SF: Areas of confusion, infinity

jstevh_at_msn.com
Date: 04/14/05 

Date: 14 Apr 2005 11:58:30 -0700

One of the problems with surrogate factoring in terms of understanding
it, is that it utilizes infinite sets, notably the set of rationals.

The naive view is that since in the set of rationals every number
except 0 is a factor of every other number that you can't use it in
factoring, which may be why I discovered the surrogate factoring
theorem, while others did not, as it necessarily has to use rationals
because of equations like

yz^2 - Az + j^2 = 0

and I say the naive view as I've already proven that is is naive with
the surrogate factoring theorem.

How?

Well, the surrogate factoring theorem links rational factorizations,
but in so doing, it shows no inclination for trivial versus non-trivial
factorizations.

It simply doesn't indicate a preference either way.

So you can pick rational factors as you see fit, and you'll get
rational factors in exchange, where there's no reason I've yet seen or
heard for the math to be choosy.

That means that I can use rationals and rely on human choice: a person
will pick factors.

The mathematics then gives you factors in exchange.

Now here's where it's not really tricky, but I've seen posters working
to try and force the issue that the mathematics IS picky, and they rely
on pseudo-mathematics.

If you in picking factors choose to pick trivial and non-trivial
factors, why, in response to your choices, should the theorem only
provide trivial factors?

There's no mathematical reason why.

But posters confuse on this issue by pointing out that in the set of
rationals every rational except 0 is a factor of every other rational,
so they argue that in exchange for your trivial and non-trivial factors
you will get trivial factors because if you randomly pick a rational
from the set of rationals it will tend to have a numerator coprime to
any integer you might want to factor.

Basically, they argue as if there isn't a link.

However, the surrogate factoring theorem is not playing social games.
It's a mathematical theorem which allows you to choose factors and in
exchange you get factors.

For the theorem to pick trivial factors only in exchange would be a
choice.

In mathematics there has to be a reason for a theorem to make a choice.

Posters don't give any reason.

Some of you rely on others to try and learn mathematics. I've seen
posts where people reply at how happy they are to be learning this or
from posters replying to me, when the sad reality is that posters here
who know mathematics are usually replying to me to confuse a particular
issue.

So they're teaching you bogus stuff.

Ok, so naturally, you may tell yourself, I'd say that posters are
teaching your wrong information, when you may feel confident that I'm
the person who is wrong.

But, notice, the surrogate factoring theorem simply links factors.

You have factors of j^2 T, where j is some number you choose, and T is
given by

T = M^2 - j^2

where M is presumably the number you're trying to factor.

If you get factors of j^2 T, then using the theorem you get factors of

M^2 T

and if you are doing the factoring of j^2 T, you can use trivial and
non-trivial factors, right?

For those confused on trivial versus non-trivial, consider 15.

15 is a factor of 15, since 15(1) = 15, but it's a trivial, as in easy,
factor, as it doesn't take any work for people to figure that out.

However 3 is a non-trivial factor, as 3(5) = 15, and you need to know a
little more to realize that it's a factor.

Human beings distinguish between hard and easy factors.

Now, if the surrogate factoring theorem, like human beings,
distinguishes between hard and trivial factors then it must have a
reason, as mathematics is that way.

There is a reason for everything in mathematics.

If you choose trivial and non-trivial factors to use with the theorem,
why should it link your factor to only or mostly trivial factors?

If it does there has to be a mathematical reason. Understand?

However, if it does not, then guess what?

If it does not then it means that people could develop ideas from that
theorem and build algorithms that could factor very efficiently, and
very quickly.

If they do so, then while we're arguing out these points on Usenet,
there may be some people who are factoring rather large numbers.

All it takes is for them to be less gullible than those of you who
listen to people who lie to you about basic mathematics.

Remember the link aspect of the surrogate factoring theorem, and ask
yourself, why should the theorem give only trivial factors in exchange
for trivial and non-trivial factors?

I've been looking at that question as I want to know the actual answer,
but posters are working to convince others for whatever reasons
motivate these people, so they basically just say it will only give
trivial factors for really big numbers, with only two very large prime
factors.

Why?

Well really big numbers are important for encryption schemes used to
protect the Internet and lots of other stuff.

So they just pick an area where this work would be dramatic, and say
that it's not.

They are acting on social realities, and not mathematical ones.

Notice, what happened when I presented the surrogate factoring theorem.
 Some posters promptly tried to challenge whether or not it was a
theorem. Then most settled on calling it trivial and challenging me to
factor some number with it.

However, the theorem is enough to explain the link. The link between
factors is enough to show importance.

Making it work practically is a whole other arena.

But I fear it can be done, and I'm not going to do it.

So we're all waiting for those people who will, and we're waiting to
see what they do.

We can talk here as much as we want, but the real power has passed to
the people who are checking, and making it work, assuming they're out
there.

And I think they would be out there, as not everyone is gullible and
willing to listen to sci.math'ers with an agenda, who just always say
that whatever I have is wrong or unimportant.

Some people are bound to check.

James Harris

Relevant Pages

  • Re: SF: Areas of confusion, infinity
    ... One of the problems with surrogate factoring in terms of understanding ... it, is that it utilizes infinite sets, notably the set of rationals. ... Well, the surrogate factoring theorem links rational factorizations, ... The mathematics then gives you factors in exchange. ...
    (sci.crypt)
  • Re: Now you can see, my "crank" status
    ... >> Now you can see from the surrogate factoring theorem, ... rationals, as there's a mapping. ... The same argument can apply to any mapping if you say that a mapping is ... For people who've learned a lot of advanced mathematics, ...
    (sci.crypt)
  • Re: SF: Areas of confusion, infinity
    ... >> clearly that from the theorem only, but math people are pushing me ... > rationals will produce non-trivial factorisations of M, ... the mathematics does not distinguish between trivial and non-trivial ... The surrogate factoring theorem does in fact connect two infinite sets. ...
    (sci.crypt)
  • JSH: Explaining surrogate factoring, again
    ... Now I figure that many of you don't have a clue about the mathematics ... behind what I call surrogate factoring, as you listen to people who ... The aim is to find a *rational* y such that x and z are rationals. ... shown to depend on quadratic residues, such that there's about a 50% ...
    (sci.math)
  • JSH: Nearly done
    ... theory and method for factoring that I call surrogate factoring. ... The mathematics though is surprisingly simple, ... but are in the field of rationals. ...
    (sci.math)