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Article 2607 of comp.ai.philosophy:
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>From: gtall@ogre.cica.indiana.edu (Gerry Allwein)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech,sci.logic
Subject: Re: Penrose on Man vs. Machine
Message-ID: <gtall.694991248@ogre>
Date: 9 Jan 92 21:07:28 GMT
References: <1992Jan9.131829.15232@oracorp.com> <1992Jan9.110732.7279@husc3.harvard.edu> <1992Jan9.190644.331@nynexst.com>
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In <1992Jan9.190644.331@nynexst.com> gene@nynexst.com (Gene Miller) writes:

>> Lot's of uninteresting drivel.

>    1) When I think of 5 pennies, I may "see" a picture of them in my mind,
>    perhaps as the vertices of a "W".

>    2) When I think of aleph_0 pennies, I may "see" them lined up ahead
>    of me, like the ties of a railroad track, going off to the horizon,
>    with no visible end. The projective geometry that allows me to
>    "see" the infinitude of the set is unconscious, requiring no
>    symbolic reasoning.

>    3) When I think of open sets of the real line, I may "feel" the line as
>    a "necklace", with the points as little hard beads on a string. When the
>    string is broken, the bead at which it is broken terminates one of
>    necklace segments, and the other segment is left unterminated (open).

>Do not these visual and kinesthetic images serve as aids in reasoning
>about these objects?

>Similarly, could not all mathematical reasoning (including the
>consistency of arithmetic) be based on built-in or learned
>perceptual and motor capabilities intended to manipulate things
>in the physical world (occasionally aided by symbol manipulation).

>And could not this alleged "analogue computer" be simulated on a
>digital computer?

>Note: More rigorous phrasing of these ideas are welcomed.
>-- 
>Gene Miller		Phone 914 644 2834
>gene@nynexst.com	Fax 914 644 2260

Gene, what you are dangerously close to describing is something called
Visual Inference. Jon Barwise (Indiana University) and John Etchemendy
(Stanford) have done some pleasant work in the area. Jon and I taught a course
this last semester here at I.U. on visual inference (well, Jon did most of
the teaching and I did most of the helping). Jon and John have a program
in development called Hyperproof which is used to help explore a particular
form of visual reasoning (I'm one of their engineers). This seems much more
interesting than comparing the human mind to a machine. In short, who cares?
What is really fun is exploring the notion of reasoning with the help of a
machine where visual information is on all fours with sentential information.

Gerry


