From: Christian Szegedy (szegedy@or.uni-bonn.de)
Date: Thu Oct 07 2004 - 09:56:12 MDT
Bill Hibbard wrote:
>Penrose makes a very specific mistake: he uses infinite
>Turing machines to model human brains whereas they should
>be modeled by finite state machines. As I show in:
>
> http://www.ssec.wisc.edu/~billh/g/appendix.html
>
>his argument breaks down if the Turing machines are
>replaced by finite state machines.
>
>Cheers,
>Bill
>
>
>
>
>
I have explicitely stated that I am not convinced by the arguments of
Penrose.
However, it find it not just an overstatement but a completely irrelevant
statetement that he is hopelessly confused about the Theorem of Goedel.
It is a very simple theorem and I am quite sure that
he understands it at least as well as we do. Of course, the way he
applies it
to the real world can and should be disputed. I am not irritated by
criticisms on established scientists, but I don't think it is justified if
*anyone* states that the things are so and so and therefore someone else
(in this case, Penrose, who is a brilliant mathematician) is completely
wrong. A correct attitude is to say, that the observations A,B and C
combined with arguments D,E and F speak against his position on X.
(Exactly the way you did.)
If I am on it, I am not at all sure that the finite-state-machine model is
much better than the Turing machine model. The human mind is in
interaction with a practically infinite universe, so I think that both
models of computations have their specific flaws.
I found your last argument most convincing that the human thinking is
not based on any consistent formal model, but on a combination of
experimentation, probabilistic reasoning and formal logic - an inconsistent
system (not even a model in mathematical sense) but still effective for
a lot of tasks.
However I would not rule out the opinion of Penrose, after all his position
can be correct, even if some of his arguments are not convincing.
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