The Goddess of Small Victories

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The Goddess of Small Victories Page 31

by Yannick Grannec


  “Are you calling into question the principle of synchronicity?”

  “Don’t turn a subjective phenomenon into a postulate. Or a theorem. Any causal link between two personal experiences remains a happenstance, even if the particular resonance it sets up within a person’s unconscious is incontrovertible.”

  “That resonance is the absolute proof of a manifestation of immanence! Our drive to find meaning in an event implies the preexistence of such a meaning. Why else would nature give us the ability to question ourselves?”

  “The term ‘absolute proof’ is inappropriate. And are you sure you mean ‘nature’ and not ‘culture’? Why shouldn’t we hope for meaning where there is none? It wouldn’t be the first time mankind had gone on a vain quest.”

  “God has injected a maximum of meaning into the world, giving multiple values to the same events, a function on a multitude of levels.”

  “If you are going to bring God into the debate, then we can have nothing more to say to each other, Gödel!”

  “I’ve known you to be more spiritual, Robert. Where have you put your copy of the Mahabharata?”

  “I am sometimes distrustful of these ideas, because they provide a basis for charlatanism. The thirst for meaning, which everyone feels, makes some people an easy prey. It is too easy to go from synchronicity to coincidence and premonitions, to mediums …”

  “Then you take me for a charlatan, Mr. Oppenheimer.”

  “I also don’t set much store by labels. In the best case, you imagine a spiritual door where others are looking for a nice, neatly packaged answer. If memory serves, there is even a pathology associated with this. Apophenia. The tendency to see symbols or meaningful patterns in random data.”

  Charles could see his own goods being sold at clearance prices. He opted for irony.

  “Apophenia is a natural tendency. We distort reality to make it conform with our vision of the world. I know a specialist in this. My wife!”

  Putting both hands around her husband’s neck, Beate tried to strangle him. For a moment, I had had the impression that he was implicating Kurt, who was a past master at distorting reality. I had often enough seen him build cathedrals out of sand, mixing trivial details with great principles. He created a universe in his own image, both powerful and fragile, logical and absurd.

  “Before Beate kills me for real, I would like to point something out to you, Robert. Which is that psychoanalysis does not propose pretty answers. Quite the opposite, it gives us solid questions!”

  “It hardly gives them to us, dear friend. Your sessions are far from being free.”

  I decided to lead the conversation onto smoother terrain. The first commandment for a harmonious meal had been broken long before: Never talk about religion or money at table! If they started to discuss politics, our little lunch would be totally ruined. I assumed the role of silly entertainer and suggested that we attempt some actual experiments in parapsychology. Kurt would go along with this. We often indulged in this kind of game. He used to say that in the distant future, people would be surprised that twentieth-century man had discovered elementary physical particles without ever imagining the existence of elementary psychical factors. I had no idea exactly what he meant, but I was very good at telepathy. After living with a man for thirty years, guessing his thoughts is a question of simple survival. Not surprisingly, all the guests were enthusiastic.

  “I have been training for some time in ptarmoscopia … predicting the future with sneezes. I get excellent results.”

  Everyone laughed. I’d managed to put Carl Jung back on the shelf of dubious ideas where he belonged.

  “And what do you call divination based on our wives’ moods?”

  Erich Kahler suddenly appeared at the table, invigorated by his nap.

  “Good sense, Charles, plain good sense! Did I miss anything?”

  “Adele, I think I hear the telephone ringing.”

  Running toward the living room, I tripped over Penny, who was sleeping on the doorstep. I patted her in apology. What a lovely afternoon! It gave me enormous pleasure to see Kurt so lighthearted and talkative. I looked back to savor his smile again.

  I put the phone down softly. I stood there motionless, listening to the happy sounds of voices from the garden, breathing in these last minutes of happiness.

  When the shade of the poplar reached the dog, I went to Kurt. I put my hand on his shoulder. Everyone was silent. Before I’d even spoken, I saw two large tears form in my friend Lili’s eyes.

  “Albert has ruptured an aortic aneurysm. He’s been taken to the Princeton hospital.”

  45

  When the last of the dessert tarts had disappeared, Virginia invited her guests to regroup around the living room sofas. Anna decided to slip away from the crowd of smokers and visit Ernestine in her lair. The pantry had been renovated: it glistened with chrome and stainless steel. Only Tine’s collection of old china had survived. Anna had learned her first words of French there: sucre, farine, sel, sugar, flour, salt. The kitchen was spotless. To all appearances indolent, Tine organized her domain with military precision. No one was allowed to get in her way when she was cleaning up. But Anna enjoyed preferential treatment; as a child she had spent long hours watching Tine’s rubber-gloved hands at work. She had listened to Tine talk about her country, about poetry and the latest neighborhood gossip, and she had sat and read beside her, lulled by her Creole songs. She also liked Tine’s little ritual: once the dishes were all put away, Ernestine allowed herself a small glass of punch and a cigarette.

  Removing her apron, Ernestine enumerated all her age-related aches. Anna protested as a matter of form. Tine had complained of being old even when she was still the buxom nurse who terrified visiting schoolkids.

  “Have you opened my present?”

  “Don’t be daft! I haven’t had a minute to myself all evening.”

  She fished the package from a drawer and her reading glasses from another. She unwrapped the present carefully; in one of her treasure cabinets she kept a supply of neatly folded paper. She caressed the leather-bound volume: Anthologie de la poésie française. Anna had always known how to please her.

  “Comment vas-tu, mon bel oiseau? How are you, my pretty bird? You look pale.”

  There was no need for Anna to embark on a long confession, as Tine had followed every move in the war of nerves between Anna and Leonard, her two adopted children.

  “Have you spoken to Leo?”

  “Spoken about what?”

  “There you go again! Why make it simple when you can complicate it? Si c’est pas malheureux, vous deux! The two of you are hopeless! I never understood what you saw in that idiot from New York. What was his name anyway?”

  “William. He got married last year.”

  Leonard burst into the kitchen.

  “This is a private conversation, young man. What brings you poking around here?”

  “I refuse to hold a tin cup under Richardson’s nose.”

  Tine tried to smooth Leo’s hair with the flat of her hand; he skipped out of reach, too tall for her now. A last pencil mark on the doorjamb attested to it. Ernestine had had to bully the painters to keep the measurements from being erased.

  The French mathematician poked his Roman nose into the kitchen, looking for seconds on dessert. Ernestine simpered at his compliments; twenty years earlier she would have eaten him alive for an afternoon snack. Though she had always been discreet, the neighborhood buzzed with rumors about her appetites. Virginia Adams, despite her suspicions, had never caught Tine red-handed. And she was less concerned about her husband’s infidelities than she was about losing a gem of Ernestine’s caliber. For his part, Calvin was too concerned with his reputation to embark on an adventure of this kind; he made do with hotel bars in the wake of conferences.

  Tine bustled around to prepare a plate and open a bottle for her new admirer. Anna pulled out a chair for him. Leo could barely contain his irritation. By monopolizing the interest of the
two women, the Frenchman was invading his territory. Leo Adams had been at the center of everything in this house, claiming even the little attention that hadn’t already been given him by his mischief. He wanted to stay in the center, and he addressed Anna.

  “So, you’ve been assigned to recover Gödel’s papers? His widow must be at least three hundred years old. A survivor of Princeton’s heroic postwar years!”

  Pierre Sicozzi watched the young woman through his ruby-colored glass, while she, embarrassed, fingered the book of poetry.

  “Ah, yes, Calvin mentioned that to me. She must be an extraordinary character to have lived with such an unusual man.”

  “She’s not always easy company, but she is generous with her stories.”

  “You’re a research librarian who stands very close to History.”

  “She’s resisting turning over the archive to us. She has a grudge against the academic establishment. She’s never been thought well of. Yet Adele is a very engaging person.”

  As always, Leo had an opinion on the subject.

  “Gödel is an icon at MIT. We use his portrait as a target when we play darts. We even organized a ‘Gödel versus Turing’ festival.”

  “Who won?”

  “Scoreless game. An undecidable proposition, Professor Sicozzi.”

  “If such a battle ever took place, Gödel won it a long time ago.”

  “Turing’s consolation prize was being the father of modern computer science. Gödel pushed formal logic to its extremes. The Englishman gave logic reality by developing a technology for it.”

  The Frenchman attacked his plate vigorously. Leo watched him briefly before continuing.

  “Another tragic mathematical fate. Brilliance and decline. One of them died mad, while the other made a theatrical exit. He killed himself by biting an apple laced with arsenic. Poisoned like Snow White.”

  Anna decided not to correct him, although she knew the story of the English logician perfectly well. He had not committed suicide over mathematics: he had been persecuted by the British government for his homosexuality and forced to take a barbaric hormonal treatment. Yet it was thanks to him that Enigma, the German ciphering machine, had been cracked. Without Turing, the Allies would not have won the intelligence battle during World War II.

  Leonard would allow no one to contradict him in his own field of expertise. Unsurprisingly, he went on to tell the story of the Turing machine, the precursor of the modern computer. At the end of the 1930s, the British mathematician had devised a theoretical system for executing simple algorithms. He had gone from there to the idea of a metamachine that could combine all these operations infinitely. Anna had helped mount an exhibition on von Neumann and ENIAC, another great leap forward in the history of computers. She could therefore have told Leo a thing or two on the subject, but the chance to hear Leo wax enthusiastic was so rare that she swallowed her pride. She was within an ace of exclaiming, “You’re so strong!” He wouldn’t have appreciated the joke, and he didn’t need anyone to tell him what he already knew. As to trying out Adele’s theorem on a Fields medalist, she would never have dared.

  “Pushing his concept to the limit, Turing realized that his machine could only supply an answer that already existed. It wasn’t capable of deciding whether certain questions were decidable. Which is to say, deciding within a finite time whether a proposition was true or false.”

  “The incompleteness theorem is unavoidable, even to a machine.”

  “You, Anna Roth, are interested in mathematics?”

  “I’m not sure I understood the whole thing, but Adele did speak to me about the fact that they met.”

  Ernestine gave her a quiet smile before going back to banging cabinet doors; she, too, knew the technique.

  “You should write a book about it, Anna. The heroic fate of the pioneers of the computer age. Gödel, Turing, von Neumann …”

  The young woman blushed when Pierre brushed her glass with his own.

  “Leo’s idea strikes me as excellent. You’re at the source of History, with access to an intimate perspective.”

  “Adele is not a scientist. She has an emotional view of events.”

  “Life is not an exact science. A human being is more than the sum of his acts. More than a simple chronology.”

  “I’m a research librarian. I collect objective facts.”

  “Trust your intuition.”

  “If I did that, it would be fiction.”

  “Why wouldn’t it be one truth among others? Truth does not exist or … not all truths are provable.”

  He gave a small, embarrassed smile.

  “That lyrical extension of the incompleteness theorem would have made our defunct genius shudder.”

  “I understood as much! It’s wrong to use a proof of formal logic in other fields.”

  “Relax, Anna. Being a mathematician does not prevent me from enjoying music, a good novel, this sublime fruit tart, or this delicious Gevrey-Chambertin. Even if words are incapable of describing the complexity of its taste.”

  “You’re an epicurean.”

  “I feed the capricious animal of my intuition through all my senses.”

  “Even by reading fiction?”

  “It suggests clues to the universal by starting from the particular, just as poetry does. Mathematics has a great deal to do with poetry in any case.”

  Exasperated, Leo shrugged.

  “Kurt Gödel distrusted language.”

  “He was looking for another form of communication, for formal tools capable of conceptualizing reality in our sensory world, an immanent mathematical universe. For him, the mind was greater than the sum of its connections, however enormous it might be. None of your computers achieves that state of intuition or creation.”

  Leo was seething: the subject required more exactitude and less rhetoric. Gödel had compared two ideas. If the brain was a Turing machine, it shared the machine’s limits: there existed undecidable problems. Mathematics or the world of ideas, in the Platonic sense, would remain in part inaccessible to man. But if the brain was an infinitely more complex instrument, able to manipulate patterns that were inconceivable to an automaton, then man possessed an unsuspected system for managing mental activity. Unable to pinpoint it, we might simply call it “intuition,” the capacity to project oneself beyond language and beyond even the formal language of mathematics. Pierre Sicozzi listened to him attentively, a small and inscrutably ironic smile on his lips.

  “Then mind always surpasses matter, Leonard.”

  “Until we have proof to the contrary! We’re talking about a field that is seeing extraordinary development. Tomorrow’s computer may give the lie to Kurt Gödel.”

  “You’re preaching to the digital choir. Moore’s law—that microprocessors double their capacity every eight months—is only a fuzzy conjecture, intended to egg on the industry by holding out the promise of endless growth. In my humble opinion, the role of computers will be in the area of verification. When it comes to mathematical discoveries, nothing beats the natural method of using a pencil and notebook.”

  “And yet the possibilities seem infinite.”

  “What is the infinite in balance with this sublime dessert?”

  “It all depends on which infinite you mean.”

  “Another Gödelian observation. All roads lead to Gödel, right, Anna?”

  “Are you going to finish your tart, Mr. Sicozzi?”

  “Dear Ernestine, we have here reached the limits not of my mind but of my stomach. I throw in the towel. You’ve won.”

  He noticed Anna’s present on the table. Opening the book randomly, he read a few lines in his musical voice.

  “ ‘CE SERAIT … pire … non … davantage ni moins … indifféremment, mais autant … LE HASARD.’ ”

  Leo poured himself another glass, mumbling. “What is this gobbledygook? I don’t understand French.”

  “I would have an easier time demonstrating the incompleteness theorem than explaining Mallarm
é to you, Leo. I could tell you about sensations. About the pleasure of juxtaposed sounds. The white of the page and the black of the typography in this calligram speak to each other.”

  He showed him the placement of the poem on the page: a frayed cloud of lowercase and capital letters.

  “A genial intuition of the very nature of our physical world. A void in which a few motes of randomness dance.”

  “If you go that way, then Tine’s recipe books contain hidden meanings of the universe.”

  “Mécréant! Wretch! Are you then nothing but a Turing machine? How can you deny the fertility of a sentence like Mallarmé’s: ‘A throw of the dice will never abolish chance’?”

  “I don’t believe in chance. Only in algorithms. You are too fond of words for a mathematician.”

  “If mathematical inspiration can come from pizza, why not from Mallarmé?”

  Calvin Adams appeared in the doorway. He had the look of a man who discovers that the real party has been happening elsewhere, without him.

  “These youngsters have been monopolizing your time, Pierre.”

  “Not at all. Frenchmen always wind up in the kitchen.”

  Calvin apologized for calling him away from the charms of the lovely Ernestine; they needed to make some final arrangements for the conference scheduled two days hence. Pierre Sicozzi rose regretfully to his feet. He courteously kissed the two women’s hands and gave a warm handshake to Leonard, who responded with the barest courtesy. Calvin put his arm around his son’s shoulder and asked him to say a few polite words to the Richardson heir. Leo tore a page from his notebook, scribbled down a number, and handed it without a word to Anna. She put the paper in her handbag, promising herself not to make use of it. He hadn’t changed one iota, and a certain dead mathematician was adding enough complexity to her life at the moment.

 

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