Measure of the prisoner

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Mon, 28 Aug 2000 17:16:37 +0200

Suppose that the simulated prisoner is a ``digital ´´ copy of a real
prisoner. If the simulated time also corresponds exactly to real time then
the probability of the prisoner finding himself in the simulated world is
almost exactly 1/2.

 The reason is that instead of simulating the prisoner in his virtual
environment, one could have made a copy of the prisoner in the form of a
``real´´ robot. The measures of the robot and the real prisoner are clearly
equal. It clearly doesn't matter if the ``brain´´ of the robot is located in
the robot itself or in a computer somewhere else. In the latter case it
clearly doesn't matter if the computer receives its input from a real robot
or from a simulated robot.

Now suppose that it takes t seconds to simulate t' seconds of the life of
the virtual prisoner. Denote the measure of the real prisoner by m1, the
measure of the prisoner being simulated by m2, and the measure of the
prisoner in an universe where the fundamental laws of nature appear to be
those of the simulated prison by m3.

I now postulate that one has:

m2/m1 = t'/t

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)

I can motivate the postulate as follows. Suppose the computer used to
simulate the prisoner is also used to perform other calculations. A random
generator decides which calculation is performed at a particular time. If
one has t'/t = 1 and the probability that the computer is simulating the
prisoner is w, then one has an effective
t'/t of w.


S. Mitra
Received on Mon Aug 28 2000 - 08:23:12 PDT