On 10/18/2011 11:30 PM, Russell Standish wrote:
On Mon, Oct 17, 2011 at 07:03:38PM +0200, Bruno Marchal wrote:
This, ISTM, is a completely different, and more wonderful beast, than
the UD described in your Brussells thesis, or Schmidhuber's '97
paper. This latter beast must truly give rise to a continuum of
histories, due to the random oracles you were talking about.
All UDs do that. It is always the same beast.
On reflection, yes you're correct. The new algorithm you proposed is
more efficient than the previous one described in your thesis, as
machines are only executed once for each prefix, rather over and over
again for each input having the same prefix. But in an environment of
unbounded resources, such as we're considering here, that has no import.
So the histories, we're agreed, are uncountable in number, but OMs
(bundles of histories compatible with the "here and now") are surely
still countable.
If we take the no information ensemble, and transform it by applying a
universal turing machine and collect just the countable output string
where the machine halts, then apply another observer function that
also happens to be a UTM, the final result will still be a
Solomonoff-Levin distribution over the OMs. This result follows from
the compiler theorem - composition of a UTM with another one is still
a UTM.
So even if there is a rich structure to the OMs caused by them being
generated in a UD, that structure will be lost in the process of
observation. The net effect is that UD* is just as much a "veil" on
the ultimate ontology as is the no information ensemble.
Unless I'm missing something here.
Lets leave the discussion of the universal prior to another post. In a
nutshell, though, no matter what prior distribution you put on the "no
information" ensemble, an observer of that ensemble will always see
the Solomonoff-Levin distribution, or universal prior.
I don't think it makes sense to use a universal prior. That would
make sense if we suppose there are computable universes, and if we
try to measure the probability we are in such structure. This is
typical of Schmidhuber's approach, which is still quite similar to
physicalism, where we conceive observers as belonging to computable
universes. Put in another way, this is typical of using some sort of
identity thesis between a mind and a program.
I understand your point, but the concept of universal prior is of far
more general applicability than Schmidhuber's model. There need not be
any identity thesis invoked, as for example in applications such as
observers of Rorshach diagrams.
And as for identity thesis, you do have a type of identity thesis in
the statement that "brains make interaction with other observers
relatively more likely" (or something like that).
There has to be some form of identity thesis between brain and mind
that prevents the Occam catastrophe, and also prevent the full retreat
into solipsism. I think it very much an open problem what that is.
Hi Russell,
Would the conjecture that the Stone duality provide a coherent
version of this "identity thesis"? Minds, as per Comp, -> logical
algebras and Brains -> topological spaces. Not not, how so?
Onward!
Stephen
snip
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