Quick, what’s the difference between 1 million, 1 billion and 1 trillion?
You’re in trouble if you respond with something like, “What’s the difference when the figures get that high?”
If you think the Empire State Building is about a mile high, plead guilty again.
You’re an innumerate.
Help, however, is at hand.
Meet the oxymoronic John Allen Paulos, a witty mathematics professor who quotes philosophers, devours novels, once did a stand-up comedy act in a Philadelphia club and passionately hopes that his fifth-grade math teacher reads his latest book. He’s also a man who doesn’t think the world would be a better place if we were all able to work quadratic equations.
“Come to the fifth floor,” he instructs a visitor, “and go to room . . . this is rather embarrassing given the subject of the book, but it’s either room 540 or 542.”
In Russell’s Shadow
A huge poster of Bertrand Russell, one of his idols, looks over his shoulder as he works. A pyramid of blue and magenta empty Hawaiian Punch cans--fun to move around in different configurations--rests quietly now in a garish display on his windowsill.
Paulos, a 43-year-old Temple University professor, has written “Innumeracy: Mathematical Illiteracy and its Consequences,” a book whose title would not compel the average reader to snap it off the shelf. But it’s fun, and Paulos tells you it’s OK to skip the tough parts.
One of the tough parts is the title itself. The word “innumeracy,” which means the inability to deal comfortably with the fundamental notions of number and chance, has been in usage in England since the 1950s, Paulos says. He first came across it several years ago in an article in Scientific American.
“It will be in American dictionaries soon,” he says. “Dan Rather has used it a few times, and that’s got to be an imprimatur.”
Numbers Within Easy Grasp
But back to that first question. Throughout the book, Paulos has a knack of breaking things down into easily grasped units.
He wants people to have a sense of the vast difference among the members of the " . . . illion” family. He suggests that you look at it this way: One million seconds takes about 11 1/2 days to tick by. A billion seconds would take almost 32 years. A trillion seconds equals 32,000 years.
Paulos says he sometimes asks his freshman students how high the Empire State Building is.
“I don’t want them to go and look it up,” he says. “I just want to know about their sense of proportion and scale. I would consider 1,000 feet a correct answer, even 2,000 feet, because it’s in the range. (Actual footage is 1,200 feet.) But if a student said 50 feet or a mile, he has no sense of what a mile is, what a mile is like straight up in the air.”
Paulos, who teaches freshmen as well as graduate students, is a recognized expert in symbolic logic, computer languages and artificial intelligence. Born in Denver, he grew up in Milwaukee and describes himself as a bright kid but very shy.
“This is a book for educated people,” he says.
Paulos notes that he once accompanied his wife, a former French teacher turned romance novelist, to the doctor to learn more about a minor procedure she was facing.
“Within 20 minutes, the doctor said there was only a million-to-one shot of something going wrong, that it was a 99% safe procedure, and then he said that it usually went quite well,” he says. When Paulos tried to explain to the physician that he just said three entirely different things, he was met with a grim stare and incomprehension.
“Even in their areas of expertise, people just use numbers, not knowing what they mean,” he says.
Paulos has met with blank stares before. When he did the comedy club act, one of his jokes had to do with the sign suggesting citizens put litter where it belongs. Paulos pointed out that if people did that, it would no longer be litter, it would be garbage. Litter, he pointed out, is litter only when it is littering.
Not too many chuckles.
“Actually, most of it went quite well, but some of it was a little too cerebral for the club,” he says.
Not Quite Discounts
He also gets blank stares when he quips that something selling at a “fraction of its normal cost” probably is--and that the fraction is 4/3.
His quixotic quest is serious. He believes that innumeracy contributes to a lack of skepticism and lack of critical thinking, which leads to poor life decisions.
“People should know, for instance, that when they see a headline that says something like 1 million American children kidnaped every year, that it’s simply not true,” he says.
“Innumerates, if I can use that as a noun, tend to personalize things and overvalue coincidences,” he says. “They don’t have a sense of how unrare coincidences are, so they read entirely too much into them.”
These are the people, he says, who get involved with numerology, astrology, and such largely because they don’t understand the laws of probabilities, nor do they think critically. Do they ever wonder how many times the psychic was wrong, rather than boasting about the one time he was right?
Paulos has many funny examples in his book, such as the Wisconsin legislator who opposed daylight-saving time on the ground that that much more sun would fade the curtains and the carpets faster.
He blames math teachers, the social acceptability of even intelligent men and women rather proudly flaunting their innumeracy, and a general unawareness of how important these things are in a society that is rapidly becoming more and more scientific and technical.
He has no patience with people who proclaim that they do not have a head for numbers.
“Anyone can master the elements of mathematics,” Paulos says. “The unfortunate thing is that some of it is kind of ugly. It’s like learning to parse a sentence. That’s not fun, but it’s necessary to get to the fun things like literature. Before you play with patterns and structures and have fun with math, you have to go through the ugly part too.”
He partly blames the math teachers who lack imagination. As a fifth-grader, he was very proud to have computed the ERA (earned run average) of one of the worst pitchers the Milwaukee Braves ever had--a 135. He showed it to his teacher. The teacher told him to go sit down, announcing authoritatively that the highest possible ERA was 27.
At the end of the year, the Milwaukee Journal published all the ERAs, and since this guy had been kicked down to the minors and not pitched again, there it was in black and white--135.
When confronted with this, the teacher, though dead wrong, told Paulos to sit down.
“I hope that martinet is reading my book,” Paulos says. “His idea of teaching math was getting students to sit down.”
Paulos also wrote two previous books, “Mathematics and Humor,” and “I Think Therefore I Laugh,” as well as various newspaper and magazine articles. He is negotiating a contract to write a syndicated weekly column on problems great and small, sort of a Paulos on numbers and probabilities rather than a William Safire on usage.
Paulos is also concerned about a blind faith in numbers. He stresses that the human assumptions must be correct before the math is good.
He points out that even the most basic “one and one is two” is not correct if the assumptions are wrong. His example: One cup of popcorn plus one cup of water does not equal two of anything. It equals 1 1/2 cups of soggy popcorn.
The book, published by Hill and Wang, is an alternate Book-of-the-Month Club selection and has received generally good reviews.