By John Allen Paulos
Sunday, October 10, 2010; B07
The Dark Arts of Mathematical Deception
By Charles Seife. Viking. 295 pp. $25.95
The title of Charles Seife's new book, "Proofiness," is a takeoff on Stephen Colbert's notion of truthiness, the property of statements that have the ring of truth to them but upon a little reflection are seen to be bogus. Likewise, proofiness refers to numbers and statistical arguments that seem convincing but are really somewhere between unwarranted and ludicrous. Seife begins by pointing out that numbers in the news do not inhabit some ideal Platonic realm but result from very fallible measurements that are often based on vague definitions or faulty assumptions.
He tells the story of the museum guard who claimed the dinosaur on exhibit was 65,000,038 years old. When pressed about the precision of the number, the guard says that a scientist told him the dinosaur was 65 million years old when he was hired 38 years before. Seife calls this error "disestimation," the mathematical sin of underestimating the uncertainties associated with most numbers.
He gives cute names to other types of proofiness as well: Potemkin numbers, those without even a tenuous connection to reality, such as Joe McCarthy's charge of the State Department harboring 205 communists; cherrypicking, examining only data favorable to one's position; randumbness, the tendency to see patterns and order in random data; causuistry, ascribing causes to accidental associations; risk mismanagement, misjudging or even lying about risk, often so that the people assuming it are not the ones reaping its rewards; and so on.
These mathematical solecisms are illustrated with many topical examples, ranging from the non-perils of NutraSweet and the inequities of the death penalty to the numerical skullduggery behind the U.S. abandonment of the nuclear test ban treaty with the Soviet Union in 1982. That last case involved a nonsensical formula that led to a spurious allegation of Soviet cheating. The second half of the book is devoted to somewhat fuller discussions of issues such as the U.S. census and its problems; gerrymandering, which seems to be tolerated if it is politically, rather than racially, motivated; the mortgage crisis, including a particularly clear and brief discussion of it via an analogy involving fire insurance, whereby fire insurance policies are imagined to be bundled and sold the way mortgages were; and close elections, particularly the 2008 Franken-Coleman Senate race in Minnesota and the 2000 Bush-Gore contest.
With regard to the latter, Seife urges acceptance of the uncomfortable fact that some races are essentially ties, that the official and meaningless "exact totals" are sometimes overwhelmed by systemic errors in counting, the vagueness of the election laws and the unclear criteria, definitions and protocols governing them. As I wrote in 2000, trying to determine whether Gore or Bush received more votes in Florida was a bit like trying to measure bacteria with a yardstick. The official 537-vote difference between them recalls the absurdity of the 65,000,038-year-old dinosaur.
Throughout the book, Seife's practiced journalist's eye results in trenchant nonmathematical observations. He notes, for example, that in a very close election the candidate in the lead almost always takes the position that "rules are rules" and the candidate who is behind almost always argues to "count every vote."
Seife condemns the 2000 Supreme Court decision forbidding the use of statistical sampling to ascertain the number of households missed by census workers. Likening the decision to poll taxes, literacy tests and voter ID laws, he notes that its effect is an apportionment of House seats that disenfranchises millions of largely minority voters. The decision seems not only unfair but also inconsistent. For example, if an answer on a census form looks wrong -- say someone claims 1,000,000 children -- census workers are allowed to replace this number with one reflecting what statistically similar households have reported. This imputation and others in common use also violate the prohibition of statistical techniques, but the court has accepted them.
Polls, of course, play an important role in a journalist's craft(iness), and Seife writes that they are one of the primary sources of proofiness in modern life. Real, unpredictable events provide fodder for journalists and commentators, but polls and pseudoevents, which he defines as synthetic, planned and occurring at convenient times and locations, are almost as good for this purpose. Moreover, polls are subject not just to the statistical margin of error but, more crucially, to systemic shortcomings and tendentious special pleading as well.
Disposing of arithmetical mistakes, misjudgments and misunderstandings is, like trash removal, a never-ending job. Seife performs it cogently and entertainingly without resorting to arcane mathematics. The effort is important because the cumulative effect of proofiness is, as he sagely concludes, "toxic to a democracy."