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? Cheers -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---