From: Bill Hibbard (firstname.lastname@example.org)
Date: Sat Oct 09 2004 - 10:49:25 MDT
On Sat, 9 Oct 2004, Christian Szegedy wrote:
> Hi Bill,
> You wrote:
> > You are right that I do not demonstrate a mathematical
> > error in Penrose. Rather, his overall argument is wrong,
> > based on an unrealistic model of human brains.
> I restate it the last time: if you write that the human mind can
> be computationally modelled by a finite state machine, then
> you implicitely agree with him that it can be modelled by
> a Turing machine.
Good, it is time to end this thread. I agree that the
finite state machine issue does not refute Penrose's
mathematics. The real error is in holding machines to
the standard of reasoning from a fixed set of consistent
axioms while allowing humans to reason from natural
language. However, the fact that his mathematical
proof only works assuming an infinite model of computation
makes me think that he has found a property of infinite
sets rather than anything essential about humans and the
way they compute. I will be on the road for the next few
days and not following this up any more.
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