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Suppose that there was a headline in every newspaper that said that science has now proven that we do indeed live in a simulation, without any doubt. Or, some godlike aliens that created our simulation appeared to us and told us. Suppose that fact was settled.
Starting from that point, and working our way backwards, what are some of the pieces of evidence we would use to say, "Well, that makes sense, because of this fact."
I'm looking at it mostly as a computer programmer, thinking of how the simulation would work from a programming standpoint. Here are a few examples I'm looking for, see if you can think of some other similar arguments...
Individual and indivisible computations: A simulation, by definition, is an approximation. Having indivisible pieces of matter, or subatomic matter, or even strings, would be good evidence. They would be the individual pixels of our universe as it were. Or, perhaps the Planck length itself would be the invisible pixels, and the maximum resolution of our universe, and particles (or strings) would be variables.
No rendering until necessary: In a video game, there's no need to render objects that aren't in frame. You can save processor power that way. In the same way, it seems that our universe doesn't decide on a definite position, momentum, spin, etc, for a particle until it is pinned down and has to make a decision. That is the simulation saving expensive computation power.
Approximating complex systems: A black hole could be seen as merely a local system that is too complicated for a small area, considering the large number of particles are in such a small area. Especially if the processing is done as a distributed system, meaning one processor for one area of the universe, and perhaps a black hole taxes one processor too heavily. Instead of trying to simulate every particle and every particle interaction, at a certain density, just save the mass of the total amount of particles and delete all the extraneous detail about each individual particle. Approximate it with one mass parameter, one amount of angular momentum, and one amount of charge, the only 3 parameters you need for a black hole. For interactions with particles far away, the simulation would be unchanged, yet it would be much less computationally expensive locally.
Speed of light is speed of framerate: it would be prohibitively expensive to simulate every particle's interaction with every other particle in the entire universe simultaneously. It would be much easier to limit the amount of things that can influence other things, at least on a frame by frame basis. You don't have to simulate how a supernova will effect every star system right away, just simulate how it effects local particles, and then simulate the particles after that, then the ones after that, in a ring. Perhaps the speed of light is simply the set speed for computations of interactions between particles, in order to lighten the load of how fast things can influence other things.
Time dilation: It would likely be more computationally expensive to update all the info for an object such as a spaceship moving closer and closer to the speed of light, as it gets closer and closer to the edge of the framerate of the simulation. To help counter that, the framerate of the local simulation (inside the fast moving spaceship) would go down, much in the same way that video game framerates go down during fast moving parts of the game. If you run into the limit of processor power, you either have to drop frames, or slow down the speed of the frames.
Quantum entanglement: Perhaps entangled particles are created as a single class, together, and when they need to be updated, they are ran as one function, one subroutine, meaning they are both updated simultaneously, short-circuting the usual speed limit of c found in interactions between separate unrelated particles.
Nuclear fusion and the uncertainty principal: Our sun should not be hot enough or have high enough pressure for particles to overcome the Columb barrier in order to fuse, but they do anyway, and it's because of the uncertainty principle. The particles can't get close enough or move fast enough to fuse, but occasionally, the uncertainty principle makes it such that the particles were close/fast enough after all, because their position/momentum weren't really nailed down, only approximated. As a result of the imprecision of their true position/momentum, it turns out that they were close enough, and they fuse. In a way, laziness of computation of the particle interactions in the core of the sun is what makes the sun shine.
Of course there are statistical arguments about how simulations can make their own simulations and so forth, and we are unlikely to be at the top level. But that is speculation and probabilities, I'm looking more for evidence we can see in our own world, such as evidence of approximations, computational shortcuts, imprecise calculations, etc. Tricks that a programmer or a designer would make that would make a simulation easier to run.
Can you think of other clues we would use to explain why we live in a simulation?