From: Christian Szegedy (szegedy@t-online.de)
Date: Sat Oct 09 2004 - 03:31:09 MDT
> I agree that Finite State Machines are not the issue.
> What *is* the issue is the empirical fact that as far
> as we know, there is no such thing as an uncomputable
> finite physical process. That is, we think that all
> finite physical processes are computable.
I have explicitely avoided discussing this problem,
since it was not needed to refute that special line
of argumentation and starting with it would have only
increased the confusion. There are other arguments of
Penrose that revolve around this question and they are
much harder nuts and I would not try to refute them
at all.
I don't know who is included in *we* that think
that all finite physical processes are Turing-computable.
Most thoughtful people seem to avoid taking a definite
positions on this issue (and with good reasons).
> There is an ambiguity in the word 'solve'. Look at
> (2) again:...
I think, you are right on this. But I don't think
that it is the correct refutation. "Solving
something" in computational sense means producing
the correct (expected, specified mathematically)
answer. It is irrelevant wheter you are 100%
or only 0.0001% sure about your answer.
In his arguments he tried to exhibit *one specific* input
on which you *can not reach* the right conclusion
(assuming you can be modelled by a TM).
The real problem is that he
*pretended the you were exposed to that particular input*.
Then he tries to argue, that you could produce the
right answer to *that specific input*.
(It does not matter, whether you are only 51% sure,
or whether you are completely wrong on any other
issues.) If you produce the correct answer on something
you are *never supposed to*, then it would be a valid
contradiction.
However, there is a mistake at this point: the reader
was *never tested on that particular confusing input*.
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