How China changed the game for countries in default

Robin Wigglesworth and Sun Yu  in The FT

Zambia, struggling from an economic and financial crisis compounded by the Covid-19 pandemic, first missed an interest payment on its international bonds. Two and a half years later it remains in limbo, unable to resolve the default on most of its $31.6bn debts. 

That an impoverished and vulnerable country has for so long unsuccessfully laboured to reach a deal with creditors and move on from the crisis is an illustration of the messy process to deal with government bankruptcies, which some experts fear has now broken down completely. 

The consequences could be severe for the spate of countries that have recently defaulted on their debts, and the topic has been high on the agenda of this week’s spring meetings of the IMF and World Bank in Washington. 

In her opening remarks at those meetings, the IMF’s managing director Kristalina Georgieva noted that about 15 per cent of low-income countries were already in “debt distress” and almost half were in danger of falling into it. 

“This has raised concerns over a potential wave of debt restructuring requests—and how to handle them at a time when current restructuring cases are facing costly delays, Zambia being the most recent example,” she told attendees.  

While domestic laws and judges govern the bankruptcies of companies and individuals, there is no international law for insolvent countries — only a chaotic, ad hoc process that involves working through a hodgepodge of contractual clauses and tacit conventions, enduring tortuous negotiations and navigating geopolitical expediency. 

A decade ago, US-based hedge fund Elliott Management exploited that landscape to notch up several lucrative victories by suing defaulters for full repayment of their debts. But this fragile patchwork is now under threat of unravelling completely due to the emergence of a new, disruptive, opaque and powerful force in sovereign debt: China. 

Some experts say Beijing’s lending spree to developing countries and refusal to play by western-established rules represents the single greatest impediment to government debt workouts and threatens to leave some countries in debt limbo for years. 

But Yu Jie, a senior research fellow on China at think-tank Chatham House, believes Beijing’s stance “is less about economic rationalities and more about geopolitical competition”. 

“The multilateral financial institutions are run largely by Americans and Europeans. China had hoped to be able to shape the agenda of debt relief, not to have it dictated by the west,” she says. 

Jay Newman, the former Elliott fund manager who successfully sued Argentina for $2.4bn after its 2001 debt restructuring, says the emergence of China as a significant player has left the entire system in uncharted waters. “You now have one big state creditor with the power to dictate terms and the patience not to make a deal if it doesn’t suit them. It has completely changed the game.” 

The new landscape 

In a grim sign of the times, Alvarez & Marsal — one of the world’s biggest corporate bankruptcy advisers — this year set up a sovereign practice for the first time. Underscoring its expectations for the business, it hired Reza Baqir, a former senior IMF official and governor of Pakistan’s central bank, to lead the new unit. 

The potential is clear. The latest IMF data from the end of February indicates that nine poorer countries — such as Mozambique, Zambia and Grenada — are already in what it terms “debt distress”, while another 27 countries are at “high risk” of falling into it. A further 26 more are on the watchlist. Baqir points out that there are also a lot of struggling state-controlled companies in these countries that will need help as a result. 

“The timing was right” for A&M to set up a sovereign advisory unit, he says. “Given that there are more than 50 countries in various stages of debt distress there is an opportunity for a more holistic approach.” 

Baqir is among those that say the debt restructuring process is broken, largely because it was primarily designed for a bygone era, when creditors were overwhelmingly western countries and western banks. 

Decades ago, the Paris Club was formed to co-ordinate between government creditors, while bankers formed the London Club to restructure their debts. Broadly speaking, western governments drove the process, and occasionally leaned on banks to accept painful settlements. It was largely improvised and often slow, but it mostly worked. 

But the decline of bank lending and the growth of the bond market shook things up in the spate of sovereign defaults that started in the early 1990s. Creditor co-ordination became trickier with myriad bondholders trading claims around the world, rather than just a handful of banks. 

Argentina’s default on $80bn of bonds in 2001 led to years of fights between Buenos Aires and investors such as Elliott, which refused to accept the terms agreed by other creditors. At one point the hedge fund famously seized an Argentine naval vessel when it docked in Ghana. Its reputation became such that bondholders would sometimes invoke the mere spectre of Elliott to scare countries contemplating a default, while policymakers used it as prima facie evidence of the sovereign debt restructuring system’s weaknesses. 

In the wake of the Argentine debacle the IMF responded by attempting to set up a kind of bankruptcy court for countries with itself as judge. But the sovereign debt restructuring mechanism foundered after attracting little support from the IMF’s biggest shareholders. Instead, the US championed the insertion of “collective action clauses” into bonds, which compel recalcitrant creditors to accept a restructuring agreement made by a majority. After Greece’s debt restructuring in 2012 these CACs were beefed up further. 

However, many bonds still lack these clauses. Moreover, they can only help ease a restructuring agreement once it is struck. Many experts point out that they do nothing to solve the biggest fundamental problem: countries are far too slow to seek a debt restructuring as they are wary of a messy process with the potential of worsening an economic crisis and the inevitable political humiliation of defaulting. 

“If I was a finance minister, I’d find it hard to tell my prime minister that we have a clean framework to work with,” says Baqir. 

When they are finally forced into a debt restructuring, the financial relief that countries secure is often too little to ensure a durable upswing. In the few cases where it does clean up their balance sheet, it sometimes only leads to another debt binge. 

This flawed process has now been further complicated — some say wrecked — by China’s vast lending programme across the developing world over the past decade. Many of these loans are opaque in size, terms, nature and sometimes even existence. 

The overall size of the lending programmes is hard to judge, given that China does not report most of it to the likes of the IMF, OECD or Bank for International Settlements. But AidData, a development think-tank based at William & Mary’s Global Research Institute, estimates that the loans amount to about $843bn. China is not a member of the Paris Club, and in most cases the loans are made by its myriad state-owned or merely state-controlled banks, muddling things further. 

It’s like the international financial policy community spent the past decade trying to clean up around the street light, oblivious to the mounds of rubbish piling up unseen around the rest of the darkened street, says Anna Gelpern, a professor of law and international finance at Georgetown University. 

“We spent 20 years focusing on contractual tweaks, assuming that bonds were the problem,” she says. “The problem is the state of global politics, and the fate of low-income countries just isn’t a big priority anywhere.” 

Life in default 

Zambia is a prime example. Of the roughly $20bn of external debt that the IMF tallied when forming its programme in 2022, $2.7bn was lent by international development banks, $1.3bn comes from various western governments, bank loans come to $1.6bn, local kwacha-denominated bonds held by non-residents are $3.3bn and international dollar-denominated bonds account for $3.3bn. But the biggest chunk is nearly $6bn owed to China. 

The IMF has reached a support agreement with Zambia that is conditional on its debt burden becoming sustainable. But other bondholders do not want any relief they offer to simply go towards paying off China. Beijing has in principle agreed to accept a “haircut” on its debts, but experts say it appears to not want anything it offers to go towards improving the recovery of private creditors, leading to the impasse. 

In the meantime, Zambia says it has accumulated about $1.2bn in arrears since its default. Including missed payments to various government contractors, the IMF has estimated that the arrears are actually nearly $3bn. 

Highlighting how China also appears to be leveraging these situations to undermine the western-designed global financial architecture, in January it called for international organisations such as the IMF and World Bank to participate in the debt restructuring. This would overturn half a century of convention that these organisations are “super-senior” creditors exempt from debt restructurings, as participating would imperil their ability to lend to other countries. 

One senior adviser to the Chinese government says that “there is no law that requires World Bank loans to be prioritised” and that the country was “not happy” with a practice that originated in an era when western countries were generally the only creditors. “If we allow the World Bank to take precedence over us, we need to have bigger voting rights and take larger stakes at the bank. China’s duty doesn’t match its rights in development finance.” 

Another increasingly common wrinkle in debt restructuring is what to do with domestic bonds, which local banks and financial companies have often gorged upon. Here too, Zambia is a good example. 

The $3.3bn of local currency bonds held by non-residents have also been cordoned off from the debt restructuring. Lusaka fears that reducing the value of kwacha bonds could wreck its banking industry and do more damage than they are worth. But some holders of other international bonds argue that they should also be included in the restructuring. 

“In the sovereign debt restructuring business we didn’t really think much about local debts,” says Lee Buchheit, a leading lawyer in the field. “There often wasn’t much of it, and we always assumed that the sovereign has a much broader palate of mechanisms it can use to deal with domestic debt.” 

But what to do about Zambia’s Chinese loans remains the thorniest issue and has risen to the highest levels in Washington and Beijing. US Treasury secretary Janet Yellen this year raised the stand-off with Chinese president Xi Jinping’s economic adviser Liu He, and said that it had “taken far too long already to resolve this matter” when she visited Lusaka in January. 

China’s exceptionalism? 

For the most part, experts say China seems mostly content with rolling its debts rather than restructuring them, handing out new loans to ensure that its domestic banks can be repaid in full. But it prefers to act alone, at its own pace, and feels no need for transparency. 

A recent paper by several economists, including Harvard University’s Carmen Reinhart, estimated that China has made 128 bailout loans worth $240bn to 20 distressed countries between 2000 and 2021. About $185bn was extended over the last five years of the study, and more than $100bn in 2019-21. 

Reinhart says that China’s lending stands out for its “extreme” opacity but stresses that its overall behaviour is not as unusual as some people say. “China is really playing hardball because it is a major creditor. US commercial banks also played hardball back in the 1980s,” she says. Baqir agrees, saying: “Whatever the colour or creed of a creditor, creditors think like creditors.” 

The Chinese government adviser also points to factors such as the country’s relative inexperience with debt workouts. “China is still at an early stage in coming up with its debt relief programme,” he says. 

Incomplete domestic financial reforms have also made it harder to offer debt relief to overseas creditors, while some Chinese banks are also struggling with big hits from the country’s wilting real estate sector. 

“We need co-ordination from the top level, which now has other priorities,” the adviser says. He also points out that the pressure on developing countries has intensified following a series of US interest rate rises, and that as a result Washington “should be responsible for the debt trap”. 

But whatever the root cause, most agree on the end result. “All of this [creditor] fragmentation is leading to paralysis,” says Sean Hagan, a former general counsel at the IMF who now teaches international law at Georgetown. 

 There are few solutions being floated around. The IMF in February announced a new Global Sovereign Debt Roundtable to bring together the full gamut of creditors and debtors, and hopefully thrash out ways to “facilitate the debt resolution process”. It is an initiative that few experts harbour much hope for. 

Buchheit likens the impact of an assertive new player on an already fault-riddled debt restructuring system to someone having a bad cold that a doctor struggles to treat, who is then impaled by a spear. “The cold hasn’t gone away, but the doctor is likely to focus more on the spear,” he says. 

Ironically, both Buchheit and Newman — who clashed many times over the years as the leading lawyer for and suer of bankrupt countries — advocate for the same basic approach: countries should restructure the debts they can, remain in default to China, and the IMF should drop its “kumbaya” approach and accept semi-permanent arrears to its biggest shareholders. 

But most expect Zambia-like debt limbo to be the likeliest outcome for a lot of countries. “I suspect this is going to be a recurring problem,” says Reinhart. “And the longer these countries are in the [debt] netherworld . . . the [more the] fabric of the country is affected.”  

Are coincidences real?

The rationalist in me knows that coincidences are inevitable, mundane, meaningless. But I can’t deny there is something strange and magical in them, too wonders Paul Broks in The Guardian


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.

The vision thing … a solar eclipse. Photograph: Chiwi Giambirtone/Reuters

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.

---

Ihave 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”.

The theory of synchronicity. Photograph: cyano66/Getty Images/iStockphoto

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.

The black dog at John Bonham's grave. Photograph: David Sillitoe/The Guardian

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.

A golden scarab beetle (Plusiotis resplendens). Photograph: Minden Pictures/Alamy

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.