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Mathematica tries to do is to imagine all possible computations that people might want to do. And then to try to identify repeated structures—repeated lumps of computational work—that exist across all those computations.
it seems as if nature has some kind of secret that effortlessly produces all sorts of complexity. And I think we now know what that secret is. It’s that nature is sampling all sorts of programs in the computational universe.
it’s not that you can’t build complexity from mathematical primitives and so on. But what’s happened is that the exact sciences have tended to just define themselves to be about cases where that doesn’t happen. We haven’t studied the full computational universe of possibilities, only a thin set that we’ve historically found to be tractable.
