James Stanley

We're not in a simulation

Fri 2 February 2024
Tagged: philosophy

In this post I'm going to make the case that IF (big if) the universe can be simulated, then actually running the simulation has no effect on the contents of the universe. Either the universe can be simulated, in which case we exist within an abstract mathematical structure independent of any actual simulation, or the universe can not be simulated, in which case we trivially do not live inside a simulation.

I first learnt of this idea from a post Why are things? by Billy Bradley (which I recommend reading). He talks about a function U(P,t) which tells you the state of the universe with parameters P at time t. This formalism is useful as an intuition pump, but neither necessary nor sufficient for explaining the core idea. It's not sufficient because relativity tells us there is no universal "t", and it's not necessary because we don't need to define the form of the function in order to talk about what could happen IF a function existed.

I'm also aware that Max Tegmark has done a lot of thinking on this, though I didn't get very far in his book because I got bored of the classical physics long before it got to the interesting part.

The crux of the "mathematical universe hypothesis" is that IF it is in principle possible to define a mathematical structure which completely simulates the universe, then the mere "existence" (in an abstract mathematical sense) of that structure is enough, on it's own, to give the observers within the universe all of their observations. This means that there is no need for the universe to actually be instantiated anywhere (either "physically" or in a computer). And, further, that even if the universe were instantiated anywhere in particular, that this would have no effect whatsoever on the contents of the universe, that we would have no way to find out whether it was being simulated or not, and that even if the simulation were turned off, we would continue to exist.

The universe doesn't stop when the simulation is switched off for the same reason that arithmetic doesn't end when your calculator is switched off. The calculator is not creating arithmetic, it's just exposing arithmetical results to someone who exists outside of arithmetic. Similarly, a universe simulation does not create the universe, it's just exposing the contents of a universe that was always there. For observers within the universe, the existence of the simulation has no effect.

As far as I'm concerned, the argument is utterly watertight: IF the universe can be simulated, then it doesn't have to be. I normally find that people either agree straight away, or won't agree no matter how much we discuss it, but their disagreements don't make any sense and we end up talking past each other.

Please remember the "big if" at the start: IF the universe can be simulated. A counterargument along the lines of "our existence is special and beautiful and can't be created by mathematics alone" is a claim that the universe cannot be simulated.

I do think the question of whether our universe can be simulated is interesting, of course. But I don't know the answer. But IF the universe can be simulated, then that neatly answers a number of difficult questions about the nature of reality:

I think people confuse this argument with a related one: that this "mathematical universe" is an actual explanation of what our actual universe is made of. We know from the first part that IF the universe can be simulated, then that is enough and you don't need any more. So the question of whether our actual universe is made this way is really the question of whether our universe could be made this way. If it could, then by Occam's Razor it is.

I don't know how to find out whether our universe is computable. I expect it probably is, which means I think we do live in a structure that is made out of mathematics.

To argue that the universe could, in principle, be simulated, and therefore could exist as an unsupported abstract mathematical structure, but to then argue that actually that is not what is happening and we really "exist within a simulation on a computer" is akin to arguing that the number 42 lives within your calculator! It is quite obvious that the calculator contains a representation of the number 42, but that is not what the number 42 actually is. 42 existed before the calculator contained the representation, and it will exist after the calculator no longer contains it. The calculator is the simulator, and the numbers are the underlying abstract mathematical structure that reality is made out of.


How can we have consciousness if all there is is mathematics? (I don't know!)

We already have enormously complicated mathematical structures that we evaluate on computers and that we don't understand (ChatGPT, for example). It's not too hard to imagine that a mathematical structure orders of magnitudes more complicated than the observable universe could contain enough hidden complexity to create consciousness. The fact that consciousness exists and that we perceive anything at all is miraculous. But that we don't currently know how to model consciousness mathematically doesn't mean it's impossible.

Free will

If every possible path of every possible universe equally "exists" in the mathematical structure of all things, then we don't really have free will, do we? Probably not. But we also don't "physically exist", and yet we have the experience of physical existence, and we similarly have the experience of free will.

I maintain that everything after "IF the universe can be simulated, ..." is logically sound, which means if you want to cling on to literal free will, then you probably have to make the argument that it is mathematically impossible to simulate the universe.

Computational limits

Physical limits on computation don't apply to the simulation hypothesis as I consider it. Any hypothetical simulation would be outside the simulated universe, so it doesn't have to worry about using more resources than exist within the universe.

But, further, a universe that is "too large to simulate" still exists within the infinite abstract structure of all of mathematics. It exists just as well even if nobody ever figures out a way to evaluate it using their available resources.


I'm not saying that mathematics contains a representation of the universe, and that some magic process turns that into a real universe that we can experience. I'm saying that the magic process doesn't need to exist. Any "magic", if you want to call it that, is in the structure itself.

The anthropic principle

The abstract structure of all structures is obviously infinite, and contains infinitely many possible universes. Isn't it phenomenally unlikely that we find ourselves not just in a universe in which observers can exist in principle, but that we find ourselves existing as observers ourselves?

Every arrangement of particles that can not observe, can not observe. The fact that we can observe anything at all means we have already selected ourselves into the subset of universes in which observation is possible, and in which we are observers.

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