Nick Bostrom is an influential philosopher who specializes in the future. An Oxford don, he is also the founder of the Future of Humanity Institute.^{1} Bostrom’s paper, “Are You Living in a Computer Simulation?,” has been republished five times and translated into Russian, Ukrainian, and the artificial language Kah. Its title raises a question about the posthuman world that Bostrom imagines is our future. It is a world in which superintelligent human beings, or their posthuman successors, or their computers, have extraordinary powers. They may be able to harness planets and even galaxies to enhance their computing capacity.

Would they, Bostrom wonders, have the power to simulate human brain activity and the desire to simulate human beings? His argument has an enviable simplicity:

…at least one[emphasis original] of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation.^{2}

This argument is based on a fallacy.

To simplify the problem, I assume that a posthuman world, in Bostrom’s most optimistic sense, comes to pass. It has enormous, but not infinite, computing power, and devotes some of it to simulation. A human being has on the order of 10^{10} synapses, each of which at any time can fire or not. These, according to Bostrom, fire at a rate of 1,000 times per second. On Bostrom’s view, we can simulate a person’s brain by describing the firing pattern of his synapses. To simulate Bostrom, it would be sufficient to match his firing pattern over the course of his life. His firing pattern at any one time can be described by 10^{10 }bits of information, but suppose, for the sake of argument, we really only need only 10^{5} of these bits. There are more than 10^{11} thousandths of a second in his life so far, so to describe his overall pattern would require 10^{16 }bits.

If we generate simulations at random, there are 2 to the power of 10^{16 }possible patterns. The probability of a discovering a randomly generated Bostrom-pattern is much less than 1/10^{15}. The probability of getting Bostrom right at any given moment is less than 1/10^{10,000}. The probability of matching any of the roughly 10^{10} individuals in human history, rather than only Bostrom, is 10^{10} × 1/10^{10,000}.^{3} The probability of matching any person at all in 10^{1000} simulations is extraordinarily close to zero. The probability that Nick Bostrom, or anyone else, may be described by a randomly generated simulation is nil.

What is wrong with Bostrom’s argument?

If there are H individuals and N simulations, Bostrom assumes that each individual will be simulated an average of N/H times. When N/H is large, he asserts, any individual is more likely to be simulated than real. In a word of abundantly many clones, the odds that you are you are not very good.^{4} This is true only if every simulation produces a simulacrum. But the vast majority of simulations represent no one at all. The number of simulations that count as simulacra has a mean value of zero, because the number of simulations is far larger than the number of individuals. The number of possible simulations is so large that the probability that any future simulator, even one capable of performing 10^{10,000} simulations, can succeed in ever matching any living or past person even at any given moment is negligibly small. I am willing to believe that it is possible to simulate 10^{100} people, but not much more than 10^{1000} of them. Do not allow yourself to be confused by the fact that the vast majority of simulation targets will be dead. The dead, being dead, have no synapses that could be simulated. Before Bostrom’s vast project could even begin, the dead would have to be brought back to life.

Whatever the obstacles to Bostrom’s project, the fact remains that Bostrom himself cannot be identified with the set b of his synapses, even if they are firing like mad. A b-Bostrom conveys no more useful information about the real Bostrom than his social security number. An individual is comprised of his accomplishments, wit, appearance, skills, and failings. Such properties exist at a level of abstraction far removed from that of synapse firing and there is no clear way of relating one level to the other.

Could posthumanity find another way to generate all of human history? Who knows? Bostrom has based his claims on synapse firings and his conclusions on probabilities.