Re: A theorem can't be wrong

jst...@xxxxxxx wrote:
> N. Silver wrote:
> > JSH wrote:
> >
> > > It seems odd that I need to remind that a theorem cannot be
> > > wrong. So the surrogate factoring theorem (SFT) cannot be
> > > wrong. Now the issue of how well it factors can be raised,
> > > but that's separate from it's "pure" validity as a theorem.
> >
> > Yep. Posters, here, have addressed the issue of its worth.
> > In their opinions, it does not appear as a blip on the radar
> > screen. They have tested it and point out that it has not
> > factored anything non-trivial faster than at random. You
> > claim to know science. So, you should understand.
>
> So you focus on the practical question of factoring.
>
> Is that all that matters then, practicality?
>
> Just curious.
>

An obviously loaded question. You are no more curious than
I am the king's underpants.

There are 4 criteria for judging a "theorem":


1. True

2. Nontrivial

3. Esthetically pleasing

4. Having practical applications


Your "theorem" is true. That criterion is met.

Your "theorem" is trivial. In fact it is not worthy of the
name "theorem".

Your "theorem" is ugly. You cannot state it in a line or two.
You need to write out the solutions of two quadratics and
some other underbrush just to describe it. It is not a
surprising, rabbit-out-of-the-hat result. Many people here,
bright people, don't even know what it says. Try telling it
to the exemplary bright high school student. He/she is going
to either not get it, or say, "so what?"

Your "theorem" was of course intended for a very practical
purpose: efficient factoring large integers. There is no
evidence that it does so, either analytic or numerical, and
plenty of evidence that it does not. It could have been
redeemed if you can show that it had practical implications.
You have not done so, and it is clear now that you cannot.

A theorem does not have to be practical to be worthwhile.
Euclid's proof of the infinity of primes meets the first three
criteria: true, nontrivial, esthetically pleasing. It has
no practical application. It does not help one find new
primes or to factor numbers into products of primes. It
expresses a simple universal truth. The proof is stunning - the
first time you read it, it is like reading a great poem. It
is like watching a clever magic trick. These are qualities
that your "theorem" lacks.

You want to pretend that it is a great theorem precisely
*because* it is true and pure math and it has no applications.
That, you think, puts it in the same class as Euclid's theorem.
The pure mathematician doesn't care about applications. That's
you, you now claim.

That's bull. Great theorems have to be SOMETHING other
than just true. Either esthetically pleasing/surprising/clever,
or having useful applications. Your "theorem" falls short.

Esthetics, you may say, is subjective. You might conclude
that I, and others, devalue your theorem because we don't like
you or we are jealous. I would deny that, but certainly it
is possible in theory. In the end, whether a "theorem" meets the
esthetics criterion or not is a matter of taste. It is not
something that you, the author of the "theorem", get to decide.
It is a matter of consensus - yes, it is a SOCIAL thing. That
is a fact about ALL ASPECTS OF INTELLECTUAL DISCOURSE. You
have to live with it. It is not something that you can control. It
may seem unfair but there is nothing you can do about it.

Bieberbach supported the Nazis. It probably hurt his reputation,
but his mathematics is still judged of value on its own merit.
Yours is as well. The fact that you are a prick is not a
necessary or sufficient reason to consider your theorem worthless.
It is worthless on its own account. If Gauss had stated it,
people would still be saying "why?" and "so what???"

I knew a student who as an undergrad was considered extremely
bright. A prodigy, best in his class. He was a little
eccentric and a little pompous, but from his grades, test scores,
etc., he looked like he had a great future. His mathematical *taste*,
however, was, let us say, "off". He would create artificial
structures in much the same way you might make up a game with
arbitrary rules, and prove things about them. There were no
practical applications because his structures were idiosyncratic
and made up. There was no esthetic appeal because what he did
was unrelated to anything else.

His talent however got him a scholarship to grad school at
the U of Chicago, a truly great school. He spent 4 years there.
He did well in courses. The profs knew he had talent.

But he couldn't put together a decent thesis. It was
the same old arbitrary structures stuff. No applications and
no esthetics. He got out with some kind of consolation doctoral
degree - not a PhD, but something less. He has never done much
as a mathematician.

A "theorem", i.e., a string of symbols that logically arrive
at a true statement, is not enough. You originally set out to find
something more than that. Your tastes are not as terrible as
those of the student I described. What you did, in spite of
an unesthetical statement and a trivial proof, would have been
redeemed and validated IF it gave you a way to efficiently
factor large numbers. That was its only hope for greatness.
Lacking that, it is nothing - not worthy of the name "theorem."

Nora B.


>
> James Harris

.

Relevant Pages

  • Re: ProDOS Plus
    ... operating system was not considered worth the problems when it was just as easy to make the applications support 128k or more ram. ... if practicality were a concern we probably wouldn't be using old hardware. ... Any practical extension will have to fit within the memory envelope ... compatibility is a must if there is to be ...
    (comp.sys.apple2)
  • Re: ProDOS Plus
    ... operating system was not considered worth the problems when it was just as easy to make the applications support 128k or more ram. ... your suggested P-code system could do something similar by running in the aux 64k memory range $D000...FFFF or perhaps the aux ram used by the P8 /ram driver code space. ... the OS could fit in *only* the space that ProDOS now occupies. ... if practicality were a concern we probably wouldn't be using old hardware. ...
    (comp.sys.apple2)