Jerry was an extremely low-pressure salesman. “Here is an offer, but don’t take it. President Kennedy was from Boston and all-out for Cambridge, so President Johnson is all-out against it. Everybody fears major funding trouble. Several departments want you to be here, but each expects somebody else to pay. You would be the only Institute Professor without a deep and strong constituency; therefore, for you, safe funding will become increasingly hard. More generally, funding for science is becoming threatened. Believe me: for somebody like you, MIT is all wrong and the right place is IBM. Manny Piore wants people like you and is far freer to move than any university. Don’t take my offer.” With clenched teeth, I followed Jerry’s advice.
Next Jerry recalled a splendid precedent. MIT had Visiting Institute Professors: Arthur Kantrowitz and Polaroid’s Edwin H. Land (1909–91), then at the height of his fame as an inventor, scientist, and one of the richest men in the world. Neither had an office on campus, and their appointments were open-ended, with no term.
Marvelous? No, too good to be true. The possibility was killed by a better-informed Mr. No higher up. He pointed out that giving those titles to Land and Kantrowitz had drawn sharp fire from a group of activists—including Aliette’s cousin Leon Trilling. Existing Visiting Institute Professorships were allowed to continue, but new ones were out of the question.
Worn out, we watered that glorious title down to Visiting Institute Lecturer. IBM readily agreed, and for many years this compromise remained a wonderful and fruitful arrangement. I made fairly regular one-week visits to dizzyingly varied groups at MIT and elsewhere in the Boston area. More-or-less chance encounters—often like my first meeting with Houthakker—continued in a steady flow and provided an extraordinary supply of new thoughts and new directions that could be instantly explored within IBM Research.
To summarize and conclude, Chicago, Harvard, and MIT had honored me by trying to bring me in—but didn’t. The best manners were shown by gritty MIT, followed by upstart Chicago.
I contributed to each conclusion by being a truly dismal politician who preferred working to networking. However, the mismatch that was repeatedly demonstrated between academia and me was genuine. I had not a single identifying brand name for my activity. Ten more years went by until I gave up and coined the word “fractal.” Unlike me, my linguist friend Noam Chomsky had his MIT career smoothed or oiled by an attractive and assertive flag and several brilliant friends who rode along with him and found support.
The lack of choice was frustrating—but there is absolutely no question that on my return to IBM I churned out a mass of work, much of which had a rapid impact.
Lady Luck Against the Mess of Turbulence
In his Odyssey, Homer relates the problem that Ulysses encountered while sailing the long distances from Troy to his home in Ithaca—and everywhere between Scylla and Charybdis. Today those trips would not be scary at all, but in Ulysses’ day, boats were not built to fight the unpredictable turbulent weather encountered on long voyages. The problem of turbulence is so hard that every small step forward is a reason for pride. A fellow visitor at Harvard was Robert Stewart from Vancouver. He was an expert on turbulence. In one of his seminars, he analyzed records taken by a decommissioned submarine he monitored as it was slowly moving near Vancouver collecting data. Both in space and in time, the turbulence in the ocean it sailed through proved to continually come and go—by “intermittence,” as they said. During Stewart’s talk, I sat in the first row, smiling from ear to ear, rejoicing at the great gift I saw arriving. The work I was then doing on noisy channels—the next step after my 1963 paper with Jay Berger—fit Stewart’s data wonderfully and could use the same techniques. My feat in connecting the thread from an engineer’s headache to reputedly wild mathematical esoterica was not a fluke!
For years, straining to understand turbulence a little better was one of my favorite means of self-mortification. I became familiar with yet another set of experts I had not known and soon ceased following. My papers added up to books on this topic.
In 1964, when I returned to IBM, I realized that the Hausdorff dimension I had learned first from Henry McKean at Princeton and later from Paul Lévy was ready to move from esoterica to reality. In the context of prices, the measurement of volatility was the Hausdorff dimension. In the context of turbulence, the dimension of roughness was again the Hausdorff dimension.
I developed a multifractal model that addressed the intermittence of turbulence and has also turned out to be fundamental to our understanding of the variation of financial prices. Qualitative properties like the overall behavior of prices, and many quantitative properties as well, can be obtained by using multifractals at an extraordinary small cost in assumptions.
After my two years at Harvard, IBM corporate headquarters wanted me to take a job at Cornell University. This was tempting, but Cornell is in Ithaca, in upstate New York. Aliette and I had often visited, but we feared isolation and decided to return to Yorktown.
Excellent decision. I experienced the warm feeling of coming home to the delights of old-fashioned collegiality in a community far more open and “academic” than Harvard. The cafeteria had no competitors nearby, and even home-cooked lunches were eaten there. I loved particularly the varied conversation at the so-called physicists’ table—which was of course open to all comers. The mathematicians’ table was smaller, more homogeneous, and far less disputatious. The physicists and friends exchanged news—more often focused on science and scientists, and also on music and history, than on local or national politics. And frankly, nowhere else could I find a more diverse and appreciative audience for my stories.
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Based at IBM, Moving from Place to Place and Field to Field, 1964–79
THE TIME BETWEEN MY FIRST ARRIVAL at Harvard and the publication of The Fractal Geometry of Nature stands out as my life’s middle period. It began exceptionally late, so I continually felt in a great hurry and ranged in directions far more varied than I would have thought sensible or feasible.
Did I have a firm research agenda? Only in my head and mostly in a form that—whenever needed—could instantly be erased, shuffled around, or changed. To a degree that others would have found intolerable, I rarely managed to do what I was dying to do. Instead, I was doing what happened to be most desirable given what I perceived as the market for scientific ideas like mine—or, in other cases, what I viewed as easiest to undertake given some special resource that had become available in one corner or another of a very large institution.
Most fortunately for me—and for science—the physicist Richard Voss joined IBM in 1975. A freshly minted Berkeley Ph.D., he came in large part at my urging and became an essential ally and a close friend. He is a creative free spirit with extremely broad interests, and a true master of the computer. Other associates—bringing with them some specific skill—came and went; most stayed for a year or two.
Trumbull Lecturer and Visiting Professor of Applied Mathematics at Yale
Back when I was in Paris, working at Philips and writing my dissertation, a statistician named Leonard “Jimmie” Savage (1917–71) was there on a sabbatical. He had been at the University of Chicago during the “Stone age,” when the unquestioned boss was Marshall Stone. Next he moved to Michigan, then Yale. I respected him greatly for his fortitude (he was nearly blind) and the breadth of his reading. For example, he alerted American academia to the 1900 Ph.D. thesis of Bachelier. But our actual interests had little overlap. Although we never became close friends, we kept in touch and saw each other on my rather frequent visits to Yale.
Harvard’s old Lawrence Scientific School had a (less well-endowed) Yale counterpart, the Sheffield Scientific School. One of its buildings had been given to the math department, and the others were being continually reorganized. It had openings, and Savage suggested that it might be a good place for me. So I came to be tested. The 1970 spring term began with three packed Trumbull Lectures and continued with a short course—referred to as a semin
ar—on my various models of “abnormality” in the real world. It was well attended, and a few people identified themselves as being deprived of such activities. No offer came. Anyhow, I had lost interest.
To my shame, the overall stillness of Yale—contrasted with the incessant goings-on at MIT—created the impression that not much was happening. I did change my mind, but only seventeen years later.
In Paris: A Lecture Not to Be Forgotten
On January 16, 1973, I lectured at the Collège de France in Paris—an occasion that no attendee could forget. This was a very special event because, as long as Szolem was a professor there, his fear of condoning even the slightest possible appearance of nepotism was rare, extreme, and irrational. Only after he had retired could his former colleagues think of inviting me—which they did promptly.
I spoke at an interdisciplinary seminar that two senior professors organized on Saturday mornings. André Lichnerowicz (1915–98), a professor of mathematical physics, was famed for his broad curiosity, good taste, and political skills. He was scheduled to be on my Ph.D. committee, but illness had prevented it. François Perroux (1903–87) was a professor of economics. When the announcement was being drawn up for posting on bulletin boards, Perroux commented that working at IBM was undignified; any academic affiliation was far preferable. The Harvard economics department would have been great, but I was no longer there. A nominal and unpaid affiliation with the National Bureau of Economic Research was deemed satisfactory.
Preparing for this seminar turned out to be a major undertaking. It forced me to gather all I had achieved and fit it into an hour. This effort started me on my 1975 book. Invitations were sent to several luminaries in Paris, and word of mouth helped spread the news. As a result, the medium-size auditorium where I spoke was absolutely full. The talk itself was fairly general—a summary of topics I had worked on. But the discussion that followed brought out wide-ranging and very precise questions. I answered each, briefly but technically. In a sense, I gave a dozen five-minute technical presentations. As the meeting proceeded, my homecoming was palpably turning into a coming-out in the Paris big leagues—a rare major event. The discussion continued in the courtyard. A friend commented that he had never heard a strictly scientific lecture that was also so blatantly autobiographical.
A few days later, Le Figaro, a major daily, published a big column by one of those who attended and spoke, Pierre Massé (1898–1987), to whom I had been introduced. Under Charles de Gaulle, he had been a celebrated commissioner for planning. Before that, he ran the state electricity board, and early on he was one of the brilliant engineers who had built hydroelectric dams all along every suitable river in France. His endorsement may have precipitated the episode to which I shall now proceed.
Deciding Not to Compete for the Collège de France
A question arose: Would returning to Paris be either desirable or manageable? Gradually, it became clear—to put it simply—that it was not.
This decision was soon tested by a totally unexpected telephone call from André Lichnerowicz. “Your talks at the college have left a continuing and very favorable impression. François Perroux has now retired and his chair is open. Candidates are plentiful but none are impressive. Several of us would prefer you. If you express strong interest, you will be elected.”
High praise and a credible guarantee. I knew from Szolem that in Collège de France elections prominence outside one’s field generated unexpected enmities as well as support. I had only two substantial accomplishments, both very technical and undeveloped—a fraction of my present total. Marvelous to hear, this was enough to gain support and open up a unique and splendid occasion to return in the highest possible style.
I had come a very long way. The promise I had shown at those old examinations in 1944–45 had never been forgotten in Paris and was being given a chance to be fulfilled.
“You must be warned that the Collège de France is une auberge espagnole,” Lichnerowicz continued, invoking a tired old ethnic slur that implied that to eat and sleep in Spanish inns one had to bring one’s own food and bedding. “Organizing a group to help you may take much time and effort. Please think about it and call me back.”
I felt like Julius Caesar before he crossed the Rubicon to conquer Rome. The institutional forces that made me leave France in 1958 remained entrenched and invincible—but I would return in a much stronger position, perhaps sufficient to keep those forces at bay. Moreover, the Collège de France shared with IBM Research a feature not present elsewhere in academia. While I would be elected on the basis of my work in finance, I could teach anything I chose. This mattered to few persons other than me.
I realize now that I was about to be pushed out of the economic mainstream by a major step in academic economics: the 1972 revival by Black-Scholes-Merton of the formula of Louis Bachelier. Could I have both fought and outwaited them in a protected site?
Unfortunately, the downside was big. From the viewpoint of the dream that ruled my life, the timing was dreadful. Fractal geometry was on a roll, and at IBM I had squirreled away sufficient resources to prepare the 1975 French book and undertake a longer English one. Furnishing a “Spanish inn” properly would delay or perhaps even kill those plans by opening me up to the temptations that a Collège de France chair presents to an opinionated intellectual in Paris.
What I am about to say may sound ridiculous. Burning scientific ambition came first, and I would not think of endangering it. I might have considered compromising, since the yearly duties of a Collège de France professor easily fit into one term. This allowed Szolem and others who had neither a laboratory nor a growing family to spend every second term in the United States. IBM might be agreeable. In fact, that triumphal lecture in January 1973 must have contributed to my becoming an IBM Fellow a year later, making me much freer. A better politician less subject to jet lag might perhaps have accepted and continued part-time at IBM. But my position was delicate. I did not want that job enough to accept the offer tendered by Lichnerowicz; I thanked him but turned him down. I couldn’t tell if he was surprised.
Mother Dies in 1973
Paid sabbaticals were not officially offered at IBM but could be negotiated. I was scheduled to be in Paris as a Guggenheim Fellow during the year 1968–69. But political upheavals—the events of May 1968—intervened. There was no doubt that they would be followed by a bad hangover, during which visitors would be unwelcome, or at least uncomfortable, especially those with a Parisian background. Therefore, my sabbatical was postponed until 1972–73, when Mother’s health became preoccupying.
Only slightly younger than Father, Mother aged quite well. She took care of Léon’s three daughters and followed my career with swelling pride but no active influence. When Léon moved to his current flat, she moved to a smaller one in the same building. Her physician, a brilliant and colorful cousin of Aliette, admired and loved her and thought it was a good idea to send her each summer to a “cure.” Her letters to the local doctors were firm: Mother was simply old and should be given a very mild regime. One year, the local doctor was clumsy, so Mother went to a different doctor whose treatment was so vigorous that Léon had to bring her back home. Her energy had been very diminished. Aliette and I offered to relieve Léon from the burden of caring for Mother during the summer of 1971, and IBM gave me a sabbatical to spend the year 1972–73 in Paris. We were close when she deteriorated and died in January 1973. Her life had been long and endlessly complicated—but ultimately fulfilled and happy. One of the last times I saw her (barely) alive, I described a great event: my lecture at the Collège de France. I hope she heard and still had the strength to rejoice.
Visits to the Mittag-Leffler Institute
The mathematics research institute of the Royal Swedish Academy of Sciences, located in Stockholm’s elegant suburb of Djursholm, occupies the former mansion of the colorful Victorian Gösta Mittag-Leffler (1846–1927). His wife’s Finnish forests allowed him to build a mansion to his taste. It consists of a l
arge but not extravagant bourgeois apartment on the main floor, with several former servants’ quarters. A three-floor library that would make any university proud houses many valuable old books and much space for collecting. Mittag-Leffler wanted to teach mathematics without having to move to the Swedish Oxbridge, so with a few friends in Stockholm, he simply endowed the most private university imaginable, seed of the present university of Stockholm. He also created his own journal, Acta Mathematica.
The Mittag-Leffler Institute restricts itself to its namesake’s field of mathematical analysis. Each year (sometimes each term), it tackles a different topic, and its glory years were those under the lay directorship of Lennart Carleson, particularly the ones when his dynasty included his frequent coauthor, Peter Jones. A topic has to be selected several years ahead. I was thrilled that three of the topics chosen over the years were from my work. The Mandelbrot set was selected in 1984, before it became the height of fashion, with the hope of solving the Mandelbrot Locally Connected conjecture; a big effort ensued but failed … to this day. My 4/3 conjecture about Brownian motion was chosen in 1998, when its difficulty had become obvious and it seemed that a solution would be hastened if all those concerned could be brought together. As it happened, the solution came before the meeting, so the meeting was able to draw immediate consequences. The third meeting, in 2002, that my work inspired was on the mathematics of the Internet.
As you may have experienced, some non-negligible proportion of e-mail gets lost. Multiple identical messages are a pest, but the sender is actually playing it safe for the good reason that in engineering everything is finite. There is a very complicated way in which messages are assembled, separated, and sorted. Although computer memory is no longer expensive, there’s always a buffer of finite size somewhere. When a big piece of news breaks, everybody sends a message to everybody else, and the buffer fills. So what happens to the messages? They’re gone—just flow into the river.
The Fractalist Page 25