Re: Key Post 1, toward Church Thesis and Lobian machine

From: Russell Standish <lists.domain.name.hidden>
Date: Thu, 6 Dec 2007 09:23:44 +1100

On Wed, Dec 05, 2007 at 11:08:34PM +0100, Mirek Dobsicek wrote:
>
> > Each expression like that denotes now either a computable function from
> > N to N, or as we have to expect something else. And we have to expect
> > they are no computable means to distinguish which U_i represents
> > functions from N to N, and which represents the other beast.
>
> Can I say that the other beasts are only and only infinite loops? I
> assume that the machine cannot destroy itself, so it either stops after
> computing a computable function or enters some silly loop.
>

Not unless the total number of states was finite. In a Turing machine
case, the tape being infinite and readable/writeable allows the
machine to compute forever without entering a loop. For instance, a
program outputting the digits of Pi onto the tape computes forever and
never enters a loop (since Pi is irrational, periodic sequences of
digits are ruled out).

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Received on Wed Dec 05 2007 - 17:23:54 PST