It takes two, baby

(Caveat: I've got writing process on the brain, as I just started work on Chapter 3 this afternoon, in which I hope to discuss writing as process, and how to effectively stage that process, in the quantitative disciplines.)

For future reference: when asked to write a dialogue in which you're to help a hapless friend who's hopelessly lost regarding one or another mathematical concept, it helps to involve two people in the conversation.

The second interlocutor plays a crucial role: with this person in play you, playing the role of The Expert, need not anticipate every difficulty that might arise to trouble your poor partner in conversation. This partner is the one who need only act naturally in order to bring to light the most subtle and sophisticated aspects of the problem you've been posed. That is, this partner is your foil, the dunce whom you can task with asking every question that might conceivably come up when learning a tricky technique.

With two people talking it through, what might otherwise be a boring monologue or lecture (in which posing trivial questions and then immediately dispatching them would seem stilted at worst or pedantic at best) is now a dynamic dialogue, where nearly real-world interaction is possible.

Talk with your dialogue partner as though you would talk with a real-life friend; help him as you would help a real-life friend, let his ignorance and your expertise take turns driving the conversation forward as you uncover the truth together.

Could there be a better low-stakes writing-to-learn activity?