Tag Archives: Black Swan

Lessons from Billion-Dollar Start-Ups: Unicorns, Super-Unicorns and Black Swans.

A couple of colleagues informed me about Welcome To The Unicorn Club: Learning From Billion-Dollar Startups by Aileen Lee. I understand why. The article is closely connected to some of my main interests: high-growth start-ups and dynamics of entrepreneurs. Aileen Lee has analyzed start-ups in the Software and Internet fields which have reached a billion-dollar value while being less than 10 years old. She calls them Unicorns, whereas Super-Unicorns are companies which reached a $100B value!


All this reminds me of my analysis of 2700 Stanford-related start-ups (you can check Serial entrepreneurs: are they better? as well as High growth and profits) and to a lesser extent about the link between age and value creation: Is there an ideal age to create?

Aileen Lee has interesting results:
– out of 10,000+ founded companies per year, there are 4 unicorns per year (39 in the last decade – that is .07% of total) and about 1-3 super-unicorns per decade,
– they have raised more than $100M from investors (more than $300M for consumer-related). They may have been lean in their early days, but they grow fat!
– it takes 7+ years for an exit,
– founders have an average age of 34,
– they have 3 co-founders on average with a long experience together, often back from school,
– 75% of the founding CEO lead the company to an exit,
– many come from elite universities (1/3 from Stanford),
pivot is an outlier.

I found this article interesting, important, and I even felt empathy and let me tell you why. We have a tendency to underestimate the importance of hyper-growth and hyper-fast. Growth is extremely important for start-ups; reaching $100M in value is a success. Looking at the small group which reaches $1B and then $100B is interesting. You need money for this (VC), you do not need that much experience but you need trust from co-founders. The founders of super-licorns seem to be the explorer of unknown territories. You need passion and resources.


On Unicorns, I have done a similar analysis in “Is there an ideal age to create?” I also have an average age of 34 for 1st start-up experience of all founders, and regarding Super-Unicorns which I call Black Swans (highly unpredictable outcome according to Taleb), I have identified 10 Super-Unicorns (see below) and there are 1-4 such companies per decade since the 60s. The average age of their founders is 28 and even 27 if I count the 1st experience.

[My Black Swans – Ancestor: HP (1939); 60s: Intel (1968); 70s: Microsoft (1975), Oracle (1976), Genentech (1976), Apple (1977); 80s: Cisco (1984); 90s: Amazon (1994), Google (1998); 00s: Facebook (2004).
Age of founders: HP: Hewlett and Packard (27) – Intel: Noyce (41) and Moore (39) (but they had founded fairchild 11 years earlier). Andy Grove was 32 – Microsoft: Gates (20) and Allen (22) – Oracle: Ellison (33) – Genentech: Swanson (29) and Boyer (40) Apple: Jobs (21) and Wozniak (26) Cisco: Lerner and Bosack (29) Amazon: Bezos (30) Google: Brin and Page (25) Facebook: Zuckerberg (20) – Cofounder was 22.]

Now more data and statistics based on the Stanford-related companies. You can have a look first at my past slides and then I look at the Unicorn statistics.

Microsoft PowerPoint - BCERC-Stanford HTE-Lebret.ppt [Mode de co

Basic analysis of Stanford-related unicorns

Stanford unicorns by decade

Stanford unicorns by field

There are 3 super-unicorns in that group (HP, Cisco & Google). Out of 2700, there are 97 unicorns, which is a huge 3%! It probably means my sample is not exhaustive! Indeed Prof. Eesley estimates that 39’900 active companies can trace their roots to Stanford. This means now .2%. Now these are real exits whereas Lee includes private companies with no exit but a value provided by their investors. Whatever the ratio, unicorns are rare. Mine are less fat than Lee’s: they raise $30M with VCs.

I have less than 2 Stanford-related founders per company (but I do not count the ones with no Stanford link. It confirms Lee’s comment that many founders have roots back to school. It takes 8 years for an exit (fewer in recent years though) and 7 years for a graduate to decide about founding a company.

Unicorns and high-value creation is an interesting not to say important topic. Billion-dollar companies are not just a rare event, they tell us something about the impact of high-tech innovation & entrepreneurship. They are possible and desirable!

The Black Swan and Start-ups

I am not sure how many posts I wrote on Taleb’s Black Swan. Whatever, I was asked by EPFL to add a contribution to its relationship with start-ups. This is my eighth contribution on start-ups to the EPFL web site. Here it is:

08.05.13 – What do natural disasters and unusually successful high-tech businesses have in common? They are both statistical outliers, and they both have outsized impact. This is the concept of the “Black Swan.”


The concept of Black Swan was created by Nassim Nicholas Taleb in his works on risk and randomness and popularized by a best-seller published in 2007 and sold over 3 million copies! Taleb explains the concept of Black Swan as follows: “There are two very distinct classes of statistics. The first defines the Mediocristan, the second defines the Extremistan. Without going into much detail, the Mediocristan exceptions occur, but don’t carry large consequences. Add the heaviest person on the planet to a sample of 1000. The total weight would barely change. In Extremistan, exceptions can be everything (they will eventually, in time, represent everything). Add Bill Gates to your sample: the total wealth may increase by a factor of 10,000. The first kind is of “Gaussian-Poisson” nature with thin tails, the second kind is of “fractal” or Mandelbrotian nature, with fat tails. But note here an epistemological question: there is a category of “I don’t know” that I also bundle in Extremistan – simply because I don’t know much about the probabilistic structure or the role of large events.” The Black Swans are unknown events, in Extremistan. These events are rare, very rare, unpredictable and have a huge impact. Ironically, we tend to rationalize them afterwards. The fall of the Berlin Wall, the events of September 11th, the Fukushima accident are examples of Black Swans.

The world of high-tech entrepreneurship is particularly well described with the concepts of Taleb. We have hundreds of start-ups in Switzerland. Thousands of start-ups are founded each year around the world. But a small number grows and survives. An even smaller number will become a great success. Logitech, Swissquote, Actelion in Switzerland. But if it were only about that kind of success, using the concept of Black Swan here would be misleading. Google and Apple are two real Black Swans. The extent of the success of these two former start-ups was simply unpredictable. Many authors have tried to rationalize the success after the fact, but failed, I think. Apple market capitalization is about twice as large as any other company. Steve Jobs, an unlikely entrepreneur, founded it in 1976 at the age of 21 and even more incredibly, he saved it from disaster with his comeback in 1997. Read the new book “I’m Feeling Lucky” on Google’s first steps and you will understand the extraordinary exceptionality of its two founders, Sergei Brin and Larry Page. Google is less than 15 years old, counts more than 50,000 employees and has nearly $40B in revenue.

Taleb is very controversial and provocative. He denounces the excesses of the statistical discipline, which sometimes makes us believe in the elimination of risks. He hates the “wisdom” of scholars to the point of attacking them personally. I remember a conference where the president of the session “blamed” my great passion for high-tech start-ups which according to him is only a fraction of firms. I did not try to hide my bias, but simply pointed out to him that their impact is far from being marginal and also that the field is fascinating in the difficulty in anticipating the potential success. Passion sometimes has to prevail over reason…

Taleb drove the nail with the publication last November of Antifragile, which is subtitled “things that gain from disorder.” This book is a multifaceted, sometimes messy, work, praising the artisan, the souk and the experimenter; he also criticizes the expert, often worn because too rational. Again Taleb’s ideas fit perfectly with innovation. “The fragility of every start-up is necessary for the economy to be antifragile, and that’s what makes, among other things, entrepreneurship work: the fragility of the individual entrepreneurs and their necessarily high failure rate.”

The Black Swan may have a quite simple explanation. It often has its roots in the weaknesses (for disasters) and genius (for the wonders) of the human species. Albert Einstein, Leonardo da Vinci, Steve Jobs and Lionel Messi are creators of genius. It is possible to quantify through science and technology many phenomena, but it is still difficult to measure human capabilities. Black Swans would probably not be as unpredictable if they did not have their root in the human interference in nature.

After the Black Swan, Taleb strikes again with Antifragile

Antifragile, things that gain from disorder by Nassim Nicholas Taleb

Here’s probably one of the toughest post I ever had to write and I am not sure it is a good one, even if the topic I am addressing is great and important. But it’s been a challenge to summarize what I learnt: Nicholas Nassim Taleb gives in this follow-up to the Black Swan a very interesting analysis of how the world can be less exposed to Black Swans, not by becoming more robust only, but by becoming antifragile, i.e. by benefiting from random events. His views include tensions between the individual and the groups, how distributed systems are more robust than centralized ones, how small unites are less fragile than big ones. This does not mean Taleb is against orgamizations, governments or laws as too little intervention induces totally messy situations. It is about putting the cursor at the right level. Switzerland represents for Taleb a good illustration of good state organizations with little central government, a lot of local responsibility. He has similar analogies for the work place, where he explains that an independent worker, who knows well his market, is less fragile to crises than big corporations and their employees. One way to make systems less fragile is to put some noise, some randomness which will stabilize them. This is well-known in science and also in social science. Just remember Athens was randomly nominating some of its leaders to avoid excess!

You can listen to Taleb here:

Now let me quote the author. These are notes only but for serious reviews, visit the author’s website, www.fooledbyrandomness.com/. First Taleb is, as usual, unfair but maybe less than in the Black Swan. Here is an example: “Academics (particularly in social science) seem to distrust each other, […] not to mention a level of envy I have almost never seen in business… My experience is that money and transactions purify relations; ideas and abstract matters like “recognition” and “credit” warp them, creating an atmosphere of perpetual rivalry. I grew to find people greedy for credentials nauseating, repulsive, and untrustworthy.” [Page 17] Taleb is right about envy and rivalry but wrong in saying it is worse in academia; I think it is universal! In politics for example. But when money is available, maybe rivalry counts less than where there is little.

Nassim Nicholas Taleb

Now a topic close to my activity: “This message from the ancients is vastly deeper than it seems. It contradicts modern methods and ideas of innovation and progress on many levels, as we tend to think that innovation comes from bureaucratic funding, through central planning, or by putting people through a Harvard Business School class by one Highly Decorated Professor of Innovation and Entrepreneurship (who never innovated anything) or hiring a consultant (who never innovated anything). This is a fallacy – note for now the disproportionate contribution of uneducated technicians and entrepreneurs to various technological leaps, from the Industrial Revolution to the emergence of Silicon Valley, and you will see what I mean.” [Page 42] [Extreme and unfair again, even if not fully wrong!]

“The antifragility of some comes necessarily at the expense of the fragility of others. In a system, the sacrifices of some units – fragile units, that is, or people – are often necessary for the well-being of other units or the whole. The fragility of every start-up is necessary for the economy to be antifragile, and that’s what makes, among other things, entrepreneurship work: the fragility of the individual entrepreneurs and their necessarily high failure rate”. [Page 65] What surprised me later is that Taleb shows that this is true of restaurants (not many succeed) as much as of high-tech start-ups. So it is not only about the uncertainty of new markets, but about uncertainty above all.

Mathematics of convexity

I have to admit Taleb is not easy to read. Not because it is complex (sometimes his ideas are pure common sense), but because it is dense with different even if consistent ideas. The book is divided in 25 chapters, but also in 7 books. In fact, Taleb insists on it, he might have written 7 different books! Even his mathematics is simple. His definition of convexity is a little strange though I found it interested (I teach convex optimization, and you might not know, it was the topic of my PhD!).

Jensen inequality is interesting [Pages 342, 227 – Jensen was an amateur mathematician!]– the convex transformation of a mean is less or equal than the mean after convex transformation. Again individual (concave, we die) vs. collective (convex, antifragile, benefits from individual failures). So risk taking is good for collectivity if with insurance mechanisms. Risk taking + insurance vs. speculation with no value added. An example of a short and deep idea: “Decision making is based on payoffs, not knowledge”. [Page 337]

“Simply, small probabilities are convex to errors of computation. One needs a parameter, called standard deviation, but uncertainty about standard deviation has the effect of making the small probabilities rise. Smaller and smaller probabilities require more precision in computation. In fact small probabilities are incomputable, even if one has the right model – which we of course don’t.” [Taleb fails to mention Poincare yet he quoted him in the Black Swan, but whatever.]

A visible tension between individual and collective interests

Quotes again: “What the economy, as a collective, wants [business school graduates] to do is not to survive, rather to take a lot, a lot of imprudent risks themselves and be blinded by the odds. Their respective industries improve from failure to failure. Natural and nature-like systems want some overconfidence on the part of the individual economic agents, i.e., the overestimation of their chances of success and underestimation of the risks of failure in their business, provided their failure does not impact others. In other words, they want local, but not global overconfidence”. […] In other words, some class of rash, even suicidal, risk taking is healthy for the economy – under the conditions that not all people take the same risks and that these risks remain small and localized. Now, by disrupting the model, as we will see, with bailouts, governments typically favor a certain class of firms that are large enough to require being saved in order to avoid contagion to other businesses. This is the opposite of healthy risk taking; it is transferring fragility from the collective to the unfit. […] Nietzsche’s famous expression “what does not kill me makes me stronger” can be easily implemented as meaning Mithridatization or Hormesis but it may also mean “what did not kill me did not make me stronger, but it spared me because I am stronger than others; but it killed others and the average population is now stronger because the weak are gone”. […] This visible tension between individual and collective interests is new in history. […] Some of the ideas about fitness and selection are not very comfortable to this author, which makes the writing of some sections rather painful – I detest the ruthlessness of selection, the inexorable disloyalty of Mother Nature. I detest the notion of improvement thanks to harm to others. As a humanist, I stand against the antifragility of systems at the expense of individuals, for if you follow the reasoning, this makes us humans individually irrelevant. ” [Pages 75-77]

A National Entrepreneur Day

“Compare the entrepreneurs to the bean-counting managers of companies who climb the ladder of hierarchy with hardly ever any real downside. Their cohort is rarely at risk. My dream – the solution – is that we would have a National Entrepreneur Day, with the following message: Most of you will fail, disrespected, impoverished, but we are grateful for the risks you are taking and the sacrifices you are making for the sake of the economic growth of the planet and pulling others out of poverty. You are the source of our antifragility. Our nation thanks you.” [Page 80]

Local distributed systems, randomness and modernity

“You never have a restaurant crisis. Why? Because it is composed of a lot of independent and competing small units that do not individually threaten the system and make it jump from one state to another. Randomness is distributed rather than concentrated.” [Page 98]

“Adding a certain number of randomly selected politicians to the process can improve the functioning of the parliamentary system.” [Page 104]

“Modernity is the humans’ large-scale domination of the environment, the systematic smoothing of the world’s jaggedness, and the stifling of volatility and stressors. We are going into a phase of modernity marked by the lobbyist, the very, very limited liability corporation, the MBA, sucker problems, secularization, the tax man, fear of the boss…” [Page 108]

“Iatrogenics means literally “caused by the healer”. Medical error still currently kills between three times (as accepted by doctors) and ten times as many people as car accidents in the United States, it is generally accepted that harm from doctors – not including risks from hospitals germs – accounts for more deaths than any single cancer. Iatrogenics is compounded by the “agency problem” which emerges when one party (the agent) has personal interested that are divorced from those of the one using his services (the principal). An agency problem is present with the stockbroker and medical doctor whose ultimate interest is their own checking account, not your financial and medical health.” [Pages 111-112]

Theories and intervention.

“Theories are super-fragile outside physics. The very designation “theory” is even upsetting. In social science, we should call these constructs “chimeras” rather than theories. [Now you understand why Taleb has many enemies.] A main source of the economic crisis started in 2007 in the Iatrogenics of the attempt by […] Alan Greenspan to iron out the “boom-bust” cycle which caused risks to go hide under the carpet. The most depressing part of the Greenspan story is that the fellow was a libertarian and seemingly convinced of the idea of leaving systems to their own devices; people can fool themselves endlessly. […] The argument is not against the notion of intervention; in fact I showed above that I am equally worried about under-intervention when it is truly necessary. […] We have a tendency to underestimate the role of randomness in human affairs. We need to avoid being blinded to the natural antifragility of systems, their ability to take care of themselves and fight our tendency to harm and fragilize them by not giving them a chance to do so. […] Alas, it has been hard for me to fit these ideas about fragility within the current US political discourse. The democratic side of the US spectrum favors hyper-intervention, unconditional regulation and large government, while the Republican side loves large corporations, unconditional deregulation and militarism, both are the same to me here. Let me simplify my take on intervention. To me it is mostly about having a systematic protocol to determine when to intervene and when to leave systems alone. And we may need to intervene to control the iatrogenics of modernity – particularly the large-scale harm to the environment and the concentration of potential (though not yet manifested) damage, the kind of thing we only notice when it is too late. The ideas advanced here are not political, but risk-management based. I do not have a political affiliation or allegiance to a specific party; rather, I am introducing the idea of harm and fragility into the vocabulary so we can formulate appropriate policies to ensure we don’t end up blowing up the planet and ourselves.” [Pages 116-118]

“To conclude, the best way to mitigate interventionism is to ration the supply of information. The more data you get, the less you know.” [Page 128]

“Political and economic “tail” events are unpredictable and their probabilities are not scientifically measurable.” [Page 133]

The barbell strategy and optionality

“The Barbell strategy is a way to achieve anti-fragility, by decreasing downside rather than increasing upside, by lowering exposure to negative Black Swans. So just as Stoicism is the domestication, not the elimination, of emotions, so is the barbell a domestication, not the elimination, of uncertainty.” [Page 159] “It is a combination of two extremes, one safe and one speculative, deemed more robust than a monomodal strategy. In biological systems, the equivalent of marrying an accountant and having an occasional fling with a rock star; for a writer, getting a stable sinecure and writing without the pressures of the market. Even trial and error are a form of barbell.” [Glossary page 428]

“The strength of the computer entrepreneur Steve Jobs was precisely in distrusting market research and focus groups – those based on asking people what they want – and following his own imagination, his modus was that people don’t know what they want until you provide them with it.” [Page 171]

“America’s asset is simply risk taking and the use of optionality, the remarkable ability to engage in rational forms of trial and error, with no comparative shame in failing, starting again and repeating failure. In modern Japan, by contrast, shame comes, with failure, which causes people to hide risks under the rug, financial or nuclear.”

“Nature does a California-style “fail early” – it has an option and uses it. Nature understands optionality effects better than humans. […] The idea is voiced by Steve Jobs in a famous speech: “Stay hungry, stay foolish.” He probably meant “Be crazy but retain the rationality of choosing the upper bound when you see it.” Any trial and error can be seen as the expression of an option, so long as one is capable of identifying a favorable result and exploiting it.” [Page 181]

“Option is a substitute for knowledge- actually I don’t understand what sterile knowledge is, since it is necessarily vague and sterile. So I make the bold speculation that many things we think are derived by skill come largely from options, but well-used options, much like Thales’s situation [who had an option with olive presses – pages 173-174] rather than from what we claim to be understanding.” [Page 186]

Taleb is skeptical with experts, with anyone believing in a linear model academia -> applied science ->practice (“lecturing birds how to fly”); he believes in tinkering, heuristics, apprenticeship, and makes again many enemies for free! He claims the jet engine, financial derivatives, architecture, medicine were first developed by practitioners and then theorized by scientists, not invented or discovered by them.

Tinkering vs. research

“There has to be a form of funding that works. By some vicious turn of events, governments have gotten huge payoffs from research, but not as intended – just consider the Internet. It is just that functionaries are too teleological in the way they look for things and so are large corporations. Most large companies, such as Big Pharma, are their own enemies. Consider blue sky research, whereby grants and funding are given to people, not projects, and spread in small amounts across many researchers. It’s been reported that in California, venture capitalists tend to back entrepreneurs, not ideas. Decisions are largely a matter of opinion, strengthened with who you know. Why? Because innovations drift, and one needs flâneur-like abilities to keep capturing the opportunities that arise. The significant venture capital decisions were made without real business plans. So if there was any analysis, it had to be of a backup, confirmatory nature. Visibly the money should go to the tinkerers, the aggressive tinkerers who you trust will milk the option.” [Page 229]

“Despite the commercial success of several companies and the stunning growth in revenues for the industry as a whole, most biotechnology firms earn no profit.” [Page 237] [Optionality again]

“(i) Look for optionality; in fact, rank things according to optionality, (ii) preferably with open-ended, not closed-ended, payoffs; (iii) do not invest in business plans but in people, so look for someone capable of changing six or seven times over his career, or more (an idea that is part of the modus operandi of the venture capitalist Marc Andreessen); one gets immunity from the backfit narratives of the business plan by investing in people. Make sure you are barbelled, whatever that means in your business.” [Page 238]

“I did here just debunk the lecturing-Birds-How-to-Fly epiphenomenon and the “linear model”, suing simple mathematical properties of optionality. There Is no empirical evidence to support the statement that organized research in the sense it is currently marketed leads to great things promised by universities. [Cf also Thiel lamentations about the promise of technologies – https://www.startup-book.com/2010/10/12/tech-equals-salvation/ ] Education is an institution that has been growing without external stressors; eventually the thing will collapse.” [A conclusion to book IV, page 261]

Why is fragility non linear?

“For the fragile, the cumulative effect of small shocks is smaller than the single effect of an equivalent single large shock. For the antifragile, shocks bring more benefits (equivalently, less harm) as their intensity increases (up to a point).”

Via negativa

“We may not need a name for or even an ability to express anything. We may just say something about what it is not. Michelangelo was asked by the pope about the secret of his genius, particularly how he carved the statue of David. His answer was: It’s simple, I just remove everything that is not David.” [Page 302-304]

[…] “Charlatans are recognizable in that they will give you positive advice. Yet in practice, it is the negative that’s used by the pros. One cannot really tell if a successful person has skills, or if a person with skills will succeed – but we can pretty much predict the negative, that a person totally devoid of skills will eventually fail.”

[…] “The greatest – most robust – contribution to knowledge consist in removing what we think is wrong. We know a lot more what is wrong than what is right. Negative knowledge is more robust to error than positive knowledge. […] Since one small observation can disprove a statement, while millions can hardly confirm it [The Black Swan!], disconfirmation is more rigorous than confirmation. […] Let us say that, in general, failure (and disconfirmation) are more informative than success and confirmation.”

[Funnily, I remember the main critics against my book were the lack of [positive] proposal in the end. I should have said there we many about what not to do!]

“Finally, consider this modernized version in a saying from Steve Jobs: “People think focus means saying yes to the thing you’ve got to focus on. But that’s not what it means at all. It means saying no to the hundred other good ideas that there are. You have to pick carefully. I’m actually as proud of the things we haven’t done as the things I have done. Innovation is saying no to 1,000 things.” [Page 302-304]

Less is more

“Simpler methods for forecasting and inference can work much, much better than complicated ones. “Fast and frugal” heuristics make good decisions despite limited time. First extreme effects: there are domains in which the rare event (good or bad) plays a disproportionate share and we tend to be blind to it. Just worry about Black Swan exposures and life is easy. There may not be an easily identifiable cause for a large share of the problems, but often there is an easy solution, sometimes with the naked eye rather than the use of the complicated analyses. Yet people want more data to solve problems.” [Page 305-306]

“The way to predict rigorously is to take away from the future, reduce from it things that do not belong to the coming times. What is fragile will eventually break, and luckily we can easily tell what is fragile. Positive Black Swans are more unpredictable than negative ones. Now I insist on the via negativa method of prophecy as being the only valid one.” [Page 310]

“For the perishable, every additional day in the life translates into a shorter additional life expectancy. For the non perishable, every additional day may imply a longer life expectancy. On general, the older the technology, the longer it is expected to last. I am not saying that all technologies do not age, only that those technologies that were prone to aging are already dead.” [Page 319]

“How can we teach children skills for the twenty-first century, since we do not know which skills will be needed? Effectively my answer would make them read the classics. The future is in the past. Actually there is an Arabic proverb to that effect: he who does not have a past has no future.” [Page 320]

[As can be read later in the book Taleb does not like the Bay Area culture. And it is no coincidence, it is a region with nearly no past, nearly no history, but it certainly help it create Silicon Valley innovations…]

“If you have an old oil painting and a flat screen television, you will never mind changing the television, not the painting. Same with an old fountain pen and the latest Apple computer; [Taleb is really cautious with modernity and innovation, even if a user of it. With architecture, he has similar concerns. Again he prefers tradition to aggressive modernity. Same with the metric system vs. old methods] Top-down is usually irreversible, so mistakes tend to stick, whereas bottom-up is gradual and incremental, with creation and destruction along the way, thought presumably with a positive slope.” [Pages 323-24]

“So we can apply criteria of fragility and robustness to the handling of information – the fragile in that context is, like technology, what does not stand the test of time. […] Books that have been around for ten years will be around for ten more; books that have been around for two millennia should be around for quite a bit of time. […] The problem in deciding whether a scientific result or a new “innovation” is a breakthrough, that is, the opposite of noise, is that one needs to see all aspects of the idea – and there is always some opacity that time, and only time, can dissipate.” [Page 329]

“Now, what is fragile? The large, optimized, overreliance on technology, overreliance on the so-called scientific method instead of age-tested heuristics.”

“By issuing warnings based on vulnerability – that is, substractive prophecy – we are closer to the original role of the prophet: to warn, not necessarily to predict, and to predict calamities if people don’t listen.”


“Under opacity and complexity, people can hide risks and hurt others. Skin in the game is the only true mitigator of fragility. We have developed a fondness for neomanic complication over archaic simplicity. […] The worst problem of modernity lies in the malignant transfer of fragility and antifragility from one party to the other, with one getting the benefits, the other one (unwittingly) getting the harm, with such transfer facilitated by the growing wedge between the ethical and the legal. Modernity hides it especially well. It is of course an agency problem.” [Page 373]

[You can/should have a look at table 7, page 377]

“In traditional societies, a person is only respectable and as worthy as the downside he (or, more, a lot more, than expected, she) is willing to face for the sake of others.” [Page 376]

“I want predictors to have visible scars on their body from prediction errors, not distribute these errors to society.” [Page 386]

[Don Quixote was already the sign of the end of the heroism, of the ethical behavior. Taleb’s models are Malraux and Ralph Nader – “the man is a secular saint” [Page 394]. His enemies Thomas Friedman, Rubin and Stieglitz]

[Is “skin in the game” the only way? The only solution? What about transparency?]

About Science

“Science must not be a competition; it must not have rankings – we can see how such a system will end up blowing up. Knowledge must not have an agency problem. One doctoral student once came to tell me that he believed in my ideas of fat tails and my skepticism of current methods of risk management, but that it would not help him get an academic job. “It’s what everybody teaches and uses in papers” he said. Another student explained that he wanted a job at a good university, so he could make money testifying as an expert witness – they would not buy my idea on robust risk management because “everyone uses these textbooks”. [Page 419]

[So true! Check The Trouble with Physics.]


“All I want is to remove the optionality, reduce the antifragility of some at the expense of others. It is simple via negativa. […] The golden rule: “Don’t do unto others what you don’t want them to do to you”. […] Everything gains or loses from volatility. Fragility is what loses from volatility or uncertainty. […] Time is volatility. Education in the sense of the formation of the character, personality, and acquisition of true knowledge, likes disorder; label-driven education and educators abhor disorder. Innovation is precisely something that grains from uncertainty.” [Pages 420-22]

“It so happens that everything nonlinear is convex, concave or both. […] We can build Black-Swan-protected systems thanks to detection of concavity, […] and with a mechanism called convex transformation, the fancier name for the barbell. […] Distributed randomness (as opposed to the concentrated type) is a necessity.”

[General comments]

Taleb sometimes gives the feeling of contradictions: marketing is bad, but Steve Jobs is great; barbell strategy and optionality is great, but isn’t it about risks and downsides transferred to others [Isn’t Thales a pure speculator?], cigarettes are bad but traditions are good.

Also this love of tradition makes people with more background at ease to take risks with barbell strategy; but what about the poor with nothing to lose? Benefits might statistically go to those who already have… [It reminds the story told by J.-B. Doumeng: It is a millionaire who recounts his difficult beginnings: “I bought an apple 50 cents, I polished it to shine and I sold it for one franc. With this, I bought two apples 50cts, I carefully polished and I sold them 2 Fr after a moment, I could buy a cart to sell my apples and then I made a big inheritance … “]

You now know why it has been a challenge. A very strange, dense, fascinating book, but if you like these concepts, you must read Antifragile. In fact you must read the Black Swan first, if you have not and if you like it, I am sure you will read Antifragile.

The Black Swan again

If you understand French, you might be interested in how I explained the Black Swan on French-speaking radio broadcast Babylon on Espace 2. You just have to click on the picture. Many thanks to Jean-Marc Falcombello for the time he gave me to describe Taleb’s ideas. It is 19 minutes long – between 23:15 and 42:00.

I am less sure this works: http://www.rts.ch/espace-2/programmes/babylone/4203353-moi-je-ne-bluffe-pas-l-insoutenable-legerete-de-l-incertitude-30-08-2012.html?f=player/popup

The Black Swan and the danger of statistics

“Thought is only a flash in the middle of a long night. But this flash means everything.”
Henri Poincaré*

When I talked to friends and colleagues about The Black Swan (“BS”), they were surprised about my interest in the movie with Natalie Portman. I cannot say, I have not watched it. I was talking about Nassem Nicholas Taleb’s book and theory. Some other friends classified at it as American b… s…, these superficial books that give advice on anything and that seem to always become bestsellers; my colleagues would classify it as airport literature, not to be read in academic circles.

I read it and enjoyed it, but I have to admit Taleb is sometimes painful. Is it because he was so much frustrated by I do not know whom or what or is it because he is so proud of his certainties? I am not sure. But his ideas are certainly worth thinking about more than a minute. (Whereas you forget about airport American b… s… after 30 seconds). So back to the BS.

You’ll find great accounts of his book or of his theory, e.g.
– Nassim Taleb’s “The Black Swan” by Andrew Gelman,
– The Wikipedia page on the Black Swan theory
– or even another essay by Taleb, the Fourth Quadrant,
so I will not try to do the same.

However defining the Black Swan might be useful! In the Fourth Quadrant, Taleb writes the following:

There are two classes of probability domains—very distinct qualitatively and quantitatively. The first, thin-tailed: Mediocristan”, the second, thick tailed Extremistan. Before I get into the details, take the literary distinction as follows: In Mediocristan, exceptions occur but don’t carry large consequences. Add the heaviest person on the planet to a sample of 1000. The total weight would barely change. In Extremistan, exceptions can be everything (they will eventually, in time, represent everything). Add Bill Gates to your sample: the wealth will jump by a factor of >100,000. So, in Mediocristan, large deviations occur but they are not consequential—unlike Extremistan. Mediocristan corresponds to “random walk” style randomness that you tend to find in regular textbooks (and in popular books on randomness). Extremistan corresponds to a “random jump” one. The first kind I can call “Gaussian-Poisson”, the second “fractal” or Mandelbrotian (after the works of the great Benoit Mandelbrot linking it to the geometry of nature). But note here an epistemological question: there is a category of “I don’t know” that I also bundle in Extremistan for the sake of decision making—simply because I don’t know much about the probabilistic structure or the role of large events. Black Swans are the unknown deviations in Extremistan.

Here are more notes taken while reading.

[Page xxii] The black swan is characterized by “rarity, extreme impact and retrospective (though not prospective) predictability” (with additional footnote: the occurrence of a highly improbably event is the equivalent of the nonoccurrence of a highly probably one.

[Page 8] The human mind suffers from 3 aliments:
-The illusions of understanding, or how everyone thinks he knows what is going on in a world that is more complicated (or random) than they realize;
-the retrospective distortion, or how we can assess matters only after the fact, as if they were in a rearview mirror; and
-the overvaluation of factual information and the handicap of authoritative and learned people – when they platonify.

[Page 15] While in the past a distinction had been between drawn Mediterranean and non- Mediterranean (i.e., between the olive oil and the butter), in the 1970s, the distinction suddenly became between Europe and non-Europe.

[Page 54] There is a major difference and often-made mistake between no evidence of something and the evidence of its non-occurence (mental bias.)

[Page 77] The answer is that there are two varieties of rare events: a) the narrated Black Swans, those that are present in the current discourse and that you are likely to hear about on television, and b) those nobody talks about, since they escape models – those that you would feel ashamed discussing in public because they do not seem plausible. I can safely say that it is entirely compatible with human nature that the incidences of Black Swans would be overestimated in the first case, but severely underestimated in the second one.

[Page 80] One death is a tragedy; a million is a statistic. […] We have two systems of thinking. System 1 is experiential, effortless, automatic, fast, and opaque. System 2 is thinking, reasoned, local, slow, serial, progressive. Most mistakes come from using system 1 when we think we use system 2.

[Page 140] We overestimate what we know and underestimate uncertainty. Another bias, ”think about how many people divorce. Almost all of them are acquainted with the statistic that between one-third and one-half of all marriages fail, something the parties involved did not forecast while tying the know. Of course, “not us” because “we get along so well” (as if others tying the know got along poorly.)”

[Page 174-179] Poincaré is a central personality of Taleb’s theory, in particular through the 3-body problem. According to Taleb, “Poincaré angrily disparages the use of the bell curve.” Now the next figure simply illustrates the concept of sensitivity to initial conditions.


Operation 1: imagine an ice cube and consider how it may melt.
Operation 2: consider a puddle of water. Try to reconstruct the shape of the ice-cube.
The forward process is generally used in physics and engineering, the backward process in nonrepeatable, nonexperimental historical approaches. And the backward is much more complex to analyze.

[Page 198] While in theory it is an intrinsic property. In practice, randomness is incomplete information. Nonpractitioners do not understand the subtlety. A true random process does not have predictable properties. A chaotic system has entirely predictable properties, but they are hard to know.
a) There are no functional differences in practice between the two since we will never get to make the distinction.
b) The mere fact that a person is talking about the difference implies he has never made a meaningful decision under uncertainty – which is why he does not realize that they are indistinguishable in practice.
Randomness in practice, in the end, is just unknowledge. The world is opaque and appearances fool us.

[Page 204] Trial and error means trying a lot. In the Blind Watchmaker, Richard Dawkins brilliantly illustrates this notion of the world without grand design, moving by small incremental random changes. Note a slight disagreement on my part that does not change the story by much: the world, rather moves by large incremental random changes. Indeed, we have psychological and intellectual difficulties with trial and error and with accepting that series of small failures are necessary in life. “You need to love to lose”. In fact the reason I felt immediately at home in America is precisely because American culture encourages the process of failure, unlike the cultures of Europe and Asia where failure is met with stigma and embarrassment.
[It’s really Taleb writing and not the blog’s author, but I fully agree !]

[Page 207] When you have a very limited loss, you need to be as aggressive as speculative and sometimes as unreasonable as you can be. Middlebrow thinkers sometimes make the analogy with lottery tickets. It is plain wrong. First lottery tickets do not have a scalable payoff. Second, lottery tickets have known rules.

The economics of superstars

[Page 24] Who is this book written for? You need to understand who your audience is and amateurs write for themselves, professionals write for others. [This irony of the author’s is stimulating. I experienced it, I’m an amateur. But are the masterpieces not then written by amateurs? The Black Swans (The Lord of the Rings, Harry Potter) look often like a work of amateurs. The Yevgenia Krasnova example provided by Taleb is also stimulating]

[Page 214] Someone who is marginally better can easily win the entire pot. The problem is the notion of “better.” People take from the poor to give to the rich. An initial advantage follows someone through life and keep getting cumulative advantages. Failure is also cumulative. The advent of modern media has accelerated these cumulative advantages. The sociologist Pierre Bourdieu noted a link between the increased concentration of success and the globalization of culture and economic life.

[Page 221] Taleb claims new comers mitigate the cumulative advantages. “of the five hundred largest US companies in 1957, only seventy-four were still part of that select group, the S&P 500, forty year later. Only a few hundred had disappeared in mergers; the rest either shrank or went bust.

Actors who win an Oscar tend to live on average five years longer than their peers who don’t. People live longer in societies that have flatter social gradients.

[Page 277] What is poorly understood is the absence of a role for the average in intellectual production. The disproportionate share of the very few in intellectual influence is even more unsettling than the unequal distribution of wealth- unsettling because, unlike the income gap, no social policy can eliminate it. Communism could conceal or compress income discrepancies, but it could not eliminate the superstar system in intellectual life. [I am not sure]


Taleb defines himself as a skeptic and his mentor are Hayek and Popper. He links it with humility in the following: [Page 190] Someone with a low degree of epistemic arrogance is not too visible, like a shy person at a cocktail party. We are not predisposed to respect humble people, those who try to suspend judgment. Now contemplate epistemic humility. Think of someone heavily introspective, tortured by the awareness of his own ignorance. He lacks the courage of the idiot, yet has the rare gust to say “I don’t know”. He does not mind looking like a fool or, worse, an ignoramus. He hesitates, he will not commit, and he agonizes over the consequences of being wrong. He introspects, introspects, and introspects until he reaches physical and nervous exhaustion.


[Page 146] We know the difference between know-how and know-what. The Greeks made a distinction between techne and episteme, craft and knowledge. We have experts who tend to be experts: astronomers, pilots, physicists, mathematicians, accountants and experts who tend to be… note experts: stockbrokers, psychologists, councilors… Simply things that move and therefore require knowledge do not usually have experts and are often Black-Swan-prone. The negative effect of prediction is that those who have a big reputation are worse predictors than those who had none.

[Page 166] The classical model of discovery is as follows: you search for what you know (say, a new way to reach India) and find something you didn’t know was there (America). It’s called serendipity. A term coined in a letter by the writer Hugh Walpole who derived it form a fairy tale, “The Three Princes of Serendip” who “were always making discoveries by accident or sagacity, of things they were not in quest of.“ […] Sir Francis Bacon commented that the most important advances are the least predictable ones.

[Page 169] Engineers tend to develop tools for the pleasure of developing tools. Tools lead to unexpected discoveries. So I disagree with Taleb’s definition: A nerd is simply someone who thinks exceedingly inside the box. It may not be contradictory but I prefer the engineer-like one: “I think a nerd is a person who uses the telephone to talk to other people about telephones. And a computer nerd therefore is somebody who uses a computer in order to use a computer. [https://www.startup-book.com/2012/02/03/triumph-of-the-nerds/]
And [Page 170] Pasteur claims “Luck favors the prepared”

[Page 170] On the difficulty of predicting, just look at the failure of the Segway which “it was prophesized, would change the morphology of cities.”

[Page 184] Another example of Taleb’s target: optimization… Optimization consists in finding the mathematically optimal policy that an economic agent could pursue. Optimization is a case of sterile modeling [discussed also in Chpater 17].


[Page 16] Categorization always produces a reduction in true complexity. Try to explain why those who favor allowing the elimination of a fetus in the mother’s womb also oppose capital punishment. [Which reminds me of André Frossard : “The unfortunate thing is that the left does not believe much in original sin and that the right has not much faith in redemption.”]

[Page 52] “I never meant that the Conservatives are generally stupid. I meant to say that stupid people are generally conservative” John Stuart Mill once complained. The problem is chronic: if you tell people that the key to success is not always skills, they think that you are telling them that it is never skills always luck.”

[Page 227] Which may explain “we live in a society of one person, one vote, where progressive taxes have been enacted precisely to weaken the winners”. I am not sure if Taleb does not prefer the aristocratic world. At least he seems to favor his friends from that world.

[Page 255] True, intellectually sophisticated characters were exactly what I looked for in life. My erudite and polymathic father – who, were he still alive, would have only been two weeks older than Benoît Mandelbrot [his mentor on non-linear fractals] – liked the company of extremely cultured Jesuit priests. I remember these Jesuit visitors […] I recall that one has a medical degree and a PhD in physics, yet taught Aramaic to locals in Beirut’s Institute of Eastern Languages. […] This kind of erudition impressed my father far more than scientific assembly-line work. I may have something in my genes dirving me away from bildungsphilisters.


[Page 28] a scalable profession is good only if you are successful; they are more competitive, produce monstrous inequalities and are far more random. Consider the example of the first music recording, of the alphabet, of the printing press. Today a few take almost everything; the rest, next to nothing [page 30].

[Page 32] In Mediocristan,” when your sample is large, no single instance will significantly change the aggregate or the total”. In Extremistan, Bill Gates in wealth or J. K. Rowling in book selling totally change the average of a crowd. “Almost all social matters are from Extremistan.” [When giving a talk on high-tech serial entrepreneurs at BCERC last month, I was slightly criticized with a “but you are only looking at 2% of the entrepreneurs! And I replied, yes but look at the impact…”]

[Page 85] Intellectual, scientific, and artistic activities belong to the province of Extremistan. I am still looking for a single counter-example, a non-dull activity that belongs to Mediocristan.

[Page 90] You not only see that venture capitalists do better than entrepreneurs, but publishers do better than authors, dealers do better than artists, and science does better than scientists.” (I can add that gold seekers made less money than the people who sold them picks and shovels.)

[Page 102] The consequence of the superstar dynamic is that what we call “literary heritage” or “literary treasures” is a minute proportion of what has been produced cumulatively. Balzac was just the beneficiary of disproportionate luck compared to his peers.

[Page 118] The problem here with the universe and the human race is that we are the surviving Casanovas (who should not have survived and had his life without luck – no destiny].


Taleb is not against statistics, but against Gaussian law, averages, etc. [Page 37] “The near-Black Swan are somewhat tractable. These are phenomena commonly known by terms such as scalable, scale-invariant, power laws, Pareto-Zipf laws, Yule’s law, Paretian-stable processes, Levy-stable and fractal laws.”

One thousand and one days or the story of the turkey confirms to me that an individual may not owe to the society that fed them initially!

[Page 239] 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 (which includes various friends and relatives, such as the Poisson law) 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. There are other notions that have little or no significance outside of the Gaussian: correlation and worse, regression. Yet they are deeply ingrained in our methods: it is hard to have a business conversation without hearing the word correlation.

[Page 240] Taleb has nothing against mathematicians, but he refers to Hardy’s views: The “real” mathematics of the “real” mathematicians, the mathematics of Fermat end Euler and Gauss and Abel and Riemann, is almost wholly “useless” (and this is as true of “applied” as of “pure” mathematics).

[Page 252] A critical feature of Gaussian statistics is the inclusion of two assumptions: First central assumption: the flips are independent of one another. The coin has no memory. The fact that you got heads or tails on the previous flip does not change the odds of your getting heads or tails on the next one. You do not become a “better” coin flipper over time. If you introduce memory, or skills in flipping, the entire Gaussian business becomes shaky. (Whereas there is preferential attachment and cumulative advantage in non-Gaussian events.) Second central assumption: no “wild” jump. The step size in the building block of the basic random walk is always known, namely one step. There is no uncertainty as to the size of the step.
[…] I have not for the life of me been able to find anyone around me in the business and statistical world who was intellectually consistent in that he both accepted the Black Swan and rejected the Gaussian and Gaussian tools. Many people accepted my Black Swan idea but could not take its logical conclusion, which is that you cannot use one single measure for randomness called standard deviation (and call it “risk”), you cannot expect a simple answer to characterize uncertainty.

But Taleb goes one step further. [Page 272] “But fractal randomness does not yield precise answer. […] Mandelbrot’s fractals allow us to account for a few Black Swans but not all. […] A gray swan concerns modelable extreme events, a black swan is about unknown unknowns. […] I repeat: Mandelbrot deals with gray swans; I deal with the Black Swan. So Mandelbrot domesticated many of my Black Swans, but not all of them, not completely.


Taleb shows that the stock crashes are sometimes linked to bad modeling and is particularly critical of the Black-Scholes options. He is very much critical of the stock portfolio theories and related Nobel prizes (Markowitz, Samuelson, Hicks or Debreu, “wrecking the ideas of Keynes”. The story of the LTCM hedge fund is an illustration of Taleb’s points.

Business and technology

[Page xxv] Almost no discovery, no technologies of note came from design and planning – they were just Black swans. […] So I disagree with the followers of Marx and those of Adam Smith: the reason free markets work is because they allow people to be lucky thanks to aggressive trial and error, not by giving rewards or “incentives” for skill.

[Page 17] The business world – inelegant, dull, pompous, greedy, unintellectual, selfish and boring.
[…] What I saw was that in some of the most prestigious business schools in the world, the executives of the most powerful corporations were coming to describe what they did for a living and it was possible that they too did not know what was going on.

[Page 135] When I ask people to name three recently implemented technologies that most impact our world today, they usually propose the computer, the Internet and the laser. All three were unplanned, unpredicted and unappreciated upon their discovery, and remained unappreciated well after their initial use. They were consequential. They were Black Swans.

Against averages

[Page 295] Half of the time I am a hyperskeptic; the other half I hold certainties. […] Half of the time I hate Black Swans, the other half I love them. […] Half of the time I am hyperconservative; the other half I am hyperaggressive”. I could delete the quotes!

I am not fully finished with the Black Swan, I am now reading the 70-page postcript essay which Taleb added to the latest paperback edition. There might be more to say (and read if you followed me until now…)

* Poincaré is quoted in Le Monde on July 7, 2012, by Cedric Villani, who by the way also mentions Black Swans in Dans les entrailles des cygnes noirs