The Black Swan by Nassim Taleb

Summary

Changed my thinking about sudden, unexpected events. It provides models that help maximize the potential for sudden success while minimizing the risk of sudden ruin. The writing style is not for everyone.

Key Takeaways

A Black Swan
- Is an outlier that lies outside the realm of regular expectations.
- Carries an extreme impact.
- Makes us concoct explanations for its occurrence after the fact.
Being aware of what you don’t know is far more relevant than being aware of what you do know.
Ideas come and go, stories stay.
Scalable vs unscalable professions: Separate the “idea” person, who sells an intellectual product in the form of a transaction or a piece of work, from the “labour” person, who sells you his work. Pick the type that suits your nature and skill set.
Almost all social matters are from Extremistan. Another way to say it is that social quantities are informational, not physical.
You can eliminate a Black Swan by science (if you’re able), or by keeping an open mind.
Awareness of a problem does not mean much – particularly when you have special interests and self-serving institutions in play.
We can get closer to the truth by negative instances, not by verification!
Blindness to the Black Swan:
- Confirmation bias
- Narrative fallacy
- We behave as if the Black Swan does not exist
- Silent evidence
- We “tunnel”: that is, we focus on a few well-defined sources of uncertainty, on too specific a list of Black Swans (at the expense of the others that do not easily come to mind
People overreact to low-probability outcomes when you make them aware of the event.
How to avert the Narrative Fallacy
- Favour experimentation over storytelling, experience over history, and clinical knowledge over theories.
- Predict and keep a tally of the predictions.
- Use a narrative for a good purpose: write in a diary.

Silent evidence: to understand successes and analyze what caused them, we need to study the traits present in failures.
In real life you do not know the odds; you need to discover them, and the sources of uncertainty are not defined.
We are arrogant about what we think we know.
It is the lower bound of estimates (i.e., the worst case) that matters when engaging in a policy – the worst case is far more consequential than the forecast itself.
The wise one is the one who knows that he cannot see things far away.
The forward process is generally used in physics and engineering; the backward process in nonrepeatable, nonexperimental historical approaches.
Know how to rank beliefs not according to their plausibility but by the harm they may cause.
Asymmetric returns: put yourself in situations where favourable consequences are much larger than unfavourable ones.
- Barbell strategy: be as hyperconservative and hyperaggressive as you can be instead of being mildly aggressive or conservative.
- Dealing with uncertainty: focus on the payoff over the probability. Probabilities are often guesses, thus unknown.
Contagious mental categories must be those in which we are prepared to believe, perhaps even programmed to believe. To be contagious, a mental category must agree with our nature.
Capitalism is the revitalization of the world thanks to the opportunity to be lucky.
The Gaussian–bell curve variations face a headwind that makes probabilities drop at a faster and faster rate as you move away from the mean, while “scalables,” or Mandelbrotian variations, do not have such a restriction.
My technique, instead of studying the possible models generating non-bell curve randomness, hence making the same errors of blind theorizing, is to do the opposite: to know the bell curve as intimately as I can and identify where it can and cannot hold.
In the absence of a feedback process you look at models and think that they confirm reality.
Study the intense, uncharted, humbling uncertainty in the markets as a means to get insights about the nature of randomness that is applicable to psychology, probability, mathematics, decision theory, and even statistical physics.
Two common classes of Extremistan:
- Rich-get-richer
- Percolation theory

What I got out of it

While Fooled By Randomness focused on making me aware of “randomness,” The Black Swan is a much more practical and insightful book.

Nassim Taleb covers many instances in which the world is distributed more according to fractals or power laws, rather than a normal distribution, how randomness and (extreme) Black Swan events operate in these environments and the role of various biases and fallacies.

Taleb writes in a very aggressive and somewhat condescending style in this book. It made me enjoy it much less than his other works. I also feel that the book could’ve been written in 50~70% the number of pages.

Content-wise, I still like the book. It made me wonder and question many things, and all the name drops gives you plenty of deep-dive material, if wanted.

Some concepts that changed my thinking:

Scalable vs unscalable professions.
Silent evidence and the importance of studying failures.
Being aware of what you don’t know is far more relevant than being aware of what you do know.
Instead of studying and theorizing models of how something works, study the applications and limitations of the opposite.

Summary Notes

Prologue

A Black Swan is an event with the following three attributes.

It is an outlier, as it lies outside the realm of regular expectations because nothing in the past can convincingly point to its possibility.
It carries an extreme impact.
In spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

Black Swan logic makes what you don’t know far more relevant than what you do know. Consider that many Black Swans can be caused and exacerbated by their being unexpected.

What is surprising is not the magnitude of our forecast errors, but our absence of awareness of it.

Another related human impediment comes from excessive focus on what we do know: we tend to learn the precise, not the general.

Who gets rewarded, the central banker who avoids a recession or the one who comes to “correct” his predecessors’ faults and happens to be there during some economic recovery? Who is more valuable, the politician who avoids a war or the one who starts a new one (and is lucky enough to win)?

Everybody knows that you need more prevention than treatment, but few reward acts of prevention.

Models and constructions, these intellectual maps of reality, are not always wrong; they are wrong only in some specific applications. The difficulty is that

You do not know beforehand (only after the fact) where the map will be wrong, and
The mistakes can lead to severe consequences. These models are like potentially helpful medicines that carry random but very severe side effects

Ideas come and go, stories stay.

Naïve empiricism – successions of anecdotes selected to fit a story do not constitute evidence. Anyone looking for confirmation will find enough of it to deceive himself – and no doubt his peers.

We focus on the known, the repeated, but should instead use the extreme event as a starting point and not treat it as an exception to be pushed under the rug.

The Apprenticeship Of An Empirical Skeptic

The human mind suffers from three ailments as it comes into contact with history, what I call the triplet of opacity. They are:

the illusion 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 (history seems clearer and more organized in history books than in empirical reality);
the overvaluation of factual information and the handicap of authoritative and learned people

Our minds are wonderful explanation machines, capable of making sense out of almost anything, capable of mounting explanations for all manner of phenomena, and generally incapable of accepting the idea of unpredictability.

Categorizing always produces reduction in true complexity. Any reduction of the world around us can have explosive consequences since it rules out some sources of uncertainty; it drives us to a misunderstanding of the fabric of the world.

The historian Niall Ferguson showed that, despite all the standard accounts of the buildup to the Great War, which describe “mounting tensions” and “escalating crises,” the conflict came as a surprise. Only retrospectively was it seen as unavoidable by backward-looking historians. Ferguson used a clever empirical argument to make his point: he looked at the prices of imperial bonds, which normally include investors’ anticipation of government’s financing needs and decline in expectation of conflicts since wars cause severe deficits. But bond prices did not reflect the anticipation of war.

Working with (historical) prices can provide a good understanding of history.

The Speculator And The Prostitute

Get a profession that is “scalable,” that is, one in which you are not paid by the hour and thus subject to the limitations of the amount of your labour.

Separate the “idea” person, who sells an intellectual product in the form of a transaction or a piece of work, from the “labour” person, who sells you his work.

If you are an idea person, you do not have to work hard, only think intensely. You do the same work whether you produce a hundred units or a thousand. You can use leverage as a replacement for work.

The distinction between writer and baker, speculator and doctor, fraudster and prostitute, is a helpful way to look at the world of activities. It separates those professions in which one can add zeroes of income with no greater labour from those in which one needs to add labour and time (both of which are in limited supply) – in other words, those subjected to gravity.

I would recommend someone pick a profession that is not scalable! A scalable profession is good only if you are successful; they are more competitive, produce monstrous inequalities, and are far more random, with huge disparities between efforts and rewards – a few can take a large share of the pie, leaving others out entirely at no fault of their own.

Supreme law of Mediocristan: When your sample is large, no single instance will significantly change the aggregate or the total. The largest observation will remain impressive, but eventually insignificant, to the sum.

In Extremistan, inequalities are such that one single observation can disproportionately impact the aggregate or the total.

So while weight, height, and calorie consumption are from Mediocristan, wealth is not. Almost all social matters are from Extremistan. Another way to say it is that social quantities are informational, not physical: you cannot touch them.

What you can know from data in Mediocristan augments very rapidly with the supply of information. But knowledge in Extremistan grows slowly and erratically with the addition of data, some of it extreme, possibly at an unknown rate.

Mediocristan is where we must endure the tyranny of the collective, the routine, the obvious, and the predicted; Extremistan is where we are subjected to the tyranny of the singular, the accidental, the unseen, and the unpredicted.

One Thousand And One Days, Or How Not To Be A Sucker

Mistaking a naïve observation of the past as something definitive or representative of the future is the one and only cause of our inability to understand the Black Swan.

A Black Swan Is Relative to Knowledge

From the standpoint of the turkey, the nonfeeding of the one thousand and first day is a Black Swan. For the butcher, it is not, since its occurrence is not unexpected. So you can see here that the Black Swan is a sucker’s problem. It occurs relative to your expectation. You realize that you can eliminate a Black Swan by science (if you’re able), or by keeping an open mind.

Matters should be seen on some relative, not absolute, timescale: earthquakes last minutes, 9/11 lasted hours, but historical changes and technological implementations are Black Swans that can take decades. Positive Black Swans take time to show their effect while negative ones happen very quickly.

Doubting the consequences of an outcome will allow you to remain imperturbable. The Pyrrhonian sceptics were docile citizens who followed customs and traditions whenever possible, but taught themselves to systematically doubt everything, and thus attain a level of serenity. But while conservative in their habits, they were rabid in their fight against dogma.

Awareness of a problem does not mean much – particularly when you have special interests and self-serving institutions in play.

Other themes arising from our blindness to the Black Swan:

We focus on preselected segments of the seen and generalize from it to the unseen: the error of confirmation.
We fool ourselves with stories that cater to our Platonic thirst for distinct patterns: the narrative fallacy.
We behave as if the Black Swan does not exist: human nature is not programmed for Black Swans.
What we see is not necessarily all that is there. History hides Black Swans from us and gives us a mistaken idea about the odds of these events: this is the distortion of silent evidence.
We “tunnel”: that is, we focus on a few well-defined sources of uncertainty, on too specific a list of Black Swans (at the expense of the others that do not easily come to mind).

Confirmation Shmonfirmation!

The round-trip fallacy: these statements are not interchangeable.

There is no evidence of the possibility of large events.
There is evidence of no possible Black Swans.

Domain specificity of our reactions: our reactions, our mode of thinking, our intuitions, depend on the context in which the matter is presented.

We react to a piece of information not on its logical merit, but on the basis of which framework surrounds it, and how it registers with our social-emotional system.

We can get closer to the truth by negative instances, not by verification!
This asymmetry is immensely practical. It tells us that we do not have to be complete sceptics, just semisceptics. The subtlety of real life over the books is that, in your decision-making, you need be interested only in one side of the story: if you seek certainty about whether the patient has cancer, not certainty about whether he is healthy, then you might be satisfied with negative inference since it will supply you the certainty you seek.

Conjectures and refutations: you formulate a (bold) conjecture and you start looking for the observation that would prove you wrong. This is the alternative to our search for confirmatory instances.

Hempel’s raven paradox: Observing objects that are neither black nor ravens may formally increase the likelihood that all ravens are black even though, intuitively, these observations are unrelated.

We come equipped with mental machinery that causes us to selectively generalize from experiences. By doing so, we are not learning from a mere thousand days, but benefiting, thanks to evolution, from the learning of our ancestors – which found its way into our biology.

Once your mind is inhabited by a certain view of the world, you will tend to only consider instances proving you to be right. Paradoxically, the more information you have, the more justified you will feel in your views.

The Narrative Fallacy

Narrative fallacy: The fallacy is associated with our vulnerability to overinterpretation and our predilection for compact stories over raw truths. It severely distorts our mental representation of the world; it is particularly acute when it comes to the rare event.

The narrative fallacy addresses our limited ability to look at sequences of facts without weaving an explanation into them, or, equivalently, forcing a logical link, an arrow of relationship, upon them. Explanations bind facts together.

It takes considerable effort to see facts (and remember them) while withholding judgment and resisting explanations.

The central problems of probability and information theory.

Information is costly to obtain.
Information is also costly to store – like real estate in New York. The more orderly, less random, patterned, and narrated a series of words or symbols, the easier it is to store that series in one’s mind or jot it down in a book so your grandchildren can read it someday.
Information is costly to manipulate and retrieve.

Kolmogorov complexity: the more you summarize, the more order you put in, the less randomness. Hence the same condition that makes us simplify pushes us to think that the world is less random than it actually is.

How to escape the narrative fallacy:

by making conjectures and running experiments
by making testable predictions

If narrativity causes us to see past events as more predictable, more expected, and less random than they actually were, then we should be able to make it work for us as therapy against some of the stings of randomness.
How? By keeping a diary.

Adding the because makes these matters far more plausible, and far more likely.

There are two varieties of rare events:

The narrated Black Swans, those that are present in the current discourse and that you are likely to hear about on television, and
Those nobody talks about, since they escape models.

People overreact to low-probability outcomes when you make them aware of the event.

People underweigh small probabilities when they engage in sequential experiments in which they derive the probabilities themselves, when they are not supplied with the odds. It is only when you are supplied with their frequency – say, by telling you that 3 percent of the balls are red – that you overestimate it in your betting decision.

Abstract statistical information does not sway us as much as an anecdote.

As Stalin, who knew something about the business of mortality, supposedly said, “One death is a tragedy; a million is a statistic.” Statistics stay silent in us.

We feel the sting of man-made damage far more than that caused by nature.

How to avert the Narrative Fallacy

Favour experimentation over storytelling, experience over history, and clinical knowledge over theories.
Predict and keep a tally of the predictions.
Use a narrative for a good purpose. We can use our ability to convince with a story that conveys the right message – what storytellers seem to do.

Living In The Antechamber Of Hope

Linear progression, a Platonic idea, is not the norm.

Hedonic happiness: your happiness depends far more on the number of instances of positive feelings, what psychologists call “positive affect,” than on their intensity when they hit. In other words, good news is good news first; how good matters rather little.

Giacomo Casanova’s Unfailing Luck: The Problem Of Silent Evidence

One Diagoras, a nonbeliever in the gods, was shown painted tablets bearing the portraits of some worshippers who prayed, then survived a subsequent shipwreck. The implication was that praying protects you from drowning. Diagoras asked, “Where were the pictures of those who prayed, then drowned?”

The drowned worshippers, being dead, would have a lot of trouble advertising their experiences from the bottom of the sea. This can fool the casual observer into believing in miracles.

We call this the problem of silent evidence.

Silent evidence is what events use to conceal their own randomness.

The neglect of silent evidence is endemic to the way we study comparative talent, particularly in activities that are plagued with winner-take-all attributes.

To understand successes and analyze what caused them, we need to study the traits present in failures.

We generally take risks not out of bravado but out of ignorance and blindness to probability. That we got here by accident does not mean that we should continue to take the same risks.

The self-sampling assumption, which is a generalization of the principle of the Casanova bias to our own existence.

We are explanation-seeking animals who tend to think that everything has an identifiable cause and grab the most apparent one as the explanation. Yet there may not be a visible because; to the contrary, frequently there is nothing, not even a spectrum of possible explanations. But silent evidence masks this fact.

Whenever our survival is in play, the very notion of because is severely weakened. The condition of survival drowns all possible explanations.

Whenever your survival is in play, don’t immediately look for causes and effects. The main identifiable reason for our survival from such diseases might simply be inaccessible to us: we are here since the “rosy” scenario played out, and if it seems too hard to understand it is because we are too brainwashed by notions of causality and we think that it is smarter to say because than to accept randomness.

Silent evidence can actually bias matters to look less stable and riskier than they actually are. Take cancer. We are in the habit of counting survival rates from diagnosed cancer cases – which should overestimate the danger of cancer. Many people develop cancer that remains undiagnosed and go on to live a long and comfortable life, then die of something else, either because their cancer was not lethal or because it went into spontaneous remission. Not counting these cases biases the risks upward.

The Ludic Fallacy, Or The Uncertainty Of The Nerd

One of its nastiest illusions is what I call the ludic fallacy – the attributes of the uncertainty we face in real life have little connection to the sterilized ones we encounter in exams and games.

In real life you do not know the odds; you need to discover them, and the sources of uncertainty are not defined.

“Computable” risks are largely absent from real life! They are laboratory contraptions!

We respect what has happened, ignoring what could have happened.

The Scandal Of Prediction

We are arrogant about what we think we know. We certainly know a lot, but we have a built-in tendency to think that we know a little bit more than we actually do, enough of that little bit to occasionally get into serious trouble.

Epistemic arrogance bears a double effect: we overestimate what we know, and underestimate uncertainty, by compressing the range of possible uncertain states (i.e., by reducing the space of the unknown).

The longer the odds, the larger the epistemic arrogance.

The more information you give someone, the more hypotheses they will formulate along the way, and the worse off they will be. They see more random noise and mistake it for information.

Once we produce a theory, we are not likely to change our minds – so those who delay developing their theories are better off.

No matter what anyone tells you, it is a good idea to question the error rate of an expert’s procedure. Do not question his procedure, only his confidence.

Things that move, and therefore require knowledge, do not usually have experts, while things that don’t move seem to have some experts. In other words, professions that deal with the future and base their studies on the nonrepeatable past have an expert problem.

We humans are the victims of an asymmetry in the perception of random events. We attribute our successes to our skills, and our failures to external events outside our control, namely to randomness.

Plans fail because of tunnelling: the neglect of sources of uncertainty outside the plan itself.

With projects of great novelty, such as a military invasion, an all-out war, or something entirely new, errors explode upward.

Nerd effect, which stems from the mental elimination of off-model risks, or focusing on what you know. You view the world from within a model.

We use reference points in our heads, say sales projections, and start building beliefs around them because less mental effort is needed.

Corporate and government projections have an additional easy-to-spot flaw: they do not attach a possible error rate to their scenarios.

Forecasting without incorporating an error rate uncovers three fallacies, all arising from the same misconception about the nature of uncertainty.

Variability matters. Taking a projection too seriously, without heeding its accuracy. Yet, for planning purposes, the accuracy of your forecast matters far more than the forecast itself.
- Don’t cross a river if it is four feet deep on average.
- The policies we need to make decisions on should depend far more on the range of possible outcomes than on the expected final number.
Failing to take into account forecast degradation as the projected period lengthens. We do not realize the full extent of the difference between near and far futures.
The gravest one: a misunderstanding of the random character of the variables being forecast. Owing to the Black Swan, these variables can accommodate far more optimistic – or far more pessimistic – scenarios than are currently expected.

It is the lower bound of estimates (i.e., the worst case) that matters when engaging in a policy – the worst case is far more consequential than the forecast itself.

The wise one is the one who knows that he cannot see things far away.

The Black Swan has three attributes:

Unpredictability
Consequences
Retrospective explainability

How To Look For Bird Poop

To predict the spread of a technology implies predicting a large element of fads and social contagion.

Popper’s central argument is that in order to predict historical events you need to predict technological innovation, itself fundamentally unpredictable.

There is a law in statistics called the law of iterated expectations: if I expect to expect something at some date in the future, then I already expect that something at present.

There is a weaker form of this law of iterated knowledge. It can be phrased as follows: to understand the future to the point of being able to predict it, you need to incorporate elements from this future itself.

Three body problem:

In a dynamical system, where you are considering more than a ball on its own, where trajectories in a way depend on one another, the ability to project into the future is not just reduced but is subjected to a fundamental limitation. Poincaré proposed that we can only work with qualitative matters – some properties of systems can be discussed, but not computed. You can think rigorously, but you cannot use numbers.

The consequential divergence in his results arose not from error, but from a small rounding in the input parameters. This became known as the butterfly effect.

It may not “make sense” that acupuncture works, but if pushing a needle in someone’s toe systematically produces relief from pain (in properly conducted empirical tests), then it could be that there are functions too complicated for us to understand, so let’s go with it for now while keeping our minds open.

The riddle of induction: We project a straight line only because we have a linear model in our head – the fact that a number has risen for 1,000 days straight should make you more confident that it will rise in the future. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1,001.

The riddle of induction is another version of the narrative fallacy – you face an infinity of “stories” that explain what you have seen.

The severity of the riddle of induction is as follows: if there is no longer even a single unique way to “generalize” from what you see, to make an inference about the unknown, then how should you operate? The answer, clearly, will be that you should employ “common sense,” but your common sense may not be so well developed with respect to some Extremistan variables.

Fallacy of misplaced concreteness: the mistake of confusing a model with the physical entity that it means to describe.

Epistemocracy, A Dream

Black Swan asymmetry: you can be dead certain about some things, and ought to be so. You can be more confident about disconfirmation than confirmation.

Pleasant and unpleasant events. We overestimate the effects of both kinds of future events on our lives. We seem to be in a psychological predicament that makes us do so. This predicament is called “anticipated utility” by Danny Kahneman and “affective forecasting” by Dan Gilbert. The point is not so much that we tend to mispredict our future happiness, but rather that we do not learn recursively from past experiences.

We grossly overestimate the length of the effect of misfortune on our lives.

If you have the right models you can predict with great precision how the ice cube will melt – this is a specific engineering problem devoid of complexity, easier than the one involving billiard balls. However, from the pool of water you can build infinite possible ice cubes, if there was in fact an ice cube there at all. The first direction, from the ice cube to the puddle, is called the forward process. The second direction, the backward process, is much, much more complicated. The forward process is generally used in physics and engineering; the backward process in nonrepeatable, nonexperimental historical approaches.

A small input in a complex system can lead to nonrandom large results, depending on very special conditions.

A true random system is in fact random and does not have predictable properties. A chaotic system has entirely predictable properties, but they are hard to know.

There is no functional difference in practice between the two since we will never get to make the distinction – the difference is mathematical, not practical.
The mere fact that a person is talking about the difference implies that he has never made a meaningful decision under uncertainty – which is why he does not realize that they are indistinguishable in practice.

Randomness, in the end, is just unknowledge.

History is useful for the thrill of knowing the past, and for the narrative, provided it remains a harmless narrative. One should learn under severe caution. History is certainly not a place to theorize or derive general knowledge, nor is it meant to help in the future, without some caution. We can get negative confirmation from history, which is invaluable, but we get plenty of illusions of knowledge along with it.

Learn to read history, get all the knowledge you can, do not frown on the anecdote, but do not draw any causal links, do not try to reverse engineer too much – but if you do, do not make big scientific claims. Remember that the empirical sceptics had respect for custom: they used it as a default, a basis for action, but not for more than that. This clean approach to the past they called epilogism.

Appelles The Painter, Or What Do You Do If You Cannot Predict?

What you should avoid is unnecessary dependence on large-scale harmful predictions – those and only those. Avoid the big subjects that may hurt your future: be fooled in small matters, not in the large.

Know how to rank beliefs not according to their plausibility but by the harm they may cause.

The “barbell” strategy: if you know that you are vulnerable to prediction errors, and if you accept that most “risk measures” are flawed, because of the Black Swan, then your strategy is to be as hyperconservative and hyperaggressive as you can be instead of being mildly aggressive or conservative.

You need to put a portion, say 85 to 90 percent, in extremely safe instruments, like Treasury bills – as safe a class of instruments as you can manage to find on this planet. The remaining 10 to 15 percent you put in extremely speculative bets, as leveraged as possible (like options), preferably venture capital–style portfolios. That way you do not depend on errors of risk management; no Black Swan can hurt you at all, beyond your “floor,” the nest egg that you have in maximally safe investments.
Instead of having medium risk, you have high risk on one side and no risk on the other.

This can be called a “convex” combination. How to implement in all aspects of life:

Make a distinction between positive contingencies and negative ones.
1. Learn to distinguish between those human undertakings in which the lack of predictability can be (or has been) extremely beneficial and those where the failure to understand the future caused harm. There are both positive and negative Black Swans. William Goldman was involved in the movies, a positive–Black Swan business.
2. Aside from the movies, examples of positive–Black Swan businesses are some segments of publishing, scientific research, and venture capital. In these businesses, you lose small to make big
3. The “barbell” strategy of taking maximum exposure to the positive Black Swans while remaining paranoid about the negative ones.
Don’t look for the precise and the local. Simply, do not be narrow-minded.
1. The great discoverer Pasteur, who came up with the notion that chance favours the prepared, understood that you do not look for something particular every morning but work hard to let contingency enter your working life.
2. Do not try to predict precise Black Swans – it tends to make you more vulnerable to the ones you did not predict.
3. Invest in preparedness, not in prediction.
Seize any opportunity or anything that looks like an opportunity. They are rare, much rarer than you think. Remember that positive Black Swans have a necessary first step: you need to be exposed to them.
1. Collect as many free nonlottery tickets (those with open-ended payoffs) as you can, and, once they start paying off, do not discard them. Work hard, not in grunt work, but in chasing such opportunities and maximizing exposure to them. This makes living in big cities invaluable because you increase the odds of serendipitous encounters – you gain exposure to the envelope of serendipity.
Beware of precise plans by governments. Let governments predict (it makes officials feel better about themselves and justifies their existence) but do not set much store by what they say. Remember that the interest of these civil servants is to survive.
“There are some people who, if they don’t already know, you can’t tell ’em,” as the great philosopher of uncertainty Yogi Berra once said. Do not waste your time trying to fight forecasters, stock analysts, economists, and social scientists, except to play pranks on them.

All these recommendations have one point in common: asymmetry. Put yourself in situations where favourable consequences are much larger than unfavourable ones.

We can focus on the payoff and benefits of an event if it takes place. The probabilities of very rare events are not computable; the effect of an event on us is considerably easier to ascertain (the rarer the event, the fuzzier the odds). We can have a clear idea of the consequences of an event, even if we do not know how likely it is to occur.

This idea that in order to make a decision you need to focus on the consequences (which you can know) rather than the probability (which you can’t know) is the central idea of uncertainty.

You can build an overall theory of decision-making on this idea. All you have to do is mitigate the consequences.

We can easily narrow down the reasons we can’t figure out what’s going on:

Epistemic arrogance and our corresponding future blindness;
The Platonic notion of categories, or how people are fooled by reductions, particularly if they have an academic degree in an expert-free discipline;
Flawed tools of inference, particularly the Black Swan–free tools from Mediocristan.

From Mediocristan To Extremistan, And Back

Tournament effect: someone who is marginally “better” can easily win the entire pot, leaving the others with nothing.

Matthew effect, by which people take from the poor to give to the rich. He looked at the performance of scientists and showed how an initial advantage follows someone through life.

In sociology, Matthew effects bear the less literary name “cumulative advantage.” This theory can easily apply to companies, businessmen, actors, writers, and anyone else who benefits from past success.

Failure is also cumulative; losers are likely to also lose in the future, even if we don’t take into account the mechanism of demoralization that might exacerbate it and cause additional failure.

Merton’s cumulative-advantage idea has a more general precursor, “preferential attachment,” which reverses the chronology (though not the logic).

Zipf’s law, which, of course, is not a law (and if it were, it would not be Zipf’s). It is just another way to think about the process of inequality. The mechanisms he described were as follows: the more you use a word, the less effortful you will find it to use that word again, so you borrow words from your private dictionary in proportion to their past use.

Contagious mental categories must be those in which we are prepared to believe, perhaps even programmed to believe. To be contagious, a mental category must agree with our nature.

Preferential-attachment theories are intuitively appealing, but they do not account for the possibility of being supplanted by newcomers – what every schoolchild knows as the decline of civilizations.

Capitalism is the revitalization of the world thanks to the opportunity to be lucky. Luck is the grand equalizer, because almost everyone can benefit from it.

Everything is transitory. Luck both made and unmade Carthage; it both made and unmade Rome.

The long tail is a by-product of Extremistan that makes it somewhat less unfair: the world is made no less unfair for the little guy, but it now becomes extremely unfair for the big man. Nobody is truly established.

The Bell Curve, That Great Intellectual Fraud

The Gaussian–bell curve variations face a headwind that makes probabilities drop at a faster and faster rate as you move away from the mean, while “scalables,” or Mandelbrotian variations, do not have such a restriction. That’s pretty much most of what you need to know.

The rarer the event, the higher the error in our estimation of its probability – even when using the Gaussian.

Standard deviation is just a number that you scale things to, a matter of mere correspondence if phenomena were Gaussian.

The central assumptions we made in the coin-flip game led to the proto-Gaussian, or mild randomness.

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.
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. We did not encounter situations in which the move varied wildly.

If either of these two central assumptions is not met, your moves (or coin tosses) will not cumulatively lead to the bell curve. Depending on what happens, they can lead to the wild Mandelbrotian-style scale-invariant randomness.

My technique, instead of studying the possible models generating non-bell curve randomness, hence making the same errors of blind theorizing, is to do the opposite: to know the bell curve as intimately as I can and identify where it can and cannot hold. I know where Mediocristan is.

The Aesthetics Of Randomness

Fractal is a word Mandelbrot coined to describe the geometry of the rough and broken – from the Latin fractus, the origin of fractured. Fractality is the repetition of geometric patterns at different scales, revealing smaller and smaller versions of themselves. Small parts resemble, to some degree, the whole.

The fractal has numerical or statistical measures that are (somewhat) preserved across scales – the ratio is the same, unlike the Gaussian.

Fractals should be the default. They do not solve the Black Swan problem and do not turn all Black Swans into predictable events, but they significantly mitigate the Black Swan problem by making such large events conceivable. (It makes them grey. Why grey? Because only the Gaussian give you certainties.)

In the absence of a feedback process you look at models and think that they confirm reality.

Complexity theory should make us more suspicious of scientific claims of precise models of reality. It does not make all the swans white; that is predictable: it makes them grey, and only grey.

How to live life:

We don’t have the luxury of sitting down to read the equation that governs the universe.
We just observe data and make an assumption about what the real process might be.
“Calibrate” by adjusting our equation in accordance with additional information.
As events present themselves to us, we compare what we see to what we expected to see.
It is usually a humbling process, particularly for someone aware of the narrative fallacy, to discover that history runs forward, not backward.

Many study psychology, mathematics, or evolutionary theory and look for ways to take it to the bank by applying their ideas to business, I suggest the exact opposite: study the intense, uncharted, humbling uncertainty in the markets as a means to get insights about the nature of randomness that is applicable to psychology, probability, mathematics, decision theory, and even statistical physics. You will see the sneaky manifestations of the narrative fallacy, the ludic fallacy, and the great errors of Platonicity, of going from representation to reality.

Plenty of fashionable models attempt to explain the genesis of Extremistan. In fact, they are grouped into two broad classes, but there are occasionally more approaches.

The first class includes the simple rich-get-richer (or big-get-bigger) style model that is used to explain the lumping of people around cities, the market domination of Microsoft and VHS (instead of Apple and Betamax), the dynamics of academic reputations, etc.
The second class concerns what are generally called “percolation models,” which address not the behaviour of the individual, but rather the terrain in which he operates. When you pour water on a porous surface, the structure of that surface matters more than the liquid. When a grain of sand hits a pile of other grains of sand, how the terrain is organized is what determines whether there will be an avalanche.

I can make inferences about things that I do not see in my data, but these things should still belong to the realm of possibilities.

There is an invisible bestseller out there, one that is absent from the past data but that you need to account for. It makes investment in a book or a drug better than statistics on past data might suggest. But it can make stock market losses worse than what the past shows.

Locke’s Madmen, Or Bell Curves In The Wrong Places

The option payoff is so powerful that you do not have to be right on the odds: you can be wrong on the probability, but get a monstrously large payoff. I’ve called this the “double bubble”: the mispricing of the probability and that of the payoff.

The Uncertainty Of The Phony

The greater uncertainty principle states that in quantum physics, one cannot measure certain pairs of values (with arbitrary precision), such as the position and momentum of particles. You will hit a lower bound of measurement: what you gain in the precision of one, you lose in the other. So there is an incompressible uncertainty that, in theory, will defy science and forever remain an uncertainty