Re: Measure of the prisoner

From: Marchal <marchal.domain.name.hidden>
Date: Sat Sep 16 06:52:32 2000

>I now think Bruno is right. The measure doesn't depend on t'/t. But, in any
>case, consistency with other thougth experiments (e.g. simulations within a
>simulation with another relative time-dilatation factor t''/t') limits how
>the ratio of the measures can behave as a function of t'/t :
>
>m2/m1 = (t'/t) ^ x
>
>(m2 is the measure of the simulated prisoner m1 that of the real prisoner,
>and it takes t seconds to simulate t' seconds of the life of the prisoner).

I'm not sure I understand.


>A nonzero value for x can still arise in certain cases. E.g. if one
>simulates one day of the life of the prisoner with periodic boundary
>conditions, one has x = 1. To see this, suppose the prisoner is simulated on
>two different
>computers, one with t'/t = 1 and the other with t'/t = 1/2. Only one day of
>the life of the
>prisoner is simulated. After a simulated time of 24 hours the simulation
>starts all over again. Then clearly in a time interval of 2 T days, the life
>of the
>prisoner is simulated 2 T times on the fast computer and T times on the slow
>computer.

I am not sure. Perhaps you have some absolute measure in mind.
Perhaps you'r right. My own approach is still not sufficiently developped
to answer such question. A priori I would say that the number of
simulations
is not relevant. Only the relative distinguishable computational
continuations
with respect to a simulation will paly a role. But at this stage it is
only
an intuitive idea ...

We are here quite close to the long debated RSSA/ASSA question (relative
self sampling and absolute self sampling assumption).
I think the ASSA is needed for the search of our little-program-origin,
with
universal prior (cf Schmidhuber), but the RSSA is needed for the
computation
of the relative probabilities and the taking into account of the first and
third person point of view distinction ...

Bruno
Received on Sat Sep 16 2000 - 06:52:32 PDT