and Other Adventures
in Applied Mathematics
By Robert Banks
Princeton University Press
427 pp., $29.95
The noted science-fiction writer Arthur C. Clarke once observed that any sufficiently advanced technology is indistinguishable from a magic trick. In "Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics," engineer Robert Banks lifts the curtain to show off some modern technological sleight of hand. Usually, learning how a trick works disappoints, but the mathematical conjuring explained here has just the opposite effect: Instead of feeling let down, one marvels at the intricate wonders revealed.
This is not a book for the mathematically faint of heart. Banks is a former professor and dean of engineering at the University of Illinois, Chicago campus and does not scruple to include equations of intimidating complexity. Some knowledge of differential and integral calculus is necessary to follow all the math completely.
However, this book still contains much that is interesting, even fascinating, for readers whose grasp of higher mathematics stopped at high school algebra.
For example, in "The Ups and Downs of Professional Football," the author notes that for teams in the National Football League, there is a cycle of wins and losses that averages about 8.2 years.
"This desirable 'up and down' pattern of team performance is accomplished by the draft choice procedure of the National Football League. Overly simplified, the order of selection of new talent by NFL teams is in reverse order to the performance ranking of the previous season. Not surprisingly, it takes a certain amount of time for a team to turn around - for better or worse."
Mathematical patterns affect more than just football teams. The oscillations in the performance of the NFL can also be seen in areas as diverse as business, biology, ecology, and weather.
For instance, Banks describes the early experience of microbiologists trying to show that populations of organisms grow according to a mathematical curve called the logistic equation.
"All too frequently," he writes, "the bacteria concentration, after a rapid initial rise, did not level off at a constant value but instead reached a peak concentration and then plunged to zero." The startling discovery was that "the decline to extinction was due to contamination of the growth environment by lethal products generated by the bacteria themselves, or, in other words, self-poisoning of the system." The analogy, if applied to human population growth, is sobering.
Most examples in this book are descriptions of natural phenomena, from falling dominos to asteroids, icebergs to grains of sand.
The equations are not always easy, in fact quite the contrary, but they are consistent with the results technology has been able to provide. For instance, Banks includes a detailed discussion of the difficulties involved in towing icebergs from Antarctica to San Diego, in order to supply water to the southwestern urban agglomeration.
After extensive calculations of how fast the icebergs could be towed (2 knots maximum), how long it would take to reach California from the Ross ice shelf (20 weeks), and how to melt all that ice once it gets there, he briefly mentions that there might be some environmental problems as a result.
Unfortunately, the author does not give much consideration to the question of whether humankind has the right to remake the world through advanced technology. In order to be credible, partisans on both sides of this debate need to understand and use the language of mathematics and engineering.
The real value of this volume is as a basis for informed participation in the complex and often technical arguments that will shape the future of the planet. For this reason, if for no other, it is worth attempting.
* Frederick Pratter lives in Missoula, Mont.