Numbers are near and dear to nerds. Nerds like to guess how long it would take for a penny dropped off the top of the Empire State Building to hit the ground, how many jelly beans fit in a one-liter bottle, or how many piano tuners are there in Chicago.
Numbers aren't just for games, of course. Higher mathematics is the backbone of science. Practical math is the glue that keeps society together and keeps an economy functioning.
And yet, when our economy stopped functioning two years ago, few experts thought to pin the blame on numbers.
Now, I'm doing just that — with my new book, "Stop Getting Ripped Off."
Avid readers of Alan Boyle's Cosmic Log know , and most readers probably have a sense that American students often score far behind children of other countries in science tests. There has been endless hand-wringing about this failing of America's schools.
Much less has been written about our more fundamental — and more dire — inability to do math. The problem isn't complex math, like calculus, or even algebra. The problem is the basics: fractions, percentages, compound interest, and so on. If you doubt this, reflect on the last time you and your friends were challenged by the prospect of splitting a lunch bill six ways. Consumers who can’t calculate tips have no chance in a car salesman's back room or a mortgage broker's office.
The numbers are impossible to ignore. In a recent government survey:
- Only 42 percent of adults were able to pick out two items on a menu, add them, and calculate a tip.
- Only one in five people could reliably calculate mortgage interest.
- One in five were unable to calculate a weekly salary when told an hourly pay rate.
Meanwhile, American students ranked 25th of 30 industrialized nations, even though they told researchers their grades were higher than every other country in the study.
A straight line can be drawn between this hidden epidemic of math illiteracy — called "Innumercy" in a book by John Allen Paulos 10 years ago — and the recent economic collapse. Consumers who can’t do math make bad choices, raising the cost of goods for everyone else. Companies with bad products built on a house of cards survive far too long, buoyed by these bad choices. Everyone suffers. Even if you are great with numbers, you suffer. As long as some group of neighbors decide to pay $600,000 for homes in the neighborhood you want to live in, that’s the price you have to pay, even if you know the value is unsustainable.
It's a long slog to fix this problem. The solution lies in hiring more math-savvy elementary teachers, redoubling focus on mathematics education, a return to fundamentals like multiplication tables, and aggressive adult education programs to make up for lost time. But a more subtle contribution can be made by science and technology fans, who are naturally are more math inclined.
First, I call on all college math majors to take a silent oath, similar to the Hippocratic oath that doctors take, to "do no harm" with their skills. So-called "quants," who arrived on Wall Street 20 years ago with their too-clever-by-half algorithms are guilty of something even worse than fraud in the eyes of true mathematicians — their equations lacked intellectual integrity. Their math lied. There was no way to take risk out of the system. True higher math is an art, I learned in Calculus class long ago. That's the only justification for solving equations in the 6th, 7th, and 8th dimension. Abusing that art was an intellectual crime of the highest order.
And second, those who love numbers should share the love. We should become an army of advocates for math education. Preach to friends, quiz family members, ask questions about the loan that mom and dad are about to take, play math games with your little cousins. Nerds are not only sexy and smart — they also end up with bigger bank accounts, better vacations, and more relaxed retirements.
To fix out economy from the ground up, let’s help restore numbers to their proper place of honor in our society.
For much more on the problem of innumeracy, we present the following excerpt from my new book, "Stop Getting Ripped Off: Why Consumers Get Screwed and How You Can Always Get a Fair Deal."
Reprinted with permission.
The problem of adult illiteracy in America is widespread and alarming — an estimated 14 percent of Americans, or 1 in 7, can’t read. Terrible, but perhaps not surprising, as you’ve no doubt heard a statistic like that before. There are seemingly incessant studies of the problem, there are multiple institutes devoted to dealing with it, there are public service radio campaigns that draw awareness to it.
The problem of mathematical illiteracy is much less well known. In fact, it is downright obscure — so obscure that there isn’t really a ready-made term to describe the group of people who can’t calculate restaurant tips or balance their checkbook. Saying someone “can’t count” is in no way the equivalent of saying someone “can’t read.”
John Allen Paulos tried to change that in 1988 when he published the book Innumercy. In it, he describes the genesis of the widespread epidemic that has led to a gap between the “numerate” and the innumerate. Innumerates hate math and are sometimes proud of that fact. They can be easily identified when they say by phrases like, “I’m a word person.” Numerates, on the other hand, can easily win a bar bet from innumerates by asserting that in a tavern full of 50 people, there almost certainly are two people who share the same birthday. In fact, they’ll win the best most of the time even if there’s as few as 25 people in the bar (don’t believe me? Read on)
Innumerates almost never realize their precarious situation. They are often people who are otherwise quite sanctimonious about being right and precise. In describing this phenomenon, Paulos tells this story of a rather annoying character at a dinner party.
“The same people who cringe when words such as imply and infer are confused react without a trace of embarrassment to even the most egregious of numerical solecisms. 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 for rain on 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 often hidden, Mathematical illiteracy is often flaunted. (People say) “I can’t even balance my checkbook. I’m a people person, not a numbers person,” or “I’ve always hated math.”
Paulos puts his finger on one of the root causes of the economic meltdown. Think back to high school for a moment: rare is the institution where the captain of the math club wanders the hallways proudly sporting a “C” on a leather jacket. In fact, the real wearer of the “C,” the high school quarterback – or for that matter, any student, really -- is much more likely to curry favor by joking about failing algebra tests. There is, Paulos asserts, “a perverse pride in mathematical ignorance.” For a while, you may have even heard a perverse pride from people who didn’t understand their investments or their home loans. “Oh, I let my broker handle all that…”
It may be cute that the quarterback can’t add, but unless he eventually lands a multi-million dollar contract and an agent to count money for him, he will quickly become a burden on society. For example, he’ll be much more afraid of getting killed by a shark (odds: 1 in 300 million) than by a car accident (1 in 18,000) or by heart disease (1 in 7). He’ll happily drive after two or three beers at 3 a.m., and eat endless bags of potato chips, but cancel a seaside vacation after an isolated news report involving a shark attack. People who don’t understand numbers are prone to making terrible risk assessments. This puts them, and us, at grave risk.
In 2003, the U.S. Department of Education’s National Center for Education Statistics ran its third National Assessment of Adult Literacy. The test is massive, involving interviews with 19,000 Americans, so it’s only conducted about once every 10 years. Two-thirds of the test dealt with verbal literacy, but one-third focused on “quantitative literacy.” Its questions are impressive in their ability to simulate real-life situations. It’s not a math test, it’s a life test.
Overall “grades” were split into four categories: Below basic, basic, intermediate, and proficient. Originally, the top rating was to be “expert,” but researchers changed their minds, noting that basic check-balancing skills shouldn’t be labeled as expert. Here’s the final tally:
- Below Basic: 22%
- Basic: 33%
- Intermediate: 33%
- Proficient: 13%
Let’s break these numbers down a little more for you. More than half of U.S. consumers were categorized as having basic or below basic quantitative skills. But what does that mean? It means they could not:
- Determine whether a car has enough gasoline to get to the next gas station, based on a graphic of the car’s fuel gauge, a sign stating the miles to the next gas station, and information given in the question about the car’s fuel use `
- Calculate the cost of raising a child for a year in a family with a specified income, based on a newspaper article that provides the percentage of a typical family’s budget that goes toward raising children
- Calculate the total cost of ordering office supplies, using a page from an office supplies catalog and an order form.
- Determine what time a person can take a prescription medication, based on information on the prescription drug label that relates timing of medication to eating.
Naturally, as the required math proficiency increased, fewer consumers were able to complete the tasks. Only one in seven Americans qualified as “proficient.” That means that only one in 7 Americans can reliably perform tasks like these:
- Calculate the yearly cost of a specified amount of life insurance, using a table that gives cost by month for each $1,000 of coverage.
- Calculate an employee's share of health insurance costs for a year, using a table that shows how the employee's monthly cost varies with income and family size
If you’re wondering why Americans pay too much for health insurance, the fact that most people have no idea how much they pay for health insurance might be one hint.
Of course, no one starves to death because they can’t find a number on a piece of paper. But what if they can’t even calculate their own salaries? The literacy assessment found that 22 percent of Americans were incapable of:
- Calculating the weekly salary for a job, based on hourly wages listed in a job advertisement
- Calculating the cost of three baseball tickets using a form that provides the price of one ticket, and postage and handling charges
- Calculating the cost of a sandwich and salad, using prices from a menu.
It bears repeating: nearly one in four Americans can’t figure how much their lunch costs! If we are giving people high school degrees who are not capable of calculating when they will run out of gas, what their weekly salary is, or the cost of a sandwich and soup, we are doing a grave disservice. Something has gone horribly wrong.
Not surprisingly, quantitative abilities are an excellent predictor of life success and household income. Adults who earn $100,000 per year or more had an average test score right on the edge of “proficient.” Adults who scored in the “basic” range had an average income ranging from $20,000-$60,000. And those who couldn’t get out of the “below basic” rating were stuck with an average salary of less than $20,000 per year.
Breaking down the numbers by gender or race is even more disturbing. Only 1 in 10 U.S. women registered as proficient in 2003. Even more dismal, only 1 in 25 Hispanics, and 1 in 50 African Americans, scored proficient.
Education level mattered, but not as much as it should. Those with a college degree were 6 times more likely to be proficient than those who stopped their education after finishing high school. On the other hand, even the majority of those who hold a college degree weren’t rated as proficient – 69 percent, in fact, were not.
That means most college graduates (and in fact, most adults who held advanced degrees, too), were unable to answer a question asking test-takers to calculate interest payments on a home equity loan. Only 1 in 5 test-takers of any stripe could handle the question, which simulated the most basic task a home-buyer faces when trying to select a mortgage.
One vital key to running a con on someone is what economists sometimes call “asymmetric information” — one side simply knows much more than the other in a transaction. With most Americans incapable of even describing the cost of a home loan in 2003, you can assume that the vast majority of mortgages sold during the 2000s decade were classic asynchronous transactions. The stage was set for the biggest con in human history.
How did we arrive at a place where Americans had so much money and so little understanding?
Despite what you may have heard, numbers do lie, and they make an excellent tool for deception. Just like photographs, people naively grant numbers far too much credibility. Those who do are an easy target.
In another great tome on the problem of mathematical foibles called The Two-Headed Quarter, University of Maryland Professor Joseph Ganem shows how often numbers are used to trick consumers. By withholding a little bit of context, seemingly unbiased numbers can make a fair transaction unfair very quickly. A coin flip might seem like an even 50-50 bet, for example, unless one party knows that the coin being flipped has heads on both sides — the classic asynchronous transaction. Ganem sees many house, car, credit card, and insurance transactions through the lens of a two-headed quarter.
“Numbers are a perfect vehicle for making true but misleading statements,” he writes. “Deception works by not revealing the whole story. A two-headed quarter works in a magic trick by presenting a false choice.”
In the world of personal finance, he sees many two-headed quarters. Here’s a few:
- A credit card convenience check that promises, in large print, to let people transfer balances for the low interest rate of 2.9 percent — then tacks on a 3 percent transfer fee.
- Tax refund anticipation loans. The Jackson Hewitt tax preparation company says it charges a small 3 percent fee for consumers to receive their tax refunds instantly. Sounds small. But the annual percentage rate for such a loan is more than 100 percent. As Ganem points out, consumers would be better taking a cash advance from a credit card at 29.99 percent to cover the 7-days of waiting for the refund to arrive.
- A rent-to-own store he surveyed charged a low price of $17.99 per week to rent a bedroom set. Best of all, consumers who rented it would own the set after two years! Here’s the problem: the value of the set was $935, but after two years, the consumer would have paid $1,870.96. Clearly, $17.99 was a lie — the rental store was instead providing a loan with an APR of nearly 80 percent.
In each case, the key to making the number lie was in the “framing.” Simply changing the furniture rental price terms from weekly ($17.99) to monthly ($71.96) can dramatically change the perception of the appearance of the transaction. Revealing the APR unravels the lie altogether. But rental furniture is often marketed to down-on-their luck buyers who are living literally week-to-week, paycheck-to-paycheck, so the framing as a weekly payment works as a perfect trap.
There are many ways to construct a two-headed quarter. One is an outright cheat, so that the “house” knows more than the gambler — say, that the coin is fixed. But another, more subtle two-headed coin is to keep one party in the dark about the subtleties of transaction.
What a bettor became convinced, through poor education or belief in myth, that a coin flip is really a 75-25 proposition? Obviously, the house would win a lot of money. This suggestion might sound absurd until you consider our country’s fixation with casino gambling. Einstein once remarked that “No one can possibly win at roulette unless he steals money from the table while the croupier isn't looking.” And of course, he was right. Every single casino game is rigged so the house has slightly better odds than the betters. A roulette ball lands on red 47.37 percent of the time. The payout is 2-to-1, but the risk is slightly greater — about 5 percent greater. Remember this rule in all gambling, and in fact, in most financial transactions: The House always wins.
Why all this talk about gambling? To make the point that numbers often lie. Simple math would expose the lie of the $17.99 furniture rental, but we’ve already learned that much of America is blissfully ignorant of simple math. Step the complexity up just a small amount – say, imagine a “Pay Option ARM” (adjustable rate mortgage) with a teaser rate of 1.9 percent and an initial rate of 7.9 percent that adjusts to 8.9 percent after two years — and you can swindle a lot of home buyers by saying, “Look at this low monthly payment.”
Clever framing of these kinds of math problems lies at the core of the bad mortgage or the double-priced bedroom set. Numbers really can lie. No wonder people are afraid of them.
Just how afraid of mathematics are the American people? Every year, roughly 50 million Americans file their taxes using one-page, simple forms like the 1040EZ. That form rarely requires entries on more than 10 lines, and it can be boiled down to these three questions: What was your income? Which personal deduction are you entitled to (a multiple choice question)? How much taxes have you already paid. Yet fully one-third of EZ filers — perhaps 25 million Americans — pay someone else to do their taxes anyway.
That says something about fear of the IRS, of course. But on a deeper level I think it describes an utter lack of confidence is performing mathematical calculations when something important is really on the line.
*These classic Fermi problems have answers. About 20 seconds, about 240 beans, and about 100.