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
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.
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.)
Russell Standish wrote :
> Where differences lie is in the measure attached to these strings. I
> take each string to be of equal weight to any other, so that there are
> twice the measure of strings satisfying 01* as 011*. This leads
> naturally to a universal prior.
I don't understand. If all infinite strings have the same measure, what
is the meaning of "universal prior"?
> Neither Bruno's nor Max's theories give a measure,
But I extract the logic of the proposition having measure one. This is
enough to be compared with the logic of quantum certainties (described
by some quantum logic).
> but remarkably the
> Occam's razor theorem and White Rabbit result is fairly insensitive to
> the measure chosen (so long as it's not too pathological!).
I don't understand this either.
> On your comment on permitting infinite strings - the ensemble I
> describe in my book has only infinite strings, which belong to
> syntactic space.
?
> It would be possible to construct an ensemble of purely finite strings
> (all strings of length googol bits, say). This wouldn't satisfy the
> zero information principle, or your no-justification, as you still
> have the finite string size to justify (why googol and not googol+1,
> for instance). I suspect the observable results would be
> indistinguishable from the infinite string ensembles for large enough
> string string size, however.
Hmmm... I think that once we do care about the difference between 3-pov
and 1-pov, such difference (between ensemble of finite and infinite
strings) does become palpable (empirically), unless you take special
infinite set of arbitrarily long (but finite) strings, but then all
will depends on the chosen representations.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Sep 13 2007 - 09:04:50 PDT