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How Certain Are You About Uncertainty? A Knighted British Statistician Knows Your Limits

Professor Sir David Spiegelhalter at play

Ask a statistician to explain a coincidence and you will hear something like:

In large populations any strange thing can happen.
You remember only the personally charged coincidences and don’t notice the many other coincidences happening around you.

Professor Sir David Spiegelhalter is no exception. He loves coincidences. He loves studying coincidences. His website Understanding Uncertainty has collected more than 4000 coincidence stories for him to mull over. He marvels at their frequency in people’s lives and how they understand and use them. He rarely notices them himself. He wants to convince you that statistics offer the best explanation.

A Brief Bio
Sir Spiegelhalter aims to improve the way statistical evidence is used by health professionals and patients. He advises organizations and government agencies on risk communication and is a regular media commentator on statistical issues, with a particular focus on communicating uncertainty.

He is the author of Sex by Numbers, and The Art of Statistics. He was elected Fellow of the Royal Society in 2005, knighted in 2014 for services to medical statistics, and was President of the Royal Statistical Society for 2017-2018.
He considers himself a policeman of science whose job it is to make sure that data suggesting a pattern really show demonstrate a pattern. Apophenia, seeing patterns that aren’t there, is one of his favorite words. Valuable contributions!

He helps medical patients understand the probabilities involved with the prognosis of their diseases. Very important because physicians and nurses are rarely trained in probability.

A Cluster Analysis

The Quid group analyzed the content of the stories on his website. They found:

Sharing a birthday with someone (11%)
Probability easily explains sharing a birthday—you have a 1/365 chance of that happening. It has to happen.

Connections involving books, TV, radio, or the news (10%)
Connections involving books and media was difficult for Sir Spiegelhalter to explain. Media coincidences commonly occur by respondents to the Weird Coincidence Survey.

Vacation-related coincidences (6.1%)
Running into someone you know on vacation can be explained by both of your being in a similar socio-economic group that travels to similar vacation spots.

Meeting people in transit—while walking around, in airports, or on public transportation (6%)
They may be people you know, and people who become meaningful to you.

Coincidences related to marriage or in-laws (5.3%)
Coincidences related to family members, covers a wide variety of possibilities including Simulpathity (feeling the pain of a loved one at a distance)

Professor Spiegelhalter would like you to believe that statistics provide the best explanation for all of these coincidences. Would he consider the conventionally accepted psychodynamic explanation for some of them?

He reported his own remarkable coincidence:
“I was on a radio show working with several people. I was choosing a date since one of my favorite coincidence stories was about matching birthdays, and I had forgotten the date. I paused for a moment and picked this date. It matched the birthdays of 2 of the people with whom I was working. The probability that they had the same birthday was 1 in 365, and the probability that my ‘random’ choice matched it is 1 in 365, making it about 1/ 135,000 ( 1/365×1/365 = 133,225).

To listen to his lively exchange with me, click here

Two Strangers Cross Paths in a Forest; a Coincidence Blooms

Two strangers are about to pass each other on a forest trail in the city of Malden, Massachusetts.

I needed a woods walk and stumbled upon this trail, while visiting from Virginia. After the walk I would return to the house of my son and his family.

Feeling good! Singing love songs to the rhythm of my strides.

The man approaching me, appears happy and greets me warmly. We stop. I say: Life could be a musical.

He: Are you saying that because I was singing?

I: No, I was singing.

He: I was singing.

I: No, I was singing.

He: I was singing.

(This pleasant argument goes on for a while. We could not hear the other one singing because each of us was singing.))

He: What song were you singing?


“How important can it be,

that I’ve tasted other lips.

That was long before you came to me

with the wonder of your kiss.”

He: Lovely.

I: What were you singing?

He sings his song. I join him for the last few notes.

He: Why don’t you join our male acapella group as a baritone?

I: I don’t live here. Thanks for inviting me.

He: That was an easy invitation. Singing in the woods was a giveaway.

He: What’s your name?

I: Bernhardt (we had spoken a little German with each other).

He: A long story about my father who had earned a doctorate in Germany in 1933 just as the Nazi’s were limiting Jewish opportunities. He was an anti-fascist and got beaten up a lot. He moved to Israel, made up a name and continued to write against the Nazis. My mother allowed him to give me this name. For that reason my children are David and Sarah.

We say a warm goodbye.

I tell my son the story. He cuts me short and says the man’s name and describes him accurately. The man is a member of my son’s synagogue.

Ah, the joy of accidentally finding a friend of my son!

Was it an accident? Upon hearing the story, the rationalists dismissed the meaning, focusing on probabilities. The intuitives embraced the dance of it. Was there a rhythm each of us singers was following? I think so. Your choice to hear it. If you don’t listen, its not there.

Romance Breeds Coincidences, and Coincidences Fuel Romance.

Roman copy of a Greek sculpture by Lysippus depicting Eros, the Greek personification of romantic love.

Ah, the joy of romantic love. Songs, poetry, novels, and movies celebrate this wonder-filled human experience. Emotions swing from ecstasy to isolation, from merging to abandonment. The intense emotions, needs, and changes breed coincidences, and coincidences quicken romance. Enhanced by the timeless feeling of synchronicity, the relationship feels like it will go on forever. And so comes this warning.

First some stories.

Feeling together at a distance

One of my patients adored her romantic coincidences: “I really loved him, like no one else I have ever loved. We seemed to be able to communicate without being in the same room. I could tell how he was feeling when we were apart. When he was in the same building, I could feel his presence. When we held each other, I melted into him. His mother’s name was the same as my sister’s. His brother’s name was the same as my father’s. These things felt like evidence that our love would last for all time. After about two years our relationship was over.”

Mr. Fox

A string of fox coincidences accelerated an intense relationship. Amelia sensed that the man across the room wanted to meet her. She boldly crossed the crowded room to start a conversation with him. After a brief conversation, she gave him her card, hoping he would call her.

He didn’t.

Then her house burned down, and she accepted an invitation to stay at a friend’s house. That same man happened to be there. He helped her through the traumatic loss of her house and her things. They became romantically intimate, yet she became suspicious of his ability to be monogamous. Because of his wily ways, she heard herself calling him Mr. Fox. In the rural area where she lived, the same day she anointed him Mr. Fox, she had seven fox sightings.

And, then, in her new home, a mysterious fox adopted her. Whenever the fox made his/her presence known, Amelia contacted Mr. Fox. During the calls, he often reported that he was involved with something related to her relationship with him. Once, he told her that he was with a woman who was wearing a fox fur.

Like most people caught up in the wonders of repeated romantic coincidences, Amelia wanted to believe that this relationship was meant to be. It wasn’t.

The turmoil drove her to write Synchronicity: Unlock Your Divine Destiny. In American Indian lore, the fox, a relative of the coyote, is the trickster. She was tricked into believing something magical was going on between them. Through her book, she teaches her readers and herself about the synchronistic machinations of that wily creature who had entered her life.

Brad and Jen*

The two previous stories were told from the point of view of only one of the participants. I interviewed a couple who shared several coincidences and wondered about they meant.

Brad and Jen met through an online dating site. Each was widowed. Her last name was also the last name of three of his cousins. Jen’s mother-in-law and Brad’s cousin had the same name. Although they both lived in Atlanta, each had gone to high school in Norfolk, Virginia. Also, one of Brad’s college fraternity brothers in college was a friend of Jen’s husband when they lived in yet another city.

They were at the beginning of their relationship. What did all these coincidences mean?

The Warning

Lynn C posted a false-promise coincidence series on Facebook: “I know someone with whom I share so many coincidences all the way back to childhood. The way we met as adults was also full of coincidences and long shots. Yet I need this person out of my life now. I wish we never met. So I’m wondering why the heck he was put in my path.”

Swept up in a series of intense synchronicities, psychiatrist Stanislav Grof dramatically married and soon divorced. He concluded: “I learned not to trust unconditionally the seductive power of such experiences… It is essential to refrain from acting out while we are under their spell and not to make any important decisions until we have again both feet on the ground” (See When the Impossible Happens).

If you are caught up in a synchronistic romance, talk with your partner. Do you share similar feelings and interpretations of the coincidences? Consider saying this: “The synchronicities make us feel that fate has brought us together and that our relationship was meant to be. We have the power and responsibility to make it true. Let’s be alert to the inevitable conflicts that two people coming together will face. The coincidences don’t make our differences go away. No matter what happens, we can help each other grow psychologically and spiritually.”

For many people, coincidences are “all good.” Were it so simple! Coincidences offer possibilities, not promises. Your choices make the differences.

Sometimes, optimal coincidence interpretation requires nimble cognitive searching. Look for the unapparent positive in what seems to be miserably miscalculated expectations. “Sadder but wiser” could deprive future romantic entanglements of synchronistic elation. Clear-sighted expectations, encouraged by romantic synchronicities, can create a solid foundation for whatever is the best course for the two of you.

Sahmat was greatly disappointed when his low probability coincidence series failed to yield romance. The disappointment made him reflect on his recent failures to make new interpersonal connections. He realized he should instead revive older connections, specifically with his friend Larry.

It turned out that Larry was working on a project that needed Sahmat’s help. “So on the surface, my experience with the woman turned out to be a ‘false promise synchronicity,’ but, because I sought deeper guidance, it turned out not to be a false promise at all, but rather a necessary step to the next connection I needed to make.”

The Message

Amelia’s failed synchronicity romance helped create a book. Sahmat reconnected with an old friend. And I have been driven to write this post because of false romantic expectations driven by incredible coincidences.

The paradox presented by coincidences is described by cognitive scientists Thomas Griffiths of Brown University and Joshua Tenenbaum of MIT in their 2007 paper, “From Mere Coincidences to Meaningful Discoveries,” published in the journal Cognition:

“Coincidences] seem to be involved in both our most grievous errors of reasoning, and our greatest causal discoveries.”

Griffiths and Tenenbaum were primarily looking at the role of coincidence in scientific discovery. But their discussion may also be applied to romantic love: “Coincidences,” they wrote, “are events that provide support for a hypothesis, but not enough support to convince us to accept that hypothesis.” Let’s say the hypothesis is that a relationship, or even a marriage, will work out very well. A person should not wholeheartedly believe that hypothesis based on the coincidences alone.”

The other extreme would be to ignore all coincidences out of fear that they are misleading. But as these researchers point out, some of the greatest scientific discoveries have been made through coincidence and some of the greatest romantic discoveries, too.

* Names and places changed

Dr Coincidence Speaks!

dr coincidence
Dr Coincidence

Is the world ready for Dr. Coincidence? Ready or not, here he comes.

On November 1, 2018 Dr Coincidence made his first major public appearance on the radio show CC with BB, Connecting with Coincidence with Dr. Bernie Beitman, MD. He told stories about how he got started with coincidences, talking about finding his lost dog, Snapper, his simultaneous choking with his father 3000 miles away, and imagining hitting the first pitch of a big baseball game for a home run and then doing it.

He describes his research into chest pain and panic disorder and his hopes for Coincidence Studies, comparing it to Freud’s and Jung’s organizations.

The intersecting patterns of coincidences are composed 2 basic components: mind and thing.

“Mind” refers to the unobservables within you, that no one else can see—your sensations, feelings, images and thoughts. “Thing” refers to objects outside of the mind, observable by another person. These two elements create 3 species: mind-thing, mind-mind and thing-thing. Mind can intersect with things and with other minds. Things can intersect with other things.

In the last segment he describes the wide variety of things that mind can coincidentally intersect with, the mind-thing coincidences:

Helpful person
Inanimate Objects
Environment mirrors psychological conflicts
Animals reflecting your emotions
Plants comforting
Machines responding to human emotions
Seeing the future

To listen to the show, click here

Are Human Beings and Snowflakes Equally Unique? Because of your uniqueness, you alone decide the final meaning of a coincidence.

Can I compare you to a snowflake? Let me count the ways.

As far as anyone can tell, no two snowflakes have exactly the same shape. To prove this assertion would require gathering vast numbers of snowflakes and then comparing their shapes. No one has reported having done that. However, many photographs have been taken. The shapes are highly varied.

Each snowflake has the same basic structure: six arms that make a hexagram when the tips are connected. Each flake requires some bit of dust or pollen as a nucleus around which to form. Each is made out of water. Each one is formed by the atmospheric conditions, including the temperature, moisture, and air pressure through which it falls.

Each human has the same basic structure: two arms, two legs and a neck-head that form a pentagon when the tips are connected. Each of us is made out of mostly water with some protein and fat and small percentages of vitamins and carbohydrates. Each of us is influenced by the conditions through which we age including genetics, geography, society, culture, and the collective consciousness.

Like a single snowflake you occupy a unique place in time and space. We are all similarly unique in this space-time way.

Similar and Different

Each of our minds is predisposed to see either similarities or differences. When considering uniqueness, It may be easier for you to think that snowflakes and humans are equally unique. Others may more easily focus on the differences.

Simultaneously holding these opposites in mind can be challenging. Yet we are both similar to and different from a snowflake.

You are more complicated than a snowflake. Those complications lead to some important similarities among us humans.

Humans share similarities on several levels:

Similar world views bring people together, especially energized ones like hate of other groups, passion for justice and thirst for particular categories of new knowledge. You may share with some people similar personality characteristics, interpersonal energies, mental compatibilities, reciprocal loving capacities or emotional resonance.

Some people, born and raised separately, with no genetic ties find a mirror in another. That mirror can be visual–their faces look very much alike. That mirror can reflect many of the same personal characteristics and a similar life history–doppelgangers. I know someone with whom we each feel our interpersonal energy is vibrating at the same frequency–twin flames.

We are different from snowflakes in that we have many similarities.

Discerning the Meaning of a Synchronicity

When it comes to finding the meanings in coincidences, your uniqueness is primary. No one can see and experience the meaning from your viewpoint. You bring a unique history filled with personal symbolism that only you can call up to examine the coincidence. Yet you need not be alone in your analysis. By consulting with others, you at least hear yourself through the mind of the other. And some people have comments that clarify what you are thinking.

To find someone who knows a lot about your kind of coincidence can be inspiring. More striking can be finding someone who has had a very similar synchronicity series. (Maybe there will be an app to connect you with such people.) Even then, you will have to fall back on your own counsel.

You are far more unique than similar to others. Learn that, rely on that, be that. Be you!

The Manic Psychiatrist’s Experience of Synchronicity: A brilliant psychiatrist becomes flooded with coincidences.

Altered states of consciousness like meditation, psychedelics and mania are often associated with an increase in coincidences. James Williford is a psychiatrist, who at age 23, began to experience manic episodes. Coupled with his high intelligence and theoretical understanding, he provides a unique perspective on synchronicity.

During his first episode, he wanted to listen to some rock music and “for some reason” picked Synchronicity by the Police. This is an example of human GPS—getting where you need to be without knowing how.

He was astounded to find that the lyrics correlated with the thoughts going through his mind. He looked at the jacket notes and found that Carl Jung, who wrote extensively about synchronicity, had influenced the lyrics. Jim then became a student of synchronicity, deeply gratified that he was not alone in these experiences.

Through repeated manic episodes he observed that the volume of the patterns entering his awareness and the frequency of the coincidences between those patterns and his surroundings were directly proportional to the intensity of his mania. The more intense the mania, the more synchronicities. In the depressed states, his mind was devoid of patterns.

He learned that deep in our unconscious are progenitors—general patterns waiting to create specific patterns tuned to our current environment. These progenitors include personal patterns which Jung called complexes and archetypes which are more universal. These progenitors match archetypes and complexes to current personal needs. An intention, for example, activates specific patterns suited for the current situation.

During the manic episodes, he used his mind’s eye to look at the past, present and future. Like a video with occasional sound, he could be telepathic, clairvoyant and predict the future. One day he needed a comb and saw, in his mind’s eye, a yellow comb in the drawer of a desk in an office he had not been in. He walked down the hall, pulled open a drawer and found the yellow comb he had seen in his mind’s eye.

He realized that he had entered the collective mind and began exploring how it operated through the unconscious. He had involuntarily become a psychonaut.

To listen to Jim describe his experiences and understandings, please click here.

Treading the Line between Materialistic Science and Synchronicity Science: Aeon Magazine

Mainstream journalists, are people like the rest of us, yet they must hew the party line that states: “Any meaning you find in a coincidence is your projection onto randomness. Go ahead, make something useful out of what you experienced but don’t try for any explanation outside of conventional science.” In this article, the author seems to show his interest in looking beyond our current views of reality. See what you think.

On coincidence
Aeon Magazine
by Cody Delistraty

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.’

Concepts such as synchronicity are ‘very seductive, because mysteries always are’

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.’

A belief in meaningful coincidence is, from an existential perspective, surprisingly rational

‘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.

Synchronicities Reveal Tunnels Between Minds

Three coincidence stories paint a picture of a tunnels between minds.

Bombers Together

Conversations about coincidences can stir up coincidences. This theme is illustrated by my radio show about coincidences.

The day before Eben Alexander was to talk with me about his new book, I read a coincidence story involving B- 17 and B-24 Bombers. The author Frank Joseph had been writing about these bombers from WWII, when he felt the need for sunshine and a breath of fresh air. He heard a strange, deep droning coming from up in the sky. First a B-17 and then a B-24. How did that happen? It was spring, 2001.

Four hours later I received a coincidence story from Eben. While living near Boston, he was clearing out the attic. He suddenly remembered he had a radio controlled model B2 bomber but had not seen it in 2 years. He felt compelled to look for it. After not finding it in the attic, he ran down to the garage, didn’t see it. He then went out to the driveway and looked up. He saw a real B2 bomber flying right over the house at a fairly low altitude. This is the only time in his life he had ever seen one in flight. It was the spring of 2001.

Two very similar bomber stories within a few hours of each other? How does that happen?

This is evidence of a temporary connection between Eben and me in preparation for our interview. We had to reschedule twice because of various broadcast problems. We were reaching out to each other emotionally creating temporary tunnels between our minds.

A Fish Story

Karen Newell joined Eben in our conversation. She told us a fish synchronicity.

One morning Karen woke up, recalling a dream about one of their koi fish. They named him Buster (yes, they named all 18 of them), who was lying on the ground dead. Two other fish had recently gone missing but they hadn’t yet figured out the predator. She quickly put the dream image out of her mind, figuring it was due to anxiety over their safety. Later that day, she walked out to the pond and suddenly remembered the dream clearly and vividly. This prompted her and Eben to look in the pond for Buster. He wasn’t there. He was never found. Using a security camera, they discovered that a blue heron was the culprit. Now a net covers the pond. They have lost no fish since then.

Karen had a strong connection to Buster. She thought that maybe he was signaling her about his death so they could prevent the other fish from the same fate. A mind tunnel between Buster and Karen could explain this synchronicity.

Thinking together

Eben and Karen have a close relationship.

While in the final stages of editing their co-authored book, Living in a Mindful Universe, Karen was out on their porch watching the dogs in the yard, mulling over different sections of the book. One particular set of two sentences that had been bothering her came to mind. She then saw a way to make the writing smoother. At this point, she went into the house to make the edits. Eben was at his desk going through the manuscript. She looked over his shoulder. He was viewing the exact paragraph containing the sentences she wanted to change! He then made her suggested edits.

Eben and Karen do many things together beyond meditation and book writing. They have built a strong mental connection between them. Each was putting extra energy into their collaboration just as they do in other ways. An enduring mind tunnel has been constructed.

To hear Eben and Karen talk about these experiences and the nature of Consciousness please click here.

Why Do You Experience Lots of Coincidences (or Not)?

People who describe themselves as spiritual or religious report experiencing more meaningful coincidences than those who did not according to research done by my Coincidence Studies group.

In subsequent research, we proceeded to define the personality traits that were associated with high coincidence sensitivity.

This is a summary of our findings. For the full report please click here.

Participants were 280 undergraduate university students enrolled in a psychology class. Of the sample, 159 (57%) were female, and 121 (43%) were male. The mean age of the sample was 19.1 (SD = 1.1). Of the sample, 88.2% were white, 6.8% were black, 2.1% were Asian, less than 1% was Hispanic, and 2.1% reported “Other.”

Participants were presented with a prototypical coincidence scenario to prompt their understanding of “coincidence”.

The primary purpose of this study was to conduct a confirmatory factor analysis of previous work on the Weird Coincidence Scale (WCS) to help establish its psychometric reliability and validity. To accomplish this goal, we selected from a large set of personality questionnaires to compare with scores on the WCS.

The secondary benefit was the identification of personality variables that are associated with coincidence sensitivity.

Six Personality Traits

Six personality traits emerged as potential measures of coincidence sensitivity:

Referential Thinking Scale measures ideas of reference which involve the belief that outside events have a particular and unusual meaning for the person. An example of a test item is “When I see two people talking at work, I usually think they are criticizing me.”

Positive and Negative Affect Scale measures the independent dimensions of positive and negative affect. The positive affect terms are happy, joyful, pleased, and enjoyment/fun and the negative affect terms are depressed/blue, unhappy, frustrated, angry/hostile, and worried/anxious.

Vitality Scale measures subjective vitality, or positive feelings of energy and aliveness. An example of a test item is “I have energy and spirit.”

Religious Commitment Inventory measures “the degree to which a person adheres to his or her religious values, beliefs, and practices, and uses them in daily living.” A sample item is, “I spend time trying to grow by understanding my faith.”

Meaning in Life Scale measures two independent constructs — presence of meaning in life and search for meaning in life. An example of a Presence item is “I have discovered a satisfying life purpose.” An example of a Search question is “I am looking for something that makes my life feel meaningful.”

Faith in Intuition Scale measures the experiential thinking system, which is characterized as being “preconscious, rapid, automatic, holistic, primarily nonverbal, intimately associated with affect.” An example item is “I tend to use my heart as a guide for my actions.”


We compared their scores on the Weird Coincidence Survey with each of their scores on the personality questionnaires. The most statistically significant was The Referential Scale. The ranking of all 6 was:

1) Referential thinking

Referential thinking is characterized by beliefs that “events around me have to do with me.” Looking for coincidences and finding meaning in them represents a form of referential thinking.

2) Vitality and negative affect

High emotional charge is likely to generate increased associations.

3) Religious commitment

Religious commitment is often associated with the idea that God intervenes personally in people’s lives, suggesting the coincidences may be interpreted as a means by which people are being guided.

4) Search for meaning

A tendency to explore meaning in life is likely to be applied to searching for meaning in coincidences.

5) Faith in intuition (which statistically was not significant)

Faith in intuition involves finding importance in and drawing conclusions from coincidences rarely through rational means. We were surprised that this factor was not significant although others have found it to be significant using different scales.


An increased tendency to associate one idea to another is the common denominator among these personality characteristics. In various ways, each of these traits facilitates connecting an observation with a thought or a thought with an observation. To be self-referential increases the likelihood to connect an observation to a comment on the self. High emotion increases thought production which creates more connections. Religious commitment seeks thoughts and experiences to support the idea that God intervenes in our lives through “minor miracles” like coincidences. The search for meaning drives people to connect their external experiences to their internal needs as possible guides in life’s journey.

With what ease do you connect similar ideas together?