talk as if the simple instruction to “Test ideas by experiment” or the p
I think you’re missing something really big here. There is such a thing as an optimal algorithm (or process). The most naive implementation of a process in much worse than the optimal, but infinitely better than nothing. Every successive improvement to the process asymptotically brings us closer to the optimal algorithm, but they can’t give you the same order of improvement as the preceding ones. Just because we’ve gone from O(n^2) to O(n log(n)) in sorting algorithms doesn’t mean we’ll eventually get to O(1).
Aha! You say. But human brains are so inefficient that actually we haven’t even gone a smidgeon of the path to the optimal algorithm and there is a ton more space to go. But computers already overcome many of the inefficiencies of human brains. Our brains do a decent job of pruning the search space up to the near-optimal solution, and computers take care of the work intensive step of going from near-optimal to optimal. And as our software gets better, we have to prune the search space less and less before we give the problem to the computer.
Of course, maybe we still have many orders of magnitude of improvement to go. But you can’t just assume that.
talk as if the simple instruction to “Test ideas by experiment” or the p
I think you’re missing something really big here. There is such a thing as an optimal algorithm (or process). The most naive implementation of a process in much worse than the optimal, but infinitely better than nothing. Every successive improvement to the process asymptotically brings us closer to the optimal algorithm, but they can’t give you the same order of improvement as the preceding ones. Just because we’ve gone from O(n^2) to O(n log(n)) in sorting algorithms doesn’t mean we’ll eventually get to O(1).
Aha! You say. But human brains are so inefficient that actually we haven’t even gone a smidgeon of the path to the optimal algorithm and there is a ton more space to go. But computers already overcome many of the inefficiencies of human brains. Our brains do a decent job of pruning the search space up to the near-optimal solution, and computers take care of the work intensive step of going from near-optimal to optimal. And as our software gets better, we have to prune the search space less and less before we give the problem to the computer.
Of course, maybe we still have many orders of magnitude of improvement to go. But you can’t just assume that.