Three Takes on Coincidences

 

In the summer of 2021, I experienced a cluster of coincidences, some of which had a distinctly supernatural feel. Here’s how it started. I keep a journal, and record dreams if they are especially vivid or strange. It doesn’t happen often, but I logged one in which my mother’s oldest friend, a woman called Rose, made an appearance to tell me that she (Rose) had just died. She had had another stroke, she said, and that was it. Come the morning, it occurred to me that I didn’t know whether Rose was still alive. I guessed not. She’d had a major stroke about 10 years ago and had gone on to suffer a series of minor strokes, descending into a sorry state of physical incapacity and dementia.
 
I mentioned the dream to my partner over breakfast, but she wasn’t much interested. We were staying in the Midlands at the time, in the house where I’d spent my later childhood years. The place had been unoccupied for months. My father, Mal, was long gone, and my mother, Doreen, was in a care home, drifting inexorably through the advanced stages of Alzheimer’s. We’d just sold the property we’d been living in, and there would be a few weeks’ delay in getting access to our future home, so the old house was a convenient place to stay in the meantime.
 
I gave no further thought to my strange dream until, a fortnight later, we returned from the supermarket to find that a note had been pushed through the letterbox. It was addressed to my mother, and was from Rose’s daughter, Maggie. Her mother, she wrote, had died “two weeks ago”. The funeral would be the following week. I handed the note to my partner and reminded her of my dream. “Weird,” she said, and carried on unloading the groceries. Yes, weird. I can’t recall the last time Rose had entered my thoughts, and there she was, turning up in a dream with news of her own death.
 
So, what am I to make of this? Here’s one interpretation: Rose died, and her disembodied spirit felt the need to tell me and found its way into my dream. Perhaps she had first tried to contact Doreen, but for one reason or another – the impenetrable wreckage of a damaged brain? – couldn’t get through. Here’s another interpretation: the whole chain of events occurred by sheer coincidence, a chance concatenation of happenings with no deeper significance. There’s nothing at all supernatural about it.
 
If you ask me which of those two interpretations I prefer, it would, unequivocally, be the second. But here’s the thing. There is a part of me that, despite myself, wants to entertain the possibility that the world really does have supernatural dimensions. It’s the same part of me that gets spooked by ghost stories, and that would feel uneasy about spending a night alone in a morgue. I don’t believe the universe contains supernatural forces, but I feel it might. This is because the human mind has fundamentally irrational elements. I’d go so far as to say that magical thinking forms the basis of selfhood. Our experience of ourselves and other people is essentially an act of imagination that can’t be sustained through wholly rational modes of thought. We see the light of consciousness in another’s eyes and, irresistibly, imagine some ethereal self behind those eyes, humming with feelings and thoughts, when in fact there’s nothing but the dark and silent substance of the brain. We imagine something similar behind our own eyes. It’s a necessary illusion, rooted deep in our evolutionary history. Coincidence, or rather the experience of coincidence, triggers magical thoughts that are equally deep-rooted.
 
The term “coincidence” covers a wide range of phenomena, from the cosmic (in a total solar eclipse, the disc of the moon and the disc of the sun, by sheer chance, appear to have precisely the same diameter) to the personal and parochial (my granddaughter has the same birthday as my late wife). On the human, experiential, scale, a broad distinction can be drawn between serendipity – timely, but unplanned, discoveries or development of events – and what the 20th-century Lamarckian biologist and coincidence collector Paul Kammerer called seriality, which he defined as “a lawful recurrence of the same or similar things or events … in time and space”.
 
The biography of the actor Anthony Hopkins contains a striking example of a serendipitous coincidence. When he first heard he’d been cast to play a part in the film The Girl from Petrovka (1974), Hopkins went in search of a copy of the book on which it was based, a novel by George Feifer. He combed the bookshops of London in vain and, somewhat dejected, gave up and headed home. Then, to his amazement, he spotted a copy of The Girl from Petrovka lying on a bench at Leicester Square station. He recounted the story to Feifer when they met on location, and it transpired that the book Hopkins had stumbled upon was the very one that the author had mislaid in another part of London – an advance copy full of red-ink amendments and marginal notes he’d made in preparation for a US edition.
 

Hollywood provides another choice example of seriality. L Frank Baum was a prolific children’s author, best-known for The Wonderful Wizard of Oz (1900). He didn’t live to see his novel turned into the iconic musical fantasy film, yet he reputedly had a remarkable coincidental connection with the movie. The actor Frank Morgan played five roles in The Wizard of Oz (1939), including the eponymous Wizard. He makes his first appearance in the sepia-toned opening sequences as Professor Marvel, a travelling fortune-teller. Movie lore says that, when it came to screen testing, the coat he was wearing was considered too pristine for an itinerant magician. So the wardrobe department was sent on a thrift-shop mission to find something more suitable, and returned with a whole closetful of possibilities. The one they settled on, a Prince Albert frock coat with a worn velvet collar, was a perfect fit for the actor. Only later was it apparently discovered that, sewn into the jacket was a label bearing the inscription: “Made by Hermann Bros, expressly for L Frank Baum”. Baum had died 20 years before the film was released, but the coat’s provenance was allegedly authenticated by his widow, Maud, who accepted it as a gift when the film was completed.
 
Some coincidences seem to contain an element of humour, as if engineered by a capricious spirit purely for its own amusement. Not long after first moving to Bath in 2016, I made a dash across the busy London Road, misjudged the height of the kerb on the other side, tripped, fell awkwardly and fractured my right arm. Over the next five years, I lived variously in Bath, rural Worcestershire and London. Soon after moving back to Bath on a more permanent basis, I noticed a stylish mahogany chair in the window of a charity shop on London Road, went straight in and bought it. I thought I’d have no trouble lugging the chair back to my flat half a mile away, but it turned out to be heavier than I expected and awkward to carry. As I was crossing the road where I’d had my fall, the chair slipped, crashed to the ground and splintered its right arm. Hear the chuckles of the coincidence imp.
 
While some coincidences seem playful, others feel inherently macabre. In 2007, the Guardian journalist John Harris set out on “an intermittent rock-grave odyssey”, visiting the last resting places of revered UK rock musicians. About halfway through, he went to the tiny village of Rushock in Worcestershire to gather thoughts at the headstone of the Led Zeppelin drummer John Bonham, who died at the age of 32 on 25 September 1980, after consuming a prodigious quantity of alcohol. A Guardian photographer had visited the grave a few days earlier to get a picture to accompany the piece. It was, writes Harris, “an icy morning that gave the churchyard the look of a scene from The Omen”, and, fitting with one of the key motifs of that film, the photographer was “spooked by the appearance of an unaccompanied black dog, which urinates on the gravestone and then disappears”. Black Dog (1971) happens to be the title of one of the most iconic songs in the Led Zeppelin catalogue.
 
If we picture a continuum of coincidences from the trivial to the extraordinary, both the Hopkins and the Baum examples would surely be located towards the strange and unusual end. My “broken arms” coincidence tends towards the trivial. Other still more mundane examples are commonplace. You get chatting to a stranger on a train and discover you have an acquaintance in common. You’re thinking of someone and, in the next breath they call you. You read an unusual word in a magazine and, simultaneously, someone on the radio utters the same word. Such occurrences might elicit a wry smile, but the weirder ones can induce a strong sense of the uncanny. The world momentarily seems full of strange forces.
 
It’s a state of mind resembling apophenia – a tendency to perceive meaningful, and usually sinister, links between unrelated events – which is a common prelude to the emergence of psychotic delusions. Individual differences may play a part in the experience of such coincidences. Schizotypy is a dimension of personality characterised by experiences that in some ways echo, in muted form, the symptoms of psychosis, including magical ideation and paranormal belief. There is evidence to suggest that people who score high on measures of schizotypy may also be more prone to experiencing meaningful coincidences and magical thinking. Perhaps schizotypal individuals are also more powerfully affected by coincidence. Someone scoring high on measures of schizotypy would perhaps be more spooked by a death dream than I (a low scorer) was.
 
I have set naturalism and the supernatural in binary opposition, but perhaps there is a third way. Let’s call it the supranatural stance. This was the position adopted, in different ways, by Kammerer, and by the Swiss psychologist Carl Jung. Arthur Koestler’s The Roots of Coincidence (1972) introduced Kammerer’s work to the English-speaking world and was influential in reviving interest in Jung’s ideas. Kammerer began recording coincidences in 1900, most of them mind-numbingly trivial. For example, he notes that, on 4 November 1910, his brother-in-law attended a concert, and number 9 was both his seat number and the number of his cloakroom ticket. The following day he went to another concert, and his seat and cloakroom ticket numbers were both 21.
 
Kammerer’s book Das Gesetz der Serie (1919), or The Law of Seriality, contains 100 samples of coincidences that he classifies in terms of typology, morphology, power and so on, with, as Koestler puts it, “the meticulousness of a zoologist devoted to taxonomy”. Kammerer’s big idea is that, alongside causality, there is an acausal principle at work in the universe, which, as Koestler puts it, “acts selectively to bring similar configurations together in space and time”. Kammerer sums things up as follows: “We thus arrive at the image of a world-mosaic or cosmic kaleidoscope, which, in spite of constant shufflings and rearrangements, also takes care of bringing like and like together.” Albert Einstein, for one, took Kammerer seriously, describing his book as “original and by no means absurd”.
 
The theory of synchronicity, or meaningful coincidence, proposed by Jung, follows a similar line. It took shape over several decades through a confluence of ideas streaming in from philosophy, physics, the occult and, not least, from the wellsprings of magical thinking that bubbled in the depths of Jung’s own prodigiously creative and, at times, near-psychotic mind. Certain coincidences, he suggests, are not merely a random coming-together of unrelated events. They are connected acausally by virtue of their meaning. Synchronicity was the “acausal connecting principle”.
 
According to the physicist and historian of science Arthur I Miller’s book Deciphering the Cosmic Number: The Strange Friendship of Wolfgang Pauli and Carl Jung (2009), Jung considered this to be one of the best ideas he ever had, and cites Einstein as an influence. In the early years of the 20th century, Einstein was on several occasions a dinner guest at the Jung family home in Zurich, making a strong impression. Jung traces a direct link between those dinners with Einstein and his dialogue, 30 years later, with the Nobel prize-winning physicist Wolfgang Pauli, a dialogue that brought the concept of synchronicity to fruition.
 
Jung’s collaboration with Pauli was an unlikely coalition: Jung, the quasi-mystic psychologist, a psychonaut whose deep excursions into his own unconscious mind he deemed the most significant experiences of his life; and Pauli, the hardcore theoretical physicist who was influential in reshaping our understanding of the physical world at its subatomic foundations. Following his mother’s suicide and a brief, unhappy marriage, Pauli suffered a psychological crisis. Even as he was producing his most important work in physics, he was succumbing to bouts of heavy drinking and getting into fights.
 
Pauli turned for help to Jung, who happened to live nearby. His therapy involved the recording of dreams, a task at which Pauli proved remarkably adept, being able to remember complex dreams in exquisite detail. Jung also saw an opportunity: Pauli was a willing guide to the arcane realm of subatomic physics; and furthermore, Pauli saw Jung’s theory of synchronicity as a way of approaching some fundamental questions in quantum mechanics – not least the mystery of quantum entanglement, by which subatomic particles may correlate instantaneously, and acausally, at any distance. From their discussions emerged the Pauli-Jung conjecture, a form of double-aspect theory of mind and matter, which viewed the mental and the physical as different aspects of a deeper underlying reality.
 
Jung was the first to bring coincidences into the frame of psychological inquiry, and made use of them in his analytic practice. He offers an anecdote about a golden beetle as an illustration of synchronicity at work in the clinic. A young woman is recounting a dream in which she was given a golden scarab, when Jung hears a gentle tapping at the window behind him and turns to see a flying insect knocking against the windowpane. He opens the window and catches the creature as it flies into the room. It turns out to be a rose chafer beetle, “the nearest analogy to a golden scarab that one finds in our latitudes”. The incident proved to be a transformative moment in the woman’s therapy. She had, says Jung, been “an extraordinarily difficult case” on account of her hyper-rationality and, evidently, “something quite irrational was needed” to break her defences. The coincidence of the dream and the insect’s intrusion was the key to therapeutic progress. Jung adds that the scarab is “a classic example of a rebirth symbol” with roots in Egyptian mythology.
 
Whereas Kammerer hypothesised impersonal, acausal factors intersecting with the causal nexus of the universe, Jung’s acausal connecting principle was enmeshed with the psyche, specifically with the archetypes of the collective unconscious. Jung’s archetypes are primordial structures of the mind common to all human beings. Resurrecting an ancient term, he envisioned an unus mundus, a unitary or one world, in which the mental and physical are integrated, and where the archetypes are instrumental in shaping both mind and matter. It’s a bold vision, but where, we are bound to ask, is the evidence for any of this? There is more than a grain of plausibility in the suggestion that archetypal structures have an influence in shaping thought and behaviour. But the entire universe? Pauli aside, the idea of synchronicity received little support from the wider scientific community.
 
Contemporary cognitive science offers a more secure, if less colourful, conceptual framework for making sense of the experience of coincidence. We are predisposed to encounter coincidences because their detection, it might be said, reflects the basic modus operandi of our cognitive and perceptual systems. The brain seeks patterns in the flow of sensory data it receives from the world. It infuses the patterns it detects with meaning and sometimes agency (often misplaced) and, as a part of this process, it forms beliefs and expectations that serve to shape future perceptions and behaviour. Coincidence, in the simple sense of co-occurrence, informs pattern-detection, especially in terms of identifying causal relationships, and so enhances predictability. The “world” does not simply present itself through the windowpanes of the eyes and channels of the other senses. The brain’s perceptual systems are proactive. They construct a model of the world by continually attempting to match incoming, “bottom-up” sensory data with “top-down” anticipations and predictions. Raw sensory data serve to refine the brain’s best guesses as to what’s happening, rather than building the world afresh with each passing moment. The brain, simply put, is constantly on the lookout for coincidence.
 
From a wide-ranging survey of psychological and neurocognitive research, Michiel van Elk, Karl Friston and Harold Bekkering conclude that the overgeneralisation of such predictive models plays a crucial part in the experience of coincidence. Primed by deeply ingrained cognitive biases, and ill-equipped to make accurate estimates of chance and probability, we are innately inclined to see (and feel) patterns and connections where they simply don’t exist. “Innately inclined” because, in evolutionary terms, the tendency to over-detect coincidences is adaptive. Failure to detect contingencies between related events – for example, rustling in the undergrowth/proximity of a predator – is generally more costly than an erroneous inference of a relationship between unrelated events. Another driver of coincidence is what the linguist Arnold Zwicky calls the “frequency illusion”, a term that originated in a blogpost but has since found its way into the Oxford English Dictionary:
 
“frequency illusion n. a quirk of perception whereby a phenomenon to which one is newly alert suddenly seems ubiquitous.”
 
Van Elk and his colleagues were not the first to signal the unreliability of intuitive judgments of probability as a factor in the perception of coincidence. Various authors before them – such as Stuart Sutherland in his book Irrationality (1992) – have suggested that paranormal beliefs, including the belief that some coincidences are supernatural, arise because of failures of intuitive probability. The so-called birthday problem, a staple of introductory classes in probability theory, reliably exposes the flaws of our intuitions. It asks what is the likelihood that two people will share a birthday in randomly selected groups. Most people are surprised to learn that a gathering of only 23 people is required for the chances of two of them sharing a birthday to exceed 50%. I’d been meaning for some time to try a simple empirical exercise involving “deathdays” to mirror the birthday problem. When I found myself again staying briefly at my parents’ old house, a short drive from Rushock, I decided I would use Bonham’s grave as the starting point for my research, for no reason other than the vague pull of that black dog story.

 
His headstone is easy to locate, festooned as it is with drumsticks and cymbals left as offerings by the many pilgrims who make their way to the shrine from around the world. The grave lies in the shade of a spreading, blue-needled conifer and, to the right, there’s a row of three other graves – so just four graves in total (there is also a small, sandcastle-like monument at the base of the tree trunk, which I discounted for lack of name and dates). The plan was to conduct a self-terminating search. Starting with Bonham’s headstone, and with my notebook in hand, I would inspect the other graves in the row and then the rows behind and in front, working my way methodically around the graveyard, until I found any two matching dates of death, but my mission ended almost as soon as it had begun. I needed to go no further than the four graves (with five occupants) in Bonham’s row. The occupants of the two on the right shared 29 September as their date of death (21 years apart). I wish I could report that the mysterious black dog made an appearance, but it didn’t.
 
Turning to the probability of dream coincidences, suppose for the sake of argument that the probability of a dream coincidentally matching real-world events is 1 in 10,000, and that only one dream per night is remembered. The probability of a “matching” dream on any given night is 0.0001 (ie, 1 in 10,000), meaning that the probability of a “non-matching” dream is 0.9999. The probability of two consecutive nights with non-matching dreams is 0.9999 x 0.9999. The probability of having non-matching dreams every night for a whole year is 0.9999 multiplied by itself 365 times, which is 0.9642. Rounding up, this means that there is a 3.6% chance of any given person having a dream that matches or “predicts” real-world events over the course of a year. Over a period of 20 years, the odds of having a matching/precognitive dream would be greater than even.
 
Rose, the woman in the death dream I experienced, was 90 years old, and the chances of a 90-year-old woman in the UK dying before her 91st birthday are around one in six, which is to say, not unlikely. Given her medical history, the likelihood that Rose would die before her 91st birthday was probably much greater than that. But why should I dream about her in the first place? It’s true, I hadn’t been consciously thinking about Rose, but, staying in my childhood home, there would have been many implicit reminders. She used to live close by, and came to our house often. Also, visiting my ailing mother more often than usual at her care home would have me thinking about death at both conscious and unconscious levels, and perhaps (unconsciously) about her friendship with Rose.
 
Attempts at understanding coincidence thus range from extravagant conjectures conceiving of acausal forces influencing the fundamental workings of the universe, to sober cognitive studies deconstructing the basic mechanisms of the mind. But there is something else to consider. Remarkable coincidences happen because, well, they happen, and they happen without inherent meaning and independently of the workings of the pattern-hungry brain. As the statistician David Hand puts it, “extremely improbable events are commonplace”. He refers to this as the improbability principle, one with different statistical strands, including the law of truly large numbers, which states that: “With a large enough number of opportunities, any outrageous thing is likely to happen.” Every week, there are many lottery jackpot winners around the globe, each with odds of winning at many millions to one against. And, in defiance of truly phenomenal odds, several people have won national and state lottery jackpots on more than one occasion.
 

I am a naturalist, but coincidences give me a glimpse of what the supernaturalist sees, and my worldview is briefly challenged. Soon, though, for good or ill, I am back on my usual track. One final coincidence story: it was a warm afternoon in mid-June, and I was feeling sorry for myself. My partner had walked out on me just the week before, and I thought a good way to deal with self-pity would be to launch into a new project. I would do some research into the psychology of coincidence. I settled in an armchair surrounded by books and articles on the subject, including Koestler’s The Roots of Coincidence. Among other things, I’d been reading his account of Jung’s golden scarab story.
 
In need of coffee, I set Koestler aside and went to the kitchen, returning to find, set squat on the back of my armchair, a golden beetle, a rose chafer like the one that had made its way through the window of Jung’s consulting room. It must have flown in through the wide-open balcony door. I quickly took a picture in case the insect took flight again, and then nudged it on to my palm to return it to the wild, but it simply rolled on to its back and lay motionless. Dead.
 
I sent the picture to my ex, and asked how she was doing. She didn’t reply, but later that evening called with unsettling news. Zoe, an acquaintance of ours, had that afternoon killed herself. My brain by now was in magical thinking mode, and I said I couldn’t help but link Zoe’s death to the appearance, and death, of the golden beetle. I didn’t believe there was a link, of course, but I felt there might be. There was something else at the back of my mind. In Greek mythology, all that king Midas touched turned to gold. His daughter’s name was Zoe, and she too was turned to gold.
 
Ah, but rose chafers are quite common in the south of England; they are active in warm weather; the balcony opens out on a water meadow (a typical rose chafer habitat); et cetera. And it has since been suggested to me that the beetle was quite likely “playing dead” rather than truly dead. Perhaps, after I’d thrown it back out on to the meadow, there was a “rebirth” of the kind these creatures are said to symbolise.
 
Weird, though.
 
 
Are coincidences real? By Paul Bloks. The Guardian, April 13, 2023.

In the 1920s, one of Carl Jung’s female patients proved particularly frustrating to him – notwithstanding her ‘excellent education’ and ‘highly polished Cartesian rationalism’. She was ‘psychologically inaccessible’, the Swiss psychiatrist later wrote in his Synchronicity: An Acausal Connecting Principle (1960), by which he meant that she wasn’t accepting his pseudo-scientific methods.
 
To better understand her subconscious mind, Jung had her recount her recent dreams. She told him that, the night before, she had dreamed that she’d been given a golden scarab as a piece of jewellery. As she was describing the dream, there was a tapping on the window and Jung turned around. ‘I opened the window immediately and caught the insect in the air as it flew in,’ he wrote. ‘It was a scarabaeid beetle, or common rose-chafer (cetonia aurata), whose gold-green colour most nearly resembles that of a golden scarab.’ Jung knew this was just what his skeptical patient needed to see. ‘I handed the beetle to my patient with the words, “Here is your scarab.” This experience punctured the desired hole in her rationalism and broke the ice of her intellectual resistance. The treatment could now be continued with satisfactory results.’
 
Jung called this an instance of ‘synchronicity’, a concept whose application to psychology he developed with the Austrian-born theoretical physicist Wolfgang Pauli to describe the way that seemingly unrelated events can in fact be significantly related and held together by an unseen force – in this case, his patient’s dream and shared reality coalescing with the appearance of the scarab beetle. Jung believed in an unus mundus, or a unitary world, in which there is no separation between mind and matter. Everything is connected; every event has a reason behind it. It spurred his belief in even wilder ideas such as telepathy, and fed his concept of the ‘collective unconscious’, for which he claimed there were certain universal ideas, beliefs and archetypes implicitly understood by everyone from birth.
 
The Austrian biologist Paul Kammerer, a contemporary of Jung’s, built on ‘synchronicity’ with his theory of ‘seriality’, which says that coincidences are a basic force of the Universe, like gravity. Albert Einstein, always pushing the boundaries between faith and reason, found the quasi-spiritual idea of seriality intriguing, and is rumoured to have called it ‘original and by no means absurd’.

 
Today, nearly all scientists say that coincidences are just that: coincidences – void of greater meaning. Yet, they’re something we all experience, and with a frequency that is uniform across age, sex, country, job, even education level. Those who believe that they’ve had a ‘meaningful coincidence’ in their lives experience a collision of events so remarkable and unlikely that they chose to ascribe a form of grander meaning to the occurrence, via fate or divinity or existential importance. One of the most commonly experienced ‘meaningful coincidences’ is to think of your friend for the first time in a long while only to have her telephone you that instant. Any self-respecting statistician would say that if you tracked the number of times you thought of any friend, and the number of times you had that friend immediately ring you, you’d find the link to be statistically insignificant. But it is not necessarily irrational to attribute grander significance to this occurrence. To those who believe in meaningful coincidences, statistical insignificance does not undermine an event’s causality or importance. To them, just because something could happen doesn’t mean it wasn’t also fated to happen.
 
It’s a mindset that applies equally to our habit of weaving relationships between coincidental events into epic myths, religious stories, even conspiracy theories. Longwinding, Dickensian stories of interconnected coincidences leading to a cathartic conclusion can provide us with a sense of meaning, of life holding subtler, unseen mysteries that make even our suffering worthwhile – as if our lives were really a series of sophisticated, interconnecting puzzle pieces. This largely explains the seductiveness of most mainstream religions as well: a divine hand orchestrating our lives is a particularly comforting notion, even if, scientifically, there’s little to lend credence to such beliefs.
 
But just because we might ‘know’ that meaningful coincidences don’t really exist doesn’t mean that they don’t still move us. The poet John Keats in 1817 accused Isaac Newton of trying to ‘unweave the rainbow’, by which he meant that Newton was attempting to take the magic out of life by paring it down to its scientific basis. The young poet might have been wishful in his thinking, but such a statement also raises the question of how we should grapple with mysteries – with or without a belief in a greater meaning to life? Even if every possible coincidence could be scientifically explained, we shouldn’t necessarily discount its importance. You can watch a movie or read a novel, and be at once aware of its nonreality while also being moved by it. Must these ideas therefore be incompatible? Indeed, might the continued belief in meaningful coincidences even be rational and necessary to our experience of existing in the world? And, is a belief in meaningful coincidences something vital to our survival as humans?
 
After the so-called Freud Wars starting in the 1970s, led by the American essayist Frederick Crews, any orthodox adherence to Freudian or Jungian ideas has since been frowned upon in the mainstream scientific community. Statistical and evolutionary arguments against notions of synchronicity, seriality and meaningful coincidences at large have come to seem ironclad, and the existential aspects of coincidence have been wholly discounted. Those who do believe in meaningful coincidences also haven’t been doing many favours for themselves. People who strongly believe in the paranormal and in conspiracy theories, for instance, tend to be significantly worse at probabilistic and statistical reasoning than those who don’t believe in them, according to studies from the University of Bristol and Goldsmiths, University of London, respectively. In truth, most of us are surprisingly poor at gauging the probabilities of events, so when we receive that phone call from the friend we’re thinking of, we’re prone to ascribe to it a significance disproportionate to its relative commonness.
 
A good example of our lack of statistical logic is when gamblers interpret a run of black or red numbers in roulette as meaningful, in spite of the fact that each time one colour comes up, the next spin has exactly the same 50 per cent probability of landing on black or red. Or, take ‘the birthday problem’, which simply asks: how many people would you need to get into the same room in order to statistically assure that at least two share the exact birth month and day? Given that there are 365 days in a non-leap year, and that most people you know probably don’t have the same birthday, you might reasonably suppose that you’d need quite a high number to find an exact match. Hundreds, perhaps, and even then you’d be lucky to find two people with the same birth month and day. Statistically, however, you need only 23 people in the room for a greater than 50 per cent (hence ‘statistically probable’) chance of finding two people with the exact same birth month and day. For a 99.9 per cent chance, you need only 70 people.
 
We ascribe exceptional meaning to what we perceive as exceptionally low-probability events, but they’re often not as low-probability as we think. And, even if they are unlikely, the most unlikely events are – with 7 billion people on Earth – actually relatively common, thanks to the so-called law of truly large numbers, the statistical adage of Frederick Mosteller and Persi Diaconis, in which a big sample size will eventually lead to essentially any result. Many people have survived being struck by lightning (even multiple times). Many have won the lottery (even multiple times). Plus, we’re culturally trained to see meaning in intrinsically meaningless events: Thomas Jefferson and John Adams died hours apart on the 50th anniversary of the Declaration of Independence; Mark Twain was born and died on days in which Halley’s Comet could be viewed from Earth. There’s statistically nothing further to be derived from these events, but we talk about them regardless as evidence of a greater, often spiritual, meaning. Every coincidence can be statistically explained. Even Plutarch understood this. Writing in ‘The Life of Sertorius’, a volume in his Parallel Lives series (1st century CE), he noted: ‘It is no great wonder if in the long process of time, while fortune takes her course hither and thither, numerous coincidences should spontaneously occur.’

 
Irrespective of the mathematics of coincidence, there are still psychology specialists unwilling to give up on adapting theories of synchronicity and seriality. Bernard Beitman, a psychiatrist in Virginia and the author of the bestselling Connecting with Coincidence: The New Science for Using Synchronicity and Serendipity in Your Life (2016), believes that meaningful coincidences both exist and can be proven. One story he likes to tell about coincidence is extremely personal. He was 31 years old and living in San Francisco. One night, at about 11pm, he began violently choking over the sink. He hadn’t been eating or drinking, and the attack seemed to come out of nowhere. He drank some water, recovered, and then went to bed wondering what had spurred his choking fit. The next morning, he received a call from his brother, who told him that their father had died at two in the morning in Connecticut – which, because of the three-hour time difference, made it the same time as when Beitman had begun choking. His father had died choking to death on his own blood. Beitman found this pair of events incredibly significant, but he couldn’t find a sufficiently scientific explanation for them other than random chance. So he developed his own explanation, taking, in part, from Jung’s idea of synchronicity.
 
Beitman called this experience ‘simulpathity’ – or the experience of another person’s suffering, even from afar. He has since tried to provide a scientific basis for other Jungian ideas such as serendipity and seriality, and his overarching view is inherently Jungian, invoking the unus mundus while adding a distinctly New Age twist. ‘I use a term called “the psycho-sphere”,’ Beitman told me, ‘by which I mean only that mental atmosphere that surrounds Earth, in which we are immersed right here.’ Admittedly, trying to find a scientific basis for believing in meaningful coincidence is not a widespread pursuit (Iris Bell, a psychiatrist at the University of Arizona, with whom Beitman has co-written a book, is another rare exception). Statisticians still push back.
 
‘I find it very surprising, given the incontrovertible mathematical arguments,’ says David Hand, a prominent statistician and emeritus professor of mathematics at Imperial College London. ‘If you look at the relative numbers – especially of statisticians and probabilists, who are expert in such matters – you will find a vanishingly small percentage who would agree with concepts like synchronicity.’ But, perhaps, Hand reasons, the popularity of Beitman’s ideas isn’t all that surprising given human nature. ‘It’s very seductive, because mysteries always are.’
 
In fact, Beitman has taken a clever tack in recognising that just because something is random doesn’t also mean it’s not significant. It’s a similar argument that an atheist will eventually face when debating with a religious person who believes that God pulls the strings of life. Just because the atheist can use the law of truly large numbers to statistically prove that every event that happens within the boundaries of the physically conceivable world is possible without a god, this proof doesn’t also mean that those chance events are not somehow hiding meaning. (Or indeed, that some magical string-puller might not be behind at least some of them)
 
Meaning cannot be quantified or even clearly and routinely identified. The difficulty that Beitman faces is in trying to make meaningful coincidence into a scientific concept. Like a religious person, the greatest asset to believing in meaningful coincidence is that you cannot prove that something is devoid of meaning since ‘meaning’ is not scientifically testable. Where Beitman is most successful – even rational – is when he shows how experiencing a coincidence can encourage psychological shifts. He tells the story of a patient who told him that she was letting her abusive husband return to living with her. But before she went to get him from the airport, she received a phone call. The woman on the other end had the wrong number; yet, for reasons unexplained, they continued to talk, and it came out that the other woman had an abusive boyfriend. The other woman sounded fearful and unstable, and after hanging up the married woman decided to separate from her husband after all. This, Beitman says, is a meaningful coincidence that fundamentally altered her psychology and outlook on life. It is also why meaningful coincidences are so important. With the exception perhaps of the chilliest of rationalists, these types of events tend to have deeply visceral, sometimes life-changing effects.
 
Cynically, one could reason that trying to add a scientific patina to the belief in meaningful coincidence is driven by greed: there will always be money to be made in writing books about or giving talks that exploit people’s desire to see chance coincidences as significant. We want evidence of a hidden meaning in life – and we’re willing to pay for it. Beitman might be one of the few trying to provide an academic spin to meaningful coincidences, but there are literally thousands of books and movies about the beauty, significance and importance of coincidences (not to mention how they’re used to win religious adherents). Coincidences, write Yitta Halberstam and Judith Leventhal in their bestselling book Small Miracles: Extraordinary Coincidences From Everyday Life (1997), show ‘the rich promise of a bounteous universe and the splendour lying dormant within your soul. Coincidences are everywhere and can happen any time. When your soul is ready, they will come. All that is required is that you open your heart.’ This is obviously just a bit of feelgood hocus pocus. But it’s not actively harmful either, other than in taking advantage of people’s willingness to pay to hear what they want to hear.
 
Where a belief in meaningful coincidences can become dangerous, however, is when it begins to impair your judgment. For one, it can make you think illogically. For instance, ‘overfitting’ occurs when you fit your belief model to the noise rather than the signal, like suddenly ‘seeing’ UFOs after your friend has been talking about them. ‘Hidden meanings’ come out of the Jungian and Freudian ideas of the collective and individual unconscious, in which ‘slips’ of words or phrases are viewed not merely as linguistic errors but as pointing towards a greater subconscious, psychological meaning that’s not really there. Or the aforementioned ‘gambling fallacy’, which occurs when you begin to see seemingly hidden patterns in outcomes that result only by chance.
 
But while these might seem like small-time issues – UFOs, Freudian slips – there are sometimes larger questions at play. For instance, when the anti-vaccination movement was embraced in the United States, children died or had their health imperilled by parents who aligned rising rates of autism in children to the rising number of vaccines being given. It’s true that autism tends to be diagnosed around the same time that vaccinations are administered, but anti-vaxxers confused correlation with causality, relying, in part, on a belief in meaningful coincidence. Something has to be making certain children around the age of vaccinations get sick, they thought. But as study after study has shown, there’s no stock in the claim that vaccines make children autistic or even sick. Scientists, therefore, need to help ‘people to make decisions on the basis of concrete evidence, not half-baked pseudoscience,’ says Hand, the statistician. ‘Scientists have a public duty to help to disperse the mists of confusion.’

 
‘When we experience coincidences, we experience a pattern of events, sometimes perceived to be very rare, and that are surprising to us, that feel like they are caused by something,’ adds Magda Osman, who teaches experimental psychology at Queen Mary University of London. But just because we can’t say why, exactly, certain events happen at certain times doesn’t give them meaning, she says. ‘Coincidences are just an inevitable part of our cognitive system. That is it.’
 
What so much of the question around meaningful coincidence comes down to is how you choose to fill the vacuum of life’s mysteries. Is the realm of the unknown a place of spirituality and existential significance for you, or does the world remain entirely material?
 
Beneath the statistical incorrectness, beneath any economic ploys, beneath even the potentially grave errors that can result, a belief in meaningful coincidence is, from an existential perspective, surprisingly rational. If your father were to choke to death across the country at the same time that you felt a phantom choking, you might know, intellectually, that there was no mysterious, invisible connection at play. But, if you did let your mind wander to that possibility, it would allow you a new way to grieve your father’s death, giving you a sense of intimacy or a fatalist understanding of events. Beitman claims that science is ‘fairly flexible’, which seems like a red flag to serious researchers. But behind such a statement – and motivating the millions of people who buy books on, watch movies about, or have ever thought about what the many links between the events in one’s life mean – is the sometimes-necessary need to fabricate meaning.
 
We do this in infinite ways, not least via the apparatus of religion, but one way of finding meaning is to marry the mental and material worlds, signing up to what Jung called the ‘collective unconscious’ – an invisible realm that binds together our lives. It’s a belief that’s scientifically disproven, of course, and it’s flawed from its start; but, like so many other non-scientific beliefs, from a psychological angle, it makes some sense. There is, after all, a difference between statistical significance and human significance – one does not always dictate the other. Wrong and right all at once. A beetle is just a beetle until you decide that it’s not.
 
On Coincidence. By Cody Delistraty.  Aeon, July 10, 2018.

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 middle-school bands traveled. (I imagine it still is.)  They had this indoor roller coaster there, called the Disaster Transport. My friends and I were standing 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 amount of money. I don’t remember now exactly how much, but for the purposes of this retelling, let’s say it was $134. That sounds close.

 We had barely had time to whiplash from marveling at our good fortune to guiltily suggesting we should find somewhere to turn it in before a group of older kids ahead of us snatched the cash wad out of our hands. They claimed it was theirs; it was not theirs—they counted it in front of us and exchanged “Whoa”s and high fives. We were hapless, gangly middle schoolers (I was growing out my bangs; it was a rough year). They were confident we would do nothing to stop them, and they were right. So that was the end of that.

 Until, Part Two:

 A little more than a year later, I went to a summer program at Michigan State University, a nerd camp where you take classes like genetics for fun. One evening, as we were sitting around in the common area, chatting and doing homework, I overheard a kid telling his friends how he’d lost a bunch of money last year at Cedar Point.

 With very little attempt at chill I interrupted their conversation and grilled him on the particulars.

 Was he there on May whatever date I was also there? He was.

 Did he lose the money in line for the Disaster Transport? 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 not just something that was unlikely to happen. The overstuffed crate labeled “coincidences” is packed with an amazing variety of experiences, and yet something more than rarity compels us to group them together. They have a similar texture, a feeling that the fabric 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 it’s just 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 event,” but decided “this includes too much to permit careful study.” Instead, they settled on, “A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.”

 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 time. “Extremely improbable events are commonplace,” as the statistician David Hand says in his book The Improbability Principle. But humans generally aren’t great at reasoning objectively about probability as they go about their everyday lives.

 For one thing, people can be pretty liberal with what they consider coincidences. If you meet someone who shares your birthday, that seems like a fun coincidence, but you might feel the same way if you met someone who shared your mother’s birthday, or your best friend’s. Or if it was the day right before or after yours. So there are several birthdays that person could have 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, any 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 you go and all the places they go, chances are good that you’ll run into someone you know, somewhere, at some point. But it’ll still seem like a coincidence when you do. When something surprising happens, we don’t think about all the times it could have happened, but didn’t. And when we include near misses as coincidences (you and your friend were in the same place on the same day, just not at the same time), the number of possible coincidences is suddenly way greater.

 To demonstrate how common unlikely seeming events can be, mathematicians like to trot out what is called the birthday problem. The question is how many people need to be in a room before there’s a 50/50 chance that two of them will share the same birthday. The answer is 23.

 “Oh, those guys and their birthdays really get 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’s not the way the average 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?” but something more like, “What are the odds that this specific thing would happen to me, here and now?” And with anything more complicated than a birthday match, that becomes almost impossible to calculate.

 It’s true that people are fairly egocentric about their coincidences. The psychologist Ruma Falk found in a study that people rate their own coincidences as more surprising than other people’s. They’re like dreams—mine are more interesting than yours.

 “A coincidence itself is in the eye 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 Point story on the phone—I couldn’t help 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 5,000 stories since 2011. Unfortunately, he and his colleagues haven’t done much with this treasure trove of information, mostly because a pile of free-form stories is a pretty hard data set to measure. They’re looking for someone to do text-mining on it, but so far all they’ve been able to analyze is how many coincidences fall into the different categories you can check off when you submit your story:

 Common Types of Coincidences AFB

 

 

David Spiegelhalter

 

 

He says he’d categorize mine as “finding a link with someone you meet.” “But it’s a very different sort of connection,” he says, “not like having lived in the same house or something like that. And it’s a very strong one, it’s not just like you were both at the theme park. I love that. And you remember it after all this time.”

 And the craziest thing is not that I found someone’s 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 up? Or “you might not have heard him if you’d been somewhere slightly away,” Spiegelhalter says. “And yet the coincidence would have been there. You would have been six feet away from someone who lost their money. The coincidence in a sense would have physically occurred. It was only because you were listening that you noticed it. And so that’s why the amazing thing is not that these things occur, it’s that we notice them.”

 “This is my big theory about coincidences,” he continues, “that’s why they happen to certain kinds of people.”

 Beitman in his research has found that certain personality traits are linked to experiencing more coincidences—people who describe themselves as religious or spiritual, people who are self-referential (or likely to relate information from the external world back to themselves), and people who are high in meaning-seeking are all coincidence-prone. People are also likely to see coincidences when they are extremely sad, angry, or anxious.

 “Coincidences never happen to me at all, because I never notice anything,” Spiegelhalter says. “I never talk to anybody on trains. If I’m with a stranger, I don’t try to find a connection with them, because I’m English.”

 Beitman, on the other hand, says, “My life is littered with coincidences.” He tells me a story of how he lost his dog when he was 8 or 9 years old. 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 wrong way home, and there was the dog … I got into [studying coincidences] just because, hey, look Bernie, what’s going on here?”

 For Beitman, probability is not enough when it comes to studying coincidences. Because statistics can describe what happens, but can’t explain it any further than chance. “I know there’s something more going on than we pay attention to,” he says. “Random is not enough of an explanation for me.”

 Random wasn’t enough for the Swiss psychiatrist Carl Jung either. So he came up with an alternative explanation. Coincidences were, to him, meaningful events that couldn’t be explained by cause and effect, which, so far so good, but he also thought that there was another force, outside of causality, which could explain them. This he called “synchronicity,” which in his 1952 book, he called an “acausal connecting principle.”

 Meaningful coincidences were produced by the force of synchronicity, and could be considered glimpses into another of Jung’s ideas—the unus mundus, or “one world.” Unus mundus is the theory that there is an underlying order and structure to reality, a network that connects everything and everyone.

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

 This is the trouble with trying to find a deeper explanation 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 “like an early 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, mind-environment interactions, and mind-mind interactions.

 Environment-environment are the most obvious, and easiest to understand. These coincidences are objectively observable. Something, or a series of things, happens in the physical world. You’re at a gin joint in Morocco and your long-lost love from Paris shows up. I found some money 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 three crashes of its ill-fated fleet of ocean liners. She was on the Olympic when it collided with the HMS Hawke in 1911. In 1912, she was there for the big one: the Titanic. And four years later, when White Star’s Britannic, reportedly improved after its sister ship’s disaster, also sank, Jessop was there. And she survived. That one, I guess, is an environment-environment-environment.

 Mind-environment coincidences are premonition-esque—you’re thinking of a friend and then they call you, for example. But unless you happen to write down “I am thinking of so-and-so [timestamp]” before the call happens, these are cool for the person they happen to, but not really measurable. “We banned premonitions from our site,” Spiegelhalter says. “Because, where’s the proof? Anybody could say anything.”

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

This is an effect that the Stanford linguistics professor Arnold Zwicky calls “the frequency illusion,” and it’s not the same as a premonition. It’s just that once you’ve noticed something, your brain is primed to notice it again the next time you encounter it. A word or a concept you’ve just learned feels relevant to you—you may have seen it hundreds of times before and just never noticed. But now that you’re paying attention, it’s more likely to pop out at you the next time it whizzes by.

 And then the final category, mind-mind, of course, is straight-up mystical. One example of this is “simulpathity,” a term Beitman coined to describe feeling the pain or emotion of someone else at a distance. His interest in this particular type of coincidence is deeply personal.

 “In San Francisco, in 1973, February 26, I stood at a sink uncontrollably choking,” he says, clarifying, “There was nothing in my throat that I knew [of].”

 “It was around 11 o’clock in San Francisco. The next day my brother called, and told me my father had died at 2 a.m. in Wilmington, Delaware, which was 11 in San Francisco, and he had died by choking on blood in his throat. That was a dramatic experience for me, and I began to look to see if other people had experiences like this. And many people have.”

 * * *

 This is where we 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 nothing more than a curiosity may be a more evidence-based mindset, but it’s not fair to say that the people who make meaning from coincidences are irrational. The process by which we notice coincidences is “part of a general cognitive architecture which is designed to make sense of the world,” says Magda Osman, an associate professor in experimental psychology at Queen Mary University of London. It’s the same rational process we use to learn cause and effect. This is one way to scientifically explain how coincidences happen—as by-products of the brain’s meaning-making system.

 People like patterns. We look for them everywhere, and by noticing and analyzing them we can understand our world and, to some small degree, control it. If every time you flick a switch, a lamp across the room turns on, you 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 mechanism for it,’ because I’d have to know the world perfectly to be able to say that,” Osman says.

 Instead what we do is weigh whether it seems likelier that the event was caused by chance, or by something else. If chance is the winner, we dismiss it. If not, we’ve got a new hypothesis about how the world works.

 Take the case 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 strong, that even when identical twins are separated, their lives play out the same way. In fact, the twins were part of a University of Minnesota study on twins reared apart that was asking just that question, though it didn’t suggest that there was any 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 consistent. Take learning language as an example. There isn’t going to be a dog, or even a picture of a dog, nearby every time a child hears the word “dog.” But if dad points at the family Fido enough times while saying “dog,” the kid will learn what the word means anyway. 

 “Small children are justified in being conspiracy theorists, since their world is run by an inscrutable and all-powerful organization possessing secret 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. It can still be very useful, especially for scientists who are working on unsolved questions, but for most adults in their daily lives, any new coincidental connection is likely 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 evidence 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 really 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 you a person who believes there’s something going on here that maybe we gotta pay more attention to? On the continuum of explanation, on the left-hand side we’ve got random, on the right-hand side we’ve got God. In the middle we’ve got little Bernie Beitman did something here, I did it but I didn’t know how I did it.”

 In the middle zone lie what Griffiths calls “suspicious coincidences.”

  “To me, that’s a key part of what makes something a coincidence—that it falls in that realm between being certain that something is false and being certain that something is true,” he says. If enough suspicious coincidences of a certain nature pile up, someone’s uncertainty can cross over into belief. People can stumble into scientific discoveries this way—“Hmm, all these people with cholera seem to be getting their water from the same well”—or into superstition—“Every time I wear mismatched socks, my meetings go well.”

 But you 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 evidence for some kind of hidden but as-yet undiscovered ordering principle for reality, be that synchronicity or a sort of David Mitchell–esque “Everything Is Connected” web that ensnares us in its pattern. Meaningful connections can seem created by design—things are “meant to be,” they’re happening for a reason, even if the reason is elusive. Or as Beitman puts it, “Coincidences alert us to the mysterious hiding in plain sight.”

 I suppose no one can prove there isn’t such a thing, but it’s definitely impossible to prove that there is. So you’re left with … not much. Where you fall on the continuum of explanation probably says more about you than it does about reality.

 * * *

 In The Improbability Principle, Hand cites a 1988 U.S. National Academy of Sciences report that concluded that there was “no scientific justification from research conducted over a period of 130 years for the existence of parapsychological phenomena.”

 “One 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 experience if there ever was one.”

 But I disagree. It may be that researching the paranormal is partly an act of hope that you’ll find something where no one has found anything before. But it seems like, often, experiences are the building blocks of belief in the paranormal, or in an underlying force that organizes reality. Even if they’re not doing formal research, people are seeking explanations for their experiences. And structure is a much more appealing explanation than chance.

 Where you fall on the chance-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 string of numbers, people who believe in ESP are even worse. Even more so than skeptics, believers tend to think that repetitions in a sequence are less likely to be random—that a coin flip sequence that went “heads, heads, heads, heads, tails” would be less likely to come up randomly than one that went “heads, tails, heads, tails, heads,” even though they’re equally probable.

 So we have psychology to explain how and why we notice coincidences, and why we want to make meaning from them, and we have probability to explain why they seem to happen so often. 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 about any other coincidence.

 Jung seems to have been annoyed by this. “To grasp these unique or rare events at all, we seem to be 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 result in a chaotic collection of curiosities, rather like those old natural-history cabinets where one finds, cheek by jowl with fossils and anatomical monsters in bottles, the horn of a unicorn, a mandragora manikin, and a dried mermaid.”

 This is supposed to be unappealing (surely these things should be put in order!), but I rather like the image of coincidences as a curio cabinet full of odds and ends we couldn’t find anywhere else to put. It may not be what we’re most comfortable with, but a “chaotic collection of curiosities” is what we’ve got.

 Coincidences and the Meaning of Life. By Julie Beck. The Atlantic, February 23, 2016.