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Dr. Bostrom assumes that technological advances could produce a computer with more processing power than all the brains in the world, and that advanced humans, or “posthumans,” could run “ancestor simulations” of their evolutionary history by creating virtual worlds inhabited by virtual people with fully developed virtual nervous systems.

Some computer experts have projected, based on trends in processing power, that we will have such a computer by the middle of this century, but it doesn’t matter for Dr. Bostrom’s argument whether it takes 50 years or 5 million years. If civilization survived long enough to reach that stage, and if the posthumans were to run lots of simulations for research purposes or entertainment, then the number of virtual ancestors they created would be vastly greater than the number of real ancestors.

There would be no way for any of these ancestors to know for sure whether they were virtual or real, because the sights and feelings they’d experience would be indistinguishable. But since there would be so many more virtual ancestors, any individual could figure that the odds made it nearly certain that he or she was living in a virtual world.