Thanks for the comment. I mostly agree, but I think I use “reducible” in a stronger sense than you do (maybe I should have specified it then) : by reducible I mean something that would not entail any loss of information (like a lossless compression). In the examples you give, some information—that is considered negligeable—is deleted. The thing is that I think these details could still make a difference in the state of the system at time t+Δt, due to how sensitiveness to initial conditions in “real” systems can in the end make big differences. Thus, we have to somehow take into account a high level of detail, if not all detail. (I guess the question of whether it is possible or not to achieve a perfect amount of detail is another problem). If we don’t, the simulation would arguably not be accurate.
So, yes I agree that “the extremely vast majority of physical phenomena in our own universe” are reducible, but only in a weak sense that will make the simulation unable to reliably predict the future, and thus non-sims won’t be incentivized to build them.
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.
Thanks for the comment. I mostly agree, but I think I use “reducible” in a stronger sense than you do (maybe I should have specified it then) : by reducible I mean something that would not entail any loss of information (like a lossless compression). In the examples you give, some information—that is considered negligeable—is deleted. The thing is that I think these details could still make a difference in the state of the system at time t+Δt, due to how sensitiveness to initial conditions in “real” systems can in the end make big differences. Thus, we have to somehow take into account a high level of detail, if not all detail. (I guess the question of whether it is possible or not to achieve a perfect amount of detail is another problem). If we don’t, the simulation would arguably not be accurate.
So, yes I agree that “the extremely vast majority of physical phenomena in our own universe” are reducible, but only in a weak sense that will make the simulation unable to reliably predict the future, and thus non-sims won’t be incentivized to build them.
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.