Reference no: EM133626158

The principle of indifference states that when we lack adequate data or reasons for accepting one option over any other, then all options have an equal prior probability. So, given two options A and B, if we have no more reason to accept A than to accept B, then P(A) = .50 and P(B) = .50, assuming that these options are jointly exhaustive.

Now, what is the probability that we live in a Matrix-like simulation rather than in a base reality-meaning a reality that is not simulated? Until recently, we've had no evidence to incline us either way on this question. So, the principle of indifference tells us that P(simulation)=.50. However, we must now consider the evidence of recent developments.

• Advances in computer gaming simulations and AI over the last 20 years make it almost certain that humans are capable of creating totally realistic and immersive simulations as well as conscious AIs before going extinct. Furthermore,
• it is also very probable that those humans would make a simulation of their ancestral past, including a past in which they are on the verge of creating immersive simulations and conscious AIs, a past like our present. Moreover,
• if humans have created one simulation, then it is almost certain that the humans in that simulation would create simulations of their 'reality' in which those humans would in turn create simulations and so on.

So, given that humans are able to create one simulation, it is almost certain that there are billions of simulations. It seems, then, that Elon Musk was right when he asserted, "There's a billion to one chance we're living in base reality," meaning that the probability that we live in a base reality, rather than in one of the billion or so simulations, is 1 in 1 billion. But is Musk right?

Let's symbolize the new evidence expressed in propositions 1-3 with the letter E and the hypothesis that we live in a simulation with the letter S. Now, that we would live in a base world in which E is the case would be highly unlikely on the assumption that we do not live in a simulation, but let's propose the modest estimate of P(E | ~S)=.10. On the other hand, E would not be surprising at all if we lived in a simulation, so let's say P(E | S)=.90. Based upon these modest estimates and using Bayes' Theorem, what is the probability that we live in a simulation given evidence E? In other words, what is P(S | E)? How strong is this argument? Is it cogent?