It is a common belief that bad things happen in sets of three. From natural disasters to celebrity deaths to household mishaps, the idea is embedded in the Western cultural psyche.
Furthermore, the anecdotal evidence seems to support it. Just two weeks in February 2014, for example, saw the deaths of actors Philip Seymour Hoffman, Shirley Temple, and Sid Caesar. Surely this is more than simple coincidence.
As a matter of fact, it is more than coincidence. However, the reason has more to do with the human psyche than some sort of cosmic triple conspiracy.
Patterns, Clusters, and Coin Flips
If you were to look at a bowl of colored candies, you may find yourself seeing patterns or even clumps of colors in the bowl. Four green candies over here, five reds over there, six purples in the middle of the bowl. It may even seem to you that the colors are organizing themselves, or are attracted to each other by some form of candy-coated magnetism.
What you are seeing is not a candy conspiracy, but a bit of human psychology known as the clustering illusion. We tend to see patterns in random events, be it the distribution of candies in a bowl or a series of coin flips. Random events are naturally clumpy - candies of the same color will sometimes be next to each other and sometimes be separated. A series of coin flips will have streaks of heads or tails. In fact, streaks are one of the telltale signs of randomness.
Mathematicians can often tell a fake coin flip sequence from a real one due to the streaks. According to several studies on the topic, participants faking a series of coin flips will generally avoid making streaks of the same coin face six or more times in a row, thinking that the long streaks will look suspicious. However, in an actual random coin flip sequence of 200 flips, a streak of six heads or tails in a row is a statistical near-certainty.
The reason we think long streaks look suspicious is because we over-estimate the probability of alternation. If we flip one coin and it comes up heads, the probability of the next flip being tails is 50%. However, several studies of human psychology have found that we expect an alternation rate of about 70%. To illustrate - the coin flip sequences HHHHTTTT and HTHHTHTT are equally probable, but the latter sequence "looks more random" because it contains more alternations.
This clustering illusion is why we tend to have a selective perception of random events, focusing narrowly on the clumps and streaks. We ignore the big picture in which these clumps and streaks are just part of the noise of randomness.
From Coins to Celebrities
Our selective focus on streaks and clumps is also known as the Texas sharpshooter fallacy. This fallacy is named for an old joke in which a Texan fires a few rifle shots randomly at a barn, then paints a bullseye around the tightest cluster of bullet holes and claims to be a sharpshooter. (Why a Texan was singled out to be the butt of this joke is outside the scope of this article - sorry, Texans!)
The fallacy can apply to any argument that focuses on a small subset of outcomes from a large random sample. Claims of psychic abilities or ancient prophecies often hinge on this fallacy - looking at the small subset of predictions in which the psychic or prophet did better than chance, but ignoring the larger body of incorrect predictions.
This logical fallacy is particularly problematic in epidemiology. Public health researchers may misidentify an area as a cancer cluster by drawing too small a circle around a clump of cases, rather than looking at the wider region and seeing that the clump of cases is just the result of random chance.
The fallacy also applies when we selectively look at celebrity deaths. If we selectively draw our circle around a clump of three deceased celebrities, we ignore the big picture in which these are simply normal streaks in a series of random events. How we draw our circle also depends on who we consider to be a celebrity.
In December 2012 there were 517 deaths of notable individuals around the world, according to a list compiled by Wikipedia - an average of 16.6 per day. To most Americans, individuals like Indian cricketer B.B. Nimbulkar and Argentine actress Olga Zubarry would not be considered celebrities. To enthusiasts of Indian cricket or Argentinian cinema, however, these would be big names.
Similarly, we could narrowly focus on musicians. On December 5, we lost jazz legend Dave Brubeck, Tampa "singing twins" vocalist Sammy Arena, and 80s punk musician Sarah Kirsch. Looking at the entire month, however, there were 36 deaths of notable musicians around the world during the month, an average of 1.16 per day. Some days had one, some had two, others had zero. Three musician deaths in one day seems unusual when we focus just on that day, but if we zoom out to look at the entire month it reveals itself for what it is - random streakiness.
Why we have an affinity for the number three is a mystery, but it may be due to our natural tendency toward narrative. This is more than just a societal trait, but is wired into the cognitive processes of our brains.
Three is an important number in the Western literary tradition. Aside from its religious significance in the Christian concept of the Holy Trinity and in Hebrew Numerology, the number three is at the root of the narrative structure.
Most Western literature follows a three act structure, introducing characters and concepts in act I, developing the plot through conflict in Act II, and resolving the conflict in Act III. In addition, the Rule of Three is a key rhetorical device used in children's literature, comedy, and public speaking.
Fairy tales such as The Three Pigs, Goldilocks and the Three Bears, and The Three Billy Goats Gruff invoke this rule by setting a pattern in the first two interactions between characters, then breaking it in the third. [Spoiler Warning!] The wolf blows two houses down, then fails on the third. Goldilocks finds the bears' porridge too hot, too cold, and just right. The troll passes on eating the first two goats and gets soundly beaten by the third.
This format is also at the root of many jokes, setting up a pattern with two anecdotes and delivering a punchline with the third. Public speakers will also employ it when using three points to make an argument, or three adjectives to describe something the speaker wishes to emphasize.
With this tradition of threes so deeply ingrained in our literary culture, it is little wonder we look for patterns of three in random events such as celebrity deaths and natural disasters. However, these patterns only exist in our minds.
Sources and Further Information
- clustering illusion - The Skeptic's Dictionary - Skepdic.com
The clustering illusion is the intuition that random events which occur in clusters are not really random events. The illusion is due to selective thinking based on a counterintuitive but false assumption regarding statistical odds.
- Kouritzin, Newton, Orsten, Wilson: On Detecting Fake Coin Flip Sequences
In this paper, we apply nonlinear filtering to a simplified fraud-detection problem: classifying coin flip sequences as either real or faked.
- The Texas Sharpshooter Fallacy - You Are Not So Smart
The Misconception: You take randomness into account when determining cause and effect. The Truth: You tend to ignore random chance when the results seem meaningful or when you want a random event to have a meaningful cause.
- The Hot Hand Fallacy
Describes and gives examples of the hot hand fallacy.
- Why Do We Believe That Catastrophes Come in Threes? - ABC News
A column by John Paulos debunking the idea that the number three repeats more in nature than do other numbers, writing specifically about three recent celebrity deaths (Jackson, Fawcett, McMahon) and the election in Iran.
- Our Gift for Good Stories Blinds Us to the Truth - Bloomberg
As commentators, politicians and academics struggle to make sense of the recent financial crisis and its ramifications, many of their accounts seek to identify a root cause or the “beginning of the story.”
- The Book of Threes
The Book of Threes - A Subject Reference Encylclopedia of concepts in threes.
Nathan Bernardo from California, United States of America on May 19, 2015:
Very fascinating, I've wondered why things seem to happen in 3's and now I know; it's in our minds. I was thinking about how standard writing is taught to be done in 3 parts; introduction, body and conclusion. We do use 3's a lot in Western culture.
joe on October 05, 2013:
this is fascinating!