[theWheez]

I think going through The Little Schemer by Daniel Friedman and Matthias Felleisen helped me a lot. It builds up your knowledge in a conversational way to achieve understanding of quite complex ideas in simple terms. In that case, it builds up to an understanding of the halting problem, and then to the Y Combinator.

The click felt to me similar to understanding recursion for the first time--it doesn't fit into your head naturally. Once it does "click", even then you have to re-remember it later, and trace your logic on how you "realized" recursion.

Godel's Theorem brings that "feeling" of recursion and takes it to the extreme, in that its subject matter is "meta"-mathematical. So in the same way that recursion can't be grokked in terms of only loops, Godel's Theorem can't be grokked only in terms of equations.

I don't know if that made sense, I've also seen some links in this thread which I think may help as well