It's not actually a true statement to say that "if recursively-simulated universes are possible it becomes vanishingly unlikely that we do not live in one."
Yes, I've read Bostrom's paper[0], but he misses a key point: the number of rational beings in each simulated universe may decrease exponentially. If, on average over all universes, each rational being simulates only 0.5 rational beings during his or her lifetime, the total number of simulated rational beings would be exactly equal to the total number of unsimulated rational beings, making it equally plausible that we are in the root universe or one of the simulations.
The possibility that rational beings diminish in number exponentially as universes are simulated seems not only plausible, but likely given the nature of the simulations necessary to replicate our universe in all its detail.
I think it might be heading down the wrong path to talk in terms of "rational beings" as atomic units rather than in terms of energy (or rather information) balance.
Remember that you do live in a simulation of the universe so compressed it fits between your ears, and it does contain many simulations of other rational actors. They're nowhere near as complex as your whole universe, but I bet they're complex enough to know that they're complex enough.
I don't see how this philosophical argument is going to change anything. Each human has a rather small finite number of 'rational beings' they can handle processing at once. It doesn't recurse very well, the limit is a total. The exponential argument against simulation is unaffected.
"The glitch arises from the possibility that the average number of people living in the preposthuman phase might be different in civilizations that produce ancestor simulations than in civilizations that do not."
No, that's not the problem. The simulation argument essentially depends on the fact that a universe that reaches simulation-capability ends up simulating more rational beings than half of the beings that exist in the universe itself. But it's possible that the simulations themselves are so limited that they can only simulate some fraction of the universes' number of rational beings. In fact, that seems likely: it seems that any simulation of this universe which obeys the same laws as this universe must be smaller than this universe. "How much smaller?" is the glitch. The simulated universes have to be sufficiently large (as measured by the number of rational minds they ultimately simulate) to exceed an average of 0.5 simulated minds per real mind in order for the simulation argument to hold.
Exactly. To draw a computing analogy, in order for it to work we'd have to be able to make virtual machines that outperform the machines they're running on, and recursively. In order for it to work, each simulated universe would have to progress to the point we have in ours, and also be able to simulate getting to this point much faster than it took to get there itself. It quickly starts to sound like perfect compression or perpetual motion.
Yes, I've read Bostrom's paper[0], but he misses a key point: the number of rational beings in each simulated universe may decrease exponentially. If, on average over all universes, each rational being simulates only 0.5 rational beings during his or her lifetime, the total number of simulated rational beings would be exactly equal to the total number of unsimulated rational beings, making it equally plausible that we are in the root universe or one of the simulations.
The possibility that rational beings diminish in number exponentially as universes are simulated seems not only plausible, but likely given the nature of the simulations necessary to replicate our universe in all its detail.
[0] http://www.simulation-argument.com/simulation.html