## JSH: So why tautological spaces?

Lost in all the arguing around this or that research of mine is the tool used to find mathematical solutions like the simplification to binary quadratic Diophantine equations which I call a tautological space.

At its simplest it's just an identity like: x+y+vz = x+y+vz, but written as x+y+vz = 0(mod x+y+vz), and I'd guess that few of you are into modular arithmetic or it's also called congruences, if you are physics people as I was not, but learned their utility.

Notice you have x, y and z, plus an extra variable I call v. (I picked v as the variable for various reasons.)

That extra variable v is your handle on the space. It can be ANY VALUE you wish! And I invented this approach because I was frustrated fiddling with an equation where I'd exhausted all possible ways I could think of, of manipulating x, y and z.

ALL the major controversy you see with Usenet posters who relentlessly reply to my postings is around the research given by tautological spaces. The paper that went to the math journal that published it, withdrew it, and then died, was from tautological spaces.

The postings I've done on binary quadratic Diophantine equations is with research I did using tautological spaces.

To me it's simple enough: math people will kill one of their own journals, stalk me relentlessly, and spread as much disinformation as possible to distract people from using this technique I call tautological spaces. So I understand what they're doing. While for the rest of you it's probably a mystery, as to what could be the big deal with such a thing?

Well tautological spaces again are just identities. Because they are identities the basic tautological space is always true, and you just take the identity, manipulate it algebraically a bit, and subtract ANY equation you wish, where I'd assume it'd have only x, y and z, and then you analyze the residue.

The residue then has all its properties from the equation you subtracted from it, which I call the conditional, but it also has this extra variable v, which is YOURS. You can make v whatever you wish, which means your creative mind can come into play and you can actually talk to the mathematics you might say, and at times I feel like it's more of a conversation with the math.

It's like you are partners.

The story here is way screwy as yes, math people already killed one of their own math journals fighting this research. And you can see the arguing over my latest use of it with binary quadratic Diophantine equations in recent threads all over the sci.physics newsgroup.

Oh, I'd like to leave you with one more thing, which I re-discovered because of these latest musings, and let you ponder why mathematicians would let this be lost, or mainly just not noted as important!

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

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

and

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.

I think that is beautiful and yet it was known to Fermat. Why isn't it taught today in even baby physics courses? The D is related to eccentricity. You can produce every ellipse or hyperbola—just a small, I guess unit-like version with ellipses—by just fiddling with that D number.

But you see, mathematicians don't see that as an equation for use with rationals as they call it "Pell's Equation" and only care about it as a Diophantine equation, that is, only for integers.

Math people are quirky. They can do the damndest things. So yeah, I invented this technique I call tautological spaces and in warring against it they've killed one of their OWN math journals, and you can see the continual stalking on the newsgroups.

Why? Ask them. I dare you. Just even the rational parameterization. Ask some math person why that is buried within the math literature rather than being trumpeted as an interesting way, at a minimum, to graph ellipses and hyperbolas.

And who knows? What if the D number said something about orbits that eccentricity does not, when you look at the data laid out?

What if our universe cares more about the D number than it does about eccentricity?

Can you say right now whether the physics looks different with one number or the other when you consider orbit classification?

## JSH: So what is the best explanation for Google search results?

One thing that I have puzzled over for years has been high rankings on certain Google search results, which certain stalking posters think is me trying to brag. It's not. When I first noticed it I thought, hey, maybe my amateur research is heading towards acceptance! But now YEARS later, with no change, I'm mostly puzzled.

The problem can be considered to be loosely a physics problem like analyzing traffic flows is a physics problem. The question here is, why is Google ranking certain search results for a Usenet "crackpot" or "crank" so highly?

Anywhere in the world where you have access to the Internet the following Google searches should bring up a page on my math blog at #1:

define mathematical proof

But why?

I have other #1's. My open source programming project will come up #1 on ALL major search engines with the search:

class viewer

And here's the weird one which will work only in the United States I think:

Superman plot idea

That brings up a plot idea I had for a Superman movie! And goes to one of my non-math blogs.

I've already noted that I've discounted the significance of these results as I've had years to ponder the mystery.

I'm opening it up to explanation as a physics problem.

And no, I don't post links to any of the above. To my knowledge only the open source project has a lot of other pages linking to it.

And my non-math blog with the Superman plot idea according to stats from various sources averages only 1 hit per day, which could be me as I visit it regularly.

Any thoughts or idea beyond the knee-jerk dismissal of the stalker-azi who plague my threads with inane replies?

## JSH: Impossible to predict

One problem I'm having is that I didn't expect this scenario. It didn't seem possible to me that a person could have easily demonstrated mathematical results, clearly demonstrating things never before done, and the world just, sort of, do nothing.

The first surprise was with my prime counting research, as it lead to a partial differential equation, which, just so happened to give simple answers to questions that motivated Riemann.

Easy to show. Easy to show the introduction of the calculus in this unique way. But that was done by me back in 2002.

Since then I've considered areas where I thought breakthrough could not just be ignored, like with the factoring problem, and focused on extreme simplification in applied mathematics, like with my solution to binary quadratic Diophantine equations.

Inexplicably to me, not only could experts in the field blissfully ignore major advances, but the world let them.

Over the years I've worked at several theories to explain the social dynamics which allow this series of events to occur, but regardless of any intellectual appreciation for the bizarre depths of the problem, the hardest thing is just to SEE these things routinely that I'm sure most people would say are impossible.

I mean, like I defined mathematical proof! Just an off-hand thing in a way one day for me, but now years later, to see it come up #1 in Google searches? Bizarre. But weirder, the rationalizations by Usenet posters to explain it away as if it were nothing, which necessarily for logical reasons, lead them to attacking Google itself. Despite the ever growing strength of one of the world's major companies.

Impossible to predict.

Re-thinking history I've gone back to more carefully review the lives of past major discoverers and realized a lot more tragedy was evident than even I accepted before. So what I'm facing is not new! There is something weird that happens, where society punishes people like me.

IF only I'd known that before!!! Like when I was a kid!!!

But of course, if world society does punish instead of reward for major discoveries, why would it want that realized?

Smart people would simply not make them.

Increasingly I'm turning to working at warning.

Alan Turing was mentioned by me in a tweet where I introduced memes noting that major problem solvers are often destroyed by society versus being cheered. Often society will kill them: Archimedes killed, Boltmann pushed to suicide, Socrates pushed to suicide, Alan Turing pushed to suicide, Martin Luther King, Jr. killed, John Lennon killed

All remarkably enough can be considered to be major problem solvers.

The message I'm beginning to carefully and with a lot of special force introduce worldwide is that the penalty you may pay for being a major discoverer is death at the hands of your society.

It is a scary reality for me now. The behavior of Usenet posters is a tame version of what can happen. My society is very likely going to try and kill me, for doing what I thought was great, what I thought was a good thing, what I naively believed was the way to go.

Impossible to predict.

But with the lessons now learned, I can warn.

## JSH: Math is easy, people are hard

Short of it is, I found this nifty way to handle mathematics around things called binary quadratic Diophantine equations, which come up in quantum mechanics or something, I think.

Given a Diophantine equation of the form:

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

which is called a binary quadratic Diophantine equations, because x and y are the unknowns—the c's are known constants—I have a way to transfer solving, like figuring out if integer solutions exist or not, to handling a simpler equation:

(2A(x+y) - B)^2 - 4As^2 = B^2 - 4AC

where A, B and C are defined by the c's and are:

A = (c_2 - 2c_1)^2 + 4c_1(c_2 - c_1 - c_3)

B = 2(c_2 - 2c1)(c_6 - c_5) + 4c_5(c_2 - c_1 - c_3)

and

C = (c_6 - c_5)^2 - 4c_4(c_2 - c_1 - c_3).

Now x+y and s are unknowns where s is actually a function of x and y. (You can solve for s if you wish by substituting and simplifying, where I recommend letting a computer program do it for you.)

If you substitute everything and simplify then you just get back:

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

So you will go in a circle which confirms the correctness of the equations.

Turns out that mathematicians had not accomplished that task. And it currently is not part of mainstream literature or techniques for handling these equations.

What is part of the mainstream are several techniques to handle them, so yes, there are known methods for doing so, where there are several when I can give one, which has only one special case.

It may give 0=0, in specific situations, and the fix is to substitute x = z-y. Which gives you a binary quadratic Diophantine with z and y, which will work, and then you find x easily enough.

The mathematics I've given is new to me. If you search the literature you will not find a simpler way to handle these equations.

There can be computational benefits to a simplified approach.

Here is some literature I've found doing a search which shows an area where these equations might be applicable.

<quote>
W. A. Beyer1, J. D. Louck1 and P. R. Stein1

(1) Los Alamos National Laboratory, 87545 Los Alamos, NM, U.S.A. Received: 11 February 1986 Revised: 22 August 1986

Abstract The interface between Racah coefficients and mathematics is reviewed and several unsolved problems pointed out. The specific goal of this investigation is to determine zeros of these coefficients. The general polynomial is given whose set of zeros contains all nontrivial zeros of Racah (6j) coefficients [this polynomial is also given for the Wigner-Clebsch-Gordan (3j) coefficients]. Zeros of weight 1 3j- and 6j-coefficients are known to be related to the solutions of classic Diophantine equations. Here it is shown how solutions of the quadratic Diophantine equation known as Pell's equation are related to weight 2 zeros of 3j- and 6j-coefficients. This relation involves transformations of quadratic forms over the integers, the orbit classification of zeros of Pell's equation, and an algorithm for determining numerically the fundamental solutions of Pell's equation.

The symbol manipulation program MACSYMA was used extensively to effect various factorings and transformations and to give a proof.
</quote>

All the arguing with various Usenet posters can give the wrong impression that the mathematics is in doubt. It is not.

It is rather simple algebra that is easily checkable with a computer program, but regardless, it was previously unknown.

Mathematicians CURRENTLY teach more convoluted techniques which are less efficient.

I do not have Ph.D in mathematics or a Ph.D at all, as I only have an undergraduate degree in physics. Maybe I don't know all the rules to the game to try and get academics to recognize this find.

And yes, I argue a lot on Usenet, and I challenge the status quo, but if I have found something useful I'm just one person with an opinion when it comes to the rest, while the knowledge should belong to the entire human race.

One man with an opinion shouldn't scare you.

People ignoring an important mathematical result, should.

## JSH: Hard part is discovery, but…

When I was a kid in elementary school I dreamed of being a great discoverer. I'd read the little kid biographies of Newton and Einstein and I'd ask myself a simple question, if I'd lived in their times, and known what they did, would I have made the discoveries they made?

As I grew older and read more in-depth biographies I learned to also worry about acceptance, as while it was a dream of mine to have my own major discoveries I also had to realize that the odds were long and I might never. But if, somehow, I did, then what?

I think it's amazing how many people seem to either think that great discoveries are just accepted, or the slightly more annoying people who think that for the great discoverer, life is tragic and usually they're never recognized until long after they're dead.

Oh, you thought that was great artists? A great discoverer is just an artist by another name.

Albert Einstein was working as a patent clerk. Seems he couldn't get an academic position. Hmmm…

One of my favorite stories about Einstein which I only learned recently despite having read quite a few biographies on him was that he promised the money from the Nobel Prize he EXPECTED to win, long before he ever got it, to his wife Mileva as part of a divorce settlement.

Talk about confidence, eh? Or was it simply arrogance?

Recently there has been more press about Galileo Galilei and I was reading an article in the Smithsonian magazine I think it was where it was noted that Galileo was a relentless promoter of his own research.

Can you imagine him today? On Usenet? How many posters would line up to deride him as a crank and crackpot, the more he promoted himself and his research.

Boltzmann had a paper published in his local town newspaper. But he IS one of the more tragic figures, and committed suicide before he was recognized.

Alan Turing was pushed to suicide and the British government recently apologized for his treatment.

But then again, Galileo ran afoul of the Roman Catholic Church and spent his latter years imprisoned in his own home.

Einstein spent his later years distanced from the physics community. Someone who was considered just famous for his past work, with his current ideas considered well, not worth seriously considering.

One of my favorites though for perspective is Nikolai Tesla. A man who can be said to have given us the means to have our modern world, as he pioneered AC electricity—along with so much else—having to fight a bruising battle against Thomas Edison, who pushed for DC current, and would even torture elephants to death in demonstrations to claim it was dangerous. Edison brought us the electric chair as a means of execution as part of his fight against the technology without which we would not have our modern world.

Nikolai Tesla reportedly believed aliens talked to him from outer space, liked pigeons so much he fell in love with one, and would only stay in hotel rooms divisible by 3.

He died in one, alone, and it was days before his body was found.

You are not a discoverer for your world to treat you well.

And you are lying to yourself if you expect that it will just appreciate you.

Instead it may very well kill you. Archimedes was cut-down by a Roman soldier.

But IF you are a discoverer, you'll find out things anyway, and you know why?

What else would you do with yourself?

People can like you or hate you or whatever but that's about them. It's never really about your discoveries.

Those make you because you are their way into this world, like a line through which current flows.

The discoverer is the link for knowledge into our world. Nothing more. It's not about greatness or personality or wanting it.

It is about being someone through which the knowledge WILL flow, whether you like it or not, and whatever consequences follow, for you, and your world.

Discovery is destiny.

## JSH: Here's the weird thing

I'll point out something and I get these Usenet posters dismissing it as if I'm just some "crank" or "crackpot" looking for self-promotion as if that proves that nothing I say can be worth puzzling over, when to me this Google search thing is actually rather weird.

Years ago when I first started noticing ideas of mine taking over in Google searches I was excited about it, thinking that meant my research was heading towards immediate acceptance.

But here we are years later…

Yet it seem so strange to me, while the lack of curiosity displayed by attack Usenet posters to me is about their tiny intellects. They're a primitive sub-species that sees insulting people on Usenet as the height of good living. It makes their reptilian brains all giddy or something.

So they're not a surprise. These are dumb people. The surprise would be if they DID find it odd that my research dominates in these searches.

Now I like taking the definition of mathematical proof partly because I figure it annoys math people!!! Talk about sticking it them in a sensitive spot, eh?

A guy some Usenet posters have painted as a "kook", "crank" and a "loon", if you consider that Erik Max Francis guy who runs Crank.net, who yes, I argued with in the past on sci.math so if you thought he was an outsider to Usenet, you were fooled, by that fool.

To me he's just another angry sci.math poster and I've seen a lot of them over the years.

But I digress…so for ME to take over the definition of mathematical proof is such a cool thing which drives Usenet people on sci.math freaking butt crazy nuts, so much that they can't help attacking Google searches themselves! To hear the math Usenet freaks talk (ok you can't HEAR them literally typing away but anyway), Google is this third rate company that produces meaningless search results that no one cares about, which mean NOTHING.

LOL. They're so much fun those Usenet math people. They're bizarrely brainless to supposedly know math.

BUT as here is a physics newsgroup, I will emphasize that mathematics is a tool, so the math, yes, will work for physics people.

So what do the Google searches mean really?

Best guess I have is that there ARE people around the world who discover that my math works!!! But they're terrified of having themselves or their research connected with a "crank", so they hide their interest as best they can.

Either that or some people at Google are playing around with me.

I actually at one point got so frustrated on this issue that I wrote my Congress people, and as I live in San Francisco, they are Nancy Pelosi and Dianne Feinstein. My peeps. I love those two.

Maybe I should take a road trip down to Google's offices, eh? Start banging on the doors demanding someone take me to see the Google guys—you know whoever those two guys are who started the thing—and get some damn answers!!!

Why oh why does Google indicate that I defined mathematical proof for the world?

Search string: define mathematical proof

Try that anywhere in the world you have Internet access.

Hey, can we get a march on Google started here? Who's with me? Who is ready to march down to Google and demand why they would DARE let some guy branded on Usenet as a CRANK for God's sake, take over the definition of mathematical proof and irritate math weenies all over the world?

Like, if the Google guys aren't looking out for the feelings of math weenies? Who is?

Math weenies around the world are tearing up as they read this post (of course they MUST be secretly reading, somewhere).

Cheer up guys. Mommies probably right there as you live at home anyway. Go cry on her shoulders and maybe she'll give you a cookie to help you feel better.

Last year I found a nifty mathematical short-cut for handling with integers equations of the form

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

which are called binary quadratic Diophantine equations, where x and y are unknown and the c's are known constants, and my understanding is that they come up in quantum mechanics.

There ARE various methods for getting from the general equation to an equation of the form u^2 + Dv^2 = F, which I've seen called the general Pell's Equation, where solving it allows you to solve the original, but I found the fastest short-cut out there:

(2A(x+y) - B)^2 - 4As^2 = B^2 - 4AC

where A, B and C are defined by the c's and are:

A = (c_2 - 2c_1)^2 + 4c_1(c_2 - c_1 - c_3)

B = 2(c_2 - 2c1)(c_6 - c_5) + 4c_5(c_2 - c_1 - c_3)

and

C = (c_6 - c_5)^2 - 4c_4(c_2 - c_1 - c_3).

The s is actually I think x-y, but I usually just give it as s, as it's still just another unknown.

That IS the short-cut approach to generally handling binary quadratic Diophantine equations which has only one special case, when c_2 = 2c_1, and c_2 - c_1 - c_3 = 0, which is handled with a substitution, like y = x + z, and then it all works, as otherwise you get 0 = 0.

Now I discovered that mathematical tool last year and as I'm proud of it, I've talked about it and I've sent it to mathematicians and even tried to get a paper published, to no avail.

So I'm back on Usenet trying to reach the physics community directly, as it IS a tool. And yes, there are Usenet posters who make it their business to insult people but that's because that's what they do—insult people.

There is no other method that works as directly as a short-cut for binary quadratic Diophantine equations and it is a shame that academics around the world have built a system that allows someone like me to be blocked possibly just because I don't have a math Ph.D, or any Ph.D and you all know that's a really close club.

Math Ph.D's might piss on themselves rather than admit that someone without even a math degree, as my undergrad is in physics, might figure out something really BIG.

Maybe they're afraid it'd be the end of the world as they know it.

Regardless, they've fought me before to a standstill and killed a math journal to do it. Google: SWJPAM

I've countered by putting information out there and pointing out when Google pulls the world to it, like do this search in Google.

Search string: binary quadratic Diophantine equations

I call these the Math Wars. I discover things, math people ignore my discoveries, while some fringe Usenet freaks insult me.

The Math Wars are about math society as an institution foolishly believing that in its numbers and influence it can stop the research of one man, me.

We are battling to see if they are right. And the world feels the heat of that massive exchange.

You can side with the mathematicians in the Math Wars if you wish, and use weaker techniques that are not as fast or as effective, or you can advance the human species.

Mathematicians are mostly Ph.D's who are too small-minded to understand that human Progress is bigger than even their massive egos, and sure, maybe they can block my research for a few more years, but when it breaks through, they diminish all academics, as if mathematicians can ignore simple mathematics easily proven, why can't ANY academic ignore the truth?

Why should the world then trust academia?

Why not just shatter it entire and start over?

The Math Wars can only last so long. For me to lose this research must be lost…

And humanity must then work harder than it need, and do less than it can, so some petty people can protect their turf.

## JSH: Factoring with general solution?

One of the things I've noted is that last year I derived a general solution for binary quadratic Diophantine equations using what I call tautological spaces. I've been talking about it on the sci.physics newsgroup because such a solution has relevance to quantum mechanics where such equations come up.

But some sci.math'ers have come over and hijacked the discussion and the focus has shifted to factoring, as yes, a general solution to binary quadratic Diophantine equations must also handle factoring because xy= T is a binary quadratic Diophantine, which I didn't even think of with these equation until the poster Enrico brought it up.

But that's not something that interests physics people, so I want a thread here on sci.math for THAT discussion and sci.math'ers can quit bugging me about it on the sci.physics newsgroup.

The general solution that I found allows you to take any binary quadratic Diophantine of the form

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

and relate solving it to instead resolving u^2 + Dv^2 = F, which is related to prior art, that is, the ways people solve such equations anyway before my research, but my method allows you to do that in one step, across the board for all such equations (with one exception easily handled).

That is not in debate.

What is debated is getting the solution after, where the math I've given turns to an easy relation that follows from the research but is easily verified without it:

Given: x^2 + Dy^2 = F,

(x-Dy)^2 + D(x+y)^2 = F(D+1)

which is why it's a lift, as you repeat using that identity you get a higher power of D+1, for instance, next is:

((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F(D+1)^2

so you can solve for u and v, with

u^2 + Dv^2 = F(D+1)^j

where j is arbitrarily high and step back down the chain to your original equation.

THAT is the second piece and it's important to note that the general solution I've found is VERY easy and has two parts:
1. It allows you to get to the form u^2 + Dv^2 = F, to solve any binary quadratic Diophantine of the form:

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

2. A simple relation that follows from the method gives you

u^2 + Dv^2 = F(D+1)^j

where j can be arbitrarily high and any solution to it can be used to get a solution to the original equation by stepping down the chain (there are j steps I think).
Now then to try to use this to factor you need:

x^2 - k^2*y^2 = T

where T is the target and that also just gives a difference of squares, and (x-ky)(x+ky) = T, so it's easy to see WHY it factors if you get solutions.

My approach then would require solving

u^2 - k^2*v^2 = T(1 - k^2)^j

where you need to pick k, where I'd guess it'd need to be large, maybe approximately sqrt(T), and then you'd use:

u^2 = k^2*v^2 mod T(1-k^2)^j

and

u^2 = T(1-k^2)^j mod k^2*v^2

where I say just guess at v, like assume v = 1, use the Chinese Remainder Theorem to get

u^2 mod k^2*T(1-k^2)^j

and if u^2 mod k^2*T(1-k^2)^j is a perfect square you have a solution.

Notice you may get fractions with this approach (probably will get fractions) which STILL may factor T in the original equation.

In any event THAT is the full approach for people who wish to criticize it, and you don't need to post to sci.physics about factoring!!!

An immediate criticism is guessing at the residue of v. If that never works, ok, prove it. If you say I haven't proven it works, fine.

But that I think covers all the territory. If it does work and with large j you tend to get a perfect square, with a guessed at residue for v, then that should allow solution.

## JSH: Web searches reveal Usenet reality

There is one way that the Google search results have helped me tremendously and that is in appreciating how absolute is the denial of certain posters who obsessively reply with negatives in my threads as a reality as easily testable as sending people to do Google searches would SEEM to be a powerful way to make a point.

But you can peruse recent threads to see how it doesn't pause them at all—like when I got published in a formally peer reviewed math journal it didn't pause them then either.

They simply attacked the journal, and it is actually rather appalling that Usenet was instrumental in destroying an actual journal because of them, and it should be a chilling warning to those of you using electronic only journals.

I've emphasized recently that posters claim there is all this hostility to my research when they ARE it. Hostility to my research is some Usenet posters, including Erik Max Francis, who runs the Crank.net website, and I'm emphasizing that so that people realize they are making themselves out to be something they are not. They are a fringe.

An angry rude fringe that lies about its own size and influence.

The search result demonstration is about as powerful as you can give when a discipline like the mathematical one refuses to follow its own rules and properly acknowledge your research:

Search string: solving binary quadratic Diophantine equations

That is a string that demonstrates a need to solve equations of the form:

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

in integers for x and y, which comes up in quantum mechanics.

If you think that's too specialized of a search and are suspicious for that reason here's one where I don't take #1.

Search string: solving quadratic Diophantine equations

There you can also see the kind of search string competition that interests me as I'm beaten out by Dario Alpern at #1 and MathWorld at #2.

One of the more interesting search string results is for the definition of mathematical proof. Here Google again is the source (the strings above may work with Yahoo!).

Search string: define mathematical proof

There you can see where the Wikipedia went, when my definition beat it out for the top spot.

(Yeah, that's right. I defined mathematical proof. The search results are a leading indicator that somewhere down the line it is likely to be THE definition, so it will eventually end up dictionaries—if the web is correct. The Internet is a force that is still not fully understood at this time.)

For those of you who argue on Usenet with people who are often rude and nasty you can see here just how impossible it can be to EVER get them to behave rationally. They simply will not. So evidence is not useful. Reasoning with them is a waste of time.

Like I GOT published. They simply ripped on journals (and some of them managed to kill the journal). Google: SWJPAM

They are deliberately doing what they are doing.

Their desired impact on you is to infuriate and frustrate you, as they live to try and give pain to others. Inflicting pain IS their purpose. They wish to inflict as much pain as possible on their designated targets.

If you are one, there is no answer you can give that will bring reason from one of them.

## JSH: Increasingly the world's math reference

People on Usenet who aren't rabid who know much about physics probably understand that a general solution to binary quadratic Diophantine equations if it exists is an important mathematical tool for physicists:

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

That is an example of a general form for a binary quadratic Diophantine equation—x and y are unknown while the c's are known constants. I found a general way to solve equations of that form for integers, which yes, do come up in physics because of a certain little thing called quantum mechanics.

Yes, there are integers in physics, if you know where to look.

Now certain rabid posters track my threads and proceed to fill them with as much nonsense in reply as they can, but the reality of my research as a potent force is not about what I say, but about what you can check. And I like Google. I like Google because Google is the top search engine in the world (did you know that?) and rather than give links, I give searches to try in Google.

In a saner world that would be it. After all the mathematics is not hard for any physicist with a Ph.D to verify, and even the concept I call tautological spaces which gave me the tools to derive the method is not terribly complicated: I subtract equations from identities and analyze the residue.

Easy math. Easily verified. And you get directed to it by the world's search leader.

So why are rabid Usenet people stalking my postings claiming it's worthless and often attacking Google in the process?

Simple. Because they're angry.

Why are they angry? Who knows. People are angry all over the world. Usenet simply amplifies anger and lets angry people feel powerful. So I say Google links to my research. They say, no it doesn't. I say, well people can check and SEE it does. They reply, no it doesn't and call ME crazy. Or they claim that Google search results don't mean anything.

Those of you in the real world with the rest of us are aware I'm sure that there are web metrics measuring tools available by which people can get an idea of the kind of interest there is in their website. One of those tools is Google Analytics (yup, there's that "Google" name again, it comes up a lot).

Google Analytics says that so far in 2009 there have been visits to my math blog from people in 1816 cities in 112 countries/territories around the world (not a lot of people so I don't give the number as it's only a few thousand).

Um, actually, wow, those 112 countries are most of the world. The countries themselves include most of the planets 6.78 billion or so people.

Regardless of what a handful of posters can say in rants against my research, or rants against me, the reality is that the evidence shows that increasingly the world is turning to my math as a resource. Check in Google: mymath

I think I come up #4.

So why aren't math professors talking about my research? I don't know. Maybe they are. I don't claim to know all that happens in the world.

Why am I not in math journals? Well, I got one paper published and some USENET rabid people mounted an email campaign against it, editors pulled it, journal died. I'm being nice to journals now. Ha ha.

Jokes aside, the mathematical world is very in-bred. They like math people with Ph.D's in, guess what? Mathematics. Go figure.

Math society seems intent on ignoring reality for as long as the world will let them, but physicists don't care! Physicists use math as a tool, and now they have a tool that lets them solve binary quadratic Diophantine equations! Yeah!!! Wonderful world.

Reality is that things can get messy with even important research when various interests and people's FEELINGS get involved, as history has shown. But at the end of the day, objective measures are a good way to go.

And what's more objective? A Google search giving you a particular method when you ask about solving something rather technical and mathematically specific?

Or Usenet posters ranting about some person they clearly hate, who also will tell you that Google really isn't, well, Google! And oh yeah, don't forget Erik Max Francis the Usenet poster who also has Crank.net, a guy who once told me some choice things when I got into arguments with him, years ago. He's angry too. Yeah, Erik Max Francis is one angry dude.

Angry people are just angry people. Objective reality is what physics people do. I suggest you go with the easily checkable facts.

Increasingly my math is a world resource.

And a post like this one is to help those people who will come across the negatives, will wonder when they read these posters saying horrible nasty things about me, and get bothered because they trust that people are more decent than that and I'm just here to say, no, some people aren't.

## JSH: Back to conic section parameterization result

To understand that there really is something wrong here, you need only reflect back now on a rather simple mathematical result that has been known for centuries:

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

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

and

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: http://mathworld.wolfram.com/Circle.html eqns. 16 & 17

That allows you to, say, graph ellipses or hyperbolas adjusting a single D number which is related of course to eccentricity.

That has been known for CENTURIES.

One would think that would be an undramatic thing, but the posting assaults against me when I noted the result and questioned why it's not more well-known should give you a clue.

These people killed an entire math journal. See: http://www.emis.de/journals/SWJPAM/

If you think it's rational to just say I'm some crackpot, and I can show you my re-discovery of a nifty little result known for centuries—except mathematicians look at "Pell's Equation" as a Diophantine equation so classified away from rational solutions—and know about a DEAD math journal killed in a spectacular way, then you cannot escape my assessment that your brain is screwed up.

Math journals don't just die. And physics people don't just ignore nifty little simple equations that can draw ellipses and hyperbolas where you just fiddle with one D number versus eccentricity, if their brains are working properly.

Try to think through the special circuitry that gets you to do dumb things.

It is the same circuitry that requires human misery, war and strife—for the good of the species.

Our species can now do better. Try to transcend your programming. It may be the biggest intellectual challenge most of you will ever face in your lives—understanding that your own brain is tricking you, for the good of your species.

## JSH: Would a major result get picked up?

I'll admit that as someone with an undergraduate degree in physics and probably even without that as just an educated adult I'd say that a major mathematical find important in both mathematics and the sciences including physics should rapidly be picked up around the world and celebrated, regardless of the source of the result.

So that in and of itself makes suspect any position I might make for myself having found major mathematical results important in mathematics and the sciences that have mostly been ignored!

Now then though, for the sake of argument, how exactly do you suppose it would occur for such a thing to happen? For a major mathematical find to get known?

Mathematics professors talking? Maybe grad students? Doing what? Citations in papers? A paper to a journal? Or as one posters recently suggested in a thread, a talk by me at a conference? Or something?

How is it supposed to happen?

Turns out that if you look carefully you'll find that the mechanisms available presuppose that a Ph.D'd mathematician or a Ph.D in some other field with substantial ties to the academic community and a lot of skills in producing papers or talks is the only person who could make such a find.

Built into the system IS an expectation of the source of the knowledge, and that expectation is a Ph.D'd person with substantial academic ties.

## JSH: Something wrong in your brains

The nice thing about mathematics is you can determine truth, absolutely, and what I've found is that the world has responded oddly to various mathematical truths I've found. What's weird is that some people have claimed those are not true (and some have been very insulting) while the world has mostly appeared to ignore them, but also seems to be slyly using the research as revealed by Google web search results.

That's all remarkably strange.

The answer to the mystery I've concluded is that evolution designed into the human brain some peculiar circuitry designed to allow people to do all of the above and more in a quest to keep the species viable.

If my theory is correct then built into human beings is an ability to think illogically for a purpose, which requires strife, war and religion (where that can be flexible as to what constitutes a religion) in order to prevent the dominance of middle class societies as middle class societies tend to have too low birth-rates. For example, consider modern day Japan and its quest to stay alive, as make no mistake, if that country's birthrate stays low, it will cease to exist.

But human beings can also be quite logical! Physics is a dominant force today because of things that work! Theories that work wonderfully. Technology that allows human beings to do quite well for themselves—yet war and strife still continue!

My point is that is deliberately built into the human animal.

Put there by evolutionary forces that are keeping the human species from dying out from low birthrates associated with too much success.

Your are built to think non-rationally in highly particular ways in very specific areas, and you have no idea when you are doing it.

## JSH: Understand the split and math strategy

What appears to have occurred is that the mathematical community concentrated on insulting me personally and discrediting me as a human being, which has been a successful campaign, which Google searches also show with a page slamming me as a "crank", "crackpot" and "kook" coming up highly under search by my name. I can't even find any of my own research coming up in the first hundred search results on my own name, only negative pages against my research.

But what's really interesting and fascinating is that while the world accepted the designation of me as a "kook" evidence from other search results, show it found and values the mathematical research I discovered.

You see, math people focused on the person. The research simply took off on its own, disconnected from any human being.

So now, you can try a series of search results where most come up highly in Google but others do so in other search engines:

define mathematical proof
mymath

What makes this story just incredible to me is that math people STILL focus on character attacks as if they deeply believe on a fundamental level that it is personality not real results that matter!

And I think they do so believe.

Simply look at these threads. (It may show how "Uncle Al" is really different from physics people as well as consider how dedicated he is! He's like a machine with a program it cannot quit running. He is in a loop he cannot exit.)

Mathematicians have focused on personality for years now, putting up one mathematician or the other as the latest "beautiful mind", and I think they have a cult of personality so to them their strategy should work!

And the mystery to them may be this bizarre thing where the world simply takes the research and NOT the person as to them that does not exist!

To them, the person IS the research.

As this saga unfolds it is of massive interest to me how easily the world does this trick.

My research moves without me. It is a power unto itself.

It loops the world every 30 days in country after country, city after city, with a relentlessness that is about ideas that can act 24 hours a day, 7 days a week—never tiring. The Internet is the mechanism for the idea exchange and it operates with extreme efficiency.

To the world I am a "kook", "crackpot" and a "loon" as math people are very good at slamming people and dedicated in their energy and focus in that activity.

But my ideas move the world regardless.

My ideas change the world anyway.

## JSH: Hard to explain

Web search results did help me a lot as I've been working my way through a fascinating situation that it seems has not occurred before in this particular way in human history. As of now I am dominant in quite a few topics on web search results while the mathematical community still is recalcitrant in acknowledging my research so that it appears that the old guard is determined to run full tilt into the currently unknown full power of our modern Internet.

Old against the new. That part is classic.

What is different in this case is the weirdness of such a sharp disparity in the reach I know I have from new technologies like the web, and the disdain, insults and continual talking down that still occurs in forums like this one.

At this point, for instance, my math blog is according to Google Analytics, which is important as of course I don't have the technology on my own to know so I rely on the cutting edge of our modern world, being visited every 30 days from 50+ countries. For a while that was 60+ countries, but for some reason it dropped recently, and for instance, was only 54 countries, or I should say, "countries/territories" as Google Analytics puts it, in the LAST 30 days.

For the year? 112 countries/territories. 1805 cities, around the world.

The distribution of hits that I see when I do the city counts looks like a miniature version—like a little fractal—of the hits that Google itself gets, and shows me on a daily basis the use of the Internet worldwide, roughly. So I know the top countries where there is the most Internet usage, just from looking at my own hits for my math blog.

Obviously then, I am disconnected from MUCH impact from insults from posters. They're like miscreants on the street in the little neighborhood in the bad section of the city, built in the valley, hollering up at the guy on the mountain, but I find them intriguing for various reasons. Their rationalizations interest me, and also despite my reach I am still hampered somewhat simply from being still this fringe figure because of the bizarre aspects of this saga.

The mathematical community refuses to acknowledge the importance of my research, and seems intent on letting me hammer at their prestige in a long, slow drawn out process.

But the world is already voting against academia—quietly, for the moment. Processes that before were probably mostly invisible when there was a major conflict of the more powerful new knowledge against old processes and ideas are now more visible—because of the Internet.

And it is all very hard to explain. Posters will probably reply to this post like they usually do with insult or whatever, but that is as irrelevant to this reality as if they were ranting at any world figure.

Of course, it is interesting to have a collection of such rants, for study later. And I like the perspective to wonder what these people are thinking. How important they think what they're doing is. How effective they think it is?

They are interesting enough for me to make posts like this one, as this forum is tiny compared to my reach in other areas. And I do try to be more careful as I tend to distort the normal flow on newsgroups like these, so I'm trying to take smaller steps, post more carefully, interfere less.

As you watch technology continue to evolve as we move further into the Information Age, you should know that I gain more tools. And I gain more ways to watch what is going on in the world, so your words mean less and less.

I don't care nearly so much about what you say, as why you say it. My efforts more often are about probing what is going on inside your brains than anything else.

I feel a continuing need to know, to understand.

## JSH: What puzzles me, discovery ignored

One of the more important discoveries from my research last year was a general solution to binary quadratic Diophantine equations. That is, a way of finding integer solutions to x and y with equations of the form:

c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y

For those who wonder what good is that to physics, well, in quantum mechanics wherever any discrete equations of that (remember a lot of the c's can be 0) form pop-up, my mathematical theory can be used to determine if integer solutions for x and y exist, and also tell you how to find them.

A general solution had never been given before. If you doubt me you can go to your local library, or do what most of people who live in the modern world do and go onto Google and do a search! (Of course some of you may know my research pops up highly.)

For reasons that escape me, some posters have gotten away with attacking the high ranking SOME of my research gets in Google with bizarre rationalizations. On sci.math newsgroups when I brought it up—some people attacked Google search results themselves! Others seem to think I post lots of links or something, when if you notice, I don't post links to my research—why should I? I can just refer

IF you could do it. You would too. Why bother posting links?

Now then, for those results to come up highly there are people around the world DOING something, which causes that to occur, which would indicate use! But I don't know of any citations that refer back to my work. And I haven't seen any indication that the mathematical community has any desire to acknowledge my research, despite the ease of proving its value.

So I'm puzzled by a situation that before, years ago before I ran into how dedicated some academics apparently can be in the defense of what they may see as their area, as in they OWN it—human beings can be so recidivistically petty—I would have thought that a demonstrably useful mathematical result where there is no doubt of correctness would be cheered. Instead my research it would seem based on search results gets silently used, and I continue to get jeered.

That general solution to binary quadratic Diophantine equations is actually so dominating I find it depressing as I have other research it relates to, which I just think is more fun, because the general solution comes from my most powerful research idea—tautological spaces.

Tautological spaces allow you to encompass all prior human knowledge in a particular area of mathematics, and go beyond, to infinite levels of knowledge, and draw conclusion from infinity. So it's depressingly powerful.

You can put xy = T into the theorem. It doesn't care. You can put x^2 = a mod N into the theorem using x^2 = a + Nj, and it doesn't care. Damn thing will just solve it for you. Boringly easily.

Tautological spaces are way awesome in their power, so they are depressing in their reach as that whole encompassing all human knowledge in a particular area and also including infinite mathematical knowledge just is kind of overwhelming.

Tautological spaces can conceivably encompass all human knowledge entire. And keep going to handle all possible knowledge in a particular area. Infinite knowledge, in reach to pitiful little humans. Scary.

Their use is beyond anything that human beings have ever come close to having, and thankfully the human species except for me seems to be intent on ignoring them! I say thankfully as, have you looked around? Human beings seem to be best at hurting each other, destroying things, and creating lots and lots of garbage.

In any event, some people seem to be using the fruits of tautological spaces—as quietly as they can. With their footprints being revealed by Google.

So there is a general solution to binary quadratic Diophantine equations available. It allows a simple approach to solving all such equations of that type. It was derived using mathematical techniques beyond normal belief, which allow one to encompass all human knowledge in a mathematical area plus infinite knowledge in that area.

And the mathematical community is so far not acknowledging the research.

Did you know I defined mathematical proof? Don't believe me? Google it!!!