Thursday, November 25, 2004


JSH: Living and learning

I've been watching "Everybody Loves Raymond" and they just had this great episode where Raymond's father decides to paint his house and is his usual self so Raymond fires him, but of course his mother convinces him to go talk to his father again, and his dad says something about people being the problem when all that should matter
is if you're right.

And I used to actually think that way.

I figured that, hey, this is a PUBLIC forum, and I can come out here and talk about whatever math related thing I want—following the RULES you know as it's math related—and then people would give me grief, which to me just showed you that people were the problem. I mean if it's a PUBLIC forum, and you're posting about math then BY THE RULES I should just be able to post, but I got all this flak.

Sure I had lots of ideas that were wrong that I thought were right, but hey, I was following the rules, and in the real world problem solving is a difficult process where you brainstorm ideas, eventually critique them, and then hopefully come out at the end with something.

I FOLLOWED THE RULES of Usenet and twerps gave me grief—still give me grief—and for a while I decided that people were the problem.

But now I realize that some people are the problem and I don't have to let them get to me. So I follow the rules, talk about math related as I see fit, and hey, I have a paper at a math journal anyway, so let the losers keep at it, as if they have no lives.

So hey, yeah, I'm not the nicest guy around, and I don't mind dishing it out, challenging people, or making big claims when I feel they are justified, but at least I'm following the freaking rules of Usenet.

These other people, they steal posts and put them on their own webpages. Hound me all over Usenet, and spend all sorts of effort to control my postings and I'm supposed to be the bad guy?

Like Frank I'm misunderstood. People cheat. But hey, they're still important, and at the end of the day, it's better when you make the effort to be nice. So I'm making the effort. I'm being nice now. This is me being nice.

Tuesday, November 23, 2004


JSH: Better now

I don't know if you noticed but I had a tremendous drop in confidence concomittant with a dramatic grip of existential crisis.

But I feel much better now and my confidence is restored, and I've learned to handle better the implications of my own research.

I guess there's no way any of you would understand what it's like to end up with some research result far bigger than you ever wanted, finding something you didn't want to find, where that makes everything so much harder.

It would have been easier for me in many ways for there not to be this problem with algebraic integers which is so HUGE where it impacts so many areas in mathematics and extends out into the physics world through group theory—though not so much in a bad way!

It's like the screw-up in the math world might have helped physics as group theory got developed, so what if the underlying mathematical ideas were slightly off?

Hey, in physics, if it works, it works.

In any event, for me, there was that lagging doubt that maybe somewhere along the way someone would find something just WRONG with what I had, and why would that be a surprise or not a good thing?

But a lot of people having looked over my work, with a lot of criticisms considered lead me to finally just have to accept that it is correct, despite my severe misgivings.

You know that technique of non-polynomial factorization may lead to new physics theories that can probe into a finer mathematical structure of electron, quarks and other physical particles than anyone ever even dreamed might exist?

Sigh. Of course you don't. That's ok though as it'd shock the hell out of me if any of you had even a minor grasp of how big all of this is, as that would mean you are, um, different in important ways than what I've gathered over years of making these posts and watching the effects.

Now the wait is on a math journal. I'm still not sufficiently motivated to re-write my other papers. So far the paper I wrote on surrogate factoring got a nice paper, but not for us, please send to another journal from a journal in the top 5, while Combinatorica passed on my paper deriving the prime counting function, which is kind
of ok, as it had a minor, sort of error, which they didn't notice. I kind of wonder about this peer review thing.

Hey, NONE of them have given me copies of comments from reviewers. When do you get those? Southwest Journal of Pure and Applied Mathematics didn't either.

Is there some kind of weird rule going on where I don't get comments from reviewers? Maybe from fear I'll just post them?

Tuesday, November 16, 2004


JSH: Legacy of error

Basically the latter 1800's and early 1900's represent a period when a substantial amount of errors, mathematical and logical entered into the math field, and then, in what has been a covering action, the concept of "pure math" was emphasized, which helped to hide the errors.

There is more than just the problem with the ring of algebraic integers that I've discussed so much.

Like, consider the Riemann Hypothesis. I find it hard to face the issue myself at times, but my find of a three dimensional formula that counts primes gives a rather clear and readily understandable explanation for the closeness of the prime distribution to continuous functions.

It's just simple. But you have these complex ideas that got a lot of attention, get a lot of attention, and I know that nothing will come of them.

If you look at Riemann's actual work, you'll find a section where he talks about certain terms looking like they'll tend to zero, as they look like they should balance out.

But has anyone ever proven that they will?

Goldstone had what he thought was a proof shot down for using the same type reasoning just recently. So why wouldn't anyone go back to Riemann's work with the same analysis?

Yet, why is my work still just supposedly the rantings of some "crank" when all of it is now rigorously proven?

You are in a field with a legacy of error.

Andrew Wiles didn't prove Fermat's Last Theorem. Riemann's Hypothesis can be shown to probably be wrong on some very basic grounds, but no one will admit it. And that's not all of the error.

I have research I don't bother even talking about in public, as what's the point?

Actually it's just freaking depressing. The mistakes cluster around 1900, both before and after it, and it's just weird looking at them, wondering.

Like think about this algebraic integer thing. Why wouldn't it occur to people that maybe they might want to consider roots of non-monic polynomials irreducible over Q that might correlate to integer examples like

3x^2 + 4x + 1 = (3x + 1)(x + 1)?

I mean, it's not like it takes brilliance to consider that maybe some non-monics—even if they were irreducible over Q—might have roots that have integral properties despite being irrational.

It doesn't take brilliance to consider possibilities.

And as for counting primes, why not have a p(x,y) function that gives a count with p(x,sqrt(x))? Why couldn't the answer to linking the prime distribution to continuous functions like x/ln x come from multi-variable functions?

Why not ask why?

Have you seen my derivation of the prime counting function?

Such a simple derivation could have been done a thousand years ago. Maybe it was and lost.

If I knew a few years ago what I know now, I'd have never made these discoveries—if I could have stopped myself. Ignorance is bliss. There is no profit in it after all, and I'm not talking about money. I never really was.

Sunday, November 14, 2004


JSH: Contradiction shown

Now it turns out that having thought it all through I finally realized that I could show a direct contradiction using the objections raised against my work.

Notice here I'll actually use constants where before I talked about variables being held constant.

I start with

P(x) = 14706125 x^3 - 900375 x^2 - 17640 x + 1078

which can be factored into non-polynomial factors by using

P(x)= 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3

which looks complicated but if you multiply it all out and simplify, you get the first, and I just have an analysis method for breaking up a polynomial in a certain way to factor it—into non-polynomial factors—and here the factorization is

P(x) = (5 a_1(x) + 7)(5 a_2(x) + 7)(5 a_3(x) + 7)

where the a's are roots of

a^3 + 3(-1 + 49x)a^2 - 49(2401 x^3 - 147 x^2 + 3x).

And it's easy to get that cubic by solving for one of the a's using

(5 a_1(x) + 7)(5 a_2(x) + 7)(5 a_3(x) + 7) = 7^2(2401 x^3 - 147 x^2 + 3x) (5^3) - 3(-1 + 49 x )(5)(7^2) + 7^3.

Now I've pointed out that setting x=0, will show that two of the a's equal 0 at that point, while one equals 3, which others have argued is a "special case".

The cubic with x=0 is

a^3 -3a^2 = 0

so two of the a's equal 0, while one equals 3.

Usually I arbitrarily select a_1, and a_2 to equal 0, at x=0, which is what I'll do now. Then, with

P(x) = (5 a_1(x) + 7)(5 a_2(x) + 7)(5 a_3(x) + 7)

at x=0, you have two of the a's equal 0, while one equals 3, to give

P(0) = 7(7)(22) = 1078

which fits with

P(x) = 14706125 x^3 - 900375 x^2 - 17640 x + 1078.

Then for the first two factors (5a_1(x) + 7) and (5a_2(x) + 7) the 7's visible in the expressions are factors of the constant term of P(x).

But P(x) is a multiple of 49 as each coefficient has 49 as a factor, so I divide out the 49 to get

P(x)/49 = 300125 x^3 - 18375 x^2 - 360 x + 22.

Now assume each of the a's has some non-unit factor in common with 7, for a given x, which in fact they do in the ring of algebraic integers whenever all the a's are irrational, which is a point that has been brought up repeatedly by people arguing with me. For a while I resisted that fact, but now as I've said before I concede that they are in fact correct—each of the a's, in the ring of algebraic integers does in fact share a non-unit factor with 7 when all of the a's are irrational.

So let w_1(x) w_2(x) w_3(x) = 49, where the w's are those factors, so

a_1(x) = w_1(x) b_1(x),

a_2(x) = w_2(x) b_2(x),


a_3(x) = w_3(x) b_3(x)

and where

w_1(x) v_1(x) = 7, w_2(x) v_2(x) = 7, and w_3(x) v_3(x) = 7,

and divide through by 49 to get

P(x)/49 =

(5 b_1(x) + v_1(x))(5 b_2(x) + v_2(x))(5 b_3(x) + v_3(x))

and if you allow that the factors are each factors of the constant term as before, then you have

v_1(0) v_2(0)(15 + v_3(0)) = 22

at x=0, and when x does not equal 0, you have

v_1(x) v_2(x)(5u_3(x) + v_3(x)) = 22

where I introduce u_3(x) to handle any further weirdness with how a_3(x) behaves, where u_3(0) = 3, to agree with previous results, and remember

P(x)/49 = 300125 x^3 - 18375 x^2 - 360 x + 22

and the constant term doesn't change, as, well, it's constant, as it's 22.

So, notice, I now have that v_1(x) and v_2(x) are factors of 22.

Provably, they cannot be units in the ring of algebraic integers when a_1(x), a_2(x), and a_3(x) are all irrational as that's what people argued with me about for so long.

The full result was just so weird that it escaped even me for a while, as following their arguments to their logical conclusion 22 and 7 must share non-unit factors in the ring of algebraic integers.

But you can also appear to prove that 22 and 7 are coprime in the ring of algebraic integers using various accepted definitions of coprimeness, like you can find algebraic integers x, and y such that

22x + 7y = 1

and claim to have proven that they are coprime.

So, in the ring of algebraic integers, using what's commonly accepted you can prove that 22 and 7 are both coprime and that they share non-unit algebraic integer factors.

That's the full result.

Now, of course, posters arguing with me on Usenet wouldn't follow through to the full result, probably because they weren't smart enough to see it, as make no mistake, that's the kind of result that's quite big.

That's a career maker, or could have been one. For me, it's just one of my results. Nice, sure, but still just one, with techniques I introduced in a couple of lines in another paper.

The ring of algebraic integers is quirky. That arbitrary selection of roots of monic polynomials with integer coefficients allows you to do all kinds of wacky things, including believing that you're doing all kinds of great math, when you have nothing at all.

Make no mistake, the big names in math today have just about zero reason to accept these results. Would you if you were them?

But you're not them.

You are students. You have the future to make your names, with real math that is actually correct.

I'm offering you your future. Follow the math, and then if you have what it takes, then accept what is true without holding your breath waiting for old men who are trying to stave off ruin to do the right thing.

They are cowards. They will admit the truth when they no longer believe they can get away with lying.

Come on, do you really think results like these could have been missed by the top "mathematicians" of the world?

Well, maybe, maybe they don't know. But I think they do. After all, I've contacted people all over the math world, as I've been quite bold in pushing forward this issue, in warning about the error.

I think they do know and they are waiting to see what you do.

I think they are waiting to see if you will let them get away with the lies.

Maybe you will—or at least, maybe you'll try. LOL. Some of you probably will try because you're young, and foolish, and so eager to please them.

Monday, November 08, 2004


JSH: At the Annals

I basically looked over the paper Advanced Polynomial Factorization, considered all the arguments and various comments from journals, editors and various people I've talked to about it, and rewrote and renamed it.

The result went to the Annals, which accepted it for review.

So, no, I'm not concerned about sci.math posters coming later and trashing the journal and yes I'm assuming few problems. After all, I've gone over every step in the argument repeatedly to quite a few people, from Barry Mazur, to Ralph McKenzie at my alma mater in-person, to, yes, Usenet posters.

There is no error.

And also, I'm not terribly concerned about how it will be handled by reviewers because I have so much information from what happened with the older paper.

Essentially, it's over, but I'm sure many of you will cherish your ability to continue to badmouth my work and act as if it's nothing for as long as you can because that's really all you can do at this point.

I have included non-polynomial factorization, stepped out each step, and noted the conflict with what follows from the ring of algebraic integers, and noted it as an error within the discipline.

The paper is quite solid.

I don't know how long you people have exactly, but you may have until next year, early.

So enjoy that time if you feel that being wrong is something to enjoy, and be thankful for whatever it is that you people are thankful for, as I wish you cared about mathematics itself.

Sure, egos can get caught up in something, and it's hard to finally swallow your pride—I know—but at the end of the day if you care about mathematics then you care about what is TRUE, and your ego be damned.

At the end of the day, it's not really my work, but the world's. Information valuable to humanity is not something to be blocked, fought, and maligned becaus it makes you feel bad or scared.

Unfortunately, since humanity's beginning there have been minority groups who feel threatened by new information to the extent that they fight it, long past the point when the fighting should stop.

But there is progress because those people lose. And that is what you should really be thankful for.

Now, it's drift time. Waiting. Time to think. Time to consider before the hammer finally falls.

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