Proofiness: The Dark Arts of Mathematical Deception

  • Charles Seife
Viking: 2010. 295 pp. $25.95 9780670022168 | ISBN: 978-0-6700-2216-8

The statement, published in a newspaper, that only 0.027% of US felony convictions are wrongful is false. Based on a back-of-the-envelope calculation, it was nevertheless quoted in a court case that ended with a prisoner being sent to his death. Such bad figures are “toxic to democracy”, argues science journalist and former mathematics student Charles Seife in his latest book Proofiness, a field guide for spotting the numeric impostors. Seife's polemic against the reporters, politicians, scientists, lawyers and bankers who spread tenacious and specious statistical claims is strident but sobering.

Credit: ILLUSTRATIONS BY G. POTENZA

Seife coins the term “proofiness” to refer to the misuse of numbers, deliberate or otherwise. He dubs the simplest quantitative sins “fruit-packing”. These include: “cherry-picking” the data, as he says Al Gore did when describing climate change in An Inconvenient Truth; “comparing apples to oranges”, as economics pundits do when they neglect to adjust for price inflation; and “apple-polishing”, as when advertisers use graphics to mislead.

Seife finds bogus figures in every corner of public life — where there are numbers, they will be fudged. He does not spare his fellow hacks, citing the opinion poll as a method for journalists to manufacture their own stories. Surveys, no matter how large their sample sizes and small their margins of random error, may be skewed by slanted questions, biased samples and lying respondents, he explains.

Even the simple act of counting ballots can be fraught with controversy, as in the contested Florida presidential recount in 2000. Claiming the margin of error to have been larger than the 537-vote difference between George W. Bush and Gore in that state, Seife suggests that the race should have been declared too close to call — and therefore, by Florida law, settled by the drawing of lots. He also describes economist Kenneth Arrow's impossibility theorem, which expresses how no voting system can fully capture the preferences of a group.

Seife faults some scientists, too, for overinterpreting their data and making extravagant causal inferences when the evidence is slim. This is particularly problematic in health and nutrition research, he argues, casting doubt on studies alleging, for example, that an artificial sweetener causes brain cancer and that debt causes illness. He criticizes a handful of peer-reviewed articles, including some published in Nature, for making claims that, in his eyes, go beyond common sense. For example, Seife thinks it unlikely that wearing red helps Olympic fighters to win, offering his own analysis of results from the 2008 Beijing Olympics as proof. He dismisses other assertions, such as that wide-hipped women give birth to more sons than daughters, as mixing up cause and effect. Seife highlights how scientists can sometimes be seduced by models whose curves fit their data, attributing misguided efforts to find causal relationships to a “misfiring of our pattern-seeking behavior”.

Moving on to the legal system, Seife describes how probabilities may be taken out of context in court. Statistics showing that particular crimes or events are rare have wrongly been cited as proof of innocence and guilt — delivering what Seife calls “judicial nonsense”. In business, problems arise when numbers are used to under- or overstate potential dangers. Whereas the media tend to overplay risk, Seife reminds us that “underestimating risks, not exaggerating them, is where the money is”. He points to prominent company directors who hid their firms' liabilities, and corporate banks that had to be bailed out by governments because of their reckless underestimation of credit risk.

Seife can overstate his case, as when he claims that proofiness is robbing us of “the democratic right to think for ourselves”, oiling the “machinery of death” and “crippling our economy”. He does little to explain why, given the onslaught of phony figures, many people remain susceptible to them, and he provides few practical suggestions for reducing their influence. Yet there is plenty of healthy scepticism and common sense in Seife's taxonomy of statistical malfeasance. In a world of unreliable numbers, Proofiness is a helpful guide.