My new paper on historical simulations has finally appeared in print in the August issue of the Journal of Futures Studies. George Dvorsky has posted some comments about it on Sentient Developments, where it spawned an interesting little thread on the stacked simulation issue, (simulations within simulations) involving Robert Bradbury and others. George quoted an earlier passage (written prior to my paper) from Bradbury stating that simulated realities will run slower than the host reality, therefore allowing at least "trillions of trillions of trillions" of simulations and therefore the universe is unlikely to run out of computing power due to stacked simulations.
This quote from Bradbury also indicated that if we live in a simulation, then we cannot extrapolate the size of the host or "basement" universe from examining the size of the simulated universe that we inhabit, since future societies might simulate "weird" universes with different physical laws and dimensions than the real one they occupy. George thus concludes that it is arbitrary and unfounded to conclude that our simulation will terminate around 2050 when we start on a widespread basis to create historical simulations of our own. There are several problems with George's concerns:
1) He ignores the point in the paper that there is another reason for the simulation to be unplugged when it reaches 2050, i.e. that a simulation depicting a period after that date would lose the element of deception of its inhabitants necessary to produce genuine behavior for observational and experimental purposes. Robert Bradbury's comments in the thread discussing my paper even concede that it is possible that we could be in a simulation designed "to study evolutionary paths of advanced civilizations up to the point where they begin to simulate the evolutionary paths of advanced civilizations" in which case we may be indefinitely "suspended" (nice euphemism for "terminated") at that point.
2) George's quote states that due to the simulations running much more slowly than the host reality, the universe would be capable of at least "trillions of trillions of trillions of simulations". However, this is merely 1036 simulations, which still doesn't come anywhere close to the 1096simulations that would be produced after only 16 generations of stacking starting with an initial one million simulations.
World of Warcraft currently has at least 6 million subscribers, so it is easy to project a starting point of at least 1 million fully realistic simulated worlds by 2050. In any event, Robert concedes in his comments that if the hardware is intentionally engineered to facilitate simulations, (e.g. a nanotechnology or femtotechnology graphics card!) it will run at close to the speeds of the reality being simulated. Presumably if a future society wants to create simulations, then it will dedicate special technology to the task and won't use a generic form of hardware. Robert also notes in his comments that the simulation could develop abstractions (shortcuts or heuristics) that would enable computational speedups which exceed the reduction in speed inherent in the simulation.
3) In his comments on the paper, Robert also notes that there is the issue of whether the abstractions or shortcuts developed in the simulation can be translated back into the reality that produced the simulation. If the rules in the simulation are vastly different, (e.g. the "weird universe"), then extracting the inventions of the simulation may be impossible. Robert then wonders whether the "gods" would intentionally design simulations from which extraction is difficult or impossible. I think that the answer to this question must be in the negative. If a future society goes to the trouble of creating a historical simulation, it must be for the purpose of extracting information from it. If we are in a simulation now (which we probably are), then it is likely not a depiction of a "weird" universe that is fundamentally different from that of the host reality. We can therefore extrapolate from observing the simulated universe that we inhabit what the total computational power of the host universe is likely to be.
I am looking forward to further comments. The stacked simulation problem, which was only a small part of my Historical Simulations paper, could easily justify a paper of its own.