From: Bill Hibbard (email@example.com)
Date: Thu Oct 07 2004 - 10:52:32 MDT
On Thu, 7 Oct 2004, Christian Szegedy wrote:
> 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.
> I have explicitely stated that I am not convinced by the arguments of
> However, it find it not just an overstatement but a completely irrelevant
> statetement that he is hopelessly confused about the Theorem of Goedel.
Then I guess its a good thing I didn't say that Penrose 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.
Given the current state of physics it is impossible to
be sure whether our universe if finite or infinite, but
there have been numerous recent papers in quantum mechanics
estimating the finite number of states of the universe.
Even in classical physics, the second law of thermodynamics
tells us that only a finite amount of state is usable, in
a finite region of space. Given the current limit on human
life spans and the speed of light limit, all humans who
have lived are properly modeled as finite state machines,
and Penrose's argument is about current humans.
If you are using "practically infinite" to mean "large but
finite", that's enough for Penrose's proof to fail.
> 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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