Why is Simulation Difficult

Say you are making a movie and need to shoot an India Mela. You could either locate a real Mela and go shoot there or you could simulate one on your set. Except at the cost of tremendous effort, one can tell the simulated one from the real one (maybe it is too clean or too organized). This is a question that arises everywhere. Why is simulation so difficult? Why is it so difficult to simulate liquids but the liquids themselves use no compute at all?

I think, a good start to understanding this situation to ask ourselves why we expect simulation to be easy. Most of the phenomena that we care about lack centralized control. Numerous agents interact with each other on the basis of simple local rules (think fish schools). While simulating, we try to mimic this interaction using either some overall deterministic relation or if the complexity is too much, randomized relations. But the fact of the matter is that "the real thing" is neither of these. The source of complexity is in the interactions among numerous agents based on simple rules. You may come up with statistical properties of these interactions or you may try to replicate the interactions using "one" set of rules. But "the real thing" is a collection of simple rules. A "simplified" relation may describe the interaction in simple terms to a human brain, but it can only be an approximation.

So now we have this one equation that we think can describe the fluid dynamics. Only if we had sufficient compute. The issue is again that we are trying to simulate numerous agents using (say) one central unit. There is no reason why this should be efficient or easy. For a system in a certain state, that follows a fixed set of deterministic rules, there is only a limited number of possible future states. Contrast that with a computer trying to simulate that system's future state. The computer's current state and its rules are very different from the system's. Hence, the computer needs a hell lot of extra compute and information to really zero down on (an approximation) of the system's future state.

Reality is not a mystical computer with unlimited compute.

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