The Fractalist Page 11

  A wandering scientist should never say never, and history shows that beautiful parts of abstract mathematics can well slumber for a while and become disconnected from their roots in reality. They may seem to be stone dead—yet should never be called exhausted.

  A second example concerns the intellectual landscape previously visited by Szolem and his students and friends. In due time, a persistent scientific study of roughness led me to encounter increasing depths of wild complexity—and therefore to cease to expect the world to be fundamentally mild and simple. To my initial astonishment and ultimate delight, I encounter again and again the hard messiness found in Szolem’s mathematics. Its practical applicability revealed that it reflects the irreducible messiness of where I have chosen to work—the scientific frontier.

  An Unexpected and Much-Needed Pause

  The last-minute switch from Normale to Carva was made possible in January 1945 because of a wartime quirk. Normale had vacant dormitory space, but Carva did not. So, from February to August 1945, my class waited for space to become available. The army drafted my future classmates into a special unit. I volunteered to join them but, being a foreigner, was turned down. Thus, for half a year, my schooling was interrupted once again—by odd jobs.

  Many people I know and respect value efficient processing of youths and view “wasted time” as harmful, even threatening, or immoral. I had no choice. Moreover, I think it helped me grow up—a valuable gift from fate. Much later on, I was happy when both my sons had reason to take years off.

  Let me elaborate. Good wine or cheese must not be rushed. So why rush good humans by pressing a cookie cutter on a malleable young mind? As that stuff sets in, it preserves for life the shape of the mold. Today, taking time off is tolerated, but still not in the hard sciences. Among my old classmates, many acknowledge lifelong distress at having never been given a break.

  Sirens Hawking All Kinds of New Propaganda

  I was waiting for a top school to be ready, but money and food were a constant issue. I did not mind eating quite often at a soup kitchen in Belleville, probably supported by some American Jewish charity. Most of the habitués of that soup kitchen had dreams of victory soon followed by revolution, and conversation was always lively.

  The aftermath of the war provided fertile ground for all kinds of would-be messiahs, and that mood seemed to extend to every activity of concern to me. A moral imperative—as we were told from many sides—was total commitment to a great and well-organized cause, or perhaps to several compatible ones. Many of the noises I had already heard before the war in Warsaw hit the older me more strongly, and they were joined by fresh ones.

  Communist parties following different schools of thought were constantly competing with one another in their proselytizing. A growing number of people in France and elsewhere in Europe had come to believe that to tackle the gigantic problems ahead, democracy and individualism were outdated. They had to be sacrificed to concerted collective action—a political secular religion with a charismatic leader. Empires had been destroyed by the world wars, but most of their key structures remained popular and many countries promptly reinstated them, often in a smaller but more brutal form.

  The century-old default option at Carva was to become exclusively devoted to bringing back the glory of the French state and its institutions—to become a mandarin, or grand commis. But after the war, many of my roommates there considered the opposite option: fearing that France would not rebuild in their lifetime, they spoke of moving to a more promising place far away—not the United States (oddly, as I thought then and continue to think today) but Argentina or Brazil. A glance at the alumni directory shows that this talk was not followed by action.

  There was constant talk in 1945 of adopting some form of sacerdoce (vocation) or other ready-made commitment. Catholics were offered several strengthened or modernized versions of their faith. Blaming Rome for compromising too willingly, some became Calvinists. Every serious form of commitment imitated the rules that organizations like the Freemasons and the Catholic Church had themselves adopted from their predecessors. Everyone “wed a discipline”—as Jesuits wed the church and bear witness by wearing an iron ring on their finger. French society being stable, commitment was often inherited.

  The celebrated writer Jean-Paul Sartre belonged to a prominent family from Alsace, the Schweitzers. A demagogue, he wrote clumsy French but had a silver tongue. I once attended a political rally that featured him. The chairman concluded by wishing to see him become a political leader. I soon came to shudder at the very thought.

  The levelheaded writer Raymond Aron—whom, shamefully, I failed to appreciate until much later—was Jean-Paul Sartre’s classmate at Normale. He once complained to the effect that “I have always been right but no one knows me, while Sartre is consistently wrong but famous” (well, no longer). I was urged by friends to recognize Aron as a kindred spirit, but I discounted him because he wrote for Le Figaro, a stolid, conservative newspaper no one I knew would touch.

  The crosscurrents of that period affected me profoundly. Almost all my friends joined loud causes. The skepticism my family had instilled in me during the 1930s was amplified, and against odds—and like the Raymond Aron I missed knowing—I elected to be a dissenter. I believed that to dissent from one church, one need not create another. My ambition, my megalomania, was to help the church change. In mathematics, who was the self-appointed messiah? For better or worse, that person was André Weil of Bourbaki.

  Total commitment to causes benefited some of my friends, at least for a while. But I was never tempted to join. Instead, I began to continually customize my life in a way that history might reward but society had left unfulfilled. This choice may have contributed to the length of my active life, but it also guaranteed that I would be anything but precocious. In the absence of a well-defined set of rules to play by, the very notion of precocity ceases to make sense.

  One look at France after 2000 suffices to show that, in some ways, two hot wars and a cold one had little effect on the country. Political Marxism and Gaullism—as well as their intellectual counterparts in Bourbakism, existentialism, and Freudianism—appear to have burned out … but who knows.

  9

  A (Then Rare) Foreign Student at the École Polytechnique, 1945–47

  “POUR LA PATRIE, LES SCIENCES ET LA GLOIRE” has been Carva’s motto for years. The link to the fatherland resides in the school’s focus on providing the French state and society with technical elites—both civilian and military.

  Carva graduation rank is perceived as extremely important and as justifying gigantic investments by both society and individuals. A very high graduation rank provides a splendid state job, which is often followed by a splendid career in business. Those aiming for the top had to work very hard, and—like in the taupe—efficiently, as their lives were relentlessly packed. Most of my Carva classmates found the competition excessive. They preferred to coast along, confident that being ancien élève (antique or alumnus) would serve them well in any career they chose.

  The many perks that come with the degree give few graduates an incentive to live outside of France—ordinarily, a prerequisite to renown abroad. A special case might be me—of Lithuanian extraction and Polish birth. For me, at first Carva meant a great deal; I became a French citizen while a student there. But then it became less and less important until it faded into a nice memory of youth. When I graduated, I really finished Carva, while for the typical alum, being ancien élève was a welcome life sentence.

  Student Life at Carva, the Military Academy

  Carva was founded in 1794 as a school of civil engineering, but Napoléon made it a military academy for artillery officers and military engineers, together with a few high civil servants. Some alumni were also part-time scientists who contributed mightily to the glory days of French science—1800 to 1850, later extended by Henri Poincaré (class of 1873). Science suffered a long and painful low between my teacher Paul Lévy’s class (1904) and—
roughly—mine (1947).

  In my years, very few graduates became officers, yet the school was run like a strict military academy. Entering students immediately became state employees, and therefore had to have been French citizens for at least five years. I was a special foreign student. As mentioned, I had taken the regular exam, and I was promised a diploma if my record was better than that of the worst regular student. With the exception of a classmate who died, I was the school’s only foreign student over a period of nearly ten years.

  Most all the students lived in barracks. We 1945 freshmen did so on the comparatively elegant campus in town—on 5, rue Descartes, a few steps behind that majestic gate that Father had pointed out to me just after I came to Paris. As 1946 seniors, we lived in a cookie-cutter barracks called Lourcine, a good walk south of the Latin Quarter.

  We were organized in units of twelve called caserts (short for casernements): tightly packed beds in a small dorm and desks in a common study room. Three caserts formed a “group” for recitations, gym, and foreign language classes. Serendipitously, two birds were killed with one stone—the school favored proficiency for language and a blend of talent for gym and the key subjects. Therefore, first we were ranked by our entrance grades in English or German, then we were divided into caserts.

  Given the strict rationing on the “outside,” this military academy fed us surprisingly well. Though gym was considered important, the crowded neighborhood left us limited facilities within the school. A swimming pool in a basement was so busy that we were able to use it only very early or late in the day. I still recall with dread those long jogs along the quais of the Seine under a fine drizzle before sunrise. (The joke is that Paris has no rainy season, because it rains a little bit every day.) Overcrowding became a reason for moving the school lock, stock, and barrel to a windy and remote suburb.

  Carva Dress Code: Always in Uniform

  Many of my otherwise conventional classmates continually grumbled about the uniform, but being the impoverished oddball that I was, I rarely complained. I had entered the school literally in rags. Léon and I piled our clothes together, and I put on my worst shoes, pants, and top. A few hours later—bliss—I tossed them all into the garbage can. This was long before dressing down created its own universal uniform. Without that dress code, the differences between rich and poor students would have been intolerably conspicuous.

  The school’s basic uniforms included a soldier’s battledress (an accepted French word) for every day and an officer’s town uniform (mine lacked certain insignia). Both were khaki colored, hence the school’s military academy status—though only skin-deep—was highly visible and brought some incidental perks.

  (Illustration Credit 9.1)

  In addition, very special occasions demanded le grand U, the grand uniform, custom-tailored in heavy black wool with long rows of gilded buttons and red and gold trim. It could be worn with either a very long coat or a billowing cape. The two-cornered hat was vaguely Napoleonic, except that the corners pointed to the front and back. Each of us also received a straight sword, which—unlike the uniforms—had to be returned upon graduation. Mine was a hundred years old, and I took it for granted that it had never touched blood.

  A recent move revealed that two of the four pieces of my grand U have survived all my previous moves. I was reminded of my serial number (1179) and of the pride I had felt when—shortly after I had trashed my rags—I was measured for a masterpiece of custom tailoring. Somehow, it no longer fits—but one day it just might again.

  (Illustration Credit 9.2)

  The grand U was essential for the many elegant parties to which I was never invited and for the rather frequent parades down the Champs-Élysées. Out of a class of some two hundred, the tallest students paraded in twelve rows and twelve columns, and 144 grand Us—including mine—figured in every pre-TV newsreel. In terms of precision drills, the hardest were the few minutes when each row had to remain straight as we fanned around the Arc de Triomphe. Fortunately, the big stand with officials and guests was safely farther down, on the sunny side where the Champs-Élysées widens into a park.

  To march in the first row during a parade is extremely stressful. I often failed to avoid this fate. My classmate André Giraud (1925–97), a bit shorter in stature, invariably arranged to march just behind me, admonishing me each time my drawn sword—tangente—deviated even a bit from the required vertical direction. He became an admired but ruthless high civil servant and, in due time, one of the few ministers (of industry and then of defense) who continue to be remembered. In school, we were anything but kindred souls, and I am glad my fate never came into his hands.

  But on a much later occasion, when our paths crossed in New York, we shared a connivance that must link old dogs who recall playing together as puppies. Marching in grand U, we had performed for Charles de Gaulle, Winston Churchill, and other lesser historical figures. Most oddly—and memorably—we honored Ho Chi Minh! This Vietnamese leader was visiting Paris to iron out some remaining details of a peaceful withdrawal of French troops. That very night—without authority from Paris—Admiral Georges Thierry d’Argenlieu, the French naval commander in Indochina, bombarded the northern port of Haiphong. Ho flew back home in a rage, and the rest is history. Who was this d’Argenlieu? A naval officer who became a Carmelite monk, but received wartime leave from the order to join de Gaulle in London and was made admiral. Having defied the Vietnam policy of his country’s postwar government, he returned to the Carmelites, and so could not be indicted, and was never heard from again.

  Côte d’Amour and Hazing

  We all received a grade for military bearing. Most officers did not want this grade to affect ranking; therefore, most students received a grade of 15/20. But there were exceptions. For example, André Giraud’s first-year grade was something like 18/20—hence the grade was rudely referred to as the côte d’amour. My first-year grade was a lowly 2/20. The second year, I improved to a 13/20. Years later, someone having fun let me read my file. I saw that after the second year, Captain Wolf commented that although my 2/20 suggested a willful troublemaker, it only meant that I had no concept of the role of military authority. This was indeed the case—and my whole life’s orbit was to show that professional authority did not awe me either.

  The man who gave me the grade of 2/20 had an ax to grind. During the fall, while he was a lieutenant hanging around without obvious assignment, we (at least I) did not know that he was being groomed to take over our company. Then, over the Christmas break, he took a few of us to Fort de Briançon, near the Italian border in the Alps. Without an instructor, we were struggling to learn to ski by gliding down a highway. I almost crashed into him, making him scream, which was quite an embarrassment. Upon returning to Paris, he was promoted to my captain, and remembered everything vividly.

  Gaudeamus igitur, juvenes dum sumus (While we are young, let us rejoice). In that spirit, and knowing we were going to be forced into dull and ordered lives, Carva allowed a great deal of (frankly sophomoric) tomfoolery. I barely participated, and it is well documented, so let me be brief.

  Hazing of freshmen by seniors was permitted, but this was not a big deal. On a certain festive occasion, select incoming freshmen were given nicknames, sometimes mildly degrading ones. A classmate’s surname, Godet, denoted a cup in French, so he became Fanofbooze and was ordered to spend an induction ceremony pretending to drink from an oversize empty cup. My name was recognized as being German for cake, something edible, so I became Fanamagnan—that is, Fanofchow—and was ordered to pretend to chew on a large cooked bone.

  The Gamma Point is a special day for astronomers. Carva celebrated it with an open house. It is widely claimed that its grossly inflated prices sustained the Carva counterpart of U.S. high school student councils. Partaking of the bubbly that I was selling, I verified by repeated experiment that with good champagne it is very hard to get drunk.

  Matchmaking and the Carva Alumni House

  Coeducational U.S.
universities are essential to matching life partners. In my time, all Carva students were men, hence the need for special arrangements such as the dances with live orchestras that the GPX—Groupe Parisien des X—hosted at Carva’s alumni house in the elegant Faubourg Saint-Germain in the Seventh Arrondissement. It had servants’ quarters in a building on the road, a paved courtyard, a garden behind, and a main house entre cour et jardin.

  Students paid no admission, and alumni acted as discreet chaperones of their eligible daughters. Many of my classmates found a wife and a father-in-law eager to become their patron. Only once, several years after graduation, did curiosity make me visit. Yet my wife, Aliette, and I held our wedding reception there, and when needed, we take advantage of its intended role as a grand home away from home.

  Home Economics

  Financially, the regular students at Carva (and also Normale) could fairly be described as extremely privileged—or, less politely, as utterly spoiled. This helped explain the school’s attractiveness. Although it is true that those students were constrained by a long-term legal commitment to serve in the nation’s army or some branch of civil service—one entirely determined by their school record—an alumnus could in fact buy back his freedom, either by paying his tuition retroactively or by performing acceptable good deeds. While at school, all regular students—rich or poor—were exempt from paying room, board, and tuition.

  As a foreign student, I received a bill for tuition and board. But this was an accounting fiction: the grant from a government agency that would have gone to Normale went instead to Carva. When I became a French citizen, I lost that support, and the invoice I received was equal to the buyback of a regular student’s contract. When set up in 1943, the amount was more or less equivalent to tuition and board at Yale. But by 1946, postwar inflation had reduced it to practically nothing. So, instead of making me seek another scholarship with different strings attached, Father bought me the joys and sorrows of independence—at a historically low bargain rate.