“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.”
46. 1958: Papa Albert’s Dead and Gone
Dear Posterity,
If you have not become more just, more peaceful, and generally more rational than we are (or were) — why then, the Devil take you. Having, with all respect, given utterance to this pious wish, I am (or was) Yours, Albert Einstein
— message written for a time capsule
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!”