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From: jwl@ernie.Berkeley.EDU (James Wilbur Lewis)
Newsgroups: comp.ai
Subject: Randomness, the universe, and Turing machines
Message-ID: <26154@ucbvax.BERKELEY.EDU>
Date: 20 Sep 88 02:25:21 GMT
References: <1369@garth.UUCP> <2346@uhccux.uhcc.hawaii.edu> <1383@garth.UUCP> <372@quintus.UUCP> <1390@garth.UUCP> <388@quintus.UUCP> <7059@aw.sei.cmu.edu>
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In article <7059@aw.sei.cmu.edu> firth@bd.sei.cmu.edu (Robert Firth) writes:
>In article <388@quintus.UUCP> ok@quintus.UUCP (Richard A. O'Keefe) writes:
>
>>But is there any reason to suppose that the universe _is_ a Turing machine?
>
>None whatever.  The conjecture is almost instantly disprovable: no Turing
>machine can output a true random number, but a physical system can.  Since
>a function is surely "computable" if a physical system can be constructed
>that computes it, the existence of true random-number generators directly
>disproves the Church-Turing conjecture.

Two comments.  First, I think "deterministic automaton" is a more apt
(putative) metaphor for the universe than a Turing machine.  Turing machines 
have infinite tapes, symbols, read/write heads, etc.;  it is a model of 
computation, and bandying it about as an analogy for the workings of the
universe in this sort of discussion is sloppy, and bound to make theorists
wince. ;-)

Regarding "true randomness": randomness, in a theoretical sense, is more
closely related to predictability than determinism.  Turing machines are
certainly capable of outputting highly unpredictable sequences which would
satisfy any statistical criteria of randomness you care to invent.  If, by
"random", you mean to imply nondeterministic behaviour, the existence of
"true", physically realizable random number generators is contingent upon
the Copenhagen interpretation of quantum mechanics (no hidden variables).
Can you supply a proof that God does indeed play dice with the universe?

-- Jim Lewis
   U.C. Berkeley