How Much Art Can the Brain Take?

Steven Pinker

This article is adapted from How the Mind Works (Penguin paperback, 1999).

Man does not live by bread alone, nor by know-how, safety, children, or sex. People everywhere spend as much time as they can afford on activities that, in the struggle to survive and reproduce, seem pointless. In all cultures, people tell stories and recite poetry. They joke, laugh, and tease. They sing and dance. They decorate surfaces.

As if that weren't enough of a puzzle, the more biologically frivolous and vain the activity, the more people exalt it. Art, literature, and music are thought to be not just pleasurable but noble. They are the mind's best work, what makes life worth living. Why do we pursue the biologically trivial and futile and experience them as sublime? To many educated people the question seems horribly philistine, even immoral. But it is unavoidable for anyone interested in the makeup of [Homo sapiens]. Members of our species do mad deeds like living for their art and (in India) selling their blood to buy movie tickets. Why? How might we understand the psychology of the arts within the modern understanding of the brain as a biological organ shaped by the forces of evolution?

Every university has a faculty of arts, which usually dominates the institution in numbers and in the public eye. But the tens of thousands of scholars and millions of pages of scholarship have shed almost no light on the question of why people pursue the arts at all. The function of the arts is almost defiantly obscure, and I think there are several reasons why.

One is that the arts engage not only the psychology of aesthetics but the psychology of status. The very uselessness of art that makes it so incomprehensible to the evolutionary biologist makes it all too comprehensible to the economist and social psychologist. What better proof that you have money to spare than your being able to spend it on doodads and stunts that don't fill the belly or keep the rain out but that require precious materials, years of practice, a command of obscure texts, or intimacy with the elite?

Thorstein Veblen's and Quentin Bell's classic analyses of taste and fashion, in which an elite's conspicuous displays of consumption, leisure, and outrage are emulated by the rabble, sending the elite off in search of new inimitable displays, nicely explains the otherwise inexplicable oddities of the arts. The grand styles of one century become tacky in the next, as we see in words that are both period labels and terms of abuse ([gothic, mannerist, baroque], [rococo]). The steadfast patrons of the arts are the aristocracy and those who want to join them. Most people would lose their taste for a musical recording if they learned it was being sold at supermarket checkout counters or on late-night television, and even the work of relatively prestigious artists, such as Pierre Auguste Renoir and Claude Monet, draws derisive reviews when it is shown in a popular "blockbuster" museum show. Modern and postmodern works are intended not to give pleasure but to confirm or confound the theories of a guild of critics and analysts, to e'pater la bourgeoisie, or to baffle the rubes in Peoria.

The banality that the psychology of the arts is partly the psychology of status has been repeatedly pointed out, not just by cynics and barbarians but by erudite social commentators such as Quentin Bell and Tom Wolfe. But in the modern university, it is unmentioned, indeed, unmentionable. Academics and intellectuals are culture vultures. In a gathering of today's elite, it is perfectly acceptable to laugh that you barely passed Physics for Poets and Rocks for Jocks and have remained ignorant of science ever since, despite the obvious importance of scientific literacy to informed choices about personal health and public policy. But saying that you have never heard of James Joyce or that you tried listening to Mozart once but prefer Andrew Lloyd Webber is as shocking as blowing your nose on your sleeve or announcing that you employ children in your sweatshop, despite the obvious [un]importance of your tastes in leisure-time activity to just about anything. The blending in people's minds of art, status, and virtue is an extension of Bell's principle of "sartorial morality": people find dignity in the signs of an honorably futile existence removed from all menial necessities.

I mention these facts not to denigrate the arts but to clarify an important mystery in understanding ourselves. To understand the psychology of the arts, we have to look at the phenomena with the disinterested eye of an alien biologist trying to make sense of the human species rather than as a member of the species with a stake in how the arts are portrayed. *OF COURSE* we find pleasure and enlightenment in contemplating the products of the arts, and not all of it is a pride in sharing the tastes of the beautiful people. But to understand the psychology of the arts that remains when we subtract out the psychology of status, we must leave at the door our terror of being mistaken for the kind of person who prefers Andrew Lloyd Webber to Mozart. We need to begin with folk songs, pulp fiction, and paintings on black velvet, not Mahler, Eliot, and Kandinsky. And that does *not* mean compensating for our slumming by dressing up the lowly subject matter in highfalutin "theory" (a semiotic analysis of [Peanuts], a psychoanalytic exegesis of James Bond, a deconstruction of [Vogue]). It means asking a simple question: What is it about the mind that lets people take pleasure in shapes and colors and sounds and stories and myths?

That question might be answerable, whereas questions about Art in general are not. Theories of Art carry the seeds of their own destruction. In an age when any Joe can buy CDs, paintings, and novels, artists make their careers by finding ways to avoid the hackneyed, to challenge jaded tastes, to differentiate the cognoscenti from the dilettantes, and to flout the current wisdom about what art is (hence the fruitless attempts over the decades to define art). Any discussion that fails to recognize that dynamic is doomed to sterility. It can never explain why music pleases the ear, because "music" will be defined to encompass atonal jazz, chromatic compositions, and other intellectual exercises. It will never understand the bawdy laughs and convivial banter that are so important in people's lives because it will define humor as the arch wit of an Oscar Wilde. Excellence and the avant-garde are designed for the sophisticated palate, a product of years of immersion in a genre and a familiarity with its conventions and cliches. They rely on one-upmanship and arcane allusions and displays of virtuosity. However fascinating and worthy of our support they are, they tend to obscure the psychology of aesthetics, not to illuminate it.

Another reason the psychology of the arts is obscure is that they are not adaptive in the biologist's sense of the word. I believe there is much insight to be gained in studying the adaptive design of the major components of the mind, but that does not mean that everything the mind does is biologically adaptive. The mind is a neural computer, fitted by natural selection with algorithms for reasoning about plants, animals, objects, and people. It is driven by goal states that served biological fitness in ancestral environments, such as food, sex, safety, parenthood, friendship, status, and knowledge. That toolbox, however, can be used to assemble Sunday afternoon projects of dubious biological value.

Some parts of the mind register the attainment of increments of fitness by giving us a sensation of pleasure. Other parts use a knowledge of cause and effect to bring about goals. Put them together and you get a mind that rises to a biologically pointless challenge: figuring out how to get at the pleasure circuits of the brain and deliver little jolts of enjoyment without the inconvenience of wringing bona fide fitness increments from the harsh world. When a rat has access to a lever that sends electrical impulses to an electrode implanted in its medial forebrain bundle, it presses the lever furiously until it drops of exhaustion, forgoing opportunities to eat, drink, and have sex. People don't yet undergo elective neurosurgery to have electrodes implanted in their pleasure centers, but they have found ways to stimulate them by other means. An obvious example is recreational drugs, which seep into the chemical junctions of the pleasure circuits.

Another route to the pleasure circuits is via the senses, which stimulate the circuits when they are in environments that would have led to fitness in past generations. Of course a fitness-promoting environment cannot announce itself directly. It gives off patterns of sounds, sights, smells, tastes, and feels that the senses are designed to register. Now, if the intellectual faculties could identify the pleasure-giving patterns, purify them, and concentrate them, the brain could stimulate itself without the messiness of electrodes or drugs. It could give itself intense artificial doses of the sights and sounds and smells that ordinarily are given off by healthful environments. We enjoy strawberry cheesecake, but not because we evolved a taste for it. We evolved circuits that gave us trickles of enjoyment from the sweet taste of ripe fruit, the creamy mouth feel of fats and oils from nuts and meat, and the coolness of fresh water. Cheesecake packs a sensual wallop unlike anything in the natural world because it is a brew of megadoses of agreeable stimuli which we concocted for the express purpose of pressing our pleasure buttons. Pornography is another pleasure technology. At least to some extent, art may be a third.

The visual arts are one example of a technology designed to defeat the locks that safeguard our pleasure buttons and to press the buttons in various combinations. Vision solves the unsolvable problem of recovering a description of the world from its projection onto the retina by making assumptions about how the world is put together. Optical illusions, including paintings, photographs, movies, and television, cunningly violate those assumptions and give off patterns of light that dupe our visual system into seeing scenes that aren't there. That's the lock-picking. The pleasure buttons are the content of the illusions. Everyday photographs and paintings (the ones that most people hang in their living rooms, though not necessarily the ones you would see in a museum) depict plants, animals, landscapes, and people. Many biologists believe that the geometry of beauty is the visible signal of adaptively valuable objects: safe, food-rich, explorable, learnable habitats, and fertile, healthy dates, mates, and offspring.

Fiction and drama may be a mixture of the non-adaptive and the adaptive. John Dryden defined a play as "a just and lively image of human nature, representing its passions and humours, and the changes of fortune to which it is subject; for the delight and instruction of mankind." It's helpful to distinguish the delight, perhaps the product of a useless technology for pressing our pleasure buttons, from the instruction, perhaps a product of a cognitive adaptation.

The technology of fiction delivers a simulation of life that an audience can enter in the comfort of their cave, couch, or theater seat. Words can evoke mental images, which can activate the parts of the brain that register the world when we actually perceive it. Other technologies violate the assumptions of our perceptual apparatus and trick us with illusions that partly duplicate the experience of seeing and hearing real events. They include costumes, makeup, sets, sound effects, cinematography, and animation. Perhaps in the near future we can add virtual reality to the list, and in the more distant future the feelies of [Brave New World]. When the illusions work, there is no mystery to the question "Why do people enjoy fiction?" It is identical to the question "Why do people enjoy life?" When we are absorbed in a book or a movie, we get to see breathtaking landscapes, hobnob with important people, fall in love with ravishing men and women, protect loved ones, attain impossible goals, and defeat wicked enemies. Not a bad deal for seven dollars and fifty cents!

Even following the foibles of ordinary virtual people as they live their lives can press a pleasure button, the one labeled "gossip." Gossip is a favorite pastime in all human societies because knowledge is power. Knowing who needs a favor and who is in a position to offer one, who is trustworthy and who is a liar, who is available (or soon to become available) and who is under the protection of a jealous spouse or family --- all give obvious strategic advantages in the games of life. That is especially true when the information is not yet widely known and one can be the first to exploit an opportunity, the social equivalent of insider trading. In the small bands in which our minds evolved, everyone knew everyone else, so all gossip was useful. Today, when we peer into the private lives of fictitious characters, we are giving ourselves the same buzz.

Literature, of course, not only delights but instructs. Fictional narratives might work a bit like experiments. The author places a fictitious character in a hypothetical situation in an otherwise real world, and allows the reader to explore the consequences. Once the fictitious world is set up, the protagonist is given a goal and we watch as he or she pursues it in the face of obstacles. We watch what happens to them and mentally take notes on the outcomes of the strategies and tactics they use in pursuing their goals.

What are those goals? A Darwinian would say that ultimately organisms have only two: to survive and to reproduce. And those are precisely the goals that drive the human organisms in fiction. Most of the thirty-six plots in Georges Polti's catalogue "The Thirty-Six Dramatic Situations" are defined by love or sex or a threat to the safety of the protagonist or his kin (for example, "Mistaken jealousy," "Vengeance taken for kindred upon kindred," and "Discovery of the dishonor of a loved one"). The difference between fiction for children and fiction for adults is commonly summed up in two words: sex and violence. The American movie critic Pauline Kael got the title for one of her books from an Italian movie poster that she said contained "the briefest statement imaginable of the basic appeal of the movies": Kiss Kiss Bang Bang.

Sex and violence are not just the obsessions of pulp fiction and trash TV. The writers Richard Lederer and Michael Gilleland present the following tabloid headlines:

DOCTOR'S WIFE AND LOCAL MINISTER EXPOSED FOR CONCEIVING ILLEGITIMATE DAUGHTER

TEENAGERS COMMIT DOUBLE SUICIDE; FAMILIES VOW TO END VENDETTA

STUDENT CONFESSES TO AXE MURDER OF LOCAL PAWNBROKER AND ASSISTANT

MADWOMAN LONG IMPRISONED IN ATTIC SETS HOUSE ON FIRE, THEN LEAPS TO DEATH

PRINCE ACQUITTED OF KILLING MOTHER IN REVENGE FOR MURDER OF HIS FATHER

Sound familiar? They are the plots of [The Scarlet Letter], @I[Romeo and Juliet], [Crime and Punishment], [Jane Eyre], and [Eumenides]. The intrigues of people in conflict can multiply out in so many ways that no one could possibly play out the consequences of all courses of action in the mind's eye. Fictional narratives supply us with a mental catalogue of the fatal conundrums we might face someday and the outcomes of strategies we could deploy in them. The cliche that life imitates art is true because the function of some kinds of art may be for life to imitate it.

Of course, there is far more to the arts than pressing our pleasure buttons and playing out lurid scenarios. Art can help us see the world in new ways, give us a sense of harmony with the cosmos, and allow us to experience the sublime. But if we really want to understand this strange and eternally fascinating quirk of the human brain, we cannot just exalt the finest examples. We have to look at the typical exa

By Umberto Eco An English modification of an essay for La Repubblica, 15 October 2001. Excerpted from Counterpunch). Original Article: Le guerre sante passione e ragione All the religious wars that have caused blood to be shed for centuries arise from passionate feelings and facile counter-positions, such as Us and Them, good and bad, white and black. If western culture is shown to be rich it is because, even before the Enlightenment, it has tried to "dissolve" harmful simplifications through inquiry and the critical mind. Of course it did not always do this. Hitler, who burned books, condemned "degenerate" art and killed those belonging to "inferior" races; and the fascism which taught me at school to recite "May God Curse the English" because they were "the people who eat five meals a day" and were therefore greedy and inferior to thrifty Italians, are also part of the history of western culture. It is sometimes hard to grasp the difference between identifying with one's own roots, understanding people with other roots, and judging what is good or bad. Should I prefer to live in Limoges rather than, say, Moscow? Moscow is certainly a beautiful city. But in Limoges I would understand the language. Everyone identifies with the culture in which he grew up and the cases of root transplants, while they do occur, are in the minority: Lawrence of Arabia dressed as an Arab, but he ended up back home in England. The west, often for reasons of economic expansion, has been curious about other civilisations. The Greeks referred to those who did not speak their language as barbarians, that is stammerers, as if they did not speak at all. But a few more mature Greeks, like the Stoics, noticed that although the barbarians used different words, they referred to the same thoughts. From the second half of the 19th century, cultural anthropology developed as an attempt to assuage the guilt of the west towards others, and particularly those others who had been defined as savages; societies without a history, primitive peoples. The task of the cultural anthropologist was to demonstrate that beliefs which differed from western ones existed, and should be taken seriously, not disdained and repressed. In order to say -- as Italian prime minister Silvio Berlusconi did, controversially, this month -- whether any one culture is superior to another, parameters have to be established. A culture can be described objectively -- these people behave like this; believe in spirits or in a single divine being that pervades the whole of nature; meet in family clans according to these rules; consider it beautiful to pierce their noses with rings (this could be a description of western youth culture); consider pork to be impure; circumcise themselves; raise dogs for the pot on public holidays or, as the English and Americans still say of the French, eat frogs. Obviously, the anthropologist knows that objectivity is always limited by many factors. The criteria of judgment depend on our own roots, preferences, habits, passions, our system of values. For example: do we consider that the prolonging of the average life span from 40 to 80 years is worthwhile? I personally believe so, but many mystics could tell me that, between a glutton who lives for 80 years and Saint Luigi Gonzaga, who only survived for 23, it was the latter who had the fuller life. Do we believe that technological development, the expansion of trade, and faster transport is worthwhile? Many think so, and judge our technological civilisation as superior. But, within the western world itself, there are those who primarily wish to live in harmony with an uncorrupted environment, and are willing to relinquish air travel, cars and refrigerators, to weave baskets and travel on foot from one village to another, as long as the ozone hole isn't there. So in order to define one culture as better than another, it is not enough to describe it (as the anthropologist does), but it is advisable to have recourse to a system of values which we do not feel we can relinquish. Only at this point can we say that our culture is better, for us. How absolute is the parameter of technological development? Pakistan has the atom bomb, not Italy. So is Italy an inferior civilisation? Better to live in Islamabad than Arcore? Shouldn't we respect the Islamic world by being reminded that it has given us men like Avicenna (who was actually born in Buchara, not far from Afghanistan) and Averroes, as well as Al-Kindi, Avenpace, Avicebron, Ibn Tufayl, or that great historian of the 14th century Ibn Khaldoun, whom the west considers as the father of the social sciences. The Arabs of Spain cultivated geography, astronomy, mathematics or medicine when the Christian world was lagging far behind in those subjects. We might recall that those Arabs of Spain were fairly tolerant of Christians and Jews, while we gave rise to the ghettoes, and that Saladin, when he reconquered Jerusalem, was more merciful to the Christians than the Christians had been to the Saracens when they took over Jerusalem. All very true, but in the Islamic world there are fundamentalist and theocratic regimes today which the Christians do not tolerate, and Bin Laden was not merciful to New York. The Taliban destroyed the great stone Buddhas with their cannon: conversely, the French carried out the St Bartholomew's day massacre, but this gives no one the right to say they are barbarians today. History is a two-edged sword. The Turks were impalers (and that's bad) but the orthodox Byzantines put out the eyes of their dangerous relatives and the Catholics burned Giordano Bruno; Saracen pirates did many wicked things, but the buccaneers of his British majesty set fire to the Spanish colonies in the Caribbean; Bin Laden and Saddam Hussein are ferocious enemies of western civilisation, but within western civilisation there were men like Hitler and Stalin. No, the problem of parameters is not set within history, but in our times. One of the praiseworthy aspects of western culture (free and pluralistic, and these are values which we consider basic and essential) is that it has been long held that the same person can employ different parameters which may be mutually contradictory on different matters. For example, the prolonging of life is considered good, and atmospheric pollution bad, but we can very well see that maybe in big laboratories where they study how to prolong life, there might be power systems which themselves produce pollution. Western culture has developed the capacity to freely lay bare its own contradictions. Maybe they remain unresolved, but they are well known and admitted: how can we manage some positive globalisation while avoiding the risks and injustices that follow; how can we prolong life for the millions of Africans dying of AIDS (while at the same time prolonging our own lives) without accepting a planetary economy which causes people to die of hunger and AIDS, and makes us eat polluted food? But it is just this criticism of parameters, pursued and encouraged by the west, that makes us understand how delicate the matter is. Is it just and proper to protect bank secrets? Many people think so. But if this secrecy allows terrorists to keep their accounts in the City of London then is this defence of so-called privacy a positive value or a doubtful one? We are always calling our parameters into question. The western world does so to such an extent as to allow its own citizens to turn down technological development and become Buddhists, or go and live in communities where no tyres are used, not even for horse-drawn carts. The west has decided to channel money and effort into studying other customs and practices, but no one has really given other people the chance to study western customs and practices, except at schools maintained by white expatriates, or by allowing the rich from other cultures to study in Oxford or Paris. What happens then is that they return home to organise fundamentalist movements, because they feel solidarity with those of their compatriots who lack the opportunity for such education. An international organisation called Transcultura has been campaigning for an "alternative anthropology" for some years. It has taken African researchers, who have never been to the west before, to describe provincial France and society in Bologna. Both sides started to take a genuine look at each other, and some interesting discussions took place. At present, three Chinese -- a philosopher, an anthropologist and an artist -- are completing a Marco Polo voyage in reverse, culminating in a conference in Brussels in November. Imagine Muslim fundamentalists being invited to research Christian fundamentalism (not the Catholics this time, but American Protestants, more fanatical than ayatollahs, who try to expunge all reference to Darwin from schools). In my opinion the anthropological study of other people's fundamentalism leads to a better understanding of one's own. Let them come and study our concept of holy war (I could commend many interesting texts to them, including some quite recent ones). They might then take a more critical view of the idea of holy war back home. We are a pluralist civilisation because we allow mosques to be built in our countries, and we are not going to stop simply because Christian missionaries are thrown into prison in Kabul. If we did so, we too would become Taliban. The parameter of tolerating diversity is certainly one of the strongest and least open to argument. We consider our culture mature because it can tolerate diversity, and those who share our culture, while rejecting diversity to be uncivilised, period. We hope that, if we allow mosques in our countries, one day there will be Christian churches in their countries, or at least Buddhas won't get blown up there. If we believe we have got our parameters right, that is. But there is a great deal of confusion. Funny things happen these days. It seems that defending western values has become a rightwing prerogative, while the Left, as ever, is pro-Islamic. Now, apart from the pro-third world, pro-Arab stance of some rightwing and Catholic activist circles, and so on, this ignores a historical phenomenon which is there for all to see. The defence of scientific values, of technological development and modern western culture in general, has always been characteristic of secular and progressive political circles. Indeed, all communist regimes have relied on an ideology of technological and scientific progress. The 1848 Communist Manifesto opens with a dispassionate eulogy on the expansion of the bourgeoisie. Marx does not say it is necessary to change direction and go over to Asian means of production. He merely says that the proletariat must learn to master these values and successes. Conversely it has always been reactionary thought (in the best sense of the word), at least starting from the rejection of the French revolution, which has opposed the secular ideology of progress and propounded a return to traditional values. Only a few neo-Nazi groups have a mythical notion of the west and would be ready to slit the throats of all Muslims at Stonehenge. The more serious traditionalist thinkers have always looked to Islam as a source of alternative spirituality, in addition to the rites and myths of primitive peoples and the teachings of Buddhism. They have always made a point of reminding us that we are not superior, but impoverished by our ideology of progress, and that we must seek the truth among the Sufi mystics or the whirling dervishes. Thus a strange dichotomy is now opening on the right. But perhaps it is only a sign that, at times of great bewilderment (such as the present), no one knows quite where they stand any more. But it is at times of bewilderment that the weapon of analysis and criticism comes into its own, to be applied to our own superstitions and those of others. Umberto Eco (c) 2001

THE FOURTH QUADRANT: A MAP OF THE LIM...

THE FOURTH QUADRANT: A MAP OF THE LIMITS OF STATISTICS [9.15.08]

By Nassim Nicholas Taleb

An Edge Original Essay

Introduction



When Nassim Taleb talks about the limits of statistics, he becomes
outraged. "My outrage," he says, "is aimed at the scientist-charlatan
putting society at risk using statistical methods. This is similar to
iatrogenics, the study of the doctor putting the patient at risk." As a
researcher in probability, he has some credibility. In 2006, using FNMA
and bank risk managers as his prime perpetrators, he wrote the
following:

The
government-sponsored institution Fannie Mae, when I look at its risks,
seems to be sitting on a barrel of dynamite, vulnerable to the
slightest hiccup. But not to worry: their large staff of scientists
deemed these events "unlikely."

In the following Edge original
essay, Taleb continues his examination of Black Swans, the highly
improbable and unpredictable events that have massive impact. He
claims that those who are putting society at risk are "no true
statisticians", merely people using statistics either without
understanding them, or in a self-serving manner. "The current subprime
crisis did wonders to help me drill my point about the limits of
statistically driven claims," he says.

Taleb, looking at the cataclysmic situation facing financial institutions today, points out that "the banking system, betting against Black Swans, has lost over 1 Trillion dollars (so far), more than was ever made in the history of banking".

But, as he points out, there is also good news.

We can identify where the danger zone is located,
which I call "the fourth quadrant", and show it on a map with more or
less clear boundaries. A map is a useful thing because you know where
you are safe and where your knowledge is questionable. So I drew for
the Edge readers a tableau showing the boundaries where
statistics works well and where it is questionable or unreliable. Now
once you identify where the danger zone is, where your knowledge is no
longer valid, you can easily make some policy rules: how to conduct
yourself in that fourth quadrant; what to avoid.

—John Brockman

NASSIM
NICHOLAS TALEB, essayist and former mathematical trader, is
Distinguished Professor of Risk Engineering at New York University’s
Polytechnic Institute. He is the author of Fooled by Randomness and the international bestseller The Black Swan.

Nassim Taleb's Edge Bio Page

REALITY CLUB: Jaron Lanier, George Dyson

BLOGWATCH

---

THE FOURTH QUADRANT: A MAP OF THE LIMITS OF STATISTICS

Statistical and applied probabilistic knowledge is the core
of knowledge; statistics is what tells you if something is true, false, or
merely anecdotal; it is the "logic of science"; it is the instrument of
risk-taking; it is the applied tools of epistemology; you can't be a modern
intellectual and not think probabilistically—but... let's not be suckers.
The problem is much more complicated than it seems to the casual, mechanistic
user who picked it up in graduate school. Statistics can fool you. In fact it
is fooling your government right now. It can even bankrupt the system (let's
face it: use of probabilistic methods for the estimation of risks did just blow up the banking system).

The current subprime crisis has been doing wonders for the
reception of any ideas about probability-driven claims in science, particularly
in social science, economics, and "econometrics" (quantitative economics).  Clearly, with current International
Monetary Fund estimates of the costs of the 2007-2008 subprime crisis,  the banking system seems to have lost
more on risk taking (from the failures of quantitative risk management) than
every penny banks ever earned
taking risks. But it was easy to see from the past that the pilot did not have
the qualifications to fly the plane and was using the wrong navigation tools:
The same happened in 1983 with money center banks losing cumulatively every
penny ever made, and in 1991-1992 when the Savings and Loans industry became
history.

It appears that financial institutions earn money on transactions (say
fees on your mother-in-law's checking account) and lose everything taking risks
they don't understand. I want this to stop, and stop now— the current
patching by the banking establishment worldwide is akin to using the same
doctor to cure the patient when the doctor has a track record of systematically
killing them. And this is not limited to banking—I generalize to an
entire class of random variables that do not have the structure we thing they
have, in which we can be suckers.

And we are beyond suckers: not only, for socio-economic
and other nonlinear, complicated variables, we are riding in a bus driven a blindfolded driver, but we refuse to
acknowledge it in spite of the evidence, which to me is a pathological problem
with academia. After 1998, when a "Nobel-crowned" collection of people (and the
crème de la crème of the financial economics establishment) blew up Long Term
Capital Management, a hedge fund, because the "scientific" methods they used
misestimated the role of the rare event, such methodologies and such claims on
understanding risks of rare events should have been discredited. Yet the Fed
helped their bailout and exposure to rare events (and model error) patently increased exponentially (as
we can see from banks' swelling portfolios of derivatives that we do not
understand).

Are we using models of uncertainty to produce certainties?

This masquerade does not seem to come from statisticians—but from the commoditized, "me-too" users of the products. Professional
statisticians can be remarkably introspective and self-critical. Recently, the
American Statistical Association had a special panel session on the "black
swan" concept at the annual Joint Statistical Meeting in Denver last August.
They insistently made a distinction between the "statisticians" (those who deal
with the subject itself and design the tools and methods) and those in other
fields who pick up statistical tools from textbooks without really
understanding them. For them it is a problem with statistical education and
half-baked expertise. Alas, this category of blind users includes regulators
and risk managers, whom I accuse of creating more risk than they reduce. 

So the good news is that we can identify where the danger zone is located, which I call "the fourth
quadrant", and show it on a map with more or less clear boundaries.  A map is a useful thing because you
know where you are safe and where your knowledge is questionable. So I drew for
the Edge readers a tableau showing the boundaries where statistics works well
and where it is questionable or unreliable.  Now once you identify where the danger zone is, where your
knowledge is no longer valid, you can easily make some policy rules: how to
conduct yourself in that fourth quadrant; what to avoid.

So the principal value of the map is that it allows for
policy making. Indeed, I am moving on: my new project is about methods on how
to domesticate the unknown, exploit randomness, figure out how to live in a world we don't understand very well. While
most human thought (particularly since the enlightenment) has focused us on how
to turn knowledge into decisions, my new mission is to build methods to turn
lack of information, lack of understanding, and lack of "knowledge" into
decisions—how, as we will see, not to be a "turkey".

This piece has a technical appendix that presents
mathematical points and empirical evidence. (See link below.) It includes a battery of tests
showing that no known conventional tool can allow us to make precise
statistical claims in the Fourth Quadrant. While in the past I limited myself
to citing research papers, and evidence compiled  by others (a less risky trade), here I got hold of more than
20 million pieces of data (includes 98% of the corresponding macroeconomics
values of transacted daily, weekly, and monthly variables for the last 40
years) and redid a systematic analysis that includes recent years.

What Is Fundamentally Different About Real Life

My anger with "empirical" claims in risk management does not
come from research. It comes from spending twenty tense (but entertaining)
years taking risky decisions in the real world managing portfolios of complex
derivatives, with payoffs that depend on higher order statistical properties
—and you quickly realize that a certain class of relationships that "look
good" in research papers almost never replicate in real life (in spite of the papers making some claims with a "p"
close to infallible). But that is not the main problem with research.

For us the world is vastly simpler in some sense than the
academy, vastly more complicated in another. So the central lesson from
decision-making (as opposed to working with data on a computer or bickering
about logical constructions) is the following: it is the exposure (or payoff) that creates the complexity
—and the opportunities and dangers— not so much the knowledge (
i.e., statistical distribution, model representation, etc.). In some
situations, you can be extremely wrong and be fine, in others you can be
slightly wrong and explode. If you are leveraged, errors blow you up; if you
are not, you can enjoy life.

So knowledge (i.e., if some statement is "true" or "false")
matters little, very little in many situations. In the real world, there are
very few situations where what you do and your belief if some statement is true
or false naively map into each other. Some decisions require vastly more
caution than others—or highly more drastic confidence intervals. For
instance you do not "need evidence" that the water is poisonous to not drink from it. You do not
need "evidence" that a gun is loaded to avoid playing Russian roulette, or
evidence that a thief a on the lookout to lock your door. You need evidence of
safety—not evidence of lack of safety— a central asymmetry that
affects us with rare events. This asymmetry in skepticism makes it easy to draw
a map of danger spots.

The Dangers Of Bogus Math

I start with my old crusade against "quants"
(people like me who do mathematical work in finance), economists, and bank risk managers, my
prime perpetrators of iatrogenic risks (the healer killing the patient). Why
iatrogenic risks? Because, not only have economists been unable to prove that their models work, but
no one managed to prove that  the
use of a model that does not work is neutral,
that it does not increase blind risk taking, hence the accumulation of hidden
risks.

 

Figure
1
My classical metaphor: A Turkey is fed for a
1000 days—every days confirms to its statistical department that the
human race cares about its welfare "with increased statistical significance".
On the 1001^st day, the turkey has a surprise.

 

Figure

2

The graph above shows the fate of close to 1000
financial institutions (includes busts such as FNMA,
Bear Stearns, Northern Rock, Lehman Brothers, etc.). The banking system
(betting AGAINST rare events) just lost > 1 Trillion dollars (so far) on a
single error, more than was ever earned in the history of banking. Yet bankers
kept their previous bonuses and it looks like citizens have to foot the bills.
And one Professor Ben Bernanke pronounced right before the blowup that we live in an era of stability
and "great moderation" (he is now piloting a plane and we all are passengers on
it).

 
 

Figure

3

The graph shows the daily variations a
derivatives portfolio exposed to U.K. interest rates between 1988 and 2008.
Close to 99% of the variations, over the span of 20 years, will be represented
in 1 single day—the day the European Monetary System collapsed. As I
show in the appendix, this is typical with ANY socio-economic variable
(commodity prices, currencies, inflation numbers, GDP, company performance,
etc. ). No known econometric statistical method can capture the probability of
the event with any remotely acceptable accuracy (except, of course, in
hindsight, and "on paper"). Also note that this applies to surges on
electricity grids and all manner of modern-day phenomena.

Figures 1 and 2 show you the classical problem of the turkey
making statements on the risks based on past history (mixed with some
theorizing that happens to narrate well with the data). A friend of mine was
sold a package of subprime loans (leveraged) on grounds that "30 years of
history show that the trade is safe." He found the argument unassailable
"empirically". And the unusual dominance of the rare event shown in Figure 3 is
not unique: it affects all macroeconomic data—if you look long enough
almost all the contribution in some classes of variables will come from rare
events (I looked in the appendix at 98% of trade-weighted data).

Now let me tell you what worries me. Imagine that the Turkey
can be the most powerful man in world economics, managing our economic fates.
How? A then-Princeton economist called Ben Bernanke made a
pronouncement in late 2004 about the "new moderation" in economic life: the
world getting more and more stable—before becoming the Chairman of the
Federal Reserve. Yet the system was getting riskier and riskier as we were
turkey-style sitting on more and more barrels of dynamite—and Prof.
Bernanke's predecessor the former Federal Reserve Chairman Alan Greenspan was
systematically increasing the hidden risks in the system, making us all more
vulnerable to blowups.

By
the "narrative fallacy" the turkey economics department will always
manage to state, before thanksgivings that "we are in a new era of
safety", and back-it up with thorough and "rigorous" analysis. And
Professor Bernanke indeed found plenty of economic explanations—what I
call the narrative fallacy—with graphs, jargon, curves, the kind of
facade-of-knowledge that you find in economics textbooks. (This is the
find of glib, snake-oil facade of knowledge—even more dangerous because
of the mathematics—that made me, before accepting the new position in
NYU's engineering department, verify that there was not a single
economist in the building. I have nothing against economists: you
should let them entertain each others with their theories and elegant
mathematics, and help keep college students inside buildings. But
beware: they can be plain wrong, yet frame things in a way to make you
feel stupid arguing with them. So make sure you do not give any of them
risk-management responsibilities.)

Bottom Line: The Map

Things are made simple by the following. There are two distinct types of decisions, and
two distinct classes of
randomness.

Decisions: The first type of decisions
is simple, "binary", i.e. you just care if something is true or false. Very
true or very false does not matter. Someone is either pregnant or not pregnant.
A statement is "true" or "false" with some confidence interval. (I call these
M0 as, more technically, they depend on the zero^th moment, namely just on probability of events, and not their magnitude
—you just care about "raw" probability). A biological experiment in the
laboratory or a bet with a friend about the outcome of a soccer game belong to
this category.

The second type of decisions is more complex. You do not
just care of the frequency—but of the impact as well, or, even more
complex, some function of the impact. So there is another layer of uncertainty
of impact. (I call these M1+, as they depend on higher moments of the
distribution). When you invest you do not care how many times you make or lose,
you care about the expectation: how many times you make or lose times the amount made or lost.

Probability structures: There are two
classes of probability domains—very distinct qualitatively and
quantitatively. The first, thin-tailed: Mediocristan",
the second, thick tailed Extremistan. Before I get
into the details, take the literary distinction as follows:

In
Mediocristan, exceptions occur but don't carry large consequences. Add
the heaviest person on the planet to a sample of 1000. The total weight
would barely change. In Extremistan, exceptions can be everything (they
will eventually, in time, represent everything). Add Bill Gates to your
sample: the wealth will  jump by a factor of
>100,000. So, in Mediocristan, large
deviations occur but they are not consequential—unlike Extremistan.

Mediocristan corresponds to "random walk" style randomness
that you tend to find in regular textbooks (and in popular books on
randomness). Extremistan corresponds to a "random
jump" one. The first kind I can call "Gaussian-Poisson",
the second "fractal" or Mandelbrotian (after the
works of the great Benoit Mandelbrot linking it to the geometry of nature). But
note here an epistemological question: there is a category of "I don't know"
that I also bundle in Extremistan for the sake of
decision making—simply because I don't know much about the probabilistic
structure or the role of large events.

The Map

Now it
lets see where the traps are:

First
Quadrant: Simple binary decisions, in Mediocristan: Statistics does
wonders. These situations are, unfortunately, more common in academia,
laboratories, and games than real life—what I call the "ludic fallacy".
In other words, these are the situations in casinos, games, dice, and
we tend to study them because we are successful in modeling them.

Second Quadrant: Simple decisions,
in Extremistan: some well known problem studied in
the literature. Except of course that there are not many simple decisions in Extremistan.



Third Quadrant: Complex decisions
in Mediocristan: Statistical methods work
surprisingly well.



Fourth Quadrant: Complex decisions in Extremistan:
Welcome to the Black Swan domain. Here is where your limits are. Do not base
your decisions on statistically based claims. Or, alternatively, try to move
your exposure type to make it third-quadrant style ("clipping tails").

The four quadrants. The South-East area (in orange) is
where statistics and models fail us.

Tableau Of Payoffs

Two Difficulties

Let me refine
the analysis. The passage from theory to the real world presents two distinct
difficulties: "inverse problems" and  "pre-asymptotics".

Inverse Problems.
It is the greatest epistemological difficulty I know. In real life we
do not observe probability distributions (not even in Soviet Russia,
not even the French government). We just observe events. So we do not
know the statistical properties—until, of course, after the fact. Given
a set of observations, plenty of statistical distributions can
correspond to the exact same realizations—each would extrapolate
differently outside the set of events on which it was derived. The
inverse problem is more acute when more theories, more distributions
can fit a set a data.

This inverse problem is compounded
by the small sample properties of rare events as these will be naturally rare
in a past sample. It is also acute in the presence of nonlinearities as the
families of possible models/parametrization explode
in numbers.

Pre-asymptotics. Theories are, of
course, bad, but they can be worse in some situations when they were derived in
idealized situations, the asymptote, but are used outside the asymptote (its
limit, say infinity or the infinitesimal). Some asymptotic properties do work
well preasymptotically (Mediocristan),
which is why casinos do well, but others do not, particularly when it comes to Extremistan.

Most statistical
education is based on these asymptotic, Platonic properties—yet we live
in the real world that rarely resembles the asymptote.  Furthermore, this compounds the ludic fallacy: most of what students of statistics do is
assume a structure, typically with a known probability. Yet the problem we have
is not so much making computations once you know the probabilities, but finding
the true distribution.

The Inverse Problem Of The Rare Events

Let us start with the inverse problem of rare events and proceed
with a simple, nonmathematical argument. In August 2007, The Wall Street
Journal published a statement by one financial economist, expressing his
surprise that financial markets experienced a string of events that "would
happen once in 10,000 years". A portrait of the gentleman accompanying the
article revealed that he was considerably  younger than 10,000 years; it
is therefore fair to assume that he was not drawing his inference from his own
empirical experience (and not from history at large), but from some theoretical
model that produces the risk of rare events, or what he perceived to be rare
events.

Alas, the rarer
the event, the more theory you need (since we don't observe it). So the rarer the event, the worse its
inverse problem. And theories are fragile (just think of Doctor
Bernanke).

The tragedy is as follows. Suppose that you are deriving
probabilities of future occurrences from the data, assuming (generously) that
the past is representative of the future. Now, say that you estimate that an
event happens every 1,000 days. You will need a lot more data than 1,000 days
to ascertain its frequency, say 3,000 days. Now, what if the event happens once
every 5,000 days? The estimation of this probability requires some larger
number, 15,000 or more. The smaller the probability, the more observations you
need, and the greater the estimation error for a set number of observations.
Therefore, to estimate a rare event you need a sample that is larger and larger
in inverse proportion to the occurrence of the event.

If small probability events carry large
impacts, and (at the same time) these small probability events are more
difficult to compute from past data itself, then: our empirical knowledge about the potential contribution—or role—of rare events (probability × consequence) is
inversely proportional to their impact. This is why we should worry in the
fourth quadrant!

For rare
events, the confirmation bias (the tendency, Bernanke-style, of finding samples
that confirm your opinion, not those that disconfirm it) is very costly and
very distorting. Why? Most of histories of Black Swan prone events is going to
be Black Swan free! Most samples will not reveal the black swans—except
after if you are hit with them, in which case you will not be in a position to
discuss them. Indeed I show with 40 years of data that past Black Swans do not predict future Black Swans
in socio-economic life.

 

Figure

4
The Confirmation Bias At Work. For left-tailed fat-tailed
distributions, we do not see much of negative outcomes for surviving
entities AND we have a small sample in the left tail. This is why we
tend to see a better past for a certain class of time series than
warranted.

Fallacy Of The Single Event Probability

Let us look at events in Mediocristan. In a developed country a newborn female is expected to die at around 79,
according to insurance tables. When she reaches her 79th birthday, her life expectancy, assuming that
she is in typical health, is another 10 years. At the age of 90, she should
have another 4.7 years to go. So
if you are told that a person is older than 100, you can estimate that he is
102.5 and conditional on the person being older than 140 you can estimate that
he is 140 plus a few minutes. The conditional expectation of additional life drops as a person gets older.

In
Extremistan things work differently and the conditional expectation of
an increase in a random variable does not drop as the variable gets
larger. In the real world, say with stock returns (and all economic
variable), conditional on a loss being worse than the 5 units, to use a
conventional unit of measure units, it will be around 8 units.
Conditional that a move is more than 50 STD it should be around 80
units, and if we go all the way until the sample is depleted, the
average move worse than 100 units is 250 units! This extends all the
way to areas in which we have sufficient sample.



This tells us that there is "no typical" failure and "no typical"
success.  You may be able to predict the occurrence of a war, but you
will not be able to gauge its effect! Conditional on a war killing more
than 5 million people, it should kill around 10 (or more). Conditional
on it killing more than 500 million, it would kill a billion (or more,
we don't know).  You may correctly predict a skilled person getting
"rich", but he can make a million, ten million, a billion, ten
billion—there is no typical number. We have data, for instance, for
predictions of drug sales, conditional on getting things right. Sales
estimates are totally uncorrelated to actual sales—some drugs that were
correctly predicted to be successful had their sales underestimated by
up to 22 times!

This absence of "typical" event in Extremistan is what makes prediction markets ludicrous, as they make events look binary. "A
war" is meaningless: you need to estimate its damage—and no damage is
typical. Many predicted that the First War would occur—but nobody
predicted its magnitude. Of the reasons economics does not work is that the
literature is almost completely blind to the point.

A Simple Proof Of Unpredictability In The Fourth Quadrant

I show elsewhere that if you don't know what a "typical"
event is, fractal power laws are the most effective way to discuss the extremes mathematically. It does not mean that the real
world generator is actually a power law—it means you don't understand
the structure of the external events it delivers and
need a tool of analysis so you do not become a turkey. Also, fractals simplify
the mathematical discussions because all you need is play with one parameter (I
call it "alpha") and it increases or decreases the role of the rare event in
the total properties.

For instance, you move alpha from 2.3 to 2 in the
publishing business, and the sales of books in excess of 1 million copies
triple!  Before meeting Benoit
Mandelbrot, I used to play with combinations of scenarios with series of
probabilities and series of payoffs filling spreadsheets with clumsy
simulations; learning to use fractals made such analyses immediate. Now all I
do is change the alpha and see what's going on.

Now the problem: Parametrizing a power law lends itself to monstrous estimation errors (I said that
heavy tails have horrible inverse problems). Small changes in the "alpha" main
parameter used by power laws leads to monstrously large effects in the tails. Monstrous.

And
we don't observe the "alpha. Figure 5 shows more than 40 thousand
computations of the tail exponent "alpha" from different samples of
different economic variables (data for which it is impossible to refute
fractal power laws). We clearly have problems figuring it what the
"alpha" is: our results are marred with errors. Clearly the mean
absolute error is in excess of 1 (i.e. between alpha=2 and alpha=3).
Numerous papers in econophysics found an "average" alpha between 2 and
3—but if you process the >20 million pieces of data analyzed in the
literature, you find that the variations between single variables are
extremely significant.

Figure

5—Estimation error in "alpha" from 40 thousand
economic variables. I thank Pallop Angsupun for data.

Now this mean error has massive consequences. Figure 6 shows
the effect: the expected value of your losses in excess of a certain
amount(called "shortfall") is multiplied by >10 from a small change in the
"alpha" that is less than its mean error! These are the losses banks were
talking about with confident precision!

Figure

6—The value of the expected shortfall
(expected losses in excess of a certain threshold) in response to changes in
tail exponent "alpha". We can see it explode by an order of magnitude.

What if the distribution is not a power law? This is a
question I used to get once a day. Let me repeat it: my argument would not
change—it would take longer to phrase it.

Many researchers, such as Philip Tetlock,
have looked into the incapacity of social scientists in forecasting
(economists, political scientists). It is thus evident that while the
forecasters might be just "empty suits", the forecast errors are dominated by
rare events, and we are limited in our ability to track them. The "wisdom of
crowds" might work in the first three quadrant; but it certainly fails (and has
failed) in the fourth.

Living In The Fourth Quadrant

Beware the Charlatan. When I was a quant-trader in complex derivatives, people
mistaking my profession used to ask me for "stock tips" which put me in a state
of rage: a charlatan is someone likely (statistically) to give you positive
advice, of the "how to" variety.

Go
to a bookstore, and look at the business shelves: you will find plenty
of books telling you how to make your first million, or your first
quarter-billion, etc. You will not be likely to find a book on "how I
failed in business and in life"—though the second type of advice is
vastly more informational, and typically less charlatanic. Indeed, the
only popular such finance book I found that was not quacky in nature—on
how someone lost his fortune—was both self-published and out of print.
Even in academia, there is little room for promotion by publishing
negative results—though these, are vastly informational and less marred
with statistical biases of the kind we call data snooping. So all I am
saying is "what is it that we don't know", and my
advice is what to avoid, no more.

You can live longer if you avoid death,
get better if you avoid bankruptcy, and become prosperous if you avoid blowups
in the fourth quadrant.

Now you would think that people would buy
my arguments about lack of knowledge and accept unpredictability. But many kept
asking me "now that you say that our measures are wrong, do you have anything
better?" 

I used to give the same
mathematical finance lectures for both graduate students and practitioners
before giving up on academic students and grade-seekers. Students cannot
understand the value of "this is what we don't know"—they think it is not information, that they are learning
nothing. Practitioners on the other hand value it immensely. Likewise with
statisticians: I never had a disagreement with statisticians (who build the
field)—only with users of statistical methods.

Spyros Makridakis and I are editors of a special issue of a decision science journal, The International Journal of Forecasting.
The issue is about "What to do in an environment of low predictability". We
received tons of papers, but guess what? Very few addressed the point: they
mostly focused on showing us that they predict better (on paper).  This convinced me to engage in my new
project: "how to live in a world we don't understand".

So for now I can produce phronetic rules (in the Aristotelian sense of phronesis,
decision-making wisdom). Here are
a few, to conclude.

Phronetic Rules: What Is Wise To Do (Or Not Do) In The Fourth Quadrant

1) Avoid Optimization, Learn to Love Redundancy.
Psychologists tell us that getting rich does not bring happiness—if you
spend it. But if you hide it under the mattress, you are less
vulnerable to a black swan. Only fools (such as Banks) optimize, not
realizing that a simple model error can blow through their capital (as
it just did). In one day in August 2007, Goldman Sachs experienced 24 x
the average daily transaction volume—would 29 times have blown up the
system? The only weak point I know of financial markets is their
ability to drive people & companies to "efficiency" (to please a
stock analyst’s earnings target) against risks of extreme events.



Indeed some systems tend to optimize—therefore become more fragile.
Electricity grids for example optimize to the point of not coping with
unexpected surges—Albert-Lazlo Barabasi warned us of the possibility of
a NYC blackout like the one we had in August 2003. Quite prophetic, the
fellow. Yet energy supply kept getting more and more efficient since.
Commodity prices can double on a short burst in demand (oil, copper,
wheat) —we no longer have any slack.  Almost everyone who talks about
"flat earth" does not realize that it is overoptimized to the point of
maximal vulnerability.



Biological systems—those that survived millions of years—include huge
redundancies. Just consider why we like sexual encounters (so redundant
to do it so often!). Historically populations tended to produced around
4-12 children to get to the historical average of ~2 survivors to
adulthood.



Option-theoretic analysis: redundancy is like long an option. You
certainly pay for it, but it may be necessary for survival.



2) Avoid prediction of remote payoffs—though
not necessarily ordinary ones. Payoffs from remote parts of the
distribution are more difficult to predict than closer parts.



A general principle is that, while in the first three quadrants you can
use the best model you can find, this is dangerous in the fourth
quadrant: no model should be better than just any model.



3) Beware the "atypicality" of remote events.
There is a sucker's method called "scenario analysis" and "stress
testing"—usually based on the past (or some "make sense" theory). Yet I
show in the appendix how past shortfalls that do not predict subsequent
shortfalls. Likewise, "prediction markets" are for fools. They might
work for a binary election, but not in the Fourth Quadrant. Recall the
very definition of events is complicated: success might mean one
million in the bank ...or five billions!



4) Time. It
takes much, much longer for a times series in the Fourth Quadrant to
reveal its property. At the worst, we don't know how long. Yet
compensation for bank executives is done on a short term window,
causing a mismatch between observation window and necessary window.
They get rich in spite of negative returns. But we can have a pretty
clear idea if the "Black Swan" can hit on the left (losses) or on the
right (profits).


The point can be used in climatic
analysis. Things that have worked for a long time are preferable—they
are more likely to have reached their ergodic states.



5) Beware Moral Hazard.
Is optimal to make series of bonuses betting on hidden risks in the
Fourth Quadrant, then blow up and write a thank you letter. Fannie Mae
and Freddie Mac's Chairmen will in all likelihood keep their previous
bonuses (as in all previous cases) and even get close to 15 million of
severance pay each.



6) Metrics.
Conventional metrics based on type 1 randomness don't work. Words like
"standard deviation" are not stable and does not measure anything in
the Fourth Quadrant. So does "linear regression" (the errors are in the
fourth quadrant), "Sharpe ratio", Markowitz optimal portfolio, ANOVA
shmnamova, Least square, etc. Literally anything mechanistically pulled
out of a statistical textbook.



My problem is that people can both accept the role of rare events, agree with me, and still use these metrics, which is leading me to test if this is a psychological disorder.  



The technical appendix shows why these metrics fail: they are based on
"variance"/"standard deviation" and terms invented years ago when we
had no computers. One
way I can prove that anything linked to standard deviation is a facade
of knowledge: There is a measure called Kurtosis that indicates
departure from "Normality". It is very, very unstable and marred with
huge sampling error: 70-90% of the Kurtosis in Oil, SP500, Silver, UK
interest rates, Nikkei, US deposit rates, sugar, and the dollar/yet
currency rate come from 1 day in the past 40 years, reminiscent of
figure 3. This means that no sample will ever deliver the true
variance. It also tells us anyone using "variance" or "standard
deviation" (or worse making models that make us take decisions based on
it) in the fourth quadrant is incompetent.



7) Where is the skewness? 
Clearly the Fourth Quadrant can present left or right skewness. If we
suspect right-skewness, the true mean is more likely to be
underestimated by measurement of past realizations, and the total
potential is likewise poorly gauged. A biotech company (usually) faces
positive uncertainty, a bank faces almost exclusively negative shocks.
I call that in my new project "concave" or "convex" to model error.

8) Do not confuse absence of volatility with absence of risks.
Recall how conventional metrics of using volatility as an indicator of
stability has fooled Bernanke—as well as the banking system.

Figure

7

Random Walk—Characterized by volatility. You
only find these in textbooks and in essays on probability by people who have
never really taken decisions under uncertainty.

 

Figure

8

Random Jump process—It is not characterized by
its volatility. Its exits the 80-120 range much less often, but its extremes
are far more severe. Please tell Bernanke if you have the chance to meet him.

9) Beware presentations of risk numbers. Not only we have mathematical
problems, but risk perception is subjected to framing issues that are acute in
the Fourth Quadrant. Dan Goldstein and I are running a program of
experiments in the psychology of uncertainty and finding that the perception of
rare events is subjected to severe framing distortions: people are aggressive
with risks that hit them "once every thirty years" but not if they are told
that the risk happens with a "3% a year" occurrence. Furthermore it appears
that risk representations are not neutral: they cause risk taking even when
they are known to be unreliable.