Re: relevant probability distribution

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Fri, 7 Jun 2002 00:58:22 +0200

Hello Bruno:
----- Oorspronkelijk bericht -----
Van: "Bruno Marchal" <marchal.domain.name.hidden>
Aan: "Saibal Mitra" <smitra.domain.name.hidden>; "everything"
<everything-list.domain.name.hidden>
Verzonden: dinsdag 4 juni 2002 19:50
Onderwerp: Re: JOINING posts


> Hi Saibal,
>
> At 0:26 +0200 1/06/2002, Saibal Mitra wrote:
> >I think that statistical physics, and especially renormalization group
> >techniques, are essential if one wishes to derive the physics that we
> >observe from abstract concepts like a measure defined on a set of
computer
> >programs.
>
> As I said I agree with you. But do you really mean a measure defined
> on a set of computer programs, or a set of computer program *states*?

I think that you can derive one from the other. I have thought about this
before, and I now think that the observer should associate himself with a
(to himself unknown) program, or better, a set of programs, that could
generate him.

E.g. there exists a program that only calculates me and nothing else. This
program e.g. could compute me in an infinite dream. Many such (very complex)
programs must exist. I think that these programs define our identities (or
vice versa, but then not uniquely). Now, if conscious objects correspond to
programs then you don't have the paradox that any clock or lookup table has
intelligence. The fact that I don't live in my own personal universe, but
that my universe is generated by a simpler one, suggests that simpler
programs have larger probabilities.

If you now have an a priory probability over the set of all programs, you
can compute (in principle) the probability that I will observe a certain
outcome if I perform a certain experiment. At least you can formulate this
question in a mathematical unambiguous way.

> In my setting it is the latter although it can and must eventually lead
> to a measure on consistent *sequences* of computer program states.
> (This is reminiscent of the passage made by Isham going from the Quantum
> logics of states to the quantum logics of histories).
>
> The states must be considered also as seen by the machines themselves,
> should I add. cf the 1-person/3-person distinction (which I attempt to
> capture by the variant of self-reference logics.
>
> I said we meet but of course we are not yet at the Stanley-Livingston
Junction,
> but let us say we each begin to appear on our respective horizon :)

Maybe, one can already try to do calculations without knowing the correct
probability distribution. Many different models have the same critical
behaviour. This is called universality. The effect arises, because different
models at criticality can sometimes be mapped to the same fixed point under
the renormalization group map. I think that to apply such techniques further
assumptions need to be made. Like e.g. in statistical mechanics one makes
the assumption that the system under investigation is ergodic.

Regards,
Saibal
Received on Thu Jun 06 2002 - 16:02:19 PDT