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THE MYSTERY
Fortune brings in some boats that are not steer’d.
 —William Shakespeare
Simply Unbelievable
In the summer of 1972, the actor Anthony Hopkins was signed to play a leading role in a film based on George Feifer’s novel The Girl from Petrovka, so he traveled to London to buy a copy of the book. Unfortunately, none of the main London bookstores had a copy. Then, on his way home, waiting for an underground train at Leicester Square tube station, he saw a discarded book lying on the seat next to him. It was a copy of The Girl from Petrovka.
As if that was not coincidence enough, more was to follow. Later, when he had a chance to meet the author, Hopkins told him about this strange occurrence. Feifer was interested. He said that in November 1971 he had lent a friend a copy of the book—a uniquely annotated copy in which he had made notes on turning the British English into American English (“labour” to “labor,” and so on) for the publication of an American version—but his friend had lost the copy in Bayswater, London. A quick check of the annotations in the copy Hopkins had found showed that it was the very same copy that Feifer’s friend had mislaid.1
You have to ask: What’s the chance of that happening? One in a million? One in a billion? Either way, it begins to stretch the bounds of credibility. It hints at an explanation in terms of forces and influences of which we are unaware, bringing the book back in a circle to Hopkins and then to Feifer.
Here’s another striking incident, this time from the book Synchronicity, by the psychoanalyst Carl Jung. He writes: “The writer Wilhelm von Scholz … tells the story of a mother who took a photograph of her small son in the Black Forest. She left the film to be developed in Strassburg. But, owing to the outbreak of war, she was unable to fetch it and gave it up for lost. In 1916 she bought a film in Frankfurt in order to take a photograph of her daughter, who had been born in the meantime. When the film was developed, it was found to be doubly exposed: the picture underneath was the photograph she had taken of her son in 1914! The old film had not been developed and had somehow got into circulation again among the new films.”2
Most of us will have experienced coincidences rather like these—if not quite so extraordinary. They might be more akin to thinking of someone just before she phones you. Strangely enough, while I was writing part of this book, I had precisely this sort of experience. A colleague at work asked me if I could recommend some publications on a specific aspect of statistical methodology (the so-called “multivariate t-distribution”). The next day, I did a little research and managed to identify a book on exactly that topic by two statisticians, Samuel Kotz and Saralees Nadarajah. I had started to type an e-mail to my colleague, giving him the details of this book, when I was interrupted by a phone call from Canada. During the conversation, the caller happened to mention that Samuel Kotz had just died.
And so it goes on. On September 28, 2005, The Telegraph described how a golfer, Joan Cresswell, scored a hole in one with a fifty-yard shot at the thirteenth hole at the Barrow Golf Club in Cumbria in the UK. Surprising, you may think, but not outlandishly so—after all, holes in one do happen. But what if I tell you that, immediately afterward, a fellow golfer, the novice Margaret Williams, also scored a hole in one?3
There’s no getting away from it: sometimes events occur which seem so improbable, so unexpected, and so unlikely, they hint that there’s something about the universe we don’t understand. They make us wonder if the familiar laws of nature and causality, through which we run our everyday lives, occasionally break down. They certainly make us doubt that they can be explained by the accidental confluence of events, by the random throwing together of people and things. They almost suggest that something is exerting an invisible influence.
Often such occurrences merely startle us, and give us stories to tell. On my first trip to New Zealand, I settled down in a café, and noticed that the notepaper being used by one of the two strangers at the neighboring table was from my own university back in the UK. But at other times, these uncanny events can significantly alter lives—for the better, as with a New Jersey woman who won the lottery twice, or for the worse, as with Major Summerford, who was struck by lightning several times.
Humans are curious animals, so we naturally seek the underlying cause of strange coincidences. What was it that led two strangers from the same university to travel to the far side of the world and end up sitting at neighboring tables in the same café at exactly the same time? What was it that led the woman to pick those two winning sets of lottery numbers? What was it that brought huge electrostatic forces to hit Major Summerford time and time again? And what steered Anthony Hopkins and The Girl from Petrovka through space, and through time, to the same seat in the same underground station at the same moment?
Beyond that, of course, how can we take advantage of the causes underlying such coincidences? How can we manipulate them to our benefit?
So far all my examples have been very small-scale—at the personal level. But there are countless more-profound examples. Some seem to imply that not only the human race, but the very galaxies themselves wouldn’t exist if those very unlikely events hadn’t occurred. Some relate to how sequences of tiny random changes in our genetic constitution could end up producing something as complicated as a human being. Others relate to the distance of the earth from the sun, the existence of Jupiter, and even the values of the fundamental constants of physics. Again the question arises as to whether blind chance is a realistic explanation for these apparently staggeringly unlikely events, or whether there are in fact other influences and forces directing the course of events behind the scenes.
The answers to all these questions hinge on what I call the Improbability Principle. This asserts that extremely improbable events are commonplace. It’s a consequence of a collection of more fundamental laws, which all tie together to lead inevitably and inexorably to the occurrence of such extraordinarily unlikely events. These laws, this principle, tell us that the universe is in fact constructed so that these coincidences are unavoidable: the extraordinarily unlikely must happen; events of vanishingly small probability will occur. The Improbability Principle resolves the apparent contradiction between the sheer unlikeliness of such events, and the fact that they nevertheless keep on happening.
We’ll begin by looking at prescientific explanations. These often go far back into the mists of time. Although many people still hold to them, they predate the Baconian revolution: that is the idea that the way to understand the natural world is to collect data, conduct experiments, take observations, and use these as test beds through which to evaluate proposed explanations for what’s going on. Prescientific notions predate...