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Message from discussion AI direction to approach. //Quanta
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Albert Lai  
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 More options Jul 12 2003, 1:35 am
Newsgroups: comp.lang.functional
From: Albert Lai <tre...@vex.net>
Date: 12 Jul 2003 01:18:35 -0400
Local: Sat, Jul 12 2003 1:18 am
Subject: Re: [OT]Re: AI direction to approach. //Quanta
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Costin Cozianu <c_cozi...@hotmail.com> writes:
> I recently discovered the very opinionated and probably very well
> informed thoughts of one Jean Yves Girard who has some well deserved
> fame and notoriety in computer science and mathematics.

> He basically affirms without too much argumentation that automatic
> proof doesn't work and will never work (basically because of the
> halting problem),

1. Automated reasoning suffers from the Turing halting problem.
0. Mathematics suffers from the Goedel incompleteness and inconsistency
   problem.  (I know this is arguable, depending on what you consider
   as the purpose of mathematics.)
2. Code optimization suffers from the Kolmogorov complexity problem.

They are all the same problem in different incarnations.

The days when people worried about mathematics because of #0 has long
gone.  No one has ever used #2 to dismiss code optimization.  In fact
both are now viewed optimistically and jokingly:

Theorem 0: Permanent employment of mathematicians.  You will never run
out of new axioms and new models to study.

Theorem 2: Permanent employment of researchers in code optimization.
You will always be able to publish new, better optimizations.

So I don't see why we have to view #1 as a limitation rather than a
gift:

Theorem 1: Permanent employment of researchers in automated reasoning.
You can always find a way to beat your rival's automatic theorem
prover.


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