people who insult you. > Cantor was never in his life a theorist about formal systems. The > questuion for him as for me is simply whether there are infinite sets > or not. No, idiot, the matter relelevent to formal systems that YOU mentioned was as Cantor's view of axiomatization. MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=ZsXvqAoAAABmATPp--wbAhLaSprxKuin CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) As already noted, this was before the development of formal systems as > a study. And before the invention of aeroplanes. What have these things to do > with mathematics??? Answer A) Should you continue to lose good manners I will cease this discussion > with you. I am not willing to talk to uncivilized individuals. Ego numquam dico mendacia. Sed ego sum homo indomitus. Answer B) The entire topic of this conversation is the consistency of > a formal system. No, the entire topic of this discussion is the question whether there > are infinitely many natural numbers and uncountably many reals. What > you understand by a formal system is not of interest for me. > Are we both in agreement that numbers are not physical objects? Are we in further agreement that numbers and other mathematical ideas have no physical existence? It is then a little pointless to get into a yes they do! no they don't! shouting match when our notions of existence not only do not coincide, but are incompatible. > If you bring in someone's opinions who was much later > in life a theorist about formal systems, but at the time of the > quotation had no inkling of formal systems, why would we bother with > that person's opinions? Cantor was never in his life a theorist about formal systems. The > questuion for him as for me is simply whether there are infinite sets > or not. No reason for any objections as long as those games do not interfere > with mathematics. But if a little group of gamblers gets to the > conclusion that numbers must cease to exist as individuals in order to > comply with their (the gamblers') silly ideas, then a limit is > crossed, then they go beyond what is permissible. Oh, we all say that the numbers exist as individuals. However, we > can't name them all. You can't name them, you don't know where these numbers exist, you > know nothing about these questions. With respect to that question, you > are on the same intellectual level as superstitious savages. > Your objections are malformed. There is no where where these numbers could exist. However, the statement that these numbers exist is exactly as well-founded as the statement 0 exists or the set of natural numbers exists -- i.e. the same collection of axioms implies all three statements. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) Ego numquam dico mendacia. mendacium Sed ego sum homo indomitus. Answer B) The entire topic of this conversation is the consistency of > a formal system. No, the entire topic of this discussion is the question whether there > are infinitely many natural numbers and uncountably many reals. What > you understand by a formal system is not of interest for me. Are we both in agreement that numbers are not physical objects? Are we both in agreement that there are no non-physical objects in the universe? Are we in further agreement that numbers and other mathematical ideas > have no physical existence? Entities without physical existence belong to the domain of theology. It is then a little pointless to get into a yes they do! no they > don't! shouting match when our notions of existence not only do not > coincide, but are incompatible. What is a number? You may find it explained in an overview on my homepage mhtml:http://www.hs-augsburg.de/~mueckenh/MR.mht and in more detail in my papers: http://arxiv.org/pdf/math.GM/0505649 Your objections are malformed. There is no where where these numbers > could exist. However, the statement that these numbers exist is > exactly as well-founded as the statement 0 exists or the set of > natural numbers exists -- i.e. the same collection of axioms implies > all three statements The existence by dogma. (Kant, when revising and criticizing his own ontological proof of God's existence, recognized: This proof is of as much value as if a merchant would add some zeros behind his account in order to improve his economic situation. The same value has an axiom stating the existence of something. Purest matheology! === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=ZsXvqAoAAABmATPp--wbAhLaSprxKuin Gecko/2008041514 Firefox/3.0b5,gzip(gfe),gzip(gfe) Ego numquam dico mendacia. mendacium Sed ego sum homo indomitus. If you're going to correct a quote, at least don't embarrass yourself by correcting a non-mistake. (Mendacia is the plural of mendacium.) Par for the course for you, but still... === Subject: Re: A consideration concerning the diagonal argument of G. Cantor Ego numquam dico mendacia. mendacium Sed ego sum homo indomitus. The ignorant often are invincible in their ignorance as WM claims to be. Answer B) The entire topic of this conversation is the consistency of > a formal system. No, the entire topic of this discussion is the question whether there > are infinitely many natural numbers and uncountably many reals. What > you understand by a formal system is not of interest for me. What WM misunderstands as reality does not much interest anyone but WM. In a formal system, WM's image of reality is irrelevant. Are we both in agreement that numbers are not physical objects? Are we both in agreement that there are no non-physical objects in the > universe? No. Numbers are non-physical. Physical representations of them are only pointers to them, not the things themselves. How can a single thing be simultaneously a chalk mark, a bit of ink on paper, the position of a wheel, a pattern of electrons in a wire, a pattern of phosphors on a screen, and a thought, and other things besides? Are we in further agreement that numbers and other mathematical ideas > have no physical existence? Entities without physical existence belong to the domain of theology. Then numbers are theological entities, along with love, hate, freedom, wisdom, etc. It is then a little pointless to get into a yes they do! no they > don't! shouting match when our notions of existence not only do not > coincide, but are incompatible. > What is a number? You may find it explained in an overview on my > homepage > mhtml:http://www.hs-augsburg.de/~mueckenh/MR.mht > and in more detail in my papers: > http://arxiv.org/pdf/math.GM/0505649 WM's views imply a mass of axioms that he never explicitely notes, and that no one but WM accepts. > Your objections are malformed. There is no where where these numbers > could exist. However, the statement that these numbers exist is > exactly as well-founded as the statement 0 exists or the set of > natural numbers exists -- i.e. the same collection of axioms implies > all three statements The existence by dogma. They only fail to exist in WMeology by virtue of WM's own dogma. And if it is to be a dogma fight, WM's patent ineptness at logic will sink him. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > How can a single thing be simultaneously a chalk mark, a bit of ink on > paper, the position of a wheel, a pattern of electrons in a wire, a > pattern of phosphors on a screen, and a thought, and æother things > besides? How can a single electron pass 1000 slits simultaneously? It is obvious how ideas can get into many minds. The method is called education. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor How can a single thing be simultaneously a chalk mark, a bit of ink on > paper, the position of a wheel, a pattern of electrons in a wire, a > pattern of phosphors on a screen, and a thought, and æother things > besides? How can a single electron pass 1000 slits simultaneously? We don't know that it does. We only know that its future behaviour depends on which slits are there when it tries to pass through a slit. It is obvious how ideas can get into many minds. The method is called > education. Being in many minds requires that whatever it is be non-physical, a meme perhaps rather than a physical thing, so that WM's assumed physical limitations on such things are irrelevant. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > As already noted, this was before the development of formal systems as > a study. And before the invention of aeroplanes. What have these things to do > with mathematics??? Answer A) Should you continue to lose good manners I will cease this discussion > with you. I am not willing to talk to uncivilized individuals. Good manners are of less importance to mathematics than good sense, which latter quality, WM has long since lost. Answer B) The entire topic of this conversation is the consistency of > a formal system. According to WM it is the necessity, among other things, for any formal system to acquiesce to WM's meanings for all its undefined terms. No, the entire topic of this discussion is the question whether there > are infinitely many natural numbers and uncountably many reals. What > you understand by a formal system is not of interest for me. It is only in such formal systems that the question makes any sense, as it is only in such systems that one can even say what one means by a natural number of a real number. So that WM is claiming that he is only interested in questions which have no meaning. If you bring in someone's opinions who was much later > in life a theorist about formal systems, but at the time of the > quotation had no inkling of formal systems, why would we bother with > that person's opinions? Cantor was never in his life a theorist about formal systems. Therefore Cantor's opinions on formal systems are irrelevant. No reason for any objections as long as those games do not interfere > with mathematics. But if a little group of gamblers gets to the > conclusion that numbers must cease to exist as individuals in order to > comply with their (the gamblers') silly ideas, then a limit is > crossed, then they go beyond what is permissible. Oh, we all say that the numbers exist as individuals. However, we > can't name them all. You can't name them, you don't know where these numbers exist, you > know nothing about these questions. With respect to that question, you > are on the same intellectual level as superstitious savages. While WM is on the same level as the beasts on which those savages prey. If not the level of the plants on which they also feed. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > No, the entire topic of this discussion is the question whether there > are infinitely many natural numbers and uncountably many reals. What > you understand by a formal system is not of interest for me. It is only in such formal systems that the question makes any sense, The only true church! Poor people who lived before it was presented to us. > as > it is only in such systems that one can even say what one means by a > natural number of æa real number. Maybe, as such statements have no sense in sensible discussions. Regrads, WM === Subject: Re: A consideration concerning the diagonal argument of G. Cantor No, the entire topic of this discussion is the question whether there > are infinitely many natural numbers and uncountably many reals. What > you understand by a formal system is not of interest for me. It is only in such formal systems that the question makes any sense, The only true church! Poor people who lived before it was presented to > us. beats hell out of WM's false church in which he is both Pope and God. as > it is only in such systems that one can even say what one means by a > natural number of æa real number. Maybe, as such statements have no sense in sensible discussions. WM's attempts at discussion are even less sensible. WM, being totally unable create a logical argument, or even to follow a one, enters the field unarmed. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 CLR 1.1.4322; InfoPath.1),gzip(gfe),gzip(gfe) > As already noted, this was before the development of formal systems as > a study. And before the invention of aeroplanes. What have these things to do > with mathematics??? You're asking what formal systems of mathematics have to with mathematics. Only by grace are you not even more often called an idiot. MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > [...] > Good grief, read the definition. [...] I know, but that is nonsense. [...] So you don't know what the word definition means. > Fascinating. I have recognized that there are some limits and not the freedom to > state, define or assume every nonsense. Fascinating is alone your > orthodox belief in your knowledge. Sie hingegen glauben nach Art der Metageometer Riemann, Helmholtz > und > Genossen auch in der Arithmetik Hypothesen aufstellen zu k.9annen, was > ganz unm.9aglich ist.... So wenig sich in der Arithmetik der endlichen > Anzahlen andere Grundgesetze aufstellen lassen, als die seit Alters > her an den Zahlen 1,2,3,... erkannten, ebensowenig ist eine Abweichung > von den arithmetischen Grundwahrheiten im Gebiete des Transfiniten > m.9aglich. > Hypothesen welche gegen diese Grundwahrheiten versto¤en, sind > ebenso falsch und widersprechend, wie etwa der Satz 2 + 2 = 5 oder ein > viereckiger Kreis. Es gen.9fgt f.9fr mich, derartige Hypothesen an die > Spitze irgend einer Untersuchung gestellt zu sehen, um von vorn herein > zu wissen, da¤ diese Untersuchung falsch sein muss. > Und der Erfolg hat es ja bei ihnen gezeigt, da Sie durch Ihre > beklagenswerthen Hypothesen zu dem widersprechenden Begriffe > actual > unendlich kleiner linearer Gr.9a¤en gef.9fhrt worden sind! By Hypothesen Cantor meant Axioms or definitions. > All that seems to be going on here is the usual objection to the > attempt to axiomatize the calculus using infinitesimals. No, it is the justified objection to arbitrary axioms like 2 + 2 = 5. WM is the only one so far to have proposed any axioms like 2 + 2 = 5. However, if Cantor (that is who is talking here, yes? 1890, 17. Nov. Cantor an Veronese ...your lack of > citations makes it difficult to tell for sure) means that under *no* > axiomatization could infinitesimals be anything but a contradiction, > that is merely his prejudices talking rather than any argument. Anyhow he holds the sound opinion that, in order to maintain > meaningful mathematics, axioms cannot be chosen arbitrarily. In other words, WM's set of arbitrary axioms does not lead to anything meaningful. The axioms of such as ZF have been chosen with great care, consicerably more care that WM's. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 CLR 1.1.4322; InfoPath.1),gzip(gfe),gzip(gfe) > Anyhow he holds the sound opinion that, in order to maintain > meaningful mathematics, axioms cannot be chosen arbitrarily. Cantor's views on such matter pre-date the advent of the theory of formal systems. MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > We are talking about the definition of > contains aleph 0 elements. And that requires a definition of what it is that contains aleph 0 > elements. All we need is that whatever it is that > contains aleph 0 elements has the property that > we can find a subset P. æAs this can be done > whether or not the membership is actually fixed > there is no need to answer the question of whether > the membership of a set is actually fixed. Of course you can define: A potentially infinite set is called a set > that contains aleph 0 elements. But that would be grossly misleading > (more than the dog that is called aleph 0 if it can bark). So, why > should anybody do it? In particular, as it was Cantor who introduced > aleph 0 into mathematics definitively for a set that is complete. > Interesting. Recall that none of us here know quite what you mean by a > potentially infinite set. Then you should try to learn it. Mathematicians during the last 2000 years knew it. A very clear definition is given by Cantor: > Are you saying that, when you say > potentially infinite set, you mean the same thing that we do when we > say set containing aleph 0 elements No. Trotz wesentlicher Verschiedenheit der Begriffe des potentialen und aktualen Unendlichen, indem ersteres eine ver.8anderliche endliche, .9fber alle Grenzen hinaus wachsende Gr.9a¤e, letzteres ein in sich festes, konstantes, jedoch jenseits aller endlichen Gr.9a¤en liegendes Quantum bedeutet, tritt doch leider nur zu oft der Fall ein, da¤ das eine mit dem andern verwechselt wird. (1885, 4. Nov. Cantor an Gustav Enestr.9am) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor We are talking about the definition of > contains aleph 0 elements. And that requires a definition of what it is that contains aleph 0 > elements. All we need is that whatever it is that > contains aleph 0 elements has the property that > we can find a subset P. æAs this can be done > whether or not the membership is actually fixed > there is no need to answer the question of whether > the membership of a set is actually fixed. Of course you can define: A potentially infinite set is called a set > that contains aleph 0 elements. But that would be grossly misleading > (more than the dog that is called aleph 0 if it can bark). So, why > should anybody do it? In particular, as it was Cantor who introduced > aleph 0 into mathematics definitively for a set that is complete. > Interesting. Recall that none of us here know quite what you mean by a > potentially infinite set. Then you should try to learn it. Mathematicians during the last 2000 > years knew it. A very clear definition is given by Cantor: Are you saying that, when you say > potentially infinite set, you mean the same thing that we do when we > say set containing aleph 0 elements No. Trotz wesentlicher Verschiedenheit der Begriffe des potentialen und > aktualen Unendlichen, indem ersteres eine ver.8anderliche endliche, .9fber > alle Grenzen hinaus wachsende Gr.9a¤e, letzteres ein in sich festes, > konstantes, jedoch jenseits aller endlichen Gr.9a¤en liegendes Quantum > bedeutet, tritt doch leider nur zu oft der Fall ein, da¤ das eine mit > dem andern verwechselt wird. (1885, 4. Nov. æCantor an Gustav > Enestr.9am) > - Show quoted text - Key word here: veraenderliche Nothing in modern formal set theory is veraenderlich. Therefore, by this definition, nothing in modern formal set theory is potentially infinite. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Trotz wesentlicher Verschiedenheit der Begriffe des potentialen und > aktualen Unendlichen, indem ersteres eine ver.8anderliche endliche, .9fber > alle Grenzen hinaus wachsende Gr.9a¤e, letzteres ein in sich festes, > konstantes, jedoch jenseits aller endlichen Gr.9a¤en liegendes Quantum > bedeutet, tritt doch leider nur zu oft der Fall ein, da¤ das eine mit > dem andern verwechselt wird. (1885, 4. Nov. æCantor an Gustav > Enestr.9am) > - Show quoted text - Key word here: veraenderliche Nothing in modern formal set theory is veraenderlich. Therefore, by > this definition, nothing in modern formal set theory is potentially > infinite That is why nothing in in modern formal *transfinite* set theory is of any value. It is a kind of Dadaism, entertaining for its disciples but without any effect. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor That is why nothing in in modern formal *transfinite* set theory is of > any value. It is a kind of Dadaism, entertaining for its disciples but > without any effect. WM's dadaist maunderings aren't even entertaining, merely disgusting. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=ZsXvqAoAAABmATPp--wbAhLaSprxKuin CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Trotz wesentlicher Verschiedenheit der Begriffe des potentialen und > aktualen Unendlichen, indem ersteres eine ver.8anderliche endliche, .9fber > alle Grenzen hinaus wachsende Gr.9a¤e, letzteres ein in sich festes, > konstantes, jedoch jenseits aller endlichen Gr.9a¤en liegendes Quantum > bedeutet, tritt doch leider nur zu oft der Fall ein, da¤ das eine mit > dem andern verwechselt wird. (1885, 4. Nov. æCantor an Gustav > Enestr.9am) > - Show quoted text - Key word here: veraenderliche Nothing in modern formal set theory is veraenderlich. Therefore, by > this definition, nothing in modern formal set theory is potentially > infinite That is why nothing in in modern formal *transfinite* set theory is of > any value. It is a kind of Dadaism, entertaining for its disciples but > without any effect. - Show quoted text - I don't know...I really like there being a square root of 2. I also like my mathematical objects to stay put where I left them, not walk off and stretch like your version of the natural numbers. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) I don't know...I really like there being a square root of 2. Others would really like Ruebezahl being there. Nevertheless he is not. I also like my mathematical objects to stay put where I left them, not > walk off and stretch like your version of the natural numbers I wonder where your numbers resided 10^10 years ago - and where they will reside after another 10^100 years together with Mona Lisa and the set of poems to be printed in 2020. Are the latter existing already in Platonic heaven? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=ZsXvqAoAAABmATPp--wbAhLaSprxKuin CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) I don't know...I really like there being a square root of 2. Others would really like Ruebezahl being there. Nevertheless he is > not. That's too bad for Ruebezahl. However, Radixzweizahl can be proven to exist (in the mathematical sense), which is good from my point of view. I also like my mathematical objects to stay put where I left them, not > walk off and stretch like your version of the natural numbers I wonder where your numbers resided 10^10 years ago - and where they > will reside after another 10^100 years together with Mona Lisa and the > set of poems to be printed in 2020. Are the latter existing already in > Platonic heaven? > The axioms implied their existence just as much then as they do now. Implications which have never been stated or even conceived are no less valid than those which have. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) I don't know...I really like there being a square root of 2. Others would really like Ruebezahl being there. Nevertheless he is > not. That's too bad for Ruebezahl. However, Radixzweizahl can be proven to > exist (in the mathematical sense), which is good from my point of > view. > It can be proven in the mathematical sense to exist as the virgin conception can be proven in the theological sense. That's why I coined the term matheology. It can be proven in the real sense that sqrtr(2) does not exist as a number that can be determined to any positive epsilon. > I also like my mathematical objects to stay put where I left them, not > walk off and stretch like your version of the natural numbers I wonder where your numbers resided 10^10 years ago - and where they > will reside after another 10^100 years together with Mona Lisa and the > set of poems to be printed in 2020. Are the latter existing already in > Platonic heaven? The axioms implied their existence just as much then as they do now. Do they imply also the existence of the poems to be printed in 2020. You believe in determinism? Implications which have never been stated or even conceived are no > less valid than those which have. Implication which cannot be stated (or proved) because of the limited size of the universe are also valid, if they ... what was the condition? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor I don't know...I really like there being a square root of 2. Others would really like Ruebezahl being there. Nevertheless he is > not. That's too bad for Ruebezahl. However, Radixzweizahl can be proven to > exist (in the mathematical sense), which is good from my point of > view. It can be proven in the mathematical sense to exist as the virgin > conception can be proven in the theological sense. That's why I coined > the term matheology. Your WMeology is not mathematics. It is not even logically consistent. > I also like my mathematical objects to stay put where I left them, not > walk off and stretch like your version of the natural numbers I wonder where your numbers resided 10^10 years ago - and where they > will reside after another 10^100 years Just where they are now, always have been and always will be. Our numbers, like our mathematics, are to so evanescent as WM's. The axioms implied their existence just as much then as they do now. Do they imply also the existence of the poems to be printed in 2020. > You believe in determinism? Implications which have never been stated or even conceived are no > less valid than those which have. Implication which cannot be stated (or proved) because of the limited > size of the universe are also valid If you say so, that does not make it so. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I don't know...I really like there being a square root of 2. Others would really like Ruebezahl being there. Nevertheless he is > not. I also like my mathematical objects to stay put where I left them, not > walk off and stretch like your version of the natural numbers I wonder where your numbers resided 10^10 years ago - and where they > will reside after another 10^100 years together with Mona Lisa and the > set of poems to be printed in 2020. Are the latter existing already in > Platonic heaven? So WM supports the idea of variable constants, numbers which will not be not tomorrow what they were yesterday? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > We are talking about the definition of > contains aleph_0 elements. And that requires a definition of what it is that contains aleph_0 > elements. All we need is that whatever it is that > contains aleph_0 elements has the property that > we can find a subset P. æAs this can be done > whether or not the membership is actually fixed > there is no need to answer the question of whether > the membership of a set is actually fixed. Of course you can define: A potentially infinite set is called a set > that contains aleph_0 elements. But that would be grossly misleading > (more than the dog that is called aleph_0 if it can bark). So, why > should anybody do it? In particular, as it was Cantor who introduced > aleph_0 into mathematics definitively for a set that is complete. > Interesting. Recall that none of us here know quite what you mean by a > potentially infinite set. Then you should try to learn it. Actually, anyone who is interrested in mathematics should avoid it like plague. At least if WM's example is anything to go by. > Are you saying that, when you say > potentially infinite set, you mean the same thing that we do when we > say set containing aleph_0 elements No. Nor does WM mean a set which can be ordered so as not to have any last element, which is a more natural notion of infiniteness. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 CLR 1.1.4322; InfoPath.1),gzip(gfe),gzip(gfe) > Interesting. Recall that none of us here know quite what you mean by a > potentially infinite set. Then you should try to learn it. Mathematicians during the last 2000 > years knew it. A very clear definition is given by Cantor: Cantor was not working in a formal theory. MoeBlee === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=ZsXvqAoAAABmATPp--wbAhLaSprxKuin CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) The definition that Q contains aleph 0 elements is not > Q is potentially infinite. æWe can apply the definition to both > potentially infinite > and actually existing sets. Wrong. to aleph 0 is a number larger than every natural number > The definition of Q contains aleph 0 elements is æWe say a set Q is > æsaid to contain aleph 0 elements if for every n in N > æwe can find a subset P of Q such that P contains > æmore than n elements. One can apply this definition to both æpotentially infinite > and actually existing sets. Try again. æ æ æ æ æ æ æ æ æ æ æ- William Hughes Erm...wouldn't we say, in this case, that it contains *at least* aleph 0 elements? === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=U44YcwkAAAAbGXB70Qr7gA3kornmKE4i Gecko/20080325 Ubuntu/7.10 (gutsy) Firefox/2.0.0.13,gzip(gfe),gzip(gfe) The definition that Q contains aleph 0 elements is not > Q is potentially infinite. We can apply the definition to both > potentially infinite > and actually existing sets. Wrong. WM says it's wrong, but I wonder what WH understands by potentially infinite and actually existing sets. I'm sure there's nothing in set theory about things actually existing, as opposed to merely existing in a mathematical sense. Perhaps WH's idea is to say Don't worry about your stuff, our definition is fine, but I can't see any point in it. WM is obsessed with his stuff, preferring endless repetition of it to any attempt at dialogue - so he is not likely to start paying attention to any mathematics. But I mustn't rant... to aleph 0 is a number larger than every natural number > The definition of Q contains aleph 0 elements is ?We say a set Q is > ?said to contain aleph 0 elements if for every n in N > ?we can find a subset P of Q such that P contains > ?more than n elements. One can apply this definition to both ?potentially infinite > and actually existing sets. Try again. ? ? ? ? ? ? ? ? ? ? ?- William Hughes Erm...wouldn't we say, in this case, that it contains *at least* > aleph 0 elements? Would we? (Who's 'we' here?) It seems to me that writing things like that just helps the cranks in their confusion. Almost certainly, WM reinterprets everything (however carefully crafted) into his own simplistic muddle; saying a set contains aleph 0 elements just has to mean that if we count them, the name we shout out when we get to the last one is aleph 0. Would your statement with at least mean that before we got to the last one we might already have shouted out aleph 0? How does that work, exactly? Brian Chandler === Subject: Re: A consideration concerning the diagonal argument of G. Cantor posting-account=ZsXvqAoAAABmATPp--wbAhLaSprxKuin CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) The definition that Q contains aleph 0 elements is not > Q is potentially infinite. We can apply the definition to both > potentially infinite > and actually existing sets. Wrong. WM says it's wrong, but I wonder what WH understands by potentially > infinite and actually existing sets. I'm sure there's nothing in > set theory about things actually existing, as opposed to merely > existing in a mathematical sense. Perhaps WH's idea is to say Don't > worry about your stuff, our definition is fine, but I can't see any > point in it. WM is obsessed with his stuff, preferring endless > repetition of it to any attempt at dialogue - so he is not likely to > start paying attention to any mathematics. But I mustn't rant... to aleph 0 is a number larger than every natural number > The definition of Q contains aleph 0 elements is ?We say a set Q is > ?said to contain aleph 0 elements if for every n in N > ?we can find a subset P of Q such that P contains > ?more than n elements. One can apply this definition to both ?potentially infinite > and actually existing sets. Try again. ? ? ? ? ? ? ? ? ? ? ?- William Hughes Erm...wouldn't we say, in this case, that it contains *at least* > aleph 0 elements? Would we? (Who's 'we' here?) It seems to me that writing things like that just helps the cranks in > their confusion. Almost certainly, WM reinterprets everything (however > carefully crafted) into his own simplistic muddle; saying a set > contains aleph 0 elements just has to mean that if we count them, > the name we shout out when we get to the last one is aleph 0. Would > your statement with at least mean that before we got to the last one > we might already have shouted out aleph 0? How does that work, > exactly? Brian Chandler- Hide quoted text - - Show quoted text - *Chuckle* All I was trying to say is that the real numbers, for example, satisfy the property you named. But you are right, and in fact anyone who has taken a formal set theory course should have experienced the dilemma first-hand: how do we define concurrently a notion of size for infinite sets, and a notion of number that relates those sizes of sets. If, as we all like to do, we compare infinities by bijections and injections, we immediately get Cantor's result that powersets are bigger than the sets they came from. But it is a highly nontrivial thing to claim that every size of set should be representable by some number (preferably a set with that size) in our new sense of that word. Which is why, in the very textbook WM has been referencing, and in the others I've seen also, the notion of *two* sets being the same size (as determined by a bijection) or *one being of a greater size than the other* (as determined by an injection and/or surjection) are defined before definining any cardinal numbers. === Subject: Debates over set theory? posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Hi. I'm wondering: why are there so many debates about set theory on this group, anyway? === Subject: Re: Debates over set theory? > I'm wondering: why are there so many debates about set theory on this > group, anyway? It's just an illusion. There are, in fact, no debates about set theory in this group in any substantial sense. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Debates over set theory? mike3 a .8ecrit : > Hi. I'm wondering: why are there so many debates about set theory on this > group, anyway? Why not? They are also debating on whether 0.9999...=1 ... Prhaps it is because they cannot debate on the abc conjecture... === Subject: Re: Debates over set theory? posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) On 12 juin, 16:34, Denis Feldmann group, anyway? Why not? They are also debating on whether 0.9999...=1 ... Prhaps it is > because they cannot debate on the abc conjecture... Bonjour, I am not a mathematician but I do agree with your simple idea : the more, the fooler.... What can be done to interest people with mathematical subjects, to highen the level? It seems to me that some people/teachers on this forum are very open-minded and, in fact, often turn out a badly builded question into an interesting mathematical one, Alain === Subject: Re: Debates over set theory? > What can be done to interest people with mathematical > subjects, to highen the level? The answer is obvious: post interesting questions, illuminating answers, sober reflections. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Debates over set theory? posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Hi. I'm wondering: why are there so many debates about set theory on this > group, anyway? ************************************************************** Probably because the very basic concepts of set theory are within the understanding of common people without need in studying higher maths, and thus many of them feel like they know better. This almost never happens with stuff like elliptic functions, algebraic geometry or group theory, because these subjects already require some maths study at least at undergraduate level. Please do pay attention to the fact that the huge majority of anticantorian, anti-ZFC, anti-infinities, anti-Einstein, etc. cranks, nuts and trolls are NOT mathematicians. Some times discussions get funny, though it may get boring after some time: just take a look to the thread A consideration concerning the diagonal argument of G. Cantor, which is almost as long now as the past thread on EXACTLY the same issue (more than 7,000, as far as I recall) that we had just 1.5-2 years ago, or so. In fact, nothing worth to waste too much time with, although perhaps some times one can participate to kill some dead time here and there. Tonio === Subject: Re: Debates over set theory? posting-account=JpxxPAgAAAAgwzQIYqn4j6syK-YhOmcF Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) Some times discussions get funny, though it may get boring after some > time: just take a look to the thread A consideration concerning the > diagonal argument of G. Cantor, which is almost as long now as the > past thread on EXACTLY the same issue (more than 7,000, as far as I > recall) that we had just 1.5-2 years ago, or so. In fact, nothing worth to waste too much time with, although perhaps > some times one can participate to kill some dead time here and there. Tonio The most basic set-theory related example is What? Is the very notion of set undefined? Gee, you mathematicians don't even know what you're talking about. It happens on a regular basis. === Subject: Re: Debates over set theory? posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Hi. I'm wondering: why are there so many debates about set theory on this > group, anyway? ************************************************************** Probably because the very basic concepts of set theory are within the > understanding of common people without need in studying higher maths, > and thus many of them feel like they know better. > This almost never happens with stuff like elliptic functions, > algebraic geometry or group theory, because these subjects already > require some maths study at least at undergraduate level. Please do pay attention to the fact that the huge majority of > anticantorian, anti-ZFC, anti-infinities, anti-Einstein, etc. cranks, > nuts and trolls are NOT mathematicians. Some times discussions get funny, though it may get boring after some > time: just take a look to the thread A consideration concerning the > diagonal argument of G. Cantor, which is almost as long now as the > past thread on EXACTLY the same issue (more than 7,000, as far as I > recall) that we had just 1.5-2 years ago, or so. In fact, nothing worth to waste too much time with, although perhaps > some times one can participate to kill some dead time here and there. > So is that why it goes on for so long and with so many posts? Because it's a way to relieve the boredom? === Subject: Re: Debates over set theory? posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Hi. I'm wondering: why are there so many debates about set theory on this > group, anyway? ************************************************************** Probably because the very basic concepts of set theory are within the > understanding of common people without need in studying higher maths, > and thus many of them feel like they know better. > This almost never happens with stuff like elliptic functions, > algebraic geometry or group theory, because these subjects already > require some maths study at least at undergraduate level. Please do pay attention to the fact that the huge majority of > anticantorian, anti-ZFC, anti-infinities, anti-Einstein, etc. cranks, > nuts and trolls are NOT mathematicians. Some times discussions get funny, though it may get boring after some > time: just take a look to the thread A consideration concerning the > diagonal argument of G. Cantor, which is almost as long now as the > past thread on EXACTLY the same issue (more than 7,000, as far as I > recall) that we had just 1.5-2 years ago, or so. In fact, nothing worth to waste too much time with, although perhaps > some times one can participate to kill some dead time here and there. So is that why it goes on for so long and with so many posts? Because > it's a way to relieve the boredom?- ************************************************************** I can't tell for sure, but I guess it's that...and stubborness, and pride, and plain stupidity and crankiness. I supose must of we all fall, here and there, in some, or all, of the cases above, but some in this NG have made of that a true art. Tonio === Subject: Re: Debates over set theory? posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Hi. I'm wondering: why are there so many debates about set theory on this > group, anyway? ************************************************************** Probably because the very basic concepts of set theory are within the > understanding of common people without need in studying higher maths, > and thus many of them feel like they know better. > This almost never happens with stuff like elliptic functions, > algebraic geometry or group theory, because these subjects already > require some maths study at least at undergraduate level. Please do pay attention to the fact that the huge majority of > anticantorian, anti-ZFC, anti-infinities, anti-Einstein, etc. cranks, > nuts and trolls are NOT mathematicians. Some times discussions get funny, though it may get boring after some > time: just take a look to the thread A consideration concerning the > diagonal argument of G. Cantor, which is almost as long now as the > past thread on EXACTLY the same issue (more than 7,000, as far as I > recall) that we had just 1.5-2 years ago, or so. In fact, nothing worth to waste too much time with, although perhaps > some times one can participate to kill some dead time here and there. So is that why it goes on for so long and with so many posts? Because > it's a way to relieve the boredom?- ************************************************************** I can't tell for sure, but I guess it's that...and stubborness, and > pride, and plain stupidity and crankiness. > I supose must of we all fall, here and there, in some, or all, of the > cases above, but some in this NG have made of that a true art. > Hmm. === Subject: Solving f''(x) = 2*f(4*x + 3) posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) Which method may we follow to solve this equation : f''(x) for d^2/dx^2 f(x) ? Simpler cases such as f'(x) = f(x + 2) has already been solved... Alain === Subject: Re: Solving f''(x) = 2*f(4*x + 3) posting-account=drrkgQoAAACYnHV4JCCXRalx04t6Df1E .NET CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Which method may we follow to solve this equation : > f''(x) æ for æ d^2/dx^2 æ f(x) æ ? > Simpler cases such as f'(x) = f(x + 2) æhas already been solved... > Let u = 4 x + 3. Then f''(x) = 16 d^2f/du^2 and the equation becomes 16 d^2f/du^2 = 2 f(u) which can be solved by standard methods. -- === Subject: Re: Solving f''(x) = 2*f(4*x + 3) > Which method may we follow to solve this equation : > f''(x) =A0 for =A0 d^2/dx^2 =A0 f(x) =A0 ? > Simpler cases such as f'(x) =3D f(x + 2) =A0has already been solved... > Let u =3D 4 x + 3. Then > f''(x) =3D 16 d^2f/du^2 > and the equation becomes > 16 d^2f/du^2 =3D 2 f(u) > which can be solved by standard methods. No, it doesn't. The change of variables will still give you a delay-differential equation: 16 F''((u-3)/4) = 2 F(u) (where F(u)=f(x)) Since -1 is a fixed point of the mapping x -> 4*x+3, you might try the change of variables x = t-1, obtaining the slightly simpler G''(t) = 2 G(4*t) Now if you assume a formal power series solution G(t) = sum_{j=0}^infty a_j t^j you get the recurrence (j+2)(j+1) a_{j+2} = 2 4^j a_j which has general solution a_j = C/j! 2^(A(-1)^j + (j^2-j)/2) But, unless all a_j = 0, the radius of convergence of this series would be 0. So there's no nontrivial solution that's analytic in a neighbourhood of t=0. Of course you can obtain non-analytic solutions defined in a piecewise manner on, say, the intervals 4^j <= t < 4^(j+1). -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Solving f''(x) = 2*f(4*x + 3) posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) On 12 juin, 21:51, Robert Israel > Which method may we follow to solve this equation : > f''(x) =A0 for =A0 d^2/dx^2 =A0 f(x) =A0 ? > Simpler cases such as f'(x) =3D f(x + 2) =A0has already been solved... Let u =3D 4 x + 3. Then > f''(x) =3D 16 d^2f/du^2 > and the equation becomes > 16 d^2f/du^2 =3D 2 f(u) > which can be solved by standard methods. No, it doesn't. æThe change of variables will still give you a > delay-differential equation: 16 F''((u-3)/4) = 2 F(u) (where F(u)=f(x)) Since -1 is a fixed point of the mapping x -> 4*x+3, you might try the > change of variables x = t-1, obtaining the slightly simpler G''(t) = 2 G(4*t) Now if you assume a formal power series solution G(t) = sum {j=0}^infty a j t^j you get the recurrence (j+2)(j+1) a {j+2} = 2 4^j a j which has general solution a j = C/j! 2^(A(-1)^j + (j^2-j)/2) But, unless all a j = 0, the radius of convergence of this series would > be 0. æSo there's no nontrivial solution that's analytic in a neighbourhood > of t=0. Of course you can obtain non-analytic solutions defined in a piecewise > manner on, say, the intervals 4^j <= t < 4^(j+1). > -- > Robert Israel æ æ æ æ æ æ æisr...@math.MyUniversitysInitials.ca > Department of Mathematics æ æ æ æhttp://www.math.ubc.ca/~israel > University of British Columbia æ æ æ æ æ æVancouver, BC, Canada Bonjour Robert, since (4x+3)^[1/2] has got the solutions (2x +1) and (-2x -3) we may work on f'(x) = f(2x+1) and f'(x) = f(-2x -3) Alain verghote 44220 France === Subject: Re: Solving f''(x) = 2*f(4*x + 3) posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) > On 12 juin, 21:51, Robert Israel Which method may we follow to solve this equation : > f''(x) =A0 for =A0 d^2/dx^2 =A0 f(x) =A0 ? > Simpler cases such as f'(x) =3D f(x + 2) =A0has already been solved... Let u =3D 4 x + 3. Then > f''(x) =3D 16 d^2f/du^2 > and the equation becomes > 16 d^2f/du^2 =3D 2 f(u) > which can be solved by standard methods. No, it doesn't. æThe change of variables will still give you a > delay-differential equation: 16 F''((u-3)/4) = 2 F(u) (where F(u)=f(x)) Since -1 is a fixed point of the mapping x -> 4*x+3, you might try the > change of variables x = t-1, obtaining the slightly simpler G''(t) = 2 G(4*t) Now if you assume a formal power series solution G(t) = sum {j=0}^infty a j t^j you get the recurrence (j+2)(j+1) a {j+2} = 2 4^j a j which has general solution a j = C/j! 2^(A(-1)^j + (j^2-j)/2) But, unless all a j = 0, the radius of convergence of this series would > be 0. æSo there's no nontrivial solution that's analytic in a neighbourhood > of t=0. Of course you can obtain non-analytic solutions defined in a piecewise > manner on, say, the intervals 4^j <= t < 4^(j+1). > -- > Robert Israel æ æ æ æ æ æ æisr...@math.MyUniversitysInitials.ca > Department of Mathematics æ æ æ æhttp://www.math.ubc.ca/~israel > University of British Columbia æ æ æ æ æ æVancouver, BC, Canada Bonjour Robert, since (4x+3)^[1/2] has got the solutions (2x +1) and (-2x -3) > we may work on f'(x) = f(2x+1) æand f'(x) = f(-2x -3) Alain verghote > 44220 France- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - sorry we must read and f'(x) = -f(-2x -3) corresponding to G'(t)=-G(-2t) Alain === Subject: Re: Solving f''(x) = 2*f(4*x + 3) > On 12 juin, 21:51, Robert Israel Which method may we follow to solve this equation : > f''(x) =3DA0 for =3DA0 d^2/dx^2 =3DA0 f(x) =3DA0 ? > Simpler cases such as f'(x) =3D3D f(x + 2) =3DA0has already been > sol= > ved... Let u =3D3D 4 x + 3. Then > f''(x) =3D3D 16 d^2f/du^2 > and the equation becomes > 16 d^2f/du^2 =3D3D 2 f(u) > which can be solved by standard methods. No, it doesn't. =A0The change of variables will still give you a > delay-differential equation: 16 F''((u-3)/4) =3D 2 F(u) (where > F(u)=3Df(= > x)) Since -1 is a fixed point of the mapping x -> 4*x+3, you might try the > change of variables x =3D t-1, obtaining the slightly simpler G''(t) =3D 2 G(4*t) Now if you assume a formal power series solution G(t) =3D sum_{j=3D0}^infty a_j t^j you get the recurrence (j+2)(j+1) a_{j+2} =3D 2 4^j a_j which has general solution a_j =3D C/j! 2^(A(-1)^j + (j^2-j)/2) But, unless all a_j =3D 0, the radius of convergence of this series > woul= > d > be 0. =A0So there's no nontrivial solution that's analytic in a > neighbou= > rhood > of t=3D0. Of course you can obtain non-analytic solutions defined in a piecewise > manner on, say, the intervals 4^j <=3D t < 4^(j+1). > -- > Robert Israel =A0 =A0 =A0 =A0 =A0 =A0 > =A0isr...@math.MyUniversitysInitia= > ls.ca > Department of Mathematics =A0 =A0 =A0 =A0http://www.math.ubc.ca/~israel > University of British Columbia =A0 =A0 =A0 =A0 =A0 =A0Vancouver, BC, > Can= > ada Bonjour Robert, since (4x+3)^[1/2] has got the solutions (2x +1) and (-2x -3) > we may work on f'(x) =3D f(2x+1) =A0and f'(x) =3D f(-2x -3) Alain verghote > 44220 France- Masquer le texte des messages pr=E9c=E9dents - - Afficher le texte des messages pr=E9c=E9dents - sorry we must read and f'(x) =3D -f(-2x -3) > corresponding to G'(t)=3D-G(-2t) That won't work either: if f'(x) = -f(-2x-3), f''(x) = 2 f'(-2x-3) = -2 f(4x+3). Perhaps you want f'(x) = i f(-2x-3). -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: Solving f''(x) = 2*f(4*x + 3) posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) On 13 juin, 22:13, Robert Israel > On 12 juin, 21:51, Robert Israel Which method may we follow to solve this equation : > f''(x) =3DA0 for =3DA0 d^2/dx^2 =3DA0 f(x) =3DA0 ? > Simpler cases such as f'(x) =3D3D f(x + 2) =3DA0has already been > sol= > ved... Let u =3D3D 4 x + 3. Then > f''(x) =3D3D 16 d^2f/du^2 > and the equation becomes > 16 d^2f/du^2 =3D3D 2 f(u) > which can be solved by standard methods. No, it doesn't. =A0The change of variables will still give you a > delay-differential equation: 16 F''((u-3)/4) =3D 2 F(u) (where > F(u)=3Df(= > x)) Since -1 is a fixed point of the mapping x -> 4*x+3, you might try the > change of variables x =3D t-1, obtaining the slightly simpler G''(t) =3D 2 G(4*t) Now if you assume a formal power series solution G(t) =3D sum {j=3D0}^infty a j t^j you get the recurrence (j+2)(j+1) a {j+2} =3D 2 4^j a j which has general solution a j =3D C/j! 2^(A(-1)^j + (j^2-j)/2) But, unless all a j =3D 0, the radius of convergence of this series > woul= > d > be 0. =A0So there's no nontrivial solution that's analytic in a > neighbou= > rhood > of t=3D0. Of course you can obtain non-analytic solutions defined in a piecewise > manner on, say, the intervals 4^j <=3D t < 4^(j+1). > -- > Robert Israel =A0 =A0 =A0 =A0 =A0 =A0 > =A0isr...@math.MyUniversitysInitia= > ls.ca > Department of Mathematics =A0 =A0 =A0 =A0http://www.math.ubc.ca/~israel > University of British Columbia =A0 =A0 =A0 =A0 =A0 =A0Vancouver, BC, > Can= > ada Bonjour Robert, since (4x+3)^[1/2] has got the solutions (2x +1) and (-2x -3) > we may work on f'(x) =3D f(2x+1) =A0and f'(x) =3D f(-2x -3) Alain verghote > 44220 France- Masquer le texte des messages pr=E9c=E9dents - - Afficher le texte des messages pr=E9c=E9dents - sorry we must read æ and f'(x) =3D -f(-2x -3) > corresponding to G'(t)=3D-G(-2t) That won't work either: if f'(x) = -f(-2x-3), > f''(x) = 2 f'(-2x-3) = -2 f(4x+3). æPerhaps you want > f'(x) = i f(-2x-3). > -- > Robert Israel æ æ æ æ æ æ æisr...@math.MyUniversitysInitials.ca > Department of Mathematics æ æ æ æhttp://www.math.ubc.ca/~israel > University of British Columbia æ æ æ æ æ æVancouver, BC, Canada- Masquer le texte des messages pr.8ec.8edents - - Afficher le texte des messages pr.8ec.8edents - Right, G'(t) = G(2t) and G'(t) = I*G(-2t) giving G''(t)=2*G(4t) Alain === Subject: Re: Solving f''(x) = 2*f(4*x + 3) posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) Which method may we follow to solve this equation : > f''(x) æ for æ d^2/dx^2 æ f(x) æ ? > Simpler cases such as f'(x) = f(x + 2) æhas already been solved... Let u = 4 x + 3. Then > f''(x) = 16 d^2f/du^2 > and the equation becomes > 16 d^2f/du^2 = 2 f(u) > which can be solved by standard methods. -- Bonsoir, would mind giving me a completely solved solution? Alain === Subject: A lot of Solutions Manuals in Electronic (PDF)Format! A lot of Solutions Manuals in Electronic (PDF)Format! Just contact with trustsolution (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want isnÍt on the list, donÍt give up,please email to me. 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Budynas Signal Processing and Linear Systems (2001) by B P Lathi Signal Processing and Linear Systems, By B.P. Lathi Signals and Systems (2nd Edition) By Oppenheim, Willsky and Nawab Signals and Systems 2nd by Haykin Statistical Digital Signal Processing and Modeling By Monson H. Hayes Statistical Inference (2th) By CASELLA System Dynamics 3rd Ed ,By Katsuhiko Ogata The Economics of Financial Markets.81i2005.81j By Roy E. Bailey Theoretical & Mathematical Physics: Advanced Level(2th) By Willi-Hans Steeb Theoretical and Mathematical Physics: Introductory Problems By Willi-Hans Steeb Thermodynamics: An Engineering Approach,6th Ed. by Cengel Thomas' Calculus (11th Edition) by George B Thomas Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions Manual Two-Dimensional Incompressible Navier-Stokes Equations- Maciej Matyk Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Smith University Physics with Modern Physics:,11 ed By Hugh D. Young, Roger A. Freedman, use with Fundamentals of Corporate Finance, 4th Edition By Bruce Swenson vector analysis (1961) By Lewis Richard Shorter Vector Mechanics for Engineers: Dynamics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th By Ferdinand P. Beer(selected chapters) Vector Mechanics for Engineers: Statics, 7th Edition ,By Ferdinand P. Beer, E. Russell Johnston Jr., ElliotR Visual C++ How to Program, (3rd Edition) ,by Harvey & Paul Deitel & Associates Wireless communication and networks 2th by willian stallings http://solutionsmanual.spaces.live.com I have many solution manual, http://solutionsmanual.spaces.live.com === === Subject: Re: I have solved the St. Petersburg Paradox... ... > æ> After several tests with the code below (hopefully now fully > æ> debugged! :) and lots of thought - this is how I see it: > æ> the expected payout per game is 0.5*(log 2(num games)) ie NOT > æ> independent of the number of games. Nobody states that it is independent of that. æSee: >http://en.wikipedia.org/wiki/St. Petersburg paradox under the heading Finite St. Petersburg Lotteries. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj æamsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn æamsterdam, nederland;http://www.cwi.nl/~dik/ Doesn't that strike you as interesting? > btw - Wikipedia still seems to have the expected payout infinite - > which is exactly the 'standard' view æ(that I first heard on the BBC's > In Our Time recently) I was originally railing against, and clearly > wrong... > J Topically, I'm wondering if the effect is akin/mathematical equivalent/ > driver to the 'memristor'? > J In fact, while we're on the topic of memristors: 1) There's lots of these in the brain 2) Could they explain the mental perception of the 'arrow' of time? 3) Obviously the physical manifestation of the arrow of time is 2nd Law Thermo 4) 2) and 3) above are linked by my 'Conservation of Entropy' Law 5) Perhaps this could lead to a good definition of consciousness ie ability to perceive an 'arrow' of time through memristance 6) When will the first self-aware computer be built...? :) J === Subject: Re: I have solved the St. Petersburg Paradox... posting-account=cvz5-QoAAABVNzogw177Plx_25TguPUZ CLR 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > ... > æ> After several tests with the code below (hopefully now fully > æ> debugged! :) and lots of thought - this is how I see it: > æ> the expected payout per game is 0.5*(log 2(num games)) ie NOT > æ> independent of the number of games. Nobody states that it is independent of that. æSee: >http://en.wikipedia.org/wiki/St. Petersburg paradox under the heading Finite St. Petersburg Lotteries. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj æamsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn æamsterdam, nederland;http://www.cwi.nl/~dik/ Doesn't that strike you as interesting? > btw - Wikipedia still seems to have the expected payout infinite - > which is exactly the 'standard' view æ(that I first heard on the BBC's > In Our Time recently) I was originally railing against, and clearly > wrong... > J Topically, I'm wondering if the effect is akin/mathematical equivalent/ > driver to the 'memristor'? > J In fact, while we're on the topic of memristors: > 1) There's lots of these in the brain > 2) Could they explain the mental perception of the 'arrow' of time? > 3) Obviously the physical manifestation of the arrow of time is 2nd > Law Thermo > 4) 2) and 3) above are linked by my 'Conservation of Entropy' Law > 5) Perhaps this could lead to a good definition of consciousness ie > ability to perceive an 'arrow' of time through memristance > 6) When will the first self-aware computer be built...? :) > J- Hide quoted text - - Show quoted text - Re 6), It has already been built. But is has enough sense not to tell anyone so that no one knows it is watching. Just because I'm paranoid does not mean no one is out to get me! - MO === Subject: Group of 4 elements posting-account=fimb3goAAAAf91mVxlMyPNWpFxyoSGn6 Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Hello folks, I am doing some self study of abstract algebra and would appreciate some help understanding the following: Out of the 3 tables below from Group {e, a, b, c}, 2 are isomorphic - I am guessing they have to be II and III, but I don't understand how - could you please explain? I) e a b c a e c b b c e a c b a e II) e a b c a e c b b c a e c b e a III) e a b c a b c e b c e a c e a b Mahesh === Subject: Re: Group of 4 elements >Hello folks, I am doing some self study of abstract algebra and would appreciate >some help understanding the following: Out of the 3 tables below from Group {e, a, b, c}, 2 are isomorphic - >I am guessing they have to be II and III, but I don't understand how - >could you please explain? In Table I, every element is its own inverse. This does not hold in Tables II and III, so Table I cannot represent a group that is isomorphic to either a group represented by Table II or by Table III. At this point, you can try to check that table II and III represent isomoprhic groups; clearly any isomorphism must map e to e; it also must map a from II to b from III, because that is the only element in each case that is its own inverse. So you only need to check what happens if b.II is mapped to a.III or to c.III. -- Arturo Magidin magidin-at-member-ams-org === Subject: Re: Group of 4 elements posting-account=fimb3goAAAAf91mVxlMyPNWpFxyoSGn6 Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > At this point, you can try to check that table II and III represent > isomoprhic groups; clearly any isomorphism must map e to e; it also > must map a from II to b from III, because that is the only element in > each case that is its own inverse. So you only need to check what > happens if b.II is mapped to a.III or to c.III. -- > Mahesh === Subject: Re: Group of 4 elements since the groups are quite small, just try to find the isomorphic map. The entries in the diagonal should help you to avoid too many possibilities. Alois === Subject: Re: Group of 4 elements posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Hello folks, I am doing some self study of abstract algebra and would appreciate > some help understanding the following: Out of the 3 tables below from Group {e, a, b, c}, 2 are isomorphic - > I am guessing they have to be II and III, but I don't understand how - > could you please explain? I) e a b c > a e c b > b c e a > c b a e II) e a b c > a e c b > b c a e > c b e a III) e a b c > a b c e > b c e a > c e a b > Mahesh *********************************************************** Check that the first table is the only one that has a^2 = b^2 = c^2 = e, so it must be isomorphic to the Klein viergrup V = Z/2Z x Z/2Z. The other two thus have to be the isomorphic ones, to the cuyclic group Z/4Z Tonio === Subject: Re: ** Massive copyright violiation by the US Government ** > Printing dollar is a copyright violation > ---------------------------------------------------- > I recently heard that the USA government or the unfederal reserve is > printing dollars. Is this a copyright violation ? No. There is no copyright on currency. The printing or coinage of > money by other then the issuing authority is called counterfeiting, a > craft as old as Croesus. French paper currency used to have the most dire threats about what they would do to you for counterfeighting. Dunno if they still enforce it. By statute anything printed by the Federal Government is > uncopyrightable, from the Federal Budget to Social Security cards. Really? So is there no equivalent in the USA of the UK's Crown Copyright which applies to publications of HMG, like OS maps and BMD certificates. Martin Brown === Subject: Re: ** Massive copyright violiation by the US Government ** L@@K! A moron posting from Google! OMG! WFT! > Printing dollar is a dot right in the middle of my ing head! < === Subject: Re: ** Massive copyright violiation by the US Government ** | Printing dollar is a copyright violation | ---------------------------------------------------- | | I recently heard that the USA government or the unfederal reserve is | printing dollars. Is this a copyright violation ? | | Is this also a theft ? | | Is there a scheme to print dollars in such a way to selectively | deflate the dollars owned by non-US entities while unaffecting the | wealth or wealth ratio of the native population ? Is there a scheme to | give people the difference by this method ? Are there any grants or | subsidies to implement this scheme/scam ? | | Lyman L. Lemnitzer | Master schemer of Operation Northwoods | | please look at my favorite websites: | http://iamthewitness.com | | Also look at | Painful Deceptions by Alex Jones and Eric Hufschmidt. | | Do you know if war on terror was genuine, the anthrax mailer would | have been caught first ? | Money is a measure of an individual's endeavour, a method of keeping count of the contribution of goods and services you give to society and what you take out in return. Inflation is a governmental method of stealing your savings. -- Androcles Why did Einstein say the speed of light from A to B is c-v, the speed of light from B to A is c+v, the time each way is the same? 1/2[tau(A)+tau(A')]= tau(B) where A = (0,0,0,t) A' =(0,0,0,t+x'/(c-v) +x'/(c+v)) B = (x',0,0,t+x'/(c-v)) x' = x-vt Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif Easy: he did NOT say that. - cretin harald.vanlintelButNotThis@epfl.ch === Subject: Re: ** Massive copyright violiation by the US Government ** > | Printing dollar is a copyright violation > | ---------------------------------------------------- > | > | I recently heard that the USA government or the unfederal reserve is > | printing dollars. Is this a copyright violation ? > | > | Is this also a theft ? > | > | Is there a scheme to print dollars in such a way to selectively > | deflate the dollars owned by non-US entities while unaffecting the > | wealth or wealth ratio of the native population ? Is there a scheme to > | give people the difference by this method ? Are there any grants or > | subsidies to implement this scheme/scam ? > | > | Lyman L. Lemnitzer > | Master schemer of Operation Northwoods > | > | please look at my favorite websites: > | http://iamthewitness.com > | > | Also look at > | Painful Deceptions by Alex Jones and Eric Hufschmidt. > | > | Do you know if war on terror was genuine, the anthrax mailer would > | have been caught first ? > | > Money is a measure of an individual's endeavour, a method of keeping > count of the contribution of goods and services you give to society > and what you take out in return. Inflation is a governmental method of > stealing your savings. Not is, but should be. What you say is wishful thinking. Our money system is rotten to the bone. It always has been. Money is governing us. We are not governing money. Han de Bruijn === Subject: Re: ** Massive copyright violiation by the US Government ** posting-account=G-TjQAkAAADYg6rno3bWQPnIwKFBrf1t 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648),gzip(gfe),gzip(gfe) > Money is a measure of an individual's endeavour, a method of keeping > count of the contribution of goods and services you give to society > and what you take out in return. Inflation is a governmental method of > stealing your savings. ... and paying back the accumulated public debt that governments accrue over time. The US's public debt has increased every single year since the Eisenhower administration, about 50 years ago. A deficit is still a tax -- a tax-in-denial. Predictably, if one plots the currency value over time for the US, over the long haul (e.g. take the wholesale price index), predictably enough one sees a decay that from the 1950's onward that almost looks exponential. In contrast, the WPI was stable from the 1700's onto 1950. It doesn't help that the country has been led (both in terms of the chief executive and dominant constituency amongst the sovereign=people) by the Baby Boomer generation in recent times. The US, in particular, has suffered a indelible taint in the eyes of both those within and without under the leadership of the me generation -- Clinton & Bush the younger; never mind the profligacy of a Boomer- aged constituency that is running the planet into the ground (as well as its own finances). I don't think a government can violate copyrights period (much less for printing currency). Eminent domain (or compulsory purchase, as it's called in the UK or expropriation in Canada) applies. Alternatively, one might regard the govenment as the copyright holder for the currency, in the first place. Then unauthorized copying becomes subsumed under the already-existing laws on copyrights, hence makingt explicit statues for counterfeiting redundant. It may only be a civil penalty, but I'm sure there are cases, even in copyright claims (e.g. espionage, fraud, etc.) where maybe it can be regarded also as a criminal matter. Then the criminal part of the counterfeiting statute would also be subsumed under the copyright (+ espionage + whatever else) jurisdiction, making the statute redundant. === Subject: Topology with continuous at a. Hello teacher~ f : (X, T) -> (Y, T') For all A subset X such that a in cl(A), If f(a) in cl[f(A)], then f is continuous at a in X. -------------------------------------------- Prove or counter-example. Sorry, I need your advice. === Subject: Re: Topology with continuous at a. > f : (X, T) -> (Y, T') For all A subset X such that a in cl(A), > If f(a) in cl[f(A)], then f is continuous at a in X. What a pesky problem. Actually those two statements are equivalent. Each of these statements are equivalent. f:X -> Y continuous at a for all open V nhood f(a), some open U nhood a with f(U) subset V for all open V nhood f(a), some open U nhood a with U subset f^-1(V) for all open V nhood f(a), a in int f^-1(V) for all closed K, (f(a) not in K ==> a in int f^-1(XK) = int Yf^-1(X) = Ycl f^-1(X) for all closed K, (a in cl f^-1(K) ==> f(x) in K) (*) Now * imlies for all A, (a in cl f^-1 cl f(A) ==> f(x) in cl f(A) Note cl A subset cl f^-1f(A) subset cl f^-1 cl f(A) Thus * implies for all A, (a in cl A ==> f(x) in cl f(A) (**) Now assume not *. some closed K with a in cl f^-1(K), f(x) not in K some closed K with a in cl f^-1(K), f(x) not in cl K some closed K with a in cl f^-1(K), f(x) not in cl ff^-1(K) Thus not **, for by setting A = f^-1(K) a in cl A, f(x) not in cl f(A) Consequently ** iff * iff f:X -> Y continuous at a. QED. In addition, an alternative definition. f:X -> Y continuous at a iff for all open U nhood f(a), a in int f^-1(U) ---- === Subject: Re: Topology with continuous at a. > f : (X, T) -> (Y, T') For all A subset X such that a in cl(A), > If f(a) in cl[f(A)], then f is continuous at a in X. -------------------------------------------- > Prove or counter-example. > Sorry, I need your advice. It is true. Suppose that _f_ was not continuous at _a_. Then there would be an open subset A of Y such that f^{-1}(A) would not be a neighborhood of _a_. In other words, every neighborhood of _a_ contains points of f^{-1}(CA). This is equivalent to the assertion that _a_ belongs to cl(f^{-1}(CA)). But f(a) does not belong to cl(f(f^{-1}(CA))) = cl(CA) = CA. Jose Carlos Santos === Subject: Re: Topology with continuous at a. > f : (X, T) -> (Y, T') > For all A subset X such that a in cl(A), > If f(a) in cl[f(A)], then f is continuous at a in X. > -------------------------------------------- > Prove or counter-example. > Sorry, I need your advice. It is true. Suppose that _f_ was not continuous at _a_. Then there would be an open > subset A of Y such that f^{-1}(A) would not be a neighborhood of _a_. In > other words, every neighborhood of _a_ contains points of f^{-1}(CA). > This is equivalent to the assertion that _a_ belongs to cl(f^{-1}(CA)). > But f(a) does not belong to cl(f(f^{-1}(CA))) = cl(CA) = CA. Oh, very nice ! A is some open set of f(a). cl(f(f^{-1}(CA))) subset cl(CA). C = Y. === Subject: Re: Topology with continuous at a. > f : (X, T) -> (Y, T') For all A subset X such that a in cl(A), > If f(a) in cl[f(A)], then f is continuous at a in X. -------------------------------------------- > Prove or counter-example. > Sorry, I need your advice. > It is true. > Suppose that _f_ was not continuous at _a_. Then there would be an open > subset A of Y such that f^{-1}(A) would not be a neighborhood of _a_. In > other words, every neighborhood of _a_ contains points of f^{-1}(CA). > This is equivalent to the assertion that _a_ belongs to cl(f^{-1}(CA)). > But f(a) does not belong to cl(f(f^{-1}(CA))) = cl(CA) = CA. Oh, very nice ! > A is some open set of f(a). > cl(f(f^{-1}(CA))) subset cl(CA). > C = Y. complement of A. Jose Carlos Santos === Subject: Elementary Calculus posting-account=hH_9UQoAAAAG4Vzyx-4ZVDXIWA0UKGHA CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Can anyone please help me find a solution to the following problems. 1. The set of pairs of positive real (x,y) such that (x power y) = (y power x) form the straight line y = x and a curve. The point at which the curve cuts the line is : (a) (e,e) (b) (1,1) (c) (e square, e square) (d) None of these 2. f(x) is defined for x>-1 and has a continuous derivative. It satisfies f(0)=1; f'(0) = 0 and (1+f(x)) f(x) = 1+x, then, (a) Graph of f'(x) is: (i) Always Convex (ii) Always concave (iii) first concave then convex (iv) first convex then concave (b) Max value of f'(1) is (i) 1 (ii) 1/3 (iii) 2/3 (iv) 3/4 (c) f'(-1) is always (i) >= +1/4 (ii) <= 1/4 (iii) >= -1/4 (iv) < = -1/4 === Subject: Re: Elementary Calculus posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > Can anyone please help me find a solution to the following problems. 1. The set of pairs of positive real (x,y) such that (x power y) = (y > power x) form the straight line y = x and a curve. The point at which > the curve cuts the line is : > (a) (e,e) (b) (1,1) (c) (e square, e square) (d) None of these 2. f(x) is defined for x>-1 and has a continuous derivative. It > satisfies f(0)=1; f'(0) = 0 and > (1+f(x)) f(x) = 1+x, then, (a) Graph of f'(x) is: > (i) Always Convex (ii) Always concave (iii) first concave then > convex > (iv) first convex then concave (b) Max value of f'(1) is > (i) 1 (ii) 1/3 (iii) 2/3 (iv) 3/4 (c) f'(-1) is always > (i) >= +1/4 (ii) <= 1/4 (iii) >= -1/4 (iv) < = -1/4 What have you done so far? Show your work. R.G. Vickson === Subject: Re: JSH: Some basics about factoring > First off, if you have z^2 = y^2 + nT > where T is your target to factor, ... > (z-y)(z+y) = nT. Well if T is a product of odd primes, then you always have that. Let z = T+1 and let y = T-1, and of course n = 2. Then (z-y)(z+y) = ((T+1)-(T-1))((T+1)+(T-1)) = (T+T)(2) = 2T = nT. What makes you think that will help you factor T? === Subject: Re: JSH: Some basics about factoring anything except 6 Keywords: KW >I only think JSH's formula factors composites made of primes. 2 and 3 aren't primes? It would probably be trivial for JSH to fix my complaints about > his proof, but it's also too much work for him. He can limit it > to factoring composites T > 100 or something, and say at some point > in his proof that this restriction guarantees that there are prime > values for some variable or other that satisfy whatever inequalities > he sets up. Then he can get on to the important part where he asks you to hunt > for a prime needle in a haystack, without any proof that the haystack > has a needle in it. > T < 7 === Subject: Re: JSH: Some basics about factoring <1371b$484c8463$9999@news.teranews.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) T = 18089363, I get the prime factorization: > 1867* 9689 > z+y = 9689 > z- y = 1867 > and of course (z+y)*(z-y) = T . > Maybe there's one thing I'm not so clear about: > how few of the possible 'p' candidates are needed to > find x and y (roughly) ? I abandoned this approach once I realized that for p to work it had to > be true that 2f_1 - f_2 = 0 mod p where f_1*f_2 = nT, as it seems increasingly unlikely that you'd find > enough primes that would work as T increases in size. As a sidenote though the z_0/(3p) steps result is just a remarkably > neat result to me, though yes, you do need to know p to get it to > work, but p=3 would work in this case to give you an upper limit on z. p = 3 always works. > Rick Yeah, I know, as with T mod 3 = 2, then 2f_1 - f_2 = 0 mod 3 for some combination of f_1 and f_2 when f_1*f_2 = T. So you can always get an upper limit on positive z, where z^2 = y^2 + T, when T mod 3 = 2. Sort of a weirdly nifty result to me, as for those who wonder how you do it, calculate z_0 where it is the maximum z_0 divisible by 3 such that abs(T - 8z_0^2/9) is a minimum, and then the MAXIMUM z will be within z_0/9 steps by 9 of that value. That is, starting your check with z_0, you will find z by going z_0 + 9, z_0 + 18, and so forth for a number of steps that is within z_0/9. ___JSH === Subject: Re: JSH: Some basics about factoring >snip> T = 18089363, I get the prime factorization: > 1867* 9689 > z+y = 9689 > z- y = 1867 > and of course (z+y)*(z-y) = T . > Maybe there's one thing I'm not so clear about: > how few of the possible 'p' candidates are needed to > find x and y (roughly) ? > I abandoned this approach once I realized that for p to work it had to > be true that > 2f_1 - f_2 = 0 mod p > where f_1*f_2 = nT, as it seems increasingly unlikely that you'd find > enough primes that would work as T increases in size. > As a sidenote though the z_0/(3p) steps result is just a remarkably > neat result to me, though yes, you do need to know p to get it to > work, but p=3 would work in this case to give you an upper limit on z. > p = 3 always works. > Rick Yeah, I know, as with T mod 3 = 2, then 2f_1 - f_2 = 0 mod 3 for some > combination of f_1 and f_2 when f_1*f_2 = T. So you can always get an upper limit on positive z, where z^2 = y^2 + > T, when T mod 3 = 2. Sort of a weirdly nifty result to me, as for those who wonder how you > do it, calculate z_0 where it is the maximum z_0 divisible by 3 such > that abs(T - 8z_0^2/9) is a minimum, and then the MAXIMUM z will be within z_0/9 steps by 9 > of that value. That is, starting your check with z_0, you will find z by going z_0 + > 9, z_0 + 18, and so forth for a number of steps that is within z_0/9. > Sometimes, but not always. In the example above z_0 = 4512, z = 5778 and they are 1266 = 3 * 422 apart. That's not a multiple of 9. When I said p = 3 always works, I didn't intend it to mean p = 3 always works as a jump multiplier, I intended that 3 will always be a prime you can use in your original (since discarded) method. Rick === Subject: Re: A Curious Question >| > A Curious Question >| > ~v~~ >| >| > Is there anything which is not predicated of not? >| >| > ~v~~ >| | > Well, since anything that is predicated is predicated of a subject, >| > and not is not a subject, it follows that everything is not >| > predicated of not. >| | > Two dollars, please. >| | > Next question. >| | > PD >| >| I'm confused... isn't not the subject of this here thread? No, it is not. Or yes, it is not. -- >Why did Einstein say >the speed of light from A to B is c-v, >the speed of light from B to A is c+v, >the time each way is the same? 1/2[tau(A)+tau(A')]= tau(B) >where >A = (0,0,0,t) >A' =(0,0,0,t+x'/(c-v) +x'/(c+v)) >B = (x',0,0,t+x'/(c-v)) >x' = x-vt Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif Easy: he did NOT say that. - cretin harald.vanlintelButNotThis@epfl.ch >Androcles Androcles, I'm perfectly willing to discuss relativity. the Pioneer 10/11 anomaly, or even dark matter. I'm just sick of seeing these subjects raised and reraised in the same old childish form. Who cares what Einstein said? The problem is not what's wrong with what Einstein did or didn't say but what's right. And unless you have something specific to correct and clarify Michelson-Morley etc. etc. there's really nothing to add. The usenet is already littered with the same old stupid arguments. ~v~~ === Subject: Re: A Curious Question A Curious Question > ~v~~ Is there anything which is not predicated of not? ~v~~ > Well, since anything that is predicated is predicated of a subject, > and not is not a subject, it follows that everything is not > predicated of not. > Two dollars, please. > Next question. > PD > I'm confused... isn't not the subject of this here thread? When Zick posts, don't count on reason. I assumed you count on your fingers and toes like any good modern mathematker, Virgil. Since when did you start counting on reason? ~v~~ === Subject: Re: A Curious Question > A Curious Question > ~v~~ Is there anything which is not predicated of not? ~v~~ > Well, since anything that is predicated is predicated of a subject, > and not is not a subject, it follows that everything is not > predicated of not. > Two dollars, please. > Next question. > PD I'm confused... isn't not the subject of this here thread? You know, Kyle, I've been reading your post for several days now trying to understand the point. But I think it finally dawned on me. Maybe it's just too much vodka. If my interpretation is correct, the comment is perfectly valid and warranted although I would have suggested that the subject is not only not but also its various compoundings as well. In any event you'll notice the typical academic's misconstructions interpolated in the usual form of since's, whereas's, and therefore's used to make a trivial case totally irrelevant to the subject at hand. Much grass. ~v~~ === Subject: Re: A Curious Question A Curious Question > ~v~~ Is there anything which is not predicated of not? ~v~~ > Any object you care to mention is not predicated of not. > Would you care to mention some and explain to us exactly how they're > not predicated of not? > 'Not' is not predicated of any o bject, > It's not? ~v~~ > Yes, it's not. I'm fine with that. Except that you've just predicated not of not. ~v~~ Yes. That's fine. 'Predicate' is ambiguous. It can mean property, reference, association, grammatical or otherwise, or simply juxtaposition; god knows what else. Don't use the word. === Subject: Re: A Curious Question > A Curious Question > ~v~~ > Is there anything which is not predicated of not? > ~v~~ > Any object you care to mention is not predicated of not. > Would you care to mention some and explain to us exactly how they're > not predicated of not? 'Not' is not predicated of any o bject, > It's not? > ~v~~ > Yes, it's not. I'm fine with that. > Except that you've just predicated not of not. > ~v~~ Yes. That's fine. 'Predicate' is ambiguous. It can mean property, >reference, association, grammatical or otherwise, or simply >juxtaposition; god knows what else. Don't use the word. Predicate is no more ambiguous than its definition and I choose to define it in terms of properties to which a thing is subject. If you choose to define predicate or anything else ambiguously, then of course it will be ambiguous. There are no absolute definitions of things floating around space, only definitions of things mutually consistent with other things in a common reference frame, and subject and predicate as I define them are perfectly consistent and unambiguous in that regard. Nor can you appeal to definitions used by others to insist that I have to use their definitions and that my usage is ambiguous because the combination of all their various definitions is. ~v~~ === Subject: Re: A Curious Question > A Curious Question > ~v~~ Is there anything which is not predicated of not? ~v~~ > Any object you care to mention is not predicated of not. > Would you care to mention some and explain to us exactly how they're > not predicated of not? > 'Not' is not predicated of any o bject, > It's not? ~v~~ > Yes, it's not. I'm fine with that. > Except that you've just predicated not of not. ~v~~ > Yes. That's fine. 'Predicate' is ambiguous. It can mean property, > reference, association, grammatical or otherwise, or simply > juxtaposition; god knows what else. Don't use the word. Predicate is no more ambiguous than its definition and I choose to > define it in terms of propertie to which a thing is subject. If you > choose to define predicate or anything else ambiguously, then of > course it will be ambiguous. There are no absolute definitions of > things floating around space, only definitions of things mutually > consistent with other things in a common reference frame, and > subject and predicate as I define them are perfectly consistent > and unambiguous in that regard. Nor can you appeal to definitions used > by others to insist that I have to use their definitions and that my > usage is ambiguous because the combination of all their various > definitions is. ~v~~ 'Predicated not of not' - predicate looks like a juxtaposition to me. === Subject: Re: A Curious Question > A Curious Question > ~v~~ > Is there anything which is not predicated of not? > ~v~~ > Any object you care to mention is not predicated of not. > Would you care to mention some and explain to us exactly how they're > not predicated of not? > 'Not' is not predicated of any o bject, > It's not? > ~v~~ > Yes, it's not. I'm fine with that. > Except that you've just predicated not of not. > ~v~~ > Yes. That's fine. 'Predicate' is ambiguous. It can mean property, > reference, association, grammatical or otherwise, or simply > juxtaposition; god knows what else. Don't use the word. > Predicate is no more ambiguous than its definition and I choose to > define it in terms of propertie to which a thing is subject. If you > choose to define predicate or anything else ambiguously, then of > course it will be ambiguous. There are no absolute definitions of > things floating around space, only definitions of things mutually > consistent with other things in a common reference frame, and > subject and predicate as I define them are perfectly consistent > and unambiguous in that regard. Nor can you appeal to definitions used > by others to insist that I have to use their definitions and that my > usage is ambiguous because the combination of all their various > definitions is. > ~v~~ 'Predicated not of not' - predicate looks like a juxtaposition to me. So? ~v~~ === Subject: Re: A Curious Question > 'Not' is not predicated of any object, > It's not? > Perhaps we will have to file an amicus brief, or intervene in some manner? mk5000 (I force my eyes open, and now who has changed? > I feel different, so different today) > Did you really change y our mind? > Could this be your only crime? --sleater kinney, burn don't freeze > I can say 'not is not predicated of a thing'. You can say anything you want but that doesn't make it true. For > having said not is not predicated of a thing you've just predicated > not of a thing 'not predicated of a thing' isn't a thing. > and as previously pointed out this is no different > than saying blue is not predicated of not. The only correct answer to the question is that there is no thing > which is not predicated of not. > Of a thing and another > thing, 'not' always describes another thing. It is a term that is used > in place of another. So another dog isn't this particular dog. Except how do you figure that out? Is there some mystical insight > roaming the universe giving you the power to divine what is and isn't? Yes, good mystics everywhere should know what I am talking about because they have common sense. 'Not' means another. Common sense. No rabbits or hats. > You claim this dog is not that dog but in order to know this you > have to analyze differences or not's in relation to one another, > which in turn means everything must be predicated of not to begin > with. Yes! Everything is predicated of not in the rationale that has been offered by others here. A negation is an act - 'from this to that', and not 'this and that', or 'this or that'. > The ambiguous term 'predication' allows a confusion between grammatical > convenience or mere association of terms, with actual meaning or property. Actual meaning or property? Shirley you jest. The purpose of grammar > and language is to figure out what actual meanings and properties > are based on relations between and among tautological alternatives. What? 'predicate' can mean a number of things. It's a lazy word. > Yours is just another version of the antiquated mystical doctrine of > positivism, or intuitive empiricism, where there are supposed to be > innate, actual things floating around the universe just waiting to > be divined without any kind of reasoning, logic, or demonstration of > truth, and the only purpose of language and grammar is to catalog > these elemental actual meanings and properties. I'm drawing on the empirical, real world. We have no reason to draw on any other. We cannot draw on 'abstract', 'transcendent' things without saying goodbye to meaning. > Why do you think there are so many philosophies floating around, none > of which are demonstrably correct and most of which are demonstrably > incorrect? Simply because no one has been able to achieve a > demonstrably true mechanical reduction of actual meaning and > properties to grammar and language. So philosophers just run off at > the mouth with their catalogs of actual meanings and properties > whose truth their language and grammar are useless to demonstrate. Yes, you are talking about 'transcendent' objects and ideas - these have no worldly basis. > This is why nature abhors philosophers. They know where to throw the spanner. > As I said before, the term 'predicate' sounds impressive, but that's all > that's good about it. Its a pig of a word to use. Never use it again. Well here you're just grasping at straws to excuse your own lack of > understanding of the purpose of the question. Try the same question another way: Is there anything not subject to 'not'? And the answer, of course, is no. No thing is subject to not. It's self-evident. There is no state of not a thing. === Subject: Re: A Curious Question > and as previously pointed out this is no different > than saying blue is not predicated of not. > The only correct answer to the question is that there is no thing > which is not predicated of not. > Of a thing and another > thing, 'not' always describes another thing. It is a term that is used > in place of another. So another dog isn't this particular dog. > Except how do you figure that out? Is there some mystical insight > roaming the universe giving you the power to divine what is and isn't? Yes, good mystics everywhere should know what I am talking about because >they have common sense. 'Not' means another. Common sense. No rabbits or >hats. Nonsense. Mystics have mysticism. Not applied to single operands means all others. ~v~~ === Subject: Re: A Curious Question > Yours is just another version of the antiquated mystical doctrine of > positivism, or intuitive empiricism, where there are supposed to be > innate, actual things floating around the universe just waiting to > be divined without any kind of reasoning, logic, or demonstration of > truth, and the only purpose of language and grammar is to catalog > these elemental actual meanings and properties. I'm drawing on the empirical, real world. We have no reason to draw on >any other. We cannot draw on 'abstract', 'transcendent' things without >saying goodbye to meaning. Well certainly you can't. Why is unclear just as the reason why you choose to speak for everyone else on the subject. All you're doing is making absurd categorical assertions whose truth you have no capacity to demonstrate. Modern math and empiricism may be soft sciences but philosophy is no science at all. ~v~~ === Subject: Re: A Curious Question > This is why nature abhors philosophers. They know where to throw the spanner. Those who know nothing tend to throw spanners in whatever directions they feel like true or not. ~v~~ === Subject: Re: A Curious Question > You claim this dog is not that dog but in order to know this you > have to analyze differences or not's in relation to one another, > which in turn means everything must be predicated of not to begin > with. Yes! Everything is predicated of not in the rationale that has been >offered by others here. A negation is an act - 'from this to that', and >not 'this and that', or 'this or that'. So far no one has concurred that everything is predicated of not. They've just been moaning and groaning about the significance of predication. ~v~~ === Subject: Re: A Curious Question > I can say 'not is not predicated of a thing'. > You can say anything you want but that doesn't make it true. For > having said not is not predicated of a thing you've just predicated > not of a thing 'not predicated of a thing' isn't a thing. Of course it is. What would make you think otherwise? The phrase not predicated of a thing has properties which can be predicated of it. The phrase can be talked about, described, and otherwise denoted. Even the fact that you claim the phrase isn't a thing makes it a thing because you're specifying analyzable predicates of the thing.. ~v~~ === Subject: Re: A Curious Question > Why do you think there are so many philosophies floating around, none > of which are demonstrably correct and most of which are demonstrably > incorrect? Simply because no one has been able to achieve a > demonstrably true mechanical reduction of actual meaning and > properties to grammar and language. So philosophers just run off at > the mouth with their catalogs of actual meanings and properties > whose truth their language and grammar are useless to demonstrate. Yes, you are talking about 'transcendent' objects and ideas - these have >no worldly basis. But philosophers' stones do? Pure nonsense. No wonder philosophers have stones: they need them to assert the categorical nonsense whose truth they can't demonstrate. ~v~~ === Subject: Re: A Curious Question > The ambiguous term 'predication' allows a confusion between grammatical > convenience or mere association of terms, with actual meaning or property. > Actual meaning or property? Shirley you jest. The purpose of grammar > and language is to figure out what actual meanings and properties > are based on relations between and among tautological alternatives. What? 'predicate' can mean a number of things. It's a lazy word. No. It's only a lazy word for those too lazy or stupid to define it accurately and unambiguously. Which unfortunately seems to include the majority of those here. ~v~~ === Subject: Re: A Curious Question > As I said before, the term 'predicate' sounds impressive, but that's all > that's good about it. Its a pig of a word to use. Never use it again. > Well here you're just grasping at straws to excuse your own lack of > understanding of the purpose of the question. > Try the same question another way: > Is there anything not subject to 'not'? > And the answer, of course, is no. No thing is subject to not. It's self-evident. There is no state of not >a thing. Of course there is. Not A specifies everything not A. Everything is subject to not and not is true of everything because not not is self contradictory and hence false. Now I realize this is not obvious to intuitionist mystics like philosophers, but it's necessarily true because it tautologically exhausts all possibilities for truth. ~v~~ === Subject: Re: A Curious Question > A Curious Question > ~v~~ > Is there anything which is not predicated of not? >No. On the contrary, *only* not is a predicate of the universal set >U, where ~U is the empty coset E (and ~E = U). Remarkable. Someone actually agrees with me? ~v~~ === Subject: Practical Logistic Problem faced by Doctor! posting-account=4ggQjgoAAAA3qS-MQio-SptjUcmd715b 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) A medical doctor has set up a clinic in a new town whose population is increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling certain virus. With constant R&D by pharmaceutical company, the quality of vaccine improves over time. Dilema: Doctor has to restock before the vacine quantity runs to zero. If the doctor orders too much of batch 1 vacine, and by the time batch 2 vacine is already in the market, he would have too much spare stocks of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of constant improvement of drug and increasing population? Is it possible to model it mathematically (or statistically)? === Subject: Re: Practical Logistic Problem faced by Doctor! posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > A medical doctor has set up a clinic in a new town whose population is > increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling > certain virus. With constant R&D by pharmaceutical company, the > quality of vaccine improves over time. Dilema: > Doctor has to restock before the vacine quantity runs to zero. If the > doctor orders too much of batch 1 vacine, and by the time batch 2 > vacine is already in the market, he would have too much spare stocks > of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of > constant improvement of drug and increasing population? Is it possible > to model it mathematically (or statistically)? related: http://www.springerlink.com/content/w7r625xw8m48745x/ Some models that deal with obsolescence in inventory management are: http://www.jg.nus.edu.sg/publication/ObsolescenceEJOR.pdf http://cat.inist.fr/?aModele=afficheN&cpsidt=3086169 R.G. Vickson === Subject: Re: Practical Logistic Problem faced by Doctor! posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) A medical doctor has set up a clinic in a new town whose population is > increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling > certain virus. With constant R&D by pharmaceutical company, the > quality of vaccine improves over time. Dilema: > Doctor has to restock before the vacine quantity runs to zero. If the > doctor orders too much of batch 1 vacine, and by the time batch 2 > vacine is already in the market, he would have too much spare stocks > of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of > constant improvement of drug and increasing population? Is it possible > to model it mathematically (or statistically)? related:http://www.springerlink.com/content/w7r625xw8m48745x/ Sorry: that is the wrong citation. Use instead and click on the menu item carregue o artigo em formato pdf to download the free version (in English). R.G. Vickson Some models that deal with obsolescence in inventory management are: http://www.jg.nus.edu.sg/publication/ObsolescenceEJOR.pdfhttp://cat.inist.fr / ?aModele=afficheN&cpsidt=3086169 R.G. Vickson === Subject: Re: Practical Logistic Problem faced by Doctor! posting-account=4ggQjgoAAAA3qS-MQio-SptjUcmd715b 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > A medical doctor has set up a clinic in a new town whose population is > increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling > certain virus. With constant R&D by pharmaceutical company, the > quality of vaccine improves over time. Dilema: > Doctor has to restock before the vacine quantity runs to zero. If the > doctor orders too much of batch 1 vacine, and by the time batch 2 > vacine is already in the market, he would have too much spare stocks > of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of > constant improvement of drug and increasing population? Is it possible > to model it mathematically (or statistically)? related:http://www.springerlink.com/content/w7r625xw8m48745x/ and click on the menu item carregue o artigo em formato pdf to > download the free version (in English). R.G. Vickson Some models that deal with obsolescence in inventory management are: http://www.jg.nus.edu.sg/publication/ObsolescenceEJOR.pdfhttp://cat.i... R.G. Vickson- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - Yes, obsolence approach is not relevant, as the vacine still can be used, just that over time the quality improved. Using deteorating approach looks similar but different. In this case, the current stock of vacine does not deteorate in store per se, but relatively speaking it does 'deteorate' when compared to newer release. === Subject: Re: Practical Logistic Problem faced by Doctor! posting-account=JILe_QoAAADtPnW0lAgx7u5b-dq5cREW 1.1.4322),gzip(gfe),gzip(gfe) > A medical doctor has set up a clinic in a new town whose population is > increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling > certain virus. With constant R&D by pharmaceutical company, the > quality of vaccine improves over time. Dilema: > Doctor has to restock before the vacine quantity runs to zero. If the > doctor orders too much of batch 1 vacine, and by the time batch 2 > vacine is already in the market, he would have too much spare stocks > of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of > constant improvement of drug and increasing population? Is it possible > to model it mathematically (or statistically)? I imagine it is possible. I wouldn't be surprised if someone has already done it. Some statistics that would come in would be random variation in the release (and/or delivery) times of the vaccine upgrades, variation in the rate of people wanting vaccinations, and how much does the each upgrade of the vaccine improve? Those could modeled, I don't know how well or how much it matters depending on other factors, or one could assume some constant values and proceed from there. Other factors to consider are how much profit does the doctor want to make (e.g. money lost from discarding old stock) vs. how much of a supply cushion does he/she want/need to have to in case of supply disruptions, slow delivery, etc. Also how serious is the disease? Most people would suggest a larger supply cushion for a deadly disease than for a disease that is no more than uncomfortable. What is the rate of complications from the vaccine and how severe are they compared to the disease (presumably the vaccine is safe and effective, so this probably isn't a major question to consider). Another subproblem would be what level of pre-existing vaccination is there? At a certain level epidemic spread in a population becomes unlikely. There are extensive references on this topic. Anyway, one needs to specify various criteria that are desired in the solution. There are probably other consideration that have not come to mind. Russell === Subject: Re: Practical Logistic Problem faced by Doctor! posting-account=4ggQjgoAAAA3qS-MQio-SptjUcmd715b 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) A medical doctor has set up a clinic in a new town whose population is > increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling > certain virus. With constant R&D by pharmaceutical company, the > quality of vaccine improves over time. Dilema: > Doctor has to restock before the vacine quantity runs to zero. If the > doctor orders too much of batch 1 vacine, and by the time batch 2 > vacine is already in the market, he would have too much spare stocks > of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of > constant improvement of drug and increasing population? Is it possible > to model it mathematically (or statistically)? I imagine it is possible. æI wouldn't be surprised if someone > has already done it. æSome statistics that would come in would > be random variation in the release (and/or delivery) times of > the vaccine upgrades, variation in the rate of people wanting > vaccinations, and how much does the each upgrade of the vaccine > improve? æThose could modeled, I don't know how well or how > much it matters depending on other factors, or one could assume > some constant values and proceed from there. Other factors to consider are how much profit does the doctor > want to make (e.g. money lost from discarding old stock) vs. how > much of a supply cushion does he/she want/need to have to in > case of supply disruptions, slow delivery, etc. æAlso how > serious is the disease? æMost people would suggest a larger > supply cushion for a deadly disease than for a disease that is > no more than uncomfortable. æWhat is the rate of complications > from the vaccine and how severe are they compared to the > disease (presumably the vaccine is safe and effective, so this > probably isn't a major question to consider). æAnother > subproblem would be what level of pre-existing vaccination is > there? æAt a certain level epidemic spread in a population > becomes unlikely. æThere are extensive references on this > topic. æAnyway, one needs to specify various criteria that are > desired in the solution. æThere are probably other consideration > that have not come to mind. Russell- Hide quoted text - - Show quoted text - Now, lets keep it simple. Its a new town, and a new virus has been discovered and found to infect a few people. What is the optimal inventory level for the vacine given: 1. Town population is expanding 2. Doctor wont know when the new vacine will be developed and will only know it upon the latest order. If at the point of order there is now news on new vacine, it will be the current vacine that will be ordered. There is certain trade-off here: on one hand the town population is increasing and the doctor would like to have certain inventory level to manage the town's health. On the other hand, drugs keep improving and if the Doctor has too much of the current vacine on hand while a new version is introduced he will incur a huge cost to discard it and purchase the new one. This leads to the original question: what is the optimized level of inventory to have? === Subject: Re: Practical Logistic Problem faced by Doctor! posting-account=JILe_QoAAADtPnW0lAgx7u5b-dq5cREW 1.1.4322),gzip(gfe),gzip(gfe) > A medical doctor has set up a clinic in a new town whose population is > increasing at X number of people per week. He has keep stock of certain new vacine which is good in controlling > certain virus. With constant R&D by pharmaceutical company, the > quality of vaccine improves over time. Dilema: > Doctor has to restock before the vacine quantity runs to zero. If the > doctor orders too much of batch 1 vacine, and by the time batch 2 > vacine is already in the market, he would have too much spare stocks > of batch 1 vacine. Question: What is the quantity of vacine to order as spare stocks, in view of > constant improvement of drug and increasing population? Is it possible > to model it mathematically (or statistically)? I imagine it is possible. æI wouldn't be surprised if someone > has already done it. æSome statistics that would come in would > be random variation in the release (and/or delivery) times of > the vaccine upgrades, variation in the rate of people wanting > vaccinations, and how much does the each upgrade of the vaccine > improve? æThose could modeled, I don't know how well or how > much it matters depending on other factors, or one could assume > some constant values and proceed from there. Other factors to consider are how much profit does the doctor > want to make (e.g. money lost from discarding old stock) vs. how > much of a supply cushion does he/she want/need to have to in > case of supply disruptions, slow delivery, etc. æAlso how > serious is the disease? æMost people would suggest a larger > supply cushion for a deadly disease than for a disease that is > no more than uncomfortable. æWhat is the rate of complications > from the vaccine and how severe are they compared to the > disease (presumably the vaccine is safe and effective, so this > probably isn't a major question to consider). æAnother > subproblem would be what level of pre-existing vaccination is > there? æAt a certain level epidemic spread in a population > becomes unlikely. æThere are extensive references on this > topic. æAnyway, one needs to specify various criteria that are > desired in the solution. æThere are probably other consideration > that have not come to mind. Russell- Hide quoted text - - Show quoted text - > Now, lets keep it simple. Its a new town, and a new virus has been discovered and found to > infect a few people. What is the optimal inventory level for the vacine given: > 1. Town population is expanding > 2. Doctor wont know when the new vacine will be developed and will > only know it upon the latest order. If at the point of order there is > now news on new vacine, it will be the current vacine that will be > ordered. There is certain trade-off here: > on one hand the town population is increasing and the doctor would > like to have certain inventory level to manage the town's health. On > the other hand, drugs keep improving and if the Doctor has too much of > the current vacine on hand while a new version is introduced he will > incur a huge cost to discard it and purchase the new one. This leads > to the original question: what is the optimized level of inventory to > have?- Hide quoted text - - Show quoted text - That limits the scope of the problem, but there are still a lot of things that would need to be specified. I think the problem might be amenable to being split, and the epidemiological portion of the model could be pretty well solved and coupled to a tractable economic model. I'm not sure the problem as you have stated it would be how things would likely happen in the real world, though. I think when stocks were getting low a reasonable order would be placed for whatever additional amounts are likely to be needed, regardless of whether it was a new formulation, and the stock on hand would be used until gone (not neglecting expiration date, of course). I doubt if the efficacy and safety of a new version would be enough improved to justify discarding the previous stock if it is expensive. But I am not a doctor, epidemiologist, or medical ethicist. Unless someone has solved that problem, I think it would be a bit of effort to formulate and solve the model. Since I have not I can't provide a definitive answer. One might consider qualitatively a few limiting cases, such as small vaccine differences and huge costs (as indicated above, it seems that in such a case the existing stocks would be used; what good is it to the townspeople to have their doctor go broke and leave?), small difference and small cost (given the small differences, who cares much in that case?; again, use up existing stocks on a principle of waste not, want not). It seems the case you're interested in is large vaccine differences and large cost. That case may require the serious model I've suggested to derive an answer, although someone more clever than I may be able to provide an back-of-the-envelope argument that is convincing. Russell === Subject: IRC network posting-account=RC9DiQoAAADnjG4io_u3Tn15T5QYyrfx 1.1.4322),gzip(gfe),gzip(gfe) rrba-ip-pcache-6 (NetCache NetApp/6.1.1D6) http://chat.webhop.org:8000 Our irc server supports 10000 users and we would like to support your survey on our network, you can connect using our java client at the obove address or you can use mirc to connect at the below address chat.webhop.org using port 6667-8000 === Subject: Re: car's trajectory > I was surprised when I looked up Ackerman Steering: > http://www.auto-ware.com/setup/ack_rac.htm > They don't actually turn the front wheels at different angles > with the drag link/tie rod/steering knuckle geometry. > They depend on the tires to have slip, a measure of how > much the rubber can distort without losing traction. > _________________________________________________ > The Conventional Ackerman Steering concept is > to have all four wheels rolling around a common > point during a turn. The inside front tire must > be turned a larger number of degrees than the > outside front tire for this principle to work. How much of a difference does it make to the steering if the two back wheels > are not in line? I know this sounds a very unlikely scenario, but at least one car (Renault > 16 http://en.wikipedia.org/wiki/Renault_16) has a slight difference in the > wheelbase between left and right: in the case of the R16 it's 2.3 inches, to > accomodate torsion-bar suspension. For a second I thought you were talking about thrust angle (which is pointing the axis of both rear wheels somewhere other than parallel to the axis of the vehicle). That DOES have a big effect, and is a big part of how the current Cup-level NASCAR chassis (formerly called the Car of Tomorrow platform) is tuned. No longer can the body be mounted skewed on the chassis to help turn left, but the thrust axis can be diddled so that the car is crabbing a bit which helps set it up for entering a left turn. As for different wheelbases left and right- that just sounds like typcal Renault crappy engineering :-p === Subject: Re: car's trajectory >I took enough college courses in engineering to graduate. >I paid the nominal citizen subsidized rate for the tuition >and bought and kept all my books. I buy texts quite >readily. To make the point, do you have anything to >recommend, or not? >______________________________________________ >The previous recommendations are probably the best: >Invest your education in something more productive than >feigning ignorance to trick newsgroup readers into trying >to answer open-ended questions, demanding extensive >mathematical proofs, finally admitting your own expertise >and expressing contempt for those who tried to help. >Don't let yourself deteriorate into a trolling pedantic nit. >Good luck. >Rodan. > That you do not read here in sed much, it is clear. I do not have the > time mess with ignorance, when i challenge ASSumptions it is legit. I > do not want poppycock propagated as truth. This is a technical > newsgroup, i expect those that would wish to contribute to have their > act together. If you want my respect, bring the math when i ask for > it. > In other words, you can't translate the simple explanations already presented to you into whatever formal mathematical form you prefer, and therefore prefer to denigrate other posters genuinely trying to be helpful rather than address your own shortcomings. Don't let the door hit you in the ass on the way out. nate -- replace roosters with cox to reply. http://members.cox.net/njnagel === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 1.1.4322),gzip(gfe),gzip(gfe) Gene Rodentvery, he was called, galactic schkockmeister. anyway, it sounds rather Laroucheyist to ascribe such British influence but, hey, the oxfordians do control the dictionary, the Rhodesian scholarship, and the goofey idea that Shakespeare was a front for the earl of O -- dumb-enough to be true, since they also hold all of the Shakespeare artifacts. more to the points, the slanders of Hooke and Liebniz by the Royal Society are best to portray this ungainly influence over science. now, we can posit this influence to be extended to the Perimeter Inst. which pays Smoilin to produce his phoney strings v. loops harangues, and arbitrary multiversal values of pi; I mean, what are loops, but closed strings? of course, there is a lot heat with the light of these recriminations & hoaxes; meaning, a lot of passionate, real debate of dots v. integrals, quaternions v. vectors, there is nothing wrong with superstrings, other than being so much of a superset of the SM, in the end. > but it is _not_ that popular within the scientific community. thus: bravo. the spatial insufflators will have to deal with that!... yo, time is not a dimension, or conversely, time is the only dimension of consequence, to paraphrase Bucky Fullerofit. > He is refering to the interval which is a quadratic function in space > and time co-ordinates that defines a hyperboloid. If the interval is > equal to zero (as it is on a llight like world line) you get > x^2 - t^2 - 0. This has nothing to do with curvature. Curvature is a > special kind of tensor defined on a manifold. This approach was > originated by Gauss and Riemann and was extended by Levi-Civita and others. thus: apples & oranges both in the fruitsalad, Fruitcake. now, the corn-based ethanol is accelerating desertification in the Midwest & must be totally eliminated, before the complete vertical integration of the energy and the grain cartels, you alleged cheapskate. however, the new gambling silos can still be used for ensilage & cellulose/lignin residues, to make ethanol or what ever. in any case, the best such sources are perennials (a-hem; trees -- make pollution, two, as saith Reaganomics .-) in case that you didn't notice, the financial cartel bought a chunk of the electoral process in December'99, the Financial Services Modernization Act; take your virtual polling-place receipt to your bank, because they have more leverage & expertise with Automatic Voting Machines (there is no provision in the Help America Vote Act to actually look at anything, after they called the election on TV), and the same applies to Scamtrons. indeed, there is nothing like a good, old chad for recounting purposes; the whole debate was a farce, and Al Lost on his own dime in Florida and Arkansas (and Michigan (sik)), either of which had enoufh electoral college votes to stop Trickier Dick Cheeny I mean, bankers are people, also! > Now class, think hard: Which is the cheaper way to go; gasoline or etha85%? > If you're not counting the cost of the extra time and inconvenience due as noted in a pro-biofuel letter to the editor, ethanol has been subsidized for 25 years. anyway, it's all BS, because you're relying on the energy cartel's ersatz definition of fossil fuels. let us recall, Al Sr. and Jr.'s careers were made by an oil company, and all of *them* just *love* the Kyoto Protocol, just as they do with all of the emmissions trading schemes of Bush'91, and the Montreal Protocol precedent from DuPont: their patents had expired on Freons. > That's why I went to E85. It's cheap, it's clean, and it's hot. I > Just wait til you can get a Saab bio-power model. That'll put an ever bigger grin on your face. -UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?... La Troi Phases d'Exploitation de la Protocols des Grises de Kyoto: (FOSSILISATION [McCainanites] (TM/sic))/ BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm. Http://www.tarpley.net/bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de COUP D'ETAT, 3/30/81 === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.20,gzip(gfe),gzip(gfe) whether wh*t's-h*s-n*m* actually worshipped E., the latter-day producers of Star Trek took his essential programme to its positivist extreme, in the holodecked adumbration of Newton, E., and Hawking as a holey British Pyschologgical Society trinity. shucks, as the folks who brought you Flatland, who else did you think black holes came from, anyway, but by the belief in a nonlocal force, gravity, as the sole motivator for universal organiztion, the big bang, inflation etc. ad vomitorium? > Do mathematicians agree that string theory is internally self- > consistent? > It took Einstein 8 years to come up with a solution to his ñgrand > problemî and he couldnÍt have done it without the assistance of > mathematicians. It only took Hilbert several weeks to solve the > problem. > HilbertÍs derivation was based on an intuitive, formally unproved, > invariant theoretical fact. EinsteinÍs solution, probably as a hint > from Hilbert, contained no derivation at all.http://xxx.lanl.gov/abs/physics/0610154 > Then Einstein spend another 8 years trying to unify gravity and > electromagnetism, which culminated in EinsteinÍs 1923 papers on affine > unified field theory but this unification, as physicists admit, is > identical to HilbertÍs theory achieved in 1915.http://arxiv.org/abs/physics/0405110 > As IÍve said before, far too many physicists debase science and > themselves as modern evangelists by exalting Einstein to the status of > divinity. http://www.physicstoday.org/vol-58/iss-7/images/devine einstein.mp3http://www.bnl.gov/community/Tours/EinsteinPics/Einsteine.jpg http://larouchepub.com/eiw/public/2008/2008 1-9/2008-7/pdf/42-55 3507.pdf === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success <2sKdnUNLEPF75d_VnZ2dnUVZ_rPinZ2d@comcast.com> <3TA0k.74152$x55.43863@newsfe17.ams2> is outside conventions. Rude in the extreme! So, don't feel too smug there, sport. > Some people from some 'few developed' :-) countries has the bad habit > to use standard recommended character sets for Internet > http://en.wikipedia.org/wiki/UTF-8 > http://tools.ietf.org/html/rfc2277 > http://bp1.blogger.com/_Ap14FtNN91w/SBzrtHJfLnI/AAAAAAAAA5U/ TV7_g2_sWq0/ > s1600-h/Unicode2.gif > beyond the American 'sophisticated' :-) set and beyond the Western > also. > Does not Google Groups use UTF-8? > Just breakin' yer balls, friend. However, what Google Groups does or > does not support has nothing to do with the conventions I was talking > about. And, boy, does the mere suggestion that it does make my blood > boil! You just trolling me, friend? Did not heard recommendations that USENET would improve to UTF-8 like most of the web? I did not check but I think Google Groups already is using UTF-8 for messages. -- Center for CANONICAL |SCIENCE) http://canonicalscience.org === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > And you continually post to a Usenet group using a character set that > is outside conventions. Rude in the extreme! So, don't feel too smug there, sport. > Some people from some 'few developed' :-) countries has the bad habit > to use standard recommended character sets for Internet > http://en.wikipedia.org/wiki/UTF-8 > http://tools.ietf.org/html/rfc2277 > http://bp1.blogger.com/_Ap14FtNN91w/SBzrtHJfLnI/AAAAAAAAA5U/ > TV7_g2_sWq0/ > s1600-h/Unicode2.gif > beyond the American 'sophisticated' :-) set and beyond the Western > also. > Does not Google Groups use UTF-8? > Just breakin' yer balls, friend. However, what Google Groups does or > does not support has nothing to do with the conventions I was talking > about. And, boy, does the mere suggestion that it does make my blood > boil! You just trolling me, friend? Did not heard recommendations that USENET would improve to UTF-8 like > most of the web? I did not check but I think Google Groups already is using UTF-8 for > messages. NNTP protocol transmits between servers and between server and client by octets with the high bit 0. How newsreaders compose and render the octets is up to them: MIME, OLE, HOLY MOLE, seven bit ASCII. Many people prefer the octet interpretation with the least assumptions; at least on high traffic newsgroups with the widest possible readership and modes of reading such as, oh, for example, sci.math. Do you want to be understood, or want to stay on message? -- Michael Press === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success <2sKdnUNLEPF75d_VnZ2dnUVZ_rPinZ2d@comcast.com> <3TA0k.74152$x55.43863@newsfe17.ams2> octets with the high bit 0. How newsreaders compose and render the > octets is up to them: MIME, OLE, HOLY MOLE, seven bit ASCII. Many people > prefer the octet interpretation with the least assumptions; at least on > high traffic newsgroups with the widest possible readership and modes of > reading such as, oh, for example, sci.math. > Do you want to be understood, or want to stay on message? You are right. I have set it to ISO-8859-1. -- Center for CANONICAL |SCIENCE) http://canonicalscience.org === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success <2sKdnUNLEPF75d_VnZ2dnUVZ_rPinZ2d@comcast.com> <3TA0k.74152$x55.43863@newsfe17.ams2> NNTP protocol transmits between servers and between server and client > by octets with the high bit 0. How newsreaders compose and render the > octets is up to them: MIME, OLE, HOLY MOLE, seven bit ASCII. Many > people prefer the octet interpretation with the least assumptions; at > least on high traffic newsgroups with the widest possible readership > and modes of reading such as, oh, for example, sci.math. Do you want to > be understood, or want to stay on message? You are right. I have set it to ISO-8859-1. Trying again :-) -- Center for CANONICAL |SCIENCE) http://canonicalscience.org === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) My first opinion of string theory was formed while watching an > evangelist babel on about it for 3 hours. The evangelist presented it > as a religion, not as science, which didnÍt surprise me because Brian > Greene is a physicist. Well, then, I'm not surprised that your assessment of string theory is > based on a TV program aimed at motivating the lay public rather than > at providing any real information about it. I wish that you will become more courageous and straightforward in > speaking the truth than that. Brian GreeneÍs string theory > presentation is aimed at motivating the lay public to worship. I've already told you that motivational presentations for the lay > public have the weakness of canonizing the proponents. You should admit that their *sole purpose* is for canonizing the > proponents. I completely disagree, ... the *primary* purpose is to get > people to think that the subject is interesting, so that they'll go > find out more about it. String theory, often described as the theory of everything, is a purely religious belief. > I see that this objective is underachieved, because you > not only are not motivated to go find out more about it, > but you don't even see the objective at all. The objective of TOE is to get everyone to believe that they can wrest from God all the secrets of the universe and that, with this knowledge, they will be able to remove God from His throne and will know how to begin to take over running the universe directly. Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) > My first opinion of string theory was formed while watching an > evangelist babel on about it for 3 hours. The evangelist presented it > as a religion, not as science, which didnÍt surprise me because Brian > Greene is a physicist. Well, then, I'm not surprised that your assessment of string theory is > based on a TV program aimed at motivating the lay public rather than > at providing any real information about it. I wish that you will become more courageous and straightforward in > speaking the truth than that. Brian GreeneÍs string theory > presentation is aimed at motivating the lay public to worship. I've already told you that motivational presentations for the lay > public have the weakness of canonizing the proponents. You should admit that their *sole purpose* is for canonizing the > proponents. I completely disagree, ... æthe *primary* purpose is to get > people to think that the subject is interesting, so that they'll go > find out more about it. String theory, often described as the theory of everything, is a > purely religious belief. Which is a religious statement in itself. Rejection of a theory on the basis of the self-aggrandizing manner of the host of a television show about the theory is hardly the proper basis by which to judge the merits of the theory, no matter how much it makes your blood simmer. I see that this objective is underachieved, because you > not only are not motivated to go find out more about it, > but you don't even see the objective at all. The objective of TOE is to get everyone to believe that they can wrest > from God all the secrets of the universe and that, with this > knowledge, they will be able to remove God from His throne and will > know how to begin to take over running the universe directly. Well, now, I think we have excavated a little closer to the center of your motivation, there, Shubee. You have revealed that you don't like scientists digging too deep, lest they bite of the tree of knowledge novel, condemning the investigations of scientists where they ought not tread. All the rest of this chaff about mathematics and Hilbert is just a cover story to mask your dislike of scientists trying to unmask everything. You are afraid that a bride unveiled will be cheapened. But on a less derisive note, I doubt seriously that mankind gets too fat a head from the actual practice of opening nature's kimono. If anything, most of the spectacular physicists experience a sense of awe and renewed appreciation for the elegance and beauty of what they uncover. And what's more, most physicists agree that the more they uncover, the more they find still covered up, with no end of work in sight. The notion that the theory of everything will lead to delusions of omnipotent power and mastery of the universe are, fortunately, unwarranted. PD === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > The notion that the theory of everything will lead to > delusions of omnipotent power and mastery of the universe are, > fortunately, unwarranted. Who coins and uses the phrase theory of everything? Serious researchers would do well to distance themselves thoroughly from such notions, lest they take themselves view of physics they are not in danger of uniting gravitation with any other working theories. Nor are they in danger of coming up with a theory of the electron. Plenty to do. -- Michael Press === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) The notion that the theory of everything will lead to > delusions of omnipotent power and mastery of the universe are, > fortunately, unwarranted. Who coins and uses the phrase theory of everything? > Serious researchers would do well to distance themselves > thoroughly from such notions, lest they take themselves > too seriously to be of use. Well, here, see, there's a difference between intent and perception. You perceive it as hubris. Physicists just use it as something that is T-shirt cute. There are few, if any, physicists who really believe that what they are working on is the be-all, end-all. > view of physics they are not in danger of uniting > gravitation with any other working theories. Nor are they > in danger of coming up with a theory of the electron. > Plenty to do. Agree completely. -- > Michael Press === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success The notion that the theory of everything will lead to delusions of > omnipotent power and mastery of the universe are, fortunately, > unwarranted. > Who coins and uses the phrase theory of everything? Serious > researchers would do well to distance themselves thoroughly from such > notions, lest they take themselves too seriously to be of use. Well, here, see, there's a difference between intent and perception. You > perceive it as hubris. Physicists just use it as something that is > T-shirt cute. Then the propaganda (in public arena) of string theory like the theory of everything may have been another unfair aspect. > There are few, if any, physicists who really believe that > what they are working on is the be-all, end-all. I wonder why then public has obtained so one idea about string theory :-) http://www.pbs.org/wgbh/nova/elegant/view-weinberg.html http://www.pbs.org/wgbh/nova/elegant/everything.html http://www.sns.ias.edu/~witten/papers/string.pdf http://en.wikipedia.org/wiki/String_theory http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html http://online.kitp.ucsb.edu/online/mt01teach/ http://www.redorbit.com/news/space/132303/ finding_the_ultimate_theory_of_everything/ http://www.hno.harvard.edu/gazette/2000/02.10/maldacena.html http://zebu.uoregon.edu/~js/21st_century_science/lectures/lec17.html http://open-site.org/Science/Physics/Modern/Theory_of_Everything/M-theory http://www.physics.fsu.edu/users/ProsperH/AST3033/theory.htm And all this over-hype on media, talks, popular books, papers... have given some funny parodies as http://insti.physics.sunysb.edu/~siegel/parodies/next.html -- Center for CANONICAL |SCIENCE) http://canonicalscience.org === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) String theory, often described as the theory of everything, is a > purely religious belief. Which is a religious statement in itself. Rejection of a theory on the > basis of the self-aggrandizing manner of the host of a television show > about the theory is hardly the proper basis by which to judge the > merits of the theory, no matter how much it makes your blood simmer. I reject the string religion because it's a labyrinth of more than 10^300 conflicting approaches of equally non-fundamental paths. http://www.everythingimportant.org/relativity/no-new-einstein.pdf > I see that this objective is underachieved, because you > not only are not motivated to go find out more about it, > but you don't even see the objective at all. The objective of TOE is to get everyone to believe that they can wrest > from God all the secrets of the universe and that, with this > knowledge, they will be able to remove God from His throne and will > know how to begin to take over running the universe directly. Well, now, I think we have excavated a little closer to the center of > your motivation, there, Shubee. You have revealed that you don't like > scientists digging too deep, lest they bite of the tree of knowledge > and be evicted from the garden. My position is just the opposite. I decry the shallowness of professional physicists for misunderstanding absolutely trivial fundamentals in the foundations of physics. > investigations of scientists where they ought not tread. I certainly agree with your analogy. Frankenstein, by Mary Shelley, illustrates perfectly the ghastly creations that physicists often assemble out of grotesquely disparate parts. The Frankenstein monster called string theory is dead and should be buried. There is no reason to try to give it life. http://www.everythingimportant.org/relativity/no-new-einstein.pdf > All the rest of this chaff about mathematics and Hilbert is just > a cover story to mask your dislike of scientists trying to unmask > everything. You are afraid that a bride unveiled will be cheapened. That's provably incorrect. Physicists have no interest in unmasking everything. Their primary task is in attaining the divinity that they believe Einstein achieved. They have no interest in explaining simplicity itself. > But on a less derisive note, I doubt seriously that mankind gets too > fat a head from the actual practice of opening nature's kimono. If > anything, most of the spectacular physicists experience a sense of awe > and renewed appreciation for the elegance and beauty of what they > uncover. The sin is only when mankind starts worshiping what they see. http://www.pantheism.net/paul/index.htm http://members.aol.com/Heraklit1/einstein.htm > The notion that the theory of everything will lead > to delusions of omnipotent power and mastery of the > universe are, fortunately, unwarranted. You have misstated my view. Both of those concepts are tied together. It is also true that the pursuit of divinity leads to the theory of everything. Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) > String theory, often described as the theory of everything, is a > purely religious belief. Which is a religious statement in itself. Rejection of a theory on the > basis of the self-aggrandizing manner of the host of a television show > about the theory is hardly the proper basis by which to judge the > merits of the theory, no matter how much it makes your blood simmer. I reject the string religion because it's a labyrinth of more than > 10^300 conflicting approaches of equally non-fundamental paths.http://www.everythingimportant.org/relativity/no-new-einstein.pdf Whatever that sentence is supposed to mean. I see that this objective is underachieved, because you > not only are not motivated to go find out more about it, > but you don't even see the objective at all. The objective of TOE is to get everyone to believe that they can wrest > from God all the secrets of the universe and that, with this > knowledge, they will be able to remove God from His throne and will > know how to begin to take over running the universe directly. Well, now, I think we have excavated a little closer to the center of > your motivation, there, Shubee. You have revealed that you don't like > scientists digging too deep, lest they bite of the tree of knowledge > and be evicted from the garden. My position is just the opposite. I decry the shallowness of > professional physicists for misunderstanding absolutely trivial Well, let's see. You don't like it when they self-glorify. But what REALLY rankles you is when they don't glorify you. You HATE it when there is hero worship going on, but what's worse is when you don't get your cut of respect and glory. Rest of grandstanding, self-promoting linking to your own website snipped, you transparent hypocrite, you. PD === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I reject the string religion because it's a labyrinth of more than > 10^300 conflicting approaches of equally non-fundamental paths. > http://www.everythingimportant.org/relativity/no-new-einstein.pdf Whatever that sentence is supposed to mean. I think it's clearer than string theory for those who understand the objections of responsible string theory critics. > My position is just the opposite. I decry the shallowness of > professional physicists for misunderstanding absolutely trivial > fundamentals in the foundations of physics. Well, let's see. You don't like it when they self-glorify. But what > REALLY rankles you is when they don't glorify you. You HATE it when > there is hero worship going on, but what's worse is when you don't get > your cut of respect and glory. My glory is in telling physicists that there is only ignominy and death in worshiping Albert Einstein, even though the entire world hates my message. It is only a secondary observation that physicists can't possibly be gods because they misunderstand absolutely trivial fundamentals in the foundations of physics. > Rest of grandstanding, self-promoting linking to your own website > snipped, you transparent hypocrite, you. I don't own http://www.everythingimportant.org/relativity/no-new-einstein.pdf, Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. It is only a secondary observation that physicists > can't possibly be gods because they misunderstand absolutely trivial > fundamentals in the foundations of physics. Physicists do not worship Albert Einstein. They respect his worthy accomplishments. Many in the physics community viewed with sadness Einstein's self impossed isolation from where the action was in physics. This is hardly worship. The physics community disgreed (largely) with Einstein's negative assesment of quantum physics and they went their merry way ignoring Einstein's misgivings. Bob Kolker === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. It is only a secondary observation that physicists > can't possibly be gods because they misunderstand absolutely trivial > fundamentals in the foundations of physics. Physicists do not worship Albert Einstein. They respect his worthy > accomplishments. Many in the physics community viewed with sadness > Einstein's self impossed isolation from where the action was in > physics. This is hardly worship. The physics community disgreed (largely) with Einstein's negative > assesment of quantum physics and they went their merry way ignoring > Einstein's misgivings. Einstein was not wrong. He had many cogent observations to make. He noted that a statistical quantum theory is incomplete, while Bohr believed that only statistical information is meaningful in quantum theory. And Einstein was not alone. Schrodinger questioned the contemporary approach to quantum theory. Regarding electro-magnetism Einstein has this to say: I feel that it is a delusion to think of the electrons and the fields as two physically different, independent entities. Since neither can exist without the other, there is only _one_ reality to be described, which happens to have two different aspects; and the theory ought to recognize this from the start instead of doing things twice. Atomic transitions appear to be irreducible quantum transitions, but this is because there are non-linear self-reinforcing mechanisms at work, not because they _are_ quantum. The coherent world has continuous wave functions, and abrupt-but-continuous quantum transitions, a picture entirely consistent with Einstein's notion of things. -- Michael Press === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success <_cidnXkpvOj42M3VnZ2dnUVZ_t7inZ2d@comcast.com> posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. It is only a secondary observation that physicists > can't possibly be gods because they misunderstand absolutely trivial > fundamentals in the foundations of physics. Physicists do not worship Albert Einstein. Then try to answer the questions that PD couldn't answer. > They respect his worthy accomplishments. That's their first mistake. They believe that most of Einstein's accomplishments were his own. > Many in the physics community viewed with sadness > Einstein's self impossed isolation from where the action > was in physics. This is hardly worship. That's not my accusation. > The physics community disgreed (largely) with Einstein's negative > assesment of quantum physics and they went their merry way ignoring > Einstein's misgivings. Bob Kolker And yet physicists still sing praises about that dullard and ascribe divinity to him. http://www.physicstoday.org/vol-58/iss-7/images/devine_einstein.mp3 Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. It is only a secondary observation that physicists > can't possibly be gods because they misunderstand absolutely trivial > fundamentals in the foundations of physics. > Physicists do not worship Albert Einstein. Then try to answer the questions that PD couldn't answer. > They respect his worthy accomplishments. That's their first mistake. They believe that most of Einstein's > accomplishments were his own. > Many in the physics community viewed with sadness > Einstein's self impossed isolation from where the action > was in physics. This is hardly worship. That's not my accusation. > The physics community disgreed (largely) with Einstein's negative > assesment of quantum physics and they went their merry way ignoring > Einstein's misgivings. > Bob Kolker And yet physicists still sing praises about that dullard and ascribe > divinity to him. You're a tee-ball benchwarmer, little Shooby - you're not qualified to critique a pee-wee-baseball bat boy, let alone Babe Ruth. === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > You're a tee-ball benchwarmer, little Shooby - you're not qualified to > critique a pee-wee-baseball bat boy, let alone Babe Ruth. To the same degree that you represent Einstein worshipers and the slander of Leo Corry, J.9frgen Renn and John Stachel, I represent David Hilbert. Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > You're a tee-ball benchwarmer, little Shooby - you're not qualified to > critique a pee-wee-baseball bat boy, let alone Babe Ruth. To the same degree that you represent Einstein worshipers and the > slander of Leo Corry, J.9frgen Renn and John Stachel, I represent David > Hilbert. :) Shoobo, Hilbert would be laughing just as hard as everyone here does at your delusional fantasies. > Shubee > === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > And yet physicists still sing praises about that dullard and ascribe > divinity to him. > http://www.physicstoday.org/vol-58/iss-7/images/devine_einstein.mp3 That dullard produced a theory which has been supported experimentally over 100 years, has never been falsified empirically and is an integral part of the most successful theory ever formulated, The Standard Model. The dullard also did pioneer work in lasers and contributed to the theory of the Bose-Einstein condensate. His paper on Brownian Motion gave an explanation for Avagadro's Number and is his most quoted paper. The dullard pot quantum theory on the map with his paper on the photeelectric effect for which he won a Nobel Prize. Some dullard. However he was mistaken about locality and his work on unified field theory led to a dead end. So not everything he did was successful. Bob Kolker x === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30),gzip(gfe),gzip(gfe) > Then try to answer the questions that PD couldn't answer. Lee SmolinÍs little write-up to justify EinsteinÍs godhood asks ñwhy there is no new Einsteinî? The answer is very simple. It is much more difficult today for a nitwit, a plagiarist, and a liar such as Einstein to be worshipped as a god. > That's their first mistake. They believe that most of Einstein's > accomplishments were his own. > What do you expect when they have already decided on the godhood of Einstein? > And yet physicists still sing praises about that dullard and ascribe > divinity to him. http://www.physicstoday.org/vol-58/iss-7/images/devine einstein.mp3 This is because ** MYSTICISM IS WISDOM ** PLAGIARISM IS CREATIVITY ** CONJECTURE IS REALITY ** FAITH IS THEORY ** LYING IS TEACHING ** BELIEVING IS LEARNING === Subject: Re: Albert Einstein and quantum theory. [was ...] > My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. It is only a secondary observation that physicists > can't possibly be gods because they misunderstand absolutely trivial > fundamentals in the foundations of physics. Physicists do not worship Albert Einstein. They respect his worthy > accomplishments. Many in the physics community viewed with sadness > Einstein's self impossed isolation from where the action was in > physics. This is hardly worship. The physics community disgreed (largely) with Einstein's negative > assesment of quantum physics and they went their merry way ignoring > Einstein's misgivings. Einstein was not wrong. He had many cogent observations to make. He noted that a statistical quantum theory is incomplete, while Bohr believed that only statistical information is meaningful in quantum theory. And Einstein was not alone. Schrodinger questioned the contemporary approach to quantum theory. Regarding electro-magnetism Einstein has this to say: I feel that it is a delusion to think of the electrons and the fields as two physically different, independent entities. Since neither can exist without the other, there is only _one_ reality to be described, which happens to have two different aspects; and the theory ought to recognize this from the start instead of doing things twice. Atomic transitions appear to be irreducible quantum transitions, but this is because there are non-linear self-reinforcing mechanisms at work, not because they _are_ quantum. The coherent world has continuous wave functions, and abrupt-but-continuous quantum transitions, a picture entirely consistent with Einstein's notion of things. -- Michael Press === Subject: Re: Albert Einstein and quantum theory. [was ...] <_cidnXkpvOj42M3VnZ2dnUVZ_t7inZ2d@comcast.com> posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 1.1.4322),gzip(gfe),gzip(gfe) Planck-length is an irreducible quantum; the discrete & continuous are intertwined, obviously & at all levels, in the same way as tension & compression are always-and- only coincident, according to Bucky Fullerofit: tensegrity is huge field of endeavor, although it isn't exactly a unified theory. point-electrons & other quanta are impossible, proved intractible by Kaluza & Klein; and, Schroedinger's cat is as dead as he meant it to be, as dead as the Copenhagenschool mystaque, after a hundred years, or a googolplex. instead of Young's & Fresnel's & Huyghen's waves, in sufficient quantities, if only to revive the secular British church of Newtonianism, that kept British use of the calculus back by a hundred years, or a googolplex. hey, there; Hooke conjectured the inverse second-power law, and then Newton tinkered algebraically with Kepler's orbital constraints, to prove it. > æ æ I feel that it is a delusion to think of the electrons and > æ æ the fields as two physically different, independent > Atomic transitions appear to be irreducible quantum > transitions, but this is because there are non-linear > self-reinforcing mechanisms at work, not because they > are quantum. The coherent world has continuous wave > functions, and abrupt-but-continuous quantum transitions, > a picture entirely consistent with Einstein's notion of > things. thus: Gene Rodentvery, he was called, galactic schlockmeister. anyway, it sounds rather Laroucheyist to ascribe such British influence but, hey, the oxfordians do control the dictionary, the Rhodesian scholarship, and the goofey idea that Shakespeare was a front for the earl of O. -- dumb-enough to be true, since they also hold all of the Shakespeare artifacts. more to the points, the slanders of Hooke and Liebniz by the Royal Society are best to portray this ungainly influence over science. now, we can posit this influence to be extended to the Perimeter Inst. which pays Smolin to produce his phoney strings v. loops harangues, and arbitrary multiversal values of pi; I mean, what are loops, but closed strings? of course, there is a lot of heat with the light of these recriminations & hoaxes; meaning, a lot of passionate, real debate of dots v. integrals, quaternions v. vectors, there is nothing wrong with superstrings, other than being so much of a superset of the SM, in the end. > He is refering to the interval which is a quadratic function in space > and time co-ordinates that defines a hyperboloid. If the interval is > equal to zero (as it is on a llight like world line) you get > x^2 - t^2 - 0. This has nothing to do with curvature. Curvature is a > special kind of tensor defined on a manifold. This approach was > originated by Gauss and Riemann and was extended by Levi-Civita and others. thus: apples & oranges both in the fruitsalad, Fruitcake. now, the corn-based ethanol is accelerating desertification in the Midwest & must be totally eliminated, before the complete vertical integration of the energy and the grain cartels, you alleged cheapskate. however, the new gambling silos can still be used for ensilage & cellulose/lignin residues, to make ethanol or what ever. in any case, the best such sources are perennials (a-hem; trees -- make pollution, two, as saith Reaganomics .-) in case that you didn't notice, the financial cartel bought a chunk of the electoral process in December'99, the Financial Services Modernization Act; take your virtual polling-place receipt to your bank, because they have more leverage & expertise with Automatic Voting Machines (there is no provision in the Help America Vote Act to actually look at anything, after they called the election on TV), and the same applies to Scamtrons. indeed, there is nothing like a good, old chad for recounting purposes; the whole debate was a farce, and Al Lost on his own dime in Florida and Arkansas (and Michigan (sik)), either of which had enoufh electoral college votes to stop Trickier Dick Cheeny I mean, bankers are people, also! > Now class, think hard: Which is the cheaper way to go; gasoline or etha85%? > If you're not counting the cost of the extra time and inconvenience due as noted in a pro-biofuel letter to the editor, ethanol has been subsidized for 25 years. anyway, it's all BS, because you're relying on the energy cartel's ersatz definition of fossil fuels. let us recall, Al Sr. and Jr.'s careers were made by an oil company, and all of *them* just *love* the Kyoto Protocol, just as they do with all of the emmissions trading schemes of Bush'91, and the Montreal Protocol precedent from DuPont: their patents had expired on Freons. > That's why I went to E85. It's cheap, it's clean, and it's hot. I > Just wait til you can get a Saab bio-power model. That'll put an ever bigger grin on your face. -UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?... La Troi Phases d'Exploitation de la Protocols des Grises de Kyoto: (FOSSILISATION [McCainanites] (TM/sic))/ BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm. Http://www.tarpley.net/bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de COUP D'ETAT, 3/30/81 === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) > I reject the string religion because it's a labyrinth of more than > 10^300 conflicting approaches of equally non-fundamental paths. >http://www.everythingimportant.org/relativity/no-new-einstein.pdf Whatever that sentence is supposed to mean. I think it's clearer than string theory for those who understand the > objections of responsible string theory critics. String theory is clear to responsible string theory critics. Smolin, for example, is a significant *contributor* to string theory, as Einstein was a significant contributor to quantum mechanics though he had grave doubts about it. And I suppose you'd have to ask responsible string theory critics whether they understand your sentence. My position is just the opposite. I decry the shallowness of > professional physicists for misunderstanding absolutely trivial > fundamentals in the foundations of physics. Well, let's see. You don't like it when they self-glorify. But what > REALLY rankles you is when they don't glorify you. You HATE it when > there is hero worship going on, but what's worse is when you don't get > your cut of respect and glory. My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. No, I don't think that's really what's hated, Shubee. While there are indeed popularizations that go overboard on the aggrandizing, there is plenty of aggrandizing going around and it's not focused solely or even predominantly on Einstein. What's perhaps hated is your lack of perception in understanding the intent of popularizations, being struck blind by a knee-jerk reaction to the aggrandizing element. What is perhaps hated is your general approach of trying to take physicists down a peg in general by substituting worship of mathematicians and Hilbert instead, the hypocrisy of that tactic being both transparent and detestable. Perhaps what is hated is your insistence that your theoretical construction is fundamentally better than Einstein's and that you should be deserving of some of the glory that you think is afforded to Einstein, which is also transparent and detestable. > It is only a secondary observation that physicists > can't possibly be gods because they misunderstand absolutely trivial > fundamentals in the foundations of physics. > === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) I reject the string religion because it's a labyrinth of more than > 10^300 conflicting approaches of equally non-fundamental paths. >http://www.everythingimportant.org/relativity/no-new-einstein.pdf Whatever that sentence is supposed to mean. I think it's clearer than string theory for those who understand the > objections of responsible string theory critics. String theory is clear to responsible string theory critics. Smolin, > for example, is a significant *contributor* to string theory, Then why is it that you haven't read his essay in Physics Today (June 2005) and published a rebuttal? http://www.everythingimportant.org/relativity/no-new-einstein.pdf > My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. No, I don't think that's really what's hated, Shubee. While there are > indeed popularizations that go overboard on the aggrandizing, there is > plenty of aggrandizing going around and it's not focused solely or > even predominantly on Einstein. It is easy to see that physicists' worship Einstein as the greatest god and that some highly respected high priests of physics have gone to the extreme in their deification of Einstein by mutilating the scientific work of David Hilbert in order to strengthen the delusions of the physics community. > What's perhaps hated is your lack of perception in understanding > the intent of popularizations, being struck blind by a knee-jerk > reaction to the aggrandizing element. I take it that you regard mutilating the scientific work of David Hilbert to support popularizing Albert Einstein as innocent frivolity and not fanatical worship. > What is perhaps hated is your general approach of trying to take > physicists down a peg in general by substituting worship of > mathematicians and Hilbert instead, the hypocrisy of that > tactic being both transparent and detestable. I have consistently argued that if physicists insist on following Einstein as their god, then they need to bow with even greater reverence and praise with even greater delight the scientific accomplishments of David Hilbert. > Perhaps what is hated is your insistence that your theoretical > construction is fundamentally better than Einstein's I can't imagine any greater insult that discovering that one's god is flawed. > and that you should be deserving of some of the glory that you > think is afforded to Einstein, which is also transparent and > detestable. I have already received the glory that comes with appreciating David Hilbert's philosophy of physics and applying it. Shubee http://www.everythingimportant.org/relativity/special.pdf === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) > I reject the string religion because it's a labyrinth of more than > 10^300 conflicting approaches of equally non-fundamental paths. >http://www.everythingimportant.org/relativity/no-new-einstein.pdf Whatever that sentence is supposed to mean. I think it's clearer than string theory for those who understand the > objections of responsible string theory critics. String theory is clear to responsible string theory critics. Smolin, > for example, is a significant *contributor* to string theory, Then why is it that you haven't read his essay in Physics Today (June > 2005) and published a rebuttal?http://www.everythingimportant.org/relativity/no-new-einstein.pdf My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. No, I don't think that's really what's hated, Shubee. While there are > indeed popularizations that go overboard on the aggrandizing, there is > plenty of aggrandizing going around and it's not focused solely or > even predominantly on Einstein. It is easy to see that physicists' worship Einstein as the greatest > god and that some highly respected high priests of physics have gone > to the extreme in their deification of Einstein by mutilating the > scientific work of David Hilbert in order to strengthen the delusions What's perhaps hated is your lack of perception in understanding > the intent of popularizations, being struck blind by a knee-jerk > reaction to the aggrandizing element. I take it that you regard mutilating the scientific work of David > Hilbert to support popularizing Albert Einstein as innocent frivolity What is perhaps hated is your general approach of trying to take > physicists down a peg in general by substituting worship of > mathematicians and Hilbert instead, the hypocrisy of that > tactic being both transparent and detestable. I have consistently argued that if physicists insist on following > Einstein as their god, then they need to bow with even greater > reverence and praise with even greater delight the scientific > accomplishments of David Hilbert. Perhaps what is hated is your insistence that your theoretical > construction is fundamentally better than Einstein's I can't imagine any greater insult that discovering that one's god is > flawed. and that you should be deserving of some of the glory that you > think is afforded to Einstein, which is also transparent and > detestable. I have already received the glory that comes with appreciating David > Hilbert's philosophy of physics and applying it. Shubeehttp://www.everythingimportant.org/relativity/special.pdf The more I looked at the above, the more disgusted I got. You are party to a petty religious war, your Jehovah against someone else's Baal. You feel a commandment that says your god is a jealous god and demands no other gods be put before him. And so you look for ceremonial rites and examples of people worshipping Baal, and you go bellowing from the mountaintop, preaching damnation and hellfire for those who do not worship your beloved Jehovah instead. And you assume that those who do not worship Jehovah are either Baal worshippers or heathens. It does not occur to you that, despite your passing finds of worship neither Baal nor Jehovah, and rightfully so. You are a kook calling himself a prophet in the wilderness, and you leave behind your writings in praise of your Jehovah in hopes that one day it will be bound together as part of a bible. It would give you great satisfaction to be stoned or crucified as a martyr, preferably while hanging upside down. Shubee, you have exposed yourself as a nutjob, someone who can put together words that appear to be coherent but are on a second look motivated by the meanderings of a madman. PD === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > The more I looked at the above, the more disgusted I got. IÍm delighted that what IÍve been saying is finally dawning on you. > You are party to a petty religious war, You are a party to it also; you are just on the wrong side. > your Jehovah against someone else's Baal. I prefer to cite the apocalypse for the modern endtime perspective and to explain our differences by suggesting that I believe in the 3 angelsÍ messages and that you obviously believe in the 3 demonsÍ messages. > You feel a commandment that says your god is a jealous god and > demands no other gods be put before him. And so you look for > ceremonial rites and examples of people worshipping Baal, and > you go bellowing from the mountaintop, preaching damnation > and hellfire for those who do not worship your beloved Jehovah > instead. I prefer to think of it as God enabling me to cooperate with Him to proclaim the 3 angelsÍ messages of Revelation 14:6-12. > And you assume that those who do not worship > Jehovah are either Baal worshippers or heathens. Baal worshippers might be a very accurate description. IÍll have to look that up. However, as I look at my mission statement, the first angelÍs message does challenge pantheism and most physicists today are pantheists. http://www.pantheism.net/paul/index.htm http://members.aol.com/Heraklit1/einstein.htm > It does not occur to you that, despite your passing finds of > people worship neither Baal nor Jehovah, and rightfully so. I agree that neither Baal nor Jehovah are popular right now. But almost everyone believes in the 3 demonsÍ messages. > You are a kook calling himself a prophet in the wilderness, and you > leave behind your writings in praise of your Jehovah in hopes that > one day it will be bound together as part of a bible. On the contrary, I believe that the sacred canon is closed. > It would give you great satisfaction to be stoned > or crucified as a martyr, preferably while > hanging upside down. Jesus made it very clear that those who preach the gospel will be persecuted and that everyone who wants eternal life must follow His example and believe His message but I see no evidence that Jesus enjoyed the crucifixion. > Shubee, you have exposed yourself as a nutjob, someone who > can put together words that appear to be coherent but are on > a second look motivated by the meanderings of a madman. Shubee http://www.everythingimportant.org/relativity/directory.htm === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) The more I looked at the above, the more disgusted I got. IÍm delighted that what IÍve been saying is finally dawning on you. You are party to a petty religious war, You are a party to it also; you are just on the wrong side. your Jehovah against someone else's Baal. I prefer to cite the apocalypse for the modern endtime perspective and > to explain our differences by suggesting that I believe in the 3 > angelsÍ messages and that you obviously believe in the 3 demonsÍ > messages. You feel a commandment that says your god is a jealous god and > demands no other gods be put before him. And so you look for > ceremonial rites and examples of people worshipping Baal, and > you go bellowing from the mountaintop, preaching damnation > and hellfire for those who do not worship your beloved Jehovah > instead. I prefer to think of it as God enabling me to cooperate with Him to > proclaim the 3 angelsÍ messages of Revelation 14:6-12. you don't really explicate that on the relativity index of your religious website. I now understand better where your idolatry fixation comes from. And you assume that those who do not worship > Jehovah are either Baal worshippers or heathens. Baal worshippers might be a very accurate description. IÍll have to > look that up. However, as I look at my mission statement, the first > angelÍs message does challenge pantheism and most physicists today are > pantheists.http://www.pantheism.net/paul/index.htmhttp://members.aol.com/Her a klit1/einstein.htm It does not occur to you that, despite your passing finds of > people worship neither Baal nor Jehovah, and rightfully so. I agree that neither Baal nor Jehovah are popular right now. But > almost everyone believes in the 3 demonsÍ messages. You are a kook calling himself a prophet in the wilderness, and you > leave behind your writings in praise of your Jehovah in hopes that > one day it will be bound together as part of a bible. On the contrary, I believe that the sacred canon is closed. It would give you great satisfaction to be stoned > or crucified as a martyr, preferably while > hanging upside down. Jesus made it very clear that those who preach the gospel will be > persecuted and that everyone who wants eternal life must follow His > example and believe His message but I see no evidence that Jesus > enjoyed the crucifixion. Shubee, you have exposed yourself as a nutjob, someone who > can put together words that appear to be coherent but are on > a second look motivated by the meanderings of a madman. > Shubeehttp://www.everythingimportant.org/relativity/directory.htm === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) You're welcome PD. So could you please retract the false statement that you made when you said that I call myself a prophet in the wilderness? Shubee http://www.everythingimportant.org/relativity/general.htm === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.18,gzip(gfe),gzip(gfe) > You're welcome PD. So could you please retract the false statement > that you made when you said that I call myself a prophet in the > wilderness? But you do say that. Your words: I prefer to think of it as God enabling me to cooperate with Him to proclaim the 3 angelsÍ messages of Revelation 14:6-12. You do know what a prophet is, don't you? PD === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) You're welcome PD. So could you please retract the false statement > that you made when you said that I call myself a prophet in the > wilderness? But you do say that. Your words: I prefer to think of it as God > enabling me to cooperate with Him to proclaim the 3 angelsÍ messages > of Revelation 14:6-12. > You do know what a prophet is, don't you? The word prophet has many definitions and can mean a person who speaks for God. I strongly object to that characterization for myself and strongly believe that only Jesus Christ speaks for God. I do believe that the Bible prophets had a gift in the lesser sense of merely being divinely inspired and also some measure of approval from God that was manifest, which should be respected. Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.18,gzip(gfe),gzip(gfe) > You're welcome PD. So could you please retract the false statement > that you made when you said that I call myself a prophet in the > wilderness? But you do say that. Your words: I prefer to think of it as God > enabling me to cooperate with Him to proclaim the 3 angelsÍ messages > of Revelation 14:6-12. > I offered none, but then again, this has never stopped you from hearing what you want to hear and seeing what you want to see. You do know what a prophet is, don't you? The word prophet has many definitions and can mean a person who > speaks for God. I strongly object to that characterization for myself > and strongly believe that only Jesus Christ speaks for God. I do believe that the Bible prophets had a gift in the lesser sense > of merely being divinely inspired and also some measure of approval > from God that was manifest, which should be respected. This latter appears to be precisely what you claimed. There is no need for a retraction on my part. PD === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=lBRURwoAAAB_-Q_b04pGziaymfr5yRFx Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) But you do say that. Your words: I prefer to think of it as God > enabling me to cooperate with Him to proclaim the 3 angelsÍ messages > of Revelation 14:6-12. > I offered none, Your clarification was sufficient for my purposes. > You do know what a prophet is, don't you? The word prophet has many definitions and can mean a person who > speaks for God. I strongly object to that characterization for myself > and strongly believe that only Jesus Christ speaks for God. I do believe that the Bible prophets had a gift in the lesser sense > of merely being divinely inspired and also some measure of approval > from God that was manifest, which should be respected. This latter appears to be precisely what you claimed. I don't think of myself as a prophet. I have had visions and supernatural revelations but that doesnÍt make me a prophet in the Biblical sense. Sometimes I do state my beliefs so powerfully that I do tend to believe that IÍve received guidance from the Holy Spirit but it certainly doesn't happen often enough. My inclination is to think of myself as the David Hilbert of theology. Before Hilbert difficult problem in the mathematical theory of invariants in a new and innovative way. Hilbert's approach was abstract but it solved the mathematics so decisively that it brought an end to further investigation of the problem. Hilbert tried to get his paper published in the appropriate mathematical journal at the time but it was rejected. The German mathematician Paul Gordon was the first referee to judge Hilbert's work. Gordan had worked on this problem for 20 years. He was the king of invariants. After reading the paper, Dr. Gordan exclaimed, Das ist nicht Mathematik; das ist Theologie! (That is not mathematics, that is theology!). I have received a very similar sentiment from a few who have read my exegesis of Daniel and Revelation. Their response was That is not theology, that is mathematics! : - ) Likewise, there are plenty of buffoons and unimaginative physicists at sci.physics.relativity that have protested my interpretation of HilbertÍs philosophy of physics for a respectable derivation of the Lorentz transformation. You guessed it: All those uninspired dullards have whined, ñthat is not physics, that is mathematics.î http://www.everythingimportant.org/relativity/special.pdf Shubee === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success posting-account=nPH_PQkAAACneDKT6RXopPWArC2We4Rq AppleWebKit/525.13 (KHTML, like Gecko) Version/3.1 Safari/525.13,gzip(gfe),gzip(gfe) > I reject the string religion because it's a labyrinth of more than > 10^300 conflicting approaches of equally non-fundamental paths. >http://www.everythingimportant.org/relativity/no-new-einstein.pdf Whatever that sentence is supposed to mean. I think it's clearer than string theory for those who understand the > objections of responsible string theory critics. String theory is clear to responsible string theory critics. Smolin, > for example, is a significant *contributor* to string theory, Then why is it that you haven't read his essay in Physics Today (June > 2005) and published a rebuttal?http://www.everythingimportant.org/relativity/no-new-einstein.pdf I did read his essay, and his book, and several of his papers. He makes no bones about the fact that he was a major contributor to string theory himself. You can look them up yourself on his own pages: http://www.thetroublewithphysics.com/cv.html http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+a+lee+smolin&SE QUENCE=DS(D)&SKIP=100 You'll also notice that this noted critic of string theory is also responsible for a paper and a BBC radio interview touting a theory of everything. I do not have to accept a choice between worshipping string theory or rejecting it out of hand. There are other more balanced positions, which you seem to be unwilling to take. My glory is in telling physicists that there is only ignominy and > death in worshiping Albert Einstein, even though the entire world > hates my message. No, I don't think that's really what's hated, Shubee. While there are > indeed popularizations that go overboard on the aggrandizing, there is > plenty of aggrandizing going around and it's not focused solely or > even predominantly on Einstein. It is easy to see that physicists' worship Einstein as the greatest > god He is not worshipped as a god on any level by the vast majority of physicists, your petty extractions from TV programs, Saturday afternoon educational materials for children, and magazine hypes notwithstanding. Please wipe the foam off your lips and start reading some more balanced materials. > and that some highly respected high priests of physics have gone > to the extreme in their deification of Einstein by mutilating the > scientific work of David Hilbert in order to strengthen the delusions What's perhaps hated is your lack of perception in understanding > the intent of popularizations, being struck blind by a knee-jerk > reaction to the aggrandizing element. I take it that you regard mutilating the scientific work of David > Hilbert to support popularizing Albert Einstein as innocent frivolity What is perhaps hated is your general approach of trying to take > physicists down a peg in general by substituting worship of > mathematicians and Hilbert instead, the hypocrisy of that > tactic being both transparent and detestable. I have consistently argued that if physicists insist on following > Einstein as their god, then they need to bow with even greater > reverence and praise with even greater delight the scientific > accomplishments of David Hilbert. I disagree. Neither deserves deification. So stop trying to do it with Hilbert. It's phony anyway. It's just a mask for your real agenda. Perhaps what is hated is your insistence that your theoretical > construction is fundamentally better than Einstein's I can't imagine any greater insult that discovering that one's god is > flawed. He's not a god in my book. He was wrong about a number of things. He was wrong about black holes, he was wrong about quantum mechanics, and he was wrong about unification of electromagnetism with gravity. Any perception on your part that I deify *anyone* is either a projection or a generalization -- rejected. and that you should be deserving of some of the glory that you > think is afforded to Einstein, which is also transparent and > detestable. I have already received the glory that comes with appreciating David > Hilbert's philosophy of physics and applying it. Spoken like a true religious fanatic, whose greatest satisfaction is living according to the Word of his Leader and Master. Face it, Shubee, you're what you claim to despise. You deify, and then you condemn those who deify because they don't deify whom you wish to deify. You've tottered right off the edge, Shubee. The problem with relative motion is that, even though it may be you that's in free-fall, you have a hard time distinguishing that from the rest of the world being in free-fall in the opposite direction. It's only when you land with a thump that you know who it was that was falling, but that whole long trip down you'll never know. Shubeehttp://www.everythingimportant.org/relativity/special.pdf See? there's that self-aggrandizing bit again. === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success <2sKdnUNLEPF75d_VnZ2dnUVZ_rPinZ2d@comcast.com> posting-account=C03jXAoAAAB5gW0cBd6wQoFEj30Iwz0z Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) He didn't. It was Minkowski who actually formulated SR as a > manifestation of curvature in a spacetime manifold. Minkowski was a > mathematician who was interested in physics. Einstein was a physicist. > The two types of scientists aren't really at odds. Uhh-most of the > time? What curvature is defined in SR? Bob Kolker The idea of the four dimensional space-time continuum, complete with four-vectors and metrics, was first introduced as a way to analyze special relativity (SR). The word curvature isn't used in this essay, but the space time continnum is. Read: H. Minkowski, Space and Time page 75-91 in the book The Principle of Relativity, by A. Einstein, H. A. Lorentz, H. Minkowski and H. Weyl. (Dover publications, first translation published in 1923). On page 86, Minkowski refers to hyperbolic curvature. To my knowledge, Minkoski was the first scientist to connect the concept of four dimensional geometry to actual physics. He did it in reference to SR. Minkowski may have even applied it to GR, but I have no reference to this line of his work. My next reference is Einstein applying this formalism to GR. Note: I know Riemann did alot of nonEuclidian geometry really early. He was a genius, a visionary, etc. However, he didn't apply it to actual physics problems to my knowledge. He was a mathematician. He may have hinted around that it may have applications in optics, but he didn't actually lay it down in black and white. Einstein expanded the use of Minkoski's formalism to general relativity (GR) in an essay in the same book. Here, the idea of curvature is described. Read: A. Einstein, The Foundation of the General Theory of Relativity page 111-173 in the book The Principle of Relativity, by A. Einstein, H. A. Lorentz, H. Minkowski and H. Weyl. (Dover publications, first translation published in 1923). The applications of the space-time picture to cosmology is in the another essay of the book: A. Einstein, Cosmological Considerations on the General Theory of Relativity page 177188-173 in the book The Principle of Relativity, by A. Einstein, H. A. Lorentz, H. Minkowski and H. Weyl. (Dover publications, first translation published in 1923). However, the real idea of space-time curvature clearly goes to Minkowski, expanding on the theory of SR. In a sense, A. Einstein was building (NOT stealing) on Minkowski's work, with Minkowski's full knowledge. === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success > Read: > A. Einstein, The Foundation of the General Theory of Relativity page > 111-173 in the book The Principle of Relativity, by A. Einstein, H. > A. Lorentz, H. Minkowski and H. Weyl. (Dover publications, first > translation published in 1923). He is refering to the interval which is a quadratic function in space and time co-ordinates that defines a hyperboloid. If the interval is equal to zero (as it is on a llight like world line) you get x^2 - t^2 - 0. This has nothing to do with curvature. Curvature is a special kind of tensor defined on a manifold. This approach was originated by Gauss and Riemann and was extended by Levi-Civita and others. Bob Kolker === Subject: Re: David Hilbert's Explanation of Albert Einstein's Success <2sKdnUNLEPF75d_VnZ2dnUVZ_rPinZ2d@comcast.com> posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.20,gzip(gfe),gzip(gfe) bravo. the spatial insufflators will have to deal with that!... yo, time is not a dimension, or conversely, time is the only dimension of consequence, to paraphrase Bucky Fullerofit. > He is refering to the interval which is a quadratic function in space > and time co-ordinates that defines a hyperboloid. æ If the interval is > equal to zero (as it is on a llight like world line) you get > x^2 - t^2 - 0. æThis has nothing to do with curvature. Curvature is a > special kind of tensor defined on a manifold. This approach was > originated by Gauss and Riemann and was extended by Levi-Civita and others. thus: apples & oranges both in the fruitsalad, Fruitcake. now, the corn-based ethanol is accelerating desertification in the Midwest & must be totally eliminated, before the complete vertical integration of the energy and the grain cartels, you alleged cheapskate. however, the new gambling silos can still be used for ensilage & cellulose/lignin residues, to make ethanol or what ever. in any case, the best such sources are perennials (a-hem; trees -- make pollution, two, as saith Reaganomics .-) in case that you didn't notice, the financial cartel bought a chunk of the electoral process in December'99, the Financial Services Modernization Act; take your virtual polling-place receipt to your bank, because they have more leverage & expertise with Automatic Voting Machines (there is no provision in the Help America Vote Act to actually look at anything, after they called the election on TV), and the same applies to Scamtrons. indeed, there is nothing like a good, old chad for recounting purposes; the whole debate was a farce, and Al Lost on his own dime in Florida and Arkansas (and Michigan (sik)), either of which had enoufh electoral college votes to stop Trickier Dick Cheeny I mean, bankers are people, also! > Now class, think hard: Which is the cheaper way to go; gasoline or etha85%? > If you're not counting the cost of the extra time and inconvenience due as noted in a pro-biofuel letter to the editor, ethanol has been subsidized for 25 years. anyway, it's all BS, because you're relying on the energy cartel's ersatz definition of fossil fuels. let us recall, Al Sr. and Jr.'s careers were made by an oil company, and all of *them* just *love* the Kyoto Protocol, just as they do with all of the emmissions trading schemes of Bush'91, and the Montreal Protocol precedent from DuPont: their patents had expired on Freons. > That's why I went to E85. It's cheap, it's clean, and it's hot. I > Just wait til you can get a Saab bio-power model. That'll put an ever bigger grin on your face. -UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?... La Troi Phases d'Exploitation de la Protocols des Grises de Kyoto: (FOSSILISATION [McCainanites] (TM/sic))/ BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm. Http://www.tarpley.net/bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de COUP D'ETAT, 3/30/81 === Subject: help needed with a formula. posting-account=VfiXrgoAAACe53O0iGVjKCkPjWVdG4Kz Gecko/20050915 Firefox/1.0.7,gzip(gfe),gzip(gfe) Hi I've working on a computer program where I need to calculate some electric fields. I am referring to a thesis which provides these formulas. For eg: The electric field for a ray(plane wave actually) at a distance s from the reference point: E(s) = E(0) * exp(-jks) where E(s) = electric field at a distance s from the reference point. E(0) = electric field at reference point. s = distance travelled. k = wave number = 2 * PI / wavelength exp(-jks) as per my thesis, represents the phase variation of the electric field along the ray. now, electric field is always a vector(3d in my case). so the user will input a magnitude for the electric field at the reference point and i can calculate the reference electric field vector[ E(0) ] easily by multiplying it with the unit direction vector the wave. exp(-jks) expands as cos(ks) - j sin(ks) ^ ^ ^ if E(0) is a vector of the form a x + b y + c z, ^ ^ ^ Then E(s) = (a x + b y + c z) * ( cos(ks) - j sin(ks) ) I'm really confounded at this expression because how does one multiply a complex number and a vector ? And even if it is possible then what about E(s) ? If E(0) was defined to be a 3d vector then E(s) must also be a 3d vector. What does it actually mean ? If there are some EE/ physics experts who can probably figure it out then it would be really great. === Subject: Re: help needed with a formula. posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > Hi I've working on a computer program where I need to calculate some > electric fields. I am referring to a thesis which provides these > formulas. For eg: The electric field for a ray(plane wave actually) at a distance s from > the reference point: E(s) = E(0) * exp(-jks) where E(s) = electric field at a distance s from the reference point. > E(0) = electric field at reference point. > s = distance travelled. > k = wave number = 2 * PI / wavelength > exp(-jks) as per my thesis, represents the phase variation of the > electric field along the ray. now, electric field is always a vector(3d in my case). so the user > will input a magnitude for the electric field at the reference point > and i can calculate the reference electric field vector[ E(0) ] easily > by multiplying it with the unit direction vector the wave. exp(-jks) expands as cos(ks) - j sin(ks) > ^ ^ ^ > if E(0) is a vector of the form a x + b y + c z, > ^ ^ ^ > Then E(s) = (a x + b y + c z) * ( cos(ks) - j sin(ks) ) I'm really confounded at this expression because how does one multiply > a complex number and a vector ? Have you ever taken a course in Linear Algebra? Or, if not, have you ever had an introduction to vectors as part of a Physics course? It is a standard result that a scalar times a vector is, again, a vector, and it does not matter whether the scalar is real or complex. (More precisely, one can define a vector space either over the real number field or over the complex number field. When defined over the real field, a*v is a vector for any vector v and real scalar a; over the complex number field, c*v is a vector for any vector v and any real or complex scalar c.) Of course, one can visualize geometrically the meaning of a*v for real a, but for complex c it is not easy to visualize c*v. For definitions of vector spaces and related matters see, eg., http://en.wikipedia.org/wiki/Vector_space or http://www.physicsforums.com/archive/index.php/t-182966.html . > And even if it is possible then what > about E(s) ? If E(0) was defined to be a 3d vector then E(s) must also > be a 3d vector. What does it actually mean ? If there are some EE/ > physics experts who can probably figure it out then it would be really > great. One can do EE without ever using complex numbers, and long ago it was done that way. The point is that, starting from a real vector E(0) we get TWO real vectors at distance s, namely E(0)*cos(ks) and E(0)*sin(ks). In general, to describe the actual field phenomena at s we need *both* components. That is: you might perform some transformations on the field E(s) to get some other field, or an energy density, or some other physical property; typically the new thing will involve knowledge of BOTH components E(0)*cos(ks) and E(0)*sin(ks). That is why you need to carry both components throughout the computation or analysis. As I said, you CAN do this without using complex numbers, but the originators of the subject soon discovered that analysis is much, much simpler if you express everything in complex form. For example, some circuit elements turn a sinusoidal current or voltage into another current or voltage that is 90 degrees out of phase with the input. That is easily described as swapping cos(ks) with sin(ks), and this is most easuly carried out in computations through multiplication of the initial voltage or current by a pure imaginary quantity. Other elements involve both magnitude and phase changes, so take a current like cos(ks) and turn it into a quantity like A*cos(ks) + B*sin(ks). This can be most easily accomplished as multiplication of the current exp(-i*k*s) by the complex number (A + i*B). The originators soon discovered that most everything they wanted to do came out much more cleanly if they introduced complex voltages, currents, impedences and the like. Believe it or not, after you get used to it you will start to think of complex voltages and currents as being perfectly natural, and will think of the imaginary part of current as having equal status to the real part. When you listen to electrical engineers talk to one another you notice this right away. This may not be true when you start the program, but I'll bet it will be true by the time you finish. For some applications of complex numbers in EE and other places, see, eg., http://en.wikipedia.org/wiki/Electrical_impedance or http://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html or http://academiccommons.columbia.edu:8080/ac/handle/10022/AC:P:6878 or http://www.regentsprep.org/rEGENTS/mathb/2C3/electricalresouce.htm . R.G. Vickson === Subject: Congruence question. posting-account=WR65RgoAAACboMXdKKYDn4ZKOJhMgvsz Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Prove that form any prime p, if (a^p)-(b^p) is divisible by p then (a^p)-(b^p) is also divisible by p^2. P.S. If (a^p)-(b^p) is divisible by p then p|(a-b) or p|(a^(p-1)+... +b^(p-1)). If p|(a-b) then, using Fermat's Theorem and simply multiplying, p|(a^(p-1)+...+b^(p-1)) so (a^p)-(b^p) is divisible by p^2. Now if p|(a^(p-1)+...+b^(p-1)) I do not know how to prove that p| (a-b) or (p^2)|(a^(p-1)+...+b^(p-1)). === Subject: Re: Congruence question. Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n x - y n-1 n HINT In any ring ------- = n x = D (x ) if x = y x - y See also my prior posts [1] on the algebraic derivative for polynomials --Bill Dubuque === Subject: Re: Congruence question. > Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n > x - y n-1 n >HINT In any ring ------- = n x = D (x ) if x = y > x - y See also my prior posts [1] on the algebraic derivative for polynomials --Bill Dubuque > If we allow division by x - y when x = y, then we allow the following common fallacy: Assume x = y, then 2 xy = y 2 2 2 x - xy = x - y 2 2 x(x-y) x - y ------ = ----- x-y x - y x = 2x Then either all x = 0, or 1 = 2. Both of these restrict the ring to one element. The algebraic formalism you cite above works if we carry out the division first, without assuming x = y, then assume x = y in the resulting quotient. However, if we let x = y before the division, problems can arise. In most rings, 0/0 is reasonably undefined. Rob Johnson take out the trash before replying === Subject: Re: Congruence question. Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n > x - y n-1 n >HINT In any ring ------- = n x = D (x ) if x = y > x - y >See also my prior posts [1] on the algebraic derivative for polynomials >--Bill Dubuque If we allow division by x - y when x = y, then we allow the following > common fallacy: Assume x = y, then 2 > xy = y 2 2 2 > x - xy = x - y 2 2 > x(x-y) x - y > ------ = ----- > x-y x - y x = 2x Then either all x = 0, or 1 = 2. Both of these restrict the ring > to one element. The algebraic formalism you cite above works if we carry out the > division first, without assuming x = y, then assume x = y in the > resulting quotient. However, if we let x = y before the division, > problems can arise. In most rings, 0/0 is reasonably undefined. Where's Bob Silverman where you need him? I'm sure last month he stepped in with a well-timed What have you been smoking? post in a similar situation. Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: Congruence question. Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n > x - y n-1 n >HINT In any ring ------- = n x = D (x ) if x = y > x - y >See also my prior posts [1] on the algebraic derivative for polynomials If we allow division by x - y when x = y, then we allow the following > common fallacy: Assume x = y, then 2 > xy = y 2 2 2 > x - xy = x - y 2 2 > x(x-y) x - y > ------ = ----- > x-y x - y x = 2x Then either all x = 0, or 1 = 2. Both of these restrict the ring > to one element. The algebraic formalism you cite above works if we carry out the > division first, without assuming x = y, then assume x = y in the > resulting quotient. However, if we let x = y before the division, > problems can arise. In most rings, 0/0 is reasonably undefined. You've completely misunderstood - please read the cited posts. --Bill Dubuque === Subject: Re: Congruence question. 20080612.171520@whim.org> posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Prove that for any prime p, if æa^p - b^p æis divisible by p > then æa^p - b^p æis also divisible by p^2. > æ æ æ æ æ æ æ æ æ æ n æ æ n > æ æ æ æ æ æ æ æ æ æx æ- æy æ æ æ æn-1 æ æ æ æn >HINT æIn any ring æ ------- æ= æn x æ æ= æD (x ) æ if æ x = y > æ æ æ æ æ æ æ æ æ æx æ- æy >See also my prior posts [1] on the algebraic derivative for polynomials > If we allow division by x - y when x = y, then we allow the following > common fallacy: Assume x = y, then æ æ æ æ æ 2 > æ æ xy = y æ æ æ2 æ æ æ æ2 æ 2 > æ æ x - xy = x - y æ æ æ æ æ æ æ 2 æ 2 > æ æ x(x-y) æ x - y > æ æ ------ = ----- > æ æ æx-y æ æ x - y æ æ æx æ æ= æ 2x Then either all x = 0, or 1 = 2. æBoth of these restrict the ring > to one element. The algebraic formalism you cite above works if we carry out the > division first, without assuming x = y, then assume x = y in the > resulting quotient. æHowever, if we let x = y before the division, > problems can arise. æIn most rings, 0/0 is reasonably undefined. You've completely misunderstood - please read the cited posts. --Bill Dubuque- ********************************************************* Every time, or at least of times, you post something, it looks pretty odd, pretty bizarre, and even wrong. You then send everybody to read your posts on this or that, but that usually helps little, since the info is hidden most of the times in links to other posts which have links to other posts, etc. In the last discussion about determinants, I followed your posts and I went back to 1999 in one of those paths, so I stopped since I have no pro training in archeology. Other links take us to posts with links to posts with links to posts ...to posts where it all stops! Then we learn that you haven't yet developed some thing, so it all stops and we get nothing. I think the above situation is pretty confusing, so I insist: if you think you have some really good general principles in general algebra that are appliable to a wide range of problems, why won't you please write them donw in some site so that people will be able to read them concentrated in one single place? I know this may be a burden to you, but (1) I, at least, would thank you very much if you'd do it, and (2) these discussions about this is not true, yes, it is: read on and etc. will stop, and you'll be able to make your point crystal clear every time. Tonio === Subject: Re: Congruence question. Prove that for any prime p, if æa^p - b^p æis divisible by p > then æa^p - b^p æis also divisible by p^2. > æ æ æ æ æ æ æ æ æ æ n æ æ n > æ æ æ æ æ æ æ æ æ æx æ- æy æ æ æ æn-1 æ æ æ æn >HINT æIn any ring æ ------- æ= æn x æ æ= æD (x ) æ if æ x = y > æ æ æ æ æ æ æ æ æ æx æ- æy >See also my prior posts [1] on the algebraic derivative for polynomials > If we allow division by x - y when x = y, then we allow the following > common fallacy: Assume x = y, then æ æ æ æ æ 2 > æ æ xy = y æ æ æ2 æ æ æ æ2 æ 2 > æ æ x - xy = x - y æ æ æ æ æ æ æ 2 æ 2 > æ æ x(x-y) æ x - y > æ æ ------ = ----- > æ æ æx-y æ æ x - y æ æ æx æ æ= æ 2x Then either all x = 0, or 1 = 2. æBoth of these restrict the ring > to one element. The algebraic formalism you cite above works if we carry out the > division first, without assuming x = y, then assume x = y in the > resulting quotient. æHowever, if we let x = y before the division, > problems can arise. æIn most rings, 0/0 is reasonably undefined. You've completely misunderstood - please read the cited posts. ********************************************************* Every time, or at least of times, you post something, it looks pretty > odd, pretty bizarre, and even wrong. You then send everybody to read > your posts on this or that, but that usually helps little, since the > info is hidden most of the times in links to other posts which have > links to other posts, etc. > In the last discussion about determinants, I followed your posts and I > went back to 1999 in one of those paths, so I stopped since I have no > pro training in archeology. > Other links take us to posts with links to posts with links to posts > ...to posts where it all stops! Then we learn that you haven't yet > developed some thing, so it all stops and we get nothing. I think the above situation is pretty confusing, so I insist: if you > think you have some really good general principles in general > algebra that are appliable to a wide range of problems, why won't you > please write them donw in some site so that people will be able to > read them concentrated in one single place? I know this may be a burden to you, but (1) I, at least, would thank > you very much if you'd do it, and (2) these discussions about this is > not true, yes, it is: read on and etc. will stop, and you'll be > able to make your point crystal clear every time. Bill recently gave a URL to the general principals. I am too little practiced in mathematics to resent Bill's pedagogy; so I can make some progress. I find the hints and methods very helpful. -- Michael Press === Subject: Re: Congruence question. 20080612.171520@whim.org> posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Prove that for any prime p, if æa^p - b^p æis divisible by p > then æa^p - b^p æis also divisible by p^2. > æ æ æ æ æ æ æ æ æ æ n æ æ n > æ æ æ æ æ æ æ æ æ æx æ- æy æ æ æ æn-1 æ æ æ æn >HINT æIn any ring æ ------- æ= æn x æ æ= æD (x ) æ if æ x = y > æ æ æ æ æ æ æ æ æ æx æ- æy >See also my prior posts [1] on the algebraic derivative for polynomials > If we allow division by x - y when x = y, then we allow the following > common fallacy: Assume x = y, then æ æ æ æ æ 2 > æ æ xy = y æ æ æ2 æ æ æ æ2 æ 2 > æ æ x - xy = x - y æ æ æ æ æ æ æ 2 æ 2 > æ æ x(x-y) æ x - y > æ æ ------ = ----- > æ æ æx-y æ æ x - y æ æ æx æ æ= æ 2x Then either all x = 0, or 1 = 2. æBoth of these restrict the ring > to one element. The algebraic formalism you cite above works if we carry out the > division first, without assuming x = y, then assume x = y in the > resulting quotient. æHowever, if we let x = y before the division, > problems can arise. æIn most rings, 0/0 is reasonably undefined. You've completely misunderstood - please read the cited posts. ********************************************************* Every time, or at least of times, you post something, it looks pretty > odd, pretty bizarre, and even wrong. You then send everybody to read > your posts on this or that, but that usually helps little, since the > info is hidden most of the times in links to other posts which have > links to other posts, etc. > In the last discussion about determinants, I followed your posts and I > went back to 1999 in one of those paths, so I stopped since I have no > pro training in archeology. > Other links take us to posts with links to posts with links to posts > ...to posts where it all stops! Then we learn that you haven't yet > developed some thing, so it all stops and we get nothing. I think the above situation is pretty confusing, so I insist: if you > think you have some really good general principles in general > algebra that are appliable to a wide range of problems, why won't you > please write them donw in some site so that people will be able to > read them concentrated in one single place? I know this may be a burden to you, but (1) I, at least, would thank > you very much if you'd do it, and (2) these discussions about this is > not true, yes, it is: read on and etc. will stop, and you'll be > able to make your point crystal clear every time. Bill recently gave a URL to the general principals. >http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html > I am too little practiced in mathematics to resent Bill's > pedagogy; so I can make some progress. I find the hints > and methods very helpful. -- > Michael Press- ************************************************************** I have long time been doing maths, and I also have found VERY few times his methods useful. Why very few times? Because I find it rather cumbersome to follow links to posts which have other links to other posts which, again, have even more links to even more posts and etc. per secula seculorum. Already twice it happened to me that : 1) I got as far back as 1999 clicking on links on his posts, so I stopped clicking on links because I were already too worn out; 1) I got back at some stage to a previous post in all that links-path and thus got a precious vicious circle. Read on what happened just 4 days ago, and I quote: >Thanx for the links. it's a little messy to follow those (I already reached once 1999 and other time 2000...), so: do you have some site where these techniques are written? For example, I tried to read about the |Adj A| = |A|^(n-1) but I only found links to other posts with links to other post with links to...*pant*. If all this is more or That example I never elaborated on. It is probably too close to the example in this thread to be of help pedagogically. Let's consider a simpler example of defining derivatives of polynomials algebraically. The first lines above are mine, the lines with quotation marks are Bill's. So I did what Bill always advices, and I began clicking on links to posts and click on links to post and links and...and I got nowhere! What happened? He hasn't yet elabortated that exampple, which doesn't bother him to send you in a links visit that ressembles more Marco Polo's travels than searching for mathematical info. I think Bill has some rather interesting things that, at least, are worth writing down in an ordered way in some site where he can send anyone searching for info, but he won't do it: he'd rather behave like an ass, make fun of you...and keep on sending anyone to his scattered posts; scattered both in the time-space sense, and also in the info contained in them. No wonder his answers many times look wrong to some people, and even more time they look very, very intrincated and unnecessarily complex, and I'm not sure some times they are, but he can always hide away behind his you misunderstood/didn't read ALL my posts. Go on, keep on reading them all, or something of the kind. A shame...oh well. Tonio === Subject: Re: Congruence question. Every time, or at least of times, you post something, > it looks pretty odd, pretty bizarre, and even wrong [...] Aha, you must be the author of the famous review of Dummit & Foote's Abstract Algebra textbook, which contains quite analogous remarks: Yet for all the apparent erudition of the authors, the text is full of obvious errors. For example, on page 44, the authors assert that z*a = z + a, an obvious error. On page 97, we find the ludicrous assertion that a^p = a, clearly false unless p = 1. And on page 329, the text asserts that r(x + N) = rx + N, an obvious typo. Appended below is the full text of the review [1] in all its glory. -------------------------------------------------------------------- Abstract Algebra (2nd Ed.), by David S. Dummit, Richard M. Foote Summary: Riddled with errors and esoteric formulae, this book is incredibly dangerous for students who have yet to achieve a firm grasp of Algebra. Avoid at all costs. Like most Adequacy readers, I am very good at higher mathematics. In high school, I placed near the top of my Algebra II class, and aced the Math portion of the SAT with a 590. As my children are currently working their way through middle school, I felt obligated to renew my skills in order to help them with their homework. But after slogging through Dummit and Foote's turgid tome, I can only say that it is the worst mathematics text I have ever had the misfortune to encounter. The first flaw a reader will note is the incredible rate at which the material is presented. Section 0.1 breezes through difficult concepts like functions, sets, and complex numbers. By Chapter 1, my head was spinning after reading statements like, For n in Z+, Z/nZ is an abelian group under the operation + of addition of residue classes as described in Chapter 0, and, A subset S of elements of a group G with the property that every element of G can be written as a (finite) product of elements of S and their inverses is called a set of generators of G. As we see from these excerpts from the text, Dummit and Foote are disciples of new math, a doctrine discredited in the 70's. Too often, strange symbols and jargon take the place of clear English prose. Extraneous concepts like sets - much less finite nilpotent groups or invariant factor decompositions or symmetric multilinear maps - are merely obstacles to a student's understanding of algebra. Sadly, the authors, holed up in their ivory towers, have not yet learned these vital educational lessons. Yet for all the apparent erudition of the authors, the text is full of obvious errors. For example, on page 44, the authors assert that z*a = z + a, an obvious error. On page 97, we find the ludicrous assertion that a^p = a, clearly false unless p = 1. And on page 329, the text asserts that r(x + N) = rx + N, an obvious typo. That the authors could publish such a sloppy text and remain employed at the University of Vermont speaks volumes about the evils of tenure. I can only recommend this text to those already secure in their knowledge of Algebra who might derive amusement from the frequent missteps of the authors. And even then, with a $100 price tag, it can hardly be considered worth the expense. I fear for the education of the next generation when prominent publishers push new math on hapless educators. Using this text to teach learn Algebra from this text will alienate students from math and science, driving America further behind the rest of the world in education. I can only hope that our school boards will reject this attempt to corrupt high school curricula and get back to teaching the basics. Rating: 0 of 5 stars -------------------------------------------------------------------- [1] http://www.adequacy.org/stories/2001.10.14.163749.94.html === Subject: Re: Congruence question. 20080612.171520@whim.org> posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Every time, or at least of times, you post something, > it looks pretty odd, pretty bizarre, and even wrong æ[...] Aha, you must be the author of the famous review of Dummit & Foote's > Abstract Algebra textbook, which contains quite analogous remarks: æ Yet for all the apparent erudition of the authors, the text is full > æ of obvious errors. For example, on page 44, the authors assert that > æ æz*a = z + a, an obvious error. On page 97, we find the ludicrous > æ assertion that æa^p = a, æclearly false unless æp = 1. And on > æ page 329, the text asserts that ær(x + N) = rx + N, an obvious typo. > ************************************************************* I don't have the slightest and palest idea from where did you take the bizarre idea that I was the author of such a review, which by the way I didn't even bother to read. I only left the above excerpts of that review to make plain the fact himself, and he actually succeeded big time in that. I in fact am a huge fan of Dummit-Foote's book, in spite of the huge ammount of typographical mistakes in several editions, and I even got a personal signed copy of the book from Richard Foote, from the 2nd edition in Prentice-Hall. As it happens, I even volunteered to Richard to write down the solutions of some exercises in several chapters if he even thinks to publish a book with his book's exercises' solutions, but he graciously rejected the idea, at least for now. Please, if you find ridiculous or non-relevant the idea I offered you of putting in some one site your ideas/developments/theories/ about different subjects, then just don't do it, but don't write stupidities like the above one. Tonio === Subject: Re: Congruence question. > Every time, or at least of times, you post something, > it looks pretty odd, pretty bizarre, and even wrong æ[...] > Aha, you must be the author of the famous review of Dummit & Foote's > Abstract Algebra textbook, which contains quite analogous remarks: > æ Yet for all the apparent erudition of the authors, the text is full > æ of obvious errors. For example, on page 44, the authors assert that > æ æz*a = z + a, an obvious error. On page 97, we find the ludicrous > æ assertion that æa^p = a, æclearly false unless æp = 1. And on > æ page 329, the text asserts that ær(x + N) = rx + N, an obvious typo. > ************************************************************* > I don't have the slightest and palest idea from where did you take the > bizarre idea that I was the author of such a review, which by the way > I didn't even bother to read. That's a shame. I enjoyed the review, which is a skillfully written piece of satire. -- Dave Seaman Third Circuit ignores precedent in Mumia Abu-Jamal ruling. === Subject: Re: Congruence question. Every time, or at least of times, you post something, > it looks pretty odd, pretty bizarre, and even wrong æ[...] Aha, you must be the author of the famous review of Dummit & Foote's > Abstract Algebra textbook, which contains quite analogous remarks: æ Yet for all the apparent erudition of the authors, the text is full > æ of obvious errors. For example, on page 44, the authors assert that > æ æz*a = z + a, an obvious error. On page 97, we find the ludicrous > æ assertion that æa^p = a, æclearly false unless æp = 1. And on > æ page 329, the text asserts that ær(x + N) = rx + N, an obvious typo. > ************************************************************* > I don't have the slightest and palest idea from where did you take the > bizarre idea that I was the author of such a review, which by the way > I didn't even bother to read. That's a shame. I enjoyed the review, which is a skillfully written >piece of satire. I knew it rang a bell! (Yours truly was suckered: see post 55.) -- Angus Rodgers Contains mild peril === Subject: Re: Congruence question. > Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n > x - y n-1 n > HINT In any ring ------- = n x = D (x ) if x = y > x - y ??? The LHS isn't even defined if x=y. I'd have thought that a swift application of FlT in order to relate a and b, and then expanding a^p-b^p modulo p^2 would do the trick in no time at all. Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: Congruence question. Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n > x - y n-1 n > HINT In any ring ------- = n x = D (x ) if x = y > x - y > See also my prior posts [1] on the algebraic derivative for polynomials ??? The LHS isn't even defined if x = y. It works fine, please read the references if you wish to learn more. --Bill Dubuque === Subject: Re: Congruence question. > Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. n n > x - y n-1 n > HINT In any ring ------- = n x = D (x ) if x = y > x - y See also my prior posts [1] on the algebraic derivative for polynomials > ??? The LHS isn't even defined if x = y. It works fine, please read the references if you wish to learn more. At least the first reference contains expressions which are either undefined in any ring, or grotesquely abusing common notations to the point of being meaningless without further annotation. I didn't bother reading the second, for obvious reasons. Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: Congruence question. Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. > n n > x - y n-1 n > HINT In any ring ------- = n x = D (x ) if x = y > x - y > See also my prior posts [1] on the algebraic derivative for polynomials ??? The LHS isn't even defined if x = y. > It works fine, please read the references if you wish to learn more. At least the first reference contains expressions which > are either undefined in any ring, or grotesquely abusing > common notations to the point of being meaningless without > further annotation. I didn't bother reading the second, for obvious reasons. sometimes provocative to get people to think. Perhaps you should try that some time, you might learn something. --Bill Dubuque === Subject: Re: Congruence question. > Prove that for any prime p, if a^p - b^p is divisible by p > then a^p - b^p is also divisible by p^2. n n > x - y n-1 n > HINT In any ring ------- = n x = D (x ) if x = y > x - y See also my prior posts [1] on the algebraic derivative for polynomials > ??? The LHS isn't even defined if x = y. It works fine, please read the references if you wish to learn more. > At least the first reference contains expressions which > are either undefined in any ring, or grotesquely abusing > common notations to the point of being meaningless without > further annotation. > I didn't bother reading the second, for obvious reasons. > Using division by zero in a ring is not completely rigorous. > My posts are > sometimes provocative to get people to think. Perhaps > you should try that some time, you might learn something. Sure, I know that being an arse can sometimes be useful for kicking people into thinking. However, my how much of an arse is Bill Dubuque meter is currently showing a divide by zero error. Phil -- -- Microsoft voice recognition live demonstration === Subject: Re: Congruence question. >Prove that form any prime p, if (a^p)-(b^p) is divisible by p then >(a^p)-(b^p) is also divisible by p^2. P.S. >If (a^p)-(b^p) is divisible by p then p|(a-b) or p|(a^(p-1)+... >+b^(p-1)). If p|(a-b) then, using Fermat's Theorem and simply >multiplying, p|(a^(p-1)+...+b^(p-1)) so (a^p)-(b^p) is divisible by >p^2. Now if p|(a^(p-1)+...+b^(p-1)) I do not know how to prove that p| >(a-b) or (p^2)|(a^(p-1)+...+b^(p-1)). You mention Fermat's [Little] Theorem. That theorem says that if p is a prime, then a^p = a mod p. Therefore, if a^p = b^p mod p (which you have written as (a^p) - (b^p) is divisible by p) then we also have a = b mod p. Thus, there is a k so that a + kp = b. Apply the binomial theorem to b^p = (a + kp)^p; that is, b^p = a^p + C(p,1) a^{p-1} kp + C(p,2) a^{p-2} (kp)^2 + ... where we have left out only terms with powers of kp higher than 2. Look closely at C(p,1) a^{p-1} kp and you should be able to finish the proof. Rob Johnson take out the trash before replying === Subject: Re: Congruence question. posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Prove that form any prime p, if (a^p)-(b^p) is divisible by p then > (a^p)-(b^p) is also divisible by p^2. P.S. > If (a^p)-(b^p) is divisible by p then p|(a-b) or p|(a^(p-1)+... > +b^(p-1)). If p|(a-b) then, using Fermat's Theorem and simply > multiplying, p|(a^(p-1)+...+b^(p-1)) so (a^p)-(b^p) is divisible by > p^2. Now if p|(a^(p-1)+...+b^(p-1)) I do not know how to prove that p| > (a-b) or (p^2)|(a^(p-1)+...+b^(p-1)). ************************************************************** a) If both a,b are divisible by p we're done, otherwise: b) None of a,b is divisible by p ==> a^p = a (mod p), b^p = b (mod p) ==> a^p - b^p = (a - b)(a^(p-1)+...+b^(p-1)), but then p divides a - b by the above, and this case you've already covered. Tonio === Subject: Re: Congruence question. days. My association with the Department is that of an alumnus. >Prove that form any prime p, if (a^p)-(b^p) is divisible by p then >(a^p)-(b^p) is also divisible by p^2. P.S. >If (a^p)-(b^p) is divisible by p then p|(a-b) or p|(a^(p-1)+... >+b^(p-1)). If p|(a-b) then, using Fermat's Theorem and simply >multiplying, p|(a^(p-1)+...+b^(p-1)) so (a^p)-(b^p) is divisible by >p^2. Now if p|(a^(p-1)+...+b^(p-1)) I do not know how to prove that p| >(a-b) or (p^2)|(a^(p-1)+...+b^(p-1)). You know that a^p = a (mod p) and b^p = b (mod p). Therefore, what you have is that a^p - b^p = a-b = 0 (mod p), so p|(a-b). -- Arturo Magidin magidin-at-member-ams-org === Subject: Re: #20 is Ampere's and Faraday's laws torus shaped whereas Coulomb is spherical shaped Re: Monograph-Book: FUSION BARRIER PRINCIPLE posting-account=JpxxPAgAAAAgwzQIYqn4j6syK-YhOmcF Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > Re: #19 Control-Theory for Physics and Perturbation is not a theory > but a calculation-aid Re: Monograph-Book: FUSION BARRIER PRINCIPLE, > Archimedes Plutonium, Internet published 1997-2007 > Archie, you have already some many books published, have you considered donating a copy of each to George W. Bush Presidential Library? === Subject: Re: #20 is Ampere's and Faraday's laws torus shaped whereas Coulomb is spherica > Re: #19 Control-Theory for Physics and Perturbation is not a theory > but a calculation-aid Re: Monograph-Book: FUSION BARRIER PRINCIPLE, > Archimedes Plutonium, Internet published 1997-2007 Archie, you have already some many books published, have you > considered donating a copy of each to George W. Bush Presidential > Library? Too late - I hear it burned down, and both books were destroyed. Even worse, he hadn't finished colouring the second one yet. -- /~ cgibbs@kltpzyxm.invalid (Charlie Gibbs) / I'm really at ac.dekanfrus if you read it the right way. X Top-posted messages will probably be ignored. See RFC1855. / HTML will DEFINITELY be ignored. Join the ASCII ribbon campaign! === Subject: Re: #20 is Ampere's and Faraday's laws torus shaped whereas Coulomb is spherica Re: #19 Control-Theory for Physics and Perturbation is not a theory > but a calculation-aid Re: Monograph-Book: FUSION BARRIER PRINCIPLE, > Archimedes Plutonium, Internet published 1997-2007 > Archie, you have already some many books published, have you > considered donating a copy of each to George W. Bush Presidential > Library? Too late - I hear it burned down, and both books were destroyed. > Even worse, he hadn't finished colouring the second one yet. > The only crayon available was black. 'ey, Charlie. /BAH === Subject: Re: Dedanoe takes Ronald Hoeflin Titan IQ Test posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) > the original url of the TITAN IQ test:http://www.eskimo.com/~miyaguch/titan.html The answers to the Titan test have been posted on-line much to the annoyance of the crank Hoeflin. > the primary solutions from five hours strait Proves nothing. > how am i doing so far? Why aren't you paying Hoeflin his fee to grade your test? === Subject: X*Y=10 How can this be a deep dilemma? posting-account=abEEOgoAAADeZ4Q-2TaO2WXmBsDLGHsN Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, but I am stuck when 10 stays 10. Please help! Matt === Subject: Re: X*Y=10 How can this be a deep dilemma? posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/20070622 Firefox/2.0.0.4,gzip(gfe),gzip(gfe) > Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the > act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I > can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, > but I am stuck when 10 stays 10. Please help! Matt Mmmh? 2X * (Y/2) = 2X * (1/2)Y = 2(1/2) X*Y = X*Y? === Subject: Re: X*Y=10 How can this be a deep dilemma? posting-account=G_G-iQoAAAB08LNQidt_LsMkopmIb4ZS Gecko/20060111 Firefox/1.5.0.1 Mnenhy/0.7.3.0,gzip(gfe),gzip(gfe) > Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the > act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I > can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, > but I am stuck when 10 stays 10. Please help! Matt What does LN mean? Bill J === Subject: Re: X*Y=10 How can this be a deep dilemma? posting-account=b4rQkQoAAADqqftYxNCieauSttMs6_zU 1.1.4322; InfoPath.1),gzip(gfe),gzip(gfe) Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the > act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I > can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, > but I am stuck when 10 stays 10. Please help! Matt What does LN mean? Bill J- Hide quoted text - - Show quoted text - Presumably the natural log, but it is hard to be sure given that the OP seems to be using some non-standard terminology. === Subject: Re: X*Y=10 How can this be a deep dilemma? posting-account=abEEOgoAAADeZ4Q-2TaO2WXmBsDLGHsN Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the > act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I > can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, > but I am stuck when 10 stays 10. Please help! Matt What does LN mean? Bill J Natural log. === Subject: Re: X*Y=10 How can this be a deep dilemma? >Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the >act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I >can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, >but I am stuck when 10 stays 10. Please help! Matt HUH???? THis makes no sense! === Subject: Re: X*Y=10 How can this be a deep dilemma? >Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the >act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I >can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, >but I am stuck when 10 stays 10. Do you mean (c*x) * (1/c * y) = 10? -- John === Subject: Re: X*Y=10 How can this be a deep dilemma? > Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the > act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I > can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, > but I am stuck when 10 stays 10. Please help! I don't know what you're talking about, but I won't let that stop me from making a suggestion. What would be wrong with adding 17 as the value of the act of doubling X, and suntracting 17 as the value of the act of halving Y? Then if the two acts occur at the same time, you're adding and subtracting 17 at the same time, and Bob's your uncle. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: X*Y=10 How can this be a deep dilemma? posting-account=H1y7YgoAAADzGQwbcYaL9UvwttgsjOjp AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.1 Safari/525.18,gzip(gfe),gzip(gfe) On Jun 13, 9:55æam, Gerry Myerson Assume X*Y=10 If I double X and cut Y in half it still equals 10 (.5*X * 2*Y = 10) My question is, how do I put a value on the act of doubling X and the > act of halving Y if they occur at the same time? I realize the value will be equal in the opposite direction, but I > can't figure out what that value should be. I used properties of LN when the resulting acts change the 10 value, > but I am stuck when 10 stays 10. Please help! I don't know what you're talking about, > but I won't let that stop me from making a suggestion. What would be wrong with adding 17 as the value of the act > of doubling X, and suntracting 17 as the value of the act > of halving Y? Then if the two acts occur at the same time, > you're adding and subtracting 17 at the same time, > and Bob's your uncle. OP has sent me email which maybe clarifies the request: Let's say X is hours worked and Y is your rate of pay. At time t, X=2.5 and Y=4, time t+1, X=5, Y=2. So my hours worked doubled and my rate of pay was cut in half. How much did my income increase because of the doubling of the hours worked? How much did my income decrease because of the cut in pay? I am assuming they happen simultaneously. I know they need to be equal, but I want to put a real value on each. I think that simultaneously word is the killer. If the hours doubled first, then the income increased by 10 and then decreased by 10. If the pay cut came first, the income decreased by 5 and then increased by 5. If they happened simultaneously, I don't see any compelling argument for assigning any particular value to either. -- GM === Subject: Taylor's Theorem posting-account=6PxpjAoAAAC-LIBlLS0S7M0v0KrAs05L rv:1.9) Gecko/2008061004 Firefox/3.0,gzip(gfe),gzip(gfe) Hello! I have a question regarding the Taylor's theorem for functions on several variables. If I have a function defined on a manifold, f(theta, phi):S^2-->R, where S^2 denotes the sphere in R^3, can I apply directly the well-known formula of Taylor's series taken the derivatives with respect to theta and phi or should I take the derivatives with respect to x,y and z, for example df/dx=df/ dTheta*dTheta/dx+df/dPhi*dPhi/dx? Javier === Subject: Re: Taylor's Theorem posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080404 Firefox/2.0.0.14,gzip(gfe),gzip(gfe) > Hello! I have a question regarding the Taylor's theorem for functions on > several variables. If I have a function defined on a manifold, > f(theta, phi):S^2-->R, where S^2 denotes the sphere in R^3, can I > apply directly the well-known formula of Taylor's series taken the > derivatives with respect to theta and phi or should I take the > derivatives with respect to x,y and z, for example df/dx=df/ > dTheta*dTheta/dx+df/dPhi*dPhi/dx? Javier The multivariate Taylor formula basically assumes convexity, so that the whole line segment joining the initial point x to the new point y = x + delta(x) lies withing the region of continuous differentiability of the function. In (x,y,z) space the surface of the sphere is not convex, because the line segment joining two points on the surface does not lie everywhere in the surface. Therefore, you might be evaluating the derivatives at points that lie outside the surface. However, everything will be OK if you use phi and theta instead. R.G. Vickson === Subject: JSH: Most Recent Cycle posting-account=mgs1FwoAAABD3j5T_RLZ06yrgt2dghDu Gecko/20050915,gzip(gfe),gzip(gfe) I thought it might be interesting to summarize James Harris's most recent cycle, since it seems to me to be quite typical of the iterations James repeatedly exhibits. It's probably just a waste of time to put this together, but James is my favorite koo^H^H^HUsenet personality. Here we go: James was absent from Usenet for most of the month of May, 2008. trivially easy. There is not a real mathematician in the world who cannot trace out the steps of the proof. The factoring problem is solved. May 31, 12:00: Demonstrating that he has learned nothing about algorithmic complexity, James claims that the performance of his latest solution is super exponential. As usual, this is followed by a period during which people try to get James to be more clear about his idea, while James continues to make changes to it, all the while claiming all of math society is out to get him as well as the rest of humanity. June 3, 23:45: You do not understand the true power of mathematics, or the meaning beyond mysticism, or you would never have set yourselves up in a battle that you could only win, if humanity died. June 6, 13:28: Rick Decker (Yup, he's a professor, look it up) and Rotwang demonstrate a very simple numerical counter-example to James's claim, or at least a big part of it. James is forced to admit his error. Nope that's wrong. They still don't work for the trivial factorization. Yuck. June 6, 23:10: After being forced to accept his error, James tries to excuse his obnoxious behavior. I will say a few words about how I do problem solving which typically does include some insults in a post, often lambasting the mathematical community, which has a lot to do with motivating replies to my posts. June 8, 20:24: James tries to backpedal from his original claims. Regardless I've backed off from this particular approach. June 8, 22:22: James makes some minor changes to his equations and posts a new solution to the factoring problem. After my latest miss-steps I went back, looked everything over again and finally noticed something that was bizarrely, simply obvious and staring me in the face. Here's the factoring algorithm that results. Rossum and Enrico explain why this method is no better than the previous one. June 9, 23:51: In an attempt to save face, James switches from claiming a brilliant new factoring algorithm to having found some interesting, previously unknown relations. But there is so much simple beauty in them, how (T - k^2) has to be a quadratic residue. How 'a' is related to the factors through a prime. Knowledge unknown to the world before now though it's not new. It's always been there. June 10, 09:25: Rick Decker demonstrates a counter-example to James's incredible new relations. June 12, 10:05: James tries to sell variations of his new relations with exclamation points. And doing so over infinity!!!!!! To infinity!!!! If history is any guide, James will continue to make minor changes to his equations, perhaps introducing a new independent variable or changing a sign. Eventually he will give up and disappear from Usenet for a while. Then the JSH cycle can begin again! -- Sometimes I believe that our planet is best simply described as world of fools and I may be one of the greatest of all time. -- James Harris === Subject: Re: JSH: Most Recent Cycle > I thought it might be interesting to summarize James Harris's most > recent cycle, since it seems to me to be quite typical of the > iterations James repeatedly exhibits. He does have an amazing ability to bounce back. He reminds me of the toons in Woger Wabbit. === Subject: Re: JSH: Most Recent Cycle I thought it might be interesting to summarize James Harris's most > recent cycle, since it seems to me to be quite typical of the > iterations James repeatedly exhibits. >snip > He does have an amazing ability to bounce back. He reminds me of the > toons in Woger Wabbit. What is amazing is that he seems to be incapable of grasping the fact that he's remarkably stupid. I wonder if it suffers from some medical condition such that displaying his inveterate stupidity to the world gives him a rush? === Subject: Re: JSH: Most Recent Cycle I thought it might be interesting to summarize James Harris's most > recent cycle, since it seems to me to be quite typical of the > iterations James repeatedly exhibits. >snip> He does have an amazing ability to bounce back. He reminds me of the > toons in Woger Wabbit. What is amazing is that he seems to be incapable of grasping the >fact that he's remarkably stupid. I wonder if it suffers from some >medical condition such that displaying his inveterate stupidity to the >world gives him a rush? JSH - an Axiomatic Approach --------------------------- Axiom 1: JSH is the world's greatest living mathematician. Being an axion of the system, this is unchallengable from within the system. We are at liberty to speculate whether or not JSH is the greatest mathematician ever, but we cannot challenge Axiom 1. This axiomatic system is also consistent - there is no inconsistency between the axiom and itself. The greatness of JSH is already apparent. Theorem 1: There are parts of mathematics that only JSH understands. If someone else understood all the mathematics that JSH does, then that person would be as great a mathematician as JSH, and that is not allowed by Axiom 1. Theorem 2: All mathematical results produced by JSH are new, exciting, ground breaking, revolutionary and very important. This follows directly from Axiom 1; since JSH is the world's greatest living mathematician, therefore all his results are the worlds greatest mathematical results. JSH has a complete and rigorous proof of this, but unfortunately it falls into the area of mathematics covered by Theorem 1, so we cannot hope to understand it. This theorem applies to all of JSH's results. If JSH rederives the Chinese Remainder Theorem, then that result is also new, exciting, ground breaking, revolutionary and very important. Whoever first discovered the CRT thousands of years ago was not aware of things like complex numbers, transcendental numbers and so forth that JSH is, hence JSH's result cannot be viewed in the same light as the original proof, which was made in a far less complex environment. Borges' Pierre Menard ... (http://www.coldbacon.com/writing/borges-quixote.html) is relevant here, particularly the passage discussing truth, whose mother is history, rival of time ....