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From: jqb@netcom.com (Jim Balter)
Subject: Re: Roger Penrose's New Book (in HTML) 1.0
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References: <JMC.94Oct23231211@white.wisdom.weizmann.ac.il> <39drsi$7nl@crl10.crl.com> <39vac3$ba6@news.halcyon.com> <CzFsw2.A4o@cogsci.ed.ac.uk>
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Date: Sat, 19 Nov 1994 04:29:51 GMT
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In article <CzFsw2.A4o@cogsci.ed.ac.uk>,
Jeff Dalton <jeff@aiai.ed.ac.uk> wrote:
>In article <39vac3$ba6@news.halcyon.com> jennings@chinook.halcyon.com (James Jennings) writes:
>>Forgive me for coming in late and for not having read Penrose's new
>>book. (I haven't yet deduced it's title from this thread.) I read
>>Penrose's "Emperor's New Mind" and have a comment on that.
>>
>>Penrose wants to show that the human mind is not merely a computer. He
>>tries to do this by exploring the theoretical limits of computation, the
>>known limits of the human mind, and alternate models of computational
>>processes.
>>
>>What it comes down to is this (in my opinion of course). Suppose there
>>is a problem A and a proved theorem that says:
>>"There is no algorithm that can solve A in finite time."
>>And suppose real people solve examples of A all the time. Penrose would
>>conclude that people do not think using algorithms. There must be
>>something "magic" about human thought.
>
>How do you get from not using algorithms to magic?

Is there some problem with your display system or communications software,
that it omits quote marks?  He said "<quote>magic<quote>", not "magic".  In
context, "magic" obviously (there's that word again) means "non-algorithmic",
be it QM microtubules or meatiness or soulfulness or whatever.

The problem is, of course, that there cannot be a valid proof that "there is
no algorithm that can solve A in finite time" where A is a specific problem
since, if the solution S is expressable, the algorithm "print S" solves it
(I'll ignore here the irrelevant problem that communication of the solution
requires "printing", i.e. transduction).

Rather, there are infinite classes of problems for which there are no
algorithms that solve all instances within various constraints, such as
polynomial time.  Of course, no human can solve every instance of these
infinite classes of problems within the constraints, either.  This isn't
terribly deep, and the entire computational and philosophical pedagogical
community should be embarrassed that this point has been so poorly
communicated that "serious" debate continues, especially after Lucas made it
so clear that such ignorance needs to be dispelled.


-- 
<J Q B>
