“When am I going to use this?” This is the quintessential complaint-cum-question from elementary school students the world over. It is also the introduction to Jordan Ellenberg’s new book dedicated to explaining exactly when and how we can and do use mathematics. In his new book, Ellenberg provides ample demonstration of Carl von Clausewitz’ assertion that mathematics is the extension of common sense. Covering statistics on the future of obesity, predicting terrorist behavior, and of course—the lottery, Ellenberg shows how significant mathematical constructs are when we want to increase the accuracy of our predictions.
"You've been using mathematics since you were born and you'll probably never stop. Use it well."Ellenberg launches his argument for mathematics with a story about Abraham Wald, a mathematician who emigrated from Vienna to New York at the start of World War II. One of Wald’s early assignments included strategically armoring fighter planes so that the planes had the ideal balance between protection and lightness. Too much armor would slow down the plane’s movements; too little would leave it vulnerable. Despite the low number of bullet holes in the engines of the returned planes, Wald concluded that the armor should in fact be concentrated on the engine (and anywhere else bullet holes were not). The reasoning was that the planes with bullet holes in their engines simply did not return because bullet holes in the engine most often meant the plane crashed. Ellenberg’s point is that looking at only numbers would have likely sacrificed a crucial (and life-saving) revelation, using mathematics as an extension of simple common sense resulted in important improvements to how the Army protected its bomber planes from WWII onward.
How Not To Be Wrong’s five parts lead readers through case after case in which math explains either the success or failure of everyday predictions or operations that many of us come in contact with frequently. Topics such as lotteries, banking and investing are the low hanging fruit, and Ellenberg makes sure to cover plenty of that terrain. But he also gets into “bigger” issues such as tax policies, showing how Reaganomics perverted the Laffer curve for the benefit of an apparently overtaxed class of high earners. Ellenberg examines “regression toward the mean”, citing Sir Francis Galton’s failed Hereditary Genius and the risk of ignoring important external influences on the performance of any specific group.
There is a crucial part of Ellenberg's argument, though it doesn't come until the end of the book. Citing the statistician-turned-celebrity Nate Silver, Ellenberg begins to delineate the important difference between an honest statistical appraisal of a scenario and simple "hedging". In his own words:
Math gives us a way of being unsure in a principled way: not just throwing up our hands and saying "huh", but rather making a firm assertion: "I'm not sure, this is why I'm not sure, and this is roughly how not-sure I am." Or even more: "I'm unsure, and you should be too."Across eighteen chapters, readers are privy to case after case in which our subjects were either wrong or would have been wrong, if not for a careful confluence of both math and everyday smarts. While the cover of this book suggests we are about to be proven how powerful mathematics is in everyday life, we get more than that. We learn how important our existing common sense can be, as long as we temper that sense with the rigors of mathematics.