On Mon, Jun 12, 2006 at 03:52:15PM +0200, Bruno Marchal wrote:
> In general, an infinite programs can still be written with a finite 
> number of symbols, like a real number can be written with a finite 
> number of symbols chosen among {0,1,2,3,4,5,6,7,8,9}. Of course in 
> general it will need an infinite number of occurences of those symbols. 
> It is the length of the program which is infinite.
> But there is no infinite programs (in arithmetical Platonia). Of course 
> like Russell, you can conceive and study them but it in general the 
> whole motivation of the notion of programs/names/description is really 
> to capture something infinite by something finite.

This is an interesting comment, that I hadn't appreciated before. The
Plenitude I study has infinite length "description", precisely because
this plenitude is the zero information object.

However, computable things are indeed finite in size, which implies
that the arithmetical Platonia is smaller, and consequently a richer
set of things.

The universal dovetailer, however, executes everything in the infinite
bitstring Plenitude does it not, or is this a misunderstanding of
Schmidhuberian proportions?


A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                                    0425 253119 (")
UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
Australia                                http://parallel.hpc.unsw.edu.au/rks
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