Path: utzoo!attcan!uunet!husc6!bloom-beacon!mit-eddie!uw-beaver!cornell!bay
From: bay@arvak.cs.cornell.edu (Paul Bay)
Newsgroups: comp.society.futures
Subject: Re: The future of AI
Summary: TM definition clarified; human brain no more powerful than 
        finite automaton
Message-ID: <18771@cornell.UUCP>
Date: 1 Jul 88 13:26:32 GMT
References: <48.22A3B84F@isishq.UUCP> <4347@killer.UUCP> <10425@stb.UUCP> <3965@saturn.ucsc.edu> <740@vsi.UUCP>
Sender: nobody@cornell.UUCP
Reply-To: bay@svax.cs.cornell.edu (Paul Bay)
Organization: Cornell Univ. CS Dept, Ithaca NY
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In article <740@vsi.UUCP> sullivan@vsi.UUCP (Michael T Sullivan) writes:
>In article <3965@saturn.ucsc.edu>, evan@saturn.ucsc.edu (Evan Schaffer) writes:
>> Actually, there are an infinite number of turning machines.  Turing machines
>> may have an infinite number of states.  In fact, one can argue that,
>> given the size of a neuron, and the size of a human head, there are a limited
>> number of neurons that will fit in a human's head, so a turing machine is
>> capable of more complex behavior then a human.
>
>Just where does one put a Turing machine with an infinite number of states?
>One could argue that with an infinite number of neurons, thus implying an
>infinite head, that a human brain can be infinitely powerful.  But of course
>we are back to the problem of where does one put an infinite head?

Turing machines have a *finite* number of states.  See Hopcroft and Ullman,
"Intro to Automata Theory, Languages, and Computation."   In theory, the human
brain, since it has only a finite number of neurons, is no more powerful than 
a finite automaton.  In fact, even if you augment the human brain with all the
libraries and all the paper in the world, it's still no more powerful than
a finite automaton, since these extra resources are finite as well.

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