I have a very vague understanding of Goedel's famous Incompleteness theorem, but I know enough to know that I see it constantly interpreted in what seem like bizarre ways that I am sure anyone who really knew the relevant math or logic or philosophy would find ridiculous. The most common of these come from "new age" sources. My question is, for someone who knows something about the theorems, what is it about them that you think attracts these sorts of odd and (to say the least) highly suspect interpretations? I mean you don't see a lot of bizarre interpretations of most technical theories/proofs in math, logic, or philosophy.

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You are quite right that Gödel's (first) incompleteness theorem attracts all kinds of bizarre "interpretations". Various examples are discussed and dissected in Torkel Franzen's very nice short book, Gödel's Theorem: An Incomplete Guide to its Use and Abuse, which I warmly recommend.

My guess is that a main source for the whacky interpretations is the claim that has repeatedly been made that the theorem shows that we can't be "machines", and so -- supposedly -- we must be something more than complex biological mechanisms. You can see why that conclusion might in some quarters be found welcome (and other technical results in logic generally don't seem to have such an implication). But as Franzen explains very clearly, it doesn't follow from the theorem.

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