The Inevitability of Unlikely Events
At 7:15 p.m. on March 1, 1950, the fifteen members of the church choir in Beatrice, Nebraska, were scheduled to meet for rehearsal. For various reasons, they were all running late. The minister’s family was delayed because his wife still had to iron their daughter’s dress. One couple was held back when their car wouldn’t start. The pianist wanted to be there thirty minutes early, but he fell into a deep sleep after dinner. And so on. At 7:25 p.m., the church exploded. The blast was heard all around the village. It blew out the walls and sent the roof crashing to the ground. Miraculously, nobody was killed. The fire chief traced the explosion back to a gas leak, even though members of the choir were convinced they had received a sign from God. Hand of God or coincidence?
Something last week made me think of my old school friend, Andy, whom I hadn’t spoken to in a long time. Suddenly the phone rang. I picked it up, and, lo and behold, it was Andy. “I must be telepathic!” I exclaimed excitedly. But telepathy or coincidence?
On October 5, 1990, the San Francisco Examiner reported that Intel would take its rival, AMD, to court. Intel found out that the company was planning to launch a computer chip named AM386, a term that clearly referred to Intel’s 386 chip. How Intel came upon the information is remarkable: By pure coincidence, both companies had hired someone named Mike Webb. Both men were staying in the same hotel in California and checked out on the same day. After they had left, the hotel accepted a package for Mike Webb at reception. It contained confidential documents about the AM386 chip, and the hotel mistakenly sent it to Mike Webb of Intel, who promptly forwarded the contents to the legal department.
How likely are stories like that? The Swiss psychiatrist C. G. Jung saw in them the work of an unknown force, which he called synchronicity. But how should a rationally minded thinker approach these accounts? Preferably with a piece of paper and a pencil. Consider the first case, the explosion of the church. Draw four boxes to represent each of the potential events. The first possibility is what actually took place: “choir delayed and church exploded.” But there are three other options: “choir delayed and church did not explode,” “choir on time and church exploded,” and “choir on time and church did not explode.” Estimate the frequencies of these events and write them in the corresponding box. Pay special attention to how often the last case has happened: Every day, millions of choirs gather for scheduled rehearsals and their churches don’t blow up. Suddenly, the story has lost its unimaginable quality. For all these millions of churches, it would be improbable if something like what happened in Beatrice, Nebraska, didn’t take place at least once a century. So, no hand of God. (And anyway, why would God want to blow a church to smithereens?)
Let’s apply the same thinking to the phone call. Keep in mind the many occasions when “Andy” thinks of you but doesn’t call; when you think of him and he doesn’t call; when you don’t think of him and he calls; when he doesn’t think of you and you call. . . . There is an almost infinite number of occasions when you don’t think of him and he doesn’t call. But since people spend about 90 percent of their time thinking about others, it is not unlikely that, eventually, two people will think of each other and one of them will pick up the phone. And it must not be just Andy: If you have a hundred other friends, the probability of this happening increases manifold.
We tend to stumble when estimating probabilities. If someone says “never,” I usually register this as a minuscule probability greater than zero since “never” cannot be compensated by a negative probability.
In sum: Let’s not get too excited. Improbable coincidences are precisely that: rare but very possible events. It’s not surprising when they finally happen. What would be more surprising is if they never came to be.