The Power of Coincidence

According to Tenenbaum, we could not learn language and syntax without the ability to notice strange coincidences. "Consider the challenge in learning just a single word," says Tenenbaum. "Every word is in a sense an infinite object. It's not just a name for an individual thing, it refers to an infinite set of things." Take the word "dog"—to understand that simple word you have to understand the name (Rover), the type (say, a black Labrador), all dogs, all mammals, all animals, all Labradors, all black Labradors (or black poodles, or black Great Danes), all running things, all furry things. "Yet even children under 5 can be given just a few relevant examples of dog and learn to use it," marvels Tenenbaum. Even more remarkable is that between the ages of 1 and 5, children are learning at least five new words a day.

Children make these cognitive leaps by noticing coincidences—Labradors and poodles and other dogs bark, pant with their tongues on hot days and, in cities at least, appear on leashes led by humans. Tenenbaum has demonstrated that we can generalize meaningfully from just a few examples of a novel word. In one study, 25 adults were shown sets of photographs (animals, vegetables, vehicles), and presented with a "novel" non-English word (such as "blick") as the name for the object. They were asked to point out instances of "blick" in additional photographs. Tenenbaum found that after seeing an object (such as a Dalmatian) with the name "blick" only once, adults were able to infer that the word either referred to all Dalmatians or all dogs. If they were shown three Dalmatians as three examples of "blick," they were much more likely to infer that "blick" referred only to Dalmatians. A pilot study found that even 4-year-old children could generalize properly if presented "blick" three times.

"Coincidences drive so many of the inferences our minds make," says Tenenbaum. "Our neural circuitry is set up to notice these anomalies and use them to drive new learning. There is an old saying that neurons that fire together wire together. So you could say that coincidence operates at the level of the synapse, whenever neurons fire at the same time." If our minds are primed to find coincidences, it's not surprising that we sometimes see connections where they don't exist. But do we fall into that trap too often?

It's Just a Coincidence!

"What are the odds of that?" asks SQuire Rushnell [sic] again and again in his best-selling book, When God Winks, an entertaining collection of confounding coincidences, from star-crossed lovers to holocaust survivors who were reunited years later. When Rushnell began writing the book, he was pondering the famous fact that John Adams and Thomas Jefferson, two men who shaped the Declaration of Independence, both died on July 4, 1826, the fiftieth anniversary of the signing of that historic document.

"I sat in my small study wondering whether there were more coincidences connecting the two men," recalls Rushnell. He pulled a reference book off his shelf, but it had no useful information. "Then I noticed a thin, homely, old volume right next to the reference book. I'd brought it back in a box of books after my grandfather's funeral and never noticed it before. It was a collection of Daniel Webster's speeches, and the first one was a eulogy for Adams and Jefferson." The speech described many coincidences linking the two men. In later research, Rushnell discovered that the book was available in only one public library in the Eastern U.S., the rare book section of the Library of Congress. "Yet here was a copy from my grandfather, sitting right there on my shelf, just when I needed it," exclaims Rushnell. "What are the odds of that?"

Not as small as you'd think, answer mathematicians who study the laws of probability. "In 10 years there are 5 million minutes," says Irving Jack Good, a professor in the department of statistics at Virginia Polytechnic Institute in Blacksburg. "That means each person has plenty of opportunity to have some remarkable coincidences in his life." Good recalls his own remarkable coincidence: He was at a conference listening to a speaker who described a mathematical proof, and later that day opened a mathematics textbook at random in the library. On the open page was a shorter proof of the same theorem. "I estimated that coincidence had a probability of 10^11."