No longer relegated to the domain of science fiction or the ravings of street corner lunatics, the "simulation argument" has increasingly become a serious theory amongst academics, one that has been best articulated by philosopher Nick Bostrom.
In his seminal paper "Are You Living in a Computer Simulation?" Bostrom applies the assumption of substrate-independence, the idea that mental states can reside on multiple types of physical substrates, including the digital realm. He speculates that a computer running a suitable program could in fact be conscious. He also argues that future civilizations will very likely be able to pull off this trick and that many of the technologies required to do so have already been shown to be compatible with known physical laws and engineering constraints.
Harnessing computational power
Similar to futurists Ray Kurzweil and Vernor Vinge, Bostrom believes that enormous amounts of computing power will be available in the future. Moore's Law, which describes an eerily regular exponential increase in processing power, is showing no signs of waning, nor is it obvious that it ever will.
To build these kinds of simulations, a posthuman civilization would have to embark upon computational megaprojects. As Bostrom notes, determining an upper bound for computational power is difficult, but a number of thinkers have given it a shot. Eric Drexler has outlined a design for a system the size of a sugar cube that would perform 10^21 instructions per second. Robert Bradbury gives a rough estimate of 10^42 operations per second for a computer with a mass on order of a large planet. Seth Lloyd calculates an upper bound for a 1 kg computer of 5*10^50 logical operations per second carried out on ~10^31 bits – this would likely be done on a quantum computer or computers built of out of nuclear matter or plasma [check out this article and this article for more information].
More radically, John Barrow has demonstrated that, under a very strict set of cosmological conditions, indefinite information processing (pdf) can exist in an ever-expanding universe.
At any rate, this extreme level of computational power is astounding and it defies human comprehension. It’s like imagining a universe within a universe -- and that's precisely be how it may be used.
Worlds within worlds
"Let us suppose for a moment that these predictions are correct," writes Bostrom. "One thing that later generations might do with their super-powerful computers is run detailed simulations of their forebears or of people like their forebears." And because their computers would be so powerful, notes Bostrom, they could run many such simulations.
This observation, that there could be many simulations, led Bostrom to a fascinating conclusion. It's conceivable, he argues, that the vast majority of minds like ours do not belong to the original species but rather to people simulated by the advanced descendants of the original species. If this were the case, "we would be rational to think that we are likely among the simulated minds rather than among the original biological ones."
Moreover, there is also the possibility that simulated civilizations may become posthuman themselves. Bostrom writes,
They may then run their own ancestor-simulations on powerful computers they build in their simulated universe. Such computers would be “virtual machines”, a familiar concept in computer science. (Java script web-applets, for instance, run on a virtual machine – a simulated computer – inside your desktop.) Virtual machines can be stacked: it’s possible to simulate a machine simulating another machine, and so on, in arbitrarily many steps of iteration...we would have to suspect that the posthumans running our simulation are themselves simulated beings; and their creators, in turn, may also be simulated beings.Given this matrioshkan possibility, the number of "real" minds across all existence should be vastly outnumbered by simulated minds. The suggestion that we're not living in a simulation must therefore address the apparent gross improbabilities in question.
Again, all this presupposes, of course, that civilizations are capable of surviving to the point where it's possible to run simulations of forebears and that our descendants desire to do so. But as noted above, there doesn't seem to be any reason to preclude such a technological feat.
Next: Kurzweil's nano neural nets.