Saibal Mitra wrote:
>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.
Well, ok. I still don't understand your premise: ``If the measure depends
on
time-dilatation, ..." Look my UDA argument
http://www.escribe.com/science/theory/m1726.html
I think `time' must be explained from the measure. Perhaps in fine you are
right, but I have no way to appreciate that now.
>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).
What do you mean by real world ? Moreover the fact that my whole life
is simulated again and again will not change my *relative* measure, unless
you introduce some bifurcation or fusion between these simulations.
That is hard to do in an intuitive way, and that is why I rely on
provability
logic or modal logics tools for the isolation of probability on the
relative
computational continuation.
Bruno
Received on Mon Sep 18 2000 - 03:48:03 PDT