RE: Turing vs math

From: Marchal <marchal.domain.name.hidden>
Date: Thu Oct 21 10:56:06 1999

Hal Finney wrote:

>Why can't the simplest possible program be taken as computing a universe
>which includes us? We tend to say "it computes all universes" as though
>it computes more than one. Then it is fair to object that the program
>is too simple, because it computes more than one universe.
>
>But this is a semantic objection based on the definition of a universe.
>How do we know how many universes a given program computes?

At least we can say that the UD (my UD, or Schmidhuber's great
programmer) computes c histories. (c is 2^aleph_0).

>Is there
>an objective, well defined measure?


Fundamental question. Very different answer according to ASSA, RSSA, etc.
The immortality question is an "easy" subproblem of that question.
I think that with comp the measure is relative to (conditionnalized by)
the "present" and defined on the (cardinality c) sets of possible
infinite continuations. We are filtered by deepness and multiply by
 simplicity if not linearity. The problem is: is that
filtration/multiplication enough for making the flying rabbit very rare.


>That seems necessary in order to
>rule out a trivial counting or dovetailing program as one which creates
>our observable universe and our minds as a subset of its output.


With comp our consciousness supervene necessarily on the set of ALL
computationnal histories. It is the way our multiple experience
recovers themselves which define our "observable universe".
(Looking below our level of substitution we can "grasp" the other
universes. With comp the "quantum" is probably such a "Galouye"
effect)


>Wei Dai proposed a solution to this, which was to say that it is not
>enough to compute a universe that matches what I see; it must compute
>a universe which includes my mind. And then, he proposes that the
>probability measure should not be calculated as just the size of the
>universe program, but rather as the size of the program that computes
>the universe PLUS the size of the program that localizes (finds, locates)
>my mind within that universe.


What do you mean by localizing your mind in a universe ?
A description of your brain ? At which level of description ?
A description of your body ?
... of your neighborhood ?
Or of your personal experience ? (In which case with comp it will
just be impossible without some kind of betting).

But I guess Wei Dai's intuition is linked to the complexity of
the (infinitely) programs which computes my mind relatively to the
complexity of the (infinitely) possible programs which generates
environment for me at some level. I mean the use of the PLUS function is
doubtfull in my setting. I guess Wei Dai's idea could be make clearer
with Bennett's notion of depth. (But as I keep telling this is just one
half of the problem).

>This provides an objective measure of the degree of
>overkill/redundancy/extra-universes produced by the universe simulation.
>Something objective like this seems necessary to reject the notion that
>we live in a universe produced by a trivial program.

Either the program is not universal (in which case I don't bet on it).
Or it is universal in which case it is not trivial at all, especially
concerning the way the "internal modalities" (the point of view of the
machines generated in it) will be related with each other.

Bruno
Received on Thu Oct 21 1999 - 10:56:06 PDT