JSH: Depressing reality, prime reality
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From: Jesse F. Hughes on 10 Mar 2010 06:23 Transfer Principle <lwalke3(a)lausd.net> writes: > There have been a few threads here at sci.math which discuss the > possibility that RH is undecidable in ZFC, or that Goldbach's > Conjecture is undecidable in ZFC or PA. Some standard theorists > wonder, if RH or GC is undecidable in ZFC, does this mean that RH or > GC are "true"? Standard theorists don't *wonder* whether GC is true if undecidable. If GC is undecidable, then it is true (no scare quotes needed). This is an obvious fact. (Maybe the claim about RH is just as obvious, but I'm don't know much about RH.) -- "And I'll reinforce the point that you are an enemy of humanity, that my predecessors are people like Gauss, Euler, Newton, Archimedes and others who you are spitting upon as you do it to me by trying to keep their discipline trashed as it is now." -- James S. Harris
From: William Hughes on 10 Mar 2010 07:34 On Mar 10, 7:23 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Transfer Principle <lwal...(a)lausd.net> writes: > > There have been a few threads here at sci.math which discuss the > > possibility that RH is undecidable in ZFC, or that Goldbach's > > Conjecture is undecidable in ZFC or PA. Some standard theorists > > wonder, if RH or GC is undecidable in ZFC, does this mean that RH or > > GC are "true"? > > Standard theorists don't *wonder* whether GC is true if undecidable. > If GC is undecidable, then it is true (no scare quotes needed). This > is an obvious fact. > True in the standard model. Whether this means "true" is an interesting question. If GC is undecidable then it is "true" in exactly the same way that the Goedel sentence is true. - William Hughes
From: Jesse F. Hughes on 10 Mar 2010 08:21 William Hughes <wpihughes(a)hotmail.com> writes: > On Mar 10, 7:23 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Transfer Principle <lwal...(a)lausd.net> writes: >> > There have been a few threads here at sci.math which discuss the >> > possibility that RH is undecidable in ZFC, or that Goldbach's >> > Conjecture is undecidable in ZFC or PA. Some standard theorists >> > wonder, if RH or GC is undecidable in ZFC, does this mean that RH or >> > GC are "true"? >> >> Standard theorists don't *wonder* whether GC is true if undecidable. >> If GC is undecidable, then it is true (no scare quotes needed). This >> is an obvious fact. >> > > True in the standard model. Whether this means "true" > is an interesting question. If GC is undecidable then > it is "true" in exactly the same way that the Goedel > sentence is true. Fair enough: true in the standard model. -- "How can people [philosophers] talk like that? Acting as if they're /glad/ they don't know things! Finding out more and more things they don't know! It's like children proudly coming to show you a full potty!" -- Terry Pratchett, /Small Gods/
From: William Hughes on 10 Mar 2010 08:26 On Mar 10, 8:48 am, "Ostap S. B. M. Bender Jr." <ostap_bender_1...(a)hotmail.com> wrote: > On Mar 9, 9:08 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > > > On Mar 9, 12:30 am, "Ostap S. B. M. Bender Jr." > > <ostap_bender_1...(a)hotmail.com> wrote: > > > On Mar 8, 8:50 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > > One standard theorist claimed that the result is true and follows > > > > from Dirichlet's theorem, but Dirichlet's theorem only shows that > > > > these sets are _infinite_, not what their density is. > > > Really? That's not what English and Russian Wikipedias say: > > >http://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_primes_in_arith.... > > > In number theory, Dirichlet's theorem, states that for any two > > > positive coprime integers a and d, there are infinitely many primes of > > > the form a + nd, where n ⥠0. In other words: there are infinitely > > > many primes which are congruent to a modulo d.  Stronger forms of > > > Dirichlet's theorem state that  different arithmetic progressions with > > > the same modulus have approximately the same proportions of primes. > > > Further, the proportion of primes in each of those is: 1/phi(m), where > > > phi is Euler's totient function. > > Actually, when I was searching for the original thread in which > > JSH first stated his "axiom," I found a thread that I had never > > noticed (since I didn't read sci.math during the first half of > > February at all, only the second half of the month). In that > > thread, Arturo Magidin explained the "axiom" completely: > > Magadin, 4th February 2010, 8:13PM Greenwich Time: > > "There is the quantitative form of Dirichlet's Theorem, and > > Chebotarev's Density Theorem. If N>=2 and gcd(a,N)=1, then the > > density > > of primes congruent to a modulo N is asymptotic to phi(N), where phi > > is Euler's totient function. This follows from Chebotarev (as someone > > pointed out ot me recently) by looking at the cyclotomic extension > > modulo N. > > This, of course, settles everything: > > -- So it's not Dirichlet's Theorem, but Chebotarev's that applies. > > -- According to the theorem, {keN | (P(k) == 1) mod 4} does have > > _asymptotic_ density 1/2, but by _another_ density measure (the > > "certain" density measure mentioned by Magadin), it differs from 1/2. > > Now Magadin doesn't recall whether it's 1 mod 4 or -1 mod 4 that has > > more primes by this other measure, but in another thread, someone > > pointed out that it's the quadratic nonresidues that have more primes. > > To be honest, I cannot follow all of your logic here. For example, why > have you  guys suddenly started talking about the "mod 4" case only? > Isn't this result true for all N, and not just for N = 4? > > > > > And so we conclude that JSH's "axiom" really isn't an axiom, > > Let me understand what you told me: the "JSH conjecture" has been > proven long time ago. That is, it is a simple corollary to the > Dirichlet Theorem and/or Chebotarev's Theorem. Correct? Yes and no. JSH has not given a very clear definition of his conjecture. On the one hand, the way he uses it, it is clear that he needs more than uniformity of residues, he also needs independence. This is known to be false. On the other hand JSH seems to think that independence and uniformity are the same thing. It depends where you put the error. If the conjecture states uniformity, then the error is in application of the conjecture. If the conjecture states independence then the error is in the conjecture. > > 1. Has anybody told JSH yet? I bet he will be very happy to hear that > he has wasted his and our time claiming that a proven result is a "new > axiom". :-) > He has been told many times and from the first. He has not commented. Add this to the list of things JSH cannot hear. > 2. Your previous posts seem to indicate that this JSH thingie is a > major step in proving the Twin Primes Conjecture. If so: now that we > have proof of this JSH thingie, why don't we just finish proving the > Twin Primes Conjecture  and share the next Abel Prize among ourselves? > Maybe we'll let JSH give an "Abel Lecture/acceptance speech" in Oslo > (if there is such a thing):-) You need more than uniformity. As you note, if uniformity was enough the twin prime conjecture would have been settled long ago. - William Hughes
From: harry on 10 Mar 2010 12:29
"JSH" <jstevh(a)gmail.com> wrote in message news:c9df7007-edde-4b12-bb32-96e5f6591ae1(a)t17g2000prg.googlegroups.com... >Try clipping your "Musatov" search in similar ways and see what you >get. > > >James Harris Musatov another troll. Or is JSH = Musatov ? No one cares abou trolls. Trolls die horrible deaths. |