MATHEMATICAL PROOF OF MATRIX:NICK BOSTROM SIMULATION ARGUMENT

NICK BOSTROM’s SIMULATION ARGUMENT

                                                                                                                                         

The actual fraction of all observers with human-type experiences that live in simulations is then

Writing   for the fraction of posthuman civilizations that are interested in running ancestor-simulations (or that contain at least some individuals who are interested in that and have sufficient resources to run a significant number of such simulations), and   for the average number of ancestor-simulations run by such interested civilizations, we have

and thus:          
                                   f_sim =    f_pNH/( f_pNH)+H

                                          (*)

Because of the immense computing power of posthuman civilizations,   is extremely large, as we saw in the previous section. By inspecting (*) we can then see that at least one of the following three propositions must be true:

    

   (1)  f_p ≈ 0

   (2)  N ≈ 0

    (3)  f_sim ≈ 1       

Where

: Fraction of all human-level technological civilizations that survive to reach a posthuman stage

: Average number of ancestor-simulations run by a posthuman civilization

: Average number of individuals that have lived in a civilization before it reaches a posthuman stage

THREE DEDUCTIONS CAN BE POSSIBLE:

1. No civilization will reach a level of technological maturity capable of producing simulated realities.
2. No civilization reaching aforementioned technological status will produce a simulated reality, for any of a number of reasons, such as diversion of computational processing power for other tasks, ethical considerations of holding entities captive in simulated realities, etc.
3. All entities with our general set of experiences are living in a simulation.