Jesse Mazer wrote:

> [...]

>But I think we do need some kind of global measure on 
>the set of "everything", 

Global? Only a relative one is necessary. But a relative
one needs a "global" definition. (If we want a TheoryOE).


>since everything obviously includes worlds (or 
>observer-moments) that seem to be identical to this one up to a certain 
>point but in which the laws suddenly break down, and we want to be able to 
>say that this is less probable somehow

Indeed.

> (I've never been sure what people 
>were talking about when they referred to 'white rabbits'

Basically what you said above. It is also the skeptical inductivism
Davis Lewis talk about in his "the plurality of worlds".

> but I think it's 
>another version of this problem...isn't white actually a pretty common color 
>for rabbits though?  Is it an Alice in Wonderland reference?)

Sure. It is *the* Wonderland's white rabbit. I'm used to that 
expression and I have been happily surprised by its success in the list,
because there is nothing wrong with a "white rabbit" indeed.
Schmidhuber has talked about "lambs eating wolves" somewhere in relation
with that problems. 


>A lot of people have a lot of different ideas about TOE's on this list, so 
>maybe the global measure issue could help clarify where we all stand in 
>relation to each other...do people have specific proposals about this?  I 
>guess the other relevant question is, what is the set of "everything" that 
>you're putting the measure on...all computations?  All mathematical 
>structures?  All observer-moments?
>
>Let me know what you think...

... Jesse Mazer wrote in the same thread:

>Russell Standish's page also mentions another option I hadn't 
>thought of: an observer-relative measure.


The question "if the measure should be absolute or relative"
has been discussed a lot in the thread around Bostrom
self-sampling assumption + some remarks by Wei Dai.
Russell Standish, George Levy and myself 
and (hopefully) some others
seems to agree on the
relative use of that measure, although I argue that both aspect
could be important, i.e. there could be an interplay between 
some absolute universal prior and relative conditional information.
If I remember correctly Jacques Mallah critisizes the nuances about
relativisation and conditionalisation: you can have an absolute
measure and consider that its relativisation are produced by 
classical conditionalisation. (I basically agree if we keep
in mind the difference of point of view).

In my thesis there is two parts: one where I show that if we are
machine then "physics" is reduced to the search of an "absolute
definition" of an observer-relative (first person plural) measure.
In the second part I have developed a road toward a purely mathematical
isolation of that measure based on the incompleteness phenomena.
I got the logic of the certainty-case P=1, and show it to be closely
related with quantum logic. And I take *that* as a confirmation
of both the comp-reversal and the way I have chosen for interviewing
the universal machine.

Schmidhuber's solution is based on a belongness relation between
observer and universes which is impossible to keep once we take
comp seriously. But even if we make sense to such a relation, it
would only eliminates third person white rabbits and not the
first person white rabbits: remember that the great programmer
emulates all (semi)computable "universe" but also all possible 
dreams.

In fact Schmidhuber assume a solution of the mind body problem
which is just incompatible with comp. Technically that makes 
his work incomplete (at least).

Bruno


http://iridia.ulb.ac.be/~marchal



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