On 13 Oct 2011, at 23:50, Russell Standish wrote:
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.
Bayes' theorem does not assume a physical universe. But some use of
bayes theorem to justify the laws of physics, presuppose that a
physical universe is an object (may be mathematical, like in Tegmark)
among other objects.
All it
assumes is a prior probability distribution. Something like the
universal prior of Solomonoff-Levin, or the distribution of observer
moments within UD*.
I don't think such a distribution makes sense. What makes sense is a
computational state, and a distribution of (competing) universal
machines relating that state with other states through the
computations that they emulate.
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.
I don't see the relation with this.
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.
?
The UD generates computations, and only computations, so in all
portion of the UD*, there is nothing random at all. randomness crops
out in the machine's epistemologies or first person views, because
they are intrinsically ignorant to which computations they can belong.
If true,
it should give rise to observable differences between my theory and
yours, which would be an interesting and important result.
Yes. You are still trying a theory which would be comp-independent,
apparently. Good luck :)
BTW - I'm not convinced by Schmidhuber's speed prior work, which prima
facie looks like an attempt in this direction. Are you?
I have a problem with all absolute "prior" to derive physical laws,
but I have no problem of the use of some relative prior, to derive
many facts in general. They might play a role in the "choice" made on
the deep computations (cosmological features).
I have also some technical problems with the speed prior based on the
version of the speed-up theorem for inductive inference. Universal
entities have that crazy property of being infinitely 'self-
speedable', both for proving (Blum) and inferring (Royer). Speed
priors might lead to persistent creative explosions, for the
observer's pov. But perhaps that might make some sense and I am just
not looking at this in the right angle.
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?
Well, because UDA shows that the laws of physics are logico-
arithmetical, and that they take the form of internal
(epistemological) relative statistics on computation.
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 :).
Is not physics is reduces to the numbers first person plural
epistemology, if we are machine?
The first person indeterminacy is epistemological. The notion of fist
person is a notion of epistemology, in a large sense of a science of
beliefs, knowledge, and eventually, with comp, of observation. Except
for arithmetical truth itself (where we can debate on the
epistemological nature or not), all other hypostases are
epistemological. That's why comp leads to a form of neoplantonist
monist 'idealism'.
Bruno
http://iridia.ulb.ac.be/~marchal/
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