The thing that always makes me shit bricks is when underlying mathematical structures turn out to be the same for two areas of investigation that were previously considered unrelated. For example the fact that mathematical proofs are computer programs and information entropy and physical entropy are so closely related as to be almost the same thing. Note also that information theory and probability theory unify perfectly under a bayesian interpretation (see here and here for easy introductions, see also Probability Theory: The Logic of Science) which gives us a rigorously formal definition of 'evidence', and shows us what we're actually doing when we do a statistical test.

I was going to say some stuff about economics and biology, but this post is already quite long so I'll just say that although you might think you understand evolution, if you don't understand the way allele frequencies change across a population through time, then you don't really get evolution. Oh and when I hear political firebrands blathering about the economy when they obviously know nothing about it, I have to lol.