FOM: Is chess as interesting as mathematics?
Vladimir Sazonov
V.Sazonov at csc.liv.ac.uk
Thu Feb 21 08:33:31 EST 2002
charles silver wrote:
>
> The discussion of intuition vs. rigor seems to have taken some strange
> turns. Isn't it the case that Godel simply "saw" the incompleteness
> results while working on something else? I believe he realized way before
> he worked out all the gory details that proofs had to be a proper subset of
> truths. I'd call having something like this pop into one's mind
> "intuition."
It seems it was said quite enough in that discussion on the
intuition vs. rigor to resolve such kind of questions.
Did Goedel think in some terms having ABSOLUTELY NO relation
to Peano Arithmetic? I cannot imagine that. Can you?
I guess, not. What then is the problem? Which "strange turns"?
On the other hand, there are accounts of mathematicians who
> have an over-abundance of ideas (read: intuitions) that turn out to be
> false. In favor of rigor, obviously it's needed to back up intuitions,
> though it has been mentioned that intuitive accounts by people like
> Thurston are sometimes acceptable even when no technical details
> at all have been provided. I have heard one mathematician in
> Thurston's area complain about this, saying that it's frustrating to
> listen to him just alluding to ideas and waving his hands while not
> presenting anything resembling a traditional proof. However,
> rigor completely uncoordinated with intuitions or insight can be
> mechanical and not very interesting.
Moreover, it is almost impossible!
Also, pure intuition without any alluding to some formalism
(already exsting or to be constructed) is something non-mathematical.
Is chess as "interesting"
> as mathematics?
This formal system of rules (unlike PA, ZFC, etc.) does not
serve to make more powerful our thought in investigating some
intuitive concept (like natural numbers, sets, movement of
planets, etc.) arising externally from the chess. However,
as a game it might serve as a god training of some specific
parts of our brains. This activity is not exactly of that
sort mathematics is. But the training could be useful.
On the other hand, we can try to investigate chess
mathematically (as a part of mathematical games theory).
Say, try to prove a theorem that whites win. Create a
winning strategy.
--
Vladimir Sazonov V.Sazonov at csc.liv.ac.uk
Department of Computer Science tel: (+44) 0151 794-6792
University of Liverpool fax: (+44) 0151 794 3715
Liverpool L69 7ZF, U.K. http://www.csc.liv.ac.uk/~sazonov
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