Philosopher Nick Bostrom investigated the possibility that we may be living in a simulation. A simplified version of his argument proceeds as such:
i. It is possible that a civilization could create a computer simulation which contains individuals with artificial intelligence.
ii. Such a civilization would likely run many—say billions—of these simulations (just for fun; for research, etc.)
iii. A simulated individual inside the simulation wouldn’t necessarily know that it’s inside a simulation—it’s just going about its daily business in what it considers to be the "real world."
Then the ultimate question is—if one accepts that these 1, 2, and 3 are at least possible— which of the following is more likely?
a. We are the one civilization which develops AI simulations and happens not to be in one itself? Or,
b. We are one of the many (billions) of simulations that has run? (Remember point iii.)
c. We could both be the simulation, and create our own set of simulation.
In greater detail, his argument attempts to prove the trichotomy, that:
either
1. intelligent races will never reach a level of technology where they can run simulations of reality so detailed they can be mistaken for reality (or this is impossible in principle); or
2. races who do reach such a level do not tend to run such simulations; or
3. we are almost certainly living in such a simulation.
Bostrom's argument uses the premise that given sufficiently advanced technology, it is possible to simulate entire inhabited planets or even larger habitats or even entire universes as quantum simulations in time/space pockets, including all the people on them, on a computer, and that simulated people can be fully conscious, and are as much persons as non-simulated people.
A particular case provided in the original paper poses the scenario where we assume that the human race could reach such a technological level without destroying themselves in the process (i.e. we deny the first hypothesis); and that once we reached such a level we would still be interested in history, the past, and our ancestors, and that there would be no legal or moral strictures on running such simulations (we deny the second hypothesis)—then
* it is likely that we would run a very large number of so-called ancestor simulations to study our past;
* and that, by the same line of reasoning, many of these simulations would in turn run other sub-simulations, and so on;
* and that given the fact that right now it is impossible to tell whether we are living in one of the vast number of simulations or the original ancestor universe, the likelihood is that the former is true.
Assumptions as to whether the human race (or another intelligent species) could reach such a technological level without destroying themselves depend greatly on the value of the Drake equation, which gives the number of intelligent technological species communicating via radio in a galaxy at any given point in time. The expanded equation looks to the number of posthuman civilizations that ever would exist in any given universe. If the average for all universes, real or simulated, is greater than or equal to one such civilization existing in each universe's entire history, then odds are rather overwhelmingly in favor of the proposition that the average civilization is in a simulation, assuming that such simulated universes are possible and such civilizations would want to run such simulations.
You never know...