Chapter 8 Magic in the Book of Changes Mathematicians are sometimes seen as the ultimate nerds. An old joke goes: "An outgoing mathematician is one who looks at your shoes dur- ing conversation." Your authors do not fall into this mode. Each of us has had show business careers and gives more than fifty talks a year (in addition to our scheduled classes). By now, nothing makes us nervous in public presentations. Except for just one time! In May 1990, John Solt invited us to give a talk at Harvard's Depart- ment of East Asian Languages and Civilizations colloquium. We are