[zh3]

Maybe it's not that hard to simulate, but let's start with looking at just two of the sand grains that happen to hit each other? They collide, how they rebound is all angles, internal structure, Young's modulus, they have electrostatic interactions, even the Van der Walls force come into play. Sand grains aren't regular, consider how determining the precise point at which two irregular objects collide is quite a challenge (and this isn't even a game, approximations to save compute time won't do what the real world does 'naturally').

So while we can - for something as simple and regular as an eggtimer - come up with some workable approximations, the approximation would surely fall short when it comes to the detail (an analytical solution for the path of every single grain).

[onlyrealcuzzo]

I guess I wasn't thinking of a PERFECT simulation.

Now it's obvious to me that you would have to simulate exactly what the universe is doing down to the smallest level to get a perfect simulation.

Thanks.

Is it really impossible to get a very close approximation without simulating down to the atomic level, though?

[zh3]

A close approximation should arguably include collapses/slides, which happen spontaneously because the pile organises itself to a critical angle; then an incredibly small event can trigger a large slide of salt/sand/whatever/rocks (or whatever else the pile is made of). Even working out something like "What's the biggest and smallest slides that could occur given a pile of some particular substance?".

Every approximation will by definition deviate from what really happens - I suppose that's why we talk of "working approximations", i.e. they work well enough for a given purpose. So it probably comes down to what the approximation is being used for.

There is the idea that we are all living in a simulation; if so maybe if we look closely enough at the detail all the way from the universe to atoms then we'll start to see some fuzziness (well, of course there's quantum physics....).

[galaxyLogic]

When the output looks the same as the original we would say that the simulation was successful. That is how computer games do it. We're not asking for the exact position of each grain, just the general outline of the pile.

[namaria]

An image of something is likely to be the simplest model of that thing that happened, and it has A LOT less information than a 3D model of arbitrary resolution would have.

[galaxyLogic]

Simulation is never an "image". It may simulate each grain, just saying it doesn't need to simulate each precisely, because the law of large numbers kicks in.

This is the basis for example Monte Carlo simulation, it simulates real world with random numbers it generates.

[namaria]

Every video game engine is a simulation and many of them are a very simplified model of images of things happening instead of simulating the actual physics. Even "physics" in these engines is often just rendering an image.