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Article 3150 of comp.ai.philosophy:
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>From: markc@smsc.sony.com (Mark Corscadden)
Newsgroups: comp.ai.philosophy
Subject: Re: Is understanding algorithmic?
Message-ID: <1992Jan26.010642.24883@smsc.sony.com>
Date: 26 Jan 92 01:06:42 GMT
References: <DIRISH.92Jan18155827@jeeves.math.utah.edu>
Organization: Sony Microsystems Corp, San Jose, CA
Lines: 75

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

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.

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


