The Fractalist

by Benoit Mandelbrot

  On my way out, the long corridor I went through was lined with Caltech undergraduates. I stopped to ask if they had any questions. No, they just wanted to see me up close. In earlier years, I too had stood in line to catch sight of a prominent lecturer. Now that prominent lecturer was me—made familiar to those students by my 1977 book!

  The next morning, I stopped by Delbrück’s office. He greeted me with, “Yesterday you mentioned the name Hausdorff. Tell me more about him so I can check if he was a man I have met.… You said such and such. I didn’t understand. Say it better.… Someone asked this or that. Your answer was weak. Can you do better now?” I suddenly realized that I was receiving the treatment—and was fielding each question and surviving. After the ordeal ended, he relaxed in his chair and, in a completely different tone of voice, concluded, “It was a very nice lecture. I learned a great deal.”

  My Keplerian Dream Acquires a Bit of Focus

  To have witnessed the birth of a field from close by was an experience I never forgot. It provided exhilarating proof that someone with my bent might have a chance after all. There was much talk of physics having dominated the first half of the twentieth century, leaving the second half for biology. Even Richard Feynman tried his hand in Delbrück’s lab. I never seriously thought of moving over, but I felt energized and kept looking for analogous openings closer to my strengths.

  The timing was ideal because several new developments that had been “bottled up” by war conditions were being revealed in a kind of fireworks I saw on no other occasion. My restless curiosity led me to read works that were widely discussed when they appeared: Mathematical Theory of Communication by Claude Shannon, Cybernetics, or Control and Communication in the Animal and the Machine by Norbert Wiener, and Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern.

  Except for a fleeting thought that I might return to mathematics in 1949 via the University of Chicago, I was beginning to think that the examples of Wiener and von Neumann might guide me to an idea big enough to make me, in some way, the Delbrück of a new field. This is precisely what I set off to do.

  But not immediately. I took the bus to New York, stopping to visit museums in Detroit and Cleveland. Next I took a boat and train to Paris—and fell into the open arms of the French air force, where I was to spend the next year.

  11

  French Air Force Engineers Reserve Officer in Training, 1949–50

  A BLESSING THROUGHOUT LIFE: I never wonder who I am. To the contrary, many successive bureaucracies wondered endlessly. The French army was certainly one of them. In trying to make sense of who I was, it improvised arrangements that had never been needed before and were likely never to be needed again.

  Remember that Carva exam hell? It ended in January 1945, but the school’s buildings were filled by returning veterans, so classes did not start until October of that year. My classmates took six months of basic training in a special military unit and were cleared of further military obligations. But being a Polish citizen, I was not called to serve. I tried to volunteer with my class but was told that foreign nationals could only join the dubious Foreign Legion. Bureaucrats tried to get me to join, but I was not persuaded.

  When I returned to France from Caltech in 1949, Léon was graduating, ending his student deferment, and about to be drafted for a year by the Air Force Engineers. It seemed right to check where I stood with the army, and my overeagerness revealed a Gordian knot that took a year to untangle.

  Carva being nominally a military academy, we students were locked in most of the time. When men in my class were called by the draft board, the authorities, knowing that they were at Carva, simply said, “This will do.” As a result, my military record was stamped “Bon pour le service” (meaning active duty), but they did not bother to call me. Later, having discovered that I was a foreign student—and hence a civilian—they declared me a bon absent. Bon because—lacking evidence to the contrary—they deemed me fit for service. Absent because I had not shown up; this was the lowest level of being a deserter.

  Had I not inquired, the contradiction would have remained buried in already ancient files. After I did, it was solved by deciding that, in effect, I had been granted a student deferment and should now be called to serve for twelve months.

  Air Force Camps: La Folie and Château Bougon

  The dictionary defines folie as “madness,” but the term also denoted the mini palaces that eighteenth-century aristocratic ladies built to entertain their very close guests. One was located in Nanterre, a northwest suburb of Paris. By 1949, that lady’s palace had become an air force camp called Camp de la Folie. Today it is the campus of the Université de Paris–Nanterre, where the famous student protests started in May 1968.

  The French air force ordered me to report to Nanterre. My first requirement when I arrived was to fill out a questionnaire about my qualifications. I was prompted by a young farmer.

  “Can you read and write?”

  “Yes.”

  “Did you finish elementary school?”

  “Yes.”

  “Did you pass the certificat d’etudes?”

  “Yes.”

  “Did you go to high school?”

  “Yes.”

  “Did you finish high school?”

  “Yes.”

  “Anything else to report, Mr. Smart Aleck?”

  “Yes.”

  “What?”

  “I graduated from the École Polytechnique.”

  The fellow became red in the face and boomed, “And I am the Virgin Mary! Don’t you city slickers lie to me.”

  “But I don’t. Everything I tell you is absolutely true.”

  “If it were true, you would not be drafted as a private in rags, but as an officer giving orders.”

  In short time, I was taken to the colonel commanding the camp. “Everybody says that you claim to be ancien Carva. Of course, nobody believes this is true, but the sergeants don’t dare order you around, and your presence creates un bordel. Carva alums are never drafted here. This must be cleared up.”

  “Colonel, I am ancien Carva. Look up the yearbook or call the school.”

  “OK, I believe you.” He became thoughtful and said that my being drafted was obviously the result of an administrative mistake. His good friends at the air force headquarters would fix everything in no time.

  When I reported again, he was subdued. “The law is the law and you must serve for a year, but certainly not as a private. You will be trained as a reserve officer and start as an aspirant de réserve [aspiring reserve officer]. In six months, they will call you to headquarters, but you must begin at a suitable camp—not here!”

  The colonel’s secretary broke in: “To be accepted as an aspirant de reserve, one must either have taken ROTC or pass a special exam.” The colonel’s response was, “For a Carva alum to be asked to take this exam would be completely undignified.” So they added to the regulations that the ROTC requirement was automatically satisfied if one was a civilian alumnus in good standing of a French military academy.

  Next the colonel was reminded by his secretary that promotion to aspirant required a formal appointment. Another call to headquarters, and a letter announced that the regulations had again been changed. “Now he fulfills all the requirements and shall be made an aspirant.”

  My military record was updated and I received a new uniform, a huge backdated raise, and a one-way railroad ticket from Camp de la Folie to Camp de Château Bougon, near Nantes, to report to the captain at base headquarters.

  I introduced myself to the captain. He was barely five feet tall and hated all six-footers, especially low-ranked ones. He asked to see my papers. “This letter simply announces that you shall be appointed. Only the president of France can sign those papers.”

  “I am sorry, but the office in Nanterre did not think the president’s letter was needed. As you see, they have already updated my military record.”

  “This is getting out of hand. Com
e back tomorrow.”

  “À vos ordres, capitaine.”

  The next day, the captain described a compromise. To update my record by demoting me, only to reappoint me in a few days or weeks, would be hard to explain. So I was ordered to keep out of sight and wait for the president’s letter. I did, and joined Léon. I soon became an expert on the muscadet wine grown near Château Bougon—dry and dangerously cheap from the barrel.

  The president’s decree arrived shortly, and they sent me off for training. That training called on the good eye and steady hand that had helped me learn to be a toolmaker in 1943. I became an excellent sharpshooter, a skill I am glad never had to be tested further.

  Camp de Cazaux and a Tutoring Arrangement

  The day after my arrival at Cazaux, I reported to camp headquarters. The colonel there asked me, “Are you familiar with who I am?” “Yes. During the war, you were a famous fighter pilot.” “Exactly. And did you notice two pilots doing acrobatics at noon?” “Yes, I noticed.” “What do you think of those pilots?” “Caltech taught me that slow rolls are unstable; those pilots are nuts.”

  The colonel informed me that he was one of those pilots. “But don’t you worry—we know what we are doing. Besides, these are World War I planes built in 1924—six years after they were needed—when they finally knew how to make them. Made of wood, cloth, and glue, but steady as rocks.”

  “I am pleased to hear that, Colonel.”

  “You studied aeronautics in America and can help me. The brass gave me all these decorations, but they refuse to make me a general because I did not go to the air academy and don’t have a high enough degree. I must become a scholar of supersonic flight, but I know nothing of it. Would you agree to review my papers and tell me sincerely if you find anything dubious or wrong?”

  “I shall be honored, Colonel.”

  He gave me his papers, and shortly after I reported back. “How is it? Tell me the whole truth.”

  “Colonel, this is a good beginning, but more work is needed.”

  Revised papers came in, and I went to see him again. “How is it now?”

  “Getting there. You could include this and that.”

  “Marvelous. You are very helpful and will be rewarded. Those planes we fly are two-seaters. You will sit in front. First you will be sick like a dog, and then you will have a high unlike any other. You will see.”

  “À vos ordres, colonel.”

  Another revision came in. “How is it?”

  “Well, actually you are backsliding a bit.” I went on being picky, until my basic training was complete and I was to be packed off to headquarters in Paris. One hour before my train, I returned the last assignment to my student. “Colonel, your piece is beautiful now. When they make you general, I would be honored to attend.”

  “Many thanks. Come tomorrow for the reward I promised.”

  “Unfortunately, at noon today I shall be boarding the train to Paris.”

  “That’s too bad. You must come back soon.”

  “À vos ordres, colonel.” I never heard from him, or of him, again.

  Paris Headquarters on the Boulevard Victor

  My next assignment was at the Office of Scientific Research on the boulevard des Maréchaux, a ring road around Paris that honors Napoléon’s closest helpers. The exact location was the boulevard Victor—a good name for a marshal, a good address for a headquarters, and a good last stop for a military “career” that had started in the Camp de la Folie.

  My colonel had heard about me and chose me to be his scientific liaison to academia. I liaised with abandon and everyone was delighted. Incidentally, I did not wear a uniform and lived at home. I wonder what living quarters would have been available had I not been a Parisian.

  (Illustration Credit 11.2)

  A few years later, I overheard a friend enthusing about his military assignment: “One thing I can tell you guys is that the Office of Scientific Research is very civilized.” Turning to me, he continued, “It seems that you don’t believe me!” I responded, “Of course I do. I tailored it to my needs, and am delighted that they also fit yours.”

  In a serious vein, liaising was a good opportunity to scout for Ph.D. topics. At Caltech, I had read the seed papers in which Claude Shannon founded information theory, and I badly wanted to know more. A get-together in London on this topic attracted me greatly, so I asked if I could attend. The air force obliged and sent me there. It was my first scientific conference.

  An Extended Sentence?

  The end of my twelve months of duty was approaching, and I was counting days. But at the last moment, to show solidarity for the U.S. effort in Korea, France extended the length of compulsory military service to eighteen months. The law excluded draftees who had been deferred as students—like Léon. I thought this clause also applied to me, but the day scheduled to be my last in the air force came and went, and no one called me to let me go.

  I inquired and was sent to the colonel. “Thank you for coming. The news is not good. As you know, your military record is … um … unusual. We treated it as if you had been deferred as a student, but nowhere does your record say that. We have been reviewing your case for days and are looking for a solution, but we cannot find one. The law states that you will have to serve another six months.”

  “But …”

  “Very sorry!”

  Fighting panic, I took matters into my own hands and rushed to Carva for assistance. The major in charge had been a captain in my time. He promptly found the carbon copy of a letter from the general commanding the École Polytechnique to the general commanding the armed forces in Paris. They knew each other, and the letter said: “Dear Friend. A graduating student, Benoit Mandelbrot, needs an exit visa to take a scholarship in the United States. His military record looks ridiculously complicated. I take it upon myself to inform the exit visa people that everything is under control and will be fixed shortly.”

  With a certified copy, I rushed back to headquarters. “Marvelous. That is all we need. Everybody agrees that the difficulty raised by your case was inadvertent. The rule extending service to eighteen months will be rewritten properly, and we have been authorized to let you go immediately.”

  In record time, I became an air force reserve lieutenant, junior grade, packed my few belongings, and walked out onto the boulevard Victor to face an altogether different set of challenges. Legal advice would probably have prevented this lost year—but I truly believe it helped me grow up.

  12

  Growing Addiction to Classical Music, Voice, and Opera

  I HAD NO TIME FOR MUSIC until a Carva roommate, Yves Charpentier, invited me to join him at a public rehearsal. The Orchestre des Concerts du Conservatoire—today’s Orchestre de Paris—was mostly made up of musicians from the Opéra who played together on Sundays in the Théâtre des Champs-Élysées. Their Saturday morning rehearsals were open to the public for a small charge. Charpentier was a regular and he liked company. And there, as he pointed out, our Carva uniforms received admiring glances.

  Curiosity and loneliness made me accept—and I was hooked for life. Beethoven’s symphonies—which I had not heard until I was twenty—were a revelation beyond words. At the second concert, the great Bruno Walter (1876–1962) conducted the Fifth, so my baptism was high-class indeed. Only a few weeks later, Charpentier declared that, having started as a complete neophyte, I had absorbed all I heard, as a dry and thirsty sponge absorbs water. In no time, I had become more knowledgeable and learned than he—who had been listening all his life.

  Charpentier also introduced me to Carva’s music room, with its sizable collection of old 78 rpm records. Hard to believe today, but the record player’s needles were made of the same wood as the reeds of wind instruments. Lighter than metal, wooden needles had to be continually sharpened using razor blades; they scratched the records and did not last long.

  I owe an immense debt to Charpentier. I thought we could become close friends. But one day, he vanished without a wo
rd. I guess that, except as music lovers, we had little in common; in fact, though he was a Parisian, I never met his family.

  After arriving at Caltech, I discovered the public “concerts”—records played in a large lounge. Next to it, a good-size control room was nearly filled with huge boxes—the top professional hi-fi equipment of the day—and shelves groaning under the weight of 78s. Three visitors were a crowd; mostly I shared that room with John McCarthy, who was to become a founder of computer science. An outspoken left-wing political extremist, he criticized Henry Wallace for timidity yet wanted him to become president in 1948. Eventually, life led him to the extreme right. In choosing what to play, John and I had to compromise. I am grateful he forced me to listen to Mahler.

  In Pasadena, I heard the pianist Vladimir Horowitz (1903–89). Shortly after one of his notorious and long “intermissions,” the big hall was quite empty! Astonishing technique, but listening to him made me fidgety and restless.

  Far more satisfying was a recital by the unknown Rosalyn Tureck (1914–2003). A “brainy” and profound interpreter, she played Bach on the piano, a marvelous maverick. Years later, we became friends, and I told her about this Caltech concert. She remembered it perfectly as a turning point. For the first time in her life, the crowd treated her not as an oddball but as a pioneer.

  While I was not yet enamored of the human voice, I heard the great diva Lotte Lehmann on one of her “last” tours. As she performed Schubert’s An die Musik, her voice cracked, and she stopped and apologized. Many elderly people in the audience were crying—but I confess wondering if she was not simply behaving like divas are supposed to during their farewell tour(s).

  At the Office of Scientific Research, my colonel’s secretary, Françoise Mer, was by no means a flawless record keeper or typist, but she was a cultured and musical upper-class lady who needed the money and liked to discuss opera with me. I had become a chamber music fan but knew almost nothing of opera. The few opera records at Caltech included the unsurpassed prewar Glyndebourne Mozart recordings conducted by Sir Thomas Beecham or Fritz Busch. Françoise conceded that my special admiration for the bass-baritone John Brownlee in the title role of Mozart’s Don Giovanni showed good taste. Long before, I had of course loved Carmen, as sung by the tenor Georges Thill, master of a vanished French singing style.