Review of the new book How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg:
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 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.
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