Saturday, March 18, 2006
SF: A hyperbolic solution
It's worth mentioning to me that what I found is technically a four-dimensonal general factorization of a composite that traces a hyperbolic slice from a hyperbloid:
The factorization
T = (x+y+vz)(vz-x)
in four dimensions: x, y, z, v
where x, y and z are defined by
x^2 + xy + k_1 y^2 = k_2 z^2
so you have the hyperbloid, and next
(2(v^2 - k_2)z + vy)^2 = ((1-4k_1)y^2+4T)v^2 + 4k_2(k_1y^2 - T)
where and first step to using the equations to factor is to pick y, k_1 and k_2, and actually picking y gives you the slice.
That may sound like nothing you've ever heard of for factoring composites
Some may even think that's the point for why it should be ignored, as if something so bizarre as factoring using four dimensions must be a crackpot bit of work.
Or you may naively think that the equations don't work, or that someone has proven that they cannot be used to practically factor.
I haven't seen any proof that a research effort couldn't turn the initial research into a powerful factoring method, as instead I've seen some Usenet posters deriding me.
They like to make things personal on Usenet in the math and sciences newsgroups.
Some people make it their business to reply to my posts on almost any subject across Usenet, deriding my research and me.
Now then, if those equations—like nothing before seen—can be the start of a research effort that leads to a practical factoring, why should anyone assume that mainstream cryptologists or mathematicians would be the ones to do it?
I increasingly fear it more likely, as that culture is proud, that desperate people who don't care about the source, but are interested in ANY way to crack security systems would be the more likely ones to just try anything.
So—mainstream mathematicians care about the source and you know and I know they are capable of ignoring anything—versus—desperate people who may be willing to try anything, with a general composite factorization using a hyperbloid and four dimensions.
With all that said, it's also has not been proven that the equations can be made into a practical method, so they may just been some eosteric pure math oddity, but you can be sure that mathematicians will do their best to ignore them even in that area as that's what these people freaking do.
So how did I even get those equations?
I discovered my own technique for mathematical analysis where I subtract what I call conditionals, in this case the equation for the hyperbloid
x^2 + xy + k_1 y^2 = k_2 z^2
from what is commonly called an identity, which I found by manipulating
x+y+vz = x+y+vz
which is one of those clever ideas that you wonder was only discovered last century, by me.
I discovered the method back in the month of December 1999 and promptly posted about it on sci.math to much derision, as usual.
The full derivation demonstrating the technique is at my blog:
http://mymath.blogspot.com/2005_08_01_mymath_archive.html
You can see that it is in my August 2005 archive and yes the equations have been around for that long, long enough that if they can be made practical there may be some person or persons out there as we speak who are cracking RSA easily, and not telling anyone.
If they can be made practical, and again, I don't know if they can, but even if they cannot be, if mathematicians were so "pure" as they claim, a solution of this type would be of some interest.
For those of you who do not understand how the real math world works, consider this is just one of my results, and I did get some research of mine published in a peer reviewed math journal, a somewhat small electronic one that had only been around for about a decade.
Well someone posted about it on sci.math and the newsgroup erupted in fury.
A group of them emailed the editors of the journal claiming my paper was wrong, and the chief editor yanked it THAT NIGHT in a clear knee-jerk reaction, giving in to the mob editorial decision, which he didn't know about—he clearly just thought he was getting emails from concerned mathematicians—not realizing he was dealing with sci.math people.
How do I know?
Because he emailed me claiming that publication was a mistake, and claimed to have a reviewers report showing the mistake, which was a faulty claim of error made by the Usenet poster W. Dale Hall, which I knew because he'd posted it the day before, when the sci.math people were planning the email assault—in posts!
That's the REAL math world.
That's real math society.
Not pretty, not a movie—a janitor with emotional problems (or without them) could not crack this world—not so brilliant or beautiful—but how things actually work in the real world of mathematics.
It is an academic world, with Ivory Tower people who can do things that most people would find incomprehensible, not because it's so brilliant, but because it's so damn stupid.
I eventually sent a revised paper—cleaning up some details and putting it upfront how big the paper was as I didn't do that before—to the Annals of Mathematics "published bimonthly with the cooperation of Princeton University and the Institute for Advanced Study."
See http://www.math.princeton.edu/~annals/
I was told that the paper was accepted for review, and months passed…
After six months I checked in and was told that a rejection had been sent a month after they got the paper, but I never got any email.
I asked for a reason for the rejection, and was told none was available, as my contact at Princeton University told me that someone else had just noted the database and there was no additional information.
They were stuck. Perfect paper with a dramatic conclusion which I now know leads to the conclusion that ideal theory is wrong, among other huge revolutionary things.
But how amateur!
Just claim an email was sent, when I have MSN and an email from Princeton through MSN is not going to just disappear without a trace all that freaking often, and then I have to contact someone nice enough on the inside to at least get the info out that someone had put that in their database, but, no more info available.
If these stories sound impossible to you, you do not know the real math world.
It is quite possible that I have put up one of the most important research finds in the history of factoring, and it is just being ignored by people you do not understand.
[A reply to someone who wrote that James' work can be ignored can be ignored because the author is a crackpot.]
I'm not a crackpot. And, hey, at least I understand the distributive property, unlike you.
The reality is that there is nothing else out there like pulling points from a hyperbloid plus one variable to generally factor a composite.
It's the kind of simple but brilliant idea that would generate a lot of excitement, if I weren't the person pointing out the obvious, as then it just sounds self-serving.
Like, just consider a sample headline:
Amateur Mathematician Finds Way to Factor in 4-d
The real story here is that most academics are not creative people and know nothing about what it really takes to make a major discovery.
They can read about people who made great discoveries in the past but have no clue about what it actually takes or how hard it is, and how frustrating the process is, or how long it is.
So I take years to figure things out with a lot of mistakes and messy stuff along the way, and you people push that as proof that I must just be some crackpot, and then you refuse to acknowledge even simple things about the correct results once I've finally refined them to the level of total rigor.
What, you think that it was easy for any of them in the past?
Have you any clue what it took?
At the end of the day, people re-write history and make it seem so nice and glamorous or like it's about eureka moments in the bathtub.
Or you just have some dream and suddenly you have it all figured out!
Many a morning I've awakened wishing I'd get that dream.
It's hard work on a level you cannot begin to comprehend. YEARS of effort, working hard to understand, to find some truth.
It's actually about years of hard, very hard work, lots of failure, and finally emerging battle-scarred and wiser with knowledge that has never before been known.
And people like me are supposed to get at least a nod of appreciation here or there as if we don't pay that cost and take all that pain and misery to figure out these things, they just never get found, as who else is going to do it?
You?
Want to take years of pain and misery, knocking your head against the wall of a hard problem, fail again and again, have to get back up and keep trying just with the hope that some day you MAY figure it out?
You people think it's about being brilliant so it's easy. So stuff just comes to you.
No. It's about working damn hard, night and day for years until you finally figure things out.
It's not about brilliance but about HARD WORK.
And because you can't comprehend that, you keep up your nonsense in replies to me, as you have no comprehension of what I've been through.
The factorization
T = (x+y+vz)(vz-x)
in four dimensions: x, y, z, v
where x, y and z are defined by
x^2 + xy + k_1 y^2 = k_2 z^2
so you have the hyperbloid, and next
(2(v^2 - k_2)z + vy)^2 = ((1-4k_1)y^2+4T)v^2 + 4k_2(k_1y^2 - T)
where and first step to using the equations to factor is to pick y, k_1 and k_2, and actually picking y gives you the slice.
That may sound like nothing you've ever heard of for factoring composites
Some may even think that's the point for why it should be ignored, as if something so bizarre as factoring using four dimensions must be a crackpot bit of work.
Or you may naively think that the equations don't work, or that someone has proven that they cannot be used to practically factor.
I haven't seen any proof that a research effort couldn't turn the initial research into a powerful factoring method, as instead I've seen some Usenet posters deriding me.
They like to make things personal on Usenet in the math and sciences newsgroups.
Some people make it their business to reply to my posts on almost any subject across Usenet, deriding my research and me.
Now then, if those equations—like nothing before seen—can be the start of a research effort that leads to a practical factoring, why should anyone assume that mainstream cryptologists or mathematicians would be the ones to do it?
I increasingly fear it more likely, as that culture is proud, that desperate people who don't care about the source, but are interested in ANY way to crack security systems would be the more likely ones to just try anything.
So—mainstream mathematicians care about the source and you know and I know they are capable of ignoring anything—versus—desperate people who may be willing to try anything, with a general composite factorization using a hyperbloid and four dimensions.
With all that said, it's also has not been proven that the equations can be made into a practical method, so they may just been some eosteric pure math oddity, but you can be sure that mathematicians will do their best to ignore them even in that area as that's what these people freaking do.
So how did I even get those equations?
I discovered my own technique for mathematical analysis where I subtract what I call conditionals, in this case the equation for the hyperbloid
x^2 + xy + k_1 y^2 = k_2 z^2
from what is commonly called an identity, which I found by manipulating
x+y+vz = x+y+vz
which is one of those clever ideas that you wonder was only discovered last century, by me.
I discovered the method back in the month of December 1999 and promptly posted about it on sci.math to much derision, as usual.
The full derivation demonstrating the technique is at my blog:
http://mymath.blogspot.com/2005_08_01_mymath_archive.html
You can see that it is in my August 2005 archive and yes the equations have been around for that long, long enough that if they can be made practical there may be some person or persons out there as we speak who are cracking RSA easily, and not telling anyone.
If they can be made practical, and again, I don't know if they can, but even if they cannot be, if mathematicians were so "pure" as they claim, a solution of this type would be of some interest.
For those of you who do not understand how the real math world works, consider this is just one of my results, and I did get some research of mine published in a peer reviewed math journal, a somewhat small electronic one that had only been around for about a decade.
Well someone posted about it on sci.math and the newsgroup erupted in fury.
A group of them emailed the editors of the journal claiming my paper was wrong, and the chief editor yanked it THAT NIGHT in a clear knee-jerk reaction, giving in to the mob editorial decision, which he didn't know about—he clearly just thought he was getting emails from concerned mathematicians—not realizing he was dealing with sci.math people.
How do I know?
Because he emailed me claiming that publication was a mistake, and claimed to have a reviewers report showing the mistake, which was a faulty claim of error made by the Usenet poster W. Dale Hall, which I knew because he'd posted it the day before, when the sci.math people were planning the email assault—in posts!
That's the REAL math world.
That's real math society.
Not pretty, not a movie—a janitor with emotional problems (or without them) could not crack this world—not so brilliant or beautiful—but how things actually work in the real world of mathematics.
It is an academic world, with Ivory Tower people who can do things that most people would find incomprehensible, not because it's so brilliant, but because it's so damn stupid.
I eventually sent a revised paper—cleaning up some details and putting it upfront how big the paper was as I didn't do that before—to the Annals of Mathematics "published bimonthly with the cooperation of Princeton University and the Institute for Advanced Study."
See http://www.math.princeton.edu/~annals/
I was told that the paper was accepted for review, and months passed…
After six months I checked in and was told that a rejection had been sent a month after they got the paper, but I never got any email.
I asked for a reason for the rejection, and was told none was available, as my contact at Princeton University told me that someone else had just noted the database and there was no additional information.
They were stuck. Perfect paper with a dramatic conclusion which I now know leads to the conclusion that ideal theory is wrong, among other huge revolutionary things.
But how amateur!
Just claim an email was sent, when I have MSN and an email from Princeton through MSN is not going to just disappear without a trace all that freaking often, and then I have to contact someone nice enough on the inside to at least get the info out that someone had put that in their database, but, no more info available.
If these stories sound impossible to you, you do not know the real math world.
It is quite possible that I have put up one of the most important research finds in the history of factoring, and it is just being ignored by people you do not understand.
[A reply to someone who wrote that James' work can be ignored can be ignored because the author is a crackpot.]
I'm not a crackpot. And, hey, at least I understand the distributive property, unlike you.
The reality is that there is nothing else out there like pulling points from a hyperbloid plus one variable to generally factor a composite.
It's the kind of simple but brilliant idea that would generate a lot of excitement, if I weren't the person pointing out the obvious, as then it just sounds self-serving.
Like, just consider a sample headline:
Amateur Mathematician Finds Way to Factor in 4-d
The real story here is that most academics are not creative people and know nothing about what it really takes to make a major discovery.
They can read about people who made great discoveries in the past but have no clue about what it actually takes or how hard it is, and how frustrating the process is, or how long it is.
So I take years to figure things out with a lot of mistakes and messy stuff along the way, and you people push that as proof that I must just be some crackpot, and then you refuse to acknowledge even simple things about the correct results once I've finally refined them to the level of total rigor.
What, you think that it was easy for any of them in the past?
Have you any clue what it took?
At the end of the day, people re-write history and make it seem so nice and glamorous or like it's about eureka moments in the bathtub.
Or you just have some dream and suddenly you have it all figured out!
Many a morning I've awakened wishing I'd get that dream.
It's hard work on a level you cannot begin to comprehend. YEARS of effort, working hard to understand, to find some truth.
It's actually about years of hard, very hard work, lots of failure, and finally emerging battle-scarred and wiser with knowledge that has never before been known.
And people like me are supposed to get at least a nod of appreciation here or there as if we don't pay that cost and take all that pain and misery to figure out these things, they just never get found, as who else is going to do it?
You?
Want to take years of pain and misery, knocking your head against the wall of a hard problem, fail again and again, have to get back up and keep trying just with the hope that some day you MAY figure it out?
You people think it's about being brilliant so it's easy. So stuff just comes to you.
No. It's about working damn hard, night and day for years until you finally figure things out.
It's not about brilliance but about HARD WORK.
And because you can't comprehend that, you keep up your nonsense in replies to me, as you have no comprehension of what I've been through.
# posted by James Harris @ 03:39 
