2012/9/4 William R. Buckley <[email protected]>

> Seems funny that Turing “…assumed that machines could not operate with
> infinite numbers…” given that the tape is assumed to be infinite.
>

Not really infinite but it has no boundaries, it can always extend if
needed. At any given time the used tape is of finite length.

Quentin


> ****
>
> ** **
>
> wrb****
>
> ** **
>
> *From:* [email protected] [mailto:
> [email protected]] *On Behalf Of *John Clark
> *Sent:* Tuesday, September 04, 2012 8:59 AM
> *To:* [email protected]
> *Subject:* Re: Two reasons why computers IMHO cannot exhibit intelligence*
> ***
>
> ** **
>
> On Mon, Sep 3, 2012 at 9:11 AM, benjayk <[email protected]>
> wrote:****
>
> ** **
>
> > Showing scientifically that nature is infinite isn't really possible.***
> *
>
>
> Maybe not. In Turing's proof he assumed that machines could not operate
> with infinite numbers, so if there is a theory of everything (and there
> might not be) and if you know it and if you can use nothing but that to
> show independently of Turing that no machine can solve the Halting Problem
> then that would prove that irrational numbers with a infinite number of
> digits play no part in the operation of the universe; on the other hand if
> this new physical theory shows you how to make such a machine then we'd
> know that nature understands and uses infinity. I admit that I used the
> word " if " a lot in all that.
>
>    John K Clark
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