Re: Measure of the prisoner

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Mon, 28 Aug 2000 22:11:52 +0200

> George Levy wrote:

> In a message dated 08/28/2000 8:23:06 AM Pacific Daylight Time,
> smitra.domain.name.hidden writes:
>
> > The probability P that the prisoner finds himself in the ``simulated´´
> > universe is thus given as:
> >
> > P = (t'/t+m3/m1 )/(1+t'/t+m3/m1)
>
> This is the probability that observer B in the real world observes
observer A
> in a simulated world, given that observer B is in the real world (though I
> don't quite understand the purpose of m3). In this sense it is a
conditional
> probability.

This is not what I meant by P (I should have explained this better). P is
defined as follows. We start with one (real) prisoner. The prisoner is told
that in the middle of the night (when he is sleeping) a virtual copy of him
will be made. When he wakes up, he thus doesn't know where he is (assuming
that his room is also simulated perfectly). But let's assume that he will
know the moment he is allowed to leave his room, because the other parts of
the prison look totally different.

When the prisoner leaves the room next morning he can thus find himself in
two different situations. P is the probability that he opens the door and
finds that he is in the virtual prison. Now even if the virtual prison is
not simulated there exists an universe consisting of just the virtual prison
and the prisoner. The measure of this universe is denoted as m3 (it should
be clear that m3<< m1). The above formula for P was actually not correct. It
should read:

P = (t'/t + m3/m1 )/(1 + t'/t + m3/m1 + X/m1)

X is the combined measure of the prisoner in all other universes (X<<m1). If
the ratio t'/t is zero the virtual prison is effectively not simulated. Even
in that case there is an extremely small probability for the prisoner to
wake up in the virtual prison simply because such an universe exists. Of
course, there are many other universes the prisoner could wake up in and
these are accounted for by X.

S. Mitra
Received on Mon Aug 28 2000 - 13:38:50 PDT