Simulation does not imply infinite regress
As we develop powerful technologies like Augmented/Virtual Reality, we seem to be getting closer to a time where we might be able to create virtual worlds of our own, with a much greater fidelity than you might find in a game such as Minecraft.
The mere fact that such a future now seems within our grasp gives some motivation to consider Nick Bostrom’s simulation argument from 2003. The argument itself does not merely claim that we are in a simulation, but states that we should accept one of the following propositions as true:
- The chances that a species at our current level of development can avoid going extinct before becoming technologically mature is negligibly small
- Almost no technologically mature civilisations are interested in running computer simulations of minds like ours
- You are almost certainly in a simulation.
I do not intend to develop and defend the simulation argument itself, but to consider a particular consequence of accepting it. Because the simulation argument does not tell us which of the three statements above is true — merely that one of them is — we might assign different credences to the three statements.
I will focus on the third prong: the possibility that we are in a simulation. In his paper “Theological Implications of the Simulation Argument,” Eric Steinhart re-imagines some classic philosophical arguments for the existence of God in light of Bostrom’s argument.
In particular, Steinhart looks to the consequences of iterating the Simulation Argument. If we are in a simulation, then there might be some other population, “one level up” from ours, who is simulating us. Given that this (presumably technologically mature) civilization is not only interested in running a computer simulation of another civilization but is actually doing so, Bostrom’s argument would press that civilization to consider the fact that they themselves might be simulated by another civilization, one more level up.
And so on to infinity: to Steinhart, “The Simulation Argument supports the general thesis that below every level, there is a deeper level. There is an endless series of ever deeper levels.”
Steinhart formalizes this a bit: there is an “initial” universe U_0, our universe, which has level-0 computers. Our universe is a software process running on some level-1 computer, existing in the universe U_1 one level up from ours. This argument extends inductively.
Steinhart’s thesis is interesting when we examine the implications when the third prong of the Simulation Argument holds. If we subscribe to a more probabilistic interpretation of the Argument, i.e. that there is some (possibly very high) probability that we are in a simulation (we might even read almost certainly as merely indicating a high probability and not certainty, meaning that Steinhart actually takes the statement further), then the iteration debate becomes something different entirely.
Infinite regresses are a frequently considered problem in metaphysics: if everything has a cause, then where do those causes bottom out? Is it turtles all the way down? Does an infinite regress, a chain of causes with no terminus, even make sense as a picture of reality? Philosophers have tried to develop ways of terminating the regress, where it bottoms out in some “uncaused mover” like God — an infinite regress does, indeed, seem to be an unsatisfying picture of reality.
When reading Steinhart’s paper and the Simulation Argument, my friend Matthew raised the concern of infinite regress as a possible implication of taking the third prong of the argument seriously. If we think there is an extremely high probability we are in a simulation in our universe U_0, then by the same sort of argument the civilization in U_1 should think the same, and so on to infinity.
I am not so concerned that we encounter the infinite regress problem if we are working with the probabilistic interpretation of Bostrom’s argument, the statement that “there is an extremely high probability that we are in a simulation.” I am not making the claim that there is certainly a termination point, but that under this version of the statement, the interlocutor claiming there might be an infinite regress actually has a burden of proof, and that this burden is — at least probabilistically — more difficult than that of the opposition.
To illustrate, let’s refine the statement “there is an extremely high probability that we are in a simulation” to use a specific number: say, “there is a 99.99% probability that we are in a simulation.” If that probability is a constant across all the indexed universes, then for any universe U_n, there is a 99.99% probability that there is another universe, U_{n+1}, that. is simulating U_n.
But if we look at things from our perspective, down here in universe U_0, the probability that there is some universe n levels up is not exactly 99.99%. If there is a 99.99% probability of U_1 simulating us, and in turn a 99.99% probability that there is some U_2 simulating U_1, then the probabilities compound: there is, from our vantage point, a (99.99)²% probability that there is a simulator two levels up from us.
We can extend this inductively: the probability that there is some simulator U_n, n levels up from us, is (99.99)^n%. And you might already see where this is going: in the limit, even starting with a probability of 99.99% that there is a civilization one level up simulating us, the probability of there being yet another civilization eventually vanishes as n increases.
To me, this means that the claim there is an infinite regress, if we take the statement “there is a 99.99% probability we are in a simulation” to be true, needs to defend an occurrence whose probability becomes infinitesimally small as the regress approaches infinity.
One concern I had in thinking about this was whether the issue was symmetric: a 99.99% probability of our being in a simulation means there is a 0.01% probability that we are not in a simulation. But we are speaking of probabilities here: anywhere along the chain of universes U_n, that 0.01% probability could be realized and there are no further universes to consider. Wherever the termination point occurs, say at universe U_k, the probability does not vanish because k is finite: our probability of a termination point at universe U_k is [(99.99)^{k-1}*(0.01)]%.
I haven’t made a claim that there is a certainty of no infinite regress if we take seriously the third statement in the Simulation Argument, but simply wanted to consider how the possibility of an infinite regress holds up. It might be that my statement about iterated probabilities doesn’t actually make sense in the context of this regress, and I haven’t fully worked that out here. In any case, the problem of metaphysical regress in the light of the Simulation Argument is an interesting one to consider.