JSH: Random distributions and prime numbers
in [Physics]
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From: Peter on 10 Feb 2010 18:51 I could see why the notion that all residues occur with equal frequency to a physicist (since there isn't any obvious reason why one should be preferred over the other, I suppose.) But aren't there other observations in math that could suggest that the distribution might not be uniform? I'm thinking specifically of Benford's law that seems to say that not all of the digits naturally occur with the same frequency. Peter
From: JSH on 10 Feb 2010 19:50 On Feb 10, 3:51 pm, Peter <pi2over...(a)gmail.com> wrote: > I could see why the notion that all residues occur with equal > frequency to a physicist (since there isn't any obvious reason why one > should be preferred over the other, I suppose.) But aren't there other Well my bachelors is in physics, but I've based my assertion on what I call the prime residue axiom. Axioms are things considered self-evident. If it IS an axiom then the rest follows mathematically by proof. > observations in math that could suggest that the distribution might > not be uniform? I'm thinking specifically of Benford's law that seems > to say that not all of the digits naturally occur with the same > frequency. That's a different subject (though an interesting one). The primes are not actually dependent on our reality. One can posit that in any reality where there are sentient beings who count, they will get numbers, get primes, and be able to find the prime residue axiom, but who knows what physics might govern their reality. So everything really goes to the prime residue axiom. If it IS an axiom then the rest is just about mathematical proof. Now mathematicians have accidentally verified the prime residue axiom to a very large degree, by their work on twin primes, but that is not something they may like as if it is true that could mean the end of continuing research! I've studied this issue for years, and it's a great way to test out how the world works. Some people seem to believe that humanity has greatly advanced in its mathematics, science and logic. I disagree. By considering such an important issue and how people react to it, I can watch behavior versus mathematical proof. See people disagree with observable data. And study rationalizations across wide groups around the world. Here all nations are equal, and so far equally bad. Humanity may think highly of itself, but reality seems to indicate our species is still, primitive. James Harris
From: Junoexpress on 10 Feb 2010 20:55 On Feb 10, 7:50 pm, JSH <jst...(a)gmail.com> wrote: > On Feb 10, 3:51 pm, Peter <pi2over...(a)gmail.com> wrote: > > > observations in math that could suggest that the distribution might > > not be uniform? I'm thinking specifically of Benford's law that seems > > to say that not all of the digits naturally occur with the same > > frequency. > > That's a different subject (though an interesting one). > What justification do you have for this statement? While I don't know whether it is true or not, it's not obvious to me that it isn't. If any fact leads to results that contradict your axiom, then the axiom is not an acceptable one. Just because you declare something an axiom doesn't give you carte blanche to claim that no other potentially contradictory situation can occur. I think part of your trouble is that you're probably calling something an axiom that isn't James. An axiom is *not* something that is considered self-evident: think about non-Euclidean geometry for a moment before you shoot off your mouth and look stupid again. You need to learn the definitions for some of these terms before you go throwing them around like a monkey flinging feces. An axiom is an assumption that one has some freedom in the way it is chosen, as long as the final logical structure in which it is contained does not lead to a contradiction. In your case, you are dealing with a fact: either the residues have a specific distribution or they don't. Maybe someone better trained in logic, like Jesse, can make this notion a bit more rigorous, but in the end, I think you're getting a little fuzzy in your thinking James. What you're calling an "axiom" is, in reality, probably what a physicist would call an "ansatz" or a mathematician would call a "conjecture". You should probably look these terms up and learn them. HTH, M
From: JSH on 10 Feb 2010 21:05 On Feb 10, 5:55 pm, Junoexpress <mtbrenne...(a)gmail.com> wrote: > On Feb 10, 7:50 pm, JSH <jst...(a)gmail.com> wrote:> On Feb 10, 3:51 pm, Peter <pi2over...(a)gmail.com> wrote: > > > > observations in math that could suggest that the distribution might > > > not be uniform? I'm thinking specifically of Benford's law that seems > > > to say that not all of the digits naturally occur with the same > > > frequency. > > > That's a different subject (though an interesting one). > > What justification do you have for this statement? While I don't know > whether it is true or not, it's not obvious to me that it isn't. If > any fact leads to results that contradict your axiom, then the axiom > is not an acceptable one. Just because you declare something an axiom > doesn't give you carte blanche to claim that no other potentially > contradictory situation can occur. > > I think part of your trouble is that you're probably calling something > an axiom that isn't James. An axiom is *not* something that is > considered self-evident: think about non-Euclidean geometry for a > moment before you shoot off your mouth and look stupid again. You need > to learn the definitions for some of these terms before you go > throwing them around like a monkey flinging feces. An axiom is an > assumption that one has some freedom in the way it is chosen, as long > as the final logical structure in which it is contained does not lead > to a contradiction. In your case, you are dealing with a fact: either > the residues have a specific distribution or they don't. Maybe someone > better trained in logic, like Jesse, can make this notion a bit more > rigorous, but in the end, I think you're getting a little fuzzy in > your thinking James. What you're calling an "axiom" is, in reality, > probably what a physicist would call an "ansatz" or a mathematician > would call a "conjecture". You should probably look these terms up and > learn them. > > HTH, > M I defined mathematical proof. I think I know what an axiom is. I've also had over 3 years to ponder this subject. There is also a huge amount of evidence accidentally gathered by mathematicians already working on twin primes. Hard data. But the denial is actually interesting. I can test the entire world. So it doesn't matter to me if it's US or Britain. Russian or Chinese. Japanese or Brazilian. To me, you're all the same. And we're still waiting on the LHC to power up again soon. Part of what I'm doing is priming the pump ahead of its data, and also hopefully protecting it from further sabotage. Those who doubt I defined mathematical proof need only check in Google (has to be Google). Search on: define mathematical proof My job is hard, but not impossible. I'm simply stuck with a primitive species which thinks it is more advanced than it shows itself to be. But the data is being found, slowly but surely. And you can only damage the LHC for so long. When the Higgs is not found, then things can get interesting, maybe. Or I can wait for the next opportunity. It may take years, but it will come. James Harris
From: BURT on 10 Feb 2010 23:36
On Feb 10, 6:05 pm, JSH <jst...(a)gmail.com> wrote: > On Feb 10, 5:55 pm, Junoexpress <mtbrenne...(a)gmail.com> wrote: > > > > > > > On Feb 10, 7:50 pm, JSH <jst...(a)gmail.com> wrote:> On Feb 10, 3:51 pm, Peter <pi2over...(a)gmail.com> wrote: > > > > > observations in math that could suggest that the distribution might > > > > not be uniform? I'm thinking specifically of Benford's law that seems > > > > to say that not all of the digits naturally occur with the same > > > > frequency. > > > > That's a different subject (though an interesting one). > > > What justification do you have for this statement? While I don't know > > whether it is true or not, it's not obvious to me that it isn't. If > > any fact leads to results that contradict your axiom, then the axiom > > is not an acceptable one. Just because you declare something an axiom > > doesn't give you carte blanche to claim that no other potentially > > contradictory situation can occur. > > > I think part of your trouble is that you're probably calling something > > an axiom that isn't James. An axiom is *not* something that is > > considered self-evident: think about non-Euclidean geometry for a > > moment before you shoot off your mouth and look stupid again. You need > > to learn the definitions for some of these terms before you go > > throwing them around like a monkey flinging feces. An axiom is an > > assumption that one has some freedom in the way it is chosen, as long > > as the final logical structure in which it is contained does not lead > > to a contradiction. In your case, you are dealing with a fact: either > > the residues have a specific distribution or they don't. Maybe someone > > better trained in logic, like Jesse, can make this notion a bit more > > rigorous, but in the end, I think you're getting a little fuzzy in > > your thinking James. What you're calling an "axiom" is, in reality, > > probably what a physicist would call an "ansatz" or a mathematician > > would call a "conjecture". You should probably look these terms up and > > learn them. > > > HTH, > > M > > I defined mathematical proof. I think I know what an axiom is. I've > also had over 3 years to ponder this subject. > > There is also a huge amount of evidence accidentally gathered by > mathematicians already working on twin primes. > > Hard data. > > But the denial is actually interesting. > > I can test the entire world. So it doesn't matter to me if it's US or > Britain. Russian or Chinese. Japanese or Brazilian. To me, you're > all the same. > > And we're still waiting on the LHC to power up again soon. Part of > what I'm doing is priming the pump ahead of its data, and also > hopefully protecting it from further sabotage. > > Those who doubt I defined mathematical proof need only check in Google > (has to be Google). > > Search on: define mathematical proof > > My job is hard, but not impossible. I'm simply stuck with a primitive > species which thinks it is more advanced than it shows itself to be. > But the data is being found, slowly but surely. > > And you can only damage the LHC for so long. When the Higgs is not > found, then things can get interesting, maybe. > > Or I can wait for the next opportunity. It may take years, but it > will come. > > James Harris- Hide quoted text - > > - Show quoted text - Hard data? My information doesn't say that. Mitch Raemsch |