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Go figure

Can bad math undermine a democracy? An eye-opening look at the sloppy statistics and fuzzy figures that bombard and bamboozle us

By Jordan Ellenberg
Globe Correspondent / September 26, 2010

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The great Massachusetts comic Eugene Mirman has a routine about people who quote half-remembered statistics. He says he likes to tell those people that he read somewhere that 100 percent of Americans are Asian.

“But Eugene,” they say, “you’re not Asian.”

And the punchline, delivered with magnificent self-assurance: “I read that I was!”

Charles Seife’s spirited new book, “Proofiness,’’ is a nearly 300-page exposition of Mirman’s joke, which, per Seife, is on us. In every realm of life, from commerce to politics to health, we are being snookered by fake numbers, delivered with the false conclusiveness that only two or three decimal places and a percentage sign can impart. “If you want to get people to believe something really, really stupid,” Seife writes, “just stick a number on it.” “Proofiness’’ is a field guide to mathematical trickery, in the spirit of Darrell Huff’s classic “How to Lie with Statistics.’’ One hopes it will serve as a public inoculation against the malady it describes.

Seife’s targets are less ridiculous than Mirman’s, but sometimes only just. A British psychologist generated buzz in 2003 by releasing a “mathematical formula for happiness.” In 1992, an overzealous attachment to a linear statistical model led researchers to claim in the journal Nature that women marathoners would outrun men by 1998.

Seife defines proofiness as “the art of using bogus mathematical arguments to prove something you know in your heart is true — even when it’s not.’’ In its most pernicious form, it assigns exact numbers to inherently fuzzy quantities, as when an expert witness delivered a defendant to the chair by testifying he was “100 percent certain” the man would kill again; or as in the famous case of Sally Clark, sent to prison for murdering her children based in part on the testimony of a pediatrician that the probability of two cases of sudden infant death syndrome striking a single family was about 1 in 73 million.

In the same spirit, Seife revisits two disputed elections: the 2008 Minnesota Senate race between Al Franken and Norm Coleman, and the 2000 presidential election in Florida. Minnesota undertook a full recount to determine precisely which would-be senator had garnered a few thousandths of a percent more votes than the other; the exercise quickly degenerated into an absurd spectacle, in which distinguished lawyers were reduced to arguing over what to do about a ballot in which a voter both filled in the oval for Franken and wrote in the name “lizard people.’’ The Florida recount was just as close, and just as confused (featuring Pat Buchanan in that contest’s version of the lizard people).

Seife, impressively, finds something new to say about this much-picked-through mess. In both cases, he argues, all the pain and conflict arose from trying to measure a margin of error that simply didn’t exist. Saying that 537 more Floridians voted for Bush rather than Gore is like saying one person is a 10th of a millimeter taller than another; it’s spurious precision. In every mathematically meaningful sense, the election was tied. Next time this happens, Seife says, we should do the fair thing and flip a coin.

(But be warned: Seife doesn’t say exactly which elections should be decided by coin. Suppose a first count with a margin of less than 0.05 percent triggers a coin flip; pretty soon an election will end up within a few dozen votes of the threshold, and we’ll be right back to arguing about the lizard people ticket.)

Seife writes clearly and without resorting to equations, but he’s hyperbolic at times (I lost track of how many entities were “stunningly” this or “incredibly” that) and too fond of his catchphrases (“randumbness,” “causuistry,” and “proofiness” itself.) The book will also lose some readers whose political sympathies point right; Seife makes a game effort to expose mathematical deceptions by liberals as well as conservatives, but you can tell his heart’s not in it. He could easily have devoted more space to shady math popular on the left, like the old commonplaces that 10 percent of people are gay, or that the 99.5 percent of DNA all humans share means “we’re all the same beneath the skin.” And the villain of Seife’s book is not a mad mathematician using his computational power for evil; it is Justice Antonin Scalia, who first appears in “Proofiness’’ among the bad guys of Bush v. Gore, returns in the next chapter with a mathematically muddy rebuff to the use of statistical sampling in the US Census, and finally issues a peevish defense of the death penalty from the bench using a spectacularly proofy figure obtained from a newspaper column: 99.973 percent of convicted felons are guilty.

For Seife, Scalia is a master deceiver, using decimals and figures to mislead his fellow justices and the public. I think it’s more complicated than that. Scalia, like all of us, reasons backwards as well as forwards; he knows what he believes to be true and constructs a chain of argument that gets him to that belief by reasonable-looking steps. Numbers that tell us what we want to hear seem convincing; numbers that don’t get the skeptical eye. The most insidious mathematical deceptions are the ones we practice on ourselves. Seife’s book is an admirable salvo against quantitative bamboozlement by the media and the government; I wish it offered more to help each of us defeat the Antonin Scalia within.

Jordan Ellenberg is an associate professor of mathematics at the University of Wisconsin-Madison and the author of “The Grasshopper King.’’ Contact him through his blog at quomodocumque.wordpress.com or by e-mail at ellenber@math.wisc.edu.

PROOFINESS: The Dark Arts of Mathematical Deception By Charles Seife

Viking, 295 pp., $25.95