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From: kilroy@mimsy.UUCP (Darren F. Provine)
Newsgroups: talk.religion.misc,comp.ai
Subject: Re: The Ignorant assumption
Summary: The `random' disproof of Church-Turing doesn't work.
Keywords: random, algorithm, deterministic, function
Message-ID: <13763@mimsy.UUCP>
Date: 27 Sep 88 20:17:55 GMT
References: <1369@garth.UUCP> <2346@uhccux.uhcc.hawaii.edu> <1383@garth.UUCP> <1929@aplcomm.jhuapl.edu> <12512@duke.cs.duke.edu> <7167@aw.sei.cmu.edu>
Reply-To: kilroy@mimsy.umd.edu (Darren F. Provine)
Organization: University of Maryland, Dept. of Computer Sci.
Lines: 45
Disclaimer: Brandy the WonderDog knows that C-T has nothing to do with random
            processes -- why doesn't Mr. Firth?

In article <7167@aw.sei.cmu.edu>, firth@sei.cmu.edu (Robert Firth) writes:
/*
 * In article <12512@duke.cs.duke.edu> nlt@grad3.cs.duke.edu (Nancy L. Tinkham)
 *	writes:
 *
 * >     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.
 *
 * No it isn't.  The claim is that every function "which would naturally
 * be regarded as computable" can be computed by a Turing machine.  At
 * least, that's what Turing claimed, and he should know.
 */

I do not see any point to this reply.  You have merely restated the
definition she provided and did nothing to answer her objection.

You see,
	``every function "which would naturally be regarded as computable"''
and
	``the class of functions which can be computed by some algorithm''

are pretty much the same thing.  Do you have some way of computing a
function without an algorithm that nobody else in the entire world knows
about?

If so, do go and get your Turing Award & your Ph.D., and then tell us how it
works.

If not, go reread the requirement that the algorithm used for computation
must be deterministic, and tell us how a random process is relevant to the
discussion.

And you'll also need a definition of "random function" -- if it is random,
then how can it be a function, or even a mapping?

[ All of this ignores, of course, the fact that some people believe that
  physical processes cannot act randomly (and that quantum randomness is
  a misperception).  Sadly, we cannot prove this either way.  ]

Darren

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Darren F. Provine                                    UUCP: uunet!mimsy!kilroy
University of Maryland                       ARPA/CSNET: kilroy@mimsy.umd.edu