On 12 Oct 2011, at 23:48, Russell Standish wrote:
On Wed, Oct 12, 2011 at 02:54:01PM +0200, Bruno Marchal wrote:
On 11 Oct 2011, at 22:14, Russell Standish wrote:
On Tue, Oct 11, 2011 at 06:03:42PM +0200, Bruno Marchal wrote:
With COMP, and via your UDA, our observed universe is selected
from
the set of all infinite strings (which I call descriptions in my
book).
My non observed "future"; or computational extensions, is selected,
making the comp physics explainable in term of statistics on
computations. This leads to general physical laws invariant for all
observers. There is no selection of a particular computations, just
a relative indeterminacy bearing on all computations going through
my state. In particular we cannot use Bayes theorem, for example.
Like Brent, I don't follow you here.
See my answer to Brent. Basically, Bayes is induction. Conditional
probability is usual deductive-type probability.
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.
Without the anthropic principle, ISTM that your theory would
suffer
the Occam catastrophe fate. How do you avoid that?
Is that equivalent with the white rabbits?
No, it is quite the opposite problem. As Einstein purportedly said
"Everything should be made as simple as possible, but not
simpler". Occam's razor theorem, which comes from Solomonoff and
Levin's considerations of algorithmic information theory would imply
that we don't see anything interesting at all. That is the Occam
catastrophe. Something prevents the world from being too simple. I
think that something is the Anthropic Principle, but I'm
interested if
you have an alternative suggestion.
You can give me a link to this.
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.
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.
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.
I don't use
probability at all in my reasoning, except as a result (first person
indeterminacy) which transforms physics into a probability or
uncertainty or indeterminacy calculus on computations or
arithmetical relations, without using Bayes, nor #-thropic
principles.
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*.
If you explain this in your book, remind me the pages, or just the
title of your paper (which I have on some of my hard disks). I
deduce (or show how to deduce) the necessary physical laws for all
machine-observer.
IIUC, you manage to show that a von Neumann quantum logic arises in
one of your hypostases. This requires a (still questionable IMHO)
definition of knowledge (Plato's Theatetus one).
I am still not sure about that. I don't know any definition of
knowledge such that we maintain the inability of a awake person to be
unable to know for sure that she is awake. I can imagine we might add
new constraints, and probably that might be needed at some point, but
not something contradicting the Theatetus' one. And in the
arithmetical setting, Bp & p is the only definition such that knowing
implies belief (as shown by Artemov, in the case you modelize the
ideally correct machines' belief by provability (and this is natural
when you understand that from the machine's point of view; we don't
have Bp -> p.
But sure, many other approach can be made here. Iuse the simplest one,
and the miracle is that it already give what we were searching for. It
illustrate also the consistency of comp, despite the UDA based reversal.
To be hinest, I would be the first to be quite astonished that we get
physics in the first machine's interview. I am amazed that the ideally
(arithmetically) correct machine's physics is not yet refuted.
It is still a long
way from there to something like Schrodinger's equation or Born's
rule.
Hmm.. It might non correct, but the logic provide complete constraints
on what is physics. It is just harder to solve than Schroedinger which
is easy to illustrate on simple problem. But the net advantage is that
the physics is explained in a context where everything is explained in
the manner of Plotinus: we have a "god", a "divine intellect", a
"soul", and the material reality (observable and "feelable", quanta
and qualia), all this with their relations, and all this as part of
arithmetic. And we might be close to Schroedinger equation if the
logic works well, but this is work for the future. I might try to
implement again those logic and optimize them, but this is time
demanding, and also some good hand at programming ...
I don't infer anything from observations at all
(which would be needed to use an anthropic principle and Bayes).
Well excuse me for thinking that this might be the missing ingredient
in your ontology!
UDA explains how the physical laws have to be deducible from
arithmetic. Observation can only be used to refute comp, or indeed the
naivety of using the oldest classical theory of knowledge (but then I
have never heard about any another theory: Deustch use knowledge in a
different sense (where I use conjecture or inductive bet), but the
background knowledge theory is the same, I think you just need it to
have a notion of Popper falsifiability. Now you can suggest me another
theory of knowledge. Brent's critics of modeling belief by provability
is more convincing, but fails also for providing an alternative. Its
weakness is that it needs some level of "representation theory of
mind", making hard to imagine a really low level of comp substitution.
Again if people have alternative, and show to me how to translate them
in arithmetic, I will interview the LUMs accordingly :)
Bruno
http://iridia.ulb.ac.be/~marchal/
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