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

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2012/9/4 William R. Buckley <bill.buck...@gmail.com>Seems funny that Turing “…assumed that machines could not operatewith infinite numbers…” given that the tape is assumed to be infinite.Not really infinite but it has no boundaries, it can always extendif 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 wrbFrom: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com] On Behalf Of John ClarkSent: Tuesday, September 04, 2012 8:59 AM To: everything-list@googlegroups.comSubject: Re: Two reasons why computers IMHO cannot exhibitintelligenceOn Mon, Sep 3, 2012 at 9:11 AM, benjayk <benjamin.jaku...@googlemail.com> wrote:> Showing scientifically that nature is infinite isn't reallypossible.Maybe not. In Turing's proof he assumed that machines could notoperate 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 usenothing but that to show independently of Turing that no machine cansolve the Halting Problem then that would prove that irrationalnumbers with a infinite number of digits play no part in theoperation of the universe; on the other hand if this new physicaltheory shows you how to make such a machine then we'd know thatnature 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 GoogleGroups "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 GoogleGroups "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.-- All those moments will be lost in time, like tears in rain. --You received this message because you are subscribed to the GoogleGroups "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.

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