Authors: Leonard Rosen
All Cry Chaos (12 page)
"Henley," the young man said. "Wendell."
"Well, Mr. Henley. What do we have?"
The student pulled up his work. Again, the class howled.
"I tried," he said. "It looks like a telephone pole with too many cross pieces and toothpicks for leaves. I went at this hard for a solid week, changing one value after another, trying to build a curve into the form. I should have locked my fern in a room with that dude's fern. Their children might have had a chance." His tattooed classmate raised a fist in salute. "It was all good through about 20,000 iterations. Then everything stiffened up, no matter how many times I changed the equation. Brute force usually works for me. Not this time."
The students in the lecture hall were enjoying themselves, and so was Poincaré. The pressure was indeed off, they realized, because no professor would risk failing an entire class. The relief was palpable, until the young Asian woman stepped to the lectern. Poincaré knew what was coming. The student wore a thin, pale green sweater and a pleated skirt—much like a grade-school uniform. She stood with hands folded neatly before her, looking down, as the others presented their images. When she stepped forward, her straight black hair shining in the spotlights, the room went silent.
"Here is the graph and here is the equation I used to create my fern," she said, her voice difficult to hear though she spoke into a microphone. She was a flower, marveled Poincaré, with a prodigious mind. She said: "I iterated this function just over 100,000 times. Thank you very much."
She returned to her seat, and a few students rose to congratulate her. The majority sat quietly, stunned.
"Cheer up," said Chambi. "Ms. Cheng is fifteen and ran out of math classes to take in her native Taiwan. Many of us believe she has a promising career. What will count for the rest of you is your explanation of how you approached the problem. As you may have discovered along with Mr. Henley, brute force does not work with mathematical modeling. One must use the math—must be intuitive, even."
A hand shot up. "Professor Chambi. Poets are intuitive."
"So I've heard," she said.
"This is a math class."
"Good mathematicians are poets, too," she answered. "They use a different symbol system."
Another hand went up.
"Yes? Mr.—"
"Groupman. I'm confused on a point. Ms. Cheng's equation—of the fern. Would you call it a description?"
Chambi shuffled her notes into a neat pile. "Please rephrase. I'm not quite clear on what you mean by
description.
"
description.
"
The student stood. "Say I start with a fern in the forest. I could write a paragraph describing it, I could paint it, or I might take a picture. No one would confuse these with the fern itself." As Poincaré watched Chambi listen, he thought he glimpsed a smile curling her lips. She allowed the student to finish. "The equation of the fern is more of a blueprint than the painting or the paragraph would be. I'm saying that the mathematics is, or could be, the thing—the fern—itself. It's like DNA, but it's not DNA. You could add a little dirt and water to the equation, and there you go. Dr. Fenster and you have convinced me that every process in nature can be modeled with an equation. Is the point that these equations are not just descriptions of reality but reality itself?"
Chambi crossed the amphitheater stage, trailing a hand along the lab bench. "Mr. Groupman," she said. "By r
eality itself
, what do you mean?"
eality itself
, what do you mean?"
He stamped on the concrete floor. "This." He picked up his knapsack. "And this. All of it."
"I see." She adjusted the microphone. "Allow me to answer this way. For us to even consider what you suggest, the mathematics has to be good—so good that for this fern, when you run a 3-D graphing program, you think you're seeing an actual fern in an actual forest. We're talking about a model elegant enough to anticipate the way wind moves along the forest floor and the way dew settles on their fronds in the early morning. If the equation succeeds at that level, and if you're a mathematician, you would use the word
describe
. You would say that the equation
describes
what you see. But if you're a theologian, you might use a different word."
describe
. You would say that the equation
describes
what you see. But if you're a theologian, you might use a different word."
She posed the question without posing it and let the room go quiet. If Poincaré had shut his eyes and did not know better, he would have guessed there were only a few students in the cavernous hall. The seconds passed until, from a far corner, a student called out: "Gov
ern.
A theologian might say that equations govern what we see."
ern.
A theologian might say that equations govern what we see."
"Possibly," answered Chambi.
"But that would raise the question of a
governor,
" called another student.
governor,
" called another student.
"Yes," said Chambi. "Governor. Architect. What have you. Who would write the equations of nature?"
Again, silence.
The young man who had spoken earlier stood. "According to the catalog, this class fulfills a
math r
equirement."
math r
equirement."
Chambi grinned. "Never mind that. What are you, Mr. Groupman, a mathematician or a theologian? Or perhaps that's something one doesn't decide."
The student shrugged. "I can't really say. Neither. Both. Depends what time of the morning you ask."
"An honest man! If you need a second opinion, the Divinity School is around the corner, on Francis Avenue."
The students laughed, and Chambi glanced at her watch. "That's it, then. I'll review your work and send along your grades via e-mail. A final word, if you'll indulge me. I stepped in for Professor Fenster when he died unexpectedly in Amsterdam. I want you all to remember him, not me, as your instructor for this course, though he was with you for a few weeks only. These were his materials and his notes. The idea for this exam assignment was his. Dr. Fenster was a great man, and mathematics for him was not just a job but life itself. He found exquisite beauty in equations—and, yes, he was regarded around the world as an intuitive with them, a poet. As for your confusion, Mr. Groupman . . . it is the best possible confusion. Keep at it. Good day to you all, and enjoy the summer. It has been a privilege."
Applause, then a commotion of books closing and backpacks being zippered. Two dozen students descended from the amphitheater to surround Chambi. For twenty minutes Poincaré watched this animated, dynamic woman engage her students, who continued taking notes as they spoke informally. His cell phone buzzed and a text message came through from Gisele De Vries:
Analysis at European Space Agency agrees with Dutch forensics: Amsterdam explosive = ammonium perchlorate with additives. NASA says sample = military grade fuel not available on open market + additives to boost explosion. More later. GDV
Poincaré typed a return message:
Bomber had access to or knowledge of military grade rocket fuel. Send request to NASA, European Space Agency + Russian + Chinese agencies. Ask: On staff, who had knowledge to doctor AP? If Russians or Chinese balk, ask American Intel for listing of personnel at those agencies. HP
Chambi dispatched her final student with a handshake and a wave. She climbed the stairs along the far side of the theater, then crossed a long row of seats to Poincaré. She was of medium build with a round face, broad nose, and a rope-like braid of jet-black hair—Ecuadorian according to Poincaré's notes, in the country on a student visa to study the modeling of complex systems. From a biography posted on the math department's Web page, he had learned that her particular interest was the spread of drug-resistant tuberculosis. Her intention was to model the spread mathematically; then she could return home and join the Ministry of Health to combat the disease, which disproportionately affected the country's indigenous poor.
"If you're the Immigration and Naturalization Service," she said, "my visa's in order."
He laughed. "Is it that obvious? You have a gift, you know. Henri Poincaré." He extended a hand. "Excuse my not asking permission to attend, first. I hope I wasn't a distraction."
"You are now. You said P
oincaré
?"
oincaré
?"
And then he remembered. "My father's grandfather."
"Jules Henri Poincaré was your great-grandfather?"
"One doesn't choose, you know."
She walked him to a concrete alcove by the main entrance to the Science Center. "A remarkable man. Truly a giant of mathematics."
"Which I'm not, unfortunately. My parents hoped I would have the family's math gene, but I disappointed them, Dr. Chambi. I tried for a time but gave it up—turns out I wasn't a poet with equations." He smiled.
"And I'm no Doctor of Philosophy—yet. James was my thesis advisor, and when he died no one else in the department would take me on because no one understood his work, or mine. So I'm left with three-quarters of a dissertation and only a few possible mentors in the world, none of them very good. Now if your great-grandfather were around . . . Meanwhile, Harvard's forcing me out."
"Impossible. You're too good."
She wore a scarf at her neck, and Poincaré could see the edges of a large port-wine stain that discolored her otherwise smooth, honeynut skin. She adjusted the scarf when she saw him looking. "I'm expendable. The math department's chock full of grad students, and the dean's not feeling particularly loyal to me at the moment—never mind that I took over James's class with absolutely no warning. But enough," she said. "The blood of Jules Henri runs in you! You never met him?"
Poincaré laughed. "I'm old, Ms. Chambi. Not that old."
The sudden veneration bordering on awe: it was the same whenever he met a mathematician or physicist. As a young man, Poincaré felt so burdened by the family name that he considered changing it. These days he simply accepted posthumous compliments and moved on. "About all I inherited was a fondness for puzzles," he confessed. "Useful for someone in my trade. But between you and me, I can't tell a derivative from a derriere."
Chambi laughed easily and set her computer bag on a ledge. "I somehow doubt that. Your great-grandfather's talent comes along once in a generation. In fact, he was James's personal hero. He kept quotations of Poincaré's around the office, taped to his computers. I'm serious: these were words to live by for James. Einstein should have referenced Jules Henri, you know. At the very least, your greatgrandfather anticipated the general theory of relativity, if he didn't get there first. Not to mention chaos theory."
Poincaré the younger pointed across a corridor, to a small cafeteria. "I'm here on business, Ms. Chambi. I want to learn more about Dr. Fenster. I'm investigating his death." He handed her a business card.
Chambi studied it. "Interpol?"
"That's right."
"The whole subject upsets me."
"Yes, I know. It upsets me, too. A terrible loss."
"I'm sorry, Inspector. I can't talk about it." She jerked a hand in front of her face to read a wristwatch, then adjusted her scarf. "I forgot. I have to be somewhere."
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