Geometry, Statistics, Probability: Variations on a Common Theme

ion Mathematicians like to talk about how things behave, rather than what they are. Nonmathematicians often prefer the reverse. "Anything that behaves this way is a vector (because I said so)" is not a natural way of talking to the nonmathematician. Mathematicians ought to be more sensitive to this than they typically are. Repeating examples in different words, emphasizing the equivalence of the various means of expression rather than which expression came "first," is important. Once students understand the ideas expressed in some language, they will be more willing to study the logical paths between them. The choice of words is important. "Point" and "line" should be used only for the common geometric ideas they convey. "Vector" seems as good as any term for the abstract notion.