Buadrillard, Eco et alia have developed Jorge Luis Borges' idea of "the Map of the Empire which perfectly co-incided with the Empire itself" into The Philosophy of Simulation. As hard-headed "realists" we assume that we have an intuitive grasp of where reality stops and simulation begins. The cartographer who constructed the great Map of the Empire presumably knew that the Empire itself was real. Or did he? Could such an assumption be philosophically warranted?
According to Nick Bostrom, and others, the strong likelihood is that we are living in a computer simulation.
The logic is as follows: At least one of these propositions is true: (1) The chances that a species at our current level of development can avoid going extinct before becoming technologically mature is negligibly small. (2) Almost no technologically mature civilisations are interested in running computer simulations of minds like ours. (3) You are almost certainly in a simulation. Each of these propositions seems prima facie implausible but let's work through them logically: If proposition (1) is false (there may be some highly dangerous technological development which sufficiently advanced civilisations inevitably develop which then destroys them, but let's, optimistically, assume this isn't so) then we, and/or other human or alien civilisation(s), have a good chance of reaching technological maturity. It then seems most unlikely that, with the corresponding exponential growth of computer processing power, that we/they are not going to harness a fraction of their technological resources to exploring the possibility of simulating human minds within the context of greater simulated or virtual realities. If we reject propositions (1) and (2) then it is logically inconsistent to reject proposition (3) since such an advanced civilisation could reasonably be expected to generate an astronomical number of simulated minds and these would, inevitably, far outnumber the non-simulated or "real" minds powered by organic brains. We, and the world we live in, are therefore (if we accept the logic) almost certainly part of a simulation.
This theory dovetails nicely with the subject of time travel. The most likely way for future generations to "visit the past" would be, I'd suggest, for them to visit a computer-generated simulation/virtual reality. If we follow Bostrom's logic, even if, as is currently thought likely, a technologically mature civilisation is incapable of harnessing enough energy to "really" travel in time it would probably have the capacity to generate an almost infinite number of exact replicas of the past. It is very, therefore, likely that we are currently "living" in just such an "ancestor simulation".
The controversial aspect of the Nick Bostrom's argument relates to the assumption of "substrate-independence" i.e. It is not an essential property of consciousness that it is implemented on carbon-based biological neural networks inside a cranium: silicon-based processors inside a computer could in principle do the trick as well. If we accept the proposition that advanced computers are likely to be capable of simulating a human mind then the logic appears sound. If we accept that technologically mature civilisations are likely to be capable of replicating the functionality of organic brain tissue in silico then it seems inconcievable that they should choose not to devote a fraction of their technological resources to this very task and thus reach, what could be referred to as, a "posthuman" stage of development. If we also assume that technological development is not likely to be constrained by the extinction of the species then the conclusion that posthuman civilizations would have enough computing power to run hugely many ancestor-simulations even while using only a tiny fraction of their resources for that purpose is philosophically warranted.
Bostrom's logic is quite simple: The refutation of the first two, prima facie implausible, propositions, the above caveat notwithstanding, clearly warrants acceptance of the third. If either, or both, of the first two propositions are true then the third proposition is clearly false. If you accept that the first two propositions are probably false, as do I, the high likelihood is, the "substrate-independence" assumption notwithstanding, that we are indeed "living in a simulation" (hence the "almost certainly" caveat).
Having refuted the first two propositions, one reason why we might not be living in a simulation could, of course, be that we are the original civilisation approaching technological maturity but, if we accept the proposition that technologically mature civilisations would be capable of and predisposed towards running ancestor-simulations then the high likelihood is that we are not the original civilisation but rather a replicated civilisation residing in a simulation rather than the "real" world.
Indeed the simulation theory leads inevitably to the conclusion that those who created the simulation we inhabit are themselves part of a simulation devised by an even older, more technologically sophisticated race. Simulations generated by, and within, simulations are not only foreseeable but inevitable if the simulated civilisations are to "authentically" replicate the original civilisation.
What really interests me, however, is even if we could determine that we were living in a simulation would we act any differently? Would we be liberated from all moral and ethical constraints or would pragmatic consequentialism (adherence to the simulation's internal rules of reward and punishment) lead us to act in much the same way? Would liberation from the prospect of punishment in the afterlife (for the God, or Devil, fearing amongst us) prompt us to adopt a pragmatic strategy such as "everything is permitted provided you don't get caught"? Probably not. Presumably any "omniscient", "omnipotent" (or merely sadistic) simulation programmer would have thought of constructing another level to the simulation? Your fate in that "afterlife", or "aftersim", could well depend on how you behaved in your present simulated incarnation. Even if we were living in a simulation, the best way to predict what would happen next in our simulation would be the ordinary methods – extrapolation of past trends, scientific modelling, common sense and so on. If you thought you were in a simulation, you should, probably, get on with your life in much the same way as if you were convinced that you are living a non-simulated life.