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From: nlt@grad3.cs.duke.edu (Nancy L. Tinkham)
Newsgroups: talk.religion.misc,comp.ai
Subject: Re: The Ignorant assumption
Summary: "Pick a number at random" is not an algorithm.
Message-ID: <12512@duke.cs.duke.edu>
Date: 26 Sep 88 23:09:07 GMT
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     Robert Firth offers the following proposed refutation of the Church-Turing
thesis:

> 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.


     The claim of the Church-Turing thesis is that the class of functions
computable by a Turing machine corresponds exactly to the class of functions
which can be computed by some algorithm.  The notion of an algorithm is a
somewhat informal one, but it includes the requirement that the computation be
"carried forward deterministically, without resort to random methods or
devices, e.g., dice" (Rogers, _Theory of Recursive Functions and Effective
Computability_, p.2).  If it is demonstrated that a physical system, by using
randomness, can generate the input-output pairs of a function which cannot be
computed by a Turing machine, we have merely shown that there exists a
non-Turing-computable function whose output can be generated by non-algorithmic
means -- hardly surprising, and not relevant to the Church-Turing thesis.

                                            Nancy Tinkham
                                            {decvax,rutgers}!mcnc!duke!nlt
                                            nlt@cs.duke.edu