The Goddess of Small Victories (43 page)

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 Mallarmé 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.

With the pantry returned to its normal, comfortable silence, Tine poured herself a tiny glass of punch, then lit a cigarette. It was time for Anna to go home. Ernestine pressed a Tupperware container on her that there was no question of refusing, then suffocatingly mashed her to her enormous bosom. She whispered in Anna’s ear, “
Appelle-le, crétine!
” Call him, you idiot!

When the door closed on the last of his guests, Calvin reentered his personal hell; Virginia was pouring herself a gin with only approximate command of the trajectory.

“You want to have them mate? Anna is a pale copy of Rachel. You’ll have grandchildren as white as a daikon radish, with their father’s big nose. Where shall I make reservations for the bar mitzvah?”

“You’re not making any sense.”

She jiggled the ice in her glass.

“I’m perfectly lucid. You have always had a thing for her mother.”

“From what I see, you are becoming lucid earlier and earlier in the day, Virginia.”

1958

Papa Albert’s Dead and Gone

I walked around our yard looking for a place to put my new purchase: a pink flamingo made of painted cement. Kurt watched my movements from his deck chair. Despite the mild spring temperatures, he still kept his overcoat, wrapped his legs in a plaid blanket, and, in a recent mania, wore a woolen balaclava. From the steps, I spied the perfect place: next to the arbor, where the loud pink would clash wonderfully with the green of the lawn and the delicate red of my camellias. I set my trophy in place and stepped back to admire the effect: it was impossible to miss this incongruous object. I savored in advance the silent disapproval of Kurt’s mother.
See what a woman of mediocre taste can accomplish, Marianne
.

“My mother is not going to like that oddity.”

“Your mother will just have to put up with it. I like it!”

“She’s already not too pleased at having to stay at the hotel.”

“We have no choice. You couldn’t ask your mother and brother to sleep on the living room couch!”

“I don’t think it’s very elegant, asking my family to pay for a hotel on their first visit to Princeton.”

“What about the money you send them every month? Even though your brother makes a good living!”

“Your mother lives with us. But mine can’t even spend a few nights at our house.”

“Why don’t you offer to pay for your mother’s hotel room? Your brother can perfectly well afford it!”

Eighteen years had passed since we had left Vienna, and Marianne and Rudolf were finally agreeing to visit Princeton. Thrilled at the prospect of rediscovering his family, and relieved not to have to travel to Europe himself, Kurt was worried there might be a renewal of family hostilities. He couldn’t understand my resentment toward them; he had never understood the first thing about other people’s feelings. I had promised to be on my best behavior: I would feed them amply and walk them around Princeton with a smile. As long as she didn’t pick on me! I had to admit that Kurt never reproached me for the money I spent on travel or for having to give my mother a place to stay. But in this our hands were tied: I couldn’t let her die alone in a hospice. And she couldn’t find her way from the bedroom to the kitchen. I often had to rescue her in extremis from the street; she thought she was still on the Lange Gasse.

“What a shame that my mother never had a chance to meet Albert! I would so have loved to introduce them. They were the same age.”

I went and kneeled beside him.

“Would you like a nice cup of hot tea? You look petrified with cold.”

“Did you remember to order the meat for tonight? My mother loves veal.”

We were counting our dead. Papa Albert had already died three years before. The news from Europe was that Pauli was dying in a Swiss hospital.
⁵⁶
Earlier in the year, cancer had drained the last of John von Neumann’s gigantic life force.
⁵⁷
At his funeral service at the Princeton cemetery, I remembered Albert’s terrible joke about the three nuclear physicists who are told they are going to die. Each would be granted a last wish. What had John asked for? Not to meet Jean Harlow, not to see the president, not even for a second opinion; he had insisted on pursuing his research. He had had himself transported to the lab on a stretcher. What had Einstein asked for? Peace. In a letter to Bertrand Russell, he agreed to sign a new petition urging every nation to renounce nuclear weapons. In the hospital, laid low by an aneurysm, he had made Bruria bring him the papers on his desk. He had written: “Political passions, once they have been fanned into flame, exact their victims.” Protesting, warning, working, researching. Fighting until his last breath.