How often do you pick up two books, on completely different subjects, and discover, to your astonishment, that they have more in common than would seem either likely or possible?
A probability theorist would say that there is nothing improbable about this since the books do after all, have you, the reader, with your specific interests and inclinations, in common. But I am not a probabalist and I prefer to believe that it was chance that led me recently to pick up, in quick succession, Nassim Nicholas Taleb’s The Black Swan, and Carl Gustav Jung’s Synchronicity: An Acausal Connecting Principle (a translation of an essay published in 1952).
Nassim Nicholas Taleb is a mathematician who has made a fortune by betting on highly improbable market events. The Black Swan was a huge best-seller when it was published in 2007 and Taleb is a celebrated figure, in the world of business as well as in the academy.
To no small degree does Taleb owe his fame to the concept of the Black Swan which rests (and this is of course a very crude summation) on a trenchant critique of mainstream probability theory, which he demonstrates to be incapable of predicting ‘highly improbable but consequential events’. These are precisely the Black Swans of the title: these creatures are unknown, says Taleb, in the universe charted by the conventional mathematics of probability (which he calls ‘Gaussian’ after, Carl Friedrich Gauss, father of the ubiquitous bell curve).
The Black Swan, Taleb tells us, lives in a ‘fourth quadrant’ or ‘Extremistan’: this is a world of ‘fractal randomness’ and it was hidden from view until quite recently when a brand new set of mathematical instruments, invented by Benôit Mandelbrot, revealed its existence. The chaotic world of the fourth quadrant remains invisible to Gaussians whose tools suffice only for the mapping of their own, orderly universe, ‘Mediocristan’.
For the most part, says Taleb, Black Swans are content to remain on their own planet. But sometimes, although very rarely, they spin off like meteors and hit Mediocristan with a force that is out of all proportion to their frequency. This is exactly why the Black Swan confounds the mathematics of probability: the chances of their occurrence are so small, by the standard statistical measures of prediction, that they are considered safe to ignore. But unfortunately Black Swans are obdurate creatures and appear to be indifferent to the probabilities assigned to them. They burst through with disturbing frequency, and when impact occurs the consequences can be like that of Chixculub asteroid on the dinosaurs: needless to say, that too was a highly improbable event.
Oddly enough, probability is at the heart also of Jung’s Synchronicity. He too is concerned with a certain class of highly improbable events: coincidences.
The notion of Coincidence is by definition at odds with the idea of the Probable. They are like two old adversaries, sitting on a greased pole, each trying to knock the other off. The fighter known as Probable is bigger, stronger, uglier and more bad-tempered than his adversary, Coincidence. Usually it is an uneven contest and Probable has little trouble in dislodging his opponent. But Coincidence is a supple and cunning fighter, a master of the feint; sometimes, he is able to use Probable’s size against him.
These are exactly the moments that are of interest to Jung: ‘A certain M. Deschamps, when a boy in Orléans, was once given a piece of plum-pudding by a M. de Fortgibu. Ten years later he discovered another plum-pudding in a Paris restaurant, and asked if he could have a piece. It turned out, however, that the plum-pudding was already ordered – by M. de Fortgibu. Many years afterwards M. Deschamps was invited to partake of a plum pudding as a special rarity. While he was eating it he remarked that the only thing lacking was M. de Fortgibu. At that moment the door opened and an old, old man in the last stages of disorientation walked in: M. de Fortgibu, who had got hold of the wrong address and burst in on the party by mistake.’
Jung describes many other circumstances where the laws of probability seem not to obtain. Some of these are statistical (compiled from a study of astrological charts), some are experimental and some anecdotal. Some of his best stories are derived from his own experience: ‘A young woman I was treating had, at a critical moment, a dream in which she was given a golden scarab. While she was telling me this dream I sat with my back to the closed window. Suddenly I heard a noice behind me, like a gentle tapping. I turned around and saw a flying insect knocking against the window pane from outside. I opened the window and caught the creature in the air as it flew in. It was the nearest analogy to a golden scarab that one finds in our latitudes, a scarabaeid beetle, the common rose-chafer (Cetonia aurata), which contrary to its usual habits had evidently felt an urge to get into a dark room at this particular moment. I must admit that nothing like it ever happened to me before or since…’
Jung relates another curious tale: ‘The wife of one of my patients, a man in his fifties, once told me in conversation that, at the deaths of her mother and grandmother, a number of birds gathered outside the windows of the death-chamber. I had heard similar stories from other people. When her husband’s treatment was nearing its end, his neurosis having been cleared up, he developed some apparently quite inocuous symptoms which seemed to me, however, to be those of heart-disease. I sent him along to a specialist, who after examining him told me in writing that he could find no cause for anxiety. On the way back from this consultation (with the medical report in his pocket) my patient collapsed in the street. As he was brought home dying, his wife was already in a great state of anxiety because, soon after her husband had gone to the doctor, a whole flock of birds alighted on their house…’
How to account for these curious conjunctions? Could it be, for example, that the gathering of the birds caused the deaths (or the other way around)? Jung firmly rejects this possibility: to propose a causal connection, he says, would be to resort to supernatural or magical thinking. But how then is the gap to be filled? Jung suggests (and I am, of course, simplifying greatly again) the existence of a ‘connecting principle’ that is external both to the human psyche and to the phenomenal world: this is ‘meaning’ itself. ‘We are so accustomed to regard meaning as a psychic process or content that it never enters our heads to suppose that it could also exist outside the psyche.’ Expanding on this, he adds: ‘The causality principle asserts that the connection between cause and effect is a necessary one. The synchronicity principle asserts that the terms of a meaningful coincidence are connected by simultaneity and meaning.’
Jung’s ‘synchronicity’ and Taleb’s ‘Fourth Quadrant’ share nothing except their estrangement from the domain of Gaussian probability. But even so, there are certain … well, let us call them, for want of another word, ‘synchronicities’.
Both Taleb and Jung call themselves ‘empiricists’, for example, and they both seem to have a talent for collaborating with the finest mathematical and scientific minds of their day. Taleb’s work leans heavily on Mandelbrot, as will be obvious from this clip (listen especially for Taleb’s pronouncement, ‘the banking system is a monstrous giant with feet of clay’ and for Mandelbrot’s observations on the brutality and unpredictability of sudden change: ‘I sleep better perhaps than Nissim but I don’t sleep very well’.)
Jung’s scientific associations are, if anything, even more impressive than Taleb’s. ‘Professor Einstein was my guest on several occasions at dinner,’ he writes. ‘These were very early days when Einstein was developing his first theory of relativity, [and] it was he who first started me off thinking about a possible relatively of time as well as space, and their psychic conditionality. More than thirty years later, this stimulus led to my relation with the physicist Professor W. Pauli and to my thesis of psychic synchronicity.’ The last reference is of course to Wolfgang Pauli, the great Austrian physicist who was awarded the Nobel Prize in 1945 on Einstein’s recommendation.
But these are merely minor resemblances. At bottom there is only one important link between Taleb and Jung: they are both insurgents, rebelling against the tyranny of probability. But Jung’s is a discreet, almost apologetic revolt: ‘…the statistical method is in general highly unsuited to do justice to unusual events’, he says, adding later, in an almost-hushed voice: ‘we have to remind ourselves over and over again of… the effect of the statistical method in eliminating all unusual occurrences’ (66).
Jung can be forgiven his timidity: he was not, after all, a mathematician, and he was writing at a time when Probability reigned unchallenged, exercising an iron-fisted dominion over everyday life as well as Science. To question this regime was to risk a long sentence of imprisonment in the jailhouse of ridicule. Taleb, on the other hand, is a mathematician and he has the advantage of possessing a set of armaments that did not exist in Jung’s day. There is nothing discreet about his insurgency: he raises the banner of revolt with a full-throated cry, frequently mocking the tyrant, never neglecting to point to his lack of clothing: ‘If you ever took a (dull) statistics class in college, did not understand much of what the professor was excited about, and wondered what ‘standard deviation’ meant, there is nothing to worry about. The notion of standard deviation is meaningless outside of Mediocristan… Standard deviations do not exist outside the Gaussian, or if they do exist they do not matter and do not explain much. But it gets worse. The Gaussian family… are the only class of distributions that the standard deviation (and the average) is sufficient to describe. You need nothing else. The bell curve satisfies the reductionism of the deluded.’
But Taleb doesn’t stop there. He is not afraid to turn his guns on the vast cities of thought and aspiration that have been built on the foundations of probability: ‘Everyone in (the) post-Enlightenment moment was longing for the aurea mediocritas, the golden mean: in wealth, height, weight and so on…The notion of the average man is steeped in the culture attending the birth of the European middle class, the nascent post-Napoleonic shopkeeper’s culture, chary of excessive wealth and intellectual brilliance. In fact, the dream of a society with compressed outcomes is assumed to correspond to the aspirations of a rational human being facing a genetical lottery’.
Will the empire of the probable survive this assault? That remains to be seen, but in the meanwhile battle has been joined, and for myself I have no doubt about which side I am on. This is a matter on which I have known my mind for a long time.
I happen to know the exact date when the limits of probability were demonstrated to me: March 17, 1978. I was then a student in Delhi University, studying for my master’s degree.
Mid-march is a nice time of year in Delhi: the chill of winter is gone and the blazing heat of summer is yet to come; the monsoons are far away and the sky is usually clear. But on March 17 that year there was something odd about the weather. In the late afternoon dark clouds appeared and there were squalls of rain. Then followed an even bigger surprise: a hailstorm, a very rare phenomenon in that part of the country.
I’d spent most of the afternoon in a library and had planned to stay late. But the weather changed my mind: I packed up my books and decided to go back to my room, which was at the other end of the campus.
It so happened that I had arranged to drop in on a friend that day – the writer Mukul Kesavan, who was spending a few days on campus, visiting an aunt who lived on the grounds of Daulat Ram College, an undergraduate institution. I had never before stepped into this college and nor, in the ordinary run of things, would I have had any occasion to go there. But the visit had been arranged and since it didn’t involve a long detour, I decided to go.
The college was just a short walk from where I was, a little distance past a busy intersection called Maurice Nagar. By the time I found Mukul the skies had darkened ominously. It wasn’t long before I decided to head back to my room.
It was raining as I hurried out of the college compound. Stepping on the road, I heard a rumbling sound, somewhere above. I glanced over my shoulder and saw a grey, tube-like extrusion forming on the underside of a dark cloud: it grew rapidly as I watched, and came whiplashing down to earth, heading in my direction.
Across the street lay a large administrative building. I sprinted over and headed toward what seemed to be an entrance. But the glass-fronted doors were shut, and a small crowd stood huddled outside, in the shelter of an overhang. There was no room there for me so I ran around to the front of the building. I came to a small balcony and jumped over the parapet. I knelt on the floor, protecting my books with my body.
The noise rose to a deafening pitch and I could feel the wind tugging at my clothes. I raised my head and stole a glance, over the rim of the parapet. Through the whirling dust I saw a bizarre assortment of objects shooting past: bicycles, scooters, lamp-posts, sheets of asbestos, entire tea-stalls.
I lowered my head and waited until the wind died down. Then I climbed out and started to re-trace my steps.
The building’s entrance – the place where I had first thought to take shelter – was in a shambles. The glass doors had given way and people had been blown inside.
I walked on: I suppose I was in a state of mild shock.
Decades later, I am not sure when exactly, or where, I hunted down the Times of India’s New Delhi edition of March 18. I still have the xeroxes I made of it.
The first page has a banner headline. It says: 30 dead, 700 hurt as cyclone hits North Delhi.
Here are some excerpts from the accompanying report: ‘Delhi, March 17: At least 30 people were killed and 700 injured, many of them seriously, this evening when a freak funnel-shaped whirlwind, accompanied by rain, left in its wake death and devastation in Maurice Nagar, a part of Kingsway Camp, Roshanara Road and Kamla Nagar in the Capital. The injured were admitted to different hospitals in the Capital.
‘According to eyewitnesses, milling around Mall Road, Maurice Nagar and Kamla Nagar, the wind was preceded first by light showers and then by a hailstorm. The peculiar wind hit the area around 6 p.m. and lasted about five minutes (although estimates varied between 30 seconds and five minutes).
‘The whirlwind followed almost a straight line… Some eyewitnesses said the wind hit the Yamuna river and raised waves as high as 20 or 30 feet.
‘A private transport bus, proceeding from Delhi to Panipat with about 70 passengers along Mall Road, was virtually lifted off the road and deposited nose downwards in a nullah. A number of people were believed killed in this bus – according to some, as many as 15.
‘Mr. Avtar Singh, driving a DTC [Delhi Transport Corp.] bus on route number 114 from Maurice Nagar to the Railway Station said that he turned the bus into Maurice Nagar and spotted a ‘whirling thing advancing towards my bus. I stopped the vehicle, but it was pushed backwards by a mighty force and it banged into another bus behind… Fortunately only a handful of passengers in both buses were injured. The unidentified driver of another DTC bus was, however, not so lucky. Students of the Shri Ram College of Commerce said they saw the driver’s body being cut into half by a tree which fell squarely on the vehicle.
‘Three DTC buses had turned turtle and a couple of others had been hit either by falling trees or electric poles and telephone wires falling across the road.
‘It was difficult to estimate the number of scooters – both three and two-wheelers – which were crushed under trees or blown off the road in the dark.
‘The Maurice Nagar road … presented a stark sight. It was littered with fallen poles (both electric and telephone), trees, branches, wires, bricks from the boundary walls of various institutions, tin roofs of staff quarters and dhabas and scores of scooters, buses and some cars. Not a tree was left standing on either side of the road.
‘Oddly enough the freak wind followed a path so straight and true that while all the trees had collapsed in front of Khalsa College, poplars eerily continued to stand out.
‘The front of the Khalsa College main building had a huge gaping hole torn into the wall on the top floor… At Miranda House, all boundary walls had been flattened. The library roof at the rear and the wall in front had collapsed. The entire wall facing Mall Road had been blown away. Empty book racks stood testimony to the event – the books had vanished in the vortex…. The entire roof of Sewa Kutir, an orphanage in Hakeekat Nagar, had collapsed, trapping many children under the debris. Popular dhabas, frequented by students of Delhi University, were reported to have been completely blown away…
‘Mr. Devinder Mehra of Cavalry Lines, walking with a friend on Mall Road, first said: ‘I cannot describe it,’ but then added, ‘it was something like a cyclone, a round wind and lasted only three minutes.’… Mr. Puran Mongia, a lecturer in economics, said: ‘It was like a tornado which we have read about as having occurred in California.’… Mr. B.N.Nanda, second year economics student of the Ramjas College said: ‘It was white. It was funnel-shaped with the cone pointing downwards. It sounded like a jet aircraft and looked somewhat like the picture we have seen of the atomic explosion over Hiroshima…’
In the inner pages of the issue, a headline reads: ‘Moments of hell for 2 lecturers: For Mr. Prabhu Chawla and Mr. Inder Kapahi, two lecturers of Delhi University, the four minutes they took shelter in a disused urinal by the side of Satyawati Marg in the university area were literally moments of hell. Mr. Prabhu later said he could never dream of such a terrifying scene. He and Mr. Kapahi were about to ride his scooter around 6 p.m. when he saw almost everything around him quivering suddenly. A three-wheeler scooter with two passengers was lifted off the ground by the ferocious wind. The driver and the passengers were crushed under the vehicle which fell upside down.
‘Mr. Chawla said: ‘I saw my own scooter, which I had abandoned on the road, during those terrifying moments, being carried away in the wind like a kite. We saw all this happening around but were dumbfounded. We saw people dying around but were unable to help them. The two teastalls at the Maurice Nagar corner were blown out of existence. At least 12 to 15 persons must have been buried under the debris at this spot. When the hellish fury had abated in just four minutes, we saw death and devastation around.’
The exact nature of the phenomenon was not determined till the next day: ‘A very, very rare phenomenon, says met office: March 18, Delhi: It was a tornado that hit northern parts of the Capital yesterday – the first of its kind in more than a hundred years of recorded meteorological history. According to the Indian Meteorological Department, the tornado was about 50 metres wide and covered a distance of about five k.m. in the space of two or three minutes.’
What is the likelihood?
A city of around ten million people is hit by a tornado, the first in recorded history; it touches down on one straight road and travels five kilometres in three minutes.
What are the chances of being there, in precisely that place, at that moment?
I was never interested in computing the probabilities. I knew, even without knowing the words, that the winds of synchronicity had put me in the path of a Black Swan.
The tornado passed me by with serene scorn, never harming a hair of my body. But its winds penetrated deep into my mind: the walls that had sheltered the Padshaw of the Probable were swept away. Never again would the tyrant attempt to cow me into submission.
I had joined the insurgency even without knowing it.
One day the rebels will win and the citadel will be stormed. In the aftermath, if it were to fall to me to imagine the map of possibilities that would then come into being, I would draw it so that it took its bearings from the longitude of Chance – that meridian of conjunctions that unites the random with the pre-ordained (‘chance led her to…’).
It is here that the very possibility of story-telling lies, within that beautiful and inexplicable wrinkle in time that joins happenstance to destiny: and as Taleb says, in what is perhaps the single most memorable sentence of his book: ‘Ideas come and go, stories stay.’