Jean-Michel Veuillen wrote:
>
> 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.
Only if the programs were finite. However if they're infinite in
length, then the one-to-one correspondence is with the reals...
>
> 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
> >
> >----------------------------------------------------------------------------
> >A/Prof Russell Standish Director
> >High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
> >UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
> >Australia R.Standish.domain.name.hidden
> >Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
> > International prefix +612, Interstate prefix 02
> >----------------------------------------------------------------------------
>
>
----------------------------------------------------------------------------
A/Prof Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (")
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
----------------------------------------------------------------------------
Received on Wed May 21 2003 - 07:02:39 PDT