In that case, since we are here and it's Friday and everyone needs to take it easy from time to time, here's my proof that we don't live in a simulation: according to [1], ray tracing is computationally undecidable. For example, say you are in a museum at night, and a light bulb turns on in a room on the third floor, is it still dark in some room on the first floor? This problem is undecidable using the axioms of geometric optics.
Of course, geometric optics is like real numbers, and the actual world is discrete: light is a finite collection of photons. So, you can do the simulation by simply emitting a number of photons from each light source and tracing them all the way until they are all absorbed. We can still live in a simulation, but one without algorithmic shortcuts, a simulation where you simulate every single photon.
Now, I'm sure you can come up with your own version of proof that we can't live in a simulation using Nyquist's theorem. If you do, and your Friday is not too busy, please share.
