Can mathematics help you win at Powerball? Improve your chances of finding a handsome man to date who’s not a jerk? How about prove the existence of God? While we’re at it, might the promise of such provocative explorations lure you into picking up a treatise on perhaps your least favorite subject?
If you happen to open Jordan Ellenberg’s brilliantly engaging “How Not to Be Wrong” to Page 10, the answer might be no. Rows of equations spilling over with subscripts and inequality signs might induce a paralyzing Algebra I flashback. But wait — Ellenberg is only illustrating the kind of formalism he intends to steer scrupulously clear of. He pledges to entertain and edify, even if “your mathematical training stops at pre-algebra.”
Is this goal realistic? How does one communicate the “profound” mathematical ideas Ellenberg has in mind when the language needed (algebra, calculus) may not be in most readers’ repertoire? And let’s not forget the question that crushes the aspirations of so many mathematicians yearning to share their passion, the dispiriting lament heard in schools and colleges everywhere: When am I going to use this?
Ellenberg is one of a tiny group of research mathematicians with the credentials to attempt this formidable challenge. As the writer of the long-standing series “Do the Math” on Slate.com, he has brought such arcane concepts as the Poincaré Conjecture and Gödel’s Incompleteness Theorem to the huddled (and math-less) masses. His columns are adept at teasing out the practical repercussions of the math — DNA matches that might falsely implicate you, Wall Street “sucker” bets that could crack your nest egg. Oh, and in case you’re wondering how a mathematician could write such consistently inventive prose, consider that he also published a literary novel: “The Grasshopper King,” in 2003. Mathematician and novelist? What an outlandish concept!
Ellenberg hooks you from the start with the story of Abraham Wald, asked to analyze bullet-hole data from planes returning from World War II sorties. The military wanted to know whether extra armor should be added to areas of greatest need, i.e., where the most bullets had landed. Wald’s solution was the exact opposite: Put armor where you don’t see the bullet holes. The reason such holes were so infrequent in the data was that planes hit there didn’t return.
This is the kind of “mathematical thinking” referred to in the title of the book: “the extension of common sense by other means.” Ellenberg’s talent for finding real-life situations that enshrine mathematical principles would be the envy of any math teacher. He presents these in fluid succession, like courses in a fine restaurant, taking care to make each insight shine through, unencumbered by jargon or notation. Part of the sheer intellectual joy of the book is watching the author leap nimbly from topic to topic, comparing slime molds to the Bush-Gore Florida vote, criminology to Beethoven’s Ninth Symphony. The final effect is of one enormous mosaic unified by mathematics.
Or, more frequently, statistics — misleading probabilities and percentages form the perfect set of targets, given Ellenberg’s vow to simplify. Take the Wisconsin Republican Party’s 2011 claim that Gov. Scott Walker’s policies were responsible for “over 50 percent of U.S. job growth in June.” It’s true that 18,000 jobs had been added nationally, with 9,500 in Wisconsin. But job losses in other states canceled out such gains, rendering these percentages meaningless. Neighboring Minnesota, for instance, had added 13,000 jobs, so Democratic Gov. Mark Dayton could have claimed 70 percent of the national gain had he so chosen.
Ellenberg’s most satisfying debunking is of those who purport to use mathematics to prove God’s existence. Using Bayesian statistics, Ellenberg shows that such arguments point to an origin theory that is even likelier: We are all residents of a computer simulation being carried out by a more advanced civilization. His aim is not to refute anyone’s religious beliefs but, rather, to point out the limits of mathematics: One cannot use it to answer questions of faith. “Think the school board would go for this?” Ellenberg muses about his alternative creation theory, to which my response would be no — but let me be the first to contribute to his campaign if he decides to run for a slot.
Be forewarned: Ellenberg insists on having you get your hands dirty, and as he jots down his probabilities, you’ll be calculating along. This is not a coffee table math book with artfully photographed sunflower-seed whorls illustrating the golden ratio (no pandering to the public’s insatiable appetite for Fibonacci numbers, either). Instead, what you get for illustrations are small cartoons and scribbles, drawn by the author himself, much like those you would find in the notebook of a working mathematician.
But perhaps this imagery is necessary for the show. Ellenberg knows he is playing the role of magician, beguiling us with amazing feats of logic, showing his prowess and that of the methods he touts. He’s also aware of the danger that, blinded by the power of this new tool, we will proclaim ourselves to be right about everything. “Wrongness is like original sin,” he says, something we can never be free of. He even asks us to watch him carefully, lest he fall into the infallibility trap himself. In a world filled with politicians and godmen, Ellenberg, the mathematician, is too principled to position himself as either.
HOW NOT TO BE WRONG
The Power of Mathematical Thinking
By Jordan Ellenberg
Penguin Press. 468 pp. $27.95