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SilasBarta comments on Cryptanalysis as Epistemology? (paging cryptonerds) - Less Wrong
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I oversimplified there [1], but even with your corrected phrasing of the situation, that suggests some room for cryptanalysis-based improvement in science, because finding any pattern distinguishable from randomness is a win for science as well.
Given that nature does not deliberately or intelligently add the entropy that halfway-decent ciphers add, then the patterns belonging to the weaker, lower-entropy set of observable data that nature is limited to should be a much easier problem for cryptanalysts than the ciphers they normally try to attack.
In other words, when it comes to injecting entropy into ciphertexts, nature couldn't hold a candle to even the easily-broken ciphers. Right?
[1] To be precise, it would have to be something more tautologous like, "For a given cryptanalytic goal, the best cryptanalytic methods can meet that goal for a cipher with the level of complexity in the most complex cipher broken for that goal and all ciphers of lower complexity."
I'd say that science and cryptanalysis both share the ideal of (or can be viewed as) trying to approximate Bayesian updating on a Solomonoff prior. In cryptanalysis, you have the disadvantage that your opponent is intelligent and malicious (from your perspective), but you have the advantage that the encryption process doesn't have much computing power (since ciphers have to be fast to minimize computing costs). In science, nature is not malicious, but it's not limited in computing power either. Yes, they are basically similar, but each is specialized to its domain of inquiry, so I doubt science can learn much from cryptanalysis.
I just remembered EY's post that alien message, and I don't think I'm making too dissimilar an argument: In EY's story, the aliens aren't as smart as humans, so we can infer the patterns in their messages, predict new ones, and inject new code.
As aliens were to those humans, so is nature to us.
Nature's also not very intelligent, as elaborated on here and here.
I explained one historical instance of scientists going through the same process as cryptanalysis in my reply to Nancy.
That's a good distinction.