So if a time-traveling mischief maker gave the NSA a copy of "The Klingon Hamlet" in 1980, would they have been able to "decrypt" it?
That's a difficult case. It would depend on the resources thrown into it. If it were formatted as a play it wouldn't take long for someone to notice that, and the five acts would to an English speaker suggest Shakespeare. (This isn't a hypothesis someone would immediately hit upon but it is the sort of thing that someone would eventually think of.) At that point things will be much easier since we have an effective Rosetta stone. However, note that even with the Rosetta stone, the deciphering of Egyptian hieroglyphs took a very long time even after the main breakthroughs.
If the text were not the text of Hamlet but were a similar random text of the same length, then it is almost certainly not long enough to be decipherable in any reasonable span of time. I don't however have any idea how much longer the text would need to be.
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.