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From: vlsi_lib@netcom.com (Gerard Malecki)
Subject: Re: Grounding Representations: ("Grounding" is the wrong word)
Message-ID: <vlsi_libD7M4n8.K4n@netcom.com>
Reply-To: shankar@vlibs.com
Organization: VLSI Libraries Incorporated
References: <3lkrpq$kun@mp.cs.niu.edu> <3nhlk5$i7o@percy.cs.bham.ac.uk> <3njqh7$q0m@mp.cs.niu.edu>
Date: Tue, 25 Apr 1995 22:47:32 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:27235 comp.ai:29302 comp.robotics:20133 comp.cog-eng:3101 sci.cognitive:7421 sci.psychology:40691

In article <3njqh7$q0m@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:
>In <3nhlk5$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.
>

Geometry is a very good example of this. Some of the mathematical theorems
like the Cauchy Schwarz inequality or those involving trigonometry are
more easily visualized than proved on paper. Another example involving
common sense and a bit of ingenuity is the method of solving electrostatic
problems by the method of images. It is apparent that common sense and
visual perception play an important role. For in the human, I guess the
visual cortex plays as important a part in data processing as the
frontal areas. 

Not only is the human brain poor at number crunching, but also in the
absense of sufficient spatial processing, it does poorly (as attested
by the need for Lisp programmers to indent their code for readability,
though for the Lisp interpreter, all the white spaces and carriage 
returns are nothing more than a minor nuisance). 

Shankar Ramakrishnan
shankar@vlibs.com

