Says Princeton Computer Science professor Brian Kernighan: “As calculators and computers have become steadily more powerful, they have buried us in an avalanche of numbers and graphs and charts, many of which claim to present the truth about important issues. But at the same time, our personal facility with numbers has diminished, often leaving us at the mercy of quantitative reasoning and presentation that is sometimes wrong and often not disinterested.”
For the past ten years, Dr. Kernighan has been teaching a course that satisfies “QR”, Princeton’s dreaded Quantitative Reasoning requirement. Increasingly, he has come to view a significant part of the QR component as basic numeric self-defense: assessing the numbers presented by other people, and producing sensible numbers of one’s own.
Just as the education process trains us to be skeptical of what we hear and read, so too, he suggests, we should remain vigilant when we confront numbers. Nearly four years ago, Dr. Kernighan introduced this topic. In a second look at the February 3 Lunch ‘n Learn, he presented instances primarily from the past four years that suggest that the problem remains.
Recently, the idea of distributing the AIG bailout evenly to the citizenry spread virally throughout the blogosphere. The author of the idea suggested that the $85 billion bailout, divided by 200,000,000 people, would provide each of us $425,000, a tidy sum. Needless to say, readers were jubilant. One even suggested that the author of the plan ought to run for President. Unfortunately, the math actually works out to $425 per person.
Kernighan found many examples of the incorrect use of units. “The use of motor fuel in the United States could grow to 170 billion gallons a day in ten years,” suggested the Newark Star Ledger in 2007. They should have written 170 billion gallons a year.
The size of a coal ash spill in Tennessee was one billion gallons, not one billion tons as reported by the NY Times.
The Times also reported that a zettabyre “is equivalent to 100 billion copies of all the books in the Library of Congress.” Extrapolating back, says Kernighan, that would mean that the Library of Congress has only 10,000 books.
AARP reported that 48.7% of people 55 and older responded that they enjoy participating in surveys, an amusingly precise estimate given that they clearly only surveyed those who had agreed to take the survey.
Kernighan challenges his students to estimate. Showing a large tree, he asks: “How many leaves will I have to rake?” Showing a school bus, he asks: “How many golf balls will fit inside?” The students return a wide range of estimates, but interestingly, the median often tends to be on target.
In the end, what defense do we have for faulty reasoning. First, recognize the enemy. Be aware, suggests Kernighan, that the world is full of flaky numbers, excessive precision, arithmetic errors, and misused units. Consider the source. Do they have an ulterior motive in making their claims? Become more familiar with basic conversions (e.g. that a gallon of water weighs approximately eight pounds.) Use a sense check. Do the numbers make sense? Do they agree with your experience? And what would be the real-life implications if the numbers were correct?
Brian Kernighan received a BASc from the University of Toronto in 1964 and a PhD in electrical engineering from Princeton in 1969. He was in the Computing Science Research center at Bell Labs until 2000, and is now in the Computer Science Department at Princeton. His research areas include programming languages, tools and interfaces that make computers easier to use, often for non-specialist users. He is also interested in technology education for non-technical audiences. He has been a Forbes advisor since 2001.
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