I gave a fifty-minute lecture on the lambda calculus for a class last week. It was a topic I understood very well, but had never taught to someone else before. The length of the lecture was daunting enough, but I was surprised at how difficult it was to create a lesson plan. I could clearly see the ideas and their implications in my mind’s eye, but it was hard to impose an order and a rationale on them that would make sense from the perspective of someone new to the material. You have to say the right thing in the right way in the right order. Ideas and concepts have to progress naturally and logically, later ones building on earlier ones. With this new insight into teaching, I respect teachers who were able to clearly explain something to me all the more. You aren’t qualified to teach an idea to others just because you understand it.