"Ultimately, the credit for this book has to go to my editor, ...who first told me it was a math book. Initially, that came as a complete surprise," writes author K. C. Cole. The strength of this book flows directly from that surprise and from the fact that this is not a math book. Rather, it's a refreshing book about math by a keen-eyed outsider with her nose pressed tightly against the mathematics candy store window.
Cole, a science writer for the Los Angeles Times and recipient of the 1995 American Institute of Physics Award for Best Science Writing, is a perceptive, sympathetic observer. Even the goal she sets for herself reflects her astute sense of society's ambivalent attitude about mathematics:
If I could accomplish one thing in this book, it would be to show that an interest in the quality of life is in no way diminished by quantitative arguments.
If some of us who work inside the candy store find such an objective strangely defensive, perhaps we need to step outside for a little while. K. C. Cole lets us see ourselves and our discipline as others see us, even as she gives her non-scientist readers insightful glimpses of mathematics and science all around them. With the deft touch of an accomplished journalist, she chooses just the right simile or metaphor or current event to tease out enlightening, entertaining analogies between deep ideas and everyday things.
The fourteen chapters of this book are divided into four main parts, with Chapter 1, "What's Math Got to Do with It?" serving as the introduction. In this chapter, Cole sets both tone and purpose:
[M]athematics...brings a surprising clarity to an astonishing range of issues, from cosmic questions (the fate of the universe) to social controversy (O. J.'s guilt) to specific matters of public policy (race and IQ scores).... It is a language that allows us to translate the complexity of the world into manageable patterns. In a sense, it works like turning off the houselights in a theater the better to see a movie.
Part I, "Where Mind Meets Math," explores the difficulties we humans have in trying to get a reliable "gut feeling" for some fundamental mathematical ideas. The two chapters in this part contain entertaining, if frustrating, instances of the intuitive incomprehensibility of very large and very small quantities, exponential growth, and reasonable risk assessment. Cole also recounts a number of stories and images used by scientists to help us overcome this apparent mismatch between psychology and reason, such as this one by Sir James Jeans:
Empty Waterloo Station of everything except six specks of dust, and it is still far more crowded with dust than space is with stars.
The chapter on risk assessment also is rich in polite, but trenchant social commentary, leaving little doubt as to the relevance of mathematics to the pressing social problems of our world.
Part II, "Interpreting the Physical World," is by far the largest of the four parts. Its five chapters examine variants of the signal vs. noise problem---the difficulty of finding and isolating useful information from the clutter of real-world phenomena that inundate use wherever we turn. There are chapters on the reliability of measurement and of prediction, on differences related to size, distance, and time scale variation, and on isolating patterns of intelligible data amid apparent "static." Some of the anecdotes and examples in this part are quite familiar, at least in scientific circles, some less so. One of them is the key to the book's title:
"No such thing as a teacup the size of Jupiter is possible in our world," say the Morrisons. As a teacup grew to Jupiter size, its handle and sides would be pulled into the center by the planet's huge gravity until it resembled a sphere.
Part III, "Interpreting the Social World," deals with fairness---in voting, in apportionment, and in competition. Many of Cole's examples in these chapters come right out of the news headlines: the withdrawal of Law professor Lani Guinier's nomination as head of the Justice Departments civil rights division because of her mathematically correct, but unpopular writings on voting methods; division of the sea floor by the 1994 international Convention on the Law of the Sea; California's Clear Air Act of 1990; and so on. Once again, the impact of mathematical reasoning on our social order is self-evident.
Part IV, "The Mathematics of Truth," looks at mathematics as a mechanism for coping with "Why?" Despite its somewhat pretentious title, this part deals with some very down-to-earth questions, including correlation vs. causation, the differences among mathematical, experimental, and legal proof (using the O. J. Simpson trial as a literal case in point), and symmetry as a basis for conjecture about the behavior of the physical world. Although some of the material in these three chapters heads off into deep waters, Cole does a very nice job of keeping the imagery clear, the style informal, and the examples current.
Of course, no book is perfect, even by its own standards. As you might expect, Cole's admirable efforts to express complex mathematical ideas in simple, intuitive terms occasionally cross into the realm of outright distortion. However, I found only two or three instances of that---too few even to cite a "typical" example. In fact, this book is remarkably error-free, better in that regard than many college mathematics texts.
K. C. Cole has done her job well. This is a book for virtually everyone. Its informal style makes for easy, enjoyable reading, yet it offers a wealth of insight into the interplay between mathematics and a broad range of social, scientific, and political topics. It would make an excellent addition to any high school or undergraduate library, and a superb, motivational supplement to almost any textbook in a first-year college liberal arts math or "quantitative literacy" course.