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Thanks for the response Lech

"the simulation argument does not purport to show (and I do not believe) that the Sims outnumber the [non‐Sim] humans."

I was not aware of this as a common caveat to the simulation hypothesis. If it is, I still do not see a reason to believe that it is probable that conscious beings with our set of experiences should expect to exist in a simulation. It makes more sense to assume that this is the base reality if we expect those minds to be in the majority.

This presumes that we have to fully simulate the whole universe in detail, without room for approximations, and that the physical laws of the outer universe are the same as ours.

I agree with this, these approximations are related to the granularity I was describing. My belief is that there are only so many approximations you can make before the simulated universe is not detailed enough to express individual consciousness. 

I am fully open to the possibility that a civilisation in a reality with more complicated physics is simulating ours, but I see no reason to believe this is probable, or more probable than many other possible claims (eg. brain in a vat). 

Answer by nocturne81

Here is my best argument against the simulation hypothesis:

Simulations typically have a reduction in dimensionality, at least the ones we have made so far. Which is to say: you cannot simulate the whole of the universe within itself. Our simulations are more granular and smaller than the real world, even if they become remarkably close. This reduction in detail can be temporal or spatial.

The simulation hypothesis supposes that the number of simulations would be astronomically high because of recursive simulations in simulations. This is the part that I take issue with. Assume that we live in simulation level X (some point in the chain of simulations). Anything that happens in the simulation X+1 (the simulations we make) would need to be computable by a set of operations in simulation X. This is similar to how a virtual machine ultimately runs as CPU instructions on the host machine.

This means that Simulation X bounds the complexity of every nested simulation (Simulation X+1...X+∞). If you run a virtual machine A inside a virtual machine B, on physical host C virtual machine A is still expressible as a computation of the host machine. You cannot create a virtual machine with higher specs and have this run in real-time, since the complexity of this chain is bounded by the root node.

Note that there is also overhead with every layer of simulation. Our entire universe is not interested in running simulations, only a small fraction of the compute under the control of intelligent life. A god-like civilisation that has conquered the universe may be able to dedicate a significant portion, but this necessarily cannot be 100%. 

This means that the number of simulations should be much more finite than typical formulations of the simulation hypothesis depict.

This does not mean that I rule the possibility out. Even if the chain is short there may be many simulations which we could exist in. We might be the only simulation. But this possibility seems no more profound or likely than any other unprovable statement.