Jacob's Ladder

by Ludmila Ulitskaya

  “What didn’t you like about those young men? One of them was my brother, and the other his close friend! You have a funny way of beginning an acquaintance!”

  Still smiling, she stepped to the side a bit, and I understood she was not there by herself, but in the company of a formidable woman, no longer young, wearing a queer-looking net over her gray hair—by all appearances, a schoolmistress.

  I was terribly afraid that everything would fall through, that she would leave and I would never see her again. I clutched at her sleeve like a madman and held her back. She was not in the least alarmed, just brushed away my hand and said she had to go back up to the top balcony, and she hoped I would get even more pleasure out of the second part of the concert.

  It’s over, it’s all over—now she will go away, forever, and that will be the end of it! “I beg you, I beg you, don’t go upstairs to the balcony. My father gave me a ticket in the orchestra seats, for my birthday, you see … I beg you, change seats with me; it’s the fifth row, in the middle, seat number eleven.”

  She looked at me with great sympathy and began nodding her head: “Please, don’t worry yourself, I’ll gladly take your seat—especially since not only can I not see anything from mine, but the sound is also bad there. I am very grateful to you for your kindness.”

  She waved to her companion and said, in French, “Madame Leroux, I’ve just run into an acquaintance who offered to exchange his seat for mine. It’s in the orchestra.”

  The girl clutched the ticket a bit uncertainly, as though offering it to the Frenchwoman, but the woman became very animated, pushed her hand away, raised her eyebrows, and said, laughingly, something along the lines of “Run along, Marie … And keep your eye out for another acquaintance of yours in the orchestra.”

  And we exchanged our tickets, and I led her to my place and seated her, and she nodded to me gratefully, but without constraint. She was no doubt a girl of exceptionally good upbringing—that kind of simplicity of behavior is only common among well-bred people.

  By the time I rushed up to the balcony, Rachmaninoff was already seating himself behind the piano. He played the first chord—and I was lost! I have already managed to get hold of the musical score from Filimonov, a clarinet player. I looked it over, and will study it for a long time to come, but I am left with the feeling that the first part is simply unattainable. It is the principle of conversation in a higher and middle register, and the lower F in the contra-octave, the very beginning, and the mighty theme, and the introduction of the strings and clarinets … The concert was enormous in its content and meaning; there was not a single empty phrase, nothing merely decorative, only the essence itself! The audience was in a state of nervous rapture, but Rachmaninoff himself was calm and unflappable, a giant among men, a giant! Everyone applauded rhythmically, then got out of phase, then picked up the rhythm again!

  Oh my God! I forgot, I completely forgot about the marvelous girl. When the audience had grown tired of the ovations and started to disperse, I remembered about the girl and realized that I had lost her. She had already left, never to be found again. I practically flew down the stairs, and, truly, the crowd was already departing. I rushed to the coat check for my things, and although the magic of the music had still not left me and I was still happy, I was sad at the same time, because I understood that I had lost what I would never again find. I grabbed my coat and, pulling it on as I walked, made a beeline for the exit, so that I might, if I was lucky, run into her on the steps or at the trolley stop … Then I stepped on the hem of a coat belonging to some lady who was sitting on the velvet bench, putting on her boots. I apologized—and it turned out to be her! Her face looked both solemn and troubled by the music, and also radiant. She had, of course, forgotten all about me, and didn’t even recognize me at first.

  I walked her home—she lives on Mariinsko-Blagoveshchenskaya Street, a five-minute walk from our house. Her name is Maria. Maria. Maria.

  8

  The Garden of Magnitudes

  (1958–1974)

  When they were still in the eighth grade, Grisha Lieber and Vitya Chebotarev went to the Department of Mathematics and Mechanical Engineering at the university to enroll in study clubs. About twenty boys and two (chance) girls began to live there in a unique, highly rarefied atmosphere. But even in this hothouse of young talent, Vitya stood apart. That year, he took first place among all the Moscow school-age children, and, what was most surprising, he also came in first among the ninth-graders. One year later, he won a prize at the first Math Olympiad of schoolchildren in Bucharest—true, only second place. This was more of a surprise than a disappointment to him. By that time, he was already used to being the best and the brightest in his age group. But he was not conceited, because he was a natural-born scientist, and there was no greater reward for him than solving a task or problem.

  In the autumn of the ninth grade, Grisha took a book over to Vitya, who was home sick with tonsillitis. The book was Hausdorff’s Set Theory, a prewar edition, somewhat battered and dog-eared, which had passed through many hands and minds before coming to Vitya and changing his life in the most profound manner.

  In the evening, after he had taken his prescribed pills and gargled before going to sleep, Vitya sprawled out on the divan, picking up the little book Grisha had brought over with instructions to guard it carefully—it was valuable. He had never seen anything like it! His sleep, and his tonsillitis, and his very sense of reality deserted him. He was hooked. With every page he read, he felt he changed, even physically. For several years, he had been trying to solve the most disparate and intricate problems, thinking he was doing mathematics; but it wasn’t until this night that he felt he had set foot in the realm of true mathematics. It was a whole new world of wondrous and varied sets. In the morning, he looked out the window and noticed that the world had not changed a bit, and it was incomprehensible to him how buildings could even remain standing, and not collapse in a heap, when there were such wonders in the world as he had discovered in this little book.

  Vitya had never read the well-known lines of Mandelstam, but he experienced the same emotion the poet describes in his obscure, redolent, pulsing words:

  And I step out of the space of the world

  and into the garden of magnitudes

  and I rend the illusory permanence

  and self-evidence of reasons.

  And your very own primer, eternity,

  I read all alone, in solitude—

  Wild, leafless book of medicinal lore—

  problem set of enormous roots.

  In short, he had ended up in that garden. It was impossible to imagine anything more wonderful.

  By the tenth grade, Vitya had become a real mathematician. His massive, somewhat convex forehead—like that of a child with a mild case of hydrocephalus—contained the brain in which the expanding universe moved, breathed, bubbled, and frothed. All other natural functions of the organism—eating, drinking, sleeping, etc.—were mere obstacles to the constant working of the rest of his highly functioning mind. Very little interested him apart from mathematics, and even his friendship with Grisha waned a bit. Grisha no longer satisfied him as an interlocutor. To be more precise, the pleasure he got from the music of mathematics so exceeded all other joys, including that of spending time with other people, that he began avoiding everything “extraneous.” Even physiological growth into manhood was an inconvenience or a malady to him, something like tonsillitis, which prevented him from studying. During that period in adolescence when young people are in the throes of hormonal revolution, Vitya found a simple method for releasing the tension that gripped him: overtaxing his mind.

  Nora, who inhabited the outskirts of the world of Vitya’s interests, took the initiative at this timely moment to change her status from tutor in literature to friend and companion in sexual activity, and readily accepted his newfound manly maturity. She was a premature, illegitimate offspring of the sexual revolution, of which she knew nothing—if y
ou didn’t take into account Marusya’s bold but old-fashioned pronouncements about the full emancipation of women in the socialist world, spoken in a whisper for fear the neighbors would overhear her.

  Vitya was grateful to Nora for liberating him from the yoke of his hormones, a relief he experienced immediately after each one of their short, stormy meetings. Business meetings … The marriage prank they staged for the graduation ceremony had no effect on their relationship. Sometimes Vitya went to see Nora, with a friendly but purposeful aim; sometimes Nora would call him. They would come together, then part ways, without discussing when they would see each other again. Sometime or other … Vitya devoted all his energy to another romance—mathematics. Nora did her artwork with supreme pleasure, attended lectures on the history of theater, and read books.

  Vitya was admitted to the Department of Mathematics and Mechanical Engineering, and from the first year of his studies dived headlong into set theory, a field of mathematics that had arisen relatively recently, in the mid-nineteenth century—a field that seemed to appeal greatly to madmen and suicides. It also beckoned to Vitya. Human fates, characters, and biographies did not yet stand behind the names of theories. It wasn’t until a few years later, when the Russian translation appeared of a multivolume work on mathematics and its history written by a group of mathematicians who had adopted the pseudonym Nicolas Bourbaki, that Vitya found out about the founder of the entire field. Georg Cantor, born in St. Petersburg, was the originator of the notion of actual infinity. A philosopher, musician, and Shakespeare scholar, he lost his way in the world of his own creation and died in a psychiatric clinic in Halle. He left behind (in addition to all of the above) what is known as Cantor’s Problem or the Continuum Hypothesis, which, as the next generation of mathematicians would claim, was possible neither to prove nor disprove. Vitya learned about the death of Felix Hausdorff, who took his own life in 1942 before he could be sent to a concentration camp, about Hausdorff spaces and the Hausdorff Paradox, which were his legacy to his descendants, and much else besides, concerning not so much mathematics as mathematicians.

  Vitya spent the entire fourth year writing about computational functions, which thrilled his department chair, who was also quite an eccentric fellow.

  The university administration, forced to consider the outstanding achievements of the department head, a world-renowned scholar, forgave his eccentricity; but Vitya, his student, did not get off so lightly. In those days, the Communist Party representative called the shots, and the dean’s office was beholden to him. The students were kept on a tight leash—mandatory Komsomol meetings, political briefings, “volunteer” social work. From time to time, Vitya was taken to task for disregarding the laws of existence. Once, he was barred from taking an exam for skipping PE classes. Another time, he was nearly expelled from the university for what became known as the “potato-carrot incident.”

  Every September, all the students were sent “potato-picking” on communal farms. Those who were best suited to the conditions of Soviet life managed to procure medical exemptions beforehand. As secretary of the Housing Management Committee, Varvara Vasilievna had connections all over the district, and getting hold of the desired certificate would have been a breeze for her; but Vitya hadn’t even thought to ask for one, and now he had to fulfill his Komsomol obligations.

  The students worked with great enthusiasm this time, since Dennikov, the Komsomol organizer in their class, promised that they would be released as soon as they dug up all the potatoes from the immense field. Inspired by this promise, the young people worked from sunrise to sunset, took in the entire harvest in two weeks, and were glad that they had earned fifteen extra days of free time. Toward the end of the harvest, however, Dennikov disappeared. He had been recalled on important Komsomol business, and the Party comrade who replaced him announced that now they would pick carrots. The rains started the same day.

  The students howled and went into the carrot fields. Not all of them, however—some of them refused on principle, and left for home. Vitya also left—not out of principle, but because of illness. He had a terrible cold and a fever, so he took to his bed and gave himself over to mathematical dreams. He experienced what in later years he would call “intuitive visualization.” He even attempted to describe this experience of the world of sets as forests or lacework of profoundly beautiful ties and nodes, moving in space, and having no connection whatsoever with crude reality, where the teakettle boiled, and sometimes all the water boiled off; where the indestructible cockroaches persecuted by Varvara Vasilievna roamed the kitchen; where the exhaust fumes from Nikitsky Boulevard came in through the window and filled up his ground-floor basement room. The attempt failed.

  Misty visions the mind couldn’t comprehend alternated with a semiconscious state in which the shadow of Nora was present. She offered him amazing objects on a large flat plate made of bright metal, and these objects were algorithms, and they were alive—they stirred slightly and interacted with one another. Vitya felt that there was some exquisite idea he had to write down, but something was missing, something was always missing. A tall man was walking down a long corridor with a shining hole at the end and carrying the same dish that Vitya had seen in Nora’s hands, and on the dish were the same creatures—which were the theory of functions and functional analysis. The man’s name was Andrei Nikolayevich, and Vitya desperately needed to have this man notice him, but because of some unspoken law he didn’t dare call out to him, so Vitya had to wait until the man noticed him first. Then the scenery changed, and the tall man went away; the dish with the algorithms ended up in Vitya’s hands, only they were all dead and didn’t stir any longer, and horror engulfed him.

  He was sick for a long time, and there were complications. Just at the time he returned to the university, there was a meeting at which the students who had abandoned the potatoes, or, rather, the carrots, were expelled from the Komsomol. Their fate was predetermined: after expulsion from the Komsomol, expulsion from the university followed automatically. Vitya Chebotarev’s case was considered separately. He had a medical certificate attesting to his illness, but it was dated two days after the exodus from the carrot fields.

  Logically, he was guilty and did not deserve pardon; but from a humane perspective, he really had been ill. Moreover, there were other factors of a purely medical nature that had bearing on the matter: the two days prior to the issuing of the certificate could have been the incubation period of the illness, when the symptoms had not yet manifested but the infection was already hard at work trying to undermine the host organism.

  In short, taking into account the above-mentioned circumstances, they gave Vitya a break in the form of a reprimand, though all the other offenders were kicked out of the Komsomol.

  While he was sitting in the Komsomol meeting, he made an effort to remember why he had ever joined. This detail had completely vanished from his memory. Then he remembered—his mother had insisted. Yes, Varvara Vasilievna considered it necessary. She herself was a Party member, and knew there were certain matters in which you had to be like everyone else, and even a bit better—so as not to violate the laws of life. Vitya, who had never objected to his mother’s trivial demands, had submitted his application for acceptance to the Komsomol in the eighth grade with the same insouciance with which he applied for a marriage certificate two years later.

  In matters that did not interest him, Vitya never made a show of principle. This time, however, he suddenly sensed the injustice of it all: they had been deceived. They were promised that if they dug up all the potatoes, they would be allowed to leave, but they were prevented from leaving. So in what way were they to blame? For believing what they were told? This was fraud!

  “What do you think you’re doing, you idiot? Stuff it!” Slava Berezhnoi, a friend and fellow student, whispered. “You won’t help us, you’ll only make things worse for yourself.”

  And that’s just what happened: Vitya was expelled, too. Shocked and shaken to the core,
he went home and lay down on the divan. And refused to speak. Varvara Vasilievna wasn’t able to ferret out the facts from him, but she put two and two together and decided that Nora, her mythical daughter-in-law, was the culprit in Vitya’s depression. By this time, she and Nora had already met, and Varvara Vasilievna managed to get hold of her telephone number, which wasn’t all that difficult for someone who worked in the Housing Management Committee. She called Nora, but wasn’t able to get a straight answer from her. She believed Nora was beating around the bush.

  A week later, Slava Berezhnoi came to visit him and explained everything to Varvara Vasilievna. But Vitya refused to discuss anything with Slava, either, and was taciturn the whole evening. Nevertheless, Varvara Vasilievna, now that she understood everything, went to the university and straight to the Party committee, where she spoke with the department representative heart to heart, communist to communist. He understood the situation on a human level: it’s hard for a single woman, a soldier’s widow, to raise a son by herself … It must be said that Varvara Vasilievna embellished the truth somewhat, elevating the rather unseemly circumstances. She wasn’t exactly a soldier’s widow, and not really a widow at all, but she did say things that were perfectly true: Vitya had fallen into a depression, and Varvara Vasilievna had managed to pull him out of it with good medication, an effort that took her three whole months. Vitya was reinstated in the Komsomol, and they didn’t expel him from the university. The head of his department also weighed in on the matter: though frightened, the old crank didn’t want to lose an outstanding student. “The future of Soviet mathematics”—those were his very words.