Fun (And Fear) With Numbers

Quick: what’s the normal human body temperature? If you say 98.6°F, you’re almost certainly wrong. There’s an infinitesimal chance you could be right, but that would only be a tremendous cosmic coincidence, even though you’ve sliced the number down to an impressive tenth of a degree. But all measurements are imperfect, which is the exhilarating and debilitating point of a wonderful new book called PROOFINESS, by Charles Seife. Back to body temp in a moment.

This book, along with Douglas Hofstadter’s beautiful work on what he calls “innumeracy,” represents the mathematics equivalent of the many epiphanies I experienced in college logic class. You can use the “sniff test” to weed out B.S., but logic gives you precise formulas to help you determine that something may sound nice, but it has not been proven to be true. You can find logical fallacies all over political discourse — it’s the ever-yielding motherlode — and “proofiness” is the numerical equivalent, the art of using bogus mathematical arguments to “prove” something is true. A wag of my finger to Mr. Seife for failing to credit Stephen Colbert, who coined the term “truthiness” on his first broadcast; this is an obvious callback, especially given the frequent bursts of humor here, but it would still have been courteous to acknowledge the debt.

“Proofiness” is indeed rampant, and once you get used to looking for it, you become amazed at how much claptrap you yourself have fallen for over the years. It’s used by all colors of the political spectrum. “If you want to get people to believe something really, really stupid, just stick a number on it,” the author writes. “Even the silliest absurdities seem plausible the moment that they’re expressed in numerical terms.” He offers several types of red flags to watch out for.

“Potemkin numbers” are theoretically the easiest to debunk, since they are numerical claims that the speaker has simply pulled out of his posterior regions, such as Joe McCarthy’s charge that there were 205 Communists working in the State Department, or Louis Farrakhan’s proclamation that a million people actually attended his Million Man March. Of course, you have to have the truth at your disposal to oppose Potemkin numbers. McCarthy’s figure kept changing until he was finally discredited, and Farrakhan was so incensed at the Park Service’s estimate of 400,000 attendees, give or take 20%, that he charged racism and threatened a lawsuit, so the Service just quit estimating such public events. That’s why nobody can tell you authoritatively how many people attended Glenn Beck’s recent rally in Washington, allowing the Potemkin numbers to start flying the next day; proofiness expert Rep. Michele Bachmann (R-Minn.), echoing Farrakhan, told her fans not to believe anybody who told them it was less than a million, which all available evidence suggests is overstating to the second power. But these days, every “objective” estimate is suspect to people who don’t like the result.

Tougher to spot is “disestimation,” or placing more trust in precision than is warranted. For example, take the “normal” body temperature of a human being as expressed on the Fahrenheit scale; we’re one of the few countries that still uses this antiquated form of measurement, and here’s one more bit of evidence that it puts us at a disadvantage. OK, what is “normal”? It’s 98.6 degrees, of course: every schoolchild knows the answer. But our knee-jerk response to this “slam-dunk science question” is almost certainly inaccurate. The number was established by a 19^th-century German scientist who claimed (dubiously) to have measured a million people. But “normal” body temperature fluctuates, depending on where you take the measurement (Herr Doktor used the armpits), the time of day, even from person to person. Yet he came up with a suspiciously whole number: exactly 37 degrees Centigrade – which converts to the seemingly more precise 98.6°F. Far from honing the figure to a tenth of a degree, this result is actually so “rounded” that a thoughtful user of the Celsius scale would naturally be skeptical. Yet even some American medical texts say if you’re above 98.6 – precisely – then you have a fever. Mr. Seife jokes about the museum docent who gives the age of a dinosaur skeleton as “Sixty-five million and thirty-eight years.” How could he be so sure? “Because the day I started this job, I was told it was 65 million years old – and I’ve been here for 38 years.” The precision he cites really isn’t there at all – but it’s usually much harder to recognize disestimation.

Then there’s “fruit-packing,” or deliberately distorting information. One can “cherry-pick,” such as Al Gore’s dramatic AN INCONVENIENT TRUTH slides that show Florida flooding. This calamity assumes a twenty-foot rise in sea level, when most scientists – who do not doubt global warming is real – project only two feet, maybe as much as four, within the next century. Gore’s just cherry-picking the worst case, thus making it seem more likely than scientists really expect. Or “compare apples to oranges,” as in, “George W. Bush borrowed $1.05 trillion, more than all the previous presidents combined.” Now this presidential zero was a spendthrift all right, cutting taxes and fighting two wars on credit at the same time, but that statement, though mathematically accurate, is purposely misleading because it fails to take inflation into account. You can “polish fruit,” like deliberately encouraging people to mistake the mathematical average, or mean, for the midpoint, or median. You hear this all the time when a politician, including every recent president, brags about “average” tax breaks. This chestnut isn’t in the book, but if Bill Gates walks into a room full of broke people, the average net worth is now in the millions, but the median – half the people are above this figure and half below — is still $0.00. In this case, the correctly stated average abets a lie – and devious people know it can do so again and again.

We constantly find patterns or linkage where they don’t exist. The notion of NutraSweet as a cause of brain cancer is absolutely false. There is no connection. None at all. Yet a flawed research paper has haunted the product since the mid-90s; using identical logic, dismissing facts that don’t help your case, such as the incidence of brain tumors actually plummeting while NutraSweet usage was increasing, you can “prove” that the Reagan budget deficits caused brain cancer! (As the author actually did, in the Journal of Neuropathology and Experimental Neurology: “The editor in chief had a good sense of humor.”) Female sprinters’ speeds have been gaining on males very fast – probably because more young girls are participating in track and field, producing better and better world-class sprinters — yet if you believed this as continuous relative progress, they’d be beating men (in the 100-meter, sometime between 2064 and 2788, according to a particularly foolish paper actually published in Nature) and eventually running at the speed of light, in what the author calls “regression to the moon.” NASA fudged safety numbers, even lied, to keep the space shuttle program alive, until their “risk mismanagement” blew up in their faces. The much-lampooned, color-coded Homeland Security Advisory System has never been below “elevated” risk since 9/11. Every single day, it’s been “higher than usual,” the meaning of the Department’s word. As a moment’s reflection will reveal, that’s impossible.

Nowhere does ”randumbness” thrive more heartily than the political process. From the gerrymandering of congressional districts after each census (and, you’ll remember, a few years ago Tom DeLay and his pals in Texas wouldn’t even wait for that event) which unfairly preserve incumbents’ seats, to the mind-numbing minutiae of tight-race recounts, deviltry abounds on both the left and the right. Mr. Seife goes into detail about the 2008 Minnesota Senate race between Norm Coleman and Al Franken, in which only a few hundred votes, out of nearly three million cast, separated the two. He makes the argument that in a race that tight, recounts only introduce more errors and will naturally swing one way or another, never really getting anywhere. He says that basically the race ended in a tie, and should have been decided by a coin toss, since it is impossible to know who really won when the candidates are separated by only 0.007 percent. Had that happened, Minnesotans would have saved millions of dollars and had both of their senators seated when the next Congress convened. The author also believes the Florida presidential electors in 2000 should have been awarded the same way – another race in which it was impossible to be any more precise, yet the issue still dragged on for lawyer-enriching weeks.

Political polls are also subject to manipulation, most of which you never see. The “margin of error” is simple and mathematical: the more people polled, the smaller the margin of error. But there’s a difference between statistical errors and systematic ones. The “margin of error” only takes into account mathematical sample size, not which people compose the sample or what they are asked. In spring 2005, most polls seemed to show that a majority of Americans favored removing the feeding tube in the tragic Terri Schiavo case. A group called the Christian Defense Coalition hired the Zogby polling firm and armed it with questions including: “Do you agree or disagree that the representative branch of government should intervene when the judicial branch appears to deny basic rights to the disabled?” and “Michael Schiavo has had a girlfriend for 10 years and has two children with her. Considering this, do you agree or disagree that Michael Schiavo should turn guardianship of Terri over to her parents?” Needless to say, this particular poll yielded quite different results. In 1936, the Literary Digest famously blew a 2.3-million-response mailback poll on the Alf Landon-FDR presidential race by failing to realize that (1) out-of-power Republicans were more likely to be angry and send the envelope back, a phenomenon known as “volunteer bias,” and (2) the Digest itself tipped toward well-to-do households, thus favoring Republicans. They projected 54 percent for Landon, their huge sample size suggesting a margin of error of 0.06 percent. He got 37 percent, an error more than 250 times the expected margin. I’ve developed a healthy skepticism for all polls, particularly when they’re measuring disenfranchised and/or angry people.

The ultimate big-tent poll is, of course, the decennial U.S. Census. The author, and most other people who know anything about statistics, insist that by the judicious use of sampling, the census could be many times more accurate than it actually is, and would no longer require costly and time-consuming door-to-door canvassing on the households who don’t return their forms. (In 2000, it was about one third of the country.) When the Census Bureau proposed presenting its best, sampling-corrected number to Congress just before the 2000 count, House Republicans sued, and the case went all the way to the Supreme Court, where Justice Antonin Scalia led a 5-4 decision that sampling was unconstitutional. (Conservatives don’t like sampling because door-to-door canvassing tends to undercount ethnics and the poor, who sometimes don’t reveal everything to the census-taker – and they tend to vote Democratic. Sampling would correct for this, which is a Republican no-no.) We continue to spend vast fortunes to get an inaccurate census – and everybody knows it.

Lest you think this is just a bunch of harmless numbers, they influence public policy to a remarkable degree. “Experts” spout bogus statistics in court to convict the innocent and release the guilty; one such man made a handy living testifying the same predictable way in hundreds of capital cases, including many in which DNA evidence later proved the accused to be innocent. Whatever your personal views on the morality of abortion, understand this: there is no proof of a link between abortion and breast cancer. None. Just to be clear, as the author writes, “the association between abortion and breast cancer is nonsense.” It was promulgated in 1996 by an endocrinologist named Joel Brind, who analyzed two dozen studies and failed, like the Literary Digest pollsters, to account for systematic error; he saw patterns where none existed, as Mr. Seife explains cogently. But the flawed report was a welcome sword in the hand of anti-abortion activists, and it caught on. A 2003 report at a conference of the National Cancer Institute, surveying the same data and also more recent studies, concluded that it was well established that abortions did not increase the risk of breast cancer. Its acceptance was unanimous except for one conference participant: guess who? Yet just a few months later, the state of Texas – home to the country’s wackiest school-book board – passed the “Woman’s Right To Know Act,” requiring every abortion doctor to lie to his patients about, guess what? You’re getting good at this! In South Dakota, they have to warn patients about a bogus increased risk of suicide, also the result of systematic errors in analysis. This isn’t any “right to know.” It’s a calculated misuse of numbers in an effort to convince someone not to have an abortion. The end result may make you happy. But setting the social issue aside, a physician being forced by the state to scare his patients by lying to them makes me mad.

PROOFINESS can make you mad, too, no matter what your politics. It can also make you chuckle; here are some of the dumbest numbers ever conceived. (For example, in 1897, an Indiana state senator introduced a bill to change the value of pi from 3.14159 to 3.2, to make calculations easier. It got out of committee and passed the House unanimously before the head of Purdue University’s math department was able to explain and persuade the state Senate to shelve the bill indefinitely, where it remains today.) But most of all, this book does what all good commercial nonfiction should: it makes you think.

EDIT: More reasons to distrust political polls.

AND ANOTHER: In late November 2010, after nine ineffective years (except when higher-ups needed it to stir the political cauldron, as founding Sec. Tom Ridge writes that he suspected), the Department of Homeland Security finally decided it might be time to junk the color-coded terror alert system. Good riddance to bad rubbish. The same week, a Texas jury found that oleaginous gerrymanderer Tom DeLay guilty on a criminal charge of money laundering. All in all, it was a pretty nice week, for which I properly gave thanks. It took until early May 2011 to finally, physically, cast that bright and shiny but illiterate child’s-crayon system into the ether. Homeland Security Sec. Janet Napolitano did the long-overdue honors.

September 2013: A Texas court reversed the DeLay jury’s decision, citing insufficient evidence.