JSH: Random distributions and prime numbers
in [Physics]
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From: JSH on 12 Feb 2010 19:43 On Feb 12, 2:59 am, rich...(a)cogsci.ed.ac.uk (Richard Tobin) wrote: > In article <b899990f-0dd0-46ce-b468-57844c33e...(a)v20g2000prb.googlegroups..com>, > > JSH <jst...(a)gmail.com> wrote: > >What I call the prime residue axiom leads to very specific > >predictions. > > Where can I find a precise statement of this axiom? As a mathematical It's my axiom. So I've written its statement. prime residue axiom: given differing primes p_1 and p_2, where p_1 > p_2, there is no preference for any particular residue of p_2 for p_1 mod p_2 over any other. > formula, not as words. (So that it can, for example, be used in > an automated proof checker.) It's an axiom. It is like indistinguishability of quantum states, so that random holds. You could also call it prime residue indistinguishability. It immediately leads to the conclusion that given an odd primp p_2, for any prime p_1 greater than p_2, p_1 mod p_2 has an equal probability of being ANY of p_2's p_2 - 1 residues. For instance, 3 has 1 and 2 as residues. The prime residue axiom says that if you pick another odd prime p at random, p mod 3 will tend to equal 1 or 2 with 50% probability with variation following the normal distribution. Somehow I got to be the person who declared the axiom, so I got to name it, and pick the wording. James Harris
From: JSH on 12 Feb 2010 19:46 On Feb 11, 7:08 pm, William Hughes <wpihug...(a)hotmail.com> wrote: > On Feb 11, 8:49 pm, JSH <jst...(a)gmail.com> wrote: > > > On Feb 11, 7:23 am, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > On Feb 11, 11:04 am, JSH <jst...(a)gmail.com> wrote: > > > > >Well if the predictions are wrong then there is no further argument. > > > >End of story. > > > > Your prime residue axiom makes predictions about the > > > density of the twin primes. As you acknowledge, these > > > predictions are wrong (It does not matter that you think > > > Nope. With the simplest probability calculation they tend to be 1.12 > > times the actual count over time based on what others have posted. > > I.e. wrong. > > > > > I noted that was because of blocked states with higher residues with > > the larger primes in the interval. > > You think you know why the predictions are wrong. They are still > wrong. > > JSH: Well if the predictions are wrong then > JSH: there is no further argument. End of story. > > Are your predictions wrong? Please start your answer Yes or No. > > - William Hughes Statistical arguments bore me. You can say that a probability is wrong, if you wish, but you're clearly not a physics student. And you're past tedious. What do you think, you can win an argument? Ok, you win. Now then, moving on to people who might wish to actually DO something.... James Harris
From: Richard Tobin on 12 Feb 2010 19:49 In article <3ed9de84-c8d1-4445-994a-8ae7e8204e7d(a)m35g2000prh.googlegroups.com>, JSH <jstevh(a)gmail.com> wrote: >> formula, not as words. (So that it can, for example, be used in >> an automated proof checker.) >It's an axiom. It is like indistinguishability of quantum states, so >that random holds. I'm still having trouble translating it into mathematical symbols. Do you have any suggestions how one might do this? Obviously I can't feed English text into a proof checker. -- Richard -- Please remember to mention me / in tapes you leave behind.
From: JSH on 12 Feb 2010 19:59 On Feb 12, 4:49 pm, rich...(a)cogsci.ed.ac.uk (Richard Tobin) wrote: > In article <3ed9de84-c8d1-4445-994a-8ae7e8204...(a)m35g2000prh.googlegroups..com>, > > JSH <jst...(a)gmail.com> wrote: > >> formula, not as words. (So that it can, for example, be used in > >> an automated proof checker.) > >It's an axiom. It is like indistinguishability of quantum states, so > >that random holds. > > I'm still having trouble translating it into mathematical symbols. Do > you have any suggestions how one might do this? Obviously I can't > feed English text into a proof checker. I come up with things and toss them out there and see what happens over time. If what I call the prime residue axiom IS an axiom, then it will have an impact on the world. Over time, lots of people will work hard to understand it and its implications. But that could take years. It seems to me that posters routinely forget what I do. I come up with ideas and toss them out there and then move on. I first started working in this area over 3 years ago, but didn't realize then I had an axiom in mind. Now over 3 years later I realized it, and tossed it out there. As far as I'm concerned, years can go by while the world processes it. It's like with my definition of mathematical proof. I didn't think much of it when I tossed it on my math blog. I certainly didn't expect Google to pick it up and make it #1 over much of the world, but that is what happened--over years. It may not be a satisfying answer, but for many of you, this close to my first coming up with the axiom, you may see nothing happen at all. Nothing may happen for years. I kind of feel sorry for you. To me, the process is becoming second nature. For you, it may seem that resolution should happen quickly. Like in days. But I'm telling you, nope, YEARS maybe. So sorry, I'm not going to get very excited. Not going to do much or care about helping you a lot. As far as I'm concerned, nothing may happen for years or even decades. So no rush. James Harris
From: William Hughes on 12 Feb 2010 20:59
On Feb 12, 8:46 pm, JSH <jst...(a)gmail.com> wrote: > On Feb 11, 7:08 pm, William Hughes <wpihug...(a)hotmail.com> wrote: > > > JSH: Well if the predictions are wrong then > > JSH: there is no further argument. End of story. > > > Are your predictions wrong? Please start your answer Yes or No. > > Statistical arguments bore me. ... Try again. - William Hughes |