Paul Rozin, a psychologist at the University of Pennsylvania, wondered whether this way of thinking was alive and well in modern-day Western society, and whether it might even underlie certain types of prejudice and irrationality. To find out, Rozin and his colleagues conducted a series of unusual, but insightful, experiments. One of the tasks the researchers gave their subjects concerned clothing: “Rate how you would feel about wearing a nice, soft, blue sweater, big and bulky, unisex in style. It was laundered a couple of days ago, but it’s new, has never been owned or worn by anyone.”
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Not surprisingly, people said that they had no problem wearing the sweater. The experimenters also asked them to imagine that the sweater had been worn by someone who had contracted AIDS through a blood transfusion. The experimenters said that the sweater had been laundered a couple of days ago, and that the person with AIDS had only worn it for thirty minutes. Suddenly people didn’t want to wear the sweater. Even though they knew there was no health or hygiene issue, the superstitious theory of contagion kicked in, and they could not bring themselves to wear it. When Rozin and his colleagues varied the imaginary sweater owners, they discovered that the idea of the sweater’s having once belonged to someone who personified evil (such as a mass murderer or a fanatical leader) elicited the strongest reaction. In fact, Rozin’s results revealed that people would rather wear a sweater that had been dropped in dog feces and not washed (raising genuine health concerns) than a laundered sweater that had once belonged to a mass murderer.
IT’S A SMALL, SMALL WORLD, AND YEAR ON YEAR SHRINKAGE
People often develop magical beliefs about the world because they have experienced something seemingly weird. With the concept of coincidences, events appear to coincide in ways that seem meaningful and to defy the odds. Some of the best-known coincidences surround the deaths of Presidents John Kennedy and Abraham Lincoln. Lincoln was killed in the Ford Theater; Kennedy was assassinated while travelling in a Lincoln car, built by Ford. Lincoln was elected to Congress in 1846, Kennedy in 1946. Lincoln was elected president in 1860, Kennedy in 1960. The surnames of both men contain seven letters, and both killings took place on a Friday. After their deaths, both presidents were succeeded by men named Johnson. Andrew Johnson was born in 1809, Lyndon B. Johnson in 1909.
These sorts of amazing moments do not restrict themselves to American presidents but pop up from time to time in most people’s lives. In the 1920s, three strangers were traveling through Peru by train. Sitting in the same car, they introduced themselves to one another, only to find that the first man’s surname was Bingham, the second man’s was Powell, and the third man’s was Bingham-Powell. Another remarkable coincidence took place at London’s Savoy Hotel, home of Kaspar the lucky black cat, in 1953. A television reporter named Irv Kupcinet was staying at the hotel to cover Queen Elizabeth II’s coronation. Opening one of the drawers in his room, he found some items belonging to his friend Harry Hannin, manager of the well-known basketball team the Harlem Globetrotters. Just two days later, Kupcinet received a letter from Hannin in which he explained that he had been staying at the Hotel Meurice in Paris and had found one of Kupcinet’s ties in a drawer in his room. Faced with such curious incidents, many people would simply say, “What are the chances of that?” and leave it there. But some scholars, such as the Stanford mathematician Persi Diaconis, have delved deeper.
Diaconis has been invited by Las Vegas casinos to determine whether their card shuffling machines really do randomize the order of decks (they don’t); he has used high-speed cameras taking 10,000 frames per second to analyze human coin tossing (revealing that coins show a tiny bias toward landing the same way that they started), and persuaded a team of Harvard technicians to create a machine capable of producing a perfectly random coin toss. Diaconis has also written one of the seminal papers on the mathematics and psychology of coincidences, arguing that certain little-known statistical laws make some seemingly impossible events surprisingly likely. The law of large numbers is one example.
Almost every week in Britain, a truly amazing coincidence takes place, an event that we know is extremely unlikely to happen by chance alone. In fact, the odds of this event’s happening are 15 million to one: Someone wins the lottery jackpot. Why does this unlikely event routinely happen week after week? Because a huge number of people buy lottery tickets. It is exactly the same with other coincidences. There are millions of people in the world living complex lives, and so it is not surprising that once in a while someone wins the coincidence jackpot and experiences a genuinely unlikely event. Although it is tempting to see these events as a sign from the gods or evidence of a mysterious sense of connection between people, in reality it may all come down to chance. Arthur Conan Doyle put it beautifully in “The Adventure of the Blue Carbuncle”: “Amid the action and reaction of so dense a swarm of humanity, every possible combination of events may be expected to take place, and many a little problem will be presented which may be striking and bizarre.”
The same idea also applies to amazing anagrams that seem to contain hidden messages or wonderfully succinct descriptions of people or events. The words “U.S. President Ronald Reagan” are a precise anagram of “repulsed and ignorant arse”; “President Clinton of the U.S.A.” can be scrambled to make “to copulate he finds interns.”
My favorite anagram was discovered by the puzzle creator Cory Calhoun, and it involves the famous phrase from Shakespeare’s
Hamlet:
“To be or not to be: that is the question, whether ’tis nobler in the mind to suffer the slings and arrows of outrageous fortune.” This phrase is an exact anagram of a statement that provides a perfect summary of the entire play: “In one of the bard’s best-thought-of tragedies, our insistent hero, Hamlet, queries on two fronts about how life turns rotten.” Although these examples may look amazing, nothing magical is taking place. It is simply the law of large numbers at work. Given the large number of combinations of letters in the words, and the huge amount of text in plays and books, it is not surprising that once in a while amazing anagrams emerge. What
is
perhaps more surprising is that some people are prepared to invest significant amounts of their time looking for them.
Although the law of large numbers accounts for many coincidences, sometimes there is a deeper psychology at work. A 1993 survey showed that one of the most frequently experienced coincidences is that of the “small-world phenomenon,” in which two strangers meet at a party only to discover that they have a mutual acquaintance.
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Almost 70 percent of people claimed to have had this experience, and about 20 percent experienced it frequently. In the 1960s, the phenomenon intrigued the well-known psychologist Stanley Milgram.
Milgram was a remarkable man who was responsible for conducting some of the world’s most famous psychology experiments. Starting in late 1960, Milgram carried out a series of studies examining whether ordinary people would be prepared to inflict pain and suffering on others simply because they were told to do so by an experimenter.
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In the study, an experimenter asked participants to deliver increasingly dangerous electric shocks to another participant (actually an actor who was simply pretending to receive the shocks). If the participants expressed any concern about what they were doing, the experimenter encouraged them to persevere with the procedure, using phrases such as “Please continue” and “The experiment requires you to go on.” Milgram’s results revealed that about 60 percent of participants were prepared to deliver what they thought was a potentially lethal shock to the hapless victim because they were told to do so by a man wearing a white coat.
Milgram’s electric shock study is very well known. It can be found in almost every introductory psychology textbook and is one of the very few behavioral studies to have exerted a significant effect on the broader culture. In 1974, Milgram described it in a popular book called
Obedience to Authority.
In the mid-1970s, CBS broadcast a dramatization of the electric shock experiments with William Shatner playing the role of Milgram; and in 1986, the musician Peter Gabriel wrote a song titled “We Do What We’re Told (Milgram’s 37),” referring to one of Milgram’s experiments in which thirty-seven out of forty participants were fully obedient. What is not so well known is that his work inspired several equally striking follow-up studies. Professors Charles Sheridan and Richard King, concerned that participants might have correctly realized that the participant receiving the shocks was an actor, repeated the study in the 1970s; this time, real shocks were administered to puppies.
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The resulting paper, titled “Obedience to Authority with an Authentic Victim,” describes how just over 50 percent of men delivered the maximum shock to the puppies, versus 100 percent of women.
Milgram continued to devise and carry out unusual and thought-provoking experiments throughout his academic career. In fact, he had developed such a reputation for the work that when he burst into a colleague’s lecture hall on November 22, 1963, and announced the assassination of Kennedy, many of the students assumed that it was all part of yet another Milgram experiment.
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In the mid-1960s, building on theoretical work being undertaken at the Massachusetts Institute of Technology, Milgram decided to take a hands-on approach to understanding the small-world phenomenon.
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One hundred and ninety-eight people living in Nebraska were sent a letter in which they were asked to help ensure that it made its way to a “target person”—a particular stockbroker who worked in Boston and lived in Sharon, Massachusetts. There was, however, a catch. Participants could not mail the letter directly to the stockbroker; they had to send it to people they knew on first-name terms and who they thought might know the stockbroker. Each recipient was asked to do the same; and again, the recipients had to send the letter to people they knew on first-name terms.
How many people were needed to link complete strangers? Given the tens of millions of people in America, many were surprised to discover that there tended to be just six people linking the initial volunteer and the target person—giving rise to the popular notion that we are all connected by just six degrees of separation. The results suggest that society is much more closely knit than might first be imagined, and helps explain why jokes, gossip, and fads can rapidly spread simply by word of mouth. In addition, by examining the relationship between the people in each of the completed chains, Milgram was able to gain some insights into the social structure of 1960s America. People were far more likely to pass the letter onto someone of their own, rather than the opposite, sex, and most links involved friends and acquaintances rather than relatives. The implications of Milgram’s findings are not limited to social systems; they also explain a diverse range of other networks, including the operation of power grids, the spread of disease, the way in which information is passed around the Internet, and the neural circuitry underpinning brain function.
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Writing about Milgram’s work in 1995, the mathematician John Allen Paulos noted: “It’s not clear how one would carry out studies to confirm this, but I suspect that the average number of links connecting an arbitrary pair of people has shrunk over the last fifty years. Furthermore, this number will continue to shrink because of advances in communication and despite an increasing population.”
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Given the importance of Milgram’s giant game of pass the parcel, and Paulos’s speculations about a shrinking world, it’s surprising that hardly any researchers have attempted to repeat the experiment. So in 2003, my colleague Emma Greening and I teamed up with Roger Highfield, science editor of the
Daily Telegraph,
and the Cheltenham Science Festival to address this issue.
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We wanted to carry out the first British replication of Milgram’s classic piece of quirkological research and test two ideas. First, would we obtain the same number of links, or even as Paulos suggested, fewer, than Milgram? Second, was it possible to use the phenomenon to explain another mystery that had emerged during my work studying lucky and unlucky people? Lucky people claim to have lots of chance encounters, and these seem to have remarkably beneficial effects on their lives. They bump into someone at a party, discover that they know people in common, and from these connections they end up getting married or doing business. Or when they need something, they always seem to know someone who knows someone who can solve their problem. In contrast, unlucky people rarely report such experiences. We wondered whether lucky people report lots of small-world experiences because they know lots of people and so are, without realizing it, making their own good fortune by constructing, and inhabiting, an especially small world.
I published a short article in the
Telegraph
inviting readers who wished to participate in a “small-world” experiment to contact me. One hundred volunteers were then sent a package containing some instructions along with a set of postcards and envelopes. The instructions explained that the purpose of the experiment was to ensure that the parcel made its way to a certain “target person.”