Beyond Coincidence Read online

  Psychologist Professor Chris French told us that story. He has been studying superstitions. He is skeptical that certain ritual behavior or the carrying of lucky charms can have anything at all to do with the luck we get in life. He argues that any apparent correlations are pure coincidence.

  Says Professor French, “The reason we believe in these things is because it gives us some sense of control of our lives. What is interesting is that the people who tend toward superstitions about luck usually work in situations of uncertainty. By and large, accountants tend not to be superstitious. But actors, sportsmen, soldiers, sailors, students taking examinations, financial investors, gamblers … that’s a different matter. Gamblers are the most superstitious. However illusory their belief, they are convinced that throwing dice in a particular way will bring them luck. They wouldn’t do it otherwise. However, their behavior is completely counterproductive as it draws them into deeper and deeper trouble.”

  Sports athletes are another highly superstitious breed. Just watch the batter’s box antics of Red Sox shortstop Nomar Garciaparra. Chris French accepts that such rituals can have a positive effect in helping concentration and increasing confidence—but nothing more than that. “If the ritual was prevented, it would certainly have a detrimental effect on performance,” he concedes. “The problem is that we can’t put these things to the test because people won’t agree to not carry out their rituals. The Red Sox might have been even more successful if Nomar tightened his gloves in the dugout. We will never know.”

  American psychologist, Professor Stuart Vyse, provides the following anecdotal examples of superstitions among U.S. sports stars:

  Buffalo Bills quarterback Jim Kelly forces himself to vomit before every game, a habit he has practiced since high school. Former star Chuck Persons eats two candy bars before every game: two KitKats, two Snickers, or one of each. Former NFL coach George Seifert does not leave his office without patting a book and must be the last person to leave the locker room before a game. And Wayne Gretzky always tucks the right side of his jersey behind his hip pads.

  In 1967, sociologist James Henslin studied the behavior and beliefs of taxi drivers playing the game craps, which is based upon throwing a pair of dice against a backboard. Among the superstitious beliefs identified by Henslin were the following:

  • The harder the dice are thrown, the higher the number rolled

  • Rituals such as finger-snapping, blowing on or rubbing the dice, etc., can influence the outcome

  • The higher the confidence of the thrower, the more likely the desired outcome

  • Dropping the dice will adversely affect performance

  • Increasing one’s bet will positively affect performance.

  Professor French concludes that under conditions of uncertainty any belief that gives a sense of control, even if that sense of control is illusory, is likely to be adopted, maintained, and transmitted to others.

  Research suggests that women are typically more superstitious than men. Age doesn’t appear to be a significant factor, although some superstitions appear to decrease with age, while others increase or stay the same. Arts students typically show much higher levels of belief than students of the natural sciences. Social science students fall somewhere in between.

  Belief that superstitious behavior can influence one’s luck was described back in 1989 by Leonard Zusne and Warren Jones as “magical thinking.” They defined this as “the belief that (a) transfer of energy or information between physical systems may take place solely because of their similarity or contiguity in time and space, or (b) that one’s thoughts, words, or actions can achieve specific physical effects in a manner not governed by the principles of ordinary transmission of energy or information.”

  B. F. Skinner’s classic research into “superstition in the pigeon” was conducted at Indiana University in 1948. Skinner described an experiment in which pigeons were placed inside a box and were presented with a food pellet once every fifteen seconds, regardless of their behavior. After a few minutes the birds developed various little idiosyncratic rituals, such as walking round in circles, bobbing their heads up and down and so on. The pigeons appeared to have concluded that their little routines were causing the release of the food even though in reality there was no relationship whatsoever. Skinner’s explanation for this phenomenon was that the accidental pairing of the release of food early on in the process with whatever the bird happened to be doing was enough to reinforce that particular type of activity.

  But we wouldn’t make the same basic mistakes as a pigeon, would we? It’s worth bearing Skinner’s experiment in mind while thinking about these further observations by Stuart Vyse:

  Bjorn Borg, the five-time Wimbledon champion, comes from a superstitious family. He and his relatives are known for a variety of personal superstitions, several of which center around spitting. As she sat in the competitors’ box during the 1979 Wimbledon final, Borg’s mother, Margerethe, ate candy for good luck. When Bjorn reached triple match point against Roscoe Tanner, she spat out the piece she had been chewing—perhaps in preparation for a victory cheer. Before she knew it, Tanner had rallied to deuce. Sensing she had made a mistake, Margarethe retrieved the candy from the dirty floor and replaced it in her mouth. Soon her son had won the championship for the fourth time. Earlier that same year, Borg’s father, Rune, and his grandfather, Martin Andersson, were fishing and listening to the French Open final on the radio. Bjorn was playing Victor Pecci of Paraguay. Borg’s grandfather spat in the water, and just at that instant Borg won a point. Andersson continued to spit throughout the match, going home with a sore throat. Borg won in four sets.

  It seems that our innate love and respect for coincidences leads us to adopt superstitious behavior simply as a result of the accidental pairing of random pieces of behavior and reinforcing events.

  Another experiment was carried out by Professor Koichi Ono of Kyoto University in Japan in 1987, using university students as volunteers. They were led into a cubicle where a counter was mounted on the wall behind three levers. The volunteers were told to try to “earn” as many points as possible—though in fact the points registered were predetermined and bore no relation to any activity by the students. Not all of the students engaged in superstitious behavior, but most did. In the case of one female student, the behavior became quite extreme.

  About five minutes into the session, a point delivery occurred after she had stopped pulling the lever temporarily and had put her right hand on the lever frame. This behavior was followed by a point delivery, after which she climbed on the table and put her right hand to the counter. Just as she did so, another point was delivered. Thereafter she began to touch many things in turn, such as the signal light, the screen, a nail on the screen, and the wall. About ten minutes later, a point was delivered just as she jumped to the floor, and touching was replaced by jumping. After five jumps, a point was delivered when she jumped and touched the ceiling with her slipper in her hand. Jumping to touch the ceiling continued repeatedly and was followed by points until she stopped about twenty-five minutes into the session, perhaps because of fatigue.

  Why have we evolved in such a way that these strange anomalous behavioral patterns persist? Why do we have a cognitive system that is prone to such systematic errors? Or, to put it another way, shouldn’t we be smarter than the average pigeon?

  Professor French suggests: “The answer is that in evolutionary terms it probably makes more sense to have a cognitive system that works very quickly and usually produces the right answer rather than one that works more slowly but produces a slightly higher proportion of correct conclusions. Our cognition relies upon a range of ‘shortcuts,’ technically known as heuristics, which generally lead to the correct conclusion but can, under certain circumstances, systematically lead us astray. We have been so successful as a species precisely because we are good at making connections between events and spotting patterns and regularities in nature. The price we have paid is a t
endency to sometimes detect connections and patterns that are not really there.”

  Christina Richards is a seasoned rock and mountain climber, and instructor.

  Climbing is clearly a riskier activity than, for example, accountancy (although creative accountancy can have some unpleasant consequences). But is climbing intrinsically dangerous?

  “Of course, we are taking calculated risks,” says Christina. “Some climbers do it for the adrenaline rush, but most people, if they have any respect for themselves, take proper precautions. They weigh up the risks of death.”

  How big an element does luck play in mountaineering?

  “Luck is a significant factor in climbing. It’s tied up in what we call objective dangers; things we can’t control, like rock falls, holds snapping, avalanches. These can cause real problems.”

  So how do climbers deal with these uncontrollable elements? Are they superstitious?

  “A lot are. They tend to do things to make themselves feel luckier, and therefore safer. I go through certain routines with my ropes and other equipment, but mainly I carry a ring on a necklace around my neck. It was given to me by a friend, and I do consider it to be lucky.

  “Climbers go through all sorts of ritual behavior when starting on a climb. It helps them to focus, but also makes them feel better. No one will ever blaspheme during a climb—even the complete atheists. In such a dangerous environment, you don’t want to push your luck.”

  What would happen if Christina was about to start on a climb and suddenly realized she had left her ring behind at the hotel?

  “It would depend how difficult the climb was. If it was a tough one, I would want everything to be in order. If my gear wasn’t absolutely right, or I didn’t have my ring with me, I just wouldn’t do it. Everything has to be in balance.”

  Does she seriously believe her ring will help her to get safely up or down a mountain?

  “If I was embarking on something of lesser consequence—driving to visit a friend, for example—and I hadn’t got my ring then it wouldn’t be a problem. But when the potential consequence is death—it just isn’t worth taking the risk. It’s all to do with the scale of the consequences.”

  What force does the ring exert on Christina’s luck?

  “I think it is hard to say sitting comfortably talking about it, but there is a feeling that it will make me more lucky, more successful. As ridiculous as that notion sounds, it doesn’t sound so ridiculous when you are hanging from a mountain by your fingertips.”

  Christina’s ambition is to climb one of the world’s most dangerous peaks—K2. A disturbingly small proportion of climbers who tackle this monster live to tell the tale. Would Christina’s ring help give her the courage to take on such a risky climb?

  “It would make a small amount of difference. Though training and the abilities of the other climbers would be more significant. With K2 the objective dangers of weather and avalanche are much greater. I’d love to have a crack at it though. I know the chances of surviving are only fifty-fifty—but if you have to die on a mountain—what a way to die.”

  Is there a danger that climbers might come to rely too much on lucky charms or on their own sense of being a lucky person?

  “One guy I know was phenomenally lucky. Got away with stuff where anyone else would have been dead. He would fall and land on his feet or get to the bottom of a climb and his gear would come away and end up in a puddle at his feet. He was an adrenaline junkie. He would overtake on blind bends and get away with it. He considered himself lucky—right up to the time a rock came away in his hand—an objective danger—and he slid down a mountain and broke his back.”

  Richard Wiseman points out that the risk of believing too much in one’s own luck is not limited to adrenaline junkies.

  “Research being done by psychologists has revealed a growing body of people who are relying totally on the prospect of good luck on the lottery as a means of progressing in life. Rather than trying to get a job or seek promotion, they are just sitting back and waiting for their lucky numbers to come up. They are convinced it will happen, so see no point in making an effort in any other areas of their life.

  “Putting trust in superstitious beliefs in luck is disastrous. Luck simply doesn’t work like that. Research shows that unlucky people tend to be more superstitious than lucky people. Lucky people are generally more constructive about the problems in their lives. Unlucky people invest all their optimism in an outside agency. They have a magical viewpoint of luck. The problem is that all these superstitious rituals, touching wood, and lucky charms, don’t work and these people just end up getting even unluckier.”

  Professor Chris French says research proves that people who are psychologically healthy and think of themselves as lucky people are actually less in touch with reality than depressives.

  “The truth is that life really is pretty awful,” he says. “The depressives have got it right. The people who don’t suffer from depression are the ones who have what we call ‘unrealistic optimism.’ We give people questionnaires to fill in and ask them what are the chances of certain negative things happening to them—of being run over by a bus or contracting a particular illness. Most people assume that the bad things won’t happen to them and the good things will. And the truth is that they are being overly optimistic. The depressives tend to be much more accurate. But by living your life as if you were a lucky person, good things will tend to happen to you because you will be willing to take risks. By not living in an overcautious, worried, anxious way, you will get more out of life. This is a nice example of a situation where an irrational belief can be psychologically healthy.” In the final analysis, whether we go to luck school and learn to control our luck, carry lucky rabbit’s feet in the hope of warding off bad luck—or simply leave ourselves open to whatever luck is handed down to us from on high (literally in the case of forest ranger Roy Sullivan), Dame Fortune can be very mischievous.

  In June 1980, Maureen Wilcox bought tickets for both the Massachusetts and Rhode Island lotteries. She had the winning numbers for both but didn’t win a penny. Her Massachusetts numbers won the Rhode Island lottery and her Rhode Island numbers won the Massachusetts lottery.

  What on earth could she have done to deserve that?

  7

  DOES COINCIDENCE ADD UP?

  Mathematicians are not fanciful people. They are rationalists, using numbers to understand life’s mysteries. Where others see coincidences as evidence of magic or divine intervention, they see the laws of probability in action.

  So how unlikely would something have to be, how long the odds against it, before a fusty old mathematician was prepared to accept that it was beyond coincidence—that something really rather strange was going on?

  What’s the most unlikely thing you could imagine happening? Winning millions on the lottery—twice? Being struck repeatedly by lightning? These things happen, as we have already seen. They don’t happen very often, of course, and not usually to us, but they do happen. Mathematicians tell us that if a thing can occur it will occur—eventually. Only impossible things don’t happen—like discovering icebergs in the Sahara or taxis in the rain.

  How does the mathematics of probability—of coincidence—add up? What would be the odds, for example, of being struck by a meteorite just minutes after discussing the odds against such a thing happening? And if it happened, would a mathematician be prepared to believe that it was just coincidence? The answer to this a little later.

  Meanwhile, at the other end of the probability scale, how surprised should we be when we meet someone at a party who happens to have the same birthday?

  With odds of 365 to 1 against, it doesn’t seem like this should happen too often. When we find someone who shares our birth date, we tend to think something a bit special has happened. Fancy that, of all the dates in the year, we have the same birthday. What a coincidence!

  Surprisingly the (rather complicated) mathematical formula dictates that you only need twenty-thr
ee people in a room for there to be a better than 50 percent probability that two of them will share the same birthday.

  It seems an absurdly low figure—one worth putting to the test. We looked for an average sample of people. Where better to find one than on the street?

  In the event, we had to ask twenty-nine people before we found a match—a young girl waiting for a bus was born on 24 July, the same day as the sixth person we spoke to. The girl at the bus stop was not remotely surprised that we had only had to stop so few people. In fact she thought it odd we had had to ask as many as twenty-nine. Her boyfriend, and four of her friends, all shared her birthday!

  Eminent mathematician Warren Weaver once explained this at a dinner attended by high-ranking U.S. military men and then started around the table to compare birthdays. To his disappointment, he reached the last officer without turning up a single coincidence. But he was rescued by the twenty-third person in the room. The waitress, who had been listening, announced that she had been born on the same day as one of the generals.

  Mathematical truths are often counterintuitive. The reality can surprise and delight us—or, at times, disturb us. We have a natural tendency to think the likelihood of something happening is either much greater or, indeed, much smaller than it really is. Our underestimation of the odds against winning the lottery keeps us buying tickets, and our overestimation of the odds against a road accident keeps us driving our cars.

  Let’s look at some other improbable things. If you were playing bridge and received a hand containing thirteen cards of the same suit, you would be amazed. And yet that eventuality is no more likely, or unlikely, than any other combination of cards. The likelihood of receiving any predicted hand of cards is, of course, another matter. The odds against being dealt all thirteen spades, for example, has been calculated as 635,013,559,600 to 1.