Last week, I was heading out of a crew practice when the voice of my conscience began to nag me about going for a run, given that I hadn’t in over a week. So I headed out, somewhat slowly and reluctantly, for a two-bridge run—until my post-practice legs decided that two bridges might be a bridge too far. I acquiesced and began to weave through the foot traffic on JFK Bridge. Squeezing through, I bumped right into someone walking ahead of me, turned to apologize, and my mouth dropped open; of all the people I could have bumped into in that moment on that bridge, it was a good friend I hadn’t seen in five years. What a coincidence!
Once we’d parted, I marveled at my sheer inability to explain how I’d somehow, quite literally, run into someone I didn’t even know was in Massachusetts, let alone Cambridge. If just one of the factors leading to our meeting at 5:32 p.m. at the JFK Bridge crosswalk had been different—if, for example, I’d done two bridges or run more slowly, or if he hadn’t decided to take a walk when he did—we never would have coincided. Every bit of my scientific brain was working to analyze and justify the coincidence, yet I could neither rationally nor mathematically explain it.
The science of coincidence, or, more broadly, of the human need for explanation, forms an interesting bridge between mathematics and psychology. Our fascination with coincidences was around as early as the 1650s when Blaise Pascal (a.k.a. the triangle guy) and Pierre de Fermat (a.k.a. the last-theorem guy) came up with the idea of expected value and thereby probability theory itself. Interestingly, Pascal was an avid writer and philosopher on top of being a math prodigy, an early example of probability’s place in the science of explanation.
Psychologists’ study of coincidence began in the mid-20th century, spearheaded by theorists like Karl Jung. Jung classified coincidences under the concept of “synchronicity” (like the Police album), which he explained as the principle connecting seemingly random coincidences. With his introduction of synchronicity, Jung was the first person to inquire into the meaning of coincidences and their interpretation; however, his highly elaborate, and arguably unfounded, psychological theories prevented his study of coincidence from accruing widespread scientific credibility.
In the late 20th century, developmental psychology (the study of how children’s brains grow and develop) began scientific explorations into the role of uncertainty in human behavior. Jerome Kagan, founder of Harvard’s developmental psychology department, described our need to resolve uncertainties as one of the primary motivators of our behavior. Above all, Kagan emphasized that human minds, from infants to adults, find uncertainty and inexplicable events distressing. Faced with an unclear series of occurrences or a lack of causality, we involuntarily try to come up with an explanation. Then, once we have one, it’s incredibly difficult to let our theories go.
If you look around, our fascination with coincidence and random connections has clearly seeped into our culture as well. Take When Harry Met Sally, for example. Coincidental path-crossing drives the movie’s plot. Or think about the classic true-crime scene where the beleaguered detective flips around a chalkboard to reveal dozens of pictures, all connected by thumbtacked red string. We as humans want all the inexplicable factors in our lives to connect somehow, to tie together in a little bow, because it’s simply easier that way. The human brain resorts to finding patterns amidst random occurrences and assumes that fate is at work after coincidental run-ins. Even though we know life doesn’t make sense, we want it to, and there’s no changing that.
I’m no different from any other human—when coincidences occur, I want answers. That’s why I find probability theory so satisfying. Because although it can’t numerically predict my future, it can explain relatively reasonable occurrences. Perhaps the most famous example of this is the birthday problem that Math Teachers Chip Rollinson and Mark Fidler give out in Honors Geometry. It explains that in a room of 23 people, there’s over a 50 percent chance someone will share my birthday.
I’m a scientist; I can understand the math and should believe that in large audiences, someone else will have been born on November 3. But I’ve only ever met two other people with my birthday, and I’ve met a lot of people over the last near-18 years. So despite the statistical truth, when I meet someone with a November 3 birthday or run into someone I haven’t seen in five years, it doesn’t feel like a coincidence. It feels like magic. Even though coincidences remind us that we don’t have all the answers, and that’s uncomfortable, I marvel over them anyway. Sometimes we could all use a little magic to make us smile.