Toward the end of seventh grade, my middle-school band took a trip to Cedar Point, which was pretty much the theme park to which midwestern centre-school bands traveled. (I imagine it still is.)  They had this indoor roller coaster there, chosen the Disaster Transport. My friends and I were continuing in line for this roller coaster, winding up the dimly lit cement steps, when we turned a corner and came across a huge pile of money.

We picked it up and counted it; it was a very specific corporeality of coin. I don't remember now exactly how much, but for the purposes of this retelling, allow's say it was $134. That sounds close.

We had barely had time to whiplash from marveling at our adept fortune to guiltily suggesting we should find somewhere to plow information technology in before a grouping of older kids ahead of usa snatched the cash wad out of our easily. They claimed it was theirs; information technology was not theirs—they counted it in forepart of us and exchanged "Whoa"due south and loftier fives. We were hapless, gangly middle schoolers (I was growing out my bangs; it was a rough year). They were confident nosotros would do nothing to stop them, and they were right. So that was the stop of that.

Until, Role Two:

A little more than a year afterwards, I went to a summer program at Michigan State Academy, a nerd campsite where you take classes similar genetics for fun. One evening, as nosotros were sitting around in the common area, chatting and doing homework, I overheard a child telling his friends how he'd lost a bunch of money last year at Cedar Point.

With very piffling endeavor at chill I interrupted their chat and grilled him on the particulars.

Was he there on May whatsoever appointment I was also at that place? He was.

Did he lose the money in line for the Disaster Send? In fact, he did.

How much money did he lose? $134, exactly.

* * *

Though "What are the odds?" is pretty much the catchphrase of coincidences, a coincidence is non simply something that was unlikely to happen. The overstuffed crate labeled "coincidences" is packed with an amazing variety of experiences, and even so something more than rarity compels us to grouping them together. They have a similar texture, a feeling that the material of life has rippled. The question is where this feeling comes from, why we notice certain ways the threads of our lives collide, and ignore others.

Some might say information technology's merely because people don't understand probability. In their 1989 paper "Methods for Studying Coincidences," the mathematicians Persi Diaconis and Frederick Mosteller considered defining a coincidence as "a rare issue," merely decided "this includes too much to allow careful written report." Instead, they settled on, "A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connexion."

From a purely statistical point of view, these events are random, not meaningfully related, and they shouldn't be that surprising because they happen all the fourth dimension. "Extremely improbable events are commonplace," as the statistician David Hand says in his book The Improbability Principle. Merely humans generally aren't great at reasoning objectively near probability as they go about their everyday lives.

For one affair, people can be pretty liberal with what they consider coincidences. If y'all come across someone who shares your birthday, that seems similar a fun coincidence, only y'all might feel the same way if you met someone who shared your mother's birthday, or your best friend'due south. Or if it was the day correct before or after yours. So there are several birthdays that person could accept that would feel coincidental.

And there are lots of people on this planet—more than 7 billion, in fact. According to the Law of Truly Large Numbers, "with a large enough sample, whatsoever outrageous thing is likely to happen," Diaconis and Mosteller write. If enough people buy tickets, there will be a Powerball winner. To the person who wins, it's surprising and miraculous, but the fact that someone won doesn't surprise the rest of us.

Even within the relatively limited sample of your own life, there are all kinds of opportunities for coincidences to happen. When you consider all the people you know and all the places y'all go and all the places they get, chances are good that you'll see someone yous know, somewhere, at some indicate. But information technology'll still seem like a coincidence when yous exercise. When something surprising happens, we don't retrieve nearly all the times it could accept happened, merely didn't. And when nosotros include most misses every bit coincidences (yous and your friend were in the same place on the same day, just not at the same fourth dimension), the number of possible coincidences is of a sudden way greater.

To demonstrate how common unlikely seeming events tin be, mathematicians like to trot out what is called the birthday problem. The question is how many people need to exist in a room before there'south a 50/l gamble that two of them volition share the same birthday. The answer is 23.

"Oh, those guys and their birthdays really go me mad," says Bernard Beitman, a psychiatrist and visiting professor at the University of Virginia, and author of the forthcoming book Connecting With Coincidence . That'southward not the way the boilerplate person would frame that question, he says. When someone asks "What are the odds?" odds are they aren't asking, "What are the odds that a coincidence of this nature would have happened to anyone in the room?" just something more than like, "What are the odds that this specific thing would happen to me, here and at present?" And with anything more complicated than a birthday lucifer, that becomes nearly impossible to summate.

It's true that people are adequately egocentric about their coincidences. The psychologist Ruma Falk institute in a study that people rate their own coincidences every bit more surprising than other people's. They're like dreams—mine are more interesting than yours.

"A coincidence itself is in the heart of the beholder," says David Spiegelhalter, the Winton Professor for the Public Understanding of Risk at the University of Cambridge. If a rare event happens in a forest and no one notices and no one cares, it's not really a coincidence.

* * *

I told Spiegelhalter my Cedar Indicate story on the phone—I couldn't aid it. He collects coincidences, see. (A thriller novel called The Coincidence Authority has a professor character based on him.) He has a website where people can submit them, and says he's gotten about 4,000 or v,000 stories since 2011. Unfortunately, he and his colleagues haven't done much with this treasure trove of data, mostly because a pile of gratis-form stories is a pretty hard information set up to measure. They're looking for someone to practise text-mining on it, simply and so far all they've been able to clarify is how many coincidences fall into the different categories you lot tin check off when you submit your story:

Common Types of Coincidences

David Spiegelhalter

He says he'd categorize mine every bit "finding a link with someone yous see." "But information technology's a very unlike sort of connection," he says, "non like having lived in the same house or something like that. And information technology'south a very strong one, information technology'south not just similar you were both at the theme park. I dearest that. And y'all recall it subsequently all this time."

And the craziest thing is non that I establish someone'south money and then that I was in a room with him a year later, but that I found out about it at all. What if he hadn't brought it upwardly? Or "you might not have heard him if you lot'd been somewhere slightly away," Spiegelhalter says. "And yet the coincidence would have been there. You would accept been six anxiety away from someone who lost their coin. The coincidence in a sense would have physically occurred. It was just because y'all were listening that you noticed it. And and then that's why the astonishing matter is not that these things occur, it's that nosotros discover them."

"This is my large theory about coincidences," he continues, "that's why they happen to certain kinds of people."

Beitman in his inquiry has found that sure personality traits are linked to experiencing more coincidences—people who draw themselves as religious or spiritual, people who are self-referential (or likely to relate information from the external earth back to themselves), and people who are high in meaning-seeking are all coincidence-decumbent. People are also probable to see coincidences when they are extremely deplorable, aroused, or anxious.

"Coincidences never happen to me at all, because I never find annihilation," Spiegelhalter says. "I never talk to anybody on trains. If I'm with a stranger, I don't endeavor to find a connection with them, because I'chiliad English."

Beitman, on the other hand, says, "My life is littered with coincidences." He tells me a story of how he lost his canis familiaris when he was viii or 9 years onetime. He went to the police station to ask if they had seen it; they hadn't. Then, "I was crying a lot and took the incorrect way home, and there was the canis familiaris … I got into [studying coincidences] merely considering, hey, look Bernie, what'south going on here?"

For Beitman, probability is not enough when it comes to studying coincidences. Because statistics can describe what happens, just tin't explicate it any further than chance. "I know there'southward something more than going on than we pay attention to," he says. "Random is not enough of an caption for me."

Random wasn't enough for the Swiss psychiatrist Carl Jung either. So he came upward with an alternative explanation. Coincidences were, to him, meaningful events that couldn't be explained by cause and effect, which, so far so proficient, but he also idea that at that place was some other force, outside of causality, which could explicate them. This he chosen "synchronicity," which in his 1952 volume, he chosen an "acausal connecting principle."

Meaningful coincidences were produced past the forcefulness of synchronicity, and could be considered glimpses into another of Jung'southward ideas—the unus mundus, or "i world." Unus mundus is the theory that there is an underlying order and construction to reality, a network that connects everything and everyone.

For Jung, synchronicity didn't just account for coincidences, but too ESP, telepathy, and ghosts. And to this day, research shows that people who experience more coincidences tend to exist more likely to believe in the occult as well.

This is the trouble with trying to notice a deeper caption for coincidences than randomness—it can quickly veer into the paranormal.

* * *

Beitman, like Spiegelhalter, is interested in sorting and labeling different kinds of coincidences, to develop categories "similar an early on botanist," he says, though his categories are more expansive and include not only things that happen in the world but people's thoughts and feelings as well. In our conversation, he divides coincidences into three broad categories—environment-environment interactions, listen-environment interactions, and mind-mind interactions.

Environment-environment are the most obvious, and easiest to sympathise. These coincidences are objectively observable. Something, or a series of things, happens in the concrete world. You lot're at a gin joint in Kingdom of morocco and your long-lost beloved from Paris shows up. I found some coin and a year later I met the person who lost it.

A nurse named Violet Jessop was a stewardess for White Star Line and lived through 3 crashes of its ill-fated armada of ocean liners. She was on the Olympic when it collided with the HMS Hawke in 1911. In 1912, she was at that place for the large i: the Titanic. And four years later, when White Star's Britannic, reportedly improved afterwards its sister send'south disaster, also sank, Jessop was in that location. And she survived. That one, I guess, is an environment-environs-environment.

Mind-environment coincidences are premonition-esque—you're thinking of a friend and then they call yous, for example. But unless you happen to write downwardly "I am thinking of then-and-and so [timestamp]" before the call happens, these are cool for the person they happen to, but not actually measurable. "We banned premonitions from our site," Spiegelhalter says. "Considering, where'southward the proof? Anybody could say annihilation."

Another sort of mind-surround interaction is learning a new word and and then suddenly seeing information technology everywhere. Or getting a song stuck in your head and hearing it everywhere you go, or wondering almost something and then stumbling onto an article near it. The things on our minds seem to bleed out into the world around us. Merely, though it makes them no less magical, life's motifs are created not past the globe around us, just by humans, by our attention.

This is an upshot that the Stanford linguistics professor Arnold Zwicky calls "the frequency illusion," and information technology's not the same as a premonition. It's merely that in one case you've noticed something, your brain is primed to notice it again the next time you run into it. A word or a concept you've just learned feels relevant to you—y'all may take seen it hundreds of times before and merely never noticed. But now that you're paying attending, it's more than likely to pop out at y'all the adjacent time it whizzes by.

Then the final category, mind-mind, of course, is straight-up mystical. One instance of this is "simulpathity," a term Beitman coined to describe feeling the pain or emotion of someone else at a distance. His involvement in this particular type of coincidence is securely personal.

"In San Francisco, in 1973, Feb 26, I stood at a sink uncontrollably choking," he says, clarifying, "There was null in my throat that I knew [of]."

"It was effectually eleven o'clock in San Francisco. The next day my brother called, and told me my begetter had died at 2 a.thou. in Wilmington, Delaware, which was 11 in San Francisco, and he had died by choking on blood in his throat. That was a dramatic feel for me, and I began to look to come across if other people had experiences like this. And many people have."

* * *

This is where nosotros start to leave the realm of science and enter the realm of belief. Coincidences are remarkable in how they straddle these worlds. People have surprising, connective experiences, and they either create meaning out of them, or they don't.

Leaving a coincidence as nil more than than a curiosity may be a more evidence-based mindset, but it's not fair to say that the people who make pregnant from coincidences are irrational. The procedure by which we discover coincidences is "role of a full general cerebral architecture which is designed to make sense of the globe," says Magda Osman, an associate professor in experimental psychology at Queen Mary University of London. It's the aforementioned rational process nosotros apply to learn cause and effect. This is one way to scientifically explain how coincidences happen—as past-products of the brain's meaning-making system.

People like patterns. We look for them everywhere, and by noticing and analyzing them nosotros can understand our world and, to some small caste, control it. If every time you moving-picture show a switch, a lamp across the room turns on, you lot come to understand that that switch controls that lamp.

When someone sees a pattern in a coincidence, "there's no way I can say 'Yes, that was definitely a chance event,' or 'There was an actual causal machinery for it,' because I'd have to know the world perfectly to be able to say that," Osman says.

Instead what we exercise is weigh whether it seems likelier that the consequence was caused past hazard, or by something else. If take a chance is the winner, we dismiss information technology. If not, nosotros've got a new hypothesis about how the earth works.

Take the instance of two twins, who were adopted by different families when they were four weeks old. When they were later reunited, their lives had … a lot of similarities. They were both named James by their adoptive families, were both married to a Betty and had divorced a Linda. One twin's first son's name was James Alan, the other's was James Allan. They both had adoptive brothers named Larry and pet dogs named Toy. They both suffered from tension headaches, and both vacationed in Florida within three blocks of each other.

You could hypothesize from this that the power of genetics is so stiff, that even when identical twins are separated, their lives play out the same manner. In fact, the twins were part of a University of Minnesota study on twins reared autonomously that was asking just that question, though it didn't suggest that there was whatever gene that would make someone attracted to a Betty, or likely to name a dog Toy.

Drawing inferences from patterns like this is an advantageous thing to do, even when the pattern isn't 100 percent consequent. Accept learning linguistic communication as an example. There isn't going to exist a canis familiaris, or fifty-fifty a picture of a dog, nearby every time a kid hears the word "dog." Simply if dad points at the family Fido enough times while maxim "domestic dog," the kid will learn what the word ways anyway.

"Small children are justified in being conspiracy theorists, since their world is run by an inscrutable and all-powerful organization possessing hush-hush communications and mysterious powers—a world of adults, who act by a system of rules that children gradually master as they grow up," write the cognitive scientists Thomas Griffiths and Joshua Tenenbaum in a 2006 study on coincidences.

We retain this capability, even when we're older and have figured out most of these more obvious patterns. Information technology can still be very useful, especially for scientists who are working on unsolved questions, but for about adults in their daily lives, any new casual connection is probable to be specious. From a scientific perspective, anyway. If we realize that, then we wave it off as "just a coincidence," or what Griffiths, a professor of psychology and cognitive science at the University of California, Berkeley, calls a "mere coincidence."

On the flip side, for someone who believes in ESP, thinking of a friend right before she calls may not be a coincidence to them at all, but just more than show to support what they already believe. The same goes for someone who believes in divine intervention—a chance meeting with a long-lost lover may be, to them, a sign from God, not a coincidence at all.

"You actually come across a question of just what belief system you have about how reality works," Beitman says. "Are you a person who believes the universe is random or are y'all a person who believes there'southward something going on hither that mayhap nosotros gotta pay more attention to? On the continuum of explanation, on the left-hand side we've got random, on the correct-hand side nosotros've got God. In the middle nosotros've got petty Bernie Beitman did something here, I did it but I didn't know how I did it."

In the centre zone prevarication what Griffiths calls "suspicious coincidences."

"To me, that's a cardinal office of what makes something a coincidence—that it falls in that realm between being certain that something is faux and existence certain that something is truthful," he says. If enough suspicious coincidences of a sure nature pile up, someone's uncertainty tin cross over into conventionalities. People can stumble into scientific discoveries this style—"Hmm, all these people with cholera seem to be getting their water from the same well"—or into superstition—"Every time I vesture mismatched socks, my meetings go well."

Only you tin can stay in that in-between zone for a long time—suspicious, but unsure. And this is nowhere more obvious than in the coincidences that present as testify for some kind of hidden but as-nevertheless undiscovered ordering principle for reality, be that synchronicity or a sort of David Mitchell–esque "Everything Is Connected" spider web that ensnares united states in its pattern. Meaningful connections tin seem created by design—things are "meant to be," they're happening for a reason, even if the reason is elusive. Or equally Beitman puts it, "Coincidences alert u.s. to the mysterious hiding in plain sight."

I suppose no one can prove there isn't such a thing, just it's definitely incommunicable to show that at that place is. So you lot're left with … not much. Where you autumn on the continuum of caption probably says more about you than it does about reality.

* * *

In The Improbability Principle, Paw cites a 1988 U.S. National University of Sciences study that ended that there was "no scientific justification from enquiry conducted over a period of 130 years for the existence of parapsychological phenomena."

"1 hundred thirty years!" Hand writes. The fact that people kept trying to find proof for the paranormal was "a testament to the power of hope over feel if there always was one."

But I disagree. Information technology may be that researching the paranormal is partly an act of hope that you'll find something where no one has establish anything before. Simply information technology seems like, often, experiences are the edifice blocks of belief in the paranormal, or in an underlying strength that organizes reality. Even if they're not doing formal research, people are seeking explanations for their experiences. And structure is a much more highly-seasoned explanation than chance.

Where you autumn on the take chances-structure continuum may have a lot to do with what you think chance looks like in the first place. Research shows that while most people are pretty bad at generating a random cord of numbers, people who believe in ESP are even worse. Even more so than skeptics, believers tend to remember that repetitions in a sequence are less likely to be random—that a money flip sequence that went "heads, heads, heads, heads, tails" would exist less likely to come up randomly than one that went "heads, tails, heads, tails, heads," even though they're every bit probable.

So nosotros take psychology to explain how and why we notice coincidences, and why we want to make significant from them, and we have probability to explain why they seem to happen then oftentimes. But to explain why any individual coincidence happened involves a snarl of threads, of decisions and circumstances and chains of events that, even if one could untangle it, wouldn't tell you anything near any other coincidence.

Jung seems to take been annoyed by this. "To grasp these unique or rare events at all, nosotros seem to exist dependent on equally 'unique' and individual descriptions," he writes, despairing of the lack of a unifying theory offered by science for these strange happenings. "This would effect in a chaotic collection of curiosities, rather similar those one-time natural-history cabinets where ane finds, cheek past jowl with fossils and anatomical monsters in bottles, the horn of a unicorn, a mandragora manikin, and a stale mermaid."

This is supposed to be unappealing (surely these things should exist put in order!), but I rather like the epitome of coincidences every bit a curio cabinet total of odds and ends we couldn't find anywhere else to put. It may non be what we're most comfy with, just a "cluttered collection of curiosities" is what we've got.