From: Christian Szegedy (szegedy@t-online.de)
Date: Fri Oct 08 2004 - 17:42:35 MDT
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.
Your refutation attempt is analogous to:
"Penrose assumes that the humans are mammals, but of course,
this is absurd, since they are clearly apes. So his argument that
we can do something that mammals can't do is flawed, since
we are not mammals, but apes."
I think that your argumentation is wrong, since it does not matter
whether we can be modelled by FSMs or TMs. (whether we are
apes or mammals) but whether we can do something what a TM
(mammal) can not. This is the really weak point in his
argumentation. And this would remain a weak point even if the
human brain could perform arbitrarily long computations.
So I think that your refutation is flawed since it attacks at the
wrong point. You do not exhibit the real weakness in his
consideration. The real weakness has nothing to do with
finiteness, it is a much more basic matter.
Let me illuminate the error in his arguments on another analogue.
(Now, I will play the his role and try to convince you that you are
not a computer.)
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Computers cannot factor numbers with large prime factors
efficiently, can they?
Let us take a the smallest prime number with 100 digits
and multiply it with the smallest prime number with 200
digits. If you were a computer it would be a hard job for
you to factorize their product.
Hah...! But is not it quite clear to you what the factors of
the product are?
Since you can factor so efficiently, it is highly improbable
that you are a computer. Perhaps, you are quantum-coputer,
since they can factorize efficiently too!
------------------------------------------------------------------------------------
The flaw in the above arguments has nothing to do with
finiteness, or whether I have enough time or
brain-capacity to work with 300 digit numbers. It is simple
a question of input-formats. If the factors are apriori
told, than it is not a big deal to factorize their product.
In fact, you did not have to factorize at all. This is the same
in his original argument.
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