Nature does not possess this property. For example, to compute the shape of a single protein molecule from quantum electrodynamics would take longer than the estimated lifespan of the universe.

I don't understand -- if you want to compute anything, even "tractable" problems, by modeling their implementation down to the QED level, it takes too long -- even the Casesar cipher would (because I'd either have to model my neurons carrying out the operation, and their subatomic interactions, or do the same for a semiconductor).

Yes, nature has exponentially more computing power, but that doesn't make her resistant to e.g. differential cryptanalyis on at least some problems. (An experiment in which you gradually vary one parameter is just a chosen-plaintext attack using differential analysis).

What matters is whether that computing power is directed in a way that "covers up its tracks", and thus, to what extent it has obscured the relationship between the input and the output. Just as evolution, being restricted to using small local improvements, cannot refactor a system the way an engineer of human intelligence could, nature cannot direct her resources to design better one-way functions the way human cryptographers can.

conversely, most techniques of science don't work in cryptanalysis because ciphers are designed to make sure they don't work.

Yes, what happened there is this: to solve a scientific problem, scientists use some method to detect patterns that is isomorphic to a cryptanalytic attack. Because later ciphers were designed, by human intelligences, to be resistant to known mathematical techniques, the cipher designers, as you mention, destroyed this pattern.

But how does this prove that the problems of science and cryptanalysis are unrelated? It proves just the opposite: the only reason scientific pattern-finding heuristics can't be carried over to ciphers (contemporary with that science) is because an intelligence designs the ciphers that way. There is no intelligent designer working for nature that can prevent it from working in the opposite direction.