A simple appreciation for magnitude is sometimes sufficient to shed an entirely different light on a story. Of course, there are many other sorts of numerical pitfalls, but this is probably the most basic.
Pause for a bit after reading the headlines for a second mini-test on a couple of other randomly selected arithmetical misunderstandings.
4. Number of Americans with Alzheimer's Believed to Be 5,451,213.
5. Study Shows That Almost 30 Percent of Suicides Occur on Wednesdays and Thursdays. Mid-week Blahs Blamed.
6. Group Argues That a Mere Two Percent Cut in Social Security Ought to Be Diverted to Private Accounts.
So what's wrong with these headlines?
4. The problem here is that the number is ridiculously precise. Definitions of Alzheimer's vary and it's difficult to determine whether a single individual is suffering from it, much less whether five million plus are. Such impossible precision is common.
5. Wednesdays and Thursdays constitute 2/7 of a week or about 28.5 percent. No explanation for the incidence of suicides on these days is required.
6. Here, one needs to know that Social Security usually takes 6.2 percent of one's salary up to a certain maximum. For this year alone, that figure has been reduced to 4.2 percent, a whopping 32 percent reduction, not a 2 percent reduction. Percentage points are not percent! If one was arguing for diversion of a fraction of Social Security contributions to a private account, a 2 percent reduction would sound innocuous, and this is how the Bush administration framed its proposal. A 32 percent reduction does not sound so innocuous.
I suspect the computer scientist John McCarthy had elementary examples like the above in mind when he wrote, "He who refuses to do arithmetic is doomed to talk nonsense."
John Allen Paulos, a professor of mathematics at Temple University in Philadelphia, is the author of several best-selling books, including "Innumeracy," "A Mathematician Reads the Newspaper," and "Irreligion." He's on Twitter and his "Who's Counting?" column on ABCNews.com usually appears the first weekend of every month.