Friday, October 31, 2008


JSH: See the problem yet?

Mathematicians are the designated experts for things mathematical, fully expected to rapidly accept anything provable mathematically, but I can TRIVIALLY prove a major problem and they're not doing their jobs. Which leaves me stuck because they are the designated experts for things mathematical, fully expected to rapidly accept anything provable mathematically!

So it's a Catch-22: I can prove I'm right trivially, but the people who know I'm right won't acknowledge it, when society relies on them to acknowledge such a thing.

These people destroyed a math journal versus acknowledge this thing.

You really need to Google: SWJPAM

Those are the initials of the now dead math journal.

They are not following academic rules. They are not following basic rules.

So what if their title is "mathematician" and some of them work at Harvard or Princeton?

You need to know why they're breaking all the rules? Because the problem I found entered the field in the late 1800's, so it invalidates so much, maybe even their very Ph.D's so it's a devastating find.

Want to know how possible it could be that old?

Because you damn well know that "pure math" emerged as a dominant part of the mathematical field recently, and is distinguished by not being useful in the real world, so a major error could lurk there indefinitely because without real-world tests if most people in the field accepted the error you'd be back to Catch-22 above.

The facts in this situation are so overwhelming in my favor from Google searches to easy algebra you can check yourselves to the simple demonstration I recently posted for the mathematical community.

ACCEPT IT. A major error entered into number theory in the late 1800's which invalidates a lot of "pure math" which is trivially proven with easy algebra where I've figured out how to simplify down to quadratics.

But rather than admit the shattering truth mathematicians have successfully ran from acknowledging the error for years now, having killed one math journal where I go a paper published—so I'm the one who had a peer reviewed and published result here while objectors are just ranters on newsgroups—and kept up a smear campaign against me.

The story is so dramatic that in my attempts to find some way to get past the Catch-22, I put up an open source program for Java developers called Class Viewer. Google it. It dominates the search engine results despite Microsoft having their own Class Viewer (does slightly different things). And one day I came up with an idea for copying bought DVD's in a way that Hollywood could like which I called DMESE.

Google DMESE. My idea beats out the stock symbol for a company.

RealNetworks just ended up in a battle with Hollywood over an implementation of just a piece of that idea (not saying they copied from it) which I call the "self-incryption" part.

The mathematicians are lying. And part of their lie is teaching erroneous approaches to NEW STUDENTS.

And as you keep your heads in the sand, you are part of the lie as you are enabling them.

The physics community has the mathematical ability to understand this error, and the common sense to see that something must be going on. Math journals do not just die like that.

I know you have the mathematical ability to understand the error, as my B.Sc. is in physics.

I know how you were trained because I was trained the same way.

You can see what's going on. You're just choosing to let it keep happening.


Defend algebraic integers, simple challenge

I have found a problem with the established view of something called the ring of algebraic integers, but rather than acknowledge the issue the mathematical community has tried to hide from it, so here is some very basic algebra with a simple request for those defending the classical view:


175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

Step through getting the factorization:

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

I'll demonstrate how I do it.

Multiply both sides by 7 in a particular way which is my controversial way:

7*(175x^2 - 15x + 2) = (5b_1(x) + 2)(5*7*b_2(x)+ 7)

and now use the substitutions b_1(x) = a_1(x) + 1, and 7*b_2(x) = a_2(x), to get

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

and you're done. Note that b_1(x) and b_2(x) are given by this method. That is also a requirement for any answers from the mathematical community: give b_1(x) and b_2(x).

My hope is that a simple demonstration of their inability to fulfill a basic request will help some of you see the truth here as it is EXTREMELY important. The problem being highlighted here came into the mathematical field in the late 1800's so there is a devastating impact that has snowballed for over a hundred years.

Proving the problem is easier than getting people to accept that it exists.

For more information please Google: non-polynomial factorization

It is a term I invented to describe the type of factorizations shown above, as they are not polynomial factorizations. An example of a polynomial factorization is

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

I advanced the field with non-polynomial factorizations, found an astounding error, and mathematicians ran from it, and even destroyed a mathematical journal to try and keep it hidden. Google: SWJPAM

Thursday, October 30, 2008


JSH: Your broken field

So yeah, it's EASY to prove I'm right with non-polynomial factorization. Posters disagreeing with me can try to attack my proof, where remember THEIR argument was that 7 is split up by functions, so they want something like:

7 = w_1(x)*w_2(x)

but given

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

how do you force any human, or any being for that matter to multiply through in some bizarre way with functions shifting how factors multiply through by the value of x, when any idiot can just do:

7*(175x^2 - 15x + 2) = (5b_1(x) + 2)(5*7*b_2(x)+ 7)?

Answer is, you can't so I'm right that the 7 multiplies the same way for ALL x, and can prove that easily enough, but what good is proof if people simply refuse to acknowledge it?

You people killed a freaking math journal over denial of this result with emails that derailed some editors who did the right thing, until you broke the formal peer review system.

You betrayed the mathematical field.

You betrayed the entire human race.

And you kept escalating that betrayal with my other research by refusing to acknowledge key facts about my prime counting function, and the partial difference equation and partial differential equation that result from it. And in refusing to properly acknowledge my recent work solving binary quadratic Diophantine equations.

The point here is that you people are willfully enemies of the human species.

I know many of you are living off of public funds so your behavior is parasitic in nature.

You block the correct mathematical results, and block result after result after result as you are protecting your feeding grounds, and the human species be damned as like any parasites you care for yourselves first and only.

So you would betray the human species itself so I hypothesize that on some level, you are not human yourselves.

You are a parasitic sub-species living amongst the human species, genetically different, but hiding yourselves in certain areas where you can gain traction and survive.

So you carefully pick areas where you can gain critical mass and remove the need to actually work, like "pure math", and the priesthood.

So I hypothesize that your subspecies founded most human religions.

You have driven the evolution of the more dominant species for some time now, but it is finally time for you to be un-masked as your parasitic nature now has your species directly at odds with my own: the human species.

Genetic testing with an eye for a sub-species with the characteristics mentioned should be able to verify or end the hypothesis.

I would suggest that testing mathematicians in the "pure math" field would be a good place to start in revealing the presence of the subspecies.

They look human, but they are not.


Proof of problem with ring of algebraic integers

Some simple algebra with a basic polynomial reveals a serious problem with the naive use of the ring of algebraic integers, bringing into question over a hundred years of algebraic number theory. This post will step through the extremely, short, simple, but overwhelming proof of the problem.

In an integral domain, consider a simple polynomial

P(x) = 175x^2 - 15x + 2. Multiply it times 7, to get

7*P(x) = 1225x^2 - 105x + 14. Cleverly re-group terms:

1225x^2 - 105x + 14 = (49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2

and now factor into non-polynomials:

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where you'll note that the a's are functions of x that are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

But now consider our polynomial again with a factorization before any multiplying by 7:

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

Now multiply by 7, to get

7*(175x^2 - 15x + 2) = (5b_1(x) + 2)(5(7*b_2(x))+ 7)

and use the substitutions b_1(x) = c_1(x) + 1, and 7*b_2(x) = c_2(x), and you have

7*(175x^2 - 15x + 2) = (5c_1(x) + 7)(5c_2(x)+ 7)

and of course if c_1(x) = a_1(x) and c_2(x) = a_2(x), I have my original factorization, but in so doing I'm PICKING that 7 multiplies times just one of the factors of 175x^2 - 15x + 2, but what if I picked wrong?

For instance, consider again

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

and again multiply times 7, but split it up so that each factor is multiplied times sqrt(7):

7*(175x^2 - 15x + 2) = (5*sqrt(7)*b_1(x) + 2*sqrt(7))(5*sqrt(7)b_2(x) + sqrt(7))

but there's an immediate problem!

If you let x=0, then you have the factorization:

7*(2) = (5*sqrt(7)*b_1(0) + 2*sqrt(7))(5*sqrt(7)b_2(0)+ sqrt(7))

which contradicts at x= 0 with

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are functions of x that are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

unless b_2(0) divides off sqrt(7), or b_1(0) divides off sqrt(7), as

7*(2) = (5a_1(0) + 7)(5a_2(0)+ 7) = (0 + 7)(-5+ 7)

because then the a's are roots of

a^2 + a = 0.

Therefore, there is no other way to multiply

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

by 7, and get the factorization

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are functions of x that are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

as ANY other way other than multiplying (5b_2(x)+ 1) by 7, will contradict with

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

at x=0, as demonstrated above with sqrt(7).

Therefore, one of the a's must have 7 as a factor for all x, but it is trivial to show that NEITHER of them can have 7 as a factor for any integer x, for which the a's are not rational, in the ring of algebraic integers, so there is proven a problem with that ring.


Note that attacking this proof requires that you show how given any factorization

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

you can get to the factorization

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are functions of x that are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

without multiplying (5b_2(x)+ 1), by 7.

I emphasize that as mathematicians have resisted this result for years now, and in fact, destroyed an entire mathematical journal to avoid it, killing SWJPAM, and smeared me for years rather than accept it.

Since the result cannot be refuted mathematically their only choice will be to delete out the mathematics in reply, and address non-issues, because the mathematical proof is so easy.

When they do that I want you to understand they are deliberately doing so, avoiding a simple proof in order to hold on to an error, and to keep teaching it to their students which is as basic a betrayal as a professor in any field can make: to deliberately train your students in error.


How could they? How DO they. As we speak those students are still

Some easy algebra casts doubt on core algebraic number theory but that conclusion is so hard to accept despite the ease of the mathematics.

Consider a simple polynomial P(x) = 175x^2 - 15x + 2. Multiply it times 7, to get

7*P(x) = 1225x^2 - 105x + 14. Cleverly re-group terms:

1225x^2 - 105x + 14 = (49x^2 - 14x)5^2 + (7x-1)(7)(5) + 7^2

and now factor into non-polynomials:

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

But now go backwards and divide the 7 back off, or try:

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

where now the b's are unknown functions. If I multiply by 7 again, can I do this?

7*(175x^2 - 15x + 2) = (sqrt(7)*5b_1(x) + 2*sqrt(7))(sqrt(7)*5b_2(x) + sqrt(7))?

Yes. Of course I can multiply 7 through ANY way I want, or I could multiply through by 13 or some other number.

So how many ways can 7 divide off from

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0?

People arguing with me say, one way per x. So one way for x=0, and another way for x=1, and another way for x=2.

BUT if you just divide 7 off and get

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

how many ways can you multiply 7 BACK onto the expression? An infinity is the answer.

So guess what? The mathematics will not let you start with

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

where the b's are any possible algebraic integer function, multiply by 7 and get

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

You KNOW the math won't allow that because if you could do that then you could just divide the 7 off and get b_1(x) and b_2(x), as algebraic integer functions.

So the 7 cannot be divided off in general, so math people claim you have to figure it out at EACH x, so like with x=1, you have

7*(175 - 15 + 2) = 7*162 = (5a_1(1) + 7)(5a_2(1)+ 7)

where the a's are roots of

a^2 - 6a + 35 = 0, so you have a = (6 +/- sqrt(-104))/2,

so you'd look for factors of 7 to divide through that in a different way according to them than when x=2, but how does the math know how to choose?

After all, if ANY particular factorization is used, I can just multiply back through with another as

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

is bare. There is no way mathematically to force me, a quirky human being with free will, to choose to multiply that 7 in a particular way just to get

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

so how does the math know? Mathies in arguing against the obvious, claim that the tail wags the dog in that the FUNCTIONS tell the math how the factors of 7 are distributed, but that is circular as who tells the functions?

Remember, with something like

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

you can multiply times 7 ANY WAY you like and distribute its factors in an INFINITY of ways, so how does the mathematics choose a way?

How about with

x^2 + 3x + 2 = (x+2)(7x+7)?

But you say, no fair, you can SEE how a choice was made out of infinity. How does that help anyone with

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0?

How can the math pick and choose how 7 multiplies through based on the value of x, when

175x^2 - 15x + 2

is being multiplied BY 7?

How? How is that possible? It doesn't work that way with x^2 + 3x + 2. If I multiply it times 7, and get

x^2 + 3x + 2 = (x+2)(7x+7)

that is done for all x, because x is being multiplied. The tail does not wag the dog.

There is no way for 7 to multiply times a factorization in a way determined by the very thing it is multiplied against, so with

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

there is NO WAY the value of x can control how 7 multiplies. It's not possible. It's stupendously nonsensical to claim that it does, but a dead math journal SWJPAM is dead because some people argued against the possible, convincingly.

There is NO WAY that 7 on the outside is being told which of an infinity of ways to multiply times the factorization

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

by the value of x. That is impossible. There is no mathematical way that can happen.

But then you can just pick any value for x, like x=0, and find that with

7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)

where the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0

the 7 is a factor of (5a_1(x) + 7) or (5a_2(x)+ 7)

and know that is true for all x.

And then know that with x=1, only one of the roots of

a^2 - 6a + 35 = 0, so a = 3 +/- sqrt(-26)

is 7 a factor, and I remember when I was talking about these kinds of results years ago, posters would promptly ask, but which one has 7 as a factor? 3 + sqrt(-26) or 3 - sqrt(26)? And the answer is, there is no way to know.

The frustrating thing for me in being able to explain so simply why there must be this huge issue is that posters get away with claiming that given

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

there is a way to multiply by 7, on the outside, so that it is controlled by what is being multiplied on the inside, which is impossible. There is no way, with say 7*(x^2 + 3x + 2) = (7x + 14)(x + 1) for the thing being multiplied to inform me how it is to be done, so that occurs different ways with different values of x.

So like, if x=2, then it's

7*(x^2 + 3x + 2) = (7x + 14)(x+1)

but if x=3, then it's 7*(x^2 + 3x + 2) = (x + 2)(7x+7)?

The tail does not wag the dog. The value of x cannot force 7 to multiply times

175x^2 - 15x + 2 = (5b_1(x) + 2)(5b_2(x)+ 1)

one way versus another.

Now math people are not stupid. It's not hard to see what must be true mathematically and accept that 7 divides off for all x the same way, so why did they instead kill an entire math journal?

That dead math journal should tell you something. How huge this result is, and how powerful the resistance to it.

They killed a math journal that was a decade old. Trashed it in public. Berated the editors. Its hosting university scrubbed all mention of it from their site.


What could be big enough for that kind of reaction?

What in the physics field? Maybe if someone disproved quantum mechanics. But hey, quantum mechanics works in the real world, no one CAN disprove it as it works. But in "pure math" areas there is no theory to test in the real world!

The mathematical community not only could kill a math journal to protect against knowledge of this result, wage a smear campaign against me, lie to the public repeatedly in replies and in its behavior in not accepting this result, but also keep teaching the flawed mathematical ideas to NEW STUDENTS.

Which forces a responsibility on others in the academic field to do the right thing as the experts within the field have refused to do it for years now and clearly have no intention of ever doing the right thing here.

Does the tail wag the dog? Can the thing being multiplied dictate to what is multiplying times it?

How could they destroy an entire math journal like that? Lie like that? Keep teaching their students wrong information?

How could they? How DO they. As we speak those students are still being taught around the world.

Sunday, October 26, 2008


JSH: Feeling better now

Um, so I've been ranting this morning as I've been feeling sorry for myself but a poster called Enrico just elevated my mood!

He's shown a cool result related I think to what I call a massive theoretical super structure, which I also call a Diophantine supermap for binary quadratic equations.

I had two theories about how that supermap worked, where a poster called Tim Smith helped me eliminate one, and Enrico just validated the other.

Well the rants were fun so I'm glad I got them out of my system.

If my research is ever accepted in mainstream mathematical circles I probably won't get away with such activities any more.

Hmmm…before that happens I may need to do some more ranting and REALLY rip on some academics before it's too late…

Oh yeah, Enrico should write a paper and try to get published.

God knows I won't bother submitting to any more damn journals.

Been there done that—YEARS AGO—dead journal for my troubles for the only paper that ever got accepted.

Got lots of denials though. Some woman called Susan Friedlander has a lot of them. There are also quite a few from some crap journal published by some school called Princeton, as if it matters.

Far as I'm concerned, they're all crap journals.


JSH: Not a popularity contest

As I rant and rave, continually antagonize my audience, and talk about cutting public funding for basic research, or well, any research at all, I can imagine mathematicians smiling to themselves. No way people will ever listen to such nuttiness and they may smugly feel they can rest secure that I'll never be taken seriously—except I DO have major mathematical research results.

So their satisfaction in my mind is a dismissal of their own field.

These modern "mathematicians" clearly despise mathematics.

As if, as if a really unlikable guy could possibly get listened to <gasp&rt; just because he has mega mathematical discoveries of the type that come around once in a century, or more. No way, right? Not in our popularity dominated world!

Don't you know the lesson of MTV? Of The HIlls?

Popularity is all that matters, right? Substance means nothing, right?

And if you believe them you can sit back and relax, but if they're wrong then you know that an increasingly angry and frustrated major discoverer is figuring out ways to convince policymakers someday that sharp reduction in public funding for basic research is the ONLY way to bring back integrity to the system and insure that people are actually doing real research of some value. People doing valuable research will find a way. The cons will leave for easy money elsewhere.

And besides, I figured out my mathematical results without public funding and with mathematicians from around the world mostly making fun of me, the nasty bastards.

IF I can do it, others can.

So what good are you academics anyway?

Professors teach. Discoverers do.

Albert Einstein of course worked in a patent office. What if society missed the clue? The reality that maybe academia INHIBITS major discovery.

What if we got it wrong? What if our universities around the world while playing a crucial role of teaching are the last places to go to for innovation?

What if our world has created a massive system for BLOCKING major advances, where now even the would-be Einsteins of today cannot get past the professors of today?

The message I'm giving to you if you haven't picked it up, if you are an academic, is that you are probably a failure at your job, but surrounded by other failures, you all call each other successes, and condemn the human race to the muddled mess you call research.

Publish or perish. Yeah, you publish, and let the human race perish for people who are second-rate researchers at best and outright frauds in many cases in a system that does not work.

And my story proves that beyond a doubt. You block major mathematical discoveries because you are incompetent boobs living off the public in a white collar welfare system and you legitimately see me as a threat to your free money.

Yeah, you con artists. I am a threat to your free money. And you are a threat to human civilization itself.

You are the snakes in the grass.

Saturday, October 25, 2008


JSH: Contradictory data

I've actually been waiting for some indication of pick-up on my ideas for managing copy of digital media, which I call Digital Media Equipment Self-Encryption or DMESE for short (some of you may notice that can sound a lot like "dummies").

And I put the idea out there, of course, to reality test, as reality testing is a critical part of modern problem solving which I gleefully endorse, and it took over a year and a half—I first put out DMESE January 29, 2007—but here we are with RealNetworks using the self-encryption part, for DVD copying software, and promptly being sued into stopping by Hollywood.

Bizarre, or is it?

Previously with more reality testing when I pulled out and expanded one piece of my proof of Fermat's Last Theorem, and shifted things slightly to make a paper, it got published, after quite a bit of effort on my part, sending it to journals and such, only to be pulled when sci.math'ers mounted a crafty email assault against the paper to the editors, and the wankers yanked it after publication, as always Google: SWJPAM

Later the entire mathematical journal died. Cameron University wiped its existence from its websites and some freaking European group EMIS saved the American journal when its own country didn't want it any more.

10 years of math papers into the crapper just like that as if were nothing.

So now we have new and ever more dramatic evidence that the world is stranger than you previously thought, or even I previously, thought with some illuminating events indicating human interference, and interference in bizarre ways indicating strange powers to do things not previously thought possible:
  1. An entire mathematical journal can keel over and die after yanking a paper by a supposed crackpot, and not a single reporter worldwide can be motivated to give a damn (believe me, I tried).

  2. Citizens around the world including supposedly savvy and very demanding American consumers cannot legally copy DVD's they buy, despite a FREE IDEA having been given out over a year and a half ago by the world's benefactor, me, in a wonderful gesture of charity, as the idea is conservatively worth, oh, about $100 million over its patentable lifetime, if I could have gotten a patent, of course, as patent examiners are kind of bonkers, so that's not a certainty. But I digress.
So I give an idea worth hundreds of millions of dollars to test the ability of the world to remain in control of some rather powerful people who have revealed themselves by some amazing blocks requiring extraordinary political ju-jitsu, and massive balls. Or have they? Or are they a figment of my fevered imagination?

But they haven't simply killed me. (Can you imagine walking around every day wondering if you're going to be assassinated suddenly? That's my life.)

And they left me to do more mathematical research and I obliged by solving binary quadratic Diophantine equations (I know, quite a mouthful) and I'm monitoring to see how long people use the old ways which are less efficient, versus the new way which leads to a more direct, general way of solving.

Or maybe there is no weird group of strange but powerful men capable of destroying a math journal at a whim and blocking consumer products without much effort, which means a new theory is needed.

And that's where you people come in, as some of you seem to think you're very intelligent.

I need answers people. What does the data mean?

Is there some dark cabal working to keep people from knowing about advanced mathematical techniques and prevent them from legally copying their bought DVD's?

Or is it all just bizarre coincidences where the information isn't traveling? So no one KNOWS there is DMESE?

So what about its rankings in search results? Why does DMESE dominate with Google, even trouncing the stock symbol of some company with the same initials?

How about the binary quadratic Diophantine solution?

How is it possible for a better way to do still popular math with the people who do that stuff of course sit versus being picked up in our very connected world?

And if there is a conspiracy, why haven't they killed me yet?

Ok, so get to it. I need answers in 48 hours, just because. Better yet, 24 hours.

The hecklers will make their nonsense replies. Ignore them.

Part of the conspiracy theory is that they are paid agents, so their PURPOSE is to distract you.

Ok then, let's see how brilliant you are.

Resolve the conflicting data, answer the questions.

The clock is ticking…

Thursday, October 23, 2008


JSH: State of the art of mathematics

I've now successfully used tautological spaces against only two problems. Where the latest which lead me to an alternate solution for binary quadratic Diophantine equations is rather spectacular for quite a few reasons because of the history around the problem.

Obviously, I can contemplate other areas of mathematics on which to use tautological spaces.

But I also know about their limitations as the second problem I tried to use tautological spaces on, and failed with them, was the factoring problem, so they are not infallible, just unimaginably powerful.

I've been watching the television show "House" a lot lately. I've kind of become addicted to it which has impacted how I post, as in, I'm more insulting, and it feels good. But like Dr. House, my insults are for a purpose, or I think they are, though they may simply mean I'm juvenile?

In any event, the show has given me a different perspective on the problem space.

So what do we know?

This notion of using identities in such a clever way clobbered the hell out of binary quadratic Diophantines in a way so devastating it mostly shut up even the angry idiots. But not a lot has changed.There's no reason to suspect much will change, so we can move on. And when I say we, I mean me, and my team of those people who bizarrely for reasons that puzzle many, and probably themselves, help me.

So yes, I admit it. There are people who help me evaluate ideas and I mostly insult them. Like Dr. House.

So I have a paradigm around which to fit my behavior and I am watching more and more episodes of the TV show to refine my behavior, and improve my insults.

Hilbert came up with some problems. I can clobber quite a few of them but wonder if I care. Russell thought to formalize a few things, put some logic into it, but came up short, but I think a few simple ideas bridge things in a way he didn't imagine.

But at the end of the day, does anybody really care? I know I find it hard to care.

So what other problems for those who are silly enough to care might be amenable to tautological spaces in their new and raw form, which is new and raw as I just invented the concept, or discovered it, whatever, a few years ago?

(No one say Collatz. It's verboten.)

Of course I HAVE solved problems without using tautological spaces! But that's too advanced for this initial post.

I'm thinking about cleaning out some crap left over from the old geezers who used to do math before they keeled over and died, like Russell and Hilbert.

Still I'm kind of picky, so the idiots among you need not apply. Ok, anyone can of course as usual reply as if I try to put that kind of criteria on then no one is qualified but me to talk to myself and I do enough of that already.

My suspicion is that you will fail me.

That is good.

It just means I'm more brilliant than I previously thought.

So what is the state of the art of mathematics?

In flux. The old ways have failed. I've collapsed 2000 years of old ideas about some simple binary whatevers into a page or two of rather potent theory. Mathematics can be revolutionized like the sciences.

You CAN push out the old professors hogging up the works by outdoing them, re-inventing, discovering, starting from scratch, or not, if you're not smart enough.

Get started. Or not. I'll insult you either way you go. Or not.

Wednesday, October 22, 2008


JSH: Moving to real fun

Back when I was naive and stupid, and idealistic, I dreamed of making great discoveries to advance the state of humanity.

But then I made some discoveries, got years of abuse from mathematicians, and now all I want to do is make as many academics look like fools, destroy endowments, end departments and generally wreak havoc across the academic world, as I think I kind of went bonkers as a result.

And so I no longer care, can no longer be convinced, but I'm still brilliant, can keep making discoveries indefinitely, and fantasize about shutting down, Princeton!

Yup, I want to shut down Princeton.

That sounds like a better goal than stupid nonsense like furthering and advancing the state of the human species as its full of ingrates, and people who don't value knowledge, but they care about cable!

Yeah, give them their cable. Give the hoi polloi their television with its nincompoops and actors who are worth nothing but get so much from a world of fools. This ship of fools.

Well at least I can make your lives miserable. Take away your funds and force you to do what I can do.

Make you live up to my standard.

Public funding for research is stupid.

All scientists should learn to live in the free market. Do their research as best they can without welfare.

It's time for you people to grow up!

I'm tired of the world babying you, babies.

It's time for you all to start working for a living!

Like me.

Monday, October 20, 2008


JSH: Explaining for the "angry idiots"

I'm noticing some posters replying negatively in some of my recent threads in a way that shows they don't have a clue, so because I'm trying to get a few answers quickly I thought I'd remind those who I call angry idiots, how things work here:
  1. I post when I'm working on problems, as I toss ideas out there, as part of brainstorming which is part of what I call extreme mathematics.

  2. You do not know what is going on based on how you think people should reply to me, how you see people reply to me, or think you see people reply to me, but only from the mathematical content.

  3. There is always significant mathematical content lurking in there somewhere.
Now the angry idiots will unlikely heed this post but hey it's fun just pointing out that they are, angry idiots.

I'd tried to get away from posting hoping I'd finished things out as I'm feeling kind of tired, but turns out there is more to re-working binary quadratic Diophantine equations than I first thought!

After all, I thought I was done weeks ago, but am still refining theory, God help me, and still making new discoveries, damn it. Sick of new discoveries. Tired of discovering new math. Wish it would all just stop so I can spend more time chasing women.

Ok, but I digress.

Seems that non-rationals have no real role at all with Pell's Equation but only come in because of one of those weird things where non-rationals can behave a lot like the relation group:

x^2 + Dy^2 = F

means that

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

which is just one of those things as the D just stays there like with non-rationals, say 1+sqrt(2), the sqrt(2) keeps hanging around as you raise that to higher powers and a lot of math history turned on that one thing.

But understanding the RATIONAL explanation allows you to do cool things, like have a general solution method.

And, oh, you wackies know damn well that even with JUST the general solution to equations of the form

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

I've advanced the state of the art as no one had a simple, direct, general way to do it before but just quirky more roundabout ways which readers can verify at MathWorld:

Just looked at the page and puzzled at it a bit where the important point is that the equation is not directly and generally handled when I almost trivially do so with my Quadratic Diophantine Theorem.

But it gets better as if this latest insight holds then I've figured out how to determine how long it will take before continued fractions will give a solution based on when -D is not a quadratic residue modulo (D+1), where

x^2 + Dy^2 = F

in general so you can have F=1. That could be HUGE as not only would it allow you to know exactly WHY a continued fraction solution takes as long as it does, I've figured out a general technique for getting the answer.

Putting it all together it's really exciting, which is why I'm stuck posting still as I work through it all, which leaves me also seeing posts from the angry idiots. If any of you can get some of these nitwits off my back it'd be appreciated. I'm finally getting tired of them. They're so, angry, and so, idiotic.

IN any event, waiting to see how this latest research plays out, and posting just to sci.math because you are the home of the angry idiots! So you people need EXTRA explaining as otherwise you're too goddamn stupid to get things on your own.

Have I mentioned I'm getting tired of the angry idiots?

Some of you need to think about trying to put more of a leash on these people, or better yet, a muzzle, or no, as I'm a free speech advocate. AT least let them know that they know no math, speak no math, should not pride themselves on their ape behavior in the face of their godawful ignorance of what is actually going on.

Freaking apes. I feel like I can see the human species devolving when I come on this newsgroup.

Some of these people should be back swinging in the trees versus ranting and raving, and throwing crap words, like chimps throw feces, at discoverers trying to work in the only environment available because, yup, because it's a stupid world.


JSH: Explaining Pell's Equation

Oddly enough a clue that seals the explanation to Pell's Equation came up in arguments about my general solution to binary quadratic Diophantine equations, where it's spectacularly and to me, satisfyingly simple.

Essential to the argument is the simple relation that given x^2 + Dy^2 = F, it is also true that

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

which allows you to generate a series of equations. But notice what happens with F=1, D=-3:
  1. x^2 - 3y^2 = 1

  2. (x+3y)^2 - 3(x+y)^2 = (-2)

  3. (4x+6y)^2 - 3(2x + 4y)^2 = (-2)^2
and the 4 divides off!!!

So that's
  1. x^2 - 3y^2 = 1

  2. (x+3y)^2 - 3(x+y)^2 = (-2)

  3. (2x+3y)^2 - 3(x + 2y)^2 = 1.
So you can start with x=1, y=0, and get
  1. 1^2 = 1

  2. (1)^2 - 3(1)^2 = (-2)

  3. (2)^2 - 3(1)^2 = 1
and thereby get the first non-trivial solutions!!!

Key here is the requirement that

-D must be a quadratic residue modulo (D+1)^j

where j is a natural number giving the level into the series you are at minus 1, and if THAT IS NOT POSSIBLE, then factors of (D+1)^j must divide off and if all its factors divide off you can get a non-trivial solution.

So for D=-3, j=2, when (D+1)^j divides off completely, but for 7, you're looking at (-6)^j, and notice that factors of 2 routinely divide off, but the 3 is a hardy bugger, which hangs in there for some time, so you would look for when 7 is not a quadratic residue modulo 3^j (um, can someone give that answer? When is 7 not a quadratic residue modulo 3^j?).

So you really have to look by prime factors of D+1.

But then you have the explanation for why for some values of D you get solutions quickly while for others it can take a while as the mathematics is looking for when -D is NOT a quadratic residue modulo all the prime factors of D+1 raised to some even number power of j, so it dutifully goes along until it finds that situation and it can take a while.

Cool. I like explanations. So that number theoretic structure I call a Diophantine supermap is the key to understanding Pell's Equation and all its behavior.

Yeah, I knew it was important. Cool.

Saturday, October 18, 2008


JSH: It's not complicated

You are prisoners of extremely powerful men who lack significant intellectual ability, like the ability to do math or science.

But they have a lot of power through money and politics and can pay people to do fun things like reply derisively with dedication to my posts.

Or shut down a math journal.

But why? You ask?

Have you ever been a very powerful media mogul? Or some major political figure?

Me neither but I suspect it's kind of boring in a lot of ways. Doesn't live up to the hype.

Destroying other people's lives can seem entertaining and as meaningless as everything else you do, when you supposedly have everything.

Screw a beautiful woman. Buy some company. Pay some agents to post negatives about some wild, genius who can do what you will never ever do.

And the world just keeps turning…

Oh, but the genius figures it out. Of course.


JSH: Now I'm getting upset

I've been kind of mean in recent posts not really to gloat or anything but to make a point.

You can all be brought down to the level of everyone else and the Ph.D's won't matter, and what you claim are accomplishments won't matter, and pretension won't matter.

Because all people will hear is how you couldn't accept a very simple solution that they can understand.

And then I can really get mean and talk about funding and survival of the fittest and if I could figure out everything I did without public funding, why can't you?

I'm growing impatient.

In working on this problem space as I branched out from my "pure math" research when mathematical proof didn't work, and even publication didn't work (math journal published, retracted after publication, journal died) I've been analyzing the situation and dumbing down my models.

Yup. I've kept dumbing down my models for how I'd guess people in academia should react as I tried to figure out a way to break the impasse, which is partly why there is DMESE, which is a purely commercial idea.

Now maybe I can come up with another purely commercial idea. I don't know. I hope I don't need another one, but if I do need another one because I still think you're smarter as a group than you are, then it'll be the same type thing again:
  1. I put the idea out and give it away for free.

  2. I wait.

  3. Some time passes, maybe someone uses part of the idea, coincidentally or not, it doesn't matter.

  4. I come out and rant about how stupid the world is, and especially your community.
We can do those iterations for as long as you want as I look for incremental impact where part of the goal is removal of public funding for your research.

From someone who felt a part of the physics community to someone who increasingly is looking to drop public funding more and more with each passing day, it's been a very disillusioning ride.

Physicists could have ended this years ago by catching mathematicians not behaving.

The publication and death of that journal was kind of a clue.

And I know that I'm right that the best research will get done with or without public funding because I have my own experience on which to draw.

The best physics minds will find a way. The rest of you are not worth the world's time or money.

Increasingly I believe physics research will get a HUGE leap forward as what I'm seeing is not intelligent behavior:
  1. You do not test a major discoverer as major discoverers just ≤gasp≥ keep making discoveries!

  2. Pissing off someone who is more than smart enough to convince other people that you are big fat liars is not a good idea.

  3. Continuing as if you are safe when you are told over and over again that your funding will be gone is a sign of a total lack of intelligence.
Make no mistake.

I will work to remove your public funding.

I don't care where you are. I don't care if you're Cornell, or Harvard or Duke or wherever.

I will work to remove your public funding for research. Protecting only certain areas, like materials science (national interests and all of that).

I wish to cull the academic field worldwide.

Cull as in remove many of you from academia.

As in force you to do something else with your life besides pretend to be a physicist.

Is that clear yet or should I continue to rant?

And make no mistake here, what you see on the surface is the tip of an iceberg. I'm already working to make sure my ideas are traveling in political circles and to make sure that I can get the ear of policymakers.

I will beat you at that game hands down. And your departments will feel the financial pressure, hopefully, worldwide and your will feel a tremendous drop in prestige as I deliver, and deliver and deliver and make the point that you no longer do because I am very, very, very angry.

None of the arguments you can use against naive people who don't know better will work with me when it comes to funding as the best scientific minds will find a way.

Like I've found ways.
I'm so frustrated here by a situation that shouldn't be possible!!!

So maybe I'm throwing in everything but the kitchen sink here but I'm hoping there is some kind of opening.

I hate to threaten funding.

I'd prefer to dream about doing more research, but instead I'm trying to find what buttons to push to get a response that fits more in line with people who care about something.

I figure many of you care about funding.

There is no doubt about my research. No reasonable doubt. I can keep branching out from "pure math" but the mathematical research is EXTREMELY important.

Who knows fully why mathematicians have gone bizarro and can't be moved by mathematical proof, but they have.

If you force me to turn problem solving skills just to convincing people versus making more significant discoveries then I will continue to do so, but I will increasingly feel that is unavoidable proof that you are screwed up as well, like the mathematicians.

Which would mean many of you are fakes. Not really physicists doing real research but people managing the system for public funding.

Or, as I like to call it, people living off of white collar welfare.

I will solve this problem and do it hopefully without destabilizing the entire world (math people were pushing me to do that by solving the factoring problem).

But make no mistake, I'm driven by the responsibility. And as far as I know, I have wide latitude to get things done here for the good of the human species.

To history that would just make me a great man, if we survive this crap, as a species. If not, then it doesn't matter anyway because our species and its history will just have been crap.

All that effort by all those people who discovered so much, learned so much, BELIEVED in so much, all for nothing because at the end…but no. That is not how this story ends. Not on my watch.

You people do not have the power and if you force me you will understand what I can do to honor those who came before me, and to save those who are to follow, those who are still yet to be born.

I will not let you kill them.

Friday, October 17, 2008


JSH: Correction to solving binary quadratic Diophantine equations

A poster noted a problem with my original theory that I thought fully covered binary quadratic Diophantine equations as I stupidly assumed coprimeness between x and y given an equation like

x^2 - Dy^2 = F

when F can have a square as a factor.

That poster gave the example of x^2 - 3y^2 = 4, but it turns out in any case with a natural number n, not a unit, given

x^2 - Dy^2 = n^2

where D is a natural number not a unit, solutions must exist as you can reduce to

(x/n)^2 - D(y/n)^2 = 1

so the problem is with square factors, which have to be divided off to force coprimeness which I stupidly assumed.

But other than that the theory is ok. Easy fix. I boringly solved generally solved binary quadratic Diophantine equations.

Turned out it was easy. And now I'm kind of depressed as I'm beginning to wonder about you people.

Am I some kind of genetic freak with super intelligence in a world where the people around me are just too stupid to fully understand me?

If so, why am I so freaking cursed.

I'm living on the planet of the Apes.

The best explanation then for what has been happening is that you all as a group lack the intelligence level necessary for us to communicate meaningfully so it's like if you were trapped on a world of chimpanzees, who happened to be able to talk, barely, but were otherwise, just chimpanzees.

A planet of the apes.

Well that ruins my mood. Looks like all the data is in though.

It's not that you people are actually stupid. It's that I'm some kind of mutant freak of nature in a nightmare of super intelligence trapped on a world where I have no one to talk to like me.

No wonder I'm finally actually going bonkers. I have no hope.


JSH: Pondering the idea rejections

As a person with a degree in physics I find I can't just ignore what the physical world tells me, so I have repeatedly had to question myself as to whether or not I was actually wrong in facing hostility to any number of ideas of mine, with particular rejection in the mathematical field.

So what to do?

Easy. Experiment!!!

So I branched out from "pure math" and started doing problem solving in other areas, and guess what?

Ran into the same mystery rejection which I call a mystery because I could prove things clearly, beyond any reasonable doubt, and even get remarkable supporting data, but find that then the expected acceptance wouldn't happen, and I'd still get rejecting behavior on newsgroups where I was sidelined from the mainstream.

Digital Media Equipment Self-Encryption or DMESE for short is just the most spectacular and SIMPLE example so far of this bizarre phenomena which is so dramatic because the entertainment industry loses literally MILLIONS of dollars facing a problem I solved over a year ago—and gave away for free.

RealNetworks is in a court battle to try and get software used which coincidentally uses a piece of the full solution I found, the "self-encryption" part, having been blocked by a court order when the objection raised by the MPAA is solved by a solution I found over a year and 3 months ago.

Sorry people but that's not evidence of an efficient world when it comes to information.

Add to that weird stuff like, Google: define mathematical proof

In the US most of you should get my personal definition of mathematical proof in the top 5, out of 550,000 possibles according to Google when I checked just now. Or Google "definition of mathematical proof" where the quotes are needed now (not before) and I take #1.

(When I say "Google" I mean use Google. Yahoo! gives slightly different results but some are just as spectacular but I like simple exposition so I'm sticking with Google where things work best.)

In the face of this evidence on the math newsgroups where I pointed it out, I was told that Google ranking don't matter!!!

Hmmm…maybe millions of investors need to know about this profound assertion by math people, eh?

The short of it of course is blanket rejection of basic facts which is fanatical behavior.

Physicists confront it routinely.

Difference here is that in pointing it out to the physics community here I've ran into a bizarre wall, punctuated by insults from posters like "Uncle Al", so even the physics community on newsgroups doesn't behave, so what gives?

I made an open source program. Google "Class Viewer". I came up, with a plot idea for a Superman movie, Google: Superman plot idea

And yes I'm doing all kinds of things trying to outline a bizarre problem space where near as I can figure NONE of you are what you say you are, or what I'd think you say you are.

So of course I reject academia now. I feel like my physics professors lied to me. My country lied to me. My world lied to me.

I was convinced that if I got a good education, worked hard and could prove the value of my ideas I'd be rewarded but instead I've been insulted or mostly ignored when I can get bizarre validation from the new technology of web search results.

So I know there is something wrong. The world I was told existed as a child does not.

It was a lie.

So then, now we can start. What is this world really? Who actually runs it?

What do you actually believe in?

And now if I've got your attention, who in the hell are you?

Wednesday, October 15, 2008


JSH: So why no legal DVD copying?

A remarkable seeming tangent to my story is the reality that over a year ago as I contemplated ways to break the impasse over my mathematical research I came up with a solution to the problem of legally copying DVD's which I called DMESE, which stands for Digital Media Equipment Self-Encryption.

Not having a lot of routes to talk about my ideas, I put it on some of my blogs, and yup, posted about it on newsgroups, where in response I got the usual insults, tirades, and chants that I was insane, along with people claiming it was a bogus idea, but RealNetworks just tried to put out a product which is quite similar:

The similarity is in that key to my idea and part of their approach is the encryption of the copy—preventing the user from just handing it off to others.

That's the "self-encryption" part of the DMESE title I created.

Well they were promptly sued!!!

Seems the media giants don't want DVD copying software and the reason I read was that they are afraid people will just rent DVD's and copy them versus buy them, except I solved that problem months ago:

The simple idea I had was the asking for the original DVD after 30 days to be checked by the machine which then assumes you own the thing (or are a really desperate person with lots of time on your hands to try and cheat).

What makes this story almost beyond belief is the reality that millions of United States consumers CANNOT legally copy their DVD's!!!!!!!!!

The supposedly almighty American consumer, ham-strung!!!

(But of course we Americans are no longer considered so mighty these days anyway, I guess.)

I also love this story for showing you how bogus people are who rip on me and my ideas for supposedly being crappy or not working, and for the conspiracy nuts, sorry. I find it hard to believe that the mathematical community has teamed up with Hollywood to block people around the world from being able to legally copy their DVD's just to prevent interest in my research.

Fun thing about a post like this one are the replies I expect from the losers among you who rant against people like me who will claim that I'm all wrong, and that it's not a big deal and you not being able to legally copy your DVD in the United States means NOTHING because you see, they know all, I'm supposedly just a "loon" wanting attention, and there's nothing more to be said, so you just give up and keep illegally copying your DVD or don't copy at all. You nice little sheep, or, um, people who act like sheep. Or should I say think like sheep?

And hey, deep down, you know you like being inconvenienced by people like "Uncle Al" and the other crackpot haters you dote on, to keep those people happy, right?

It's a stupid world, really. Beyond the hype. I assure you. It's a stupid world.

Sunday, October 12, 2008


JSH: Why modern number theorists lie

I was just re-reading one my blog posts which explain with extremely simple mathematics why the ring of algebraic integers is flawed:

And considering how simple it is to explain there is no rational debate over the question of whether or not modern theorists know that a lot of what they are doing is wrong, so why then do they lie?

My assessment is that if you understand the error and how it works then you also know that a lot of people with prestigious positions are, well, um, not very good mathematicians! So since their careers are BUILT on the error, without it, they might just be, oh, I don't know, car salesmen or something. And no one would care about their opinion on mathematics anyway.

But they are not car salesmen. They are men and women (mostly men) who have careers—like at prestigious institutions like Harvard and Oxford and Princeton—and families and a lot of energy and time invested in, mathematical ideas that do not work.

So they are holding on to what works for them.

Now I can blow apart standard teaching on the ring of algebraic integers, and do so with some trivial algebra and emphasizing that:

a*(f(x) + b) = a*f(x) + a*b

so the VALUE of f(x) is irrelevant, but when I'm facing desperate people desperate to believe they are real mathematicians then none of that matters in the face of raw human emotion.

Mathematics is, in many ways, a cruel discipline.

But to defy it, people with social status can just call me the crackpot, and that work, for a while

But around you in the world today you are seeing how bad it can get when people do the math wrong, and how far things can drop and how quickly.

I know many of you simply lack the intellectual ability to fully comprehend what you are doing, but now you have an opportunity to get some grasp of how bad it can get for you.

When the world finally figures out what has been happening it won't be a time you can just shrug it off, and say they'd have done what you did. That they would have kept teaching kids broken math ideas and that they would have stopped a major discoverer in his tracks for years with lies to hold on to some professor jobs and public funding.

It will be a time to face lifetime consequences that seemed like some distant thing just a while before that was a risk worth taking.

It's not.

Sunday, October 05, 2008


JSH: Drama continues?

Oh well maybe it was too much to hope that one infinite series might make a difference and I have analyzed the situation and believe that mainstream mathematicians who must be aware of my research, as I routinely notify them by email, are relying on the angry idiots on the sci.math newsgroup as their cover.

My guess is they feel they can sit back indefinitely and routinely reject my papers which yes I still do send to math journals, and always say later that my research was not accepted by the mainstream math community citing sci.math which puts me in a conundrum.

Now that I've used tautological spaces again I can potentially wipe out the need for new research in some other area of number theory, but I suspect mathematicians will just act like I didn't and still do pretend research so I'm not sure if that's the way.

The angry idiots on sci.math have continually challenged me to solve the factoring problem and post a demonstration as one thing they'd have to accept. I find that fascinating as a challenge, as I've said I refuse to do research in that area as I'm worried about crashing the world economy.

But that worry is diminishing as the world economy is crashing on its own. Kind of ironic, don't you think?

Regardless, I'm not interested in adding to the misery because mathematicians can lie as a group, are heartless fiends, who pretend to like mathematics when they despise it, who are also very savvy political operators.

The political war continues and I'm up against people who could teach George W. Bush some lessons, but that is just the reality of the problem.

Wasted time. Wasted lives. But let's face it. At the end of the day, the lives of math students aren't any more important than the lives of countless other people all over the world facing so much worse than throwing their time and mental energy away learning crap math.


JSH: Google problems, start of debate against series

Google Groups is on one of their delay things again so I can't see my new messages, so I can't reply through Google Groups, which is what I use to reply, to criticisms I see that have arisen.

So I'll make this post to note the problem, which hopefully will clear up in a few days, and to point out some things:

First, my infinite series was not previously known as you would have seen something like the following in a mathematical text on the subject and as so much has been written about Pell's Equation, I doubt you'd have missed it:
  1. x^2 + Dy^2 = F

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

  3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2

  4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3
and that goes out to infinity. To get successive terms in the series you use the algebraic result that given:

u^2 + Dv^2 = C

it must be true that

(u-Dv)^2 + D(u+v)^2 = C*(D+1).

And where whenever the exponent of (D+1) is even, you can have a case where you just have a multiple of x and y, so you can solve for D, which defines possible values for F in terms of x or y.

Like with the third in the series:

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

you can consider

(1-D)x-2Dy = +/-(D+1)x or +/-(D+1)y


2x + (1-D)y = +/-(D+1)x or +/-(D+1)y

because trivially

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

and solving for those possibilities gives a value for D. I got D=1, for the case of

(1-D)x-2Dy = (D+1)x and 2x + (1-D)y = (D+1)y.

So you can map the series as a super structure, where D is set at various levels.

One poster lobs a criticism that

u^2 + Dv^2 = C

requiring that

(u-Dv)^2 + D(u+v)^2 = C*(D+1)

is derivable from an equation known to Brahmagupta. Fine, so show that Brahmagupta derived that particular result and USED it to generate an infinite series.

Hey, you people missed the result right in front of you too, which may be why I'm seeing so many angry replies with insults.

Your chance of a lifetime was a post away and you missed it so anger can be a reaction.

And missing it against me when the opportunity to upstage me was there for days may really anger people who have argued with me or listened to and believed in other posters who argued with me as well.

That social stuff is powerful with a lot of people. Having people trust and believe in you, like when you're criticizing a "crackpot" can be powerful magic making a person feel all warm and fuzzy inside like they're actually SOMEBODY.

Getting upstaged pops the bubble. Reality is so annoying at times for some people, you know?

But you are now up against the worldwide community of people interested in mathematics who might want to explore that number theoretic super structure, and hatred is not an excuse for denigrating valuable mathematical ideas…not if you wish to be taken seriously later. Ever.

Students again I remind you of your futures. Angry sci.math posters are there because they're not good enough to go anywhere else, and I'm there because I'm an amateur who has been blocked out of usual circles, so I post to several math newsgroups including the one full of angry idiots.

But it is YOUR future. Angry losers on sci.math will probably keep ripping on this result just because…well, because they're losers, who you'll notice could not see that infinite series right in front of them for days.

They were too busy still ripping on me.

Don't make it personal. It's math. You make it personal and you lose.

So you all lost round one. Easy mathematical fame escaped you with the find of the series, so now it's up to you what you do next.

Continue to listen to angry idiots, or do the math.

Saturday, October 04, 2008


JSH: How can I top that?

I'm kicking back now kind of wondering to myself as I try to get some sense of the feeling of accomplishment with the discovery of my own infinite series, and the wild thing to me is the feeling that, hey, good thing I didn't find this thing years ago as I can't see how I'd have done anything else, as how can I top it?

And what's really wacky wild is that years ago I thought it'd be this great thing to find a simple proof of Fermat's Last Theorem, and got that, and it was like nothing as the math world wouldn't accept it, and it didn't feel satisfying anyway, and I had to use this weird new analysis technique I'd invented called tautological spaces, when I wanted something that felt CONCRETE.

So I kept at it. Found my prime counting function. Non-polynomial factorization. The object ring, and nothing really had that truly solid feeling to it, no matter what I could prove, and people kept ripping on me, so I kept going.

It's so ironic.

But it does go back to when I was a kid and I'd read about series like the Taylor series and wonder about that and it didn't sink in to me until now that I really wanted my own.

So, ok, proving FLT is cool. Discovering the object ring is cooler. Inventing my own analysis technique with tautological spaces is rather awesome.

But NOTHING beats having my own infinite series which is an infinite series of equations! So it's better yet!!!
  1. x^2 + Dy^2 = F

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

  3. ((1-D)x-2Dy)^2 + D(2x + (1-D)y)^2 = F*(D+1)^2

  4. ((1-3D)x + (2D^2 - 4D)y)^2 + D((3-D)x + (1-3D)y)^2 = F*(D+1)^3
and that goes out to infinity. To get successive terms in the series you use the algebraic result that given:

u^2 + Dv^2 = C

it must be true that

(u-Dv)^2 + D(u+v)^2 = C*(D+1).

And where whenever the exponent of (D+1) is even, you can have a case where you just have a multiple of x and y, so you can solve for D, which defines possible values for F in terms of x or y.

An infinite series of equations that I like to call a huge number theoretic super structure.

My own infinite series. Finally, something I really FEEL is concrete.

Can't see how I can top that. So I'm done.

Time to kick back and rest on my laurels, drink more and chase more women.

Thursday, October 02, 2008


Huge number theoretic structure and number crunching

I noted in a previous post the find of this HUGE freaking number theoretic structure that starts out simply enough:

x^2 + Dy^2 = F

followed by

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

followed by

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

which simplifies to

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

so you just plug in for x and y from the first equation into the second, and to get the next in the series you'd plug in again from the prior, so you build recursively:

((1-D)((1-D)x-2Dy)-2D(2x + (1-D)y))^2 + D(2((1-D)x-2Dy) + (1-D)(2x + (1-D)y))^2 = F(D+1)^3

and that goes ad infinitum. (That last is complicated enough I don't feel like simplifying.)

So it's this massively recursive thing where you feed in from the prior equation to get the next one and what makes it interesting is that of course whenever you have (D+1) with an even exponent on the side then you may have a solution with x and y multiplied by some power of D+1.

But checking that idea you find it sets D, and also sets F relative to D, so this freaking massive infinite super structure of equations is the source of all behavior for Pell Equations and more generally equations of the form x^2 + Dy^2 = F.

If that didn't make sense, imagine that with the third equation:

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

you check to see if it's possible that

((D+1)x)^2 + ((D+1)y)^2 = F*(D+1)^2.

So you could check

(x-Dy)-D(x+y) = +/-(D+1)x or +/-(D+1)y

and it turns out that if you do that you'll set possible values for D. So you're setting D at each level. And setting F relative to D, so it tells you what D and F can give solutions if that's true.

But playing with the thing requires some massive number crunching and symbolic manipulation which is best done by computer, I'd think.

Once mapped out at any level, then that's it. It's set perfect and static. Unchanging.

Actually this structure has always existed but I guess no one noticed it was there even though it's FREAKING HUGE and completely controls rational solutions to x^2 + Dy^2 = F.

I'm not even going to try to play with the thing beyond noting its existence leaving that for some person or team who wants to start mapping the super structure.

As a side benefit, any equations that fit within mapped areas can be immediately solved in integers.

Obviously with 2000 years of history with research in this area there should be some interest in this massive super number theoretic structure but I'm not holding my breath.

But hey I can post! And see what happens.

But it's so cool that I have to note again that there is this HUGE, MASSIVE number theoretic super structure made up of equations recursively built, layer by freaking layer, which completely controls Pell's equation along with others and it's just such a wild thing.

An infinite structure of equations just out there, running everything, mappable, though incredibly complex, and did I say it's freaking huge? And it's a super number theoretic structure?

I'm glad I found it. Kind of cheers me up a bit. You know?

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