While at any moment the tape may be finite, that it can at need grow is the fundamental notion of infinite. One can hardly
take a set of LARGE size (like half of the infinite set) and, say by weighing or by volumetric scale, determine if it is different from any truly infinite set. The point you make is a subjective one. The net result of Turing's specification is that the tape is infinite, effective (functional) though the definition may be. wrb From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com] On Behalf Of Quentin Anciaux Sent: Tuesday, September 04, 2012 9:10 AM To: everything-list@googlegroups.com Subject: Re: Two reasons why computers IMHO cannot exhibit intelligence 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. 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com <mailto:everything-list%2bunsubscr...@googlegroups.com> . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- All those moments will be lost in time, like tears in rain. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
