On 15 Oct 2011, at 02:50, Russell Standish wrote:
On Fri, Oct 14, 2011 at 05:01:26PM +0200, Bruno Marchal wrote:
On 13 Oct 2011, at 23:50, Russell Standish wrote:
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.
Then why couldn't the physical universe be a trace (aka history) of
UD*?
Because the UDA show it to be a sum of infinitely many computations.
Even 2^(aleph_0) due to the dovetailing of the real (and complex ...)
inputs of the program generated and executed by the UD. This cannot be
generated by any programs. It can only be lived or inferred by the
internal observers experimenting their golabl (on UD*) first person
indeterminacies.
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.
Whenever an observer interprets multiple different input strings (ie
observations) as the same thing, the S-L distribution makes
sense. Particularly so if the mapping process is a computation.
I am not sure I understand 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.
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.
There is, but I'll let you reread the book if you're interested.
OK.
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.
The UDA indicates we must be supervenient on all programs passing
through our current observer moment.
It makes sense with OM = 3-OM = relative computational state. But this
is not Bostrom's OM a priori (provably with comp).
Randomness comes differentiating
between running programs (eg being in Washington or being in Moscow).
OK.
I know there are only a countable number of programs. Does this entail
only a countable number of histories too? Or a continuum of histories?
I did think the latter (and you seemed to agree), but I am partially
influenced by the continuum of histories available in the "no
information" ensemble (aka "Nothing").
It is a priori a continuum, due to the dovetailing on the infinite
real input on programs by the UD.
Could it be that there are only a countable number of histories after
all, given there are only a countable number of programs. That would
be one big difference right there.
We do agree on this. The difference is that the comp statistics is a
statistics on non-random things, even if those things include
computations (non random) with random inputs.
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 :)
Its always worth clarifying what still goes through in an argument
when
some of the assumptions are relaxed, even if the programme itself hits
a wall.
Sure.
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.
I actually don't get that conclusion from your work, so it might be
worth elaborating more.
This already happens in the UDA step 7. We don't need the
immateriality or the 'arithmeticality'. The reversal physics/computer
science appears in any big universe in which a (concrete) UD is run.
You can't prevent that UD to access infinitely often your
computational states, through infinities of possible computations. So
when you do an experiment in physics, at some point you will have to
take your first person view into account, like when you look at then
needle of the measuring apparatus. But that first person view is given
by the first person indeterminacy bearing on that concrete UD running
in that universe. So if the experience confirms a physical laws, the
measure UD* should to, and so the physics has to be given by the
statistics on the computations, from the first person points of view.
The Theatetus definition leading to the AUDA has the feel of something
"put in by hand", rather than being a logical consequence of the
UDA. Nothing wrong with that, of course, but we should be honest with
it, if it is the case.
I agree I am not always clear on that. That is why I try to
distinguish comp (used in UDA), and comp+theaetetus, used in AUDA. But
the theaetetus ca be shown to be the unique definition meeting the
requirement of computer science, provability logic, and the usual
definition of knowledge (Kp -> p, Kp -> KKp, K(p->q)->(Kp->Kq)). It
can be motivated, as it is by Socrates in the Theaetetus of Plato, by
the dream argument, which is basically step 6 of UDA.
How would you define knowledge axiomatically, accepting that you want
it to apply to an entity (a machine) whose beliefs are rational, in
the sense of obeying classical logic on the finite things?
Bruno
http://iridia.ulb.ac.be/~marchal/
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