| Josh Kornbluth performs the opening (1.9 mb) of "The Mathematics of Change" |

let's start with functions, why don't we? A function is a transformative experience. It's kind of like a machine -- you go into the function machine and you get . . . changed. Well, you don't go into the machine -- usually x goes into the machine. Mathematicians describe this situation as "f of x." X goes into f, the function machine, and it gets transformed into . . . y. No one knows the reason for this -- why x almost always gets transformed into y. But let's just accept it for now. And x is the kind of thing you'd want to put inside a transformative machine, because x is a variable. You wouldn't want to put, say, c inside the machine, because c is a constant. And a constant is . . . constant. You go up to a constant: "How're ya doing today, constant?" "Fine." Next day: "How're ya doing?" "Fine." Next day: "Fine." It's a constant! But a variable: "Well, how're ya doing today, variable?" "Oh, pretty good." Next day: "Great!" Next day: "Lousy!" You know, it's a variable! And mathematicians have focused on what happens to x when it's inside the machine, and what happens after it emerges. Less attention, I think, has been paid to that moment just before x enters the function machine. As it stands there, at the threshold of some new experience, not knowing what's about to befall it. Standing there -- trembling, tremulous... Standing, or sometimes . . . sitting -- sitting in folding chairs arrayed neatly all along the great North Lawn of the Princeton University campus. We were the incoming freshmen of Princeton, and this was our first day at college. They had announced over the loudspeaker: "Incoming freshmen!" We all ducked. Next page: What was unique about 1980?