Another time, a student asked me out of the blue—not in class, just in the course of a normal day—what I knew about counting in base 2 (a.k.a. binary numbers, the basis for digital computers). A spontaneous quasi-class ensued, as she and I looked things up, using a chalkboard to piece together the mysteries, treating it like a puzzle or a grand game: When do you add another digit? When is a 1 replaced with a 0? and so forth.