Functions

"Mathematics is conceived in the fires of the real world, and the functions that bring twitching life to the calculus represent processess beyond the closed coffin of a coordinate system -- things that take place in time and that take place in space. The maturation of an egg and the education of an undergraduate both represent processess; so does the circumnavigation of the moon, the beating of the human heart, and the dense shifting of the seas under the influence of the lunar tides. But not every functional relationship, it is important to recall, is a relationship between numbers. There is a world of relationships beyond the world of mathematics in which men and women pair off, children are raised, scores are settled, and fathers age and then die, and none of this correlated with the real numbers. And not every relationship between numbers expresses an interesting mathematical function. Surrounded somewhere in Las Vegas by blue-haired women and hard-eyed men, a roulette wheel spins in the soulless night. It generates a string of random numbers. The association between those numbers and the time at which they are generated describes a matching of numbers to numbers and so a function. It is an association without structure and so without interest. The functions of the calculus represent, they embody, the mathematician's canonical instruments for the depiction of change. They have up to now appeared as a collection. Mathematics is, in part, a rhapsodic subject, full of dark mystery; but it is also a discipline like comparative anatomy in which things are put in their mathematical places and places found for mathematical things." David Berlinski, A Tour of the Calculus