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Edge 334 — December 2, 2010
(13,600 words)


By Emanuel Derman


By Jeremy Bernstein

An Edge Special Event!

Garniss Curits, Marcel Kinsbourne, M.D., Paul Kedrosky


Fast Company, Big Think, New York Times, Boing Boing, Discover


By Emanuel Derman

Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.


Writing in the New York Times ("They Tried To Outsmart Wall Street" March 9, 2009) , Denis Overbye observed:

Dr. Derman, who spent 17 years at Goldman Sachs, and became managing director, was a forerunner of the many physicists and other scientists who have flooded Wall Street in recent years, moving from a world in which a discrepancy of a few percentage points in a measurement can mean a Nobel Prize or unending mockery to a world in which a few percent one way can land you in jail and a few percent the other way can win you your own private Caribbean island.

They are known as "quants" because they do quantitative finance. Seduced by a vision of mathematical elegance underlying some of the messiest of human activities, they apply skills they once hoped to use to untangle string theory or the nervous system to making money.

Derman, Overbye noted, "fell in love with a corner of finance that dealt with stock options."

"Options theory is kind of deep in some way. It was very elegant; it had the quality of physics" Derman told him.

— JB

EMANUEL DERMAN is physicist and a former managing director and head of the Quantitative Strategies group at Goldman, Sachs & Co., is a professor in Columbia University's Industrial Engineering and Operations Research Department, as well as a partner at Prisma Capital Partners. He is the author of My Life As A Quant.

Emanuel Derman's Edge Bio Page




Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.



Sleep is the interest we have to pay on the capital which is called in at death; and the higher the rate of interest and the more regularly it is paid, the further the date of redemption is postponed.

So wrote Arthur Schopenhauer, comparing life to finance in a universe that must keep its books balanced. At birth you receive a loan – consciousness and light borrowed from the void, leaving an absence in the emptiness.  Nightly, by yielding temporarily to the darkness of sleep, you restore some of the emptiness and keep the absence from growing limitlessly. Finally you must pay back the principal, make the void complete again, and return the life originally lent you.

By focusing on the common periodic nature of both sleep and interest payments, Schopenhauer extends the metaphor of a loan to life itself.  The principal is life and consciousness, and death is the final repayment. Along the way, sleep is the periodic little death that keeps the borrower solvent.

Good metaphors are expansive; they compare something we don’t understand (sleep), to something we think we do (finance). They let you see in a new light both the object of interest and the substrate you rest it on, and enlighten upwards and downwards.

The common basis of Schopenhauer’s metaphoric extension is periodicity.  Taking an analogy based on matching regularities and then extending it into distant regions is a time-honored trick of mathematicians. You can see it at work in the extension of the definition of the factorial function .

Using the exclamation point is traditional but clumsy. Since  is a function of , it’s more elegant to express it via the function  defined by , which satisfies the recursive property . You can regard this property as almost a definition of the factorial function. If you define , then  for all integers  greater than 1 can be found from the recursive definition.

The definition  works only for positive integers n. The definition  seems more malleable. Why shouldn’t there be some function   that satisfies the relation  where x is not necessarily a positive integer? Why shouldn’t the factorial function exist both for   and, say, ?

The Swiss mathematician Leonhard Euler discovered (invented?) the gamma function  that does indeed satisfy  for all . For integer values of x, it agrees with the traditional factorial function. For non-integer or even complex values of x,  serves as a smooth extrapolation or interpolation of the factorial from integer to non-integer arguments. It’s smooth because it coincides with the factorial function for positive integer arguments, but maintains the crucial recursive property for non-integers. Mathematicians call this kind of extension called analytic continuation.

The gamma function is a metaphorical extension of the factorial, in which one property, its recursion, becomes its most important feature and serves as the basis for extending it. It’s a bit like calling an automobile a horseless carriage, preserving the essence of carrying and removing the unnecessary horsefulness, or like calling a railroad ferrovia in Italian or Eisenbahn in German, focusing on the fact that it’s still a road, but one made instead of iron.  Analytic continuation is a method of modeling a function. But whereas most models are restrictive – a model train is less than a real train – in mathematics, a new model can be something greater rather than diminished. That’s because mathematics deals entirely with its own world, and everything you do extends it rather than confines it.

Most of the words we use to describe our feelings are metaphors or models. To say you are elated is to say you feel as though have been lifted to a high place. But why is there something good about height? Because in the gravitational field of the earth all non-floating animals recognize the physical struggle necessary to rise, and experience wonder when they see the world spread out beneath them. Being elated is feeling as if you’d overcome gravity. People dream of flying.

Conversely, we speak of feeling depressed, as though we’d been pushed down to a low place. Things are looking up, we say, looking brighter, or less dark. These are metaphors too, derived from our physical senses. Metaphors nest, recursively. When we say the economy is depressed we are comparing the economy’s spirits (another metaphor) to the spirits of a person who feels as though he or she were pulled down by gravity.

Language is a tower of metaphors, each “higher” one resting on older ones “below”. Not every word can be a metaphor or else language would be meaningless. At the base of the tower are words like push and down, two of the non-metaphorical word-concepts on which the tower rests. Push and down are understood by us viscerally, because we are wetware, collections of chemicals rather than silicon or computer code, that experience the world through the sensations that chemicals are capable of. You cannot have lived without knowing what it is to have struggled against gravity and responded to light and warmth, and hence to know that down and dark are bad and up and light are good.

Had life arisen in outer space, free of gravity and light, there would be no perceptible down or up, and hence no possibility of depression or elation. You could be disheartened perhaps, but not depressed. You could feel full or empty, but not light or heavy, bright or dark. And you couldn’t take a dim view of your surroundings.


We use the word model in many contexts. A model airplane is a scaled-down version of an actual plane, similar in some respects, but not all. The four-year-old’s plastic plane, the twelve-year-old’s radio-controlled glider and the aeronautical engineer’s wind-tunnel airplane are all model airplanes, though they differ from each other. The similarities to the real thing are important, but different users require different similarities.

What do we mean when we call some construct a model?

The Model T is a version of a Ford, one of a class of things belonging to the Ford category. Model T is an instance, less general, not everything a Ford might be.

A fashion model can be an actual person used to display clothing or cosmetics. It’s not everything a person might be. When you’re a model, only parts of you are important. A person is complete, the real thing.

An artist’s model is a proxy for the real thing. A mannequin is a proxy for a proxy. (The work of art that uses the proxy becomes a real thing again.)

A computer model of the weather tries to predict the weather in the future from the weather today. “Weather” is an abstraction for a collection of an indefinite number of qualities and quantities and the way they vary over the short term, among them temperature, pressure, humidity, wind speed. A weather model’s equations focus on a limited number of features of a limitlessly complex system. Even with the right equation, there is always the danger that one has omitted something ostensibly negligible but whose tail effects over long times are crucially important.

An economic model aims to do for the economy what the weather model does for the weather. It too embodies a set of equations that attempts to represent the behavior of the people and institutions interacting in an economy. But just as the notion of weather is more abstract than the notion of an airplane, so the concept of an economy is even more diffuse. Money, supply, demand and utility, just a few of the many variables in an economic model, are much harder to define (let alone quantify) than temperature and pressure. A “market” and an “economy” are even more clearly a construct of the mind. When you model the economy you are modeling abstractions.

Hayek pointed out that in the physical sciences the macroscopic concepts (gases, pressure, etc.) are concrete and the microscopic one (atoms and molecules) abstractions. But in economics, he argues, individuals are concrete and the “economy” is the abstraction.

The Black-Scholes Model tells you how to estimate the value of an option in terms of its underlying risk. It’s a recipe, an engineering model, a Sol LeWitt painting that contains instructions for how to create a work of art. Just as a weather model makes assumptions about how fluids flow and how heat undergoes convection, just as a souffle recipe makes assumptions about what happens when you whip egg whites, so the Black-Scholes model makes assumptions about how stock prices fluctuate up and/or down. But our assumptions about the behavior of stock markets are much less believable than our assumptions about how egg whites turn fluffy. Fluids and egg protein don’t care what people think about them; markets and stock prices do. Like a weather model (but even more so), Black-Scholes is a limited, ingeniously clever mental model of a complex system, a small box that tries to imitate the actual world outside.

The Standard Model, for which Sheldon Glashow, Abdus Salam and Steven Weinberg received the 1979 Nobel prize in physics, is a unified description of the smallest elementary particles (quarks and leptons) and the forces between them. The description incorporates into one coherent framework Maxwell’s 19th century theory of electromagnetism, the 1928 Dirac theory of the electron and Fermi’s 1934 theory of beta decay in which all of these apparently disparate forces are only superficially different aspects of a single more general force. The standard model is not really a “model” at all, but rather a description, and hence a theory.

A theory, as I will argue below, attempts to provide an accurate description of the nature of things, unifying the outward with the inward, not just saving the appearances but identifying their essence. A model arises out of conscious analogy. A theory arises out of a deep intuitive identification of the inner and the outer.


A model airplane, however complex, is simple when compared to the real thing.

There is a gap between the model and the object of its focus. The model is not the object, though we may wish it were.

A model is a metaphor of limited applicability, not the thing itself. Calling a computer an electronic brain once cast light on the function of computers. Nevertheless, a computer is not an electronic brain. Calling the brain a computer is a model too. In tackling the mysterious world via models we do our best to explain the thus-far incomprehensible by describing it in terms of the things we already partially comprehend. Models, like metaphors, take the properties of something rich and project them onto something strange.

A model focuses on parts rather than the whole. It is a caricature which overemphasizes some features at the expense of others.

A model is a fetish in which the importance of one key part of the object of interest is obsessively exaggerated until it comes to represent the object’s quintessence, a shoe or corset standing in for a woman. (Is that perhaps why most modelers are male?). But the shoe or corset isn’t the woman, just the most important part of the woman for this model user.

The most valuable knowledge is unconscious. Until you can do something without thinking, you can’t move farther up the hierarchy of metaphors of description in language or science. In Zen in the Art of Archery, Eugen Herrigel recounts the struggle to make mental knowledge visceral. Thinking for yourself is hard work. Models provide ways of letting other people do the thinking for you. With Feynman diagrams, almost anyone can calculate elementary particle cross sections mechanically.

In physics or finance, the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform that intuition into something more formulaic, a set of rules anyone can follow, rules that no longer require the original insight itself. One person’s breakthrough becomes everybody’s possession.

The world is multi-dimensional. Models allow us to project the object into a smaller space and then extrapolate or interpolate within it. At some point the extrapolation will break down. What’s amazing is how well it sometimes works, especially in the physical sciences.

But extrapolation based on limited information is dangerous; extrapolation depends on a model, not a fact. Estrogen supplements cause their own problems, and margarine only seemed better than butter.

When unconsciously used models result in paradoxes or conflicts, it becomes necessary to expose and then examine unconscious assumptions. This is what Einstein did with the concept of simultaneity, what Lee and Yang did with parity invariance.


Models are analogies, and always describe something relative to something else. Theories, in contrast, are the real thing. They don’t compare; they describe the essence, without reference. Every fact, as Goethe wrote, is a theory.

In that sense, a theory is the ultimate non-metaphor.

Moses, tending the flock of his father-in-law Jethro near the mountain of Horeb, saw a burning bush whose flame would not consume it. God, from within the bush, declared himself to Moses and commanded him to deliver the Israelites from Pharaoh.

Whom shall I tell them sent me? asks Moses.
Tell them: I am that which I am, said the voice.

God is riffing on his true name: the Hebrew word for I will be is EHYH. Its root is HVH, the last three letters of God’s name. HVH means being, and is also the name of the present tense in Hebrew grammar.  YHVH (Yahweh or Jehovah) is the irreducible substance, the ultimate non-metaphor too, the bottom-level primitive out of which everything else is constructed. Hence, no graven images, no models, are possible. You can’t ask ‘Why?’ about YHVH; you can ask only ‘How?’.

Theories tell you what something is. Models tell you only what something is more or less like. Unless you constantly remember that, therein lies their danger.

My favorite theory is Dirac’s 1928 theory of the electron, still correct today. He sought an equation that satisfied both quantum mechanics and special relativity. The one he found had four solutions. Two of them described the electron that physicists already knew about, a particle with negative charge and two spin states. But Dirac’s equation had two additional solutions, similar to the ones he’d already found, but with incomprehensibly negative energy. The positive-energy solutions described the electron so well that Dirac felt obliged to make sense of the negative-energy ones too.

Dirac postulated that the void, the medium that we call empty space, what physicists call the vacuum, is in fact filled to its rim with negative-energy electrons, and they constitute an infinite sea. This metaphorical Dirac sea is the vacuum we inhabit, and, accustomed to it, we don’t notice the infinite number of negative charges surrounding us. (We smell only pollutants, not air itself.) If this is true, argued Dirac, then when you shoot light into the vacuum and eject a negative energy electron, a hole is left behind. This absence of an electron and its negative charge  behaves exactly like an electron with positive charge. Anderson discovered this so-called positron in 1932, and astounded all the physicists uncomfortable with what had been a metaphorical stretch. Just as life is a temporary hole in the darkness, so here too absence becomes a presence.

Dirac’s equation transcended its metaphor and became a theory of reality. A brain may be like a computer, an atom may be like a miniature solar system, but an electron is the Dirac equation. Dirac’s theory of the electron stands on its own two feet, beyond metaphor, the thing itself. Like God in the burning bush identifying himself to Moses, the theory of the electron pronounces, “I am that which I am.”

Theories are deep and inexplicable, difficult to find; they require verification; they are right when they are right. Models are shallow and somewhat easier to invent; they require explanation. We need models as well as theories.


Spinoza approached what he called the affects, human emotions, in the same way that Euclid approached triangles and squares, aiming to understand their inter-relations by means of principles, logic and deduction. Spinoza’s avowed aim was to find a method to escape the violent sway emotions inflict on human beings caught in their grip.

The Primitives
Spinoza’s primitives are pain, pleasure and desire. Every adult with a human body knows by direct experience what these feelings are, though Spinoza, following Euclid’s definitions of points and lines, makes an attempt to define them.

Desire, he writes, is appetite conscious of itself.

Its cohorts are two more primitives: pleasure and pain.

Though he defines them,  as is the case with Euclid’s points and lines, we can recognize neither   pain nor pleasure from their verbal definitions; we need to have experienced them directly and had them named. They lie beneath all the other affects and can conveniently be thought of as closer to organic conditions than psychic ones.

Spinoza distinguishes finely between local and global sensations. “Pleasure and pain,” he writes, “Are ascribed to a man when one part of him is affected more than the rest, whereas cheerfulness and melancholy are ascribed to him when all are equally affected.” Suffering, therefore, is localized pain, while melancholy is globalized pain.

His definitions of good and bad are utilitarian at the individual level. “By good I here mean every kind of pleasure, and all that conduces thereto, especially that which satisfies our longings, whatsoever they may be. By evil, I mean every kind of pain, especially that which frustrates our longings.” Good is that which brings pleasure and bad is that which brings pain.

The Derivatives
The primitives are the most fundamental affects, and the more complex emotions bear a more indirect link to the three just named. Just as financial stock options are derivatives that depend on the underlying stock price, so more complex human emotions derive their force from their relation to the three underlying sensations of pain, pleasure and desire. Spinoza elaborates:

Love is pleasure associated with an external object.

Hate is pain associated with an external object.

Hope is the expectation of future pleasure when the outcome is uncertain and doubtful.

Joy is the pleasure we experience when that doubtful expectation is fulfilled.

Disappointment is the pain of unfulfilled pleasure.

Pity is pain accompanied by the idea of evil which has befallen someone else whom we conceive to be like ourselves.

More complex emotions, like exotic financial derivatives, depend on two underlying primitives.

Envy is pain at another's pleasure, like a convertible bond whose value depends on stock prices and interest rates.

Conversely, though Spinoza doesn’t name it, Schadenfreude is pleasure at another’s pain.

Cruelty involves all three primitives: Spinoza defines it as the desire to inflict pain on someone we love or pity.

Financially speaking, Cruelty is a convertible bond whose value depends on the stock price of the underlying stock, riskless interest rates and credit spreads.

Spinoza adds to his system three additional primitives that are meta-emotions. The first is Vacillation, the state of oscillation between two emotions. Thus Jealousy, he explains, is the vacillation between hate and envy towards an object of love in the presence of a rival for it. Jealousy is a derivative of envy, and envy is a derivative of pleasure and pain. If we follow the links far enough, we end up always at pain, pleasure and desire.

The second addition is Wonder. Wonder is what we experience when confronted by something that fills the mind to the exclusion of all else, something unrelated to anything else. Wonder is what we experience in the presence of Yahweh in the burning bush, who is what he is, and bears no relation to anything else.

Spinoza’s final primitive is Contempt, the feeling we have when we contemplate something that most forcibly reminds us of all the qualities it lacks. An absence becomes a nameable presence.

I call what Spinoza created a theory rather than a model. He doesn’t make analogies; he doesn’t attempt to explain how humans behave by comparing them to some other system we already understand. He begins with observations about human beings, obtained through experience, introspection and intuition. He produced a theory accessible to everyone because it analyzes everyday human experiences.

The figure below illustrates the dependency of all the emotions on Desire, Pleasure and Pain.

double click to enlarge

6. Intuition
It takes intuition to discover theories. Intuition may sound casual but it results from intimate knowledge acquired by careful observation and painstaking effort. John Maynard Keynes wrote a speech for the Newton tercentary in which he commented on Newton’s qualities:

Newton came to be thought of as the first and greatest of the modern age of scientists, a rationalist, one who taught us to think on the lines of cold and untinctured reason. I do not see him in this light. Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago …

I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection … His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary - 'so happy in his conjectures', said De Morgan, 'as to seem to know more than he could possibly have any means of proving'.

This perception – that his insight arose independent of his proof – was also James Clerk Maxwell’s opinion about André-Marie Ampère, who, in 1820, discovered the connection between electricity and magnetism. Referring to Ampère as the “Newton of electricity”, Maxwell, who extended Ampère’s discoveries into Maxwell’s equations and found that they described light, wrote:

“We can scarcely believe that Ampere really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process which he has not shown us, and that when he had afterwards built up a perfect demonstration, he removed all traces of the scaffolding by which he had built it.”

When you struggle with a field of inquiry for a long long time and you eventually master and incorporate not only its formalism but its content, you can make use of it to build things one level higher.

Intuition is a merging of the understander with the understood. It is the deepest kind of knowledge.

7. Models in Finance
There are no genuine theories in finance. Financial models are always models of comparison, of relative value. They are metaphors. The efficient market model assumes stock prices behave like smoke diffusing through a room. These are comparisons that have some reasonableness, but they’re not even remotely fact. Newton’s laws and Maxwell’s equations are. There is almost no gap between the object and their description. You can say that stock prices behave like smoke. You cannot say that light behaves like Maxwell’s equations. Light is Maxwell’s equations.

All concepts, perhaps all things, are mental. But there are no genuine theories in finance because finance is concerned with value, an even more  subjective concept than heat or pressure. Furthermore, it is very difficult to find the scientific laws or even regularities governing the behavior of economies: there are very few isolated economic machines, and so one cannot carry out the repeated experiments that science requires. History is important in economics. Credit markets tomorrow won't behave like credit markets last year because we have learned what happened last year, and cannot get back to the initial conditions of a year ago. Human beings and societies learn; physical systems by and large don't. 

For an experiment to be approximately repeatable, history has to be unimportant. That requires that the system couple very weakly to the rest of the universe. A coin flip can be repeated ad infinitum under almost the same conditions, because external conditions affect its outcome hardly at all. That’s not the case in finance.

What is the point of a model in finance?

It takes only a little experience to see that it’s not the same as the point of a model in physics or chemistry. Mostly, the point of a model is not prediction or divination. Here’s a simple but prototypical financial model that has most of the characteristics of more sophisticated models.

How do you estimate the price of a seven-room apartment on Park Ave. if someone tells you the market price of a typical two-room apartment in Battery Park City? Most likely, you figure out the price per square foot of the two-room apartment. Then you multiply by the square footage of the Park Ave. apartment. Finally you make some rule-of-thumb higher-order corrections for location, park views, light, facilities and so on. You might develop a model for those too.

The model’s critical parameter is the implied price per square foot. You calibrate the model to Battery Park City. Then you use it to interpolate or extrapolate to Park Ave. The price per square foot is implied from the market price of the Battery Park City apartments; it’s not the realized construction price per square foot because there are other variables – exposure, quality of construction, neighborhood – that are subsumed into that one implied number.

Calibration is dangerous; it’s always the fitting a wrong model to the only world we know, and then using it to extrapolate or interpolate. The closer your model to the behavior of the world, the less dangerous your extrapolation.

The Aim of Financial Models
The way property markets use implied price per square foot illustrates the functions of financial models more generally.

Models are used to rank securities by value.
Apartments have manifold features. Implied price per square foot can be used to rank and compare many similar but not identical apartments. It provides a simple one-dimensional scale on which to begin ranking apartments by value. The single number given by implied price per square foot doesn’t truly reflect the value of the apartment; it provides a starting point after which more qualitative factors must be taken into account.

Models are used to interpolate from liquid prices to illiquid ones
In finance, models are used less for divination than in order to interpolate or extrapolate from the known prices of liquid securities to the values of illiquid securities at the current time – in the example above from the Battery Park City price to the Park Ave. value. The Black-Scholes model proceeds from a known stock price and a riskless bond price to the unknown price of a hybrid, an option, similar to the way one estimates the value of fruit salad from its constituent fruits.

No model is correct – a model is not a theory – but models can provide immensely helpful ways of initial estimates of value.

Models transform intuitive linear quantities into nonlinear dollar values
In finance a model is also a means of translating acquired intuition into dollar values. The apartment-value model transforms price per square foot into the value of the apartment. It’s easier to begin with an estimate of price per square foot because that quantity captures so much of the variability of apartment prices. Similarly, it’s easier to convert one’s intuition about future volatility into current options prices than it is to guess at the appropriate prices themselves.


Research papers in quantitative finance look superficially like those in natural science, but the similarity is deceptive. There are no deep laws or theories in finance that can be expressed in mathematics.

The one law you can rely on in finance is the law of one price, which roughly put, dictates: “If you want to know the value of a financial security, use the known price of another security that’s as similar to it as possible.”

The wonderful thing about this law – it’s valuation by analogy – when compared with almost everything else in economics, is that it dispenses with utility functions, the unobservable hidden variable whose ghostly presence permeates most of faux-quantitative economic theory.

The law of one price is not a law of nature. It’s a general reflection on the practices of human beings, who, when they have enough time and enough information, will grab a bargain when they see one. The law usually holds in the long run, in well-oiled markets with enough savvy participants, but there are always short- or even longer-term exceptions that persist.

How do you use the law of one price to determine value? If you want to estimate the unknown value of a target security, you must find some other replicating portfolio, a collection of more liquid securities that, collectively, is similar to, i.e. has the same future payoffs as the target, no matter how the future turns out. The target’s value is then simply that value of the replicating portfolio.

Where do models enter? It takes a model to demonstrate similarity, to show that the target and the replicating portfolio have identical future payoffs under all circumstances. To demonstrate the identity of future payoffs, you must (1) specify what you mean by “all circumstances,” for each security, and (2) you must find a strategy for creating a replicating portfolio that, in each future scenario or eventuality, will have payoffs identical to those of the target. That’s what the Black-Scholes options model does – it tells you precisely how to replicate an option  out of stocks and bonds, under certain assumptions. It’s like a recipe that tells you how to make fruit salad – an option – out of fruit, the stocks and bonds. And, ingeniously used, it tells you how to do the inverse – to figure out the value of one type of fruit given the price of other fruits and fruit salad.

Most of the mathematical complexity in finance involves the description of the range of future behavior of each security’s price. Trying to specify all circumstances always reminds me of  the 1967 movie Bedazzled, starring Peter Cook and Dudley Moore. In this retelling of the German legend of Faust, Dudley Moore plays a short-order cook at a Wimpy’s chain restaurant in London who sells his soul to the devil in exchange for seven chances to specify the circumstances under which he can achieve his romantic aims with the Wimpy’s waitress he desires. Each time that the devil asks him to specify the romantic scenarios under which he believes he will succeed, he cannot get them quite specific enough. He says he wants to be alone with the waitress in a beautiful place where they are both in love with each other. He gets what he wants—with a snap of the devil’s fingers, he and his beloved are instantly transported to a country estate where he is a guest of the owner, her husband, whom her principles will not allow her to betray. In the final episode, he wishes for them to be alone together and in love with each other in a quiet place where no one will bother them. He gets his wish: The devil makes them both nuns in a convent where everyone has taken a vow of silence. This difficulty is the same difficulty we have when specifying future scenarios in financial models—like the devil, markets always eventually outwit us. Even if markets are not strictly random, their vagaries are too rich to capture in a few sentences or equations.

So die the dreams of financial theories. Only imperfect models remain.


Given that finance’s best tools are shaky models, the best strategy is to use models as little as possible, and to replicate making as little assumptions as you can. Here are some other rules I’ve found to be useful as a practitioner.

Avoid too much axiomatization
Axiomatization is for mathematics. Finance is about the real world. Every financial axiom is pretty much wrong; the practical question is: how wrong, and can you still make use of it?

Good Models are Vulgar in a Sophisticated Way
In physics it pays to drop down deep, several levels below what you can observe (think of Newton, Maxwell, Dirac), formulate an elegant principle, and then rise back to the surface to work out the observable consequences. In financial valuation, which lacks deep scientific principles, it’s better to stay shallow and use models that have as direct as possible a path between observation of similarity and its consequences.

Markets are by definition vulgar, and correspondingly the most useful models are wisely vulgar too, using variables that the crowd uses, like price per square foot, to describe the phenomena they observe. Build vulgar models in a sophisticated way.

 Of course, over time crowds and markets get smarter and the definition of vulgarity changes to encompass increasingly sophisticated concepts.

Sweep Dirt Under The Rug, But Let Users Know About It
One should be very humble in applying mathematics to markets, and be extremely wary of ambitious theories, which are, when you face facts, trying to model human behavior.

Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister's foot into Cinderella's pretty glass slipper. It doesn't fit without cutting off some essential parts. Models inevitably mask as well as expose risk. You must start with models and then overlay them with common sense and experience.

The world of markets doesn’t exactly match the ideal circumstances a model assumes, but a robust model allows a savvy user to qualitatively adjust for those mismatches. A user should should know what has been assumed when he uses the model, and he should know exactly what has been swept out of view.

Think of Models as Gedanken Experiments
It’s impossible to make a correct financial model. Therefore, I like to think of financial models as gedanken experiments, like those Einstein carried out when he pictured himself surfing a light wave or Schrodinger when he pictured a macroscopic cat subject to quantum effects.

I believe that’s the right way to use mathematical models in finance, and the way experienced practitioners do use them. Models are only models, not the thing in itself. So, we can’t expect them to be truly right. Models are better regarded as a collection of parallel thought universes you can explore. Each universe should be consistent, but the actual financial and human world, unlike the world of matter, is going to be infinitely more complex than any model you make of it. You are always trying to shoe-horn the real world into one of the models to see how useful an approximation that is.

Beware of Idolatry
The greatest conceptual danger is idolatry, imagining that someone can write down a theory that encapsulates human behavior and relieves you of the difficulty of constant thinking. A model may be entrancing but no matter how hard you try, you will not be able to breath true life into it. To confuse the model with a theory is to embrace a future disaster driven by the belief that humans obey mathematical rules.

Financial modelers must therefore compromise, must firmly decide what small part of the financial world is of greatest current interest, decide on its key features, and make a mock-up of only those. A model cannot include everything. If you are interested in everything you are interested in too much. A successful financial model must have limited scope; you must work with simple analogies; in the end, you are trying to rank complex objects by projecting them onto a low-dimensional scale.

In physics there may one day be a Theory of Everything; in finance and the social sciences, you have to work hard to have a usable Model of Anything.

By Jeremy Bernstein

"Financial crisis is by definition something that had not been anticipated. If it had been anticipated it could have been arbitraged away." — Alan Greenspan

JEREMY BERNSTEIN is a professor emeritus at the Stevens Institute of Technology and a fromer staff writer for the New Yorker. He is a frequent contributor to the New York Review of Books. His latest book is Quantum Leaps published by the Harvard Press.

Jeremy Bernstein's Edge Bio Page



At the outset you need to know that I am a theoretical physicist and not a stock broker or commodities trader. But I have been trying to follow the news. It is full of terms such as "mark to market" ,"credit default swaps", "quantative easing" which at first meant about as much to me as "Bell's Inequality" might mean to some of you. But I am stubborn and decided that if these things are going to determine my financial future I better know what they mean.

The first thing that becomes clear when you look into the matter is that these concepts are part of a virtual economy. They are not like the "real economy" where, after you go into a grocery store to buy eggs and milk, you come out of the store with eggs and milk and not an option to buy eggs and milk at an agreed price at a later time. If you buy a "credit default swap" you come out of the transaction with a piece of paper-or more likely a computer file-which has no intrinsic value. If you imagine a situation in which you are confronting an aboriginal tribe you might get somewhere if you have beads to swap, but not if you have a credit default swap. These financial instruments are rather new. The commodity they trade in is money. They are very clever devices that were thought up by very smart people to make money from money and they are in the process of doing us all in. I am somehow reminded of something that the great German mathematician David Hilbert said about astrology. If the ten smartest people in the world got together they could not think of anything as stupid as astrology. Now to the glossary.


This is such a complex subject, and so fundamental, that I am dividing this entry in the primer in three parts. This one,101, gives the basics.

A derivative is a financial instrument whose value is derived from the values of other financial instruments that do have value.[1] For example if I buy an option to buy some stock in the future at some present price, what determines the value of the option depends on the  future value of the stock. The question is, what is such an option worth to me now? To understand this better let us consider a specific example.

Suppose you are given the following information-in reality you are never given this much information but that is for Derivatives 201. You are told that the Horse Feather company, whose stock is presently worth 100$ a share, will in six months be worth $120 with a probability ¾ or $80 with a probability ¼. You are offered an option to buy this stock in six months at $100 a share. What should you pay for this option?  This form of option is called a "European" option since it can be exercised only after six months. A so called "American" option can be exercised any time. Your expectation for a gain after six months is, in dollars,
3/4x20+1/4x0 =15 which reflects that fact if the stock drops to $80,  the option is worth nothing. This calculation appears to show that the option is worth $15. But never underestimate the ingenuity of people interested in making money. In this case there is the concept of "arbitrage."

Let us suppose you  are willing to buy the option from me for $15.I will take the $15 and pocket $5 which you will never see again. I then go to my friendly bank and borrow $40. This is the "leverage". In all these transactions I am assuming that there are no stock commissions and no bank interest. Since the people who thought these things up often had a background in physics they called these transactions "frictionless." It is not difficult to take the "frictions" into account. I take the $40 and the $10 and buy a half share of the Horse Feather company. (If you object to half shares I can modify my example to make it full shares.) This purchase of the half share is known as the "hedge." This sort of thing raised to many powers is what "hedge funds" do. I will now show you that I can't lose.

There are two cases the final price is $120 or the final price is $80. In the former case you will exercise your option  which was our agreement.But you are not interested in owning the stock, but simply pocketing the twenty dollar profit which I owe you.  I will now sell my half share for $60. Forty of this I will give back to the bank and the remaining twenty I give to you . Note two things. In the first place I get to keep the five dollars. In the second place the true cost of the option was ten dollars since the rest was money borrowed from the bank. You overpaid for the option by five dollars. Now take the second case. The stock has dropped to $80. You do not exercise your option so I owe you nothing. But I sell my half share for $40 which I give back to the bank still pocketing the five dollars.

This seems too good to be true and it is. In Derivatives 201 I will  begin to discuss the real world.


In 101 I presented a "toy model" to illustrate the basics. I ignored the "friction" of such inconveniences as broker commissions and bank interest. But, by somewhat complicating the mathematics ,these can readily be taken into account. What makes the model a "toy" is the assumption that we know the possible future values of the stock and the probabilities of the stock having one of these values by some sort of clairvoyance. In the real world one replaces clairvoyance by mathematical modeling, although the way things have turned ,out one often longs for a spirit medium.

The idea of such a mathematical model goes back to the year 1900 when the French mathematician Jean Louis Baptiste Alphonse Bachelier published his PhD thesis Théorie de la Spéculation.  Bachelier was already thirty years old and had spent time working at the Bourse-the French stock exchange. The question he asked was precisely the one that interests us; How can we predict the future probable values of a stock given our present information? To answer this he proposed the idea that stocks follow a "random walk." As far as I know he never  later connected this to a problem in physics solved in 1905 by Einstein. Einstein surely had never heard of Bachelier. Very few people had until he was rediscovered in the 1950s by mathematical economists like Paul Samuelson.

The problem in question was stimulated by a discovery that the Scottish botanist Robert Brown made in 1827. He noticed that if microscopic pollen grains were suspended in water then these grains performed an odd random movement which is now fittingly called "Brownian motion." At first Brown reasonably thought that these grains might be alive which explained the motion. But he tried all sorts of other suspended particles including soot from London and all of them exhibited the same motions. Throughout the 19th century this remained a puzzle although the correct solution was conjectured; namely that the suspended particles were being bombarded from all sides by the agitated and invisible molecules belonging to the liquid in which the particles were suspended. It is amusing that one objection to this is one that people first exposed to this idea often make. Such people argue that if the particle is being bombarded from all sides how does it get anywhere? But after the first lurch in some direction it is infinitesimally probable that the second one will reverse the first. The particle will go off in a new direction. It was Einstein who in 1905 made all of this quantitative. He was able to show that the average distance such a particle would travel from its origin in a time t was proportional to the square root of t which could and was tested experimentally. [2] As I mentioned, I find no reference to Brownian motion in anything that Bachelier wrote.

The problem that Bachelier posed was suppose you know the price of some stock now, what is the probability that the stock will have some given price at a later time? He did this by supposing that the later probability was achieved with a number of steps in which any motion of the stock was equally likely to be up or down. This random walk implies an "efficient market". In this kind of market prices are set by market conditions and that fluctuations do not matter.  No scheme will help you to beat the market. In fact all market speculation is based on the assumption that at least in the short run this is false. As a student of probability theory, Bachelier understood that with his assumptions the probability, as the number of ups and downs increased, would approach a "normal" distribution-a bell-shaped curve. From this he could predict the most likely future price. Here we must mention something crucial for what has happened. A property of the bell-shaped curve is that it has "wings". No matter how far you are away from the most likely there is always a non-zero probability for something that is very unlikely. You may say that it is irrational to worry about the unlikely but keep in mind what Lord Keynes noted," The market can remain irrational longer than you can remain solvent."

Bachelier applied his methodology to derivatives-options, but one thing did not seem to have occurred to him-arbitrage-beating the system by hedging.

This was corrected in the 1970s primarily by three mathematical economists, Myron Scholes, Fischer Black and Robert Merton. Merton and Scholes were then at MIT. while Black was a consultant for the Arthur D.Little Company. Scholes and Merton shared the 1997 Nobel  Memorial Prize in Economics. Black had died two years earlier. The work was done independently by Black and Scholes, and by Merton. The mantra of the quantitative financial analysts-the "quants" as they are called-is the so-called Black--Scholes equation. It is derived in a way that Bachelier would have understood. The same sort of assumptions about Brownian motion are used. The solutions tell you how to price options. For a scientist like myself it is a curious affair. In quantum mechanics, to take an example, using the mathematics of the theory we can predict the probable results of future experiments from present data. Here we use the probable future to retrodict the present. In quantum mechanics we cannot even describe the past. There are several possible pasts with different probabilities.

Merton's  approach was different and it is the one that is most commonly used by people who deal in these things. He showed that the actual option could be replaced by a "synthetic" option consisting of stocks and cash that reproduced the results of the real option. In fact you need never make reference to the real option. We saw this in the toy model. The stock purchased using the borrowed cash along with the ten dollars replicated the option. Once this was understood the quants had a field day. This was especially true since, as  market conditions changed, the mixture of stocks and cash had to be continually adjusted. This could not be done by hand. It had to be done by computers. Dealing with derivatives was like dealing with a black hole. Moreover there was no a priori check on the model. You only knew that it didn't work when it led to a financial disaster. This happened in 1987 and again in  1998 and now again in 2008. It is the subject of the next entry-301.


John Meriwether was born in Chicago in 1947. In his teens he won a caddie scholarship-a scholarship only open to caddies-which he used to attend Northwestern University. After a year of postgraduate teaching he went to the University of Chicago to study business. One of his classmates was  Jon Corzine. In 1973, Meriwether  took a job at Solomon in New York. This was just before the financial engineering revolution. After it took over, Meriwether formed the arbitrage group at Solomon. His modus operandi was always the same. He looked for the smartest people he could find even if they were smarter than he was. It did not matter how gooky they were. My feeling about Meriwether was while he certainly liked to make money he was much more interested in showing that he and his people we smarter than anyone.

In 1994 Meriwether founded a hedge fund named Long Term Capital Management-LTCM-in Greenwich, Connecticut. He hired, among others, Merton and Scholes. They don't get any smarter than that. They brought to bear every bit of wizardry you could get out of computer models. For awhile it worked marvels. It was scoring returns of 40% for its investors. It had a trillion dollars under management. This was more than any of the large investment banks. But by four years later the bubble had burst and in less than four months in 1998 they lost close to five billion dollars. What was worse was that they were not playing with their own money. They were leveraged to the hilt which might have been all right if the institutions that  had lent them money had not wanted it back once they saw that  the ship had hit an iceberg. In the event, LTCM did not have the money to repay these loans. In fact Meriwether tried to borrow more on the theory that, given a bit more time, the hole in the side of the ship would repair itself. What happened?

In the three disasters I mentioned there is a common element. Some financial instrument was created that could not fail so long as the market functioned rationally. The wings of the bell curves didn't matter. As a physicist I think of these things in terms of thermal equilibrium. If you have a gas at some temperature you can predict what the average energy of the molecules that compose it has. But there are fluctuations-deviations from the average. Under most circumstances these fluctuations dissipate. If there was a circumstance in which they didn't we would be in hot water at least for awhile. In the case of LTCM the instrument was what is known as "convergent trades." I will discuss the ones that characterize the other debacles in due course. First convergent trades.

Let us take a simple example. Suppose you have two treasury bonds, one that matures in thirty years and one that matures in twenty-nine years. Let us further suppose that we spot the fact that the second bond is trading for somewhat less than the first. It is reasonable to assume that this is a temporary fluctuation and that the spread between the two bonds will approach zero as the bonds mature and the price of the cheaper bond rises and that of the more expensive bond declines. Here is how we play the game. We "short" the expensive bond. We borrow the shorted bonds from some willing bank, or what have you, and then immediately sell them. If, as expected, the price of this bond drops as the two converge we can then replace the bonds we borrowed at less cost. But suppose instead the price of this bond rises and the cost of covering the short then increases.  If this is a brief fluctuation then we can sit tight until things sort themselves out and behave as they are supposed to. But suppose they don't and the spread gets wider and wider? Then, not to put too fine a point on it, our goose is cooked. This is what happened to LTCM.

The first intimation of trouble was  in Thailand in the summer of  1997 with the collapse of the currency which caused people in the Pacific rim countries  to look for investments such as our treasury bonds  that seemed more secure. This turned into a panic when Russia stopped payment on its debt payments in August of 1998. There was a flight for safety everywhere. LTCM had been using its convergent trade strategy everywhere. They had even opened an office in Japan. The spreads kept getting wider and LTCM more desperate. The obvious response would normally have been tough nuggets. But LTCM was in hock to the tune of about a hundred and twenty billion to its lenders-some of the most prestigious and important financial institutions in the country. In light of what has happened it is interesting to recall the role of Bear Stearns in this. Bear Stearns was the broker of record for LTCM. They kept a reserve of LTCM assets-"cash in the box". The condition was that if this reserve fell below 500 million Bear Stearns would no longer trade for LTCM and the party would be over. By September when it became clear to Bear Sterns that the assets of LTCM were declining they asked for an additional 500 million. Meriwether tried to borrow more money from everyone including his old class mate Jon Corzine at Goldman Sachs all to no avail. One problem was that as an unregulated enterprise LTCM's books were closed and no one from the outside could find out the details.

The dénouement began on Sunday, September 20 when representative of the New York Fed along with bankers from Goldman Sachs and JPMorgan made the short trip from New York to Greenwich to examine the condition of LTCM first-hand. It turned out that these bankers had no inkling of LTCM's off-book trading strategies even though they were counterparties to billions of dollars in loans. It was also clear that LTCM was too big to fail. That would bring down a number of other major financial institutions and the financial structure might collapse like a house of cards. The portfolio of LTCM had to be bought out in a fire sale. One of the bidders was none other than Warren Buffet  who attached very stiff conditions such as the firing of the entire management team of LTCM. Meriwether rejected this offer and in the end ,13 banks bought LTCM out and closed the fund.

Before I turn to the other two cases-1987 and the present-it will be helpful if I add a few more primer entries. They will come up later.


Some years ago I made a small investment in a fund offered by Merrill Lynch. I was informed that the returns were adjusted to something called LIBOR. When I asked what that was I was told that it was short for London Interbank Offered Rate. How you get "LIBOR" out of this I am not sure. Though I had no idea why a London offered bank rate should have anything to do with much of anything, I did not at the time have the intellectual curiosity to inquire further. I contented myself by going around and saying that I was in Libor-which would have been marginally more funny if I had been Australian. I have long ago sold the fund and would have given it no more thought except that LIBOR has come back big time in the present economic crisis. This has motivated me to look into the matter.

I was surprised to learn that LIBOR is a fairly recent institution. It had begun informally in 1984 but only became official on January 1,1986. It was a response to the fact that a variety of new financial instruments had appeared with a variety of different interest rate policies. It was thought that it would be a good idea to bring some uniformity to the process. In essence there are sixteen London banks which supply by 11 a.m. London time to a central office the rate at which they could borrow money, based only on their own assets as collateral, from other banks at that time. How this is determined is as much an art as a science because the banks in question do not have to have made such a transaction.

To a suspicious mind like my own, the first question that occurs is that if these rates are used to set a variety of other rates all over the world, would not some of these sixteen banks be tempted to put a little "body English" on their numbers. The tiny staff that receives these numbers at an office in London's Docklands looks for anomalies. Moreover when it averages them to produce the daily LIBOR it throws out the highest and lowest number it has gotten from the banks. Nonetheless. Why has the LIBOR come to special prominence now? This has to do with its relation to the federal  funds rate. This is a rate that is set monthly by the Federal Reserve Open Market Committee. It determines the rates at which American banks in the system will lend money to each other and the rate at which the fed will lend to member banks. Its purpose is normative. Raising the rate will cool the economy while lowering it will in principle do the opposite. The LIBOR, like the canary in the mine shaft, simply reports. When things are normal the federal funds rate and the LIBOR track each other with the funds rate being a percent or so  lower than the LIBOR. But recently the two have gotten out of alignment. The funds rate, is as of this writing something like  %.25, while the LIBOR is  about twice as large.  This reflects the reluctance of these London banks to lend to each other.


A "credit default swap" is a form of insurance pure and simple-well impure and not so simple. It is called a "swap" rather than an insurance policy because that way it is exempt from regulation unlike an insurance sale. To understand the magnitude of these transactions note that world-wide the value of the loss that is covered is estimated to be some fifty five trillion dollars! This is about equal to the gross domestic product of the world! But they do not add a scintilla of productivity to anyone. They are simply financial instruments for making or losing huge sums of money fast. The buyer of a credit default swap pays the seller an amount of money to insure against the default of something like a mortgage-or a sliced and diced bundle of mortgages. But these swaps are themselves tradable. Since the whole market is unregulated no one knows who owns what until there is a default  and someone has to pay up. Since the market is unregulated there is no specified amount that the sellers of these swaps have to keep on hand to pay the piper in case of default. A run on the swaps such as what is occurring in the mortgage market can put the counterparties into bankruptcy. This is what was about to happen to the American International Group-A.I.G.-which had about $440 billion in outstanding swaps for which they were responsible. The government bailed them out and several executives of the company celebrated by going on a very expensive partridge hunt in England. Let them eat partridge.


"Mark to market" sometimes called "mark to the market" is an accounting protocol that seeks to apply the same accounting methods to other financial instruments that are routinely applied to stocks. If you own a stock you know that after the market closes its value is posted. This is marking the value of the stock to the  market. If someone wanted to know your net worth and you wanted to include this stock this is the value you would give and not some possible value six months from now. But what if the value of the stock were undefined or ambiguous? Then if you were a clever and not particularly ethical accountant you could mark to the market of expected future earnings and inflate the present value of your enterprise. This is something that was done by Enron in spades. Conversely suppose that you held instruments that you were sure would increase in value in the future, but were distressed now, then mark to the market accounting might show that you were going bankrupt even though at some future time you might recover. This sort of thing was one of the elements that put Lehman Brothers out of business.


The 1987 stock market crash, with its Black Monday on October 19th in which the Dow lost 22.6% of its value, is a perfect model of what can go wrong when very smart people do not think things out clearly. In this case the proximate cause was what is known as "portfolio insurance." To illustrate this let us return to the toy model. Suppose I own a share of Horse Feather which is now worth $100 and is paying a very nice dividend. I want a scheme by which I can hold the stock for awhile with absolutely no risk of loss. Here is what I can do. I can short one share. I borrow a share from my friendly broker and sell it for $100. Now after the time of interest there are two possibilities; either the share will be worth $120 or it will be worth $80. Let us consider the first case first. I have to return one share to the friendly broker. I can if I want to be a little long-winded, sell my share for $120. Take the $100 I have and add $20 and buy a new share to give back or I can just give the broker the share I have. Now let us analyze the second case. I take my $100 and use 80 of it to buy a new share which I give to the broker. I now have $20 plus one share worth $80. In either case I have lost nothing. The insurance worked marvels. What could possibly go wrong?

The underlying assumption in the scheme is that the short selling people have to do to cover their positions, will not influence the market. But so many people had jumped on this insurance that once the market began to fall, and they had to sell into this depressed market, they depressed the market further-a text book example of negative feed back. It seems never to have occurred to geniuses that thought up this scheme that such a thing would be possible.


We are still too close to this to see how it is going to end. There is no doubt that it began with the collapse of the housing bubble. There is a point I would like to make that I have not seen much discussed. Suppose instead of housing we were talking about, say, a collapse in the price of tulip bulbs. Then if the normal laws of supply and demand are followed, then as the number of tulip bulbs decreases, assuming that people still want them, the price will start to go up. But housing is different. As the prices go down people get into more and more trouble with their mortgages. Hence there are more foreclosures and the stock of available housing increases depressing the prices still further-again a case of negative feedback. As I write this I do not see what is going to halt the slide


There was a kind of physics which the late an much lamented Wolfgang Pauli used to call "desperation physics." "Quantitative Easing" seems to the casual observer like desperation economics. It is a short hand for printing money. Rather than the Federal Reserve simply dropping bundles of money from air planes they propose to buy some 600 billion dollars worth of bonds from banks thus increasing the money supply. With this refreshed liquidation the banks are then supposed to begin lending money to one and all. The problem is that the banks can now borrow money from the Federal Reserve more or less free and then make money by lending it. The only reason the change this game is if the Federal Reserve interest rates go up. There is a  claim that quantitative easing might accomplish this. It seems to me like hoping to push a locomotive with a rope.



1. Emanuel Derman made the point to me that money itself is a kind of derivative. It used to be linked to gold and now to other material things.

2. For the fastidious reader I note that what I have called the "distance" here is the square root of the mean square distance and that Einstein's reasoning was somewhat different. The Polish physicist Marian Smoluchowski at about the same time analyzed Brownian motion as a random walk.

By Cliff Kuang

This is surely one of the most remarkable infographics we've ever posted. Created by social scientist Eduardo Salcedo-Albarán, it documents the organizational structure and almost limitless influence of Mexico's Michoacan drug family. And it teaches you a great deal about why, exactly, the family is so hard to combat -- and why its power seems so pervasive.

The infographic itself details various wings of the Michoacan cartel -- or La Familia as it's better known -- alongside various government agencies. (The short hand for the acronyms: Anything starting with "FUN" is a Michoacan drug cell; those starting with "NAR" are government drug agencies.) The arrows show links between each one, meaning they're sharing information. But what's most interesting is that the size of the bubbles shows how much information each cell of the organization is able to share: ...


David Berreby on November 27, 2010

If you were a sophisticated and up-to-the-minute science buff in 17th century Europe, you knew that there was only one properly scientific way to explain anything: "the direct contact-action of matter pushing on matter," (as Peter Dear puts it The Intelligibility of Nature). Superstitious hayseeds thought that one object could influence another without a chain of physical contact, but that was so last century by 1680. Medieval physics had been rife with such notions; modern thought had cast those demons out. To you, then, Newton's theory of gravity looked like a step backwards. It held that the sun influenced the Earth without touching it, even via other objects. At the time, that just sounded less "sciencey" than the theories it eventually replaced.

This came to mind the other day because, over at Edge.org, Richard H. Thaler asked people to nominate examples of "wrong scientific beliefs that were held for long periods." He also asked us to suggest a reason that our nominee held sway for too long. ...


November 24, 2010

By Andrew C. Revkin

There's a fascinating list of scientific ideas that endured for a long time, but were wrong, over at Edge.org, the Web site created by the agent and intellectual impresario John Brockman.

The cautionary tale of the fight over the cause of stomach ulcers, listed by quite a few contributors there, is the kind of saga that gives science journalists (appropriately) sleepless nights. One of my favorites in the list is the offering of Carl Zimmer, the author and science journalist, who discusses some durable misconceptions about the stuff inside our skulls:

"This laxe pithe or marrow in man's head shows no more capacity for thought than a Cake of Sewet or a Bowl of Curds."

This wonderful statement was made in 1652 by Henry More, a prominent seventeenth-century British philosopher. More could not believe that the brain was the source of thought. These were not the ravings of a medieval quack, but the argument of a brilliant scholar who was living through the scientific revolution. At the time, the state of science made it was very easy for many people to doubt the capacity of the brain. And if you've ever seen a freshly dissected brain, you can see why. It's just a sack of custard. Yet now, in our brain-centered age, we can't imagine how anyone could think that way.
The list grew out of a query from Richard Thaler, the director of the Center for Decision Research at the University of Chicago Graduate School of Business and coauthor, with Cass Sunstein, of " Nudge: Improving Decisions About Health, Wealth, and Happiness." (He also writes a column for The Times.)

Here's his question:

The flat earth and geocentric world are examples of wrong scientific beliefs that were held for long periods. Can you name your favorite example and for extra credit why it was believed to be true?


November 24, 2010

Maggie Koerth-Baker

Science can contradict itself. And that's OK. It's a fundamental part of how research works. But from what I've seen, it's also one of the hardest parts for the general public to understand. When an old theory dies, it's not because scientists have lied to us and can't be trusted. In fact, exactly the opposite. Those little deaths are casualties of the process of fumbling our way towards Truth*.

Of course, even after the pulse has stopped, the dead can be pretty interesting. Granted, I'm biased. I like dead things enough to have earned a university degree in the sort of anthropology that revolves around exactly that. But I'm not alone. A recent article at the Edge Foundation website asked a broad swath of scientists and thinkers to name their favorite long-held theory, which later turned out to be dead wrong. The responses turn up all sorts of fascinating mistakes of science history—from the supposed stupidity of birds, to the idea that certain, separate parts of the brain controlled nothing but motor and visual skills.

One of my favorites: The idea that complex, urban societies didn't exist in Pre-Columbian Costa Rica, and other areas south of the Maya heartland. In reality, the cities were always there. I took you on a tour of one last January. It's just that the people who lived there built with wood and thatch, rather than stone. The bulk of the structures decayed over time, and what was left was easy to miss, if you were narrowly focused on looking for giant pyramids.

What's your favorite dead theory?

Edge: Wrong Scientific Beliefs That Were Held for Long Periods of Time ...




Earlier this week Richard H. Thaler posted a question to selected Edge contributors, asking them for their favorite examples of wrong scientific theories that were held for long periods of time. You know, little ideas like "the earth is flat."

The contributor's responses came from all different fields and thought processes, but there were a few recurring themes. One of the biggest hits was the theory that ulcers were caused by stress–this was discredited by Barry Marshall and Robin Warren, who proved that the bacteria H. pylori bring on the ulcers. Gregory Cochran explains:

One favorite is helicobacter pylori as the main cause of stomach ulcers. This was repeatedly discovered and then ignored and forgotten: doctors preferred 'stress' as the the cause, not least because it was undefinable. Medicine is particularly prone to such shared mistakes. I would say this is the case because human biology is complex, experiments are not always permitted, and MDs are not trained to be puzzle-solvers–instead, to follow authority.

Another frequent topic of disbelief among Edge responders was theism and its anti-science offshoots–in particular the belief in intelligent design, and the belief that the Earth is only a few thousand years old. Going by current political discussions in America it may seem that these issues are still under contention and shouldn't be included on the list, but I'm going to have to say differently, and agree with Milford Wolpoff:

Creationism's step sister, intelligent design, and allied beliefs have been held true for some time, even as the mountain of evidence supporting an evolutionary explanation for the history and diversity of life continues to grow. Why has this belief persisted? There are political and religious reasons, of course, but history shows than neither politics nor religion require a creationist belief in intelligent design. ...


An Edge Special Event!

The flat earth and geocentric world are examples of wrong scientific beliefs that were held for long periods. Can you name your favorite example and for extra credit why it was believed to be true?

65 Contributors: Garniss Curtis, Marcel Kinsbourne, M.D., Paul Kedrosky


Geochronologist Emeritus, University of California, Berkeley; Coauthor, Java Man

For years I believed the Government's insistence that UFO's did not exist until I saw one under circumstances that could leave no doubt. Subsequently over many years I have seen three more. Being a scientist and professor at U.C. Berkeley, I quizzed many graduate students, asking them if they think they have seen UFO's would they come to my office and tell me about them. To my surprise, several of them did, and some went on to teach at various universities such as CalTech, and Johns Hopkins. They found, as I have, if a person hasn't seen one, he/she won't believe you. I have convinced only one scientist, and this was by giving him two excellent books on the subject which he read carefully, He came to me and said, "I am now a believer, but why this government secrecy?" I replied that I didn't know but that it must be extremely important to some branch of the government in the military.

Neurologist & Cognitive Neuroscientist, The New School; Coauthor, Children's Learning and Attention Problems

Overthrowing a presumption of symmetry, Broca revealed in 1862 that the left forebrain alone subserves language. The left hemisphere’s many specializations were cumulatively uncovered in the course of the next hundred years. Yet the "minor" right hemisphere was not similarly investigated until the 1960s. How could the plentiful specializations of the right hemisphere have been so long overlooked? The problem was not technological. The right hemisphere’s specializations were ultimately revealed by the same methods that had uncovered those of the left. What finally oriented investigators to the profuse specializations of the right hemisphere: spatiotemporal, emotional, interpersonal, creative?

Perhaps it was culture change (Kinsbourne 2000). Rigidly hierarchical thinking about human affairs prevailed: master/slave, boss/worker, king/subject, priest/sinner, God/angel, along a continuum of power, influence and assumed merit, projected to notions about the brain. Language, and the left hemisphere were placed at the peak. Simpler functions shared with other animals, were conceived as bilaterally represented. Thus the right hemisphere was denied its own specializations.

As the great empires fragmented into patchworks of independent states after World War Two, vertical value rankings no longer seemed self-evident or sufficient. Cultural constructs expanded to encompass horizontally interactive, collaborative organization (Crumley 1995). This upheaval of ideas at last permitted focus on the right hemisphere as a highly specialized collaborator of the left. In time it overthrew the antiquated notion of the cerebral network as a tangle of centers and connections, and recognized it as a heterarchical democracy (McCulloch 1945):  uncentered, unsupervised, parallel, and self-organizing.

Unquestioned and even unconscious cultural premises obstructed the natural progress of discovery. Perhaps "self-evident" but false culture-based assumptions still hold us up.

Editor, Infectious Greed; Senior Fellow, Kauffman Foundation

My favorite example is about science itself. For the longest time scientists didn't believe that their own discipline followed rules, per se, but then Imre Lakatos, Thomas Kuhn, Karl Popper and, my favorite, Paul Feyerabend showed how science was sociology, was prone to enthusiasms, fashions, and dogma, and so on. It was one of the most important realizations of my doctoral program.


Edited by John Brockman

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Contributors include: RICHARD DAWKINS on cross-species breeding; IAN McEWAN on the remote frontiers of solar energy; FREEMAN DYSON on radiotelepathy; STEVEN PINKER on the perils and potential of direct-to-consumer genomics; SAM HARRIS on mind-reading technology; NASSIM NICHOLAS TALEB on the end of precise knowledge; CHRIS ANDERSON on how the Internet will revolutionize education; IRENE PEPPERBERG on unlocking the secrets of the brain; LISA RANDALL on the power of instantaneous information; BRIAN ENO on the battle between hope and fear; J. CRAIG VENTER on rewriting DNA; FRANK WILCZEK on mastering matter through quantum physics.

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