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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

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

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