(Note: This is not a review of the best-selling book, The Black Swan, The Impact of the Highly Improbable, by Nassim Nicholas Taleb : I shall merely discuss its relevance to the scientific study of events and their interactions, what I call ‘Eventrics’. S.H.)

Before Westerners colonised Australia, it was assumed that all swans were white. However, it is now known that a few (very few) are black. The term ‘Black Swan’, though a brilliant choice of name for an important phenonenon, is somewhat misleading. For Taleb is not concerned with unusual birds but exclusively with unusual events. Moreover, although the term could, by extension, be applied to any kind of event, Taleb seems to be entirely concerned with human events, either general historical ones like wars and financial crashes, or, on an individual level, serendipitous circumstances leading to an important discovery like penicillin or a chance encounter in a bar leading to  a career change.
Taleb lists three characteristics of Black Swan events : “rarity, extreme impact, retrospective (though not prospective) predictability” (Note 1). These are best broken down into four : rarity, unpredictability, extreme impact, subsequent plausibility. Taleb rightly emphasizes how readily commentators and historians are to list the causes of, say, the outbreak of WWI the 1929 Wall Street Crash after the event, but how slow people living at the time were to even realise that anything special was about to happen. Human blindness and inveterate bias is an important issue but it is not my main concern : I wish to determine whether there are any discernable ‘general principles’ controlling the occurrence of events. Nonetheless, the fact that a reasonable attempt at showing the steps leading up to a devastating crisis like the outbreak of WWI or the 1929 and 2008 Wall Street crashes does show that a Black Swan event is not only possible — because it took place — but can be made to appear plausible, even inevitable (after the event).  Had the event under scrutiny been totally fantastic, historians would have had a much harder job trying to trace such an event’s antecedents, and, unless it was a very well verified and important event, they would have  been very happy to ignore it completely. ( Scientists and rationalists do this all the time when confronted with aberrant apparently ‘psychic’ phenomena on the principle that what they cannot explain casually cannot exist and, if they do, are best left well alone.)
The restrospective ‘plausibility’ of a Black Swan event is something to be born in mind for future reference, but the really important features of a Black Swan event are (1) unpredictability and (2) extreme impact with rarity  coming very much in third place (since Black Swan events turn out not to be so rare as all that) (Note 2). Nassim Taleb has in effect divides (human and hisotrical) events into two classes, one comprising ‘ordinary events’, those taking place in Mediocristan as he puts it, and one containing Black Swan events — those taking place in Extremistan.  The difference between these two classes is not so much the rarity of  Black Swan events as (1) their apparent lack of causal antecedents combined with (2) their sudden appearance and (3) their colossal consequences.
‘Normal’ human event-chains proceed by small increments that can be roughly figured out in advance : a nation becomes steadily wealthier as new markets open up or alternatively poorer as sources of valuable raw materials become exhausted, an individual gets promoted every five years until he retires and so on. Each step is defined by the previous one and such progress, if it is modelled mathematically, gives a so-called ‘continuous’ function. In the terms of Eventrics, there is a steady flow of what I call ‘dominance’ from one macroscopic event to the next — dominance, to be explained in due course, is roughly  causality viewed as a perfectly real ‘force’.
Black Swan events are not like this at all : they seem to appear from nowhere,  strike like a ‘bolt out of the blue’ (a significant expression) and have consequences that may last centuries in the case of historical turning-points  or a lifetime in the case of personal reversals of fortune. As an example of historical Black Swans take the rise of Islam, a movement that swept through half the known world, emerging from an insignificant, arid, scarcely civilized region no one bothered about, or, even more incredibly, the largest land Empire the world had yet seen emerging like a volcano from the steppes of Outer Mongolia. More recently, we have had 9/11,  the financial crisis of 2008, the sudden appearance of China as the twenty-first century’s super-power when not so long ago we had people in laundromat suits reading the Little Red Book and collecting scrap iron for “backyard steel foundries” (Mao’s own prhase). The examples are endless : it is actucally more difficult to find examples of ‘ordinary’, predictable events that have been turned out to be historical turning points, though there are one or two.
As for personal life :”Look into your own existence. Count the significant events, the technological changes, and the inventions that have taken place in our environment since you were born and compare them to what was expected before their advent. How many of them came on schedule ? Look into your own personal life….. How often did these things [important changes] occur according to plan?” (The Black Swan p. xix)
I would certainly concur with Taleb when he says that history is discontinuous (“History and societies do not crawl. They make jumps” (p. 11)), that history is dominated by Black Swan events and that such events seem to be on the increase (“The modern world being Extremistan, is dominated by rare — very rare — events“(p. 61) (Note 3).
Two questions immediately spring to mind : (1) Are Black Swan events truly random, or only unpredictable because of insufficient data? (2) Is there a ‘hidden pattern’ to Black Swan events, a driving force concealed from our vision ?
On the first point, Taleb is adamant that Black Swan events are truly random,  unpredictable through and through, not just because our instruments are too coarse or our information inadequate. He makes this an article of faith, not to say an obsession, and, in a sense, he ought to know what he is talking about since he has spent much of his adult life as a trader.  He is careful to distinguish true indeterminism even from the sort of randomness we associate with Chaos Theory since the latter somehow combines strict determinism with unpredictability (amongst other reasons, because the systems studied in Chaos Theory are very sensitive to the initial conditions). What do I think? I remain open minded  for the moment : though there is no doubt in my mind that Black Swan ‘causality’, if it exists at all, is totally different from the usual “Event A brings about event B” sort of causality. Black Swan events do not seem to originate in the everyday world, as if there were some sort of underground well of events which occasionally forces itself through to the surface, spewing out molten lava.
So, what of ‘hidden patterns’, ‘hidden historical sources’? Taleb, as a systematic  Sceptical Rationalist, gives any such ideas short shrift :  those who think they can read the writing on the wall, people like Plato, Hegel, Marx, Spengler et al. are deluding themselves — and doubtless he would say the same about my own humble attempts in the same direction. Few people living after the 2008 financial crash would quarrel with Taleb’s scathing attacks on economic experts, all of whom despite their sophisticated mathematical and computer telescopes, somehow managed not to see the hurricane that was blowing their way. Indeed, I would go further than Taleb (who sensibly suggests that the Nobel Prize for Economics be abolished) by also suggesting that Economics Faculties be closed down world-wide, especially the London School of Economics. However, market analysis, like weather forecasting, is a notoriously complex area and the ‘experts’ are not so much to blame for getting it wrong as for arrogantly refusing to admit that they did get it wrong. Weather forecasters have in fact been challenged and have mended their ways : after getting long-term (month or more) weather forecasting palpably wrong they have (in the UK) decided to restrict themselves to short-term forecasting where they do a good job.
But there is certainly no need to abandon the whole principle of drawing inferences from previous instances — which Taleb tends to rubbish as ‘tunneling’. The adage, “Where there is pattern, there is significance”, though it can at times mislead, has underpinned almost all of mankind’s greatest intellectual and cultural developments, whereas nothing great has ever been achieved by doubt — certainly not the great scientific discoveries such as gravitation and evolution which were wild generalisations from very inadequate evidence. The human mind and psyche does not work well with negatives : scepticism is a useful restraining force, a counter weight, but no more than that.
Taleb resuscitates the ‘Turkey Paradox’ (orginally Chicken Paradox) invented by Bertrand Russell, a man who has a deeply destructive influence on modern logic and mathematics. The ‘paradox’ goes something like this. A turkey, well-fed and well-protected by its owner for a good period of time, say forty days, concludes (or would conclude if it could reason) that, on the basis of the past record, it is going to continue to be well-fed and well-protected indefinitely. On Day 41 the turkey is slaughtered since it is Thanksgiving Day. “”Jumping to conclusions!” Unsound inference!” “Incomplete Induction!” scream Hume and Russell and all the rest of the rationalist posse. Not really. On Day 41, unbeknown to the turkey, the conditions of the problem have dramatically changed and that is why the forecast, based on outmoded conditions, turns out to be wrong. The lesson to draw is not that ‘incomplete induction is risky’ (we know that already) but rather that one should make sure that the conditions have not suddenly changed in a way that is not at first sight evident. Neither Hume nor Russell nor Popper was a practising scientist, businessman or military commander — and they would have failed in all three areas. The adroit general or businessman knows that there will never be enough data relating to economic conditions or the movements of enemy troops, he thus learns to make rapid conclusions on the basis of thoroughly inadequate data : a skill that can only really be learned by practise in the market place or on the  battlefield. In terms of the Turkey Problem, one tries to guess whether the conditions have remained the same or not and one develops a certain flair or scent for this — Taleb himself, who is dismissive of  the ability of most millionnaires, recognizes that Soros had this.
Science is a somewhat different case.  The very existence of science rests on the unprovable (and conceivably mistaken)  assumption that identical conditions produce identical results (Note 3). If we did not believe this, we would not trouble ourselves to repeat a scientific test : the very same experiment carried out in a different laboratory on a different day might well give completely different results. The ancient Greeks, likewise the Chinese, did not have make this assumption which is one reason why neither quite managed to develop natural science as we understand it today though they came very close. The Greeks, under the influence of Plato, considered that the sublunary world was subject to random influences, ‘chaotic’ in our terms, and thus could not be reduced to behaviour governed by a handful of ‘physical laws’. Heavenly bodies were different : they were regular in their movements. The result was a very advanced astronomy and mathematics but a somewhat defective mechanics despite Archimedes (no science of movement, dynamics). We have extended the application of ‘natural law’ to the entire universe, “One universe, one set of laws”. This enormous intellectual gamble seems to have paid off by and large, though it has been found necessary to exclude the inflationary period of the early universe, and there are some indications that the basic physical ‘constants’ have changed over time.  The “one universe. one set of laws” assumption is by no means self-evident: it is justified, not by its inherent plausibility, since it is not plausible, but uniquely only by its results — “One judges a tree by its fruits”. Similarly, the adage “Where there is pattern, there is significance” — which Taleb catigates as the ‘narrative fallacy’ —  has, by and large, served humanity very well and will continue to do so despite all the dreadful cautionary tales of poitivists and sceptics. You learn to distinguish between the important and unimportant patterns, false prophecies and true, on the job, not in the study, and in some cases, errors of judgement can be as fruitful as genuine discoveries, witness the wild guesses of intuitive mathematicians such as Fermat and Ramanujan (Note 4).
So, can any reasonable conclusions be drawn from Taleb’s discussion of Black Swan events, other than “Take care how you go” ? I think, yes, and Taleb, even though he categorically declined to provide specific forecasts on repeated occasions when interviewed, does as a matter of fact sneak in one or two predictions  — remarkably (since the book was written before the 2008 Wall Street crash) he says that “the government-sponsored institution Fanny Mae, seems to be sitting on a barrel of dynamite” (Note 5).
If we consider large historical Black Swans like the two world wars of the 20th century, we see that there is a family resemblance — the same big European powers opposed each other on much the same terrain — but the second Black Swan was not an identical repeat, indeed with respect to tactics it was almost exactly the reverse. WWI was a trench war that lasted nearly four years; WWII, as far as France was concerned, was a Blitzkrieg that lasted a few weeks. Likewise, the 2008 financial meltdown has a family resemblance to 1929 in America but is not an identical repeat. One can, from this and other evidence, hazard a good guess that successive large-scale Black Swans are never identical repeats : the preparations made for the ‘next’ Black Swan (the Maginot Line) tend to be quite useless, indeed counter-productive, since they draw attention away from the coming danger, and thus increase its eventual effects. This, combined with the very plausible guess that Black Swan events are becoming more and more frequent, allows one to hazard certain guesses about the 21st century.
Taleb remarks shrewdly that the supposedly ‘safe bets’ in the case of both banks and regimes may well be the most dangerous of all : not so long ago Iceland was considered a pretty safe country to invest in and standard economic wisdom says that government bonds are the safest of all investments, even though it is now whole countries, including Spain and Italy, that are on the verge of defaulting. Taleb says at one point that apparently ‘safe’ (but oppressive) regimes may be the very ones to fall, on the principle that the taller you are, the harder you fall. He mentions as examples Syria and Saudi Arabia and, since his book was written long before the Arab Spring, this is pretty good going.
I will myself stick my neck out and hazard a few guesses. It may well be that one of the affluent Arab Middle Eastern kingdoms, which no one pays much attention to at the moment, will precipitate the next financial crisis — as nearly happened with Abu Dhabi. I also predict that the natural resource that will most likely precipitate war and economic turmoil is not oil that everyone is bothered about but water (Note 6) .
What about science and technology? It seems clear that the leading science of the 21st century will be biology, but biology, though something of a Black Swan science when DNA was discovered, is hardly an outlier at the moment, is on the contrary advancing steadily year by year, the difference being that the steps it takes are getting larger. Traditional mathematics — or rather modern traditional mathematics — will decline in importance and (hopefully) be largely replaced by more flexible modelling such as computer simulations, cellular automata, ‘evolutionary computing’ and so forth.  The trouble with current mathematics is that it is fixed, inert, capable of m0delling change and motion (up to a point) but, by definition, incapable of growing from within itself. Everything unexpected is kept outside the hallowed domain which is both mathematics’s strength and elegance, but also its hopeless limitation. In the turbulent environment of today, we need symbolic systems that do not exclude the random and the uncontrollable, the source of evolutionary innovation but, on the contrary, welcome it into the system while nonetheless keeping it under control — “The price of freedom is endless vigilance”. We want computer programmes that advance by trial and error and take initiatives themselves : strangely enough, since writing these lines yesterday I have come across two articles in back issues of the New Scientist dealing with this very issue (Note 7).  As for theoretical physics, it looks like it will continue cascading into total unintelligibility until the basic concepts are rigorously re-examined and a radically new outlook emerges. Enough of all that, the rest is history.
Notes : (1) “What we call here a Black Swan… is an event with the following three attributes :
First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can con vincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable. I stop and summarize the triplet : rarity, extreme impact, and retrospective (though not prospective) predictability.”

(2) An actual Black Swan (the bird) has Taleb’s first attribute, ‘rarity’ and his third ‘unpredictability’ (since it was not even known to exist) but it completely lacks his second attribute, ‘extreme impact’. Who, apart from a few professionals, cares whether the bird is classed as a swan or not ? Viruses and  archaea are closer to being true ‘Black Swans’ since their belated and very unexpected discovery has provoked a mini-revolution in biology.

(3) Of course, it is not true in Quantum Mechanics that “the same conditions produce identical results” but this is precisely why QM, in the orthodox Copenhagen interpretation, is so worrisome.

(4) Fermat was an amateur mathematician — he was a jurist by profession  — and, though regarded as the founder of an important branch of mathematics, Number Theory, gave few proofs. He claimed to have the proof of his famous Last Theorem, but famously noted that “it was too long to go into the margin” of the book where he noted it down, Diophantus’s Arithmetica. Modern mathematicians think his proof was almost certainly spurious.
The  strange largely self-taught Hindu mathematician, Ramanujan, produced a whole lot of stunning mathematical theorems while working with chalk and slate-board (because he couldn’t afford ink and paper) on the verandah of his parents’ house near Madras in the early twentieth century. Hardy, the leading British pure mathematician of the day and himself a model of mathematical ‘rigour’, nonetheless had the breadth of vision to recognize Ramanujan’s genius and invited him to come to Cambridge. This was perhaps a mixed blessing for mathematics since it seems that Ramanujan’s really creative work, some of which turned out to be wrong, wilted in the aridity of modern ‘prove it or be damned’ mathematics (Ramanujan didn’t bother with proofs) and only flowered again briefly when he returned to India to die at the age of 32. Hardy said that “Ramanujan’s mistakes were as remarkable as his correct theorems” — or something to that effect.  Today, Ramanujan would stand even less chance of being recognized (except perhaps via the Internet) as few universities, let alone the Royal Society, would welcome such a maverick into their ranks and I doubt if any contemporary Hardy would have the vision  and above all the generosity to aid such a person.

(5) “The Black Swan” footnote p. 225 Penguin edition. Taleb also writes (p. 226), “We have moved from a diversified ecology of small banks, with varied lending policies, to a more homogeneous framework of firms that all resemble one another. True, we now have fewer failures, but when they occur… I shiver at the thought. I rephrase here : we will have fewer but mroe severe crises”.

(6)  Since writing this I have come across the following :  “A shortage of water is a more serious peril than any of the others mentioned in this report [concerning Pakistan]. Combined with fast growth of population, it is the true existential threat to Pakistan. (…) The study forecasts that by 2025 Pakistan’s annual water supply will fall short of demand by around 100 billion cubic metres, about half of the entire present flow of the Indus {!!]. In parts of the country the shortage is already acute.” (Going with the Flow in The Economist, February 11th 2012).    
Also, “We are facing a planet without enough water and with a rapidly warming atmosphere….” (Princess Sumaya of Jordan, Interview in New Scientist 18 February 2012)

(7)  This  development has already taken place though the mathematical fraternity, which even now does not accept an innovator such as Mandelbrot into its ranks, has not yet woken up to the fact :
“Evolutionary computing allows computers to do things they haven’t been programmed to do and is already being used to solve problems as diverse  as creating train timetables to designing aircraft” (“Move Over Einstein” by Justin Mullins, New Scientist, 19 March 2011)
        “Genetic algorithms mimic natural selection by describing a design as if it were a genome conbstructed from segments. Each segment describes a parameter of the invention, varying from its shape, say, to much finer grained aspects, such as electrical resistance or a chemical’s molecular affinities. By randomly changing some segments — or ‘mutating them’ — the algorithm improves the design. The best results are then bred together to improve things further (“The Next Wave” by Paul Marks, New Scientist, 14 May 2011).