Innumeracy: Mathematical Illiteracy and its Consequences by John Allen Paulos

«

I remember once listening to someone at a party drone on about the difference between “continually” and “continuously.” Later that evening we were watching the news, and the TV weathercaster announced that there was a 50 percent chance of rain for Saturday and a 50 percent chance for Sunday, and concluded that there was therefore a 100 percent chance of rain that weekend. The remark went right by the self-styled grammarian, and even after I explained the mistake to him, he wasn’t nearly as indignant as he would have been had the weathercaster left a dangling participle. In fact, unlike other failings which are hidden, mathematical illiteracy is often flaunted: “I can’t even balance my checkbook.” “I’m a people person, not a numbers person.” Or “I always hated math.”

<...>

Even more ominous is the gap between scientists’ assessments of various risks and the popular perceptions of those risks, a gap that threatens eventually to lead either to unfounded and crippling anxieties or to impossible and economically paralyzing demands for risk-free guarantees. Politicians are seldom a help in this regard since they deal with public opinion and are therefore loath to clarify the likely hazards and trade-offs associated with almost any policy.

Because the book is largely concerned with various inadequacies&mash;a lack of numerical perspective, an exaggerated appreciation for a meaningless coincidence, a credulous acceptance of pseudosciences, an inability to recognize social trade-offs, and so on—much of the writing has a debunking flavor to it. Nevertheless, I hope I’ve avoided the overly earnest and scolding tone common to many such endeavors.

The approach throughout is gently mathematical, using some elementary ideas from probability and statistics which, though deep in a sense, will require nothing more than common sense and arithmetic.

»

From the introduction by the author

«

There is a strong general tendency to filter out the bad and the failed and to focus on the good and the successful. Casinos encourage this tendency by making sure that every quarter that’s won in a slot machine causes lights to blink and makes its own little tinkle in the metal tray. Seeing all the lights and hearing all the tinkles, it’s not hard to get the impression that everyone’s winning. Losses or failures are silent. The same applies to well-publicized stock-market killings vs. relatively invisible stock-market ruinations, and to the faith healer who takes credit for any accidental improvement but will deny responsibility if, for example, he ministers to a blind man who then becomes lame.

This filtering phenomenon is very widespread and manifests itself in many ways. Along almost any dimension one cares to choose, the average value of a large collection of measurements is about the same as the average value of a small collection, whereas the extreme value of a large collection is considerably more extreme than that of a small collection. For example, the average water level of a given river over a twenty-five-year period will be approximately the same as the average water level over a one-year period, but the worst flood over a twenty-five-year period is apt to be considerably higher than that over a one-year period. The average scientist in tiny Belgium will be comparable to the average scientist in the United States, even though the best scientist in the United States will in general be better than Belgium’s best (we ignore obvious complicating factors and definitional problems).

So what? Because people usually focus upon winners and extremes whether they be in sports, the arts, or the sciences, there’s always a tendency to denigrate today’s sports figures, artists, and scientists by comparing them with extraordinary cases. A related consequence is that international news is usually worse than national news, which in turn is usually worse than state news, which is worse than local news, which is worse than the news in your particular neighborhood. Local survivors of tragedy are invariably quoted on TV as saying something like, “I can’t understand it. Nothing like that has ever happened around here before.”

»

From the chapter “Probability and Coincidence”