Isn’t this a remarkable situation to be in, from a scientific perspective? I can predict the outcome of a process, without being able to predict any of the intermediate steps of the process.
Reductio ad absurdum: I cannot predict each fair coin toss but I can be quite confident that the outcome of many coin flips will be close to 50% heads.
Is the coin an intelligent optimizer? Presumably not. At least I hope it isn’t. So then, where does simple math (statistics) end and complicated math (optimization) begin? My guess is that one has to estimate the Kolmogorov complexity of the optimizer’s algorithm. But then how is it relevant that each step cannot be predicted? Might as well abandon this superfluous idea of local unpredictability.
Reductio ad absurdum: I cannot predict each fair coin toss but I can be quite confident that the outcome of many coin flips will be close to 50% heads.
Is the coin an intelligent optimizer? Presumably not. At least I hope it isn’t. So then, where does simple math (statistics) end and complicated math (optimization) begin? My guess is that one has to estimate the Kolmogorov complexity of the optimizer’s algorithm. But then how is it relevant that each step cannot be predicted? Might as well abandon this superfluous idea of local unpredictability.