Forgive me.
Forgive me.
Forgive me.
[ IV ]
The Axiom of Equality
1
THE NIGHT BEFORE he leaves for Boston for their friend Lionel’s wedding, he gets a message from Dr. Li telling him that Dr. Kashen has died. “It was a heart attack; very fast,” Dr. Li writes. The funeral is Friday afternoon.
The next morning he drives directly to the cemetery, and from the cemetery to Dr. Kashen’s house, a two-story wooden structure in Newton where the professor used to host a year-end dinner for all of his current graduate students. It was understood that you weren’t to discuss math at these parties. “You can talk about anything else,” he’d tell them. “But we’re not talking about math.” Only at Dr. Kashen’s parties would he be the least socially inept person in the room (he was also, not coincidentally, the least brilliant), and the professor would always make him start the conversation. “So, Jude,” he’d say. “What are you interested in these days?” At least two of his fellow graduate students—both of them PhD candidates—had mild forms of autism, and he could see how hard they worked at making conversation, how hard they worked at their table manners, and prior to these dinners, he did some research into what was new in the worlds of online gaming (which one of them loved) and tennis (which the other loved), so he’d be able to ask them questions they could answer. Dr. Kashen wanted his students to someday be able to find jobs, and along with teaching them math, he also thought it his responsibility to socialize them, to teach them how to behave among others.
Sometimes Dr. Kashen’s son, Leo, who was five or six years older than he, would be at dinner at well. He too had autism, but unlike Donald’s and Mikhail’s, his was instantly noticeable, and severe enough so that although he’d completed high school, he hadn’t been able to attend more than a semester of college, and had only been able to get a job as a programmer for the phone company, where he sat in a small room day after day fixing screen after screen of code. He was Dr. Kashen’s only child, and he still lived at home, along with Dr. Kashen’s sister, who had moved in after his wife had died, years ago.
At the house, he speaks to Leo, who seems glazed, and mumbles, looking away from him as he does, and then to Dr. Kashen’s sister, who was a math professor at Northeastern.
“Jude,” she says, “it’s lovely to see you. Thank you for coming.” She holds his hand. “My brother always talked about you, you know.”
“He was a wonderful teacher,” he tells her. “He gave me so much. I’m so sorry.”
“Yes,” she says. “It was very sudden. And poor Leo”—they look at Leo, who is gazing at nothing—“I don’t know how he’s going to deal with this.” She kisses him goodbye. “Thank you again.”
Outside, it is fiercely cold, and the windshield is sticky with ice. He drives slowly to Harold and Julia’s, letting himself in and calling their names.
“And here he is!” says Harold, materializing from the kitchen, wiping his hands on a dish towel. Harold hugs him, which he had begun doing at some point, and as uncomfortable as it makes him, he thinks it’ll be more uncomfortable to try to explain why he’d like Harold to stop. “I’m so sorry about Kashen, Jude. I was shocked to hear it—I ran into him on the courts about two months back and he looked like he was in great shape.”
“He was,” he says, unwinding his scarf, as Harold takes his coat. “And not that old, either: seventy-four.”
“Jesus,” says Harold, who has just turned sixty-five. “There’s a cheery thought. Go put your stuff in your room and come into the kitchen. Julia’s tied up in a meeting but she’ll be home in an hour or so.”
He drops his bag in the guest room—“Jude’s room,” Harold and Julia call it; “your room”—and changes out of his suit and heads toward the kitchen, where Harold is peering into a pot on the stove, as if down a well. “I’m trying to make a bolognese,” he says, without turning around, “but something’s happening; it keeps separating, see?”
He looks. “How much olive oil did you use?”
“A lot.”
“What’s a lot?”
“A lot. Too much, obviously.”
He smiles. “I’ll fix it.”
“Thank god,” says Harold, stepping away from the stove. “I was hoping you’d say that.”
Over dinner, they speak of Julia’s favorite researcher, who she thinks might be trying to jump to another lab, and of the latest gossip circulating through the law school, and of the anthology of essays about Brown versus Board of Education that Harold is editing, and of one of Laurence’s twin daughters, who is getting married, and then Harold says, grinning, “So, Jude, the big birthday’s coming up.”
“Three months away!” Julia chirps, and he groans. “What are you going to do?”
“Probably nothing,” he says. He hasn’t planned anything, and he has forbidden Willem from planning anything, either. Two years ago, he threw Willem a big party for his fortieth at Greene Street, and although the four of them had always said they’d go somewhere for each of their fortieth birthdays, it hasn’t worked out that way. Willem had been in L.A. filming on his actual birthday, but after he had finished, they’d gone to Botswana on a safari. But it had been just the two of them: Malcolm had been working on a project in Beijing, and JB—well, Willem hadn’t mentioned inviting JB, and he hadn’t, either.
“You have to do something,” says Harold. “We could have a dinner for you here, or in the city.”
He smiles but shakes his head. “Forty’s forty,” he says. “It’s just another year.” As a child, though, he never thought he’d make it to forty: in the months after the injury, he would sometimes have dreams of himself as an adult, and although the dreams were very vague—he was never quite certain where he was living or what he was doing, though in those dreams he was usually walking, sometimes running—he was always young in them; his imagination refused to let him advance into middle age.
To change the subject, he tells them about Dr. Kashen’s funeral, where Dr. Li gave a eulogy. “People who don’t love math always accuse mathematicians of trying to make math complicated,” Dr. Li had said. “But anyone who does love math knows it’s really the opposite: math rewards simplicity, and mathematicians value it above all else. So it’s no surprise that Walter’s favorite axiom was also the most simple in the realm of mathematics: the axiom of the empty set.
“The axiom of the empty set is the axiom of zero. It states that there must be a concept of nothingness, that there must be the concept of zero: zero value, zero items. Math assumes there’s a concept of nothingness, but is it proven? No. But it must exist.
“And if we are being philosophical—which we today are—we can say that life itself is the axiom of the empty set. It begins in zero and ends in zero. We know that both states exist, but we will not be conscious of either experience: they are states that are necessary parts of life, even as they cannot be experienced as life. We assume the concept of nothingness, but we cannot prove it. But it must exist. So I prefer to think that Walter has not died but has instead proven for himself the axiom of the empty set, that he has proven the concept of zero. I know nothing else would have made him happier. An elegant mind wants elegant endings, and Walter had the most elegant mind. So I wish him goodbye; I wish him the answer to the axiom he so loved.”