Article View: sci.logic
Article #461Re: Church's Heresy and the Unsolveability of chess
From: Mark
Date: Tue, 06 Oct 1992 20:23
Date: Tue, 06 Oct 1992 20:23
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1375 bytes
I expound on The Church's Heresy: > The strong version of Church's Heresy: the set of all functions that have >been, are being, ever will be, or ever could be computed is a finite subset >of the recursive functions bounded above in size by 2-to-the-256. >Corollary: Every computable function can be represented uniquely by 32 bytes. >Theorem: This 32-byte coding is not computable, but is finite and recursive. In article <1992Oct6.112819.16016@odin.diku.dk> torbenm@diku.dk (Torben AEgidius Mogensen) writes: >No. It is only the size of the functions that can be represented in 32 >bytes. The functions themselves needs 2^256 bytes. There are 2^256 32 byte integers. Therefore there is a one-to-one correspondence between 32 byte integers and computeable functions (which there are less than 2^256 of). Furthermore, this mapping is finite, therefore it is a recursive function. It's just not computeable.
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Path: arc1-ca.pugleaf.net!sparky!uunet!caen!uwm.edu!csd4.csd.uwm.edu!markh From: markh@csd4.csd.uwm.edu (Mark) Newsgroups: sci.logic Subject: Re: Church's Heresy and the Unsolveability of chess Date: 6 Oct 1992 20:23:34 GMT Organization: Computing Services Division, University of Wisconsin - Milwaukee Lines: 18 Message-ID: <1assk6INN64g@uwm.edu> References: <1ar16rINNp9e@uwm.edu> <1992Oct6.112819.16016@odin.diku.dk> NNTP-Posting-Host: 129.89.7.4