As n goes to [sideways 8]

As I've been preparing to teach calculus this summer -- amid the pressure and excitement to get things right -- I've been reminded of some of the beautiful ideas behind the big C. One of these ideas is that we little creatures of limited faculties -- who would destroy ourselves if we had the chance just to prove we were right -- might be able to predict what happens when some variable goes to infinity, like time. "Find the limit as n goes to infinity," the directions say. It's a bold claim, that we might be able to say anything about infinity. But all the same, it's a beautiful idea.

It's the idea of counting until you can't count anymore and then pushing on. It's taking measurements that are either so small in size or so large in number that you can't count them on your fingers, on paper, or even on a computer, so what's the use? but you do it anyway. You look for patterns. You stand on the shoulder of giants. You take a breath and make a guess. It's the idea of looking forever in the face and being unafraid.

Something about this idea -- or maybe something about the changes happening in my own life -- reminded me of that old PBS series Cosmos. With Carl Sagan and his sonorous drawl that issued forth science like depth charges. In one episode, he talked about the Hindu idea of infinity -- another beautiful idea -- that the universe exists as long as God is awake and ends when God goes to sleep. God wakes again, and the universe starts over. Expansion / contraction, the oscillating universe, death / rebirth. It's all in there: taking what we see, making a model (or a myth) to explain it, and asking what happens when n goes to infinity.