Can you (without being an asshole) explain why exactly each tape position may contain only a simple integer? It's perfectly reasonable to define the tape alphabet to be an arbitrary set; can the set not be uncountably infinite? If not, why not?
| GOOD TIME FOR MOVIE - GOING ||| Mike McNally <m5@tivoli.com> |
Sorry for jumping in here, despite promising myself not to. I've been deleting all of the circular debate on quantum computers, Turing machines, etc. But for some reason my tape stopped on this one. Turing machines are what they are: storage for finite symbols on a tape, read by some gadget that looks at what a storage site has in it and makes some decision, possibly moving to another site, writing a new symbol, etc. This, by the way, echoes reality pretty well: all actual machines store finite symbols in actual locations. Steven Smale of Berkeley has studied what happens if a machine can store *real numbers* in the memory locations. Amazing things happen. But this ain't the real world. And it ain't crypto. --Tim May -- .......................................................................... Timothy C. May | Crypto Anarchy: encryption, digital money, tcmay@netcom.com | anonymous networks, digital pseudonyms, zero 408-688-5409 | knowledge, reputations, information markets, W.A.S.T.E.: Aptos, CA | black markets, collapse of governments. Higher Power: 2^859433 | Public Key: PGP and MailSafe available. "National borders are just speed bumps on the information superhighway."