In “Are you living in a computer simulation?”, Nick Bostrom presents a probabilistic analysis of the possibility that we might all be living in a computer simulation. He concludes that it is not only possible, but rather probable that we are living in a computer simulation. This argument, originally published in 2001, shook up the field of philosophical ontology, and forced the philosophical community to rethink the way it conceptualizes “natural” laws and our own intuitions regarding our existence. Is it possible that all of our ideas about the world in which we live are false, and are simply the result of our own desire to believe that we are “real”? Even more troubling, if we are living in a computer simulation, is it possible that the simulation might be shut off at any moment? In this paper, I plan to do two things. First, I hope to consider what conclusions we might draw from Bostrom’s argument, and what implications this might have for how we affect our lives. Second, I plan to discuss a possible objection to Bostrom’s argument, and how this might affect our personal probability for the possibility that we are living in a computer simulation.

Bostrom begins his argument by making a few assumptions necessary to the probabilistic claims he makes. The first is substrate-independence. This is simply the claim that if we were able to model the mind with enough detail, then we would be able to create artificial minds capable of thought in the same way that we are. He goes further to assume that, if we were able to simulate the entire world in sufficient detail, and feed this world into the artificial minds we have created in the form of sensory inputs, the artificial minds would be incapable of determining that they were in a simulation, unless they were given explicit knowledge of it by the creators of the simulation.

Bostrom then goes on to assert that it would be theoretically possible to create a machine with enough computing power to simulate both the human mind and the universe in sufficient detail to create a simulation that would be indistinguishable from our universe by the population of the simulation. This is based on projections of the advancement of current technology as well as on current theoretical designs of possible computing machines. This assumption, although a grand one, will be considered a valid one for the purposes of this review of the argument.

This moves Bostrom into the main part of his argument. Although Bostrom uses some formal probability theory to make this argument here, it is unnecessary to reproduce it verbatim in order to understand the general argument that he is making. Instead, I will give a general form of the argument in prose, and reproduce a small section of the probability theory later during my critique of the argument.

Bostrom begins by giving an estimate of the fraction of all people in existence that are simulated people, who don’t exist at the fundamental level of reality. He estimates this as the expectation of the number of simulated people divided by the expectation of the number of simulated people plus the number of real people. The expectation of the number of simulated people is equal to the probability of simulations being done times the average number of simulations that would be done if simulations were done times the average number of people in each simulation. Bostrom argues that this calculation gives us the fraction of all people in existence that are actually simulated people and not “real” people.

Bostrom then makes an appeal to the principle of indifference. This principle states that when there is no independent reason to believe one proposition over another, the probability that the proposition is true is equal to the number of possible ways that the proposition could turn out to be true divided by the total number of possible outcomes. This principle, when applied to the case of simulation, says that the probability that we are living in a simulated world instead of a real one is equal to the fraction of all people that are actually simulated people.

By reviewing the probability assignments that Bostrom has just given, it becomes clear that several things have to be the case. Because the number of simulations run by a civilization capable of running them would be very great, if simulations are done, then the number of people that are simulated would be much greater than the number of people that are not simulated, which would mean that the probability that we are living in a simulated universe is almost unity. So, it becomes clear that one of two things must be the case. Either the probability that simulations are run is very small (practically null), or it is almost certain that we ourselves are living in a simulation.

Bostrom asserts that, because we have no reason to believe that either of these possibilities is more likely than the other, we have no reason to change the way we live our lives because of this argument. However, this isn’t quite accurate. If we know that one of the two of these options must be the case, then utility theory tells us that our personal utility that we assign to any particular action should be the weighted utility of this action, given the probability of these two scenarios. In other words, we should live our lives as if we are half sure that we are living in a simulated universe.