Let me begin with the first of two simple tests. Below are three headlines. Before reading any further, think about them for a bit and note your response to them.
1. After the Packers' Super Bowl victory, an exuberant Aaron Rogers Shook Hands with Everyone in the Stadium.
2. Experts Fear Total US Housing Costs (Rents plus Mortgage Payments) Will Top $2 Billion in 2011.
These are just three of countless headlines or pseudo-headlines I might have chosen, but there's no need to belabor my point. Many people will recognize what should be clearly wrong with them, yet many people will not.
I have no formal statistics on the percentages in each class, but it never ceases to strike me how much public misunderstanding of issues derives from not paying any attention to numerical magnitudes in news stories. For too many people, numbers are there to provide decoration, not information.
Of course, in the artificial context of this test, not paying close attention is quite excusable. These are not real news stories after all. In any case, here is a brief account of a glaring problem with each of the three headlines above.
1. Making a few assumptions and carrying out a rough calculation shows that this story has to be bogus.
Any reasonable guess about the stadium capacity would be somewhere between 40,000 and 100,000, so let's say the stadium holds 70,000 or so people.
If they were all perfectly disciplined and lined up and proceeded past Rogers at a steady rate of 20 people per minute, the time needed would be 70,000 people/20 people/minute, or 3,500 minutes, or 58 hours or, assuming an 8-hour hand-shaking day, more than a week.
The hand-chafing that would result might be enough to end Rogers' passing career.
2. Again, a little arithmetic shows the headline to be absurd.
There are approximately 300 million Americans, which translates into very roughly 100 million households. Dividing $2 billion by 100 million households yields an annual expenditure per household of about $20.
Nothing to fear about paying only $20 annually for housing! Most people I've tricked into responding to this story talk about the mortgage crisis or housing prices and don't seem to notice the $2 billion figure. As long as it's a big number, they probably assume, it's OK.
3. This is a little trickier because some numerical facts are needed to reveal the nonsensical nature of this, unfortunately, very popular policy choice.
Roughly speaking, the U.S. spends about $30 billion annually on foreign aid and development. (What to include in the figure varies.) The recent record deficit of approximately $1.5 trillion is about 50 times this figure.
To make this ratio more visceral, assume a household must borrow $15,000 this year to make ends meet. What would you think if it resolved to cut back next year by saving $300, the cost of a once-daily soft drink?
Similar disproportions exist between some hot-button relatively inexpensive expenditure, say, the $350 million budgeted for Planned Parenthood services (not abortion) versus the $2.2 billion cost of a single B-2 bomber or the approximately $500 billion for this year's military budget.
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.