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Article 3152 of comp.ai.philosophy:
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>From: zeleny@zariski.harvard.edu (Mikhail Zeleny)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: Is understanding algorithmic?
Message-ID: <1992Jan26.014607.8073@husc3.harvard.edu>
Date: 26 Jan 92 06:46:06 GMT
Article-I.D.: husc3.1992Jan26.014607.8073
References: <DIRISH.92Jan18155827@jeeves.math.utah.edu> <1992Jan26.010642.24883@smsc.sony.com>
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In article <1992Jan26.010642.24883@smsc.sony.com> 
markc@smsc.sony.com (Mark Corscadden) writes:

>In article <DIRISH.92Jan18155827@jeeves.math.utah.edu> 
>dirish@math.utah.edu (Dudley Irish) writes:

>DI>...  It seems to
>DI>me much more important to understand why we are unwilling to assert
>DI>that a Turing machine can refer.  I therefore invite all and sundry to
>DI>attempt to convince us (I have admitted it now, I am one of those
>DI>rabid skeptics) that a Turing machine can refer.
>DI>Dudley Irish

MC:
>Well, I don't know whether I can convince you, but I can give you the
>following scenario in which two machines use a symbol to refer to an
>object in the real world.  It isn't by any means a proof that Turing
>machines can refer, but I'd sincerely like to know where a "rabid skeptic"
>sees flaws in the following demonstration.
>
>Strictly speaking, this scenario involves physical machines, which are
>not Turing machines: Turing machines are a mathematical abstraction.
>However, the control portions of these machines will implement procedures
>which are Turing machine programmable.  I realize this might not be good
>enough for some skeptics.  If so, I would like to hear more about why the
>physical/abstract difference is essential *in this specific scenario*.
>That point aside, here is the scenario.
>
>There are two "pickup stations" (physical locations in a laboratory), one
>of which is empty and the other of which contains a box.  A guide rail
>leads out from "home station" and then diverges, one path leading
>to each pickup station:
>
>			  M1   M2
>		       [home station]
>			     |
>			     |
>		    +--------+--------+
>		    |		      |
>	        [pickup 1]	  [pickup 2]
>		  +---+
>		  |box|            (empty)
>		  +---+
>
>The two machines start at home station.  The machine M1 is programmed,
>using a conventional assembly language running on a conventional chip,
>to follow the guide rail to the branch point, to take the right branch,
>and to move to pickup station 1.  It then lowers an "arm" which can detect
>(via sensing restance) whether or not a box is present.  The machine M1
>then leaves pickup station 1, travels to pickup station 2, and performs
>the same determination.  Finally M1 returns to home station.
>
>At home station, M1 lowers a mechanical sweeper to smooth a patch of
>dirt at the center of home station, and then draws a large "X" in
>the dirt if it detected the box at pickup 1, otherwise it draws a
>large "O".
>
>Now M2 uses an optical scanner to "view" the dirt at the center of home
>station and uses a pretty straightforward (but not trivial) fixed pattern
>recognition program to determine whether an "X" or an "O" is present.
>If an "X" is present, it follows the guide rail to pickup 1 and retrieves
>the box; if an "O" is present is moves directly to pickup 2 and retrieves
>the box from there.
>
>By now my intent should be obvious:  to claim that both machines are using
>the symbol at home station to refer to a specific physical location within
>the laboratory.  Several intelligent posters to c.a.p have supported
>proofs which demonstrate that Turing machines are incapable of referring,
>which brings up the following suggestion.
>
>Consider a mathematical proof which demonstrates that all objects of
>a certain general class possess a given property.  Occasionally I have
>found it useful to pick a specific object of that class and to apply
>the details of the proof, a step at a time, to that specific object, in
>order to gain insight into the proof.  Analogously, I'd like to suggest that
>someone who believes it possible to prove that Turing machines cannot
>refer help me to apply such a proof, step by step, to the scenario above.

It's a pleasure.  Your machines merely succeed in matching an internal
representation of the laboratory location, as well as of some objects
likely to be found there with a preprogrammed description, perhaps through
the use of a visual pattern matching algorithm.  Should you like to argue
that human referential capabilities could be uncharitably characterized in
the same fashion, I would like to point out the following facts:

(a) It is intuitively evident that we are capable of referring to objects
with which we have no direct perceptual acquaintance, in particular to
abstract objects like numbers and sets.

(b) No existing machine is capable of solving the general problem of visual
pattern recognition, e.g. matching a three-year old infant's capacity to
recognize a human face.  There seems to be no reason to suppose that this
problem is effectively computable.

>Mark Corscadden
>markc@smsc.sony.com
>work: (408)944-4086


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