Short version: Why can't cryptanalysis methods be carried over to science, which looks like a trivial problem by comparison, since nature doesn't intelligently remove patterns from our observations? Or are these methods already carried over?
Long version: Okay, I was going to spell this all out with a lot of text, but it started ballooning, so I'm just going to put it in chart form.
Here is what I see as the mapping from cryptography to science (or epistemology in general). I want to know what goes in the "???" spot, and why it hasn't been used for any natural phenomenon less complex than the most complex broken cipher. (Sorry, couldn't figure out how to center it.)
EDIT: Removed "(cipher known)" requirement on 2nd- and 3rd-to-last rows because the scientific analog can be searching for either natural laws or constants.
I was basically saying (tautologically) that we can break any cipher except for the ones where we can't. So if you use any of those broken ciphers, an attacker can infer the cipher, key, or plaintext, to the extent that it's possible.
My non-tautological inference, then, is that nature isn't able to intelligently design ciphers, and so her patterns should be much easier for a cryptographer to discern than those that exist in many human-designed ciphers. A good cipher destroys the patterns that would otherwise clue in the attacker on the key or plaintext, and nature should be a lot worse at this, and a lot more limited in her "cipher design". (For example, unlike with AES, she can't layer a cipher so that it first destroys linearity, then permutes the whole thing to resist differential analysis, etc.)
Furthermore, cryptographers warn against using a secret cipher you designed, and this is partly because you won't be able to find all the possible attacks on your own. In other words, for the average person, even if you intelligently design a cipher, an attacker can infer the cipher (by finding its patterns) and plaintext, even if they didn't know the cipher to begin with. Since nature's "designs" will be even less intelligent, they probably aren't resistant to the cryptanalytic methods used in the unknown-cipher case.
Also see my reply to Nancy where I argue that discoveries in astronomy followed the same pattern as frequency analysis.
An interesting thought. Do you think that code-breakers are likely to have anything to teach scientists? I am having visions of taking code-breaking software, inputting scientific data, and unraveling the secrets of the universe.