At 11:01 AM 5/21/2003 +1000, Russell Standish wrote:
>Bruno Marchal wrote:
> > In computability
> > the models
> > (object of semantics, that is one of the logician's approach to the
> > "meanings") are the
> > "real" things, for example the description can be <a program for factorial
> > written in fortran> and
> > the real thing will be the infinite set of couples {(0,1) (1,1) (2,2)
> > (3,6), (4,24), (5,120), ...}.
> >
>
>This is where we make closest contact. There are an uncountable
>infinity of factorial programs written in Fortran.
I can spot a mistake here: There is a one to one correspondance between
computer programs and integers. Think of a computer program as another way
of writing an integer, in another base.
Jean-Michel Veuillen
> (All the programs
>with junk data after the final "END" statement also count). However,
>there is only one meaning (namely {(0,1) (1,1) (2,2) (3,6), (4,24),
>(5,120), ...}). In this case, one can identify the meaning with the
>set of programs producing that output.
>
>When talking about measure, the measure of a particular program is
>zero (in the space of all programs). However, the measure of the
>meaning is not - it turns out to be approximately 2^{-K(x)} where K is
>the Kolmogorov complexity of the program x. (Result of the coding
>theorem).
>
>I agree that in some sense the program x is a finite object, and the
>meaning is infinite, but that is irrelevant to the discussion of measure.
>
> Cheers
>
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>A/Prof Russell Standish Director
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Received on Sat May 24 2003 - 18:14:02 PDT