On Thu, Oct 13, 2011 at 05:20:11PM +0200, Bruno Marchal wrote:
> On 12 Oct 2011, at 23:48, Russell Standish wrote:
> >I certainly appreciate you don't use Bayes' theorem in your work, but
> >don't understand why you say you cannot use it.
> I am not saying that we cannot use it in some context. I am not sure
> we can use it to explain the physical laws in the comp frame,
> because, it seems to me that it assume that we belong in a physical
> universes among other possible one. But when we assume comp, we do
> not belong to a universe, our bodies (at the subst level)  "belong"
> in infinitely many computations at once, and the appearance of the
> universe results from the competition among those infinities of
> computations.
> It seems to me that in the comp theory Bayes's theorem can be used
> to justify some geographical aspect, but not laws which have to e
> independent of any observers.

I don't see why Bayes' theorem assumes a physical universe. All it
assumes is a prior probability distribution. Something like the
universal prior of Solomonoff-Levin, or the distribution of observer
moments within UD*.

> >It is discussed in my book (page 83). The terminology (Occam
> >catastrophe) is mine, but it is certainly possible that other people
> >may have raised the issue by a different name.
> I will look at this again asap. I thought we discuss all this during
> the ASSA/RSSA debate.

I don't recall this issue being discussed during that debate. There
was some discussion on it after my book came out, but more about the
conclusion that self-awareness is required for consciousness, which
apparently people found counter-intuitive for some reason. 

> >
> >>Does the OCCAM catastrophe relies on Bayes?
> >
> >It is a consequence of the Occam's razor theorem, which in turn relies
> >on the Solomonoff-Levin universal prior, and the working assumption of
> >living in an ensemble. It doesn't rely on Bayes'
> >theorem itself, but you can apply Bayes' theorem to the universal
> >prior to get the only effective form of induction known. Li and
> >Vitanyi has a good technical discussion of this, though not of the
> >"catastrophe", as they don't assume an ontology.
> But this is closer to Hal Finney Universal Distribution theory,
> based on ASSA.
> Like in the doomsday argument, the reference base seems to me undefined.
> I am not oppose to such an approach, I just don't understand how it
> could work, and I prefer to avoid it.

I take observer dependent reference base. The beauty of something like
COMP is one can show that all observers must generate equivalent
reference bases - agreeing up to some additive constant independent of
the complexity of what's being opbserved.

> >
> >>What would it be with respect of UD*?.
> >
> >IFAICT, UD* should be equivalent to the all strings ensemble.
> I don't think so at all. This is missing the highly non trivial
> structure on the set of all computations coming from the non trivial
> notion of computations. Allmost all strings are random, but no
> computations at all is random, except the result of the application
> of the identity program on the arbitrary inputs when dovetailing on
> inputs. But that is just a part of UD*. Most of UD* is not random at
> all, and it has an extreme redundancy. There is the presence of deep
> computations, self-referential entities, etc.

You may be right, but I think that needs to be demonstrated. If true,
it should give rise to observable differences between my theory and
yours, which would be an interesting and important result.

BTW - I'm not convinced by Schmidhuber's speed prior work, which prima
facie looks like an attempt in this direction. Are you?

> >It wasn't a critique of your UDA and AUDA reasoning, (which I agree
> >does not use probability, nor anthropic principle) but of your
> >statement that Bayes' and the Anthropic Principle is inapplicable.
> Not in all context. The anthropic principle might been use for
> deriving cosmological principles, but not the physical *laws*.

Why not?

> Again if people have alternative, [to Theatetus]
> and show to me how to translate them in arithmetic, I will interview
> the LUMs accordingly :)

Sorry - I don't really have a good suggestion either. Epistemology is
not my field :).


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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