By Nick Bostrom
Department of Philosophy, Oxford University

IV. THE CORE OF THE SIMULATION ARGUMENT

The basic idea of this paper can be expressed roughly as follows: If there were a substantial chance that our civilization will ever get to the posthuman stage and run many ancestor-simulations, then how come you are not living in such a simulation?

We shall develop this idea into a rigorous argument. Let us introduce the following notation:

: 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

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:

                                     (*)

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)

(2)

(3)

Next Page