Book Review : U.S. Math: Is Our Number Up?
Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos (Hill & Wang: $18.95; 126 pages)
If it’s unusually hot for a few days, newspapers proclaim that it’s the greenhouse effect. (Remember the greenhouse effect?) If it’s unusually cold for a few days, newspapers proclaim that it’s nuclear winter. They don’t give much attention to the real explanation for statistical variations in the weather: chance.
When the stock market goes up, learned analysts trot out a bagful of “explanations”: renewed confidence, lower interest rates (or higher interest rates), or corporate profits or whatever. When the stock market goes down, knowledgeable-sounding explanations are offered: the federal deficit or higher interest rates (or lower interest rates) or profit taking or whatever.
Plenty Happening
There are always plenty of things happening on any given day to enable analysts to sound as if they know what they’re talking about. They rarely admit that daily fluctuations in the market are best explained by chance.
Soon the baseball season will get under way. Zillions of statistics will be compiled, a few of which will differ wildly from the past. Home runs will be up or home runs will be down, or left-handed pitchers will win all of their games played at night, or a lifetime .250 hitter will be hitting near .400 at midseason, or something. The sports pages will be full of stories analyzing why this is happening. They will ignore the real reason: chance.
John Allen Paulos, a mathematician at Temple University in Philadelphia, has a name for the public’s failure to understand these matters and its hunger for explanations where there are none. He calls it “Innumeracy,” and he has written a book by that title in an effort to set the world straight. Good luck.
A few months ago in this space I made a passing remark in which I referred to Laetrile as “quackery.” A few days later I received a long and very nice letter from a woman who told me that her husband had been a victim of pancreatic cancer and had been told by his doctors that there was no hope.
He went to Mexico, was treated with Laetrile, and now, several years later, the cancer is gone. As far as she’s concerned, Laetrile cured him. Does it make any sense to tell her that there are always a few unexplained spontaneous remissions?
Medicine a Fertile Field
If her husband had taken aspirin or orange juice or had rubbed mashed potatoes on his head, his cancer would also have gone away, and she would now be singing the praises of those “cancer cures.” People believe what they want to believe.
“Medicine is a fertile area for pseudoscientific claims for a simple reason,” Paulos writes. “Most diseases or conditions (a) improve by themselves; (b) are self-limiting; or (c) even if fatal, seldom follow a strictly downward spiral. In each case, intervention, no matter how worthless, can appear to be quite efficacious.”
At another point in the book he puts the matter more starkly: “There’s always enough random success to justify almost anything to someone who wants to believe.”
So Many Coincidences
Innumeracy, Paulos writes, is all around us, and it’s not just a matter of looking for explanations where there are none and believing them when they are proffered. There are so many things going on in the world, so many bits and pieces of information that come by each of us each day, that the wonder is not that there are coincidences. The wonder is that there aren’t more of them.
Psychologically, though, we tend to overvalue the coincidences and undervalue the vast majority of non-coincidences. Nobody ever talks about dreaming of a plane crash and then no plane crash occurs. Considering that there are billions of people in the world, all dreaming regularly, it’s not surprising or noteworthy that when a plane crash does occur, occasionally somebody, somewhere, has dreamed about a plane crash just beforehand.
Paulos is very good at explaining all of this, though sometimes with a hectoring, bitter tone, for which he apologizes at the very end. He notes correctly that the public’s failure to understand chance phenomena, statistics, probability and the nature of many numerical assertions opens the way for all manner of belief in nonsense. Perhaps more important, it leads to distortions in the making of public policy.
Television frequently portrays old people as poor, living on Social Security, eating dog food. But as a group, old people are financially better off than their children. If you make that argument, you’re accused of being “coldly rational”--”as if ‘warmly rational’ were some kind of oxymoron,” Paulos writes.
Facts Not Examined
Yet, public policy is frequently swayed by anecdotal evidence rather than by facts. And facts themselves are frequently not subjected to rigorous scrutiny.
“The simple expedient of asking oneself, ‘Percentage of what?’ is a good one to adopt,” Paulos writes. “If profits are 12%, for example, is this 12% of costs, of sales, of last year’s profits, or of what?”
“Innumeracy” identifies a pervasive problem very well, but Paulos’ prescription for what to do about is somewhat weaker. Better education, he says. In the last decade, a shelf full of reports has decried the state of mathematics education in this country and called for improvements. None of them seems to have made much difference.
