Re: SF: Areas of confusion, infinity

From: C. Bond (cbond_at_ix.netcom.com)
Date: 04/16/05 

Date: Sat, 16 Apr 2005 15:41:49 GMT

Proginoskes wrote:

> C. Bond wrote:
> > jstevh@msn.com wrote:
> >
> > > One of the problems with surrogate factoring in
> > > terms of understanding it, is that it utilizes
> > > infinite sets, notably the set of rationals.
> >
> > That is, indeed, a problem -- but not in the sense
> > you suggest.. The reason is that factoring, as is
> > the term is used in mathematics, involves finding
> > *integer* factors, not rational divisors. Since you
> > have completely misunderstood the problem, there is
> > no hope of your finding a solution.
>
> Harris has his own terminology, because he hasn't learned the real
> terminology. From what I've read, a formal definition for a
> "non-trivial rational factor of M = p*q" is a (non-zero) rational
> number a/b where exactly one of p or q divides evenly into a. Then,
> when you take the gcd(a,M), you get an integer factor of M (which is
> also prime, to boot). So "non-trivial rational factors" are just as
> good as integer factors.
>
> --- Christopher Heckman

I certainly don't object to the notion that James can whip up something
that actually works from time to time. After all, his prime counting
algorithm does get correct results. But it's difficult to determine
exactly what he is getting at about 99% of the time because of his
sloppy language and militant hostility to defining his terms. Frankly, I
even doubt that he would acknowledge your formal characterization of
'non-trivial rational factor' above -- although it seems to fit his
usage.

However, if you have the time and inclination to post a worked example
using his SF method with an explanation of how you interpret the
ambiguous points, it would serve as a touchstone for others to find out
1) whether the method does work, 2) whether the method can be made to
work by suitable modifications, 3) whether the method can be established
by rigorous proof, 4) whether it compares well with existing methods.
James will certainly do none of these.

Care to try? It might blow away some of the fog. 

--
There are two things you must never attempt to prove: the unprovable --
and the obvious.
--
Democracy: The triumph of popularity over principle.
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