Bruno wrote:
> 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
If the measure doesn't depend on t'/t, then F is the constant function and k
= 0. I now think that this is the correct choice.
> I think `time' must be explained from the measure. Perhaps in fine you are
> right, but I have no way to appreciate that now.
I agree, but I don't think one has to wait until a complete theory is
formulated before one can try to answer some questions.
>
>
> >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.
Maybe I didn't understand you correctly, but in
http://www.escribe.com/science/theory/m1726.html
you make the point that if a person is simulated, it doesn't matter how
often that person is simulated, as long as the simulations are identical.
Assuming you are right, I intended to show that without any form of
(quantum) suicide, you can change the probabilities of observing rare
events. Maybe the above example was not so clear, so let's look at a slight
variant of this.
Suppose you want to observe some rare phenomena, such as proton-decay. You
then place a computer next to the experimental set-up. The computer is
simulating your entire life over and over again (the biological version of
you is annihilated).The computer receives information about the experiment,
but this will not influence the simulation unless evidence for proton decay
is found. In that case you are made aware of the positive result.
Now, all the simulations where you don't receive news about the experiment
are equivalent and should (according to you) be counted once. The
simulations where you do receive information are all different, because a
positive result could come at any time during your simulated life.
Therefore you would have to conclude that the probability of observing
proton-decay is almost equal to 1.
Saibal
Received on Sun Sep 24 2000 - 07:34:15 PDT