the self-referential universe

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I recently came across the mathematically cute topic of self-referential sentences -- sentences that make statements about their own content. It is interesting that one can start out with a self-referential sentence that says something blatantly false about its own content, and then iterate it using a very simple technique, and you will eventually be led to a sentence that says true things about its own content (or possibly to a set of sentences that say true things about one another).

Now, ordinarily I wouldn't care too much (it's a very "pure math" type of subject), but this one gave me a very peculiar feeling. After thinking about it a while, I think I found out why. The universe can be thought of as a bunch of information (a "sentence"), and in fact it's a self-referential sentence -- we humans (scientists/physicists, specifically) are a part of the sentence, and we make statements about the rules governing the sentence itself. And in fact, we have a kind of iterative process (called science) whereby we take current statements, compares them to experiment, and then construct refined statements which get us a little closer to the truth (analogous to attraction to a "fixed point").

I'm not sure what else to say -- I suppose I'm wondering if this similarity is anything more than superficial, and if it can be used to make non-obvious statements about the nature of science, or the universe itself. Any opinions or ideas?