I've posted about this once before, but here's a more developed version of the idea. Does this pose a serious problem for the simulation hypothesis, or does it merely complicate the idea?
1. Which room am I in?
Imagine two rooms, A and B. At a timeslice t2, there are exactly 1000 people in room B and only 1 person in room A. Neither room contains any clues as to which it is; i.e., no one can see anyone else in room B. If you were placed in one of these rooms with only the information above, which would you guess that you were in? The correct answer appears to be room B. After all, if everyone were to bet that they are in room B, almost everyone would win, whereas if everyone were to bet that they are in room A, almost everyone would lose.
Now imagine that you are told that during a time segment t1 to t2, a total of 100 trillion people had sojourned in room A and only 1 billion in room B. How does this extra information influence your response? The question posed above is not which room you are likely to have been in, all things considered, but which room you are currently in at t2. Insofar as betting odds guide rational belief, it still follows that if everyone at t2 were to bet that they are in room A, almost everyone would lose. This differs from what appears to be the correct conclusion if one reasons across time, from t1 to t2. Thus, we can imagine that at some future moment t3 everyone who ever sojourned in either room A or B is herded into another room C and then asked whether their journeys from t1 to t3 took them through room A or B. In this case, most people would win the bet if they were to point at room A rather than room B.
Let’s complicate this situation. Since more people in total pass through room A than room B, imagine that people are swapped in and out of room A faster than room B. Once in either room, a blindfold is removed and the occupant is asked which room they are in. After they answer, the blindfold is put back on. Thus, there are more total instances of removing blindfolds in room A than room B between t1 and t2. Should this fact change your mind about where you are at exactly t2? Surely one could argue that the directly relevant information is that pertaining to each individual timeslice, rather than the historical details of occupants being swapped in and out of rooms. After all, the bet is being made at a particular timeslice about a particular timeslice, and the fact is that most people who bet at t2 that they are in room B at t2 will win some cash, whereas those who bet that they are in room A will lose.
2. The simulation argument
Nick Bostrom (2003) argues that at least one of the following disjuncts is true: (1) civilizations like ours tend to self-destruct before reaching technological maturity, (2) civilizations like ours tend to reach technological maturity but refrain from running a large number of ancestral simulations, or (3) we are almost certainly in a simulation. The third disjunct corresponds to the “simulation hypothesis.” It is based on the following premises: first, assume the truth of functionalism, i.e., that physical systems that exhibit the right functional organization will give rise to conscious mental states like ours. Second, consider the computational power that could be available to future humans. Bostrom provides a convincing analysis that future humans will have at least the capacity to run a large number of ancestral simulations—or, more generally, simulations in which minds sufficiently “like ours” exist.
The final step of the argument proceeds as follows: if (1) and (2) are false, then we do not self-destruct before reaching a state of technological maturity and do not refrain from running a large number of ancestral simulations. It follows that we run a large number of ancestral simulations. If so, we have no independent knowledge of whether we exist in vivo or in machina. A “bland” version of the principle of indifference thus tells us to distribute our probabilities equally among all the possibilities. Since the number of sims would far exceed the number of non-sims in this scenario, we should infer that we are almost certainly simulated. As Bostrom writes, “it may also be worth to ponder that if everybody were to place a bet on whether they are in a simulation or not, then if people use the bland principle of indifference, and consequently place their money on being in a simulation if they know that that’s where almost all people are, then almost everyone will win their bets. If they bet on not being in a simulation, then almost everyone will lose. It seems better that the bland indifference principle be heeded” (Bostrom 2003).
Now, let us superimpose the scenario of Section 1 onto the simulation argument. Imagine that our posthuman descendants colonize the galaxy and their population grows to 100 billion individuals in total. Imagine further that at t2 they are running 100 trillion simulations, each of which contains 100 billion individuals. Thus, the total number of sims equals 10^25. If one of our posthuman descendants were asked whether she is a sim or non-sim, she should therefore answer that she is almost certainly a sim. Alternatively, imagine that at t2 our posthuman descendants decide to run only a single simulation in the universe that contains a mere 1 billion sims, ceteris paribus. Given this situation: if one of our posthuman descendants were asked whether she is a sim given this information, she should quite clearly answer that she is most likely a non-sim.
With this in mind, consider a final possible scenario: our posthuman descendants decide to run simulations with relatively small populations in a serial fashion, that is, one at a time. These simulations could be sped up a million times to enable complete recapitulations of our evolutionary history (as per Bostrom). The result is that at any given timeslice the total number of non-sims will far exceed the total number of sims—yet across time the total number of sims will accumulate and eventually far exceed the total number of non-sims. The result is that if one takes a bird’s-eye view of our posthuman civilization from its inception to its decline (say, because of the entropy death of the cosmos), and if one were asked whether she is more likely to have existed in vivo or in machina, it appears that she should answer “I was a sim.”
But this might not be the right way to reason about the situation. Consider that history is nothing more than a series of timeslices, one after the other. Since the ratio of non-sims to sims favors the former at every possible timeslice, one might argue that one should always answer the question, “Are you right now more likely to exist in vivo or in machina?” with “I probably exist in vivo.” Again, the difficulty that skeptics of this answer must overcome is the ostensible fact that if everyone were to bet on being simulated at any given timeslice—even billions of years after the first serial simulation is run—then nearly everyone would lose, whereas if everyone were to bet that they are a non-sim, then almost everyone would win.
The tension here emerges from the difference between timeslice reasoning and the sort of “atemporal” reasoning that Bostrom employs. If the former is epistemically robust, then Bostrom’s tripartite argument fails because none of the disjuncts are true. This is because the scenario above entails (a) we survive to reach technological maturity, and (b) we run a large number of ancestor simulations, yet (c) we do not have reason to believe that we are in a simulation at any particular moment. The latter proposition depends, of course, upon how we run the simulations (serially versus in parallel) and, relatedly, how we decide to reason about our metaphysical status at each moment in time.
In conclusion, I am unsure about whether this constitutes a refutation of Bostrom or merely complicates the picture. At the very least, I believe it does the latter, requiring more work on the topic.
Bostrom, Nick. 2003. Are You Living in a Computer Simulation? Philosophical Quarterly. 53(211): 243-255.