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Article #450Church's Heresy and the Unsolveability of chess
From: Mark
Date: Tue, 06 Oct 1992 03:29
Date: Tue, 06 Oct 1992 03:29
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1064 bytes
Call this Church's Heresy: the set of all computable functions is a finite set, and a proper subset of the recursive functions. Application: The game solving algorithm is not (yet) computable with the input being the game of chess. Thus, by Church's Heresy, chess is not (yet) computable. 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.
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Path: arc1-ca.pugleaf.net!sparky!uunet!gumby!wupost!uwm.edu!csd4.csd.uwm.edu!markh From: markh@csd4.csd.uwm.edu (Mark) Newsgroups: sci.logic Subject: Church's Heresy and the Unsolveability of chess Date: 6 Oct 1992 03:29:31 GMT Organization: Computing Services Division, University of Wisconsin - Milwaukee Lines: 13 Message-ID: <1ar16rINNp9e@uwm.edu> NNTP-Posting-Host: 129.89.7.4