June 25, 2012
Categories: Films . . Author: simondrax
Turing did not explicitly discuss the question of the speed of his elementary actions. It is left implicit in his discussion, by his use of the word ‘never,’ that it is not possible for infinitely many steps to be performed in a finite time. Others have explored the effect of abandoning this restriction. Davies (2001), for instance, describes a ‘machine’ with an infinite number of parts, requiring components of arbitrarily small size, running at arbitrarily high speeds. Such a ‘machine’ could perform uncomputable tasks. Davies emphasises that such a machine cannot be built in our own physical world, but argues that it could be constructed in a universe with different physics. To the extent that it rules out such ‘machines’, the Church-Turing thesis must have at least some physical content.
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