Xref: utzoo talk.religion.misc:7819 comp.ai:2301 Path: utzoo!utgpu!attcan!uunet!seismo!sundc!pitstop!sun!amdcad!ames!ncar!tank!oddjob!mimsy!kilroy 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