Tuesday, August 28, 2007
JSH: Mathematical intuition, surrogate factoring equations
Having come off a tremendous research effort that has given key answers to important questions with surrogate factoring, I find myself still curious about the math world's ability to ignore a factoring idea that has many indications that it should be possible to get it to succeed!
Consider that I have
y^2 = x^2 mod T
and
k = 2x mod T
to get
(x+k)^2 = y^2 + 2k^2 + nT
when I finally to to the explicit, and it's like, if the first and second are assumed to be true to get the last, then how can it now work to factor a target composite T?
Part of the answer is that the math can get to the same place in a different way using:
y^2 = x^2 mod a
and
k = 2x mod b
to get
(x+k)^2 = y^2 + 2k^2 + nT
as long as 'a' and 'b' are coprime to T, but that doesn't explain why the math would CHOOSE to do so, as why would it care?
What difference does it make to the mathematics if it satisfies:
y^2 = x^2 mod T and k = 2x mod T
or
y^2 = x^2 mod a and k = 2x mod b
where 'a' and 'b' are coprime to T, to get to
(x+k)^2 = y^2 + 2k^2 + nT?
Why should it care?
There are two things really that jump out at you about my surrogate factoring idea as it's so simple:
Regardless of the failures I had with these equations I needed to understand why they didn't work all the time.
In contrast, I noticed that many of you seemed satisfied with simply being told that they did not work all the time, which presents me with a puzzle, why?
Why weren't any of you more curious than that?
Why wouldn't you demand an explanation for why and wonder if with such relatively easy math, none were given?
That is, where was your human curiosity?
This post is about probing that question, which is a question of your humanity.
Given the information presented here, why wouldn't this bug some of you, like a burr under your saddle until you got an answer?
Where is your human curiosity?
Consider that I have
y^2 = x^2 mod T
and
k = 2x mod T
to get
(x+k)^2 = y^2 + 2k^2 + nT
when I finally to to the explicit, and it's like, if the first and second are assumed to be true to get the last, then how can it now work to factor a target composite T?
Part of the answer is that the math can get to the same place in a different way using:
y^2 = x^2 mod a
and
k = 2x mod b
to get
(x+k)^2 = y^2 + 2k^2 + nT
as long as 'a' and 'b' are coprime to T, but that doesn't explain why the math would CHOOSE to do so, as why would it care?
What difference does it make to the mathematics if it satisfies:
y^2 = x^2 mod T and k = 2x mod T
or
y^2 = x^2 mod a and k = 2x mod b
where 'a' and 'b' are coprime to T, to get to
(x+k)^2 = y^2 + 2k^2 + nT?
Why should it care?
There are two things really that jump out at you about my surrogate factoring idea as it's so simple:
- Why didn't anyone think of this before, as mostly it is about completing the square?
- Why doesn't it always work?
Regardless of the failures I had with these equations I needed to understand why they didn't work all the time.
In contrast, I noticed that many of you seemed satisfied with simply being told that they did not work all the time, which presents me with a puzzle, why?
Why weren't any of you more curious than that?
Why wouldn't you demand an explanation for why and wonder if with such relatively easy math, none were given?
That is, where was your human curiosity?
This post is about probing that question, which is a question of your humanity.
Given the information presented here, why wouldn't this bug some of you, like a burr under your saddle until you got an answer?
Where is your human curiosity?
# posted by James Harris @ 19:51 
