Re: Factoring, SF, and transforms

jstevh_at_msn.com
Date: 04/16/05 

Date: 16 Apr 2005 14:06:28 -0700

José Carlos Santos wrote:
> jstevh@msn.com wrote:
>
> > The factoring problem looks tractable from an approch in the set of
> > rationals using a transform that I call the surrogate factoring
> > theorem.
>
> Then why don't you actually solve it?
>

The surrogate factoring theorem is a major theorem, and is important
like my other "pure math" work.

But math people have lied about the importance of my work, and shown
their actual disregard for "pure math", so that it can be seen to
really be to them, math you can lie about.

So part of my point is that "pure math" to mathematicians means, math
you can lie about, and that can be seen with a result on the edge of
practicality.

Also, I'm a theoretician. At times I do go more experimental, but not
because I like it, but because it becomes necessary.

And also, I'd just as soon go slowly, as I'm concerned about what might
happen if I too quickly forced the issue.

> > It's a one-to-one linking between infinite sets, and it has
relevance
> > to factoring because even though trivially in rationals every
number
> > but 0 is a factor of every other number, you can focus on the
numerator
> > of rationals as that is an integer, and check to see if it's a
trivial
> > or non-trivial factor.
>
> So your method gives an infinite amount of rational numbers. Let's
call
> r_1, r_2, r_3, ... to the rational numbers that you get and let b_1,
> b_2, b_3, ... be their numerators. For each numerator, you check
whether
> or not it is a trivial factor, right?!
>
> Just one question, if you don't mind: what makes you think that
there's
> some advantage in checking with the natural numbers b_1, b_2, b_3,
...
> instead of 1, 2, 3, ... ?
>

You're misrepresenting the facts.

The surrogate factoring theorem links factors.

Even in rationals a factor can be non-trivial as you can focus on its
numerator (or denominator), which is an integer.

Now in the infinity of possible factors in rationals, there is no
reason to believe that mathematically what people call trivial factors
are selected preferentially over what are called non-trivial factors.

So if you take factors of one number, and use SFT to get factors of the
other number there's no mathematical reason for the SF theorem that
I've seen presented for it to preferentially choose what we'd call
trivial factors.

Part of the problem I've seen in trying to rationally discuss what has
to happen mathematically is that posters will just keep pushing that
all factors in rationals are trivial.

But it's easy enough to explain mathematically how a factor in
rationals can still be non-trivial in that the numerator is an integer
and you can check that numerator.

BUT posters keep pushing the idea either directly or indirectly that
out of infinity what we'd call trivial factors ARE preferentially
selected.

My point is that over infinity, both trivial and non-trivial factors
are equally represented, in rationals.

> > You need to learn modern problem solving theory.
>
> Which mathematical problem have you actually solved?
>

Learning modern problem solving theory is just a good idea.

There's a whole world of advancement in a key area: problem solving.

I think that quite possibly math students believe that they are taught
modern problem solving in their classes, but if they were, then there
wouldn't have been so much hostility against the brainstorming that I
tend to do.

And, there would be evidence of use of modern problem solving
techniques in posts.

I don't see that evidence.

>>From what I see, math society today, when it comes to problem solving
as an art, is back in the Dark Ages.

James Harris

Relevant Pages

  • Re: SF: Areas of confusion, infinity
    ... > notably the set of rationals. ... choosing any integer is the same as the probability of any other ... That's what make the factoring problem interesting, i.e., not ... > is naive with the surrogate factoring theorem. ...
    (sci.crypt)
  • Re: JSH: Parameterizing conics with Pells Equation
    ... of the modern mathematical community is a parameterization of conics ... it's a result over rationals! ... You know I talk about this major error that entered the math field ... What keeps mathematicians from having that set ...
    (sci.math)
  • Re: surrogate factoring
    ... quality "SF time" than anyone other than James ... ... "surrogate factoring" doesn't really mean anything specific. ... since the set of all non-zero rationals constituted the search space ... pushing formulas around, and it may be a bona fide compulsion for him. ...
    (sci.math)
  • Re: surrogate factoring
    ... quality "SF time" than anyone other than James ... ... "surrogate factoring" doesn't really mean anything specific. ... since the set of all non-zero rationals constituted the search space ...
    (sci.math)
  • Re: JSH: Moving through it
    ... There are lots of good factoring methods that have problems with two ... Remember, x and y are rationals, so they can be fractions, and I've ... The solution is that for a given rational x the probability that it ... The mathematics proving every statement in this post is already worked ...
    (sci.math)