Brian Eggleston

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.

This might entail several things. Assuming that we don’t want the simulation to be turned off (as this would cause us to cease to exist), we should do everything in our power to keep whoever is simulating us interested in the simulation. This might cause us to pursue actions that are more likely to cause very dramatic events to happen. Also, if we believe that our simulators are willing to punish/reward people for certain behavior within the simulation, we should try to figure out what behavior they are going to reward and act on that. Thus, knowing that we are very probably living in a computer simulation should have a profound effect on the way we lead our lives.

Clearly, this argument has some real implications about how we should view our world and the future of our species, as well as implications about how we should live our lives, if we are forced to accept that we are living in a simulation. With all of this at stake, we have a lot invested in the validity of this argument. Before simply accepting it, it would be worthwhile to take a closer look at the formal probabilistic analysis that Bostrom asserts. I intend to argue here that Bostrom miscalculates the expected fraction of simulated people by ignoring the prior probabilities that are to be placed on the existence of such people.

The expectation of the number of simulated people is taken to be the number of simulations that are run (assuming that they *are* run) times the number of people in each simulation (again, assuming that these simulations are run) times the probability that these simulations are run. Bostrom asserts that this expectation is given by the formula: [1-P(DOOM)]*N*H, where [1-P(DOOM)] is the probability that our civlization (or one like ours) achieves the ability to run simulations, N is the average number of simulations that would be run by such a civilization, and H is the average number of individuals that would live in such a simulation. However, obviously we cannot count individuals from simulations that we ourselves run, because these simulated individuals don’t contribute to the possibility that we are in a simulated universe, since we know for sure that we are not them, since we created them. In fact, that only simulated individuals that can contribute the probability that we are living in a simulated universe are individuals that we haven’t (and will not) create. In other words, only individuals that aren’t *from* our universe or from universes that we might eventually simulate can be counted, as these are the only individuals for which the principle of indifference holds.

This is important because it changes the expectation of simulated individuals that Bostrom is trying to calculate. The probability that at least one civilization reaches the ability to run simulations is equal to the probability that a civilization with the potential to reach such an ability exists times the probability that that civilization actually manages to reach the ability. This would be expressed as P(W)*[1-P(DOOM)], where W stands for the proposition that a world exists in which a civilization as the potential for achieving the ability to run ancestor simulations. Before, it was okay to assume that P(W)=1, because we know that at least one world (our own) exists with the possibility of running simulations someday. This allowed us to reduce the expectation of simulated people to [1-P(DOOM)]*N*H. However, because we can’t count our world towards the expectation of simulated people if we want to maintain the principle of indifference, the proposition W must become the proposition that a world *other than our own* exists in which a civilization has the potential for achieving the ability to run simulations.

Thus, the expectation of the number of simulated people becomes P(W)[1-P(DOOM | W)]*N*H. But, it is clear that the probability P(W) is simply the prior probability that we place on the existence of a world other than our own. If this probability is taken to be very small, then the conclusion of the simulation argument doesn’t follow, and we cannot conclude that it is probable that we are living in a computer simulation.

I have attempted here to provide a critique of the simulation argument by showing that the expectation that he assigns to the number of simulated people is not independent of the prior probability of the existence of other worlds. This does not prove that we are *not* living in a simulated universe. It simply shows that the probability that we assign to our living in a simulated universe is not independent of the prior probability that we assign to the existence of universes other than our own. Depending on the prior probability that we assign to this proposition, it is possible to deny the conjunction of the denials of the following three propositions: 1) The probability that humanity will go extinct before reaching a posthuman stage is very close to unity; 2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero; 3) The probability that we are living in a simulation is very close to unity.

References

N. Bostrom, Are you living in a computer simulation?, Philosophical Quarterly 57(211): 243-255 (2003), http://www.simulation-argument.com

Bostrom actually divides the former situation into two separate possibilities: the possibility that we never achieve the ability to run simulations and the possibility that although we achieve the ability to run them, we don’t actually end up running them. This distinction isn’t important for the purposes of this paper, and so will be ignored.