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Article 1462 of comp.ai.philosophy:
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>From: G.Joly@cs.ucl.ac.uk (Gordon Joly)
Newsgroups: comp.ai.philosophy
Subject: Chinese Room Variant
Message-ID: <2094@ucl-cs.uucp>
Date: 21 Nov 91 11:49:16 GMT
Sender: news@cs.ucl.ac.uk
Lines: 59

Thomas Clarke writes:
 > [...]
 > The results of operations on singleton strings are defined by tables:
 > 
 >    & -table                  @ - table
 > 
 >     A  B  C  D ...		A  B  C  D  E
 >     ___________              ______________
 > A  | A  B  C  D ...     A   | A  A  A  A  A ...
 > B  | B  C  D  E ...     B   | A  B  C  D  E ...
 > C  | C  D  E  F ...     C   | A  C  E  G  I ...
 > D  | D  E  F  G ...     D   | A  D  G  J BC ...
 >     ...                      ...
 >         (By now you know that the system is decimal arithmetic).
 > 
 > The child is also taught the rules for forming @ and & of longer strings in  
 > terms of the tables for singleton strings.
 > 
 > After much tutelage by an expert system, the child is able to perform & and @  
 > for arbitrary pairs of strings with nearly flawless accuracy.
 > 
 > My question is:  Does the child understand the concept of number? arithmetic?  
 > 
 > I would say not; it seems to me there is more to number than computational
 > manipulations.
 > 
 > POLY   Thomas Clarke                             MATH
 > O  L   Institute for Simulation and Training     A  T
 > L  O   University of Central Florida             T  A
 > YLOP   clarke@acme.ucf.edu                       HTAM


Looks like you taught the child *Group Theory* to me. The table on the
left is the positive integers under addition. This is an infinite
group, with the operation "plus" and indentity 1; it is closed. For a
finite group, perform the arithmetic mod 4 you get a 4-group (under
addition):

             A  B  C  D 
            ___________
        A  | A  B  C  D 
        B  | B  C  D  A 
        C  | C  D  A  B
        D  | D  A  B  C

I think....? Anyway, what have we learned? That even simple
mathematics can be "ambiguous" like natural language, Chinese, French,
Latin or Russian. The symbols carry two meanings, group theoretic or
simple arithmetic.

The Chinese Room should be locked up and the key thrown away!

____

Gordon Joly                    G6DFY              +44 71 387 7050 ext 3716
Internet: G.Joly@cs.ucl.ac.uk          UUCP: ...!{uunet,ukc}!ucl-cs!G.Joly
Computer Science, University College London, Gower Street, LONDON WC1E 6BT

  he said what? - he said "hello" -- that's a bit aggressive isn't it?


