Is it possible for an infinitely nested simulation to exist?

Question

Is it possible for an infinitely nested simulation to exist? Such a scenario is impossible to imagine explicitly, and the scenario itself may seem like it is logically incoherent, but I am unable to find a clear contradiction in the concept itself. Another question I want to ask is: is it possible for a possible world to contain just an infinitely nested simulation? Call this (A).

Suppose the reality we are in right now is a simulation, and this simulation is inside another simulation and so on, ad infinitum. This is what I mean by an infinitely nested simulation. More simplistically I can "imagine" a square that is enclosed within a larger square, which is enclosed in an even larger square, and so on, ad infinitum. This is easier than trying to imagine an infinitely nested simulation, and both concepts are similar enough, so thinking about this scenario may give us more insight into whether the infinitely nested simulation is logically coherent.

It appears to me that the answer to the first question is yes, but what about the second one?

Answer 1

Suppose the reality we are in right now is a simulation, and this simulation is inside another simulation and so on, ad infinitum.

For a simulation to exist, there has to be a first simulation to exist. One that's based in a true, non-simulated, material reality. A simulation can't exist without a first material reality somewhere in the row. There has to be a first turtle on the bottom of the pile of turtles so to speak. If not, then every simulation is an empty one without reference to a real material world.
So there exists no infinitely nested simulation of realities. That is unbounded on both sides.

It's even the question if such a Matrix-like simulation can be achieved in reality. But if it can be achieved in the philosophical mind of ours, then a first simulation has to exist somewhere in the nested simulations. It's the outer one that's based in a material world.
How can I know? How will I ever be certain that there is one? How can I know that not every simulation has a simulation at its base? Well, if this not were the case then there is no way that every simulation has properties of a real material world. Every simulation must ultimately have its roots in a physical non-simulated world for the simulation to have features of a physical world.
In an infinite universe, the number of simulations can reach for infinity, but every new simulation has to be smaller than the one below it. The reason is that for a simulation computers are needed and for a computer simulation in a computer simulation there is less computer space available. Even if the universe is infinite, and the simulations are infinite, the n-th simulation must be smaller in extent than the (n-1)-th one. If the world of your n-th simulation is infinite, then still the (n-1)-th simulation is smaller in extent, even if it's infinite in extent. Considerable smaller in extent (take a look at Aleph numbers)

So, to answer your question, infinitely nested simulations are possible (in the philosophical sense, not in reality) but there has to be a first simulation based on a real, material world.

Answer 2

There is no philosophical constraint preventing this universe being a simulation running in another universe. And the same holds for that universe, infinitely.

Or in other words, if we could escape this simulation and peek into the world of the simulator, we could never know whether we see the "top" simulator or just yet another simulated world.

For that we do not even need to use simulations, we can just think of containment. Philosophically speaking, our while universe could just be some kind of paperweight on the desk of a god in their universe. And that Universe could in turn also just be contained in some larger universe.

If we assume that in every world there is any cost and time overhead to run a simulation (the simulated world runs slower than the containing world), then it becomes near impossible for this universe to be both infinitely nested and having time passing. Because computing the next state would require ever more time in some containing universe. Or otherwise said, for time to pass in this universe, FIRST time needs to pass in the containing universe, and so on, so nothing could ever move. Since we can observe time passing, we can know that either we are not infinitely nested, or our assumption about simulators is wrong for our "parent" simulators.

However, philosophically, we do not need to stick to the assumption that a simulator in a containing world would look like a simulator that we could design in our world.

Quite possibly in our world, it is not possible to build a simulator that can practically simulate infinitely nested simulations and keep time passing in all infinitely many of them (at least not with technology that we can currently imagine). But even if in our world it was impossible to simulated in infinitely nested way, this property of our world does not necessarily hold for our containing universe, so we cannot simply derive that infinite containment is impossible.

Similarly, if we stretch our definition of "world" so far, we can imagine that while in our world it might be impossible to build a simulator that contains infinitely nested simulations, the same is not true for our parent world, so infinity is philosophically possible in both directions, but for practical purposes we can be (reasonably) sure that we cannot have such a powerful simulator in our world that simulates time passing in infinitely many nested worlds. That is also true for trying to simulate infinitely many separate worlds with a simulator (no nesting).

Answer 3

This gets to one of the problems with simulation arguments. They tend, like Bostrom does, to just assume the simulated reality is the same as the reality it is simulated from, like the 'ancestor simulation' idea. In that context, there would be finite energy and finite entropy, so this nesting would not be possible.

But that need not be the case. Any unknowably different reality could be simulating ours, with us having no way to examine or access it. We may be a person dreaming of being a butterfly, or a butterfly dreaming we are a person, to paraphrase Zuangzhi. Or the case where, "some evil genius not less powerful than deceitful, has employed his whole energies in deceiving me", as Descartes put it. These are not in this case simulation argumentd, but scepticism about whether we can know anything. In terms of being useful in philosophy, rather than purely arbitrary speculation, this is pretty much limited to methodological scepticism like Descartes used, where we examine how we know what we take for granted ordinarily that we know.

I want to suggest a slightly different angle on nested realities. Nesting implies one is a subset of a more complete other reality. But there are a number of assumptions, like that the subreality can literally have no access to the supereality, but that implies vice versa the supereality can at most only observe not interact, or such interactions would provide evidence to the subreality about the supereality. So, if there is to-ing and fro-ing, are they really seperate? Can we categorically claim one more and one less 'real'?

There is an ancient Buddhist metaphor, Indra's Net, in which all the minds in the universe are pictured as jewels, each at the intersection point of a net. Each jewel contains the image in reflection of every other jewel. This is the intersubjective picture, replacing the idea of one objective reality, with the summation of interacting subjectivities, interacting and picturing each others perspective.

In a more modern metaphor, this can be described as a Peer2Peer simulation hypothesis. Like the internet, each node in the network connecting to all the other nodes, to share information. In this sense, one 'reality', one subjectivity, may have a more complex and sophisticated model of reality. Another with a simpler reality, like say a small child, might be described as having a reality 'nested' within that of adults and wider society. And such links generation to generation, can go on indefinitely, deepening and complexifying the model of the world, all while constituting aspects of the world to learn about.

Answer 4

In a word, no and no.

Such a thing is not possible physically. The simulations are a countable series, the count following the natural numbers. There is a beginning to the series, which its the first natural number, No. 1. But there is no end to the series, there is no "last natural number". Every simulation corresponds to some natural number N, as the N'th simulation. Since there is no "last" natural number, there can be no last simulation. (This argument is sometimes used by philosophers to debunk infinities of this kind. For example J.W. Dunne's infinite regresses of time and consciousness suffered essentially this argument at the hands of C.D. Broad.)

Here is essentially the same argument looked at in a different way. The first world in the chain must be a genuine physical one, in which the hardware to perform the first simulation exists. All the simulations are contingent on it (switch off the first simulation and all the others are perforce switched off along with it). That is, all the simulations are contingent on a direct relationship to some physical reality. One can of course postulate such a last item in the chain (N = infinity), but it has no constructible link back to physical reality and is therefore pure metaphysics, nothing whatever to do with actual simulations. Since the first simulation has physical hardware, there can thus be no constructible link between the first and last.