Models. Behaving. Badly. E-Book

Emanuel Derman

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 304

Veröffentlichungsjahr: 2011

Beschreibung

Emanuel Derman was a quantitative analyst (Quant) at Goldman Sachs, one of the financial engineers whose mathematical models became crucial for Wall Street. The reliance investors put on such quantitative analysis was catastrophic for the economy, setting off the ongoing string of financial crises that began with the mortgage market in 2007 and continues through today. Here Derman looks at why people -- bankers in particular -- still put so much faith in these models, and why it's a terrible mistake to do so.

Though financial models imitate the style of physics and employ the language of mathematics, ultimately they deal with human beings. There is a fundamental difference between the aims and potential achievements of physics and those of finance. In physics, theories aim for a description of reality; in finance, at best, models can shoot only for a simplistic and very limited approximation to it. When we make a model 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 of the essential parts. Physicists and economists have been too enthusiastic to acknowledge the limits of their equations in the sphere of human behavior--which of course is what economics is all about.

Models.Behaving.Badly includes a personal account of Derman's childhood encounters with failed models--the oppressions of apartheid and the utopia of the kibbutz. He describes his experience as a physicist on Wall Street, the models quants generated, the benefits they brought and the problems, practical and ethical, they caused. Derman takes a close look at what a model is, and then highlights the differences between the successes of modeling in physics and its failures in economics. Describing the collapse of the subprime mortgage CDO market in 2007, Derman urges us to stop the naïve reliance on these models, and offers suggestions for mending them. This is a fascinating, lyrical, and very human look behind the curtain at the intersection between mathematics and human nature.

Leseprobe

Dedication

Title Page

Copyright

Model I

Chapter 1: A Foolish Consistency

MODELS THAT FAILED I: ECONOMICS

THEORIES, MODELS, AND INTUITION

OF TIME AND DESIRE

MODELS THAT FAILED II: POLITICS

MODELS THAT FAILED III: THE MOVEMENT

A LOOK AHEAD

TWO IMPOSSIBLE THINGS BEFORE BREAKFAST

Chapter 2: Metaphors, Models, and Theories

THE DIRAC SEA

ANALYTIC CONTINUATION

DIG WE MUST

A MODEL AIRPLANE: THE ZIPPY

TYPES OF MODELS

THE NATURE OF MODELS

THE NATURE OF THEORIES

MONOCULAR DIPLOPIA

MAKING THE UNCONSCIOUS CONSCIOUS AGAIN

ADDENDUM: GOETHE ON SYMBOLISM

Model II

Chapter 3: The Absolute

THE TETRAGRAMMATON

THE NAME OF THE NAME OF THE NAME

THE IRREDUCIBLE NONMETAPHOR

A THEORY OF THE EMOTIONS

FIAT MONEY

LOVE AND DESPERATION

HOW TO LIVE IN THE REALM OF THE PASSIONS

THE FOUR QUESTIONS

SPINOZA’S ANSWERS

Chapter 4: The Sublime

THE BIRDS OF THE AIR

THE PHENOMENA: ELECTRICITY AND MAGNETISM

QUALITIES: POSITIVE AND NEGATIVE

QUANTITIES: COULOMB’S LAW OF FORCE BETWEEN STATIC CHARGES

VOLTA’S ITALIAN INSIGHT: CHEMISTRY IS BETTER THAN FRICTION

OERSTED: ELECTRIC CURRENTS BEHAVE LIKE MAGNETS

AMPÈRE: A LAW FOR THE FORCE BETWEEN CURRENTS

A SYMPATHETIC UNDERSTANDING

FARADAY: MOVING MAGNETS CREATE ELECTRIC CURRENTS

FARADAY IMAGINES FORCE-TRANSMITTING LINES

MAXWELL MODELS THE LINES

MAXWELL REIFIES THE LINES

MAXWELL MODIFIES AMPÈRE’S EQUATIONS

MAXWELL’S THEORY: THE FIELD ITSELF

MAXWELL’S EQUATIONS: THE FIELD’S GEOMETRY—CURLS AND DIVERGENCES

THE GREAT CONFIRMATION: LIGHT IS THE PROPAGATION OF ELECTROMAGNETIC WAVES

REALITY = PERFECTION; FACT = THEORY

THE BEASTS OF THE FIELD

ELECTROMAGNETISM AS METAPHOR

EPILOGUE

Model III

Chapter 5: The Inadequate

FINANCE IS NOT MATHEMATICS

PRICE, VALUE, UNCERTAINTY

THE EFFICIENT MARKET MODEL

UNCERTAINTY VERSUS RISK

RISK DEMANDS A POSSIBLE REWARD

A MODEL FOR RISK

RISK AND RETURN

THE ONE LAW OF FINANCE

THE CONCLUSION: EXCESS RETURN IS PROPORTIONAL TO RISK

AN ASIDE: THE PLEASURE PREMIUM

THE EMM AND THE BLACK-SCHOLES MODEL

THE CAPITAL ASSET PRICING MODEL

THE UNBEARABLE FUTILITY OF MODELING

Chapter 6: Breaking The cycle

THE PERFECT CAGE

THE MYSTERIES OF THE WORLD

MODELS THAT FAILED

WHAT IS TO BE DONE?

THE FINANCIAL MODELERS’ MANIFESTO

AN ETHICAL COROLLARY

MARKETS AND MORALS

TAT TV AM ASI

Appendix

Acknowledgments

Notes

Index

About the Author

ALSO BY EMANUEL DERMAN

My Life as a Quant: Reflections on Physics and Finance

This edition first published in 2011 Copyright © 2011 by Emanuel Derman

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I. MODELS

Chapter 1

A Foolish Consistency

Models that failed • Capitalism and the great financial crisis • Divining the future via models, theories, and intuition • Time causes desire • Disappointment is inevitable • To be disappointed requires time, desire, and a model • Living under apartheid • Growing up in “the movement” • Tat tvam asi

Pragmatism always beats principles. . . . Comedy is what you get when principles bump into reality.

—J. M. Coetzee, Summertime

MODELS THAT FAILED I: ECONOMICS

“All that is solid melts into air, all that is holy is profaned, and man is at last compelled to face, with sober senses, his real conditions of life, and his relations with his kind,” wrote Marx and Engels in The Communist Manifesto in 1848. They were referring to modern capitalism, a way of life in which all the standards of the past are supposedly subservient to the goal of efficient, timely production.

With the phrase “melts into air” Marx and Engels were evoking sublimation, the chemists’ name for the process by which a solid transmutes directly into a gas without passing through an intermediate liquid phase. They used sublimation as a metaphor to describe the way capitalism’s endless urge for new sources of profits results in the destruction of traditional values. Solid-to-vapor is an apt summary of the evanescence of value, financial and ethical, that has taken place throughout the great and ongoing financial crisis that commenced in 2007.

The United States, the global evangelist for the benefits of creative destruction, has favored its own church. When governments of emerging markets complained that foreign investors were fearfully yanking capital from their markets during the Asian financial crisis of 1997, liberal democrats in the West told them that this was the way free markets worked. Now we prop up our own markets because it suits us to do so.

The great financial crisis has been marked by the failure of models both qualitative and quantitative. During the past two decades the United States has suffered the decline of manufacturing; the ballooning of the financial sector; that sector’s capture of the regulatory system; ceaseless stimulus whenever the economy has wavered; taxpayer-funded bailouts of large capitalist corporations; crony capitalism; private profits and public losses; the redemption of the rich and powerful by the poor and weak; companies that shorted stock for a living being legally protected from the shorting of their own stock; compromised yet unpunished ratings agencies; government policies that tried to cure insolvency by branding it as illiquidity; and, on the quantitative side, the widespread use of obviously poor quantitative security valuation models for the purpose of marketing.

People and models and theories have been behaving badly, and there has been a frantic attempt to prevent loss, to restore the status quo ante at all costs.

THEORIES, MODELS, AND INTUITION

For better or worse, humans worry about what’s ahead. Deep inside, everyone recognizes that the purpose of building models and creating theories is divination: foretelling the future, and controlling it.

When I began to study physics at university and first experienced the joy and power of using my mind to understand matter, I was fatally attracted. I spent the first part of my professional life doing research in elementary particle physics, a field whose theories are capable of making predictions so accurate as to defy belief. I spent the second part as a professional analyst and participant in financial markets, a field in which sophisticated but often ill-founded models abound. And all the while I observed myself and the people around me and the assumptions we made in dealing with our lives.

What makes a model or theory good or bad? In physics it’s fairly easy to tell the crackpots from the experts by the content of their writings, without having to know their academic pedigrees. In finance it’s not easy at all. Sometimes it looks as though anything goes. Anyone who intends to rely on theories or models must first understand how they work and what their limits are. Yet few people have the practical experience to understand those limits or whence they originate. In the wake of the financial crisis naïve extremists want to do away with financial models completely, imagining that humans can proceed on purely empirical grounds. Conversely, naïve idealists pin their faith on the belief that somewhere just offstage there is a model that will capture the nuances of markets, a model that will do away with the need for common sense. The truth is somewhere in between.

In this book I will argue that there are three distinct ways of understanding the world: theories, models, and intuition. This book is about these modes and the distinctions and overlaps between them. Widespread shock at the failure of quantitative models in the mortgage crisis of 2007 results from a misunderstanding of the difference between models and theories. Though their syntax is often similar, their semantics is very different.

Theories are attempts to discover the principles that drive the world; they need confirmation, but no justification for their existence. Theories describe and deal with the world on its own terms and must stand on their own two feet. Models stand on someone else’s feet. They are metaphors that compare the object of their attention to something else that it resembles. Resemblance is always partial, and so models necessarily simplify things and reduce the dimensions of the world. Models try to squeeze the blooming, buzzing confusion into a miniature Joseph Cornell box, and then, if it more or less fits, assume that the box is the world itself. In a nutshell, theories tell you what something is; models tell you merely what something is like.

Intuition is more comprehensive. It unifies the subject with the object, the understander with the understood, the archer with the bow. Intuition isn’t easy to come by, but is the result of arduous struggle.

What can we reasonably expect from theories and models, and why? This book explains why some theories behave astonishingly well, while some models behave very badly, and it suggests methods for coping with this bad behavior.

OF TIME AND DESIRE

In “Ducks’ Ditty,” the little song composed by Rat in Kenneth Grahame’s The Wind in the Willows, Rat sings of the ducks’ carefree pond life:

Everyone for what he likes!

We like to be

Heads down, tails up,

Dabbling free!

Doubtless the best way to live is in the present, head down and tail up, looking at what’s right in front of you. Yet our nature is to desire, and then to plan to fulfill those desires. As long as we give in to the planning, we try to understand the world and its evolution by theories and models. If the world were stationary, if time didn’t pass and nothing changed, there would be no desire and no need to plan. Theories and models are attempts to eliminate time and its consequences, to make the world invariant, so that present and future become one. We need models and theories because of time.

Like most people, when I was young I couldn’t imagine that life wouldn’t live up to my desires. Once, watching a TV dramatization of Chekhov’s “Lady with a Lapdog,” I was irritated at the obtuse ending. Why, if Dmitri Gurov and Anna Sergeyevna were so in love, didn’t they simply divorce their spouses and go off with each other?

Years later I bought a copy of Schopenhauer’s Essays and Aphorisms. There I read an eloquent description of time’s weary way of dealing with human aspirations. In his 1850 essay “On the Suffering of the World” Schopenhauer wrote:

If two men who were friends in their youth meet again when they are old, after being separated for a life-time, the chief feeling they will have at the sight of each other will be one of complete disappointment at life as a whole, because their thoughts will be carried back to that earlier time when life seemed so fair as it lay spread out before them in the rosy light of dawn, promised so much—and then performed so little. This feeling will so completely predominate over every other that they will not even consider it necessary to give it words, but on either side it will be silently assumed, and form the ground-work of all they have to talk about.

Schopenhauer believed that both mind and matter are manifestations of the Will, his name for the substance of which all things are made, that thing-in-itself whose blind and only desire is to endure. Both the world outside us and we ourselves are made of it. But though we experience other objects from the outside as mere matter, we experience ourselves from both outside and inside, as flesh and soul. In matter external to us, the Will manifests itself in resilience. In our own flesh, the Will subjects us to endless and unquenchable desires that, fulfilled or unfulfilled, inevitably lead to disappointments over time.

You can be disappointed only if you had hoped and desired. To have hoped means to have had preconceptions—models, in short—for how the world should evolve. To have had preconceptions means to have expected a particular future. To be disappointed therefore requires time, desire, and a model.

I want to begin by recounting my earliest experiences with models that disappoint.

MODELS THAT FAILED II: POLITICS

I grew up in Cape Town, South Africa, in a society where most white people had Coloured servants, sometimes even several of them. Their maids or “boys” lived in miserably small rooms attached to the outside of the “master’s” house. Early in my childhood the Afrikaner Nationalist Party government that had just come to power passed the Prohibition of Mixed Marriages Act of 1949. The name speaks for itself. Next came the Immorality Act of 1950, which prohibited not just marriage but also adultery, attempted adultery, and other “immoral” acts between whites and blacks, thereby trying to deny, annul, or undo 300 years of the miscegenation that was flagrantly visible. In South Africa there were millions of “Cape Coloureds,” people of mixed European and African ancestry, who lived in the southern part of the country, their skin tone ranging from indistinguishable-from-white to indistinguishable-from-black and including everything in between.

In South Africa we all became expert at a social version of chromatography, a technique chemists use to separate the colors within a mixture. I learned how to do it in my freshman chemistry course at the University of Cape Town. You place a drop of black ink on a strip of blotting paper and then dip the end of the strip into water. As the water seeps through the paper, it transports each of the different dyes that compose black through a different distance, and, as if by magic, you can see the colors separate. How convenient it would have been for the government to put each person into a device that could have reported his or her racial composition scientifically. But the authorities came as close to that as they could: the Population Registration Act of 1950 created a catalogue in which every individual’s race was recorded. South Africa didn’t just categorize people into simple black and white; there were whites, natives (blacks), Coloureds, and Indians. Racial classification was a tortuous attempt to impose a flawed model on unruly reality:

A white person is one who in appearance is, or who is generally accepted as, a white person, but does not include a person who, although in appearance obviously a white person, is generally accepted as a Coloured person.

    A native is a person who is in fact or is generally accepted as a member of any aboriginal race or tribe of Africa.

    A Coloured person is a person who is not a white person nor a native.

Note the pragmatic combination of objectivity and subjectivity: if you are objectively white but accepted as Coloured, then you’re not white.

In disputed cases a board made decisions that determined not only who you could sleep with but which beaches you could swim at, where you could work and live, which buses you could take, and which cinemas you could attend. Given South Africa’s history of miscegenation, it was not uncommon for members of the same family to end up with different chromatography profiles. Some Coloureds attempted to be reclassified as white, and some blacks applied to be reclassified as Coloured. Evidence involved keen discussions of texture of bodily hair, nose shape, diet, and ways of earning a living, the latter two being taken as racial characteristics rather than matters of socialization or opportunity. Most Chinese, who were difficult for officials to define or even to distinguish from other Asians, were classified as nonwhite, but Chinese from Taiwan and all Japanese, for trade and economic reasons, were declared honorary whites.

The Group Areas Act of 1950 institutionalized apartheid by specifying the regions in which each race could live and do business. Nonwhites were forcibly removed from living in the “wrong” areas, thereby superimposing a legal separation over the less formal physical separation of the races that had already existed.1 Those domestics who didn’t “live in” had to commute long distances to work. In Cape Town the government razed District 6, its Coloured Harlem, and moved the entire community of inhabitants to the Cape Flats, a desolate sandy region outside the city, well described by its name. When I was at university I trekked out there several times as a volunteer on behalf of the Cape Flats Development Association to help persuade poor Coloured families to feed their children milk rather than the cheaper mashed-up squash that, though stomach-filling, had virtually no nutritional value. It was a bleak area with sparse vegetation and no running water, a gulag whose inhabitants lived in makeshift shanties constructed of corrugated iron, plywood, and cardboard. Barefoot children were everywhere. Many parts of South Africa are still like that, despite the end of apartheid.

By 1951 nonwhites were being stripped of whatever voting rights they had possessed. Though I knew all this was wrong, I grew up with it as normality. The air you breathe, once you grow accustomed to it, has no smell at all.2

When I was ten years old our neighbor down the block, a Jewish businessman in his forties with two sons a little older than I, was found on the floor of his downtown office in flagrante delicto with a young black girl. His doctor testified that he had prescribed pills for our neighbor’s heart condition that might have had aphrodisiac side effects. The black girl apparently didn’t need pills to provoke her desire, and I don’t recall what sentence, if any, either of them received.

Several years later an acquaintance of my sister’s was arrested. The police had seen him driving in his car at night with a Coloured woman seated beside him. They trailed him to his house, watched through the window, and later testified to observing the sexual act. His stained underwear was presented in court as evidence. The initial giveaway was the fact that the woman sat in the front seat, beside him. White men who gave their maids a ride somewhere commonly made them sit in the backseat to avoid suspicion.

But even white women (the “madams”) often made their maids sit in the backseat. The unarticulated aim was the avoidance of even innocuous physical intimacy. (Of course, if it had to be avoided, it wasn’t innocuous.) A native’s lack of whiteness made him or her untouchable. To avoid contamination, white families often had two sets of knives, forks, and plates: one for the family to use and one for their maids and “boys.” When I read Portnoy’s Complaint in 1969, a few years after I arrived in New York, the following passage reminded me of the visceral sense of defilement that many South African whites had been taught to feel:

Once Dorothy chanced to come back into the kitchen while my mother was still standing over the faucet marked H, sending torrents down upon the knife and fork that had passed between the schvartze’s thick pink lips. “Oh, you know how hard it is to get mayonnaise off silverware these days, Dorothy,” says my nimble-minded mother—and thus, she tells me later, by her quick thinking has managed to spare the colored woman’s feelings.

—

The Nationalist Party government that came to power in 1948 hated and feared Communism, not because the Nationalists were lovers of the individual freedom threatened by totalitarianism, but because they were totalitarian themselves. They denounced “radicals,” but as a student leader at a University of Cape Town rally once pointed out to great applause, it was the Nationalists who were the true radicals, intent on wiping out age-old conservative democratic principles. Their government periodically declared a state of emergency, which allowed for arbitrary detention. They put opponents and suspects in jail without trial for 180 days, renewable. Eventually they banned the Communist Party. Then they proceeded to ban the more gentlemanly Liberal Party, whose slogan was “One man, one vote.” Fearful people made an effort to say they were “liberal with a small l.”

When I was seventeen and spending the summer working and touring in Israel, I bought a copy of Atlas Shrugged and hid it in my luggage on my return, successfully slipping it through Customs like a copy of Playboy or Tropic of Cancer. The South African prism had shifted the political spectrum so far to the dictatorial right that Ayn Rand’s defense of the individual and of libertarian capitalism seemed to me and my friends to be subversive. At the extremes, left could not be distinguished from right. I thought of this later, when I first learned the theory of complex numbers: in the complex plane, the points at plus and minus infinity coincide, and again far left and far right become indistinguishable.

South Africa’s models were rife with internal contradictions. The most severe was the government’s policy of race separation that pretended to grant blacks independence in their supposed homelands while still keeping them available to provide the labor that kept the country running. There were smaller hypocrisies too. As young white teenagers in the 1950s, we spent the entire summer in the sun on Fourth Beach at Clifton or in the crowded Snake Pit at Muizenberg, applying fish oil or Skol so as to get as dark as possible.3 A girl I knew who devoted her time to acquiring a magnificent tan grew indignant when the train conductor mistook her for a Coloured and instructed her to go to the train carriage reserved for that race.

Coloureds were treated better than natives but much worse than whites. Their facilities weren’t separate but equal; they were vastly inferior or nonexistent. In downtown Cape Town, where I worked in a department store one summer in the early 1960s, I don’t think there was a single restaurant a black person could enter to sit down and eat. All the salesladies behind the counter, even in down-market OK Bazaars, were white.

From birth I knew no other society, and though I knew apartheid was wrong, individual blacks were pretty much invisible to me. Once, soon after I learned to drive, I took my parents’ car to the garage to get petrol. In those distant days of luxury all garages were full service, and the “boys” bustled around your car when you drove up. They pumped petrol; checked the oil, water, battery, and brake and clutch fluids; cleaned the windows; and measured the tires’ pressure and put in air if necessary. When you left, you tipped the attendant who had served you. That day, my nervous first time dealing with a garage on my own, there were three or four attendants hovering around the several cars at the petrol pumps, and as I drove away I realized with minor horror that I had mistakenly tipped the wrong man. When you weren’t used to seeing blacks as individuals, they truly did all look the same.

Enforced racial separation hadn’t always been the norm. I spent my first seven years in Salt River, a poor mixed-race suburb that was home to many immigrant Jews who hadn’t yet made it. (I remember fondly Mr. Jenkins, our Coloured plumber, who lived in the neighborhood. He spoke Yiddish, and once, when he arrived at our front door while I was in bed with a bad cold, I fearfully mistook his voice and intonation for that of our doctor, who also made home visits.) Apartheid as a legal policy reached peak efficiency only in the late 1950s and 1960s, my formative years, when I became accustomed to racism. My sisters, 9 and 12 years older than I, grew up in a less formally prejudicial world and were less racist than I was. My nephews and nieces, 16 or more years younger, grew up as the apartheid regime was collapsing, and it left a milder indentation on them.

It was only when I left to study in New York in the late 1960s that I had the chance to socialize informally with people that South Africa classified as nonwhites. One day, kidding around physically with some Indian friends in the common room of the graduate student dormitory where we all lived, I suddenly realized that I was doing what I’d never done before, and was grateful for it.

—

When I was ten I spent the winter vacation with my parents about 100 miles northeast of Cape Town, in Montagu, a small town reached by steep switchbacks that crossed a deep ravine called DuToit’s Kloof. Founded by British settlers in the mid-1800s, Montagu was a faded winter retreat, a Jewish immigrant’s colonial-style Bath or Evian, but with a local population of Coloureds and Afrikaners. The town’s main attraction was a nearby thermal spring that was reputedly good for arthritis. The refined hotel on the main street was called The Avalon. We stayed in The Baths, set in the countryside a few miles out of town. The Baths was fun but run-down. There was one toilet and bathroom at the end of each wing, and because it was a long, cold walk down the outdoor passage that connected the rooms, there was a heavy white enamel chamber pot beneath your bed in case you needed to urinate during the night. The Coloured maids emptied it in the morning, when they made up the room.

Baboons roamed the small kloof that separated The Baths from the business center of tiny Montagu. Sometimes they came onto the hotel grounds, emptying trash cans and even entering rooms. An older boy I knew climbed the hills above the hotel to shoot the baboons with an air gun, which I coveted.

The adults used to take a constitutional every morning, hiking into town through the kloof to The Avalon, to take tea and Scottish scones with local strawberry jam, butter, and thick whipped cream, but we children stuck to the grounds of The Baths, furiously socializing. My father babied me whenever I allowed him to and embarrassed me by forcing apples on me while I was with my friends. I fell in love with a twelve-year-old girl who scorned me, thanks to my father’s constant attention. It was in Montagu that someone, I don’t recall who, explained to me where babies come from. And it was in Montagu a few years later that I briefly met Adrian Leftwich.

—

Each year seasonal crazes swept through our school. One month it was silkworms that we bought and collected, keeping them in shoeboxes with airholes and feeding them mulberry or cabbage leaves until they grew into fabric-wrapped armatures. A season later came marbles. And then, outdoing all previous crazes, came hypnosis.

The sovereign of hypnosis in Cape Town was Max Collie, a professional entertainment hypnotist who had emigrated to South Africa from Scotland. His son and I went to the same school. Every year or so Mr. Collie did a couple of shows in Cape Town, some of them on our school’s premises. He began by testing the audience for suggestibility, attempting to talk their outstretched right arms into floating up into the air while their eyes were closed.4 “Your arm wants to rise up into the air. It feels light, like a balloon, so light it wants to float up towards the ceiling. Don’t resist, let it go, let it go.” Occasionally some hypersuggestible soul whose arm had spontaneously risen up would already be in a trance as a result of the test, and would fail to open his eyes at its conclusion, even before he had been officially hypnotized. Those suggestibles who were uninhibited enough to agree to participate in the show then went onstage to be hypnotized in front of the entire audience, including their own children. Soon adult men and women were under Mr. Collie’s command, shyly attending their first day at school, asking the teacher for permission to go to the washroom, scratching as though there were itching powder in their clothes, lying rigidly across two separated chairs. Finally, there was the post-hypnotic suggestion: “When you wake up and are back in the audience, whenever you hear me say ‘It is very warm in here tonight,’ you will feel as though you are sitting on a hot electric plate and jump up screaming.” Then he woke them: “As I count backwards from ten to one, you will slowly start to feel wider and wider awake. Ten, nine, eight . . . you feel light and cheerful, your eyes are beginning to open . . . seven, six, five, four . . . you are almost ready to wake up, you feel very good and full of energy . . . three, two, one, wake up! Thank you very much, ladies and gentlemen.”

It was awe-inspiring to see people under Max Collie’s power, and soon we were all trying to hypnotize each other. I bought books on hypnosis and self-hypnosis written by the aptly named Melvin Powers. The covers had mesmerizing diagrams of vertigo-inducing centripetal spirals, and some of the books included “the amazing hypnodisk,” which you could use to hypnotize yourself and your friends. My cousin and I spent hours trying to put each other under.5

In Montagu that winter of the hypnosis craze I first met the equally aptly named Adrian Leftwich, several years older than the rest of us and not really a part of our more childish circle. I didn’t see him again until a few years later, in the early 1960s, when I went to the University of Cape Town. By then Leftwich was the charismatic head of the National Union of South African Students, or Nusas, a principled anti-apartheid group. He was one in a series of Nusas student leaders who were in outspoken opposition to the government, and I admired his leadership and courage. And it truly did take courage: many student leaders of Nusas, like other foes of apartheid whom the government despised and even feared, were frequently arrested and eventually “banned,” legally forbidden to attend any public meetings or even go to the cinema or theater. A more extreme punishment was house arrest. Most of the banned had had their passports revoked, so if they chose to leave the country they had to do so on a one-time permit into permanent exile. Anti-apartheid rallies were monitored by policemen and plainclothes agents of the Special Branch, who took photographs, and even those who merely signed anti-apartheid petitions worried about getting their names on a blacklist.

As the government clamped down on all forms of legal protest, violent opposition emerged. In 1963 there were sabotage attacks on power pylons and FM transmitters in the vicinity of Cape Town. In 1964 the security police carried out nighttime searches of the houses of known anti-apartheid activists, Leftwich among them. They found him in bed with his girlfriend, his flat carelessly filled with detailed plans that incriminated him as the hitherto anonymous leader of the African Resistance Movement, which had taken responsibility for the sabotage. The police arrested Leftwich and kept him in solitary confinement. Perhaps fearful of being sentenced to death, he quickly turned state’s evidence and, in his own words in a later written reminiscence, “named the names” of his collaborators and recruits and gave testimony for the prosecution at their trial. I attended court on the day of the sentencing, where the presiding judge said that to call Leftwich a rat would be an insult to the genus Rattus.

I never had much political courage and had admired Leftwich for his bravery as head of Nusas. I don’t judge him now. Like most of us, he wasn’t what he thought he was. But thankfully, for most of us, comprehension of the disparity between who we think we are and who we truly are comes gradually and with age. We are lucky to avoid a sudden tear in our self-image and suffer more easily its slow degradation. For Leftwich the apparent union between personality and character ruptured like the fuselage of the early De Havilland Comet, in an instant, in midair, unable to withstand the mismatch between external and internal pressure. How do you ever forgive yourself for a betrayal like that?

But we have all committed acts that surprise us and are hard to forgive. You can count yourself lucky if your model of yourself survives its collision with time.

MODELS THAT FAILED III: THE MOVEMENT

I was the accidentally conceived last child of Jewish parents who emigrated from Poland (now Belarus) to Cape Town in the mid1930s to get away from what they saw as the anti-Semitic Poles. My parents’ departure from Poland turned out to be a fortuitous escape from the concentration camps, but my maternal grandparents and many of the uncles and aunts I never knew stayed behind and weren’t as fortunate. Had my mother been certain her father was dead by 1945, I would have been named Nahum Zvi. Sixteen years later, in Jewish tradition, my nephew was given his name.

When I was four years old, in late 1949, our family took a six-week trip to Israel. My mother hadn’t seen her only two surviving sisters and one brother since 1935, when she had embarked for South Africa and they had emigrated to Palestine. We took a propeller-driven DC Skymaster from Cape Town to Lydda Airport in Israel, stopping in Johannesburg, Nairobi, Entebbe, Juba, Khartoum, Wadi Halfa, Cyprus, and several other places I don’t now recall. An enormously fat man on our plane had a heart attack after eating some pickled meat somewhere over the Sudan. Officials met us on the tarmac when we next touched down, escorted us into the shade of a shack, and took him away. We had left summer behind in Cape Town; in Israel it was the now famously cold winter of 1949-1950. It snowed in Tel Aviv that year—it hasn’t happened since—and unprepared for the severity of the cold, we wore pajamas underneath our clothes all day long. It was the aftermath of the Israeli War of Independence, and food was being rationed. I recall going with my aunt to the coupon bureau, where she pleaded for an extra banana for me. I remember everything quite vividly, the rooster-shaped red lollipops they sold in the stores, the corn on the cob scooped out of steaming pots by street vendors, the grapefruit my sister and cousin and I stole off the trees of an orchard. I remember too the blood-red eyeballs of my little Israeli cousin, two years old, whose perambulator had been struck by a runaway truck.

One afternoon some friends of my parents took us for a sightseeing drive. Somewhere along the way I heard one of them point out a nearby building to my father and remark that it was a jail.

“But why is there a jail here?” I asked. “Isn’t everyone Jewish?”

The adults chuckled. It must have embarrassed me because I remember it after almost 60 years. My mental model of Jews, formed by conversations at home, didn’t contain scenarios in which we committed crimes.

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