Do we live in a simulation or in the base reality?

Elon Musk recently suggested that we likely do not live in a base reality, but in a simulation. He even puts the probability at a billion to one. Is he correct?

First of all, we have to explain what degree of a simulation we are talking about:

1. The universe and everything in it (including our minds) is computational, i.e. something like a computer program.
2. Our universe supervenes on a different (computational) universe, i.e. some other universe contains some kind of computer that runs our universe.
3. Our universe has been deliberately created by some mind in the parent universe.
4. The universe exists for our benefit, i.e. the mind in the parent universe specifically intended to create us in some way, and meant us to experience what is going on.
5. Much in our universe is “smoke and mirrors”, i.e. distant galaxies probably do not exist, because they would be very wasteful.
6. Other people probably do not exist, there is only a single, solipsistic observer (you), and everything else is just a deception. Let us start from the end: of course there is no way in which you can ever make totally sure that you are not a brain in a vat, a Boltzmann brain etc. but there are more or less useful encodings of the observable patterns, i.e. models of the world. I think that Ray Solomonoff had a good idea when he defined the limit of the quality of such a world model, as the shortest function that can best predict the present from the past, for all observed presents and pasts. The model that there are indeed other people like you, and that these people are social primates, and that they originated in an evolution, and that this evolution took place on a planetary surface and feeds off the entropy gradient delivered by the energy of nuclear fusion in the sun radiating out into interstellar space etc. seems to be much better at predicting our observations than the theory that you are just a single solipsistic mind watching a random movie. It is possible that substantial fractions of our observable universe are just “smoke and mirrors”, but it is not plausible that someone would somehow paint the sky with objects convincing enough to fool our telescopes, because being born here, we had no reason to expect to find distant galaxies, and hence no such deception would have been necessary. The same argument applies to the micro-level (and there is much more happening between here and the Planck length than between here and the boundary of the visible universe). If we can observe all these details, then they are most likely crucial parts of our universe. For this reason, I also do not think that (4) is plausible: creating a universe spanning billions of years and octillions of cubic parsecs and a googol particles just to observe the destinies of a bunch of hairless monkeys over a few millennia seems to be crazy uneconomical. Thus, if the universe is a simulation, then we are most likely an unintended byproduct. If we are indeed not the center of the universe, then a very large universe that has been created for a purpose (3) will look pretty much indistinguishable from a universe that has not been intentionally created (2), but we might come of with different probability estimates if we try to model ways in which child universes are randomly spawned rather than deliberately created. The idea that the universe is computational (1) is not a proper variant of the simulation argument, but shared by many physicists (with some debate on whether it is a deterministic, probabilistic, discrete, continous, finitist, classical, hyper-Turing or acausal computation). I think that Musk champions a variant of Nick Bostrom’s simulation argument, and thus we should look at (2)/(3). The argument is based on the idea that physics, according to (1), means that you and me live in some kind of Minecraft world, and the observation that we can build computers in Minecraft, which are in principle powerful enough to run another instance of Minecraft, i.e. a child universe, that can contain computers as well, and so on. In the same way as future scientists might be able to build a computer that runs a smaller, slower but good-enough universe to harbor intelligent life, there might be a parent universe in which scientists (or natural processes) have done just that. Because our universe has room for a great many technological civilizations of which some, as a matter of probability, will run simulation universes, there are going to be vastly more simulation universes of type (2) or (3) than base realities. Therefore, the probability that we live in a simulation would be dramatically larger than the probability that we are in a root universe. I can see some obvious complications with this argument. A computer that runs in Minecraft will have many orders of magnitude less memory and speed than the computer running Minecraft, because only a very tiny part of the computations of the parent Minecraft instance contribute to those of the child universe. Thus, a Minecraft running on a Minecraft instance in a normal PC won’t have enough space and speed to run grandchildren or even sibling universes. With each level of supervenience, we loose many orders of magnitude in computational power. Of course this won’t matter if the root universe is infinitely large and runs for an infinitely long time. Even if the parent universe is not infinite, but just many orders of magnitude larger than ours, it can harbor many universes like the one we inhabit. I cannot see how Elon Musk can put a number on this, however, because we have no way of knowing how much larger the parent universe can be. Our universe has a peculiar property that distinguishes it from Minecraft universes, however. Minecraft is built on irreversible computations: if you build something there, then there is no way to run Minecraft backwards to restore the original state. Minecraft deletes information it does not need any more. Conversely, our universe seems be built on reversible computations, which is for instance why energy cannot be created or destroyed. It seems that there is simply no way in which you can irrevocable delete a bit in our universe. Of course you can build reversible computers on top of irreversible ones: just make sure you store enough information so you can always perform an undo. You can also build irreversible computers on reversible ones, but because you cannot delete anything, you will have to squirrel the surplus bits away into some kind of landfill. Living things, planetary constellations, transistors and every other self-stabilizing system are examples of irreversible computation: they need to be robust against disturbances, i.e. they can return into the same functional state after different histories. They need to “delete” the disturbances that would otherwise destabilize and destroy them, and to do that, they need to dump, pipe, transport, radiate the garbage bits out of the system. The second law of thermodynamics reflects this: in every closed system, garbage (entropy) always accumulates. To carry the garbage bits out of the system, we need an entropy gradient: an energy source. Irreversible computation is the reason why it is possible to build perpetuum mobiles in Minecraft (such as computers that can run without consuming energy), and reversible computation is the reason why we apparently cannot build a perpetuum mobile in our universe, and our computers will always be quite small and short-lived. If we use stars as energy sources, we won’t get much of a benefit from building computers larger than a Dyson sphere, because the signal speed at interstellar distances would be too low to do interesting things before the stars burn out. This in turn puts a harsh limit on the size of the simulation we can run, i.e. based on known physics, I expect that no civilization in our universe can build a particle level simulation large enough to allow for the spontaneous evolution of intelligent life. If we are a simulation run from a vastly larger parent universe, and the parent universe allows irreversible computation, it is not clear why our creators would go to the expensive trouble of making ours reversible, thereby crippling our abilities to do interesting stuff. If the parent universe is reversible, too, it makes sense that the creators want to build ours to resemble theirs, but like us, they would still have to build an irreversible computer, so it can perform computations that deviate from the course of the computations of the parent universe. Thus, our parents have a similar entropy problem as us, and to run a universe like ours, they need to have vastly more powerful physics at their disposal (i.e. especially much more long-lived energy sources than our universe appears to contain). To me, the fact that our universe is apparently reversible indicates a somewhat higher probability that we live in the base reality than Elon Musk and Nick Bostrom suspect. I still cannot put any number on it, of course. On the other hand, I have no good answer if you ask me for the origin of the system that computes the base reality. Somehow there seems to be a primary transition function operating on some kind of primary state vector, and I see no way how to resolve this existential debt to nothingness.