Saturday, October 28, 2006
JSH: Why might factoring idea fail?
I think it very important that I talk about this latest factoring idea in a post, where I consider the possibility that it fails, as hey, maybe it does. I'm not sure at this point.
It is amazingly simple:
x^2 - y^2 = 0 mod T
and
k^2 = 2xk mod T
so
(x+k)^2 = y^2 + 2k^2 + nT
where T is the target composite to be factored and you choose k and n.
If you consider how the math can behave with that set of equations you find that it can factor T non-trivially, or it might give T back to you, or it may decide that T is 1 because if you have, say
T = 15
why can't the math go with n=15, T=1?
It doesn't know what n is, it just has nT, so it can decide that T=1, or T=3, or T=5, while with the latter two it's likely to factor for you, but with the first it is not.
So how might this idea fail? Easy, the math could preferential decide that T=1.
Why can't it do something else even more spectacular like choose numbers that have nothing to do with what you tell it for T?
Because the three relations make that impossible:
If you choose T, and the math picks some factor f out of the blue so that it is using
x^2 - y^2 = 0 mod f
and
k^2 = 2xk mod f
it runs into a contradiction at this point
(x+k)^2 = y^2 + 2k^2 + nT
if f is coprime to nT.
So the math HAS to pay attention to what you say T is, if only to decide that it is actually n and T=1, or T=-1, because it gets nT, but even then it can't just toss in any f as it has to stick with 1, so above to block a contradiction, f=1, or f=-1.
So if the math has no preference for how it chooses T, like it feels that it is too hard to pick T as anything other than 1 or -1 most of the time, then it should pick without preference, indicating this approach should factor T about 50% of the time, unless there is a mathematical reason preventing that from being true.
If it does have a preference, this idea fails, but it's still a cool idea that comes from a generalization of factoring itself:
x^2 - y^2 = 0 mod T
and
S = 2xk mod T
so
(x+k)^2 = y^2 + S + k^2 + nT
where I just used S = k^2, to lock the math to nT.
That generalized factoring idea defaults to the previously known with S=k=0, so it's a BROADER idea that includes the previous one, and it isn't then a major surprise that a leap forward in thinking should, while remaining simple, show another route to factoring, which I call surrogate factoring—as you factor some other number off the target.
In the case above you factor 2k^2 + nT, which is the surrogate.
Now these ideas are simple and clever, but our world is not, and there are people in it who make their living by not doing what's expected while claiming to do that, as they are parasitic.
So I'm sidelined to the fringe as I don't like the parasites. They know this, and to protect themselves and their offspring they have to block me out, so they have to ignore my research or downplay it. Once I convince other people of what they are, then I can get in and clear the parasites out, so they are fighting for everything.
They live by pretending and using other people, and depend on supporting themselves and theirs by you believing they do not. So I need you to use common sense: can a new idea in factoring just be smothered completely and totally ignored by "beautiful minds" in mathematics?
And until you know what kind of battle this is, you won't get it, and will help them thinking they are just like you, and see the world the way you do.
They do not.
[A reply to someone who called “parasite” to James.]
People who claim to be "mathematicians" who block mathematical research are worse than just wrong, as hey, sure I have mathematical results that people could have just missed.
But THESE people do more than just act a little embarrassed or resistant to new ideas they aren't sure of, they willfully ignore and work to block them.
That is parasitic behavior as parasites are hostile to their hosts.
These people are hostile to the intellectual growth of humanity: working to hang on to systems that protect their interests, block researchers who threaten their control, and stop human progress in certain areas of mathematics.
Consider again computer checking of mathematical arguments.
Math because it is a logical discipline SHOULD have been a natural area for growth in computer science in the area of expert systems, which instead had to grow in other areas, as to this day there is nothing of note in mathematics when it comes to expert systems checking mathematical arguments!!!
That's how these people are parasites: they not only don't do real research of any value, they BLOCK research that is threatening to them.
Parasitic behavior by creatures that have no interest in helping humanity, just themselves.
As parasites they HAVE to protect in the way they do, as they have no other options.
If they were smart enough to do real mathematical research, they wouldn't need the parasitic behavior.
What they are smart enough at is manipulating people, controlling information, and blocking results that threaten their control.
It is amazingly simple:
x^2 - y^2 = 0 mod T
and
k^2 = 2xk mod T
so
(x+k)^2 = y^2 + 2k^2 + nT
where T is the target composite to be factored and you choose k and n.
If you consider how the math can behave with that set of equations you find that it can factor T non-trivially, or it might give T back to you, or it may decide that T is 1 because if you have, say
T = 15
why can't the math go with n=15, T=1?
It doesn't know what n is, it just has nT, so it can decide that T=1, or T=3, or T=5, while with the latter two it's likely to factor for you, but with the first it is not.
So how might this idea fail? Easy, the math could preferential decide that T=1.
Why can't it do something else even more spectacular like choose numbers that have nothing to do with what you tell it for T?
Because the three relations make that impossible:
If you choose T, and the math picks some factor f out of the blue so that it is using
x^2 - y^2 = 0 mod f
and
k^2 = 2xk mod f
it runs into a contradiction at this point
(x+k)^2 = y^2 + 2k^2 + nT
if f is coprime to nT.
So the math HAS to pay attention to what you say T is, if only to decide that it is actually n and T=1, or T=-1, because it gets nT, but even then it can't just toss in any f as it has to stick with 1, so above to block a contradiction, f=1, or f=-1.
So if the math has no preference for how it chooses T, like it feels that it is too hard to pick T as anything other than 1 or -1 most of the time, then it should pick without preference, indicating this approach should factor T about 50% of the time, unless there is a mathematical reason preventing that from being true.
If it does have a preference, this idea fails, but it's still a cool idea that comes from a generalization of factoring itself:
x^2 - y^2 = 0 mod T
and
S = 2xk mod T
so
(x+k)^2 = y^2 + S + k^2 + nT
where I just used S = k^2, to lock the math to nT.
That generalized factoring idea defaults to the previously known with S=k=0, so it's a BROADER idea that includes the previous one, and it isn't then a major surprise that a leap forward in thinking should, while remaining simple, show another route to factoring, which I call surrogate factoring—as you factor some other number off the target.
In the case above you factor 2k^2 + nT, which is the surrogate.
Now these ideas are simple and clever, but our world is not, and there are people in it who make their living by not doing what's expected while claiming to do that, as they are parasitic.
So I'm sidelined to the fringe as I don't like the parasites. They know this, and to protect themselves and their offspring they have to block me out, so they have to ignore my research or downplay it. Once I convince other people of what they are, then I can get in and clear the parasites out, so they are fighting for everything.
They live by pretending and using other people, and depend on supporting themselves and theirs by you believing they do not. So I need you to use common sense: can a new idea in factoring just be smothered completely and totally ignored by "beautiful minds" in mathematics?
And until you know what kind of battle this is, you won't get it, and will help them thinking they are just like you, and see the world the way you do.
They do not.
[A reply to someone who called “parasite” to James.]
People who claim to be "mathematicians" who block mathematical research are worse than just wrong, as hey, sure I have mathematical results that people could have just missed.
But THESE people do more than just act a little embarrassed or resistant to new ideas they aren't sure of, they willfully ignore and work to block them.
That is parasitic behavior as parasites are hostile to their hosts.
These people are hostile to the intellectual growth of humanity: working to hang on to systems that protect their interests, block researchers who threaten their control, and stop human progress in certain areas of mathematics.
Consider again computer checking of mathematical arguments.
Math because it is a logical discipline SHOULD have been a natural area for growth in computer science in the area of expert systems, which instead had to grow in other areas, as to this day there is nothing of note in mathematics when it comes to expert systems checking mathematical arguments!!!
That's how these people are parasites: they not only don't do real research of any value, they BLOCK research that is threatening to them.
Parasitic behavior by creatures that have no interest in helping humanity, just themselves.
As parasites they HAVE to protect in the way they do, as they have no other options.
If they were smart enough to do real mathematical research, they wouldn't need the parasitic behavior.
What they are smart enough at is manipulating people, controlling information, and blocking results that threaten their control.
# posted by James Harris @ 09:37 
