Review
“A wonderfully readable guide to how the mathematical laws of randomness affect our lives.”--Stephen Hawking, author of A Brief History of Time
"The Drunkard's Walk is a magnificent exploration of the role that chance plays in our lives. Often historical, occasionally hysterical, and consistently smart and funny, this book challenges everything we think we know about how the world works. The probability is high that you will be entertained and enlightened by this intelligent charmer."--Daniel Gilbert, professor of psychology, Harvard University, and author of Stumbling on Happiness
"Fast, chatty, very readable, and a fine introduction to ideas that everyone should know." --David Berlinski, author of A Tour of the Calculus
“A primer on the science of probability.”–The Washington Post Book World
“Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists ...The result is a readable crash course in randomness.”–The New York Times Book Review
“A jaunty read worthy of any beach or airplane. . . . Mlodinow has an intimate perspective on randomness. . . . He draws direct links from the works of history's greatest minds to the deeds of today's not-so-great ones, explaining phenomena like the prosecutor's fallacy (which helped acquit O.J. Simpson) and the iPod shuffle function (eventually programmed not to be truly random, lest songs hit upon eerie playing streaks).”–The Austin Chronicle
“Please read The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow, a history, explanation, and exaltation of probability theory. . . . Mlodinow . . . thinks in equations but explains in anecdote, simile, and occasional bursts of neon. . . .The results are mind-bending.”–Fortune
“Challenges our intuitions about probability and explores how, by understanding randomness, we can better grasp our world.”–Seed Magazine
“[Mlodinow is] the perfect guy to reveal the ways unrelated elements can relate and connect.”–The Miami Herald
About the Author
Leonard Mlodinow received his doctorate in physics from the University of California, Berkeley, was an Alexander von Humboldt fellow at the Max Planck Institute, and now teaches about randomness to future scientists at Caltech. Along the way he also wrote for the television series MacGyver and Star Trek: The Next Generation. His previous books include Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace, Feynman's Rainbow: A Search for Beauty in Physics and in Life, and, with Stephen Hawking, A Briefer History of Time. He lives in South Pasadena, California.
From The Washington Post
Reviewed by Christopher Shea
Leonard Mlodinow has had, to speak informally, a pretty random career: He earned a PhD in physics from Berkeley, wrote for "MacGyver" and "Star Trek" and has now settled down as a science popularizer.
A far more sober instance of randomness, however, underpins his new book, The Drunkard's Walk. And it's not hard to see it as a sort of Rosebud, explaining why the author finds unpredictability so compelling. During World War II in the Nazi death-camp Buchenwald, his father and other starving inmates had been told they'd be killed one-by-one until someone confessed to stealing some bread that had gone missing. Upon confessing, Mlodinow's guilty father was not executed, as expected, but promoted to serve as the chef's assistant. A different capricious decision then, and the author Leonard Mlodinow would not exist today.
It's been said that what divides liberals and conservatives is the degree to which each thinks luck plays a role in where one ends up in life. For Mlodinow, "There but for the grace of God" is a mathematical (if not theological) truth. In A Drunkard's Walk, which takes its title from scientific slang for a purely random succession of events, Mlodinow argues that it is quintessentially human to stamp the results of largely arbitrary processes as, in retrospect, inevitable.
Shifting from his own family's encounters with fate, for example, he notes that it is hard to imagine a world without Harry Potter, yet publishers rejected J.K. Rowling's manuscript nine times before someone finally said yes. There's a self-helpish lesson here: Whether we succeed in life is partly out of our hands -- think of the other worthy authors whose manuscripts languish in desk drawers -- but by persisting we offer lightning more chances to strike.
Sandwiched in this book between a morally freighted opening and conclusion is a primer on the science of probability. "Probability is the very guide of life," Cicero wrote. If so, most of us are mapless. We put our money in the hands of moneymen with the best records over the past (say) five years, ignoring research that demonstrates that these big-swinging stockpickers are as likely as their peers to wind up at the bottom of the pile over the next five-year period.
Even the scientifically literate can be confounded by probability. Mlodinow once tested positive for HIV, at which point his doctor sadly told him that there was a 99.9 percent chance he had a death sentence. But the doctor had failed to properly balance the 1-in-1,000 chance of a false positive against the 1 in 10,000 chance that a man in Mlodinow's demographic (heterosexual, married, white, non-IV-drug-user) had the virus. Within that group, only 1 in 11 people who test positive is truly infected; Mlodinow wasn't.
Once in a while, Mlodinow sends you scurrying for a statistics textbook when he ventures into deeper mathematical waters or skips steps in his explanations, but when things get slow, there's usually a diverting historical detour. This is the kind of book in which you learn that Pascal, after he set aside his work on statistics, took to wearing "an iron belt with points on the inside so that he was in constant discomfort," lest the siren song of happiness tempt him.
Nudge, in contrast, is a much more policy-oriented book. It comes with substantial advance publicity, thanks in part to the imprimatur of Sen. Barack Obama, who has embraced some of the authors' proposals, which are underpinned by libertarian paternalism. ("Paternalism" because the authors want to steer people to make better choices; "libertarian" because they feel people should still be free to make bad ones.)
Like Mlodinow, Richard Thaler, a pioneer of so-called behavioral economics, and Cass Sunstein, a noted law professor, discuss numerous studies that show just how far short humans fall from the ideal of homo economicus. Inertia, herd behavior, ignorance of odds, and egotism conspire to cause people to make bad decisions and poor predictions. (Typically, only 5 percent of Thaler's business school students say that they will end up in the bottom half of his class.)
Thaler and Sunstein's best-known proposal has to do with 401(k) plans. When people fail to sign up for such plans, they are leaving money on the table -- especially when employers match employees' contributions -- not to mention raising the odds they'll be subsisting on chunk light tuna in retirement. One study found that enrolling workers automatically in these plans -- switching from an "opt in" system to "opt out" -- drove participation in the plans from 65 percent to 98 percent.
In the arena of organ donation, switching to an opt-out system could save thousands of lives annually. One study in Iowa found that 97 percent of residents supported organ transplantation, yet only 43 percent of those people had checked the relevant box on their driver's license application. That gap could be closed if participation in organ-donor programs were the default position. If opt-in seems too aggressive when it comes to bodily organs, even a "forced choice" could improve the situation. Demanding that people give a clear yes or no would surely raise the number of donors, given the popularity of the concept.
Some nudges might be purely informational. How much of the current mortgage crisis would have been averted had prospective homeowners been presented with a clear, readable document laying out some of the bad-case scenarios when their low, teaser interest rates ended?
And there's more! What about a debit card explicitly reserved for charitable donations, which would make it a cinch to keep track of tax deductions and encourage more giving? Or software that detects uncivil language in your e-mail and asks if you really want to send it?
In the end, it must be said, the profusion of proposals in Nudge, however worthy, and the countless summaries of studies supporting them grow a bit wearisome. As influential as the book is likely to be, it's hard to imagine it pushing its way alongside Malcolm Gladwell's Blink (inferior social science, far breezier style) on the bestseller list. Then again, who dares judge the odds of the publishing biz? None of us knows when lightning will strike.
Copyright 2008, The Washington Post. All Rights Reserved.
Excerpt. © Reprinted by permission. All rights reserved.
Peering through the Eyepiece of Randomness
I remember, as a teenager, watching the yellow flame of the Sabbath candles dancing randomly above the white paraffin cylinders that fueled them. I was too young to think candlelight romantic, but still I found it magical-because of the flickering images created by the fire. They shifted and morphed, grew and waned, all without apparent cause or plan. Surely, I believed, there must be rhyme and reason underlying the flame, some pattern that scientists could predict and explain with their mathematical equations. "Life isn't like that," my father told me. "Sometimes things happen that cannot be foreseen." He told me of the time when, in Buchenwald, the Nazi concentration camp in which he was imprisoned and starving, he stole a loaf of bread from the bakery. The baker had the Gestapo gather everyone who might have committed the crime and line the suspects up. "Who stole the bread?" the baker asked. When no one answered, he told the guards to shoot the suspects one by one until either they were all dead or someone confessed. My father stepped forward to spare the others. He did not try to paint himself in a heroic light but told me that he did it because he expected to be shot either way. Instead of having him killed, though, the baker gave my father a plum job, as his assistant. "A chance event," my father said. "It had nothing to do with you, but had it happened differently, you would never have been born." It struck me then that I have Hitler to thank for my existence, for the Germans had killed my father's wife and two young children, erasing his prior life. And so were it not for the war, my father would never have emigrated to New York, never have met my mother, also a refugee, and never have produced me and my two brothers.
My father rarely spoke of the war. I didn't realize it then, but years later it dawned on me that whenever he shared his ordeals, it was not so much because he wanted me to know of his experiences but rather because he wanted to impart a larger lesson about life. War is an extreme circumstance, but the role of chance in our lives is not predicated on extremes. The outline of our lives, like the candle's flame, is continuously coaxed in new directions by a variety of random events that, along with our responses to them, determine our fate. As a result, life is both hard to predict and hard to interpret. Just as, looking at a Rorschach blot, you might see Madonna and I, a duck-billed platypus, the data we encounter in business, law, medicine, sports, the media, or your child's third-grade report card can be read in many ways. Yet interpreting the role of chance in an event is not like intepreting a Rorschach blot; there are right ways and wrong ways to do it.
We often employ intuitive processes when we make assessments and choices in uncertain situations. Those processes no doubt carried an evolutionary advantage when we had to decide whether a saber-toothed tiger was smiling because it was fat and happy or because it was famished and saw us as its next meal. But the modern world has a different balance, and today those intuitive processes come with drawbacks. When we use our habitual ways of thinking to deal with today's tigers, we can be led to decisions that are less than optimal or even incongruous. That conclusion comes as no surprise to those who study how the brain processes uncertainty: many studies point to a close connection between the parts of our brain that make assessments of chance situations and those that handle the human characteristic that is often considered our prime source of irrationality-our emotions. Functional magnetic resonance imaging, for example, shows that risk and reward are assessed by parts of the dopaminergic system, a brain-reward circuit important for motivational and emotional processes. The images show, too, that the amygdala, which is also linked to our emotional state, especially fear, is activated when we make decisions couched in uncertainty.
The mechanisms by which people analyze situations involving chance are an intricate product of evolutionary factors, brain structure, personal experience, knowledge, and emotion. In fact, the human response to uncertainty is so complex that sometimes different structures within the brain come to different conclusions and apparently fight it out to determine which one will dominate. For example, if your face swells to five times its normal size three out of every four times you eat shrimp, the "logical" left hemisphere of your brain will attempt to find a pattern. The "intuitive" right hemisphere of your brain, on the other hand, will simply say "avoid shrimp." At least that's what researchers found in less painful experimental setups. The game is called probability guessing. In lieu of toying with shrimp and histamine, subjects are shown a series of cards or lights, which can have two colors, say green and red. Things are arranged so that the colors will appear with different probabilities but otherwise without a pattern. For example, red might appear twice as often as green in a sequence like red-red-green-red-green-red-red-green-green-red-red-red, and so on. The task of the subject, after watching for a while, is to predict whether each new member of the sequence will be red or green.
The game has two basic strategies. One is to always guess the color that you notice occurs more frequently. That is the route favored by rats and other nonhuman animals. If you employ this strategy, you are guaranteed a certain degree of success but you are also conceding that you will do no better. For instance, if green shows up 75 percent of the time and you decide to always guess green, you will be correct 75 percent of the time. The other strategy is to "match" your proportion of green and red guesses to the proportion of green and red you observed in the past. If the greens and reds appear in a pattern and you can figure out the pattern, this strategy enables you to guess right every time. But if the colors appear at random, you would be better off sticking with the first strategy. In the case where green randomly appears 75 percent of the time, the second strategy will lead to the correct guess only about 6 times in 10.
Humans usually try to guess the pattern, and in the process we allow ourselves to be outperformed by a rat. But there are people with certain types of post-surgical brain impairment-called a split brain-that precludes the right and left hemispheres of the brain from communicating with each other. If the probability experiment is performed on these patients such that they see the colored light or card with only their left eye and employ only their left hand to signal their predictions, it amounts to an experiment on the right side of the brain. But if the experiment is performed so as to involve only their right eye and right hand, it is an experiment on the left brain. When researchers performed those experiments, they found that-in the same patients-the right hemisphere always chose to guess the more frequent color and the left hemisphere always tried to guess the pattern.
Making wise assessments and choices in the face of uncertainty is a rare skill. But like any skill, it can be improved with experience. In the pages that follow, I will examine the role of chance in the world around us, the ideas that have been developed over the centuries to help us understand that role, and the factors that often lead us astray. The British philosopher and mathematician Bertrand Russell wrote,
We all start from "naive realism," i.e., the doctrine that things are what they seem. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow are not the greenness of grass, the hardness of stones, and the coldness of snow that we know in our own experience, but something very different. In what follows we will peer at life through the eyepiece of randomness and see that many of the events of our lives, too, are not quite what they seem but rather something very different.
In 2002 the Nobel committee awarded the Nobel Prize in Economics to a scientist named Daniel Kahneman. Economists do all sorts of things these days-they explain why teachers are paid so little, why football teams are worth so much, and why bodily functions help set a limit on the size of hog farms (a hog excretes three to five times as much as a human, so a farm with thousands of hogs on it often produces more waste than the neighboring cities). Despite all the great research generated by economists, the 2002 Nobel Prize was notable because Kahneman is not an economist. He is a psychologist, and for decades, with the late Amos Tversky, Kahneman studied and clarified the kinds of misperceptions of randomness that fuel many of the common fallacies I will talk about in this book.
The greatest challenge in understanding the role of randomness in life is that although the basic principles of randomness arise from everyday logic, many of the consequences that follow from those principles prove counterintuitive. Kahneman and Tversky's studies were themselves spurred by a random event. In the mid-1960s, Kahneman, then a junior psychology professor at Hebrew University, agreed to perform a rather unexciting chore: lecturing to a group of Israeli air force flight instructors on the conventional wisdom of behavior modification and its application to the psychology of flight training. Kahneman drove home the point that rewarding positive behavior works but punishing mistakes does not. One of his students interrupted, voicing an opinion that would lead Kahneman to an epiphany and guide his research for decades.
"I've often praised people warmly for beautifully executed maneuvers, and the next time they always do worse," the flight instructor said. "And I've screamed at people for badly executed maneuvers, and by and large the next time they improve. Don't tell me that reward works and punishment doesn't work. My experience contradicts it." The other flight instructors agreed. To Kahneman the flight instructors' experiences rang true. On the other hand, Kahneman believed in the animal experiments that demonstrated that reward works better than punishment. He ruminated on this apparent paradox. And then it struck him: the screaming preceded the improvement, but contrary to appearances it did not cause it.
How can that be? The answer lies in a phenomenon called regression toward the mean. That is, in any series of random events an extraordinary event is most likely to be followed, due purely to chance, by a more ordinary one. Here is how it works: The student pilots all had a certain personal ability to fly fighter planes. Raising their skill level involved many factors and required extensive practice, so although their skill was slowly improving through flight training, the change wouldn't be noticeable from one maneuver to the next. Any especially good or especially poor performance was thus mostly a matter of luck. So if a pilot made an exceptionally good landing-one far above his normal level of performance-then the odds would be good that he would perform closer to his norm-that is, worse-the next day. And if his instructor had praised him, it would appear that the praise had done no good. But if a pilot made an exceptionally bad landing-running the plane off the end of the runway and into the vat of corn chowder in the base cafeteria-then the odds would be good that the next day he would perform closer to his norm-that is, better. And if his instructor had a habit of screaming "you clumsy ape" when a student performed poorly, it would appear that his criticism did some good. In this way an apparent pattern would emerge: student performs well, praise does no good; student performs poorly, instructor compares student to lower primate at high volume, student improves. The instructors in Kahneman's class had concluded from such experiences that their screaming was a powerful educational tool. In reality it made no difference at all.
This error in intuition spurred Kahneman's thinking. He wondered, are such misconceptions universal? Do we, like the flight instructors, believe that harsh criticism improves our children's behavior or our employees' performance? Do we make other misjudgments when faced with uncertainty? Kahneman knew that human beings, by necessity, employ certain strategies to reduce the complexity of tasks of judgment and that intuition about probabilities plays an important part in that process. Will you feel sick after eating that luscious-looking seviche tostada from the street vendor? You don't consciously recall all the comparable food stands you've patronized, count the number of times you've spent the following night guzzling Pepto-Bismol, and come up with a numerical estimate. You let your intuition do the work. But research in the 1950s and early '60s indicated that people's intuition about randomness fails them in such situations. How widespread, Kahneman wondered, was this misunderstanding of uncertainty? And what are its implications for human decision making? A few years passed, and Kahneman invited a fellow junior professor, Amos Tversky, to give a guest lecture at one of his seminars. Later, at lunch, Kahneman mentioned his developing ideas to Tversky. Over the next thirty years, Tversky and Kahneman found that even among sophisticated subjects, when it came to random processes-whether in military or sports situations, business quandaries, or medical questions-people's beliefs and intuition very often let them down.
Suppose four publishers have rejected the manuscript for your thriller about love, war, and global warming. Your intuition and the bad feeling in the pit of your stomach might say that the rejections by all those publishing experts mean your manuscript is no good. But is your intuition correct? Is your novel unsellable? We all know from experience that if several tosses of a coin come up heads, it doesn't mean we are tossing a two-headed coin. Could it be that publishing success is so unpredictable that even if our novel is destined for the best-seller list, numerous publishers could miss the point and send those letters that say thanks but no thanks? One book in the 1950s was rejected by publishers, who responded with such comments as "very dull," "a dreary record of typical family bickering, petty annoyances and adolescent emotions," and "even if the work had come to light five years ago, when the subject [World War II] was timely, I don't see that there would have been a chance for it." That book, The Diary of a Young Girl by Anne Frank, has sold 30 million copies, making it one of the best-selling books in history. Rejection letters were also sent to Sylvia Plath because "there certainly isn't enough genuine talent for us to take notice," to George Orwell for Animal Farm because "it is impossible to sell animal stories in the U.S.," and to Isaac Bashevis Singer because "it's Poland and the rich Jews again." Before he hit it big, Tony Hillerman's agent dumped him, advising that he should "get rid of all that Indian stuff."
