What happens to the simulation argument if the universe is infinite?
This is an interesting issue, which is deliberately set aside in the original paper. Certainly some modifications are necessary once we admit the possibility of an infinite universe that may contain infinitely many simulated and non-simulated people. In this case, the ratio of simulated people to the total number of people is not defined. To deal with these infinite cases, we need to do something like thinking in terms of densities rather than total populations. A suitable density-measure can be finite even if the total population is infinite. It is important to note that we to use some kind of density-measure of observation types quite independently of the simulation argument. In a “Big World” cosmology, all possible human observations are in fact made by somebody somewhere. (Our world is may well be a big world, so this is not a farfetched possibility.). To be able to derive any observational consequences from our scientific theories in a Big World, we need to be able to say that cer
