Le 14-sept.-07, à 01:02, Russell Standish a écrit :

> On Thu, Sep 13, 2007 at 03:04:34PM +0200, Bruno Marchal wrote:
>> Le 13-sept.-07, à 00:48, Russell Standish a écrit :
>>> These sorts of discussions "No-justification", "Zero-information
>>> principle", "All of mathematics" and Hal Ruhl's dualling All and
>>> Nothing (or should that be "duelling") are really just motivators for
>>> getting at the ensemble, which turns out remarkably to be the same in
>>> each case - the set of 2^\aleph_0 infinite strings or histories.
>> Once you fix a programming language or a universal machine, then I can
> You don't even need a universal machine. All you need is a mapping
> from infinite strings to integers.

Which one?

> And that can be given by the
> observer,

But what is the observer? Is the observer an infinite string itself, a 
machine, ?

> where the integers are an enumeration of the oberver's
> possible interpretations.

I still don't understand what you accept at the ontic level, and what 
is epistemological, and how those things are related.

>> imagine how to *represent* an history by an infinite string. But then
>> you are using comp and you know the consequences. Unless like some
>> people (including Schmidhuber) you don't believe in the difference
>> between first and third person points of view.
>> (Youness Ayaita wrote:
>>> When I first wanted to capture mathematically the Everything, I tried
>>> several mathematicalist approaches. But later, I prefered the
>>> Everything ensemble that is also known here as the Schmidhuber
>>> ensemble.
>> Could you Youness, or Russell, give a definition of "Schmidhuber
>> ensemble", please.
> The set of all infinite length strings in some chosen alphabet.

Is not Shmidhuber a computationalist? I thought he tries to build a 
constructive physics, by searching (through CT) priors on a program 
generating or 'outputting" a physical universe. Is not the ensemble an 
ensemble of computations, and is not Schmidhuber interested in the 
finite one or the limiting one? Gosh, you will force me to take again a 
look at his papers :)

>> Also I still don't know if the "physical universe" is considered as an
>> ouptut of a program, or if it is associated to the running of a
>> program.)
> No, it is considered to be the stable, sharable dream, as you
> sometimes put it.

It is the case, by and through the idea that the observer is a lobian 
machine for which the notion of dream is well defined (roughly 
speaking: computations as seen through the spectacles of the 

The set of all infinite strings, according to the structure you allow 
on it, could give the real line, the set of subset of natural numbers, 
the functions from N to N, etc. It is not enough precise I think.

I don't understand either how you put an uniform measure on those 
infinite strings, I also guess you mean a (non-uniform) measure on the 
subsets of the set of infinite strings. Interesting things can come 

> It is the interpretation of the observer, but it
> isn't arbitrary.

Certainly not in Schmidhuber, as I remember (cf our discussions in this 
list). OK, with comp, but in some RSSA way, and not in any ASSA way 
based on an ensemble.



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