Re: Measure of the prisoner

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Sat, 16 Sep 2000 18:33:58 +0200

----- Oorspronkelijk bericht -----
Van: "Marchal" <marchal.domain.name.hidden>
Aan: "Saibal Mitra" <smitra.domain.name.hidden>; <everything-list.domain.name.hidden.com>
Verzonden: zaterdag 16 september 2000 15:47
Onderwerp: Re: Measure of the prisoner


>
>
>
>
>
> >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.

Let me try to explain. Suppose the simulated prisoner is copied again in the
computer. We then have three prisoners: the real one and two simulated ones.
Suppose that the time dilatation factor of the prisoner simulated inside the
simulation relative to the real one is t''/t. Let's denote the measure of
this prisoner by m3, that of the (first) simulated prisoner by m2, that of
the real one by m1. If the measure depends on time-dilatation, we can write:

m2/m1 = F(t'/t) (1)

m3/m1 = F(t''/t) (2)


Now the simulated person would calculate m3/m2 as

m3/m2 = F(t''/t') (3)

because t''/t' is the time dilatation factor of the prisoner simulated
inside the simulation relative to the simulated one.

>From (1) and (2) it follows that m3/m1 = F(t''/t) / F(t'/t). Equating this
to (3) gives


Log[F(t''/t')] = Log[F(t''/t)] - Log[F(t'/t)]

This is equivalent to

Log[F(x)] + Log[F(y)] = Log[F(xy)]

Now any function satisfying g(xy) = g(x) + g(y) is a logarithm, so we may
put Log[F(x)] = k* Log[x] =>
 F(x) = x ^ k.

>
>
> >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.
>
 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 ...
>

But then the probability of observing rare events can be made more likely
without any form of (quantum) suicide. E.g. suppose that your entire life
was simulated over and over again, for billions of years. The computer
simulating you will atomatically simulate an alarm if and only if in the
real world a large comet was about to hit the earth. Then, according to you,
the probability of hearing the alarm in your lifetime would be much larger
than 1/2 (note that the alarm could go of at any moment during your
simulated life, so there are many different continuations where the alarm is
sounded).

> 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
>
>

Saibal
Received on Sat Sep 16 2000 - 09:39:24 PDT