Frank writes: > I would hate to have to demonstrate that a modern computer is an instance > of a Turing Machine. Among other things they usually have multiple > processors as well as memory hierarchies. But I suppose it could be done, > theoretically.
First a passage from a chapter I contributed to a book edited by a graduate student Nick knows (Zack Beckstead); I have cut out a bit in the middle which aims at a different point not under consideration here. ===begin=== If talk of machines in the context of the human sciences seems out of place, note that Turing (1936) actually introduces his automatic machine as a formalization (thoroughly mathematical, though described in suggestive mechanistic terms like tape and scanning) of an idealized *human* calculating agent (Soare, 1996, p. 291; italics in the original), called by Turing a computer. [...] As Turing remarks, It is always possible for the computer to break off from his work, to go away and forget all about it, and later to come back and go on with it (1936, p. 253). It seems to me that then it must also be always possible for the computer to break off and never come back (in fact, this often happens in the lives, and invariably upon the deaths, of non-idealized human calculating agents). ===end=== Of course Turing's idealization of "an idealized *human* calculating agent" also idealizes away the fact that human computers sometimes make errors. A Turing machine doesn't make errors. But both the processors and the memory of a modern computer can, and *must* make errors (however rarely, and however good the error-detection). To at least that extent, then, they are not *perfect* instantiations of Turing machines. On the other hand, that very fact about them makes them (in some sense) *more* like (actual) human calculating agents. So, Nick, why are you asking what Turing machines think, instead of what modern computers think? (Be careful how you answer that...) ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
