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From: dm@DIAMOND.BBN.COM.UUCP
Newsgroups: comp.society.futures
Subject: Re: The future of AI
Message-ID: <8806291531.AA15519@quartz.BBN.COM>
Date: 1 Jul 88 14:00:10 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Organization: The Internet
Lines: 26
X-Unparsable-Date: 1988-06-29-11:31:19


>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.

>Michael Wolf                

Actually, as the person to whom you were replying pointed out,
there are only a countable infinity of Turing machines (that
is, Turing machines can be put into a one-to-one correspondence
with the integers).  I'll have to be convinced that there is an
uncountable number of problems (seems plausible at first blush,
but then, countable vs. uncountable infinities DON'T seem
plausible at first blush, so I don't like rely on mere
plausibility where levels of infinity are concerned).

As regards your second point --- that our finite heads imply
there are things we can't conceive --- Rudy Rucker explores
this idea in great detail in his _Mind tools: the five levels
of mathematical reality_.  His meditation is inspired by
Gregory Chaitin's algorithmic information theory (``You can't get
a 20 pound theorem out of a 10 pound axiomatic system''), which
is also described in the June, 1988 _Scientific American_ (in the
article ``Randomness in arithmetic'').