Saturday, February 23, 2008
JSH: How they do it
To me it's still rather neat to find this surprisingly useful relationship from considering
abs(nT - 2k^2)
and the maximum k for which that value is a minimum, when T is an odd composite to factor, and n is just there to force nT mod 3 = 2, so you can use 5, when T mod 3 = 1, but 1 otherwise.
Then that k is at or near a value such k is a solution when z = 3k/2, and
z^2 = y^2 + nT
and you have a non-trivial factorization of nT.
Now that follows from doing something out of the box as I deliberately looked at
2x = k mod p
for quite some time just so that I could complete a square, as I was speculating about factoring T by using the factorization of some other number.
So getting the full result is just about using
2x = k + pr
where r is just some integer and substituting with z = x + k, into
z^2 = y^2 + nT
and doing some basic algebraic analysis and I explain all of that to emphasize the simplicity of the approach, and many of you can do it yourself to verify or read my other recent posts to see more detail.
And it's a fascinating result for many reasons, but one of them is that the p kind of vanishes after helping you factor by helping you find the correct k.
I can also show that k^2 = 2^{-1}(nT) mod p, so you can just go looking for large primes—as the bigger the prime the quicker you can factor—when you have a large composite T, so you actually get to just go find some primes and know about where to look and can factor.
So that should be a big deal as a nice bit of interesting mathematics that could have impact on the use of RSA encryption and it's just a neat result, so why am I still the "crackpot" on newsgroups instead of celebrated in the mainstream?
Well I'm looking at posts in reply to me and not seeing much new which is why I wanted to explain to you how they do it: how they keep the truth from being mainstreamed.
I have other mathematical results and watched the same process with them.
That process is to deny, mostly ignore, or claim ignorance of the result or of the behavior around the result.
So some posters will keeps posting nastily in reply and just claim I'm wrong, while others will post puzzlement that I'm even posting! While others will post puzzlement that anything I have ever said was ever ignored as they claim none of it was and that in fact I get plenty of attention so why am I complaining.
But they'll ignore any current result. If pressed they will simply quit replying.
Years ago when I first faced this process, yes, I went off Usenet, and got a paper published. I'm sitting back waiting for math society to acknowledge that remarkable result—but monitoring Usenet just to see what happened—and some poster posts that I'm published on the sci.math newsgroup and the group erupted in fury.
Never paused for a moment to consider that maybe publication meant something.
There is what people say they believe and there is what they demonstrate they truly believe. Publication. Hmmm…
Now you can see how they react with the factoring problem.
Yes, I've said for some time that I had solved it only to be wrong, but I know this process better than you do, and my strategy is based on game theory.
And you can see what I'm up against if you understand that simple approach I outlined before about using abs(nT - 2k^2) and understand it, as well as the implications, and see how math society is STILL to this point reacting.
Lying is as old as humanity. People lie to get things they would not get otherwise.
Some of you may be going to math classes to listen to professors who would not be there if they told the truth. It's that simple. It can be easy to talk about the fate of the human race and the importance of knowledge and progress in the abstract, but if you're some middle-aged man with a mortgage, a wife who thinks you're brilliant, and other perks that may come with being a math professor (yes there are some perks for some maybe not many but some) considering accepting not being so brilliant and losing what you have, then lying can seem to be just about survival.
Perspective is an amazing thing.
Some of these people may figure that humanity is such a big thing that there's no way it can really matter if they stop intellectual progress in mathematics for a while. So they did. They stopped most progress in "pure math" areas for the entire human race across the planet.
So I went to the factoring problem.
Now then, yes, humanity is kind of big to us, and it can seem easy to think that getting your little piece today is worth blocking its progress for a little while, especially to stop some annoying guy—just some guy after all—who keeps going on and on about his mathematical research.
Because history makes the legends—so I can't be one to you now—so it's later that students will read about you and find it incomprehensible that you could have even paused with the fate of your own species in the balance, and what could have been so important to you that you'd actually deny progress for people who were just lying?
But they would also know how it's in the balance. Some of them might contemplate not getting to be born because of what you are doing now—if you weren't stopped.
But they aren't in your shoes now. Perspective.
Legacy is a word that gets tossed around, but thinking that maybe down the line your legacy can be that of THOSE people, who didn't do the right thing, who held on even when it was clear that they were wrong, and broken later, could only fumble out rationalizations or apologies and accept their branding for life, is an exercise for those who aren't thinking about their bills and just trying to have a life.
If you were brilliant you wouldn't be in this situation.
Make no mistake, the world is not a nice place when you get on the outside and are looked at as a renegade versus being one of us.
You are inside now, and if you are a math professor, then you are very inside, but think about what happens if you keep up this nonsense and you are completely out.
I'm a problem solver. I brainstormed my way through some important and difficult math problems, got the answers, and found a society that couldn't or wouldn't live up to expectations so I am working on solving that problem as well.
My mistakes are many, but I own up to them. I have been wrong many times before, said things I know I'll regret later, and often wondered how this situation is even possible—until I remember—perspective.
No criminal ever thought first, long and hard, about getting caught, enough to not do the crimes.
If they had, then they wouldn't be criminals, now would they?
abs(nT - 2k^2)
and the maximum k for which that value is a minimum, when T is an odd composite to factor, and n is just there to force nT mod 3 = 2, so you can use 5, when T mod 3 = 1, but 1 otherwise.
Then that k is at or near a value such k is a solution when z = 3k/2, and
z^2 = y^2 + nT
and you have a non-trivial factorization of nT.
Now that follows from doing something out of the box as I deliberately looked at
2x = k mod p
for quite some time just so that I could complete a square, as I was speculating about factoring T by using the factorization of some other number.
So getting the full result is just about using
2x = k + pr
where r is just some integer and substituting with z = x + k, into
z^2 = y^2 + nT
and doing some basic algebraic analysis and I explain all of that to emphasize the simplicity of the approach, and many of you can do it yourself to verify or read my other recent posts to see more detail.
And it's a fascinating result for many reasons, but one of them is that the p kind of vanishes after helping you factor by helping you find the correct k.
I can also show that k^2 = 2^{-1}(nT) mod p, so you can just go looking for large primes—as the bigger the prime the quicker you can factor—when you have a large composite T, so you actually get to just go find some primes and know about where to look and can factor.
So that should be a big deal as a nice bit of interesting mathematics that could have impact on the use of RSA encryption and it's just a neat result, so why am I still the "crackpot" on newsgroups instead of celebrated in the mainstream?
Well I'm looking at posts in reply to me and not seeing much new which is why I wanted to explain to you how they do it: how they keep the truth from being mainstreamed.
I have other mathematical results and watched the same process with them.
That process is to deny, mostly ignore, or claim ignorance of the result or of the behavior around the result.
So some posters will keeps posting nastily in reply and just claim I'm wrong, while others will post puzzlement that I'm even posting! While others will post puzzlement that anything I have ever said was ever ignored as they claim none of it was and that in fact I get plenty of attention so why am I complaining.
But they'll ignore any current result. If pressed they will simply quit replying.
Years ago when I first faced this process, yes, I went off Usenet, and got a paper published. I'm sitting back waiting for math society to acknowledge that remarkable result—but monitoring Usenet just to see what happened—and some poster posts that I'm published on the sci.math newsgroup and the group erupted in fury.
Never paused for a moment to consider that maybe publication meant something.
There is what people say they believe and there is what they demonstrate they truly believe. Publication. Hmmm…
Now you can see how they react with the factoring problem.
Yes, I've said for some time that I had solved it only to be wrong, but I know this process better than you do, and my strategy is based on game theory.
And you can see what I'm up against if you understand that simple approach I outlined before about using abs(nT - 2k^2) and understand it, as well as the implications, and see how math society is STILL to this point reacting.
Lying is as old as humanity. People lie to get things they would not get otherwise.
Some of you may be going to math classes to listen to professors who would not be there if they told the truth. It's that simple. It can be easy to talk about the fate of the human race and the importance of knowledge and progress in the abstract, but if you're some middle-aged man with a mortgage, a wife who thinks you're brilliant, and other perks that may come with being a math professor (yes there are some perks for some maybe not many but some) considering accepting not being so brilliant and losing what you have, then lying can seem to be just about survival.
Perspective is an amazing thing.
Some of these people may figure that humanity is such a big thing that there's no way it can really matter if they stop intellectual progress in mathematics for a while. So they did. They stopped most progress in "pure math" areas for the entire human race across the planet.
So I went to the factoring problem.
Now then, yes, humanity is kind of big to us, and it can seem easy to think that getting your little piece today is worth blocking its progress for a little while, especially to stop some annoying guy—just some guy after all—who keeps going on and on about his mathematical research.
Because history makes the legends—so I can't be one to you now—so it's later that students will read about you and find it incomprehensible that you could have even paused with the fate of your own species in the balance, and what could have been so important to you that you'd actually deny progress for people who were just lying?
But they would also know how it's in the balance. Some of them might contemplate not getting to be born because of what you are doing now—if you weren't stopped.
But they aren't in your shoes now. Perspective.
Legacy is a word that gets tossed around, but thinking that maybe down the line your legacy can be that of THOSE people, who didn't do the right thing, who held on even when it was clear that they were wrong, and broken later, could only fumble out rationalizations or apologies and accept their branding for life, is an exercise for those who aren't thinking about their bills and just trying to have a life.
If you were brilliant you wouldn't be in this situation.
Make no mistake, the world is not a nice place when you get on the outside and are looked at as a renegade versus being one of us.
You are inside now, and if you are a math professor, then you are very inside, but think about what happens if you keep up this nonsense and you are completely out.
I'm a problem solver. I brainstormed my way through some important and difficult math problems, got the answers, and found a society that couldn't or wouldn't live up to expectations so I am working on solving that problem as well.
My mistakes are many, but I own up to them. I have been wrong many times before, said things I know I'll regret later, and often wondered how this situation is even possible—until I remember—perspective.
No criminal ever thought first, long and hard, about getting caught, enough to not do the crimes.
If they had, then they wouldn't be criminals, now would they?
# posted by James Harris @ 17:46 
