Xref: utzoo talk.religion.misc:7809 comp.ai:2295 Path: utzoo!attcan!uunet!super!udel!gatech!mcnc!duke!grad3!nlt 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 References: <1369@garth.UUCP> <2346@uhccux.uhcc.hawaii.edu> <1383@garth.UUCP> <1929@aplcomm.jhuapl.edu> Sender: uucp@super.ORG Followup-To: talk.religion.misc Lines: 26 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