Magic by Numbers
The Weight at the Plate
Times to Remember, Places to Forget
What You Don’t Know Makes You Nervous
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October 18, 2010: Magic by Numbers
I recently wound up in the emergency room. Don’t worry, it was probably nothing. But to treat my case of probably nothing, the doctor gave me a prescription for a week’s worth of antibiotics, along with the usual stern warning about the importance of completing the full course.
I understood why I needed to complete the full course, of course. What I didn’t understand was why a full course took precisely seven days. Why not six, eight or nine and a half? Did the number seven correspond to some biological fact about the human digestive tract or the life cycle of bacteria?
My doctor seemed smart. She probably went to one of the nation’s finest medical schools, and regardless of where she trained, she certainly knew more about medicine than I did. And yet, as I walked out of the emergency room that night with my prescription in hand, I couldn’t help but suspect that I’d just been treated with magic.
Certain numbers have magical properties. E, pi and the Fibonacci series come quickly to mind — if you are a mathematician, that is. For the rest of us, the magic numbers are the familiar ones that have something to do with the way we keep track of time (7, say, and 24) or something to do with the way we count (namely, on 10 fingers). The “time numbers” and the “10 numbers” hold remarkable sway over our lives. We think in these numbers (if you ask people to produce a random number between one and a hundred, their guesses will cluster around the handful that end in zero or five) and we talk in these numbers (we say we will be there in five or 10 minutes, not six or 11).
But these magic numbers don’t just dominate our thoughts and dictate our words; they also drive our most important decisions.
Consider my prescription. Antibiotics are a godsend, but just how many pills should God be sending? A recent study of antibiotic treatment published in a leading medical journal began by noting that “the usual treatment recommendation of 7 to 10 days for uncomplicated pneumonia is not based on scientific evidence” and went on to show that an abbreviated course of three days was every bit as effective as the usual course of eight. My doctor had recommended seven. Where in the world had seven come from?
Italy! Seven is a magic number because only it can make a week, and it was given this particular power in 321 A.D. by the Roman emperor Constantine, who officially reduced the week from eight days to seven. The problem isn’t that Constantine’s week was arbitrary — units of time are often arbitrary, which is why the Soviets adopted the five-day week before they adopted the six-day week, and the French adopted the 10-day week before they adopted the 60-day vacation. The problem is that Constantine didn’t know a thing about bacteria, and yet modern doctors continue to honor his edict.
If patients are typically told that every 24 hours (24 being the magic number that corresponds to the rotation of the earth) they should take three pills (three being the magic number that divides any time period into a beginning, middle and end) and that they should do this for seven days, they will end up taking 21 pills. If even one of those pills is unnecessary — that is, if people who take 20 pills get just as healthy just as fast as people who take 21 — then millions of people are taking at least 5 percent more medication than they actually need. This overdose contributes not only to the punishing costs of health care, but also to the evolution of the antibiotic-resistant strains of “superbugs” that may someday decimate our species. All of which seems like a rather high price to pay for fealty to ancient Rome.
Magic “time numbers” cost a lot, but magic “10 numbers” may cost even more. In 1962, a physicist named M. F. M. Osborne noticed that stock prices tended to cluster around numbers ending in zero and five. Why? Well, on the one hand, most people have five fingers, and on the other hand, most people have five more. It isn’t hard to understand why an animal with 10 fingers would use a base-10 counting system. But according to economic theory, a stock’s price is supposed to be determined by the efficient workings of the free market and not by the phalanges of the people trading it.
And yet, research shows that fingers affect finances. For example, a stock that closed the previous day at $10.01 will perform about as well as a stock that closed at $10.03, but it will significantly outperform a stock that closed at $9.99. If stocks close two pennies apart, then why does it matter which pennies they are? Because for animals that go from thumb to pinkie in four easy steps, 10 is a magic number, and we just can’t help but use it as a magic marker — as a reference point that $10.01 exceeds and $9.99 does not. Retailers have known this for centuries, which is why so many prices end in nine and so few in one.
The hand is not the only part of our anatomy that gives certain numbers their magical powers. The tongue does too. Because of the acoustic properties of our vocal apparatus, some words just sound bigger than others. The back vowels (the “u” in buck) sound bigger than the front vowels (the “i” in sis), and the stops (the “b” in buck) sound bigger than the fricatives (the “s” in sis). As it turns out, in well over 100 languages, the words that denote bigness are made with bigger sounds.
The sound a number makes can influence our decisions about it. In a recent study, one group was shown an ad for an ice-cream scoop that was priced at $7.66, while another was shown an ad for a $7.22 scoop. The lower price is the better deal, of course, but the higher price (with its silky s’s) makes a smaller sound than the lower price (with its rattling t’s). And because small sounds usually name small things, shoppers who were offered the scoop at the higher but whispery price of $7.66 were more likely to buy it than those offered the noisier price of $7.22 — but only if they’d been asked to say the price aloud.
The magic that magic numbers do is all too often black. They hold special significance for terrestrial mammals with hands and watches, but they mean nothing to streptococcus or the value of Google. Which is why we should be suspicious when the steps to sobriety correspond to a half turn of our planet, when the eternal commandments of God correspond to the architecture of our paws and when the habits of highly effective people — and highly trained doctors — correspond to the whims of a dead emperor.
Here are the articles referred to in my essay:
Osborne, M. F. M. (1962). Periodic structure in Brownian motion of stock prices. Operations Research, 10, 345-379.
Coulter, K. S., & Coulter, R. A.. (2010). Small sounds big deals: Phonetic symbolism effects in pricing. Journal of Consumer Research, 37, 315-328.
el Moussaoui, R. et al. (2010). Effectiveness of discontinuing antibiotic treatment after three days versus eight days in mild to moderate-severe community acquired pneumonia: randomised, double blind study. BMJ, on line first.
Johnson, E., Johnson, N. B., & Shanthikumar, D. (2010). Round numbers and security returns. http://www.people.hbs.edu/dshanthikumar/RoundNumbers.pdf
Ross, B. R., & Engen, T. (1959). Effects of round number preferences in a guessing task. Journal of Experimental Psychology, 58, 462-468.
August 5, 2010: The Weight at the Plate
The Boston Red Sox haven’t given their fans much to cheer about this summer so we’ve had to take our pleasure where we could find it, for example, by watching Alex Rodriguez of the Yankees struggle to hit his 600th career home run — again and again and again.
Rodriguez hit his 599th home run on July 22, bringing himself and his fans to the brink of celebration. And then, for 12 long days, he not only failed to drive the ball out of the park and into the history books, he also went hitless for 17 consecutive at-bats. This wasn’t the first time Rodriguez has stood at the precipice, and then stood there some more: after hitting his 499th home run in 2007, he came to the plate an excruciating 28 times before finally hitting his 500th.
What made all this so frustrating for New Yorkers (and so delicious for Bostonians) was that everyone felt certain that Rodriguez would have slammed several homers in the past two weeks if only they hadn’t mattered so much. Watching him struggle to break the numerical barrier was like watching a man frozen with fear on the last step of a tall ladder: we knew, and he knew, that the last step was exactly the same as all the steps before it — so why couldn’t he just take it?
One of the ironies of human psychology is that desperately wanting something can make attaining that thing all the more difficult. When stakes go up, performance often goes down. In one study, subjects practiced sinking a putt and got better as they went along — better, that is, until the experimenter offered them a cash reward for their next shot, at which point their performance took a nosedive.
This is because we pay close attention to what we’re doing when what we’re doing matters, and though close attention is helpful when our task is novel or complex, it is positively destructive when our task is simple and well practiced. Golfers in another study were told either to take their time and think about their stroke or to step up and swing as quickly as possible. Although novice golfers did better when they took their time, expert golfers did worse.
The lesson from the laboratory is clear: thinking about tasks that don’t require thought isn’t just pointless, it’s debilitating. It may be wise to watch our fingers when we’re doing surgery or shaving the family dog, but not when we’re driving or typing, because once our brains learn to do something automatically they don’t appreciate interference. The moment we start thinking about when to step on the clutch or hit the alt key, our once-seamless performance becomes slow, clumsy or impossible.
That’s why milestones can be millstones. When Rodriguez stepped to the plate in recent days, he may not have heard the roar of the crowd as much as the sound of a record book opening and a pencil being sharpened. The more important his next homer became, the more he probably thought about how to hit it. The more he thought, the less he hit; the less he hit, the more he thought, and the cycle spun on.
Until Wednesday, that is, when Rodriguez finally hit his 600th home run. Forty-six agonizing at-bats separated that homer from the one before it, but the moment the ball sailed over the center field fence, Yankee fans knew that a great burden had been lifted, a great slugger had been liberated, and that a great bat would once again be free to find the ball — naturally, effortlessly, and in its own sweet time.
Or maybe not.
After all, 600 is an important number only because it’s round, and several of the numbers that follow are much more significant. For instance, Rodriguez is the seventh greatest home-run hitter of all time and hitting 600 didn’t change that. But hitting No. 610 will, because it will push him past the retired Sammy Sosa and into sixth place; hitting 631 would let him overtake Ken Griffey Jr. and put him in fifth place. Should that happen, there are a few more legends whom Rodriguez must lap on his way to supremacy: Willie Mays at 660, Babe Ruth at 714, Hank Aaron at 755 and the reigning champion Barry Bonds at 762.
Rodriguez won’t get any competition from a Red Sox hitter as he works his way up the list, but that’s O.K. Red Sox fans are nothing if not good sports. Which is why on Friday, when the Red Sox play the Yankees, we will applaud Alex Rodriguez — not just to acknowledge his new achievement, but also to remind him of the unbelievably, incredibly, really very large historical significance of each and every one of his future trips to the plate.
Posted by Dan Gilbert on August 5, 2010 | E-mail this post
January 15, 2010: Times to Remember, Places to Forget
Tonight, millions of Americans will raise a glass, sing the only three Scottish words they know and remember the past with an ineffable blend of sadness and delight. Nostalgia has all the hallmarks of a universal emotion, and it is only natural to assume that the yearning for “auld lang syne” that was shared by our grandparents will someday be shared by our grandchildren.
But maybe we’ve reached nostalgia’s end. “Nostalgia” — made up of the Greek roots for “suffering” and “return” — is literally a longing for the places of one’s past. And lately, it has become harder and harder to find things to miss about America’s places.
Downtowns were once collections of local businesses that lured us with claims of uniqueness: “Try our homemade pies,” their signs read, or “Best jazz selection in town.” Today, those signs have been replaced by familiar corporate logos that make precisely the opposite claim, promising us the same goods arranged in the same way as they are in every other place. The banks and burritos and baristas on one city block are replicated on the next — and in all the malls, in all the cities, in all the states. Americans can drive from one ocean to the other, stopping every day for the same hamburger and every evening at the same hotel. Traveling in a straight line is no longer much different than traveling in a circle.
When the industrial smoothing of our nation’s once-variegated edges has been fully accomplished, Americans may no longer need to gather at midnight on the last day of the year to yearn for their yesterdays, because wherever they are they will see the landscapes of their youths. When they remember the Starbucks where they met the one they married or the Gap where they lost the one they didn’t, they will be marinating in memories that happened everywhere but not somewhere, reliving experiences that are located in time but dislocated in space. And when they return to the places where they grew up, or went to school, or fell in love, they may not even notice that the Old Navy has been replaced by an Abercrombie, the Fridays by an Olive Garden and the once-fleeting past by an endless present.
Ours may be the last generation of Americans to suffer for return — to remember events that took place when place still mattered. So tonight let us revel in our nostalgia, and long for the days when longing was easy.
Posted by Dan Gilbert on January 15, 2010 | E-mail this post
May 21, 2009: What You Don’t Know Makes You Nervous
Okay, I admit it. This isn’t a blog.
A blog is like a garden; you can’t fuss over it for a while, forget about it for two years, and then expect it to be there when you come back. But I’ve been busy with other things — co-authoring a psychology textbook, co-editing the new edition of The Handbook of Social Psychology, filming a television series for PBS, tickling my grandchildren — and as a result I haven’t been writing the short essays that are the backbone of this blog. I hope to start doing more of that again.
So here’s a contribution to the Website Formerly Known As Blog: An op-ed that appears in today’s New York Times.
Seventy-six years ago, Franklin Delano Roosevelt took to the inaugural dais and reminded a nation that its recent troubles “concern, thank God, only material things.” In the midst of the Depression, he urged Americans to remember that “happiness lies not in the mere possession of money” and to recognize “the falsity of material wealth as the standard of success.”
“The only thing we have to fear,” he claimed, “is fear itself.”
As it turned out, Americans had a great deal more to fear than that, and their innocent belief that money buys happiness was entirely correct. Psychologists and economists now know that although the very rich are no happier than the merely rich, for the other 99 percent of us, happiness is greatly enhanced by a few quaint assets, like shelter, sustenance and security. Those who think the material is immaterial have probably never stood in a breadline.
Money matters and today most of us have less of it, so no one will be surprised by new survey results from the Gallup-Healthways Well-Being Index showing that Americans are smiling less and worrying more than they were a year ago, that happiness is down and sadness is up, that we are getting less sleep and smoking more cigarettes, that depression is on the rise.
But light wallets are not the cause of our heavy hearts. After all, most of us still have more inflation-adjusted dollars than our grandparents had, and they didn’t live in an unremitting funk. Middle-class Americans still enjoy more luxury than upper-class Americans enjoyed a century earlier, and the fin de siècle was not an especially gloomy time. Clearly, people can be perfectly happy with less than we had last year and less than we have now.
So if a dearth of dollars isn’t making us miserable, then what is? No one knows. I don’t mean that no one knows the answer to this question. I mean that the answer to this question is that no one knows — and not knowing is making us sick.
Consider an experiment by researchers at Maastricht University in the Netherlands who gave subjects a series of 20 electric shocks. Some subjects knew they would receive an intense shock on every trial. Others knew they would receive 17 mild shocks and 3 intense shocks, but they didn’t know on which of the 20 trials the intense shocks would come. The results showed that subjects who thought there was a small chance of receiving an intense shock were more afraid — they sweated more profusely, their hearts beat faster — than subjects who knew for sure that they’d receive an intense shock.
That’s because people feel worse when something bad might occur than when something bad will occur. Most of us aren’t losing sleep and sucking down Marlboros because the Dow is going to fall another thousand points, but because we don’t know whether it will fall or not — and human beings find uncertainty more painful than the things they’re uncertain about.
A colostomy reroutes the colon so that waste products leave the body through a hole in the abdomen, and it isn’t anyone’s idea of a picnic. A University of Michigan-led research team studied patients whose colostomies were permanent and patients who had a chance of someday having their colostomies reversed. Six months after their operations, patients who knew they would be permanently disabled were happier than those who thought they might someday be returned to normal.
Similarly, researchers at the University of British Columbia studied people who had undergone genetic testing to determine their risk for developing the neurodegenerative disorder known as Huntington’s disease. Those who learned that they had a very high likelihood of developing the condition were happier a year after testing than those who did not learn what their risk was.
Why would we prefer to know the worst than to suspect it? Because when we get bad news we weep for a while, and then get busy making the best of it. We change our behavior, we change our attitudes. We raise our consciousness and lower our standards. We find our bootstraps and tug. But we can’t come to terms with circumstances whose terms we don’t yet know. An uncertain future leaves us stranded in an unhappy present with nothing to do but wait.
Our national gloom is real enough, but it isn’t a matter of insufficient funds. It’s a matter of insufficient certainty. Americans have been perfectly happy with far less wealth than most of us have now, and we could quickly become those Americans again — if only we knew we had to.
Here are the articles referred to in my essay:
Arntz, A., Van Eck, M., & de Jong, P. J. (1992). Unpredictable sudden increases in intensity of pain and acquired fear. Journal of Psychophysiology, 6, 54-64.
Wiggins, S., Whyte, P., Higgins, M., Adam, S., Theilmann, J., Bloch, M., et al. (1992). The psychological consequences of predictive testing for Huntington’s disease: Canadian collaborative study of predictive testing. New England Journal of Medicine, 327, 1401-1405.
Smith, D. M., Loewenstein, G., Jankovich, A., & Ubel, P. A. (2007). The dark side of hope: Lack of adaptation to temporary versus permanent colostomy., unpublished manuscript.
March 26, 2007: Compassionate Commercialism
I have nothing against commercials. In fact, I rely on them to tell me which bank is offering the best interest rate or where I can get another pair of those cool green loafers that all my friends make fun of but secretly covet. Every one of us makes what economists call “consumption decisions” every day, and commercial communications can help us make them well.
But commercial speech does more than that. Many advertisements tell us what to want rather than how to find it. I’m not a huge fan of ads that are meant to persuade (especially when they are meant to persuade us to act against our own interests, for example, by smoking or voting against the better of two presidential candidates) but I am a huge fan of free speech and thus I tolerate them, and even defend them. As I wrote in John Brockman’s 2006 anthology, What Is Your Dangerous Idea?: Today’s Leading Thinkers on the Unthinkable:
We live in a world in which people are beheaded, imprisoned, demoted, and censured simply because they have opened their mouths, flapped their lips, and vibrated some air. Yes, those vibrations can make us feel sad or stupid or alienated. Tough shit. That’s the price of admission to the marketplace of ideas. Hateful, blasphemous, prejudiced, vulgar, rude, or ignorant remarks are the music of a free society, and the relentless patter of idiots is how we know we’re in one. When all the words in our public conversation are fair, good, and true, it’s time to make a run for the fence.
The First Amendment guarantees that we will hear unwelcome voices in the public forum, but where exactly is the public forum? Is it all around us? Or are there placesprivate places, sacred placeswhere commercial speech doesn’t belong? That’s the question that a recent ad campaign by Nissan made me ask myself, and I wrote the following essay in reply.
In an advertising campaign that began last week, Nissan left 20,000 sets of keys in bars, stadiums, concert halls and other public venues. Each key ring has a tag that says: “If found, please do not return. My next generation Nissan Altima has Intelligent Key with push-button ignition, and I no longer need these.”
This campaign is clever, but not particularly original.
It was 1997, and the man who was crouched on the sidewalk at 68th and Broadway in New York City was one of the most pathetic souls I’d ever seen. His limbs were twisted in what appeared to be arthritic agony and tears were streaming down his face. “Please,” he whimpered. “Please, somebody help me.”
Most passers-by did what they were named for, but my wife and I stopped. The man looked up. “Please,” he sobbed. “I just want to go home.” My hand needed no guidance from my brain as it reached into my wallet and extracted $10. “Thank you,” he said as I handed him the money. “Thank you so much.” My wife and I mumbled some embarrassed words and walked on.
We hadn’t gone a block when she tugged my sleeve. “Maybe we should have gotten him into a cab,” she said. “He could barely stand up. He might need help. We should go back to see.” My wife is the patron saint of lost kittens and there is no arguing, so we went back to see. And what we saw was our horribly crippled friend walking briskly and happily up 68th Street, opening the door to a late-model car, getting in and driving away after what was apparently a short day of theatrical work.
I know two things now that I didn’t know then.
First, I now know that my hand did what human hands were designed to do. Research suggests that we are hard-wired with a strong and intuitive moral impulse —- an urge to help others that is every bit as basic as the selfish urges that get all the press. Infants as young as 18 months will spontaneously comfort those who appear distressed and help those who are having difficulty retrieving or balancing objects. Chimpanzees will do the same, though not so reliably, which has led scientists to speculate about the precise point in our evolutionary history at which we became the “hypercooperative” species that out-nices the rest.
The second thing I know now that I didn’t know then is that this was the most damaging crime I had ever experienced. Like most residents of large cities, I’d been a victim before —- of burglary once, of vandalism several times. But this was different. The burglars and vandals had taken advantage of my forgetfulness (“Why didn’t I double lock the door?”) and taught me to be better.
But the actor on 68th Street had taken advantage of my helpfulness and taught me to be worse. The hand that had automatically reached for my wallet had been slapped, and once slapped was twice shy. I’ve never again given money to a stranger without scrutinizing him for the signs that distinguish suffering from its imitation. And because I don’t know what those signs are, I typically just walk by.
Now corporate America has taken a lesson from the guild of shameless grifters. Nissan’s plan to leave those 20,000 sets of keys in public venues is every bit as crafty as the fraudulent performance that a decade ago left me with holes in both my pocketbook and soul. There is no selfish reason to bend down and pick up a key ring, but Nissan knows that we will bend without thinking because the impulse to help is bred into our marrow. Our best instinct will be awakened by a key ring and then punished by a commercial. Like rubes throughout the ages, we will be lured by a false cry of distress and quickly cured of our innocence and compassion.
We are used to commercial tricks that play on our fears. The official-looking letter marked “Verification Audit” is actually a magazine subscription renewal form; the credit card company’s ominous call to “discuss your account” is actually an attempt to sell new services.
Should we now get used to commercial tricks that play on our humanity? How would we feel about a device planted in trash bins that screams “I’m stuck!” until the lid is opened, at which point it continues, “Stuck in a dead end job, that is —- and if you are too, then let us show you how to make millions in real estate with no money down”? Is it O.K. to send a thousand doleful puppies into the streets with tags that say: “Thanks for checking. And speaking of checking, our bank charges no monthly fees”?
What happens to us when greed masquerades as need, when cries for help become casting calls for chumps, when our most noble actions make us patsies? “You put an idea out there and seed it,” said the president of the advertising agency that came up with Nissan’s key ring ploy. “And people carry it for you.” Indeed they do. The idea being seeded and carried in this case is that the world cries wolf, that our moral impulse betrays us and that smart people should keep on walking.
You can learn more about the “the moral impulse” by reading
F. Warneken and M. Tomasello (2006). Altruistic helping in human infants and young chimpanzees. Science, 311, 1301-1303.
Haidt, J. (2001). The emotional dog and its rational tail: A social intuitionist approach to moral judgment. Psychological Review, 108, 814-834.
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