R Hansen says: >Did you know the math, but were unable to connect it to an analogy, or were there simply no suitable analogies to connect it to?
No, not at all. I was aware of the result, also had been thinking about physical phenomenon for a long time, but had never really sat down and thought it through for myself in step by step excruciating detail. So, when calculus class happened to me, and I felt I hadn't received the "aha!" experience I was hoping for, based on the text's development (I have no memory of what text in particular) I figured if you want something done right, you have to do it for yourself. So I did.