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Article 4779 of comp.ai.philosophy:
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>From: orourke@unix1.cs.umass.edu (Joseph O'Rourke)
Newsgroups: sci.philosophy.tech,comp.ai.philosophy
Subject: Re: A rock implements every FSA
Message-ID: <45653@dime.cs.umass.edu>
Date: 28 Mar 92 18:59:11 GMT
References: <45390@dime.cs.umass.edu> <1992Mar24.231518.10230@husc3.harvard.edu> <45426@dime.cs.umass.edu> <1992Mar28.092723.10365@husc3.harvard.edu>
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In article <1992Mar28.092723.10365@husc3.harvard.edu> 
	zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:

[A clarification of his proposal to handle inputs]

OK, so for that 2-state FSA, with inputs restricted to length 2, we
have the following mapping from abstract states to physical system
states:

        <A,00>,   ->  S1 
	<A,00>,   ->  S2
	<A,00>;   ->  S3
        <A,01>,   ->  S4
	<A,01>,   ->  S5
	<B,01>;   ->  S6
        <A,10>,   ->  S7
	<B,10>,   ->  S8
	<B,10>;   ->  S9
        <A,11>,   ->  S10
	<B,11>,   ->  S11
	<A,11>;   ->  S12

Why don't you finish the construction?  You need to identify what
in the rock corresponds to abstract state A, and what to B.  These
are the obvious choices:

	Rock state A = S1 + S2 + S3 + S4 + S5 + S7 + S10 + S11
	Rock state B = S6 + S8 + S9 + S11

But to be convincing as a realization, you need to perform a
similar identification for the inputs:  what in the rock corresponds
to input 0 at time 1?  It's (roughly) the middle-third of S1 +...+ S6.
And e.g., input 1 at time 2 is roughly the last third of S4 + S5 + S6 +
S10 + S11 + S12.
	So maybe you have to slice the physical states more finely if
you want to have something in the rock correspond to a specific input
at a specific time?  But this naive "thirds" slicing would lead
to difficulties establishing the equivalent of Putnam's causality 
argument on p.123.  The way you have set it up, it is more natural
to identify rock states with the entire input stream.  But then there
is no obvious correspondent to specific inputs, which seems necessary
for the causality part of the argument.


