Unlikely Events and Coincidence

Newspapers frequently run stories of the following kind: a man lost his University of Virginia class ring while sailing off the Carolina coast. He reached up to halt the swing of a boom, and accidentally sent his ring flying off into the sea, where it sank in about 30 feet of water. A year and a half later, another man was talking to a friend in an alley behind a restaurant in Charlottesville, Virginia, when a bright glint in some trash from the restaurant caught his eye. Investigating, he found a class ring, and from the inscription was able to locate the man who had originally lost the ring and return it to him. The two men assumed, after comparing stories, that the ring was swallowed by a fish which was later caught and sold to the restaurant, then discarded unseen in the waste from the preparation of the fish for a dinner. Of course, many other explanations are possible, but it is not important for the present discussion just HOW the lost ring made its way from the sea to an alley behind a restaurant. Whatever happened involved many remarkable coincidences… or did it?

Another news item reported how two women had met in a Tulsa, Oklahoma hospital a few years ago when they had given birth to daughters about an hour apart. Even though they had solemnly vowed to keep in touch, they had not seen or spoken to one another since— until they found themselves back in the same hospital, both having given birth to sons, this time about four hours apart.

One sometimes reads about the bridge player who receives a 13-card hand consisting of all the spades. By chance, such a hand should be dealt only once in 635,013,559,600 times! Incredible, right?

An experience reported by a number of people is that of traveling to a distant city only to encounter a friend or acquaintance from back home, on the street or in a store or some other public place. The event seems even more remarkable when we consider how easily it could NOT have taken place. Had either of the two friends decided to go to Museum X instead of Museum Y, or taken an earlier bus, or overslept, or taken longer for lunch, or gotten on a different elevator, or any of hundreds of alternatives presented in the course of daily events that preceded the encounter, the event would never have happened and the two people would never have realized that they were both in the same remote city at the same time.

Perhaps most of the people who have, or read about, such experiences accept them as being very unlikely, very uncommon, but not otherwise unusual. Most people seem to feel no need to appeal to supernatural explanations for these events. But we frequently encounter in pseudoscience the claim that such events are in fact miraculous, and that some mysterious force or influence is required to bring about the event at all. Instead of accepting such events as normal events of low probability, there are in fact international organizations devoted to the collection, preservation, and dissemination of examples of such “strange” occurrences, which the organization find highly significant, mysterious, and certainly NOT due to “mere coincidence.” There are even religious cults based on coincidence, or “synchronicity.” Often the examples are rendered more dramatic than otherwise by involving some famous person or media personality, or being part of some famous event in history. Here are some instances from an article in the January 1982 issue of Science Digest.

• British novelist Dame Rebecca West was writing a story in which a girl finds a hedgehog in her garden. Just as West finished this passage, she was interrupted by servants who informed her they had just found a hedgehog in her garden.
• When Norman Mailer began his novel Barbary Shore, there was no plan to have a Russian spy as a character. As he worked on it, he introduced a Russian spy in the US as a minor character. As the work progressed, the spy became the dominant character in the novel. After the novel was completed, the US Immigration Service arrested a man who lived just one floor above Mailer in the same apartment building. He was Colonel Rudolf Abel, alleged to be the top Russian spy working in the U.S. at that time.
• While the Allied Forces were planning the Normandy invasion of June 6, 1944, the following code words were used (and were among the best kept secrets of the war): Utah and Omaha for the beaches where the landing would take place; Mulberry, for the artificial harbor which would be put in place after the landing; Neptune, the overall plan for Naval operations; Overlord, the entire planned invasion itself. On May 3, 1944, the first code word, Utah, appeared as an answer in the London Daily Telegraph crossword puzzle; on May 23, Omaha appeared similarly; on May 31 Mulberry appeared; and on June 2, four days before the invasion, Neptune and Overlord both appeared. British Intelligence investigated intensively and extensively, but the man who had created the puzzles was found to be innocent of espionage, had no knowledge of any invasion plans, and to all intents and purposes had chosen the words at random.

There is no question that unusual events of this kind happen, and it is easy to imagine how dramatic and impressive they must have seemed to the people who were involved. When something happens that is perceived to be dramatic or unexpected, there is a tendency to look for equally “dramatic” causes for the event. That such an event is due to “mere coincidence” is usually dismissed at once as a possibility. People tend to look for something impressive, a supernatural or “psychic” or religious explanation for the event. Psychologists sometimes call this the “Oh, Wow!” Syndrome. If it seems dramatic to you, it must be totally, miraculously incredible, right?

But just how remarkable are these events? Is the hedgehog experience of Dame West more or less remarkable than the meeting of the two women in the hospital twice on occasions two years apart? Are the odds of a spy living near you at the time you decide to write a novel involving a spy that much different from the odds of being dealt a bridge hand with 13 spades? Is it less likely that Utah, Omaha, Mulberry and two other common words would be used in a crossword puzzle just at the time a secret military operation has given them a secret significance, than that the sailor would get his class ring back a year and a half after losing it in the ocean? Suppose you just happen to think of an old friend, and a few moments later, you get a telephone call... from that old friend!

Take the 13-spade bridge hand, where it is simple to calculate the odds. With 20 million bridge players dealing 30 hands a week, we should get one all-spade hand per 20 years. In fact, as bridge expert Oswald Jacoby pointed out, such hands are reported much more frequently, perhaps a dozen times per year. An obvious explanation, easily verified on many occasions, is that one or more players conspire to play a harmless practical joke on the other players by simply stacking the deck. It is a fairly safe way to get your name and photograph in the newspapers. And, of course, the probability of getting any specific bridge hand is the same as that of getting the 13-spade hand! But only one of the equally-likely 635,013,559,600 different bridge hands is newsworthy. If two people in the same profession, who routinely must travel from Austin, Texas to New York city several times per year on business, were to happen to meet in the airport or in a familiar hotel, we would hardly consider this as unusual. Yet it is not so much more unusual for two elderly friends to decide to take a vacation in Washington, DC, in May to see the cherry blossoms, independently, and to run into one another by chance at one of the places every tourist visits while in Washington. Again, if hedgehogs are fairly common in English gardens, it is not too surprising that Dame West was writing about finding one and that in fact one was found in her garden. Again, if both of the women in Tulsa were married to men in the oil business, who are regularly separated from their wives for many months while they work in overseas oil fields, and who get leave at the same time, then our view of the probability of both women being in the maternity ward at the same time is greatly changed. In the case of the call from your old friend... how many old friends do you have, how often do you think of them, how often do they think of you, and how many telephone calls do you get per day? Most important of all— how often have you gotten a call from someone you have just thought of? It is usually the fact that it has never happened before, or very rarely happens, that impresses you! It is this kind of accident that we very precisely mean by the word, “coincidence.” Generally, people tend to underestimate grossly the probability of any event that happens to them, especially one perceived as “strange.”

Pseudoscientists frequently take advantage of this inability of people to understand the nature of coincidence. Thus coincidences that are hardly remarkable are passed off as “miracles” that can only be explained by ESP, intervention by benevolent Space Brothers or guardian angels, fairies, etc. The failure to understand the odds is particularly noticeable when one hears about feats of alleged psychics, fortunetellers, astrologers, and others who claim to foresee future events.

Pseudoscientific predictors and prophets tend to stress the time or two they made a really spectacular correct guess— for some reason we don't hear about the thousand other “predictions” made by them during the same time period, that didn't quite pan out. Recall the fable about the boy who cried wolf; eventually he was correct, but he had given so many false alarms prior to that time that the villagers didn't respond to the valid warning. For some reason, many people in our society do not recognize the parallel between the boy in this fable and the alleged “psychics,” who are allowed to get away with being wrong nearly all the time, and still are taken seriously on the rare occasions they chance to be correct.

Let's take an example. Suppose you try to guess every time the telephone rings who is calling before picking up the receiver. Inevitably you will be correct if you guess often enough, just by chance. The usual practice is to remember and talk about only the times when you were correct; but if you keep track of the misses as well as the hits, you will see that the correct guesses are no more frequent than sheer chance would imply. If you dream every night and your dreams often involve relatives or friends, then once in a while, by sheer chance, you must and will have a dream about some event involving those relatives or friends that is vaguely similar to something that later actually happens to them.  If we consider the hundreds of thousands of stories that are written by Dame West, Norman Mailer, and other thousands of active writers being published over the years, we soon realize that by accident some incident described in one of these stories will eventually prove to have parallels in real life. It simply has to be that way. The remarkable thing would be if none of those plausible, everyday incidents imagined and described by writers ever happened!

The point is that each moment of each day of even the most ordinary, humdrum life of an individual is filled with events, and each of those events, no matter how ordinary, is quite improbable. It is very improbable that precisely as I sit down at my computer, a student comes into my office at the University of Texas to ask me something. But I sit down at the computer frequently, and students come into my office frequently, so it's bound to happen sometimes. Only if every time I sat down at the keyboard, a student came into my office, would something miraculous be happening. Once this is appreciated for the events of our own humble lives, it should be clear that it must pertain for the lives of famous and important people as well. A “strange” event happening to a famous person, or at a crucial moment in history, is no more or less strange than a similar event happening to you in the bathtub tonight.

What would be paranormal, what would be miraculous, what would be unexplainable, would be if NO SUCH coincidence or unlikely accidents or “strange” events every happened to anyone!

Further Reading—

  • Probabilities in Everyday Life, by J. D. McGervey, Nelson-Hall, NY, 1986.
  • Randomness, by Deborah J. Bennett, Harvard U. Press, Cambridge, 1998.
  • What are the Odds?, by Jefferson Hane Weaver, Prometheus, NY, 2001.
  • Chance Rules, by Brian S. Everitt, Springer-Verlag, NY, 1999.
  • Chance, by Amir D. Aczel, Thunder's Mouth Press, NY, 2004.
  • Turning Numbers into Knowledge, by Jonathan G. Koomey, Analytics, CA, 2001.
  • Statistical Tricks and Traps, by Mark Durm, Prycsak, LA, 2000.
  • More Damned Lies and Statistics, by Joel Best, Univ. of Ca. Press, LA, 2004.
  • Subjective Probability, ed. by George Wright and Peter Ayton, John Wiley & Sons, NY, 1994.
  • How to Take a Chance, by Darrell Huff and Irving Geis, Norton, NY, 1959
  • Lady Luck, by Warren Weaver, Anchor Press, NY, 1965; Dover, NY, 1982; see especially chapter 13, “Rare Events, Coincidences and Surprising Occurrences.”
  • • “Jumping to Coincidences: Defying the Odds in the Realm of the Preposterous,” by J. A. Hanley, American Statistician, August 1992, pp.197– 202.
  • • “Coincidences,” by Persi Daiconis and Frederick Mosteller, in Encylopedia of the Paranormal, ed. by Gordon Stein, Prometheus, NY, 1996.
  • Acknowledgments— Dr. Dennis McFadden, Professor of Psychology at the University of Texas at Austin, is the author of this fact sheet. The International Cultic Studies Association, a professional research and educational organization concerned about the harmful effects of cultic and related involvements, prints and helps distribute these fact sheets. Because such fact sheets seek to stimulate critical thinking, rather than advance a particular point of view, opinions expressed are those of the authors. These fact sheets may be copied for educational purposes, but they may not be reproduced for resale.

    Links on Coincidence—

  • Law of Large Numbers
  • Synchronicity and Karl Jung
  • New Age and Coincidence
  • “Manifesting”
  • Littlewood's Law
  • More Wikipedia Links
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