From: tcmay@netcom.com (Timothy C. May)
Date: Tue, 26 Jul 94 11:49:58 PDT
To: m5@vail.tivoli.com (Mike McNally)
Subject: Re: GUT and P=NP
In-Reply-To: <9407261542.AA03740@vail.tivoli.com>
Message-ID: <199407261849.LAA12086@netcom8.netcom.com>
MIME-Version: 1.0
Content-Type: text/plain



> 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



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