First Steps to Infinity

Infinity has many faces. The layman often perceives it as a kind of “number” larger than all numbers. For some primitive tribes infinity begins at three, for anything larger is “many” and therefore uncountable. The photographer’s infinity begins at thirty feet from the lens of his camera, while for the astronomer—or should I say the cosmologist—the entire universe may not be large enough to encompass infinity, for it is not at present known whether our universe is “open” or “closed,” bounded or unbounded. The artist has his own image of the infinite, sometimes conceiving it, as van Gogh did, as a vast, unending plane on which his imagination is given free rein, at other times as the endless repetition of a single basic motif, as in the abstract designs of the Moors. And then there is the philosopher, whose infinity is eternity, divinity, or the Almighty Himself. But above all, infinity is the mathematician’s realm, fir it is in mathematics that the concept has its deepest roots, where it has been shaped and reshaped innumerable times, and where it finally celebrated its greatest triumph.