I buy that, insofar as the use-case for simulation actually requires predicting the full state of chaotic systems far into the future. But our actual use-cases for simulation don’t generally require that. For instance, presumably there is ample incentive to simulate turbulent fluid dynamics inside a jet engine, even though the tiny eddies realized in any run of the physical engine will not exactly match the tiny eddies realized in any run of the simulated engine. For engineering applications, sampling from the distribution is usually fine.
From a theoretical perspective: the reason samples are usually fine for engineering purposes is because we want our designs to work consistently. If a design fails one in n times, then with very high probability it only takes O(n) random samples in order to find a case where the design fails, and that provides the feedback needed from the simulation.
More generally, insofar as a system is chaotic and therefore dependent on quantum randomness, the distribution is in fact the main thing I want to know, and I can get a reasonable look at the distribution by sampling from it a few times.
I buy that, insofar as the use-case for simulation actually requires predicting the full state of chaotic systems far into the future. But our actual use-cases for simulation don’t generally require that. For instance, presumably there is ample incentive to simulate turbulent fluid dynamics inside a jet engine, even though the tiny eddies realized in any run of the physical engine will not exactly match the tiny eddies realized in any run of the simulated engine. For engineering applications, sampling from the distribution is usually fine.
From a theoretical perspective: the reason samples are usually fine for engineering purposes is because we want our designs to work consistently. If a design fails one in n times, then with very high probability it only takes O(n) random samples in order to find a case where the design fails, and that provides the feedback needed from the simulation.
More generally, insofar as a system is chaotic and therefore dependent on quantum randomness, the distribution is in fact the main thing I want to know, and I can get a reasonable look at the distribution by sampling from it a few times.