I’m not sure when I first noticed that the universe appeared to be sending me coded messages through Jeopardy!, but I know it never stopped, and it never will. I’m not mad. I will explain.

Jeopardy!, for the tiny percentage of you who are unaware, is America’s favorite quiz show. Created in the 1970s and airing in its current form on national television for five days a week since 1984, Jeopardy!’s gimmick is that the contestants must answer clues, which are phrased as answers, in the form of a question.

My wife and I watch it religiously and competitively, shouting out answers and keeping score. We have been recording which of us won in a little black book since 2016. At some point, we started noticing the strange coincidences. Here’s two that stand out.

December 28, 2017: Sue Grafton, a famous author of detective novels, passed away. We’d both met her at conferences a few times and were quite sad. That evening, we sat down to catch up on Jeopardy! from a couple of days earlier. One of the first clues was “Ms. Grafton, or what she might do if you plagiarized one of her novels,” and the answer, of course, was “Sue.” What are the odds?

April 6, 2018: My wife was cooking chicken and rice. I randomly asked her how to say that in Spanish. “Arroz con pollo,” she said. An hour later, after eating the chicken and rice, we were watching Jeopardy! The $600 clue under “New to the Oxford English Dictionary” came up. It was “This, Spanish for ‘rice with chicken,’” and the question: “What is arroz con pollo?” We looked at each other and laughed. It was an amazing coincidence. I’d asked my wife a question I had never asked her before, and then the same question and answer showed up that same day!

Once we started noticing these coincidences, they seemed to come faster and faster. Sometimes they were trivial, sometimes amazing. I’m a good skeptic, and I know that Jeopardy! is not trying to send me messages. It must be coincidence, and yet some of the coincidences seem almost impossibly personal. What is going on?

Ideas of Reference

The notion that “the universe is trying to tell you something” is timeless. Historically, people have seen meaning in the most banal of occurrences. A cat crossing your path was a warning from God. The number of magpies in a tree correlated directly to something that would happen to you in the future.

In psychology, this type of thing is often referred to as “ideas of reference,” defined as the belief that random events are specifically related to a person. In more extreme cases, where the belief begins to impact a person’s life, it’s known as delusions of reference.

Delusions of reference are specifically related to mental illness. They manifest as a deep paranoia and suspicion, often about people around the person but also about the media. Paranoid schizophrenics often report that they are receiving special messages. Historically, the source has been newspapers; more recently, it’s been television, and now of course it’s the internet. But the milder form of the delusion, ideas of reference, is, I think, a pervasive but rarely discussed part of bad thinking. It is a form of cognitive bias that we would do well to understand if we want to help people out of their misconceptions. Ideas of reference permeate conspiracy, mystical, and pseudoscientific communities. “There are no coincidences” is the war cry of the conspiracy theorist. The mystic sees meaning everywhere. Some UFO fans feel that lights in the sky move in response to their thoughts.

Synchronicity

While psychologists now use ideas and delusions of reference as a diagnostic criteria for schizophrenia, it was the work of an early psychologist that unfortunately codified the concept in a way that gave it acceptance. In the 1930s, Carl Jung coined the term synchronicity to describe a hypothetical principle that explained meaningful coincidences. The notion of synchronicity was, as Jung described it, essentially magic. He argued that both “meaningful coincidences” and ESP (extrasensory perception) were real phenomena that could not be explained by conventional physics (Jung 1960).

Jung’s idea got unexpected support from a hard scientist, Austrian physicist Wolfgang Pauli, one of the pioneers of quantum physics who was often lauded as a successor to Albert Einstein. Pauli’s belief seems to have come from the joking observation by his colleagues that equipment would frequently malfunction when he was present, often ruining a complex experiment. They labeled this the “Pauli effect.”

Pauli had corresponded with Jung and came to believe that the Pauli effect was real and an example of the supernatural form of synchronicity. Pauli did not subscribe to Jung’s level of mysticism—he was critical of Jung’s inclusion of astrology in his synchronicity theories—but he was also working in a field that seemed almost magical. Elements of quantum physics, such as the observer effect and nonlocality, were initially rejected by physicists such as Einstein as being “spooky,” so perhaps being an early adopter and developer of those (accurate) theories positioned Pauli to be more accepting of Jung’s ideas. [For more on this, see Arthur Miller’s book 137: Jung, Pauli, and the Pursuit of a Scientific Obsession—Eds.] Quantum physics is still frequently misused as a justification of such beliefs.

Both Jung and Pauli were greatly influenced in their belief by coincidences that rival my Jeopardy! examples. Pauli had numerous examples of experiments going wrong when he was in town, including one where he just happened to be passing through on a train. There were other events where colleagues pranked him by rigging things to go wrong, and when those pranks failed, that too was ascribed to the Pauli effect, cementing the legend.

Jung relates a famous example where a patient was recalling a dream about a golden beetle. As he listened, he heard a tapping on the window. Turning, he saw a shiny beetle, similar to the one the woman was describing. He opened the window, caught the beetle in mid air, and handed it to the woman, leading to a breakthrough in her therapy.

What Are the Odds?

So, what causes these seemingly reasonable and highly intelligent people to reject the obvious explanation of “just a coincidence” and instead leap to some mystical phenomenon where the universe serves up synchronicities perfectly tailored to their individual situations? It boils down to a misapplication of probability. The coincidences seem so improbable, so personal and specific, that it seems impossible that they are just coincidences.

When we ask “what are the odds,” we generally understand the question in terms of very simple examples. The odds of rolling a four on a standard die are one in six. The odds of winning the Mega Millions lottery after buying one ticket are one in 302.5 million. But what are the odds that “chicken and rice” will show up on tonight’s Jeopardy!?

We can look at that in some simple ways. Out of 8,490 games, the “Spanish for chicken and rice” question has actually shown up four times. The Jeopardy! writers tend to recycle clues and topics every few years. So it’s very roughly one in two thousand. Still very unlikely. So why did it happen?

Framing the probability of a synchronicity like this is asking the wrong question. We should not be asking the odds of one specific amazingly improbable thing happening on the show, but rather the odds of any (seemingly) amazingly improbable thing happening.

Jeopardy! has 120 clues per game. These sometimes contain multiple things, so we can say that each day there are, roughly, 200 opportunities for a coincidence. What might those 200 things coincide with? Each day my wife and I read and talk about a lot of different things. It’s difficult to count, but taking into account reading the news, interacting on Twitter, doing the crossword (a rich source of synchronicity), and just a look at my browser history, we come up with maybe 500 different things over a couple of days.

So, the question now becomes, what are the odds that one of the 500 things we encounter will show up in the 200 Jeopardy! entities. This question is similar to the “Birthday Paradox,” which you might remember as the surprisingly high probability that two people in a group will have the same birthday. It’s not so much about the hits but how improbable it is that you would continually miss.

I’ll take 100,000 as my number of entities, essentially an above-average vocabulary. Think of Jeopardy! as picking 200 words at random from a 100,000-word dictionary, then I pick 500 more. The odds that I will miss their 200 with any one of mine are high: 99,800 out of 100,000. But to miss with two, we have to (roughly) square that, then cube it for three. Rapidly the odds of missing decrease, so if we have only 350, the odds are even, and at 500 it’s 2:1 in favor of a synchronicity.

Every game there’s a Jeopardy! synchronicity of some sort. Look and you shall find. Most of these coincidences are not particularly interesting, but my wife and I still notice something nearly every day. Sometimes the oddest thing we’ve discussed that day will come up—seemingly a true synchronicity—but in reality that will happen once every 300 games, or about once a season, which it does. It is inevitable.

The Synchronicity Lottery

The person who wins the Mega Millions with a single ticket might consider it a miracle. But someone had to win eventually. Likewise, because ten million people watch each episode of Jeopardy!, someone has to have the most amazing set of synchronicities imaginable—literally ten million times more improbable than mine. They may well feel the universe is trying to tell them something. But it had to happen to someone.

Jung also would have a similar intersection of real-world random events (like the beetle) and his patients’ dreams. He kept playing and eventually won the lottery when the beetle bumped against his window. It was just random chance, but he interpreted it as significant. Someone has to win. If we take all the physicists in the world, one of them is going to have the worst (but still random) luck regarding experiments going wrong. Pauli bought a lot of tickets, and he won that lottery. The events that convinced him of synchronicity’s reality would have happened to someone. The Pauli effect was a contrivance. We might as well invent a “Lustig effect” after Richard Lustig, who won the lottery multiple times—without any magic involved.

Synchronicity drives the confirmation bias feedback loop behind ideas of reference. If we understand how it works, it becomes easier to understand how some people might fall for the belief that there are no coincidences, or that magic works, or even that the universe is sending them messages via Jeopardy!.

Reference

Jung, Carl. 1960. Synchronicity: An Acausal Connecting Principle. Princeton, NJ: Princeton University Press.