On 04 Sep 2012, at 18:09, Quentin Anciaux wrote:



2012/9/4 William R. Buckley <bill.buck...@gmail.com>
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.

Right. The tape is not part of the machine. It plays the role of an extendible environment/memory space.

If we had infinite tape ourself, we would never have drawn on cave's wall, nor invented magnetic tapes.

You can always substitute the message "memory overflow" by "give me more memory space".

True, the Turing machine has an infinite tape, but that is pedagogical folklore. To be finite is part of the essence of what a machine consists in, as Turing was well aware off. For example by proving the equivalence Turing-machine with lambda term (which have no tape at all).

Also, machine can handle the infinite numbers. It can handle all the constructive infinite ordinal in an effective way, like us, and it can handle the others infinite ordinals and cardinals in a non constructive way, like us.

Bruno




Quentin




wrb



From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com ] On Behalf Of John Clark
Sent: Tuesday, September 04, 2012 8:59 AM
To: everything-list@googlegroups.com
Subject: Re: Two reasons why computers IMHO cannot exhibit intelligence



On Mon, Sep 3, 2012 at 9:11 AM, benjayk <benjamin.jaku...@googlemail.com > 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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