Explaining the Termination Risk of Simulation Technologies

Question

There is a recent article in Erkenntnis that discusses termination risks related to the simulation hypothesis [1]. That is, if we are living in a computer simulation, are there risks that might suddenly cause the simulation to end? The author proposes that there are risks:

The problem with this reasoning is that any computation performed in a simulation must ultimately be supported by computation on the basement level. The computing constraints and the objectives of the simulators on the basement level, therefore, put a limit on the amount of nesting that can occur.8 It is partly for this reason that ancestor simulations entail a termination risk to those that create them. A similar risk is mentioned by Bostrom (2003b, 253), who writes:

One consideration that counts against the multi-level hypothesis is that the computational cost for the basement-level simulators would be very great. Simulating even a single posthuman civilization might be prohibitively expensive. If so, then we should expect our simulation to be terminated when we are about to become posthuman.

I don't understand how a simulation is limited on the nesting that can occur, and therefore the conclusion that there is a termination risk does not follow.

For instance, my thought is that if the universe is already "exactly" simulated ("outside" of our time), then re-arranging components (building a computer, etc) inside the simulation to create a sub-simulation doesn't change anything in terms of resources used.

Question: How is it possible that there is a limit on the amount of nesting that can occur inside the simulation (the simulation of "the simulation hypothesis")?

[1] Greene, Preston. "The Termination Risks of Simulation Science." Erkenntnis, online https://link.springer.com/article/10.1007/s10670-018-0037-1

Answer 1

For instance, my thought is that if the universe is already "exactly" simulated

Not all simulation hypotheses consist of exact simulations. Many posit that the simulations is limited to only enough of the universe for the simulation to appear complete to the inhabitants of the simulation. So, for instance, if we are in a simulation, perhaps other galaxies are not simulated down to individual stars. If we were to create a posthuman civilization that colonizes other galaxies, then perhaps the simulation would then have to simulate individuals stars in other galaxies, requiring vastly more computing power.

Answer 2

Hmm, I think I see your intuition. If the basement-level simulation computer is already fully simulating a part of the virtual earth that houses a virtual simulation computer, then how could nesting occurring in that virtual computer increase the complexity of the computation for the basement-level computer? After all, the basement-level computer is already simulating all the atoms in that region, and nesting entails just moving them around! Do I have your view right?

At the same time, at the beginning of Section 3.1 the paper appeals to the claim that you cannot use your computer to fully simulate the operations of your computer. We could add, a fortiori, that you cannot use your computer to simultaneously fully simulate the operations of two computers of the same complexity as your computer. Does that seem right? If it is right, then perhaps the answer is that a basement-level computer is simply unable to "fully" simulate a region of the virtual earth that contains a bunch of computers (some "nested") that are of similar complexity to itself.

At the least, it seems there's some tension between these two intuitions that needs to be worked out somehow.