@johncarlosbaez I feel like many things in math and physics are that way: when you're introduced to them someone can give you an explanation that makes sense; then when you think about it more you run into contradictions or incompleteness in the simple explanation. Getting back to the point where it makes sense again can take a LOT of work. Two examples that come to mind would be Hilbert spaces in quantum mechanics including momentum and position eigenstates and the notion of infinitesimals in calculus.
@johncarlosbaez Robenson: "I think you're under-thinking it."
@internic - true!
You're making me think of Weierstrass saying "maybe I'm overthinking it...."