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From: pindor@gpu.utcc.utoronto.ca (Andrzej Pindor)
Subject: Re: Grounding Representations: ("Grounding" is the wrong word)
Message-ID: <D7rBBF.IAF@gpu.utcc.utoronto.ca>
Organization: UTCC Public Access
References: <departedD5xB4A.544@netcom.com> <3lkrpq$kun@mp.cs.niu.edu> <3nhlk5$i7o@percy.cs.bham.ac.uk> <3njqh7$q0m@mp.cs.niu.edu>
Date: Fri, 28 Apr 1995 17:59:39 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:27340 comp.ai:29384 comp.robotics:20236 comp.cog-eng:3111 sci.cognitive:7452 sci.psychology:40853

In article <3njqh7$q0m@mp.cs.niu.edu>, Neil Rickert <rickert@cs.niu.edu> wrote:
>In <3nhlk5$i7o@percy.cs.bham.ac.uk> A.Sloman@cs.bham.ac.uk (Aaron Sloman) writes:
,,,,
>>(b) In fact it may turn out easier to design and implement a
>>disembodied (or perhaps I should say "disconnected") mathematician
>>whose mind is concerned with nothing but problems in number theory
>>(and who enjoys the thrill of discovery and experiences the sorrow
>>of refutation) than it is to design and implement a robot with
>>properly functioning eyes, ears, arms, legs, etc.
>
>I am personally quite doubtful of this.  It is, after all, quite
>trivial to generate any number of proofs of true number theoretic
>propositions which have never before been published.  What is
>difficult is producing _interesting_ new propositions.  If we use a
>human standard of what is interesting, I suspect that what we
>consider interesting does not derive from the axioms alone, but has
>some relation to our experience.
>
In fact, Siemion Fajtlowicz's program Grffiti, which I have mentioned in
another posting, generated a number of conjectures (in graph theory and
planar geometry) which were found very interesting by human mathematicians, 
enough so for some of them to attempt to prove them.

Andrzej

-- 
Andrzej Pindor                        The foolish reject what they see and 
University of Toronto                 not what they think; the wise reject
Instructional and Research Computing  what they think and not what they see.
pindor@gpu.utcc.utoronto.ca                           Huang Po
