....The Sims' smoking gun for computer code, to the extent there is one, would be that the world they can sense does everything in discrete steps. So their laws of physics are all implementable on a computer.
I thought that the movements of the characters would be interpolated to about 60 frames per second... they don't have the ability to capture a video of that and slow it down.... I don't think they'd be able to determine what the framerate is.
The human eye can't distinguish 25 frames per second from continuous; but we can reason about what we see and draw inferences beyond the unaided eye. For instance, you see the wagon wheel spokes rotating slowly in the wrong direction and you deduce you're seeing a series of frames and not continuity. The Sims could do likewise -- we're presuming highly intelligent Sims here.
Similarly, the smoking gun for our world not being a simulation, to the extent there is one, is that our best guesses at laws of physics are a bunch of differential equations that don't work right unless time and space are continuous. To get that right on a computer would take an infinite amount of calculation....
If it is truly completely continuous then it seems the "Achilles and the tortoise" paradox could apply....
https://en.wikipedia.org/wiki/Zeno's_paradoxes#Achilles_and_the_tortoise
I think that's not so much a real paradox as it is an ancient Greek mortal fear of infinities. Infinite series add up to finite sums all the time.
1 + 1/2 + 1/4 + ... = 2
Discrete time and space solves this paradox. I thought the Planck time and length means that time and space are discrete (quantized?).
They don't mean that -- that's just the scale where quantum gravity effects are expected to become dominant, and we don't have a working theory of quantum gravity yet. So it's not that current theory says there are no distances and times smaller than the Planck scale; rather, our theory says we don't know what happens below that scale so we need better theories.
There are a couple of big obstacles to discrete spacetime hypotheses. One is the dilemma of how the individual discrete spacetime points are laid out. Jokodo was talking about this issue here a few years ago. If they're laid out in a regular pattern like a crystal then we'd expect to see different physics in directions lined up with the crystal's axes from what we see in directions that cut across the axes; but as far as we can tell physics is completely uniform in all directions. Contrariwise, if the discrete spacetime points are laid out randomly like atoms in glass, then we'd expect energy to leak out of propagating waves and turn into heat, the way sound waves die out so much faster in glass than in crystals; but as far as we can tell there is no energy leakage, and we can see light that's traveled half way across the universe. (Of course maybe there's some aperiodic quasicrystal pattern that resolves the dilemma; if so we haven't found it.)
The other obstacle is Relativity. Duration and distance aren't absolute -- they're relative to the motion of the observer. So if two particles are the Planck length apart from my point of view, to somebody who's moving at 9/10 the speed of light the same two particles are less than half a Planck length apart. But that's impossible if no distances are shorter than the Planck length. So it pretty much means if space and time are discrete then Relativity must be wrong; but as far as we can tell by looking, Relativity is right.
I think the simulation I think I'm in would just give the impression of things like the Sun being made up of 1057 atoms without having to have them all being continually explicitly simulated.... so it shows what we expect to see without necessarily being calculated in the way it gives the impression of... e.g. it could seem that there was a Big Bang with infinite density without having to simulate that in a simplistic brute force way. I think AI techniques like machine learning physics simulations could be used.
That's a nifty speculation. But how would a simulator know when it can get away with bulk estimates and when it needs to simulate subatomic particle by particle? It would need to be able to tell if anybody is watching closely. Glad I'm not the programmer who has to code that one...
