Mandelbrot the Magnificent

by Liz Ziemska

  “We’re celebrating the Sabbath?” We hadn’t done that since we left Warsaw, not wanting to advertise our Jewishness (the Friday arrival of Madame Derrasse’s faux challah notwithstanding).

  Father got up from his sewing table and came over to measure the circumference of my neck. “Do as your mother says, it will be dusk soon.” Then he ran the tape from my right shoulder down to the first knuckle of my thumb.

  Mother waved her hands over the candle flames to extract their illuminative power, then cupped her hands over her eyes and prayed, “Barukh ata Adonai Eloheinu melekh ha-olam.”

  “What’s the occasion?” I asked. Was all this for me? Had they already heard of my triumph in the classroom?

  “You’re the occasion,” said Léon. I hadn’t even noticed him, but there he stood at the sink, placing wildflowers into a pretty blue vase.

  “You told them?” I was upset that he had stolen my fire. And furthermore, how had he known? Léon and I ran in different circles. It would be more accurate to say that he had friends, while I had only my Book of Monsters.

  “The whole school is talking about it,” said Léon, “probably the entire town.”

  “Bring those flowers over here,” Mother snapped.

  “It’s not my fault,” Léon whined, though he obeyed without hesitation.

  “It’s nobody’s fault,” said Father.

  “But you don’t even know the best part,” I said, still not grasping the situation. “It was as if the numbers were speaking to me directly and—”

  “When will they post the class rankings?” Mother cut me off.

  “Monday afternoon,” I said. “But I already know: I will be the first.”

  “Maybe not,” Mother said to Father. “There’s still some chance they might fail him, or at least knock him back a few levels.”

  “There is no chance,” I protested. “I answered every question perfectly!”

  “We can’t be certain,” said Father. “It’s not worth the risk.”

  “Then we will have the weekend to prepare.” Mother turned to Léon and me. “And you two will leave first thing Monday.”

  “Leave?” Had my entire family gone insane?

  Mother set her raptor gaze on me. “Remember when I told you to do well, but not too well?”

  I could feel my face turning red with shame, but wounded pride made me want to push back. “What kind of mother tells her son to do anything less than his best?”

  Mother reared back as if I had slapped her. How awful I was at that moment, but I so badly wanted to be praised. She turned away and began preparing a salad of bitter greens.

  Léon looked at me with awe (was it really possible to talk to Mother that way?).

  “I like our school,” he said, suddenly bold. “Let him go. I’m not going anywhere.”

  “I’m not going anywhere,” I said.

  “You should go,” Léon said to me. “Without you, they’ll leave us alone.” (I didn’t blame him. It couldn’t have been easy being my brother.)

  Father got up and stood between us. “Why ruin the little time we have together?”

  I went over to Mother and placed a protective hand on her shoulder. I had grown that year, she seemed tiny in comparison. “I’m sorry I spoke to you that way,” I said softly, “and I know that you’re upset because you’re worried, but you have nothing to fear, Monsieur Leguay will protect us.”

  Mother turned around. “Who is this Leguay?”

  “That day I told you that I went out to gather mushrooms, and you got mad at me because I came home after dark? Well, that’s because I came upon Monsieur Leguay in the maquis,” I said, “and it turns out that he’s not just my math teacher, but an officer in the Resistance.”

  “I knew it!” Mother pulled the shawl off her head and threw it on the ground.

  “Leguay is the one who told me that I should try to beat Emile Vallat,” I said, happy that she finally understood me. “He encouraged me to be the best in class. My success is helping the war effort. It’s an act of resistance, a way of showing the Germans that we are not afraid.” I was improvising now. It felt good.

  “He set you up,” Mother said.

  “Listen, Trotsky, not everything is a conspiracy.” Father patted Mother’s hand affectionately, though I could tell that he too was concerned.

  “I saw the men and women he commanded,” I insisted, though at this point I was mostly trying to convince myself (such was the power of Mother’s skepticism). “They had guns, they will protect us.”

  “Resistance fighters don’t care about people like us,” Mother said dismissively. “They only care about glory. It’s romantic for them to play soldiers under the stars. I met many of those types in Russia during the revolution. They all had boring lives before the war, as teachers, clerks, mechanics. Guns make men feel heroic, and equal.”

  “Maybe he couldn’t help it,” Father offered. “Having such a brilliant boy in his class, it’s irresistible. Maybe for once he just wanted to reward his best student, even if he was a Jew.”

  I noted with pleasure and surprise that Father took my side, though the whole situation was painfully confusing. Had I really been a pawn in Leguay’s game? What was that game? To punish Vallat? Did it have something to do with his mother, or her lover, the owner of the Hotel St. Michel? In any case, my path was now clear.

  “Whether or not Leguay betrayed me, I am staying here,” I said.

  “So am I,” said Léon, though he did not look certain. “We’ll protect you.”

  “If that’s your decision, then tomorrow you will go see the rabbi in Brive and tell him so in person,” Mother said as she brought the salad to the table.

  “What rabbi?” At no point during our exile had my parents ever mentioned a rabbi.

  “The rabbi who has already bought your tickets to Lyon, paid your tuition at the new lycée, and arranged your new identity papers,” said Mother. “The rabbi who helped Szolem escape to America.”

  I turned to Father, my only possible ally: “I’m not leaving you, not the way Szolem did.”

  As soon as those words were out of my mouth, I regretted them. Forgive me. I tried to catch Father’s eye, but he turned away from me.

  “We should eat,” he said, and folded up the traveling suit he had been making for me.

  The benefit of this unfortunate exchange, in which I impugned Father’s ability to take care of his own family, was that I suddenly became docile.

  “Let’s eat,” I said, grateful for the distraction.

  Mother had performed the miracle of the loaves and fishes, but instead of the traditional challah bread, a pair of Romanesco cauliflowers commemorated the manna that had fallen from Heaven upon the wandering Israelites. Bright green and ornately textured, they looked like the jewel-encrusted baubles crafted by Fabergé for the Romanovs (another doomed family). Lamb neck (Vincent the butcher was getting creative) cooked with wild garlic completed the meal. The smell alone should have drawn the Gestapo to our door, but to me it all tasted like sand.

  G-d, Mathematician

  BRIVE-LA-GAILLARDE, “BRIVE THE BOLD,” is a prosperous market town twenty-nine kilometers southwest of Tulle. The road to Brive being mostly downhill through numerous twists and switchbacks, I was able to make the journey in a little over an hour using Monsieur Hubert’s rusty bicycle. It had just stopped raining when I rolled into town. The streets were coated with damp pink cherry blossoms, giving them a gruesome aspect, as if the cobblestones were carpeted with flesh.

  I rang the bell at an elegant villa on the avenue Turgot. A stern-faced girl opened the door and led me upstairs to the second floor, where my benefactor sat in his book-lined study. Rabbi David Feuerwerker was thirty-two years old the day I met him, but despite his beard and balding head, he looked more like a young pugilist than a man of G-d. He shook my hand and we sat down on a pair of chairs upholstered in faded green velvet. The girl served us tea in tall, gold-veined glasses. The rabbi offered me sugar, a rare
luxury. I accepted one cube, though I wanted three. Already I was beholden to him.

  Born in Geneva, Rabbi Feuerwerker spoke French with a Swiss accent. His ancestors had come from a small town in Transylvania. He was an expert in Aramaic, particularly its Syriac dialect, the language spoken by another famous rabbi, Jesus of Nazareth. All this I would learn later. For now I was focused on trying to figure out how to tell him that I could not accept his generosity.

  “I have heard great things about your mathematical abilities,” he said.

  My resistance began to melt under the warm breath of praise. “Who told you?”

  “Your father.”

  How? I wondered. Did they write letters to each other? But more interesting, it was the second time in two days that I discovered, with chagrin, that my father had more depth to him than I had previously realized. I had always assumed he was just a tailor and a merchant, a man lacking the sophistication to comprehend the mathematical world Uncle Szolem and I had shared.

  “That’s why your parents thought it would be wise to send you to a school that could better develop your natural talents,” the rabbi continued.

  “That’s not why they’re sending me,” I said, feeling my face turn red with shame. “In any case, I plan to remain in Tulle.”

  “I will cover all expenses,” he countered.

  “My parents are old. We are at war. This isn’t the time for selfishness,” I said, feeling very mature.

  “Selfishness is not the issue here.” The rabbi’s dark eyes probed my resolve. “Neither is shame.” He poured me another glass of tea and offered more sugar. I accepted two cubes. “The only shame is in humanity’s unquenchable desire to destroy itself.”

  I popped a cube into my mouth and crushed it between my teeth. The concentrated sweetness made my eyes water.

  “Creation and destruction,” the rabbi said after a few moments of silence. “Are you familiar with the concept of tikkun?”

  I could feel the sugar rising through the roof of my mouth, setting my thoughts a-skitter. “No.” We never talked about religious matters at home, only practical things like food, survival, and academic achievement.

  “Any positive act is tikkun,” he explained. “Simple kindness, a scientific discovery, the creation of a new masterpiece in the realm of art, music, dance, literature, even going to a different school to continue your mathematical studies: these are all examples of tikkun.”

  Nonsense, I thought, though the exact word that came to mind is unprintable. “Like my Uncle Szolem,” I said quickly, “who abandoned us to pursue his mathematical studies in Texas?”

  The rabbi nodded. “Szolem was far too talented to remain in France. We had to keep him safe.”

  Anger made me feel huge in this room of glass-lined bookcases. “And what about my parents, are they of no value?”

  “It’s not me doing the choosing,” he said, “it’s the Americans. They know what’s happening to us here, and in the rest of Europe, but they don’t want the whole rabble of us appearing on their shores. Here and there they make their selections—a musician, a painter, a physicist, a mathematician. Only the best will get on the ark. Become the best, and you can save yourself.”

  “And my family,” I said.

  The rabbi lowered his head. The gesture could have been interpreted as a nod. “In the meantime, go to Lyon,” he said. “Study hard, learn everything. Your parents will remain hidden in Tulle.”

  “Hidden where?” Would Madame Popova hide them under her voluminous skirts? Could Madame Derrasse bake them into a pie?

  Rabbi Feuerwerker got up and retrieved a sheet of paper from his desk and handed it to me. I glanced at it and found a familiar shape.

  “Uncle Szolem had one of these hanging in his study.” The diagram consisted of ten nodes labeled with Hebrew letters joined together by twenty-two connected paths.

  “What can you tell me about it?” asked the rabbi.

  “Not much. I asked Uncle Szolem about it, and he said it was just a decoration.”

  The rabbi raised an eyebrow. “It’s called the sefirot.”

  “So what is it?” I asked, annoyed that Szolem’s evasion now made me seem foolish.

  “Sefirot is Hebrew for ‘emanations.’ According to the Kabbalah, it is the filter through which the Ein Sof, the Infinite, reveals Himself into the physical and metaphysical realm. Some people believe that it contains esoteric knowledge passed down from Archangel Raziel to Adam and Eve after they had been cast out of Eden, so that they might use it to regain entrance into Paradise,” said the rabbi. “Szolem was studying its mathematical properties.”

  “Clearly neither Adam, nor Eve, and not even Szolem were able to solve it,” I said, “unless Texas is Paradise.”

  The rabbi snorted with laughter. “I have never been to Texas, so I cannot say.” He leaned forward and tapped my knee, which made me jump a little. “When you look closely at this ‘decoration,’ what do you see?”

  I put aside my hurt feelings and forced myself to look down at the sefirot again. I traced its complicated treelike structure while somewhere in the background, sounding very far away, the rabbi’s voice began to recite in Hebrew: Kether, Chochmah, Binah …

  Curves began to spin out clockwise like the little vortex created by pulling the plug in the chipped claw-footed tub in our communal bathroom. The curves drained out of the page and splashed down onto the polished wooden floor of the rabbi’s study until it appeared as though we were sitting at the edge of a deep pool filled with something more viscous than water, yet so completely clear that I could not actually perceive it as a substance, but more like an absence, its contours discernible only at the borders of itself and ordinary space.

  I kept staring into that invisible yet discernible stuff, could feel it oscillating through the soles of my shoes.

  Dimples began to disturb the non-substance like a sudden spring downpour, setting its non-surface boiling (what is the inverse of boiling?) …

  Chesed, Gewurah …

  But there were no raindrops here, only words, with their consonants and vowels, diphthongs and fricatives, hitting ping, ping, ping! …

  Tiphereth, Nezach, Hod …

  … causing even greater turbulence, until the viscous non-substance crested its banks and came sloshing up over the cuffs of my trousers, soaking me to the knee with numbing cold (not cold, more like numbness, non-being). I could feel the polyrhythmic thrumming of the rabbi’s words in the bones of my legs, my hips, climbing up my spine, as if all the atoms of my body, my blood, bones, sinew, and even my eyelashes were dissolving into a densely swarming mass of neutrinos, winking on/off, on/off, on/off, like fireflies.

  I panicked and used all my will to launch myself out of the primordial soup, like a pike leaping out of a lake to catch a fly, and suddenly I found myself back in my green velvet chair, with the rabbi examining me closely.

  I patted myself down, making sure that all parts of me were back in the mundane world of men and jackets and chairs. “Have I been here the entire time?” I asked.

  “As much as anyone is anywhere,” the rabbi said calmly, but he had a twinkle in his eye.

  “Your recitation,” I began, testing my voice, “it was very nice.”

  “The ten sefirot have beautiful names”—the rabbi nodded—“but what shapes did you see when you looked inside?”

  “Curves,” I said. How else could I describe what I had seen? “Or maybe, ripples.”

  The floor beneath my feet had resumed its solid wood-ness. There was a damp spot on the toe of my right shoe, but that could have been from the rain-soaked flower petals. My brain hurt and I felt oddly disjointed, like a chicken that had been taken apart for stewing.

  “How many curves did you see?” asked the rabbi.

  “Hundreds.” (What else could I say?)

  “Szolem was only able to see fifty.” He leaned back in his chair and crossed his arms, clearly delighted.

  “Really?” A small twinge of pleasu
re at besting Szolem brought forth a smile, though I quickly suppressed it.

  “I too was once good at math,” the rabbi said wistfully. “When I was a boy I could add numbers in my head. Stacks and stacks of numbers, without making even one mistake. But then I contracted scarlet fever, and my abilities disappeared, though I was never able to see the sefirot as you or Szolem do, even at my best.”

  I shrugged and felt my shoulders pop back into their sockets. If what I had just experienced meant being good at math, I wished it on nobody.

  “It is a gift,” he insisted, noting my doubtful expression.

  A curse.

  “One that you must protect,” he added.

  “Thanks for showing it to me.” I tried to hand the sefirot back to the rabbi.

  “You used shapes to solve mathematical equations in class.” He pushed it back to me.

  I nodded. Was this really such an extraordinary feat? It seemed so obvious to me.

  “Can you reverse the process?” he asked.

  “How so?” I said.

  “Can you extract the mathematical formula for the sefirot by examining its curves?”

  An equation that describes a set of infinite overlapping curves that contain within their center a matter-dissolving core activated by sound waves? Not even Monsieur Leguay would assign such an evil problem. “Not sure I can. Why would I want to?”

  “Every mathematical genius since Pythagoras has tried to solve the sefirot,” said the rabbi. “Isaac Newton believed that it was the key to the transmutation of matter. Others believe that it’s a metaphysical puzzle box constructed to contain the Ein Sof, the Most Hidden of the Hidden, more commonly known as G-d. But I shouldn’t have asked you. It’s too much for a young boy.”

  “How close did Uncle Szolem get?” I asked. Few mathematicians had ever made an important innovation past the age of twenty-five, I wanted to say. At sixteen, I was in my prime.

  The rabbi leaned forward and unclasped his boxer’s hands. “Maybe if you go to school and work hard, you can join your Uncle Szolem in Texas and ask him yourself.”

  “We’re back at the beginning,” I said, startled by the sudden turn of our conversation away from esoteric matters.