### Thursday, March 11, 2010

## JSH: Math, logic, pragmatic reality and primes

Years ago I noted that with math people I was stuck unable to convince them with mathematical proof, which doesn't quite make sense, and it puzzled me for years, and of course on Usenet posters claimed otherwise (I found it to be true off Usenet as well, for instance with mathematical journals), but now you can see it in action with what I call my prime residue axiom.

Years ago I noticed that you could consider twin primes probability in a fairly simple way by assuming that primes have no preferred residue modulo each other, which gives a nice little formula:

prob = ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2)

where you look at the interval p_{j-1}^2 to p_j^2, as my simple idea was to use the actual count of primes WITHIN that interval with the prob calculation, so it keeps shifting, as you go higher, you get more primes, and my simplification works rather well.

THAT is ALL from over 3 1/2 years ago. I pushed the idea further back then, realized you should be able to do something similar for prime gaps of arbitrary even size, and realized some depressing things. If true, my simple idea PROVED the twins prime conjecture and DISPROVED Goldbach's Conjecture. But in a probabilistic proof!

All that is from over 3 1/2 years ago. I argued about a few things on Usenet and wandered off, and recently brought the subject up again and decided I had an axiom which I called the prime residue axiom.

Arguments erupted and posters argued both sides: some claimed I didn't have an axiom, others claimed that what I had was already proven but so what?

Oh, and I forgot, you can also find ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2), in the twin primes constant!

See: http://mathworld.wolfram.com/TwinPrimesConstant.html

Now I know how people can ignore bold facts like seeing a formula from a probabilistic interpretation in established literature, which does a rather good job of predicting twin primes probability with a simpler formula than what is currently taught, and argue BOTH SIDES as if it were nothing at all!

People can in fact confidently proclaim that 2+2=5 and believe it, if you understand human nature and how the mind works.

So there is no doubt that this approach is a simplification, it ties in easily with prior known research, and has scary implications like that you can prove the Twin Primes Conjecture and disprove Goldbach's Conjecture with one interpretation.

But you may have noticed that the math world isn't exactly buzzing with the news!

If you know your math history you know that study of twin primes got big about the time I say a rather remarkable error entered into the mathematical field, where I've proven that the ring of algebraic integers can be trivially shown to contradict with the field of complex numbers!

That allows you to appear to prove things without having actually done so, and as it has been in the field for over a hundred years it has selected people who are tolerant of the error.

Such people can believe two different and contradictory things at the same time.

The mathematical flaw at the heart of established number theory SELECTS such people, as people who are not so capable could not be number theorists WITH THAT FLAW.

That is, if you were not a person with that peculiar ability, even if you did not understand that something was wrong with the ring of algebraic integers thoroughly, you might have some weird feeling that would push you into a different field, like topology.

Ok, so back to prime numbers! Turns out I have multiple results around prime numbers. The people who can believe two different and contradictory things always say that none of them are important! The prime residue axiom though leads to a prime gap equation. It took me a while to get that correct but I think I have the correct equation as of now on my math blog (though I haven't posted it on Usenet, having put up flawed prior versions).

So why not just use the prime gap equation over a wide range to prove I'm right?

Because it won't matter to the people who can believe two different and contradictory things at the same time, who have been selected into number theory by the core error I found, which means they cannot be moved by mathematical proof, as given ANY proof they can believe it's opposite just as easily as believe in the proof itself. Damn inconvenient, eh?

It's a conundrum. These people dominate number theory because the error dominates number theory.

I assure you they are special people whose brains allow them to believe two different and contradictory things at the same time.

The error that entered into number theory over a hundred years ago is perfect for these type of people and they found a comfortable home in number theory and fashioned "pure math" to secure that home. Notice 'pure math" came into the field at about the time of the error and at about the time that the twin primes conjecture was made.

To themselves they are normal!!!

You will NOT get anywhere trying to explain to them that it's not normal to be able to believe two opposite and contradictory things at the same time, as their brains work that way. To them it's as natural as breathing.

The situation is actually kind of fascinating in many ways. God only knows what can break the hold of these people on number theory. But I assure you that facts and therefore mathematical proof, cannot.

Years ago I noticed that you could consider twin primes probability in a fairly simple way by assuming that primes have no preferred residue modulo each other, which gives a nice little formula:

prob = ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2)

where you look at the interval p_{j-1}^2 to p_j^2, as my simple idea was to use the actual count of primes WITHIN that interval with the prob calculation, so it keeps shifting, as you go higher, you get more primes, and my simplification works rather well.

THAT is ALL from over 3 1/2 years ago. I pushed the idea further back then, realized you should be able to do something similar for prime gaps of arbitrary even size, and realized some depressing things. If true, my simple idea PROVED the twins prime conjecture and DISPROVED Goldbach's Conjecture. But in a probabilistic proof!

All that is from over 3 1/2 years ago. I argued about a few things on Usenet and wandered off, and recently brought the subject up again and decided I had an axiom which I called the prime residue axiom.

Arguments erupted and posters argued both sides: some claimed I didn't have an axiom, others claimed that what I had was already proven but so what?

Oh, and I forgot, you can also find ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*…*(1/2), in the twin primes constant!

See: http://mathworld.wolfram.com/TwinPrimesConstant.html

Now I know how people can ignore bold facts like seeing a formula from a probabilistic interpretation in established literature, which does a rather good job of predicting twin primes probability with a simpler formula than what is currently taught, and argue BOTH SIDES as if it were nothing at all!

People can in fact confidently proclaim that 2+2=5 and believe it, if you understand human nature and how the mind works.

So there is no doubt that this approach is a simplification, it ties in easily with prior known research, and has scary implications like that you can prove the Twin Primes Conjecture and disprove Goldbach's Conjecture with one interpretation.

But you may have noticed that the math world isn't exactly buzzing with the news!

If you know your math history you know that study of twin primes got big about the time I say a rather remarkable error entered into the mathematical field, where I've proven that the ring of algebraic integers can be trivially shown to contradict with the field of complex numbers!

That allows you to appear to prove things without having actually done so, and as it has been in the field for over a hundred years it has selected people who are tolerant of the error.

Such people can believe two different and contradictory things at the same time.

The mathematical flaw at the heart of established number theory SELECTS such people, as people who are not so capable could not be number theorists WITH THAT FLAW.

That is, if you were not a person with that peculiar ability, even if you did not understand that something was wrong with the ring of algebraic integers thoroughly, you might have some weird feeling that would push you into a different field, like topology.

Ok, so back to prime numbers! Turns out I have multiple results around prime numbers. The people who can believe two different and contradictory things always say that none of them are important! The prime residue axiom though leads to a prime gap equation. It took me a while to get that correct but I think I have the correct equation as of now on my math blog (though I haven't posted it on Usenet, having put up flawed prior versions).

So why not just use the prime gap equation over a wide range to prove I'm right?

Because it won't matter to the people who can believe two different and contradictory things at the same time, who have been selected into number theory by the core error I found, which means they cannot be moved by mathematical proof, as given ANY proof they can believe it's opposite just as easily as believe in the proof itself. Damn inconvenient, eh?

It's a conundrum. These people dominate number theory because the error dominates number theory.

I assure you they are special people whose brains allow them to believe two different and contradictory things at the same time.

The error that entered into number theory over a hundred years ago is perfect for these type of people and they found a comfortable home in number theory and fashioned "pure math" to secure that home. Notice 'pure math" came into the field at about the time of the error and at about the time that the twin primes conjecture was made.

To themselves they are normal!!!

You will NOT get anywhere trying to explain to them that it's not normal to be able to believe two opposite and contradictory things at the same time, as their brains work that way. To them it's as natural as breathing.

The situation is actually kind of fascinating in many ways. God only knows what can break the hold of these people on number theory. But I assure you that facts and therefore mathematical proof, cannot.