Le 14-juin-06, à 07:31, Russell Standish a écrit :

> 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.

Could you explain what is your conception of the relation between a 
description and an object?
I can understand "an infinite length object", like some putative 
infinite physical universe for example. I can understand  "a zero 
information description"; for example the empty program or some empty 
theory (I will address "theories" later though). It is harder for me to 
understand what can be the use of infinite description or a 
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?

I think the only trouble with Schmidhuber, and then with many people to 
be sure, is that they find hard to take seriously enough the 
distinction between first and third person point of views.
The UD is a (finite) program, and when it runs, like any program 
running on some universal machine, it uses only at each time a finite 
piece of its (potentially infinite) tape, etc.
Now, indeed, once you grasp that the probabilities of relative 
histories relies on the first person point of view, the case can been 
made that the infinite computations have a higher measure that the 
finite one, so that somehow physicalities emerges from the infinite set 
of those infinite (crashing-like) computations.



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