Re: Turing Machines and Physical Computation

From: JXStern (JXSternChangeX2R_at_gte.net)
Date: 11/28/04 

Date: Sun, 28 Nov 2004 17:48:55 GMT

On Sun, 28 Nov 2004 08:14:01 GMT, "Stephen Harris"
<cyberguard1048-usenet@yahoo.com> wrote:
>>... But,
>> before a mark constitutes anything interesting, it must have a
>> subject, I stand by that.
>
>Is the future something that you can grasp either with your mind or
>with your hand? With your mind you can't do better than make
>predictions which sometimes come true. In mathematics, perhaps
>the successor function, n +1, n +2, n + 3 and so implies a future.
>
>A succession of causes and effects, manifested as events, unfold
>to our perception which take time. What is the physical thing ...

I'm not sure what the question is you have in mind here, but you said
the magic word(s), "cause" and "time".

What are the proper roles of causality and of time in the world of
Turing Machines? Seems to me that many mathematicians see TMs as
outside of time and such logical results as TMs present as being
immanent.

Part of the system that must constitute any theory of phyiscal
computation, I assert, is going to have to be a recognition of time as
a dimension and causality as everywhere manifest.

This is not a matter of future, though, it is a matter of how the now
relates to the other-than-now. Physical computation depends on some
kind of time-binding, it seems to me, if that statement is not
hopelessly metaphysical. Purely abstract TMs do not require time, I
guess, and certainly one can play with nondeterministic machines that
do not even require order.

Then there's my man Wittgenstein who pretty much hated the idea of
mathematical sequences. He was dead wrong in this, I believe, and it
was perhaps this one point of his that kept him from appreciating to
even the smallest degree what Turing was doing under his very nose.

J.

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