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Tag Archives: Nassim Taleb

The Probability Distribution of the Future

The best colloquial definition of risk may be the following:

“Risk means more things can happen than will happen.”

We found it through the inimitable Howard Marks, but it's a quote from Elroy Dimson of the London Business School. Doesn't that capture it pretty well?

Another way to state it is: If there were only one thing that could happen, how much risk would there be, except in an extremely banal sense? You'd know the exact probability distribution of the future. If I told you there was a 100% probability that you'd get hit by a car today if you walked down the street, you simply wouldn't do it. You wouldn't call walking down the street a “risky gamble” right? There's no gamble at all.

But the truth is that in practical reality, there aren't many 100% situations to bank on. Way more things can happen than will happen. That introduces great uncertainty into the future, no matter what type of future you're looking at: An investment, your career, your relationships, anything.

How do we deal with this in a pragmatic way? The investor Howard Marks starts it this way:

Key point number one in this memo is that the future should be viewed not as a fixed outcome that’s destined to happen and capable of being predicted, but as a range of possibilities and, hopefully on the basis of insight into their respective likelihoods, as a probability distribution.

This is the most sensible way to think about the future: A probability distribution where more things can happen than will happen. Knowing that we live in a world of great non-linearity and with the potential for unknowable and barely understandable Black Swan events, we should never become too confident that we know what's in store, but we can also appreciate that some things are a lot more likely than others. Learning to adjust probabilities on the fly as we get new information is called Bayesian updating.


Although the future is certainly a probability distribution, Marks makes another excellent point in the wonderful memo above: In reality, only one thing will happen. So you must make the decision: Are you comfortable if that one thing happens, whatever it might be? Even if it only has a 1% probability of occurring? Echoing the first lesson of biology, Warren Buffett stated that “In order to win, you must first survive.” You have to live long enough to play out your hand.

Which leads to an important second point: Uncertainty about the future does not necessarily equate with risk, because risk has another component: Consequences. The world is a place where “bad outcomes” are only “bad” if you know their (rough) magnitude. So in order to think about the future and about risk, we must learn to quantify.

It's like the old saying (usually before something terrible happens): What's the worst that could happen? Let's say you propose to undertake a six month project that will cost your company $10 million, and you know there's a reasonable probability that it won't work. Is that risky?

It depends on the consequences of losing $10 million, and the probability of that outcome. It's that simple! (Simple, of course, does not mean easy.) A company with $10 billion in the bank might consider that a very low-risk bet even if it only had a 10% chance of succeeding.

In contrast, a company with only $10 million in the bank might consider it a high-risk bet even if it only had a 10% of failing. Maybe five $2 million projects with uncorrelated outcomes would make more sense to the latter company.

In the real world, risk = probability of failure x consequences. That concept, however, can be looked at through many lenses. Risk of what? Losing money? Losing my job? Losing face? Those things need to be thought through. When we observe others being “too risk averse,” we might want to think about which risks they're truly avoiding. Sometimes risk is not only financial. 


Let's cover one more under-appreciated but seemingly obvious aspect of risk, also pointed out by Marks: Knowing the outcome does not teach you about the risk of the decision.

This is an incredibly important concept:

If you make an investment in 2012, you’ll know in 2014 whether you lost money (and how much), but you won’t know whether it was a risky investment – that is, what the probability of loss was at the time you made it.

To continue the analogy, it may rain tomorrow, or it may not, but nothing that happens tomorrow will tell you what the probability of rain was as of today. And the risk of rain is a very good analogue (although I’m sure not perfect) for the risk of loss.

How many times do we see this simple dictum violated? Knowing that something worked out, we argue that it wasn't that risky after all. But what if, in reality, we were simply fortunate? This is the Fooled by Randomness effect.

The way to think about it is the following: The worst thing that can happen to a young gambler is that he wins the first time he goes to the casinoHe might convince himself he can beat the system.

The truth is that most times we don't know the probability distribution at all. Because the world is not a predictable casino game — an error Nassim Taleb calls the Ludic Fallacy — the best we can do is guess.

With intelligent estimations, we can work to get the rough order of magnitude right, understand the consequences if we're wrong, and always be sure to never fool ourselves after the fact.

If you're into this stuff, check out Howard Marks' memos to his clients, or check out his excellent book, The Most Important Thing. Nate Silver also has an interesting similar idea about the difference between risk and uncertainty. And lastly, another guy that understands risk pretty well is Jason Zweig, who we've interviewed on our podcast before.


If you liked this article you'll love:

Nassim Taleb on the Notion of Alternative Histories — “The quality of a decision cannot be solely judged based on its outcome.”

The Four Types of Relationships — As Seneca said, “Time discovers truth.”

The Green Lumber Fallacy: The Difference between Talking and Doing

“Clearly, it is unrigorous to equate skills at doing with skills at talking.”
— Nassim Taleb


Before we get to the meat, let's review an elementary idea in biology that will be relevant to our discussion.

If you're familiar with evolutionary theory, you know that populations of organisms are constantly subjected to “selection pressures” — the rigors of their environment which lead to certain traits being favored and passed down to their offspring and others being thrown into the evolutionary dustbin.

Biologists dub these advantages in reproduction “fitness” — as in, the famously lengthening of giraffe necks gave them greater “fitness” in their environment because it helped them reach high up, untouched leaves.

Fitness is generally a relative concept: Since organisms must compete for scarce resources, their fitnesses are measured in the sense of giving a reproductive advantage over one another.

Just as well, a trait that might provide great fitness in one environment may be useless or even disadvantageous in another. (Imagine draining a pond: Any fitness advantages held by a really incredible fish becomes instantly worthless without water.) Traits also relate to circumstance. An advantage at one time could be a disadvantage at another and vice versa.

This makes fitness an all-important concept in biology: Traits are selected for if they provide fitness to the organism within a given environment.

Got it? OK, let's get back to the practical world.


The Black Swan thinker Nassim Taleb has an interesting take on fitness and selection in the real world:  People who are good “doers” and people who are good “talkers” are often selected for different traits. Be careful not to mix them up.

In his book Antifragile, Taleb uses this idea to invoke a heuristic he'd once used when hiring traders on Wall Street:

The more interesting their conversation, the more cultured they are, the more they will be trapped into thinking that they are effective at what they are doing in real business (something psychologists call the halo effect, the mistake of thinking that skills in, say, skiing translate unfailingly into skills in managing a pottery workshop or a bank department, or that a good chess player would be a good strategist in real life).

Clearly, it is unrigorous to equate skills at doing with skills at talking. My experience of good practitioners is that they can be totally incomprehensible–they do not have to put much energy into turning their insights and internal coherence into elegant style and narratives. Entrepreneurs are selected to be doers, not thinkers, and doers do, they don't talk, and it would be unfair, wrong, and downright insulting to measure them in the talk department.

In other words, the selection pressures on an entrepreneur are very different from those on a corporate manager or bureaucrat: Entrepreneurs and risk takers succeed or fail not so much on their ability to talk, explain, and rationalize as their ability to get things done.

While the two can often go together, Nassim figured out that they frequently don't. We judge people as ignorant when it's really us who are ignorant.

When you think about it, there's no a priori reason great intellectualizing and great doing must go together: Being able to hack together an incredible piece of code gives you great fitness in the world of software development, while doing great theoretical computer science probably gives you better fitness in academia. The two skills don't have to be connected. Great economists don't usually make great investors.

But we often confuse the two realms.  We're tempted to think that a great investor must be fluent in behavioral economics or a great CEO fluent in Mckinsey-esque management narratives, but in the real world, we see this intuition constantly in violation.

The investor Walter Schloss worked from 9-5, barely left his office, and wasn't considered an entirely high IQ man, but he compiled one of the great investment records of all time. A young Mark Zuckerberg could hardly be described as a prototypical manager or businessperson, yet somehow built one of the most profitable companies in the world by finding others that complemented his weaknesses.

There are a thousand examples: Our narratives about the type of knowledge or experience we must have or the type of people we must be in order to become successful are often quite wrong; in fact, they border on naive. We think people who talk well can do well, and vice versa. This is simply not always so.

We won't claim that great doers cannot be great talkers, rationalizers, or intellectuals. Sometimes they are. But if you're seeking to understand the world properly, it's good to understand that the two traits are not always co-located. Success, especially in some “narrow” area like plumbing, programming, trading, or marketing, is often achieved by rather non-intellectual folks. Their evolutionary fitness doesn't come from the ability to talk, but do. This is part of reality.


Taleb calls this idea the Green Lumber Fallacy, after a story in the book What I Learned Losing a Million Dollars. Taleb describes it in Antifragile:

In one of the rare noncharlatanic books in finance, descriptively called What I Learned Losing a Million Dollars, the protagonist makes a big discovery. He remarks that a fellow named Joe Siegel, one of the most successful traders in a commodity called “green lumber,” actually thought it was lumber painted green (rather than freshly cut lumber, called green because it had not been dried). And he made it his profession to trade the stuff! Meanwhile the narrator was into grand intellectual theories and narratives of what caused the price of commodities to move and went bust.

It is not just that the successful expert on lumber was ignorant of central matters like the designation “green.” He also knew things about lumber that nonexperts think are unimportant. People we call ignorant might not be ignorant.

The fact that predicting the order flow in lumber and the usual narrative had little to do with the details one would assume from the outside are important. People who do things in the field are not subjected to a set exam; they are selected in the most non-narrative manager — nice arguments don't make much difference. Evolution does not rely on narratives, humans do. Evolution does not need a word for the color blue.

So let us call the green lumber fallacy the situation in which one mistakes a source of visible knowledge — the greenness of lumber — for another, less visible from the outside, less tractable, less narratable.

The main takeaway is that the real causative factors of success are often hidden from usWe think that knowing the intricacies of green lumber are more important than keeping a close eye on the order flow. We seduce ourselves into overestimating the impact of our intellectualism and then wonder why “idiots” are getting ahead. (Probably hustle and competence.)

But for “skin in the game” operations, selection and evolution don't care about great talk and ideas unless they translate into results. They care what you do with the thing more than that you know the thing. They care about actually avoiding risk rather than your extensive knowledge of risk management theories. (Of course, in many areas of modernity there is no skin in the game, so talking and rationalizing can be and frequently are selected for.)

As Taleb did with his hiring heuristic, this should teach us to be a little skeptical of taking good talkers at face value, and to be a little skeptical when we see “unexplainable” success in someone we consider “not as smart.” There might be a disconnect we're not seeing because we're seduced by narrative. (A problem someone like Lee Kuan Yew avoided by focusing exclusively on what worked.)

And we don't have to give up our intellectual pursuits in order to appreciate this nugget of wisdom; Taleb is right, but it's also true that combining the rigorous, skeptical knowledge of “what actually works” with an ever-improving theory structure of the world might be the best combination of all — selected for in many more environments than simple git-er-done ability, which can be extremely domain and environment dependent. (The green lumber guy might not have been much good outside the trading room.)

After all, Taleb himself was both a successful trader and the highest level of intellectual. Even he can't resist a little theorizing.

Frozen Accidents: Why the Future Is So Unpredictable

“Each of us human beings, for example, is the product of an enormously long
sequence of accidents,
any of which could have turned out differently.”
— Murray Gell-Mann


What parts of reality are the product of an accident? The physicist Murray Gell-Mann thought the answer was “just about everything.” And to Gell-Mann, understanding this idea was the the key to understanding how complex systems work.

Gell-Mann believed two things caused what we see in the world:

  1. A set of fundamental laws
  2. Random “accidents” — the little blips that could have gone either way, and had they, would have produced a very different kind of world.

Gell-Mann pulled the second part from Francis Crick, co-discoverer of the human genetic code, who argued that the code itself may well have been an “accident” of physical history rather than a uniquely necessary arrangement.

These accidents become “frozen” in time, and have a great effect on all subsequent developments; complex life itself is an example of something that did happen a certain way but probably could have happened other ways — we know this from looking at the physics.

This idea of fundamental laws plus accidents, and the non-linear second order effects they produce, became the science of complexity and chaos theory. Gell-Mann discussed the fascinating idea further in a 1996 essay on Edge:

Each of us human beings, for example, is the product of an enormously long sequence of accidents, any of which could have turned out differently. Think of the fluctuations that produced our galaxy, the accidents that led to the formation of the solar system, including the condensation of dust and gas that produced Earth, the accidents that helped to determine the particular way that life began to evolve on Earth, and the accidents that contributed to the evolution of particular species with particular characteristics, including the special features of the human species. Each of us individuals has genes that result from a long sequence of accidental mutations and chance matings, as well as natural selection.

Now, most single accidents make very little difference to the future, but others may have widespread ramifications, many diverse consequences all traceable to one chance event that could have turned out differently. Those we call frozen accidents.

These “frozen accidents” occur at every nested level of the world: As Gell-Mann points out, they are an outcome in physics (the physical laws we observe may be accidents of history); in biology (our genetic code is largely a byproduct of “advantageous accidents” as discussed by Crick); and in human history, as we'll discuss. In other words, the phenomenon hits all three buckets of knowledge.

Gell-Mann gives a great example of how this plays out on the human scale:

For instance, Henry VIII became king of England because his older brother Arthur died. From the accident of that death flowed all the coins, all the charters, all the other records, all the history books mentioning Henry VIII; all the different events of his reign, including the manner of separation of the Church of England from the Roman Catholic Church; and of course the whole succession of subsequent monarchs of England and of Great Britain, to say nothing of the antics of Charles and Diana. The accumulation of frozen accidents is what gives the world its effective complexity.

The most important idea here is that the frozen accidents of history have a nonlinear effect on everything that comes after. The complexity we see comes from simple rules and many, many “bounces” that could have gone in any direction. Once they go a certain way, there is no return.

This principle is illustrated wonderfully in the book The Origin of Wealth by Eric Beinhocker. The first example comes from 19th century history:

In the late 1800s, “Buffalo Bill” Cody created a show called Buffalo Bill's Wild West Show, which toured the United States, putting on exhibitions of gun fighting, horsemanship, and other cowboy skills. One of the show's most popular acts was a woman named Phoebe Moses, nicknamed Annie Oakley. Annie was reputed to have been able to shoot the head off of a running quail by age twelve, and in Buffalo Bill's show, she put on a demonstration of marksmanship that included shooting flames off candles, and corks out of bottles. For her grand finale, Annie would announce that she would shoot the end off a lit cigarette held in a man's mouth, and ask for a brave volunteer from the audience. Since no one was ever courageous enough to come forward, Annie hid her husband, Frank, in the audience. He would “volunteer,” and they would complete the trick together. In 1880, when the Wild West Show was touring Europe, a young crown prince (and later, kaiser), Wilhelm, was in the audience. When the grand finale came, much to Annie's surprise, the macho crown prince stood up and volunteered. The future German kaiser strode into the ring, placed the cigarette in his mouth, and stood ready. Annie, who had been up late the night before in the local beer garden, was unnerved by this unexpected development. She lined the cigarette up in her sights, squeezed…and hit it right on the target.

Many people have speculated that if at that moment, there had been a slight tremor in Annie's hand, then World War I might never have happened. If World War I had not happened, 8.5 million soldiers and 13 million civilian lives would have been saved. Furthermore, if Annie's hand had trembled and World War I had not happened, Hitler would not have risen from the ashes of a defeated Germany, and Lenin would not have overthrown a demoralized Russian government. The entire course of twentieth-century history might have been changed by the merest quiver of a hand at a critical moment. Yet, at the time, there was no way anyone could have known the momentous nature of the event.

This isn't to say that other big events, many bad, would not have precipitated in the 20th century. Almost certainly there would have been wars and upheavals.

But the actual course of history was in some part determined by small chance event which had no seeming importance when it happened. The impact of Wilhelm being alive rather than dead was totally non-linear. (A small non-event had a massively disproportionate effect on what happened later.)

This is why predicting the future, even with immense computing power, is an impossible task. The chaotic effects of randomness, with small inputs having disproportionate and massive effects, makes prediction a very difficult task. That's why we must appreciate the role of randomness in the world and seek to protect against it.

Another great illustration from The Origin of Wealth is a famous story in the world of technology:

[In 1980] IBM approached a small company with forty employees in Bellevue, Washington. The company, called Microsoft, was run by a Harvard dropout named bill Gates and his friend Paul Allen. IBM wanted to talk to the small company about creating a version of the programming language BASIC for the new PC. At their meeting, IBM asked Gates for his advice on what operating systems (OS) the new machine should run. Gates suggested that IBM talk to Gary Kildall of Digital Research, whose CP/M operating system had become the standard in the hobbyist world of microcomputers. But Kildall was suspicious of the blue suits from IBM and when IBM tried to meet him, he went hot-air ballooning, leaving his wife and lawyer to talk to the bewildered executives, along with instructions not to sign even a confidentiality agreement. The frustrated IBM executives returned to Gates and asked if he would be interested in the OS project. Despite never having written an OS, Gates said yes. He then turned around and license a product appropriately named Quick and Dirty Operating System, or Q-DOS, from a small company called Seattle Computer Products for $50,000, modified it, and then relicensed it to IBM as PC-DOS. As IBM and Microsoft were going through the final language for the agreement, Gates asked for a small change. He wanted to retain the rights to sell his DOS on non-IBM machines in a version called MS-DOS. Gates was giving the company a good price, and IBM was more interested in PC hardware than software sales, so it agreed. The contract was signed on August 12, 1981. The rest, as they say, is history. Today, Microsoft is a company worth $270 billion while IBM is worth $140 billion.

At any point in that story, business history could have gone a much different way: Kildall could have avoided hot-air ballooning, IBM could have refused Gates' offer, Microsoft could have not gotten the license for QDOS. Yet this little episode resulted in massive wealth for Gates and a long period of trouble for IBM.

Predicting the outcomes of a complex system must clear a pretty major hurdle: The prediction must be robust to non-linear “accidents” with a chain of unforeseen causation. In some situations this is doable: We can confidently rule out that Microsoft will not go broke in the next 12 months; the chain of events needed to take it under quickly is so low as to be negligible, no matter how you compute it. (Even IBM made it through the above scenario, although not unscathed.)

But as history rolls on and more “accidents” accumulate year by year, a “Fog of the Future” rolls in to obscure our view. In order to operate in such a world, we must learn that predicting is inferior to building systems that don't require prediction, as Mother Nature does. And if we must predict, must confine our predictions to areas with few variables that lie in our circle of competence, and understand the consequences if we're wrong.

If this topic is interesting to you, try exploring the rest of the Origin of Wealth, which discusses complexity in the economic realm in great (but readable) detail; also check out the rest of Murray Gell-Mann's essay on Edge. Gell-Mann also wrote a book on the topic called The Quark and the Jaguar which is worth checking out. The best writer on randomness and robustness in the face of an uncertain future, is of course Nassim Taleb, whom we have written about many times.

Nassim Taleb’s Life Advice: Be Careful of Life Advice

Nassim Taleb, the modern philosopher best known for his ideas on The Black Swan and Antifragility, gave his first commencement address this year, at American University in Beirut. (I suspect he's been asked in the past but declined.)

Like him or not, Taleb is a unique and uncompromising mind. He doesn't suffer any fools and doesn't sacrifice his principles for money or fame, so far as one can tell. He's willing to take tremendous personal heat if he thinks he's right. (Again, agree with him or not.) There's a certain honor in his approach that must be admired.

The most interesting part of his commencement is on the idea of life advice itself. Commencement speeches are, obviously, meant to pass advice from a wise (and famous) person to a younger generation. But Nassim goes in a bit of a different direction: He advises the students to be careful of common life advice, for if he had followed it, he'd have never become the unique and interesting person he became.

I hesitate to give advice because every major single piece of advice I was given turned out to be wrong and I am glad I didn’t follow them. I was told to focus and I never did. I was told to never procrastinate and I waited 20 years for The Black Swan and it sold 3 million copies. I was told to avoid putting fictional characters in my books and I did put in Nero Tulip and Fat Tony because I got bored otherwise. I was told to not insult the New York Times and the Wall Street Journal; the more I insulted them the nicer they were to me and the more they solicited Op-Eds. I was told to avoid lifting weights for a back pain and became a weightlifter: never had a back problem since.

If I had to relive my life I would be even more stubborn and uncompromising than I have been.

The truth is, much of the advice you receive as a young person will be pretty good. Saving money works. Marrying the right person works. Avoiding drugs works. Etc. The obvious stuff is worth following. (You don't always have to walk on your hands because everyone else walks on their feet.)

But there's a host of more subjective wisdom that, generally speaking, leads you to become a lot more like other people. “Common wisdom,” insofar as it's actually common, tends to reinforce cultural norms and values. If you want to lead a comfortable existence, that may work fine. But it won't create another Nassim Taleb, or another Steve Jobs, or another Richard Feynman. They, and many others, embraced what made them different.

Of course, many less successful people embraced their oddities, too. The silent grave is chock full of candidates. This isn't a “recipe for success” or some other nonsense — it's more complicated than simply being different. (The narrative fallacy is always right around the corner.)

But one has to suspect that a more interesting and honorable life is led by those who are a bit uncompromising on the important values like integrity, self-education, and moral courage. If you can offset that by being extremely compromising on the unimportant stuff, you may have a shot at living an interesting and different life with a heaping scoop of integrity.

You can read the rest of the commencement here. If you're still interested, check out a few other great commencement speeches.

Life Changing Books (New Guy Edition)

Back in 2013, I posted the Books that Changed my Life. In doing so, I was responding to a reader request to post up the books that “literally changed my life.”

Now that we have Jeff on board, I've asked him to do the same. Here are his choices, presented in a somewhat chronological order. As always, these lists leave off a lot of important books in the name of brevity.

Rich Dad, Poor Dad – Robert Kiyosaki

Before I get hanged for apostasy, let me explain. The list is about books that changed my life and this one absolutely did. I pulled this off my father's shelf and read it in high school, and it kicked off a lifelong interest in investments, business, and the magic of compound interest. That eventually led me to find Warren Buffett and Charlie Munger, affecting the path of my life considerably. With that said, I would probably not recommend you start here. I haven't re-read the book since high school and what I've learned about Kiyosaki doesn't make me want to recommend anything to you from him. But for better or worse, this book had an impact. Another one that probably holds up better is The Millionaire Next Door, which my father recommended when I was in high school and stuck with me for a long time too.

Buffett: Making of an American Capitalist/Buffett's Letters to Shareholders – Roger Lowenstein, Warren Buffett

These two and the next book are duplicates off Shane's list, but they are also probably the reason we know each other. Learning about Warren Buffett took the kid who liked “Rich Dad, Poor Dad” and watched The Apprentice, and might have been on a path to highly leveraged real estate speculation and who knows what else, and put him on a more sound path. I read this biography many times in college, and decided I wanted to emulate some of Buffett's qualities. (I actually now prefer The Snowball, by Alice Schroeder, but Lowenstein's came first and changed my life more.) Although I have a business degree, I learned a lot more from reading and applying the collected Letters to Shareholders.

Poor Charlie's Almanack – Peter Kaufman, Charlie Munger et al.

The Almanack is the greatest book I have ever read, and I knew it from the first time I read it. As Charlie says in the book, there is no going back from the multi-disciplinary approach. It would feel like cutting off your hands. I re-read this book every year in whole or in part, and so far, 8 years on, I haven't failed to pick up a meaningful new insight. Like any great book, it grows as you grow. I like to think I understand about 40% of it on a deep level now, and I hope to add a few percent every year. I literally cannot conceive of a world in which I didn't read this.

The Nurture Assumption – Judith Rich Harris

This book affected my thinking considerably. I noticed in the Almanack that Munger recommended this book and another, No Two Alike, towards the end. Once I read it, I could see why. It is a monument to clear and careful thinking. Munger calls the author Judith Rich Harris a combination of Darwin and Sherlock Holmes, and he's right. If this book doesn't change how you think about parenting, social development, peer pressure, education, and a number of other topics, then re-read it.

Filters Against Folly/Living within Limits – Garrett Hardin

Like The Nurture Assumption, these two books are brilliantly well thought-through. Pillars of careful thought. It wasn't until years after I read them that I realized Garrett Hardin was friends with, and in fact funded by, Charlie Munger. The ideas about overpopulation in Living within Limits made a deep impression on me, but the quality of thought in general hit me the hardest. Like the Almanack, it made me want to become a better and more careful thinker.

The Black Swan – Nassim Taleb

Who has read this and not been affected by it? Like many, Nassim's books changed how I think about the world. The ideas from The Black Swan and Fooled by Randomness about the narrative fallacy and the ludic fallacy cannot be forgotten, as well as the central idea of the book itself that rare events are not predictable and yet dominate our landscape. Also, Nassim's writing style made me realize deep, practical writing didn't have to be dry and sanitized. Like him or not, he wears his soul on his sleeve.

Good Calories, Bad Calories / Why We Get Fat: And What to do About it – Gary Taubes

I've been interested in nutrition since I was young, and these books made me realize most of what I knew was not very accurate. Gary Taubes is a scientific journalist of the highest order. Like Hardin, Munger, and Harris, he thinks much more carefully than most of his peers. Nutrition is a field that is still sort of growing up, and the quality of the research and thought shows it. Taubes made me recognize that nutrition can be a real science if it's done more carefully, more Feynman-like. Hopefully his NuSi initiative will help shove the field in the right direction.

The (Honest) Truth about Dishonesty – Dan Ariely

This book by Ariely was a game-changer in that it helped me realize the extent to which we rationalize our behavior in a million little ways. I had a lot of nights thinking about my own propensity for dishonesty and cheating after I read this one, and I like to think I'm a pretty moral person to start with. I had never considered how situational dishonesty was, but now that I do, I see it constantly in myself and others. There are also good sections on incentive-caused bias and social pressure that made an impact.

Sapiens – Yuval Noah Harrari

This is fairly new so I'm still digesting this book, and I have a feeling it will take many years. But Sapiens has a lot of (for me) deep insights about humanity and how we got here. I think Yuval is a very good thinker and an excellent writer. A lot of the ideas in this book will set some people off, and not in a good way. But that doesn't mean they're not correct. Highly recommended if you're open-minded and want to learn.


At the end of the day, what gets me excited is my Antilibrary, all the books I have on my shelf or on my Amazon wish list that I haven't read yet. The prospect of reading another great book that changes my life like these books did is an exciting quest.

The Map is Not the Territory

Map and Territory

“(History) offers a ridiculous spectacle of a fragment expounding the whole.”
— Will Durant in Our Oriental Heritage

“All models are wrong but some are useful.”
— George Box


Relationship between Map and Territory

“That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

“About six inches to the mile.”

“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”

“Have you used it much?” I enquired.

“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.
Sylvie and Bruno Concluded

In 1931, in New Orleans, Louisiana, mathematician Alfred Korzybski presented a paper on mathematical semantics. To the non-technical reader, most of the paper reads like an abstruse argument on the relationship of mathematics to human language, and of both to physical reality. Important stuff certainly, but not necessarily immediately useful for the layperson.

However, in his string of arguments on the structure of language, Korzybski introduced and popularized the idea that the map is not the territory. In other words, the description of the thing is not the thing itself. The model is not reality. The abstraction is not the abstracted. This has enormous practical consequences.

In Korzybski’s words:

A.) A map may have a structure similar or dissimilar to the structure of the territory.

B.) Two similar structures have similar ‘logical’ characteristics. Thus, if in a correct map, Dresden is given as between Paris and Warsaw, a similar relation is found in the actual territory.

C.) A map is not the actual territory.

D.) An ideal map would contain the map of the map, the map of the map of the map, etc., endlessly…We may call this characteristic self-reflexiveness.

Maps are necessary, but flawed. (By maps, we mean any abstraction of reality, including descriptions, theories, models, etc.) The problem with a map is not simply that it is an abstraction; we need abstraction. Lewis Carroll made that clear by having Mein Herr describe a map with the scale of one mile to one mile. Such a map would not have the problems that maps have, nor would it be helpful in any way.

(See Borges for another take.)

To solve this problem, the mind creates maps of reality in order to understand it, because the only way we can process the complexity of reality is through abstraction. But frequently, we don’t understand our maps or their limits. In fact, we are so reliant on abstraction that we will frequently use an incorrect model simply because we feel any model is preferable to no model. (Reminding one of the drunk looking for his keys under the streetlight because “That’s where the light is!”)

Even the best and most useful maps suffer from limitations, and Korzybski gives us a few to explore: (A.) The map could be incorrect without us realizing it(B.) The map is, by necessity, a reduction of the actual thing, a process in which you lose certain important information; and (C.) A map needs interpretation, a process that can cause major errors. (The only way to truly solve the last would be an endless chain of maps-of-maps, which he called self-reflexiveness.)

With the aid of modern psychology, we also see another issue: the human brain takes great leaps and shortcuts in order to make sense of its surroundings. As Charlie Munger has pointed out, a good idea and the human mind act something like the sperm and the egg — after the first good idea gets in, the door closes. This makes the map-territory problem a close cousin of man-with-a-hammer tendency.

This tendency is, obviously, problematic in our effort to simplify reality. When we see a powerful model work well, we tend to over-apply it, using it in non-analogous situations. We have trouble delimiting its usefulness, which causes errors.

Let’s check out an example.


By most accounts, Ron Johnson was one the most successful and desirable retail executives by the summer of 2011. Not only was he handpicked by Steve Jobs to build the Apple Stores, a venture which had itself come under major scrutiny – one retort printed in Bloomberg magazine: “I give them two years before they're turning out the lights on a very painful and expensive mistake.” – but he had been credited with playing a major role in turning Target from a K-Mart look-alike into the trendy-but-cheap Tar-zhey by the late 90’s and early 00’s.

Johnson's success at Apple was not immediate, but it was undeniable. By 2011, Apple stores were by far the most productive in the world on a per-square-foot basis, and had become the envy of the retail world. Their sales figures left Tiffany’s in the dust. The gleaming glass cube on Fifth Avenue became a more popular tourist attraction than the Statue of Liberty. It was a lollapalooza, something beyond ordinary success. And Johnson had led the charge.

With that success, in 2011 Johnson was hired by Bill Ackman, Steven Roth, and other luminaries of the financial world to turn around the dowdy old department store chain JCPenney. The situation of the department store was dour: Between 1992 and 2011, the retail market share held by department stores had declined from 57% to 31%.

Their core position was a no-brainer though. JCPenney had immensely valuable real estate, anchoring malls across the country. Johnson argued that their physical mall position was valuable if for no other reason that people often parked next to them and walked through them to get to the center of the mall. Foot traffic was a given. Because of contracts signed in the 50’s, 60’s, and 70’s, the heyday of the mall building era, rent was also cheap, another major competitive advantage. And unlike some struggling retailers, JCPenney was making (some) money. There was cash in the register to help fund a transformation.

The idea was to take the best ideas from his experience at Apple; great customer service, consistent pricing with no markdowns and markups, immaculate displays, world-class products, and apply them to the department store. Johnson planned to turn the stores into little malls-within-malls. He went as far as comparing the ever-rotating stores-within-a-store to Apple’s “apps.” Such a model would keep the store constantly fresh, and avoid the creeping staleness of retail.

Johnson pitched his idea to shareholders in a series of trendy New York City meetings reminiscent of Steve Jobs’ annual “But wait, there’s more!” product launches at Apple. He was persuasive: JCPenney’s stock price went from $26 in the summer of 2011 to $42 in early 2012 on the strength of the pitch.

The idea failed almost immediately. His new pricing model (eliminating discounting) was a flop. The coupon-hunters rebelled. Much of his new product was deemed too trendy. His new store model was wildly expensive for a middling department store chain – including operating losses purposefully endured, he’d spent several billion dollars trying to effect the physical transformation of the stores. JCPenney customers had no idea what was going on, and by 2013, Johnson was sacked. The stock price sank into the single digits, where it remains two years later.

What went wrong in the quest to build America’s Favorite Store? It turned out that Johnson was using a map of Tulsa to navigate Tuscaloosa. Apple’s products, customers, and history had far too little in common with JCPenney’s. Apple had a rabid, young, affluent fan-base before they built stores; JCPenney’s was not associated with youth or affluence. Apple had shiny products, and needed a shiny store; JCPenney was known for its affordable sweaters. Apple had never relied on discounting in the first place; JCPenney was taking away discounts given prior, triggering massive deprival super-reaction.

In other words, the old map was not very useful. Even his success at Target, which seems like a closer analogue, was misleading in the context of JCPenney. Target had made small, incremental changes over many years, to which Johnson had made a meaningful contribution. JCPenney was attempting to reinvent the concept of the department store in a year or two, leaving behind the core customer in an attempt to gain new ones. This was a much different proposition. (Another thing holding the company back was simply its base odds: Can you name a retailer of great significance that has lost its position in the world and come back?)

The main issue was not that Johnson was incompetent. He wasn’t. He wouldn’t have gotten the job if he was. He was extremely competent. But it was exactly his competence and past success that got him into trouble. He was like a great swimmer that tried to tackle a grand rapid, and the model he used successfully in the past, the map that had navigated a lot of difficult terrain, was not the map he needed anymore. He had an excellent theory about retailing that applied in some circumstances, but not in others. The terrain had changed, but the old idea stuck.


One person who well understands this problem of the map and the territory is Nassim Taleb, author of the Incerto series – Antifragile , The Black SwanFooled by Randomness, and The Bed of Procrustes.

Taleb has been vocal about the misuse of models for many years, but the earliest and most vivid I can recall is his firm criticism of a financial model called Value-at Risk, or VAR. The model, used in the banking community, is supposed to help manage risk by providing a maximum potential loss within a given confidence interval. In other words, it purports to allow risk managers to say that, within 95%, 99%, or 99.9% confidence, the firm will not lose more than $X million dollars in a given day. The higher the interval, the less accurate the analysis becomes. It might be possible to say that the firm has $100 million at risk at any time at a 99% confidence interval, but given the statistical properties of markets, a move to 99.9% confidence might mean the risk manager has to state the firm has $1 billion at risk. 99.99% might mean $10 billion. As rarer and rarer events are included in the distribution, the analysis gets less useful. So, by necessity, the “tails” are cut off somewhere and the analysis is deemed acceptable.

Elaborate statistical models are built to justify and use the VAR theory. On its face, it seems like a useful and powerful idea; if you know how much you can lose at any time, you can manage risk to the decimal. You can tell your board of directors and shareholders, with a straight face, that you’ve got your eye on the till.

The problem, in Nassim’s words, is that:

A model might show you some risks, but not the risks of using it. Moreover, models are built on a finite set of parameters, while reality affords us infinite sources of risks.

In order to come up with the VAR figure, the risk manager must take historical data and assume a statistical distribution in order to predict the future. For example, if we could take 100 million human beings and analyse their height and weight, we could then predict the distribution of heights and weights on a different 100 million, and there would be a microscopically small probability that we’d be wrong. That’s because we have a huge sample size and we are analysing something with very small and predictable deviations from the average.

But finance does not follow this kind of distribution. There’s no such predictability. As Nassim has argued, the “tails” are fat in this domain, and the rarest, most unpredictable events have the largest consequences. Let’s say you deem a highly threatening event (for example, a 90% crash in the S&P 500) to have a 1 in 10,000 chance of occurring in a given year, and your historical data set only has 300 years of data. How can you accurately state the probability of that event? You would need far more data.

Thus, financial events deemed to be 5, or 6, or 7 standard deviations from the norm tend to happen with a certain regularity that nowhere near matches their supposed statistical probability.  Financial markets have no biological reality to tie them down: We can say with a useful amount of confidence that an elephant will not wake up as a monkey, but we can’t say anything with absolute confidence in an Extremistan arena.

We see several issues with VAR as a “map,” then. The first that the model is itself a severe abstraction of reality, relying on historical data to predict the future. (As all financial models must, to a certain extent.) VAR does not say “The risk of losing X dollars is Y, within a confidence of Z.” (Although risk managers treat it that way). What VAR actually says is “the risk of losing X dollars is Y, based on the given parameters.” The problem is obvious even to the non-technician: The future is a strange and foreign place that we do not understand. Deviations of the past may not be the deviations of the future. Just because municipal bonds have never traded at such-and-such a spread to U.S. Treasury bonds does not mean that they won’t in the future. They just haven’t yet. Frequently, the models are blind to this fact.

In fact, one of Nassim’s most trenchant points is that on the day before whatever “worst case” event happened in the past, you would have not been using the coming “worst case” as your worst case, because it wouldn’t have happened yet.

Here’s an easy illustration. October 19, 1987, the stock market dropped by 22.61%, or 508 points on the Dow Jones Industrial Average. In percentage terms, it was then and remains the worst one-day market drop in U.S. history. It was dubbed “Black Monday.” (Financial writers sometimes lack creativity — there are several other “Black Monday’s” in history.) But here we see Nassim’s point: On October 18, 1987, what would the models use as the worst possible case? We don’t know exactly, but we do know the previous worst case was 12.82%, which happened on October 28, 1929. A 22.61% drop would have been considered so many standard deviations from the average as to be near impossible.

But the tails are very fat in finance – improbable and consequential events seem to happen far more often than they should based on naive statistics. There is also a severe but often unrecognized recursiveness problem, which is that the models themselves influence the outcome they are trying to predict. (To understand this more fully, check out our post on Complex Adaptive Systems.)

A second problem with VAR is that even if we had a vastly more robust dataset, a statistical “confidence interval” does not do the job of financial risk management. Says Taleb:

There is an internal contradiction between measuring risk (i.e. standard deviation) and using a tool [VAR] with a higher standard error than that of the measure itself.

I find that those professional risk managers whom I heard recommend a “guarded” use of the VAR on grounds that it “generally works” or “it works on average” do not share my definition of risk management. The risk management objective function is survival, not profits and losses. A trader according to the Chicago legend, “made 8 million in eight years and lost 80 million in eight minutes”. According to the same standards, he would be, “in general”, and “on average” a good risk manager.

This is like a GPS system that shows you where you are at all times, but doesn’t include cliffs. You’d be perfectly happy with your GPS until you drove off a mountain.

It was this type of naive trust of models that got a lot of people in trouble in the recent mortgage crisis. Backward-looking, trend-fitting models, the most common maps of the financial territory, failed by describing a territory that was only a mirage: A world where home prices only went up. (Lewis Carroll would have approved.)

This was navigating Tulsa with a map of Tatooine.


The logical response to all this is, “So what?” If our maps fail us, how do we operate in an uncertain world? This is its own discussion for another time, and Taleb has gone to great pains to try and address the concern. Smart minds disagree on the solution. But one obvious key must be building systems that are robust to model error.

The practical problem with a model like VAR is that the banks use it to optimize. In other words, they take on as much exposure as the model deems OK. And when banks veer into managing to a highly detailed, highly confident model rather than to informed common sense, which happens frequently, they tend to build up hidden risks that will un-hide themselves in time.

If one were to instead assume that there were no precisely accurate maps of the financial territory, they would have to fall back on much simpler heuristics. (If you assume detailed statistical models of the future will fail you, you don’t use them.)

In short, you would do what Warren Buffett has done with Berkshire Hathaway. Mr. Buffett, to our knowledge, has never used a computer model in his life, yet manages an institution half a trillion dollars in size by assets, a large portion of which are financial assets. How?

The approach requires not only assuming a future worst case far more severe than the past, but also dictates building an institution with a robust set of backup systems, and margins-of-safety operating at multiple levels. Extra cash, rather than extra leverage. Taking great pains to make sure the tails can’t kill you. Instead of optimizing to a model, accepting the limits of your clairvoyance.

The trade-off, of course, is short-run rewards much less great than those available under more optimized models. Speaking of this, Charlie Munger has noted:

Berkshire’s past record has been almost ridiculous. If Berkshire had used even half the leverage of, say, Rupert Murdoch, it would be five times its current size.

For Berkshire at least, the trade-off seems to have been worth it.


The salient point then is that in our march to simplify reality with useful models, of which Farnam Street is an advocate, we confuse the models with reality. For many people, the model creates its own reality. It is as if the spreadsheet comes to life. We forget that reality is a lot messier. The map isn’t the territory. The theory isn’t what it describes, it’s simply a way we choose to interpret a certain set of information. Maps can also be wrong, but even if they are essentially correct, they are an abstraction, and abstraction means that information is lost to save space. (Recall the mile-to-mile scale map.)

How do we do better? This is fodder for another post, but the first step is to realize that you do not understand a model, map, or reduction unless you understand and respect its limitations. We must always be vigilant by stepping back to understand the context in which a map is useful, and where the cliffs might lie. Until we do that, we are the turkey.