Getting soaked by the numbers
slicing pizzas, racing turtles, AND FURTHER ADVENTURES IN APPLIED MATHEMATICS
By Robert B. Banks
Princeton University Press
284 pp., $ 24.95
An optimistic corollary to Murphy's Law is that it will never rain if you remember your umbrella.
If you should forget, however, it would be good to have a copy of this handy compilation of mathematical lore. Emeritus engineering professor Robert Banks is author of "Towing Icebergs, Falling Dominos, and Other Adventures in Applied Mathematics." In that earlier volume, as in the current one, he displayed a playful imagination and love of the fantastic that one would not ordinarily associate with a mathematical engineer.
For example, in "How Fast Should You Run in the Rain?" the author takes up this momentous question from a straight-faced scientific perspective. Obviously, the faster you jog, the less time you will be out in the wet. On the other hand, your front and your shoes and socks will get splashed, adding to your sogginess.
Banks selects "an aesthetically unattractive but mathematically simple rectangular prism" as a model of the human form. He notes soberly that this problem "demonstrates the usefulness of differential calculus." It also demonstrates that mathematics does not have to be drudgery.
Banks also takes up problems that have more serious consequences. He asks, "What would happen if all the ice presently locked up mostly in the polar caps and glaciers were to melt?" Astonishingly, he calculates that the total area flooded by the melting ice would be about three times as large as the 48 states of the contiguous United States.
The chapter "The Great Explosion of 2023" should be required reading for anyone who tries to use statistics to project present trends. Using a simple model of population increase, he calculates that the earth's weight of humans is doubling every 12 years, and the period of the doubling time is decreasing. "On November 1, 2023 there will be an infinite number of people in the world, and the doubling time will have shrunk to zero." Clearly, some limiting events will have to intervene.
The author notes "that during 1995 the world's population increased by about 95 million people. If these 95 million were to comprise an entirely new country, where would it rank, in 1995 population, among the world's nations? The answer is number 11.... Just think: an enormous new country every year!"
Banks's style is entertaining but never condescending. Some of the math is pretty tough; it helps if you did well in trigonometry as well as introductory calculus and analytic geometry. It is possible to read this book without working through the math, but that would be missing the point.
The author notes, "My strong hope is that this collection of mathematical stories will be interesting and helpful to people who long ago completed their formal studies.... I think this is especially true as all of us enter a new century that assuredly will place heavy emphasis on mathematics, science, and technology."
We live in a world that has benefited immeasurably from improvements in communication, public health, and sanitation. At the same time, of course, the nuclear sword has hung over us for half a century. Surrounded by the consequences of our technology, it is essential that we have some understanding of the tools that shaped them.
*Frederick Pratter is a freelance writer in Missoula, Mont.
(c) Copyright 1999. The Christian Science Publishing Society