Monday, August 31, 2009


JSH: But what are your options?

The fury elicited by my talking about a simple relation with "Pell's Equation" can give some of you perspective on how intractable this situation is, as some of you may know that I re-discovered that result from my own general solution to binary quadratic Diophantine equations. So I did one thing that had never been done—a general solution for binary quadratic Diophantines—and found an earlier result known for hundreds of years which today I think is oddly obscure.

And I say "fury" because that's what it is. Years ago I thought it was just arguing on newsgroups and there were just some nasty people who mouthed off because they could, but as the years have gone by, and my influence has grown, and my discoveries have piled up, there is clearly a rage developing and its scary. Very scary.

For those who know I DID generally solve binary quadratic Diophantine equations and know that was a huge achievement there may be the obvious question of, why not have it published? I tried. All the math journals I sent it to, rejected it, without claiming it was wrong!

My favorite rejections came from the Bulletin of the AMS where the chief editor would send this reply saying my work wasn't suitable for that journal. I kept sending papers. She finally begged me not to send any more paper claiming it was a "survey journal" and I figured, hey, it's pointless, why not do as she says? If the chief editor is going to beg you not to send papers, why continue?

The mathematical community does not want these discoveries, and what are your options?

If the world believes that mathematicians would not do what they are doing, and you can see they are doing it, what then?

And then there is the fury. I do worry. This situation is not one that can last indefinitely I'd think, but it has gone on for longer than I thought possible.

Another weird thing is that I found a way to solve quadratic residues mod p. It's a nifty little way to do it which seems popular by web search measure. That is, do a search in Google (and Yahoo! amazingly enough last time I checked) on: solving quadratic residues

And I probably will be #1 wherever you are in the world. Mathematicians reject that research as well. Though I admit I never sent papers on it in particular. But it has been around for a while.

But what are your options?

The one time I did get a paper through the gauntlet, the math community destroyed the journal. That is, the journal pulled my paper after publication and quietly shutdown. Its parent university scrubbed all mention of the journal which had been electronic only but published for a decade. They scrubbed all mention. Google: SWJPAM

So what are your options? If I push hard enough will mathematicians completely snap? Would my life be in danger?

I try to imagine being someone out there in the world watching this situation and realizing it is happening, and there are these discoveries which are clearly true, where math people react in fury at the mere mention of them. And what can that person do?

I know I wouldn't know what to do. I don't know what to do. Mostly I just kind of keep doing a few things at the edges like this post and my earlier postings and try to understand the psychology of these people. How they motivate themselves. How they fight like they do, for what? I don't know. I have theories but only they know or maybe even they don't know why they fight so hard.

Destroyed an entire math journal. Like it was trash. And on Usenet on sci.math they gloried in the destruction and maligned the journal even in its death. I saw it as anarchy but the math community I believe sees it as a necessary defense.

Sunday, August 30, 2009


JSH: Pell's Equation war of words

A rather well-known in mathematical circles relation called Pell's Equation has become the focus of a bizarre to me war of words, where I've noted what I think is an interesting rational parameterization of an equation that is normally considered only with integers as it is a Diophantine equation.

The relation follows yet again for completeness of this post, though I have given it in two prior threads (would have thought one thread would be enough, but now I have to address some oddities with this one). The relation is NOT new having been known to Fermat, so it's been known for at least several hundred years:

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)


x = (D + t^2)/(D - t^2)

and you get hyperbolas with D>0, the circle with D=-1, and ellipses in general with D<0.

You can see the D=-1 case from a well-known mainstream source at the following link:
See: eqns. 16 & 17

Now one particularly belligerent poster has obsessively replied to me in prior threads, and I'm making this thread to note a few things.
  1. If you do a web search on Pell's Equation—yes, I know there are things not yet on the web but a lot IS on the web so it makes sense to check—there is no mention of the rational parameterization in the first 5 links I see doing the search in Google. The 6th link though is mine!!! It's a link to my freaking math blog!!!

  2. When I do the search now on Pell's Equation my math blog takes links 6 and 7 when I do that search in Google.

  3. So, sorry if I'm not going to just accept it when some poster starts ranting about me being this ignorant person, as if I should just accept that it is standard teaching that Pell's Equation has this rational parameterization which can be used in the study of ellipses and hyperbolas especially when my own ideas in this area are taking over web search results!!!
Come on! Give me a break!

And I guess some of you think that's nothing. As if the world simply puts any person up to that level of attention just, oh, I don't know, just because it's such a friendly, puffy world that can just be so nice to some people, eh?

It's not a nice world. It's a mean world, with a lot of competition. The competition in this area is fierce.

If you can use Pell's Equation to classify orbits with a D number instead of eccentricity that might show something that you don't see with eccentricity. But it might not.

Physics is about asking and answering questions.

The people who fight me, are about not asking, and most definitely, don't you ever dare, answer the questions.

These wars have changed the Internet as it exists today, having gone way beyond Usenet, to the Wikipedia and across any number of media as the mathematical community seems to believe it can win.

And I know it can't. As if it does, then human progress, stops.

So ok, if the math wars are to continue, fine. Your world will continue to change as a result and maybe that IS the point.

As we have these huge unbelievably massive battles, we push the world forward, and at the end of the day, maybe that's all that matters.

Saturday, August 29, 2009


JSH: Categorization conflict with Pell's Equation?

I've been amazed by finding out that a rather simple rational parameterization of the equation known as Pell's Equation has been known for hundreds of years, when I found it by re-discovering it, and I'm bringing this subject up again—as I have another thread on it—as I'm wondering if it is a case where because mathematicians traditionally look at Pell's Equation as a Diophantine equation, the rational parameterization of it has been dismissed and almost forgotten though it can be found if you search for it and possibly keeps getting re-discovered:

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)


x = (D + t^2)/(D - t^2)

and you get hyperbolas with D>0, the circle with D=-1, and ellipses in general with D<0.

You can see the D=-1 case from a well-known mainstream source at:
See: eqns. 16 & 17

If I'd seen that as a kid in standard texts when I liked to do things like have the computer graph curves I'd have definitely programmed that one, as it lets you go from hyperbolas to ellipses by simply changing a single number.

It would be amazing if mathematicians by categorizing Pell's Equation as a Diophantine equation created an odd situation where the human species kind of just happens to keep forgetting that you have this way to look at it with rationals!!! Over the entire planet. The entire human species.

You see, the rational parameterization is, of course, useless for solving Pell's Equation in integers only, which is what you do considering it as a Diophantine equation, and in fact, Fermat dismissed it for that reason in one of his letters, hundreds of years ago, when he and others were engaging in contests around what we now call Pell's Equation.

They'd compete to get solutions in integers for various D's that are hard.

Wednesday, August 26, 2009


Rational parameterization with certain conics

While number theorists consider Pell's Equation only with integers, it can be considered with rationals, parameterized and related then to all the conic sections except the parabola:

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)


x = (D + t^2)/(D - t^2)

and you get hyperbolas with D>0, the circle with D=-1, and ellipses in general with D<0.

You can see the D=-1 case from a well-known mainstream source at the following link:

See: eqns. 16 & 17

Tuesday, August 18, 2009


JSH: But Twitter is more fun

Sorry dudes but after years of fun arguing on newsgroups I've found a new arena where I can max supreme—Twitter. I tweet and do searches and find my tweets all over the place!

And unlike newsgroups, it's more like instant gratification. My tweets end up on political sites on economics sites and government sites and it's like, well, it's like a whole new world.

Besides, like I said, my math doesn't need me. I am still promoting it though in ways maybe because it's hard to break the habit, but arguing with "angry idiots" on newsgroups isn't gratifying.

REALITY has shifted!!!

But it is weird—my math really does not need me.

I call it my math. But it doesn't even know me.

Yeah, I can promote it if I want but it doesn't care and moves around the world at its own pace, as if I don't even matter. And wow, it MOVES. The mathematics I've discovered has no respect for the limitations of human imagination. Not even mine.

It is beyond us mere mortals: It cares not where we whither, it listens not when we speak. It is its own in all ways.

So I have Twitter. Near instant gratification. A way to feel important. To think that maybe I matter. And life moves on…

After over a decade of arguing and ranting, and often not making any sense even to myself, there's a weird melancholy at the thought of moving on…somehow I guess I'll miss it.

No more dominating newsgroups, taking over with threads that could overwhelm till the regulars screamed in posts in agony.

No more arrogant or disdainful or just plain nonsense replies.

No more to wonder if I got it right, or if it matters, or if anyone cares.

Twitter is more fun.

You losers can keep on ranting until they cut off the lights, but the world has moved on…and so have I.

Sunday, August 02, 2009


JSH: Understanding classed behavior

The recent discussions are fascinating as they help show a bizarre reality where certain posters on these newsgroups will deny ANY evidence and attack ANYONE they see as helping someone they've decided is beneath them, so now they're attacking Google because I've noted some search results related to my mathematical research where that research comes up highly.

Now it seems to me that if it's very clear that part of what I'm doing is studying their odd behavior maybe they'd think better of doing it!!! But there they go anyway, with fascinating assaults against Google where they dismiss search results, with a fascinating position that those do not matter.

Ok, so it's very clear then how the same people could dismiss publication in a mathematical journal as they did when I was published in the now defunct journal SWJPAM, and I suggest to you there is NOTHING that would work with them. Nothing.

Not reason. Not publication. Least of all, mathematical proof!

So what gives? How can such people act with such obsessiveness and WHY would they? Answer is, it's classed behavior.

Let's say you were nobility in a two-tier class society, like Old England, and you were confronted with a commoner who could out-do you on just about every level, would that matter?


Only your class mattered.

Classed societies put some people in one class and others in another class beneath them, and that is not about merit.

Now then, could you LET the commoner behave as if he or she were event at you level? No. Classed societies would exact harsh retribution against commoners who stepped over class lines so they could maintain those lines.

Classed systems are against merit. They are about social order.

So that's the explanation.

It's a class war.

So to these people mathematical proof is irrelevant. Publication in a mathematical journal just proved to them that the journal was trash. When their conniving destroyed the journal—some of them mounted an email assault against my paper, the journal pulled the paper, the journal died soon thereafter—it was the FAULT OF THE JOURNAL IN THEIR MINDS!!!

Now they despise Google because I get high rankings on some search results.

There are no limits—theirs is a classed position.

For them class rules demand they assault anything that undermines the class position they believe they have.

They are math royalty in their own minds.

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