[RC5] Beal's Problem A DN challenge?
Stephan Wonczak
sws at sherlock.pc.uni-koeln.de
Wed Jul 7 11:30:05 EDT 1999
On Tue, 6 Jul 1999, Bachrach wrote:
> >It's main drawback is that it is an open-ended problem, like SETI but
> >unlike OGR. That is, with OGR we KNOW we'll find answers, whereas with
> >Beal's conjecture and SETI we do NOT know whether we'll achieve
> >anything, which will make it more difficult to recruit.
>
> It's not so much the open ended-ness of it, but the fact that it can't
> really be done by a computer at all. To formulate a proof the person doing
> the proof must use their own mind and ingenuity to try and find a way from
> point A to point B that hasn't been discovered before. There is no set
> instructions that you could instruct a computer to follow that would result
> in an answer. The computer can't think, and proving a theorem requires just
> that.
This is not entirely correct... finding proof for something is just
following rules, and if there is one thing that a computer does well, it
is following rules. If the proof involves finding a *new* rule, then of
course the computer is doomed to fail (at least with our present
technology/software), as original thinking remains the domain of humans.
There is one interesting story though that I read in Douglas Hofstaedter's
(sp?) book 'Goedel, Escher, Bach, an Eternal Golden Braid', where they fed
a computer with some simple basic rules of geometry, and set it to
generate 'new' rules, for which it supplied the way it arrived at them. It
turned out that the computer found a very simple proof for a well known
thesis, but the way the computer proved the thesis was both shorter and
more elegant than the best proof generated by a human. The researchers
were stunned.
The point is, a computer can follow rules extremely well, and as opposed
to a human, it does not overlook possibilities. A computer is a systematic
'thinker' (for lack of a better word), which arrives at the endpoint in
small, well-defined steps. A human thinks in intuitive leaps, something a
computer cannot do.
C U, Stephan
"I haven't lost my mind; I know exactly where I left it."
"The meaning of my life is to make me crazy"
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