Reilly 11 - Case of Lies (31 page)

“What’s a number?” she answered. “It’s that thing you count with.”

“One sheep, two sheep. What’s a one?”

Nina held up a finger.

“No,” Elliott said. “That’s a finger. ‘One’ is an abstract piece of information. ‘One’ doesn’t pick your nose. True?”

“True.”

“What’s a hydrogen atom?”

Nina said, “Let me guess. Another abstract piece of information?”

“Correct. It’s the energy state of the atom, in terms of the forces that bind its electron to its nucleus, as described in Schrödinger’s equation. That and other mathematical descriptions constitute an atom. The information about its behavior is all there is. There is no other ‘there’ there.”

“You mean the hydrogen atom isn’t a thing?”

“All we can know about it is the math, which completely describes it. There’s nothing else to be said about it. It’s real in the way you and I are real. We’re made of atoms.”

“Okay. But what has the hydrogen atom got to do with locating and factoring prime numbers?”

“Prime numbers are raw information. They have the same properties as fermions-the elementary particles that make up things like hydrogen atoms.”

Nina said, “Are you telling me that you think numbers are real, like particles?”

“What does ‘real’ mean? I’m telling you they’re the same thing. They have identical properties, so they’re identical. The basic problem with both of them is the same: location, the exact location of each quantum and the exact location of each prime. The Riemann real part one-half corresponds precisely with the fermion spin of one-half. The symmetry of the Riemann zeros corresponds to fermion symmetry. And of course fermions contain odd numbers of subparticles, just as primes are odd-numbered, except for the number two, which is too close to the beginning of the number line to worry about. And the fermions behave randomly within a specific set of limits, just like the primes. The identities go on and on.”

“Very interesting.”

“And on and on,” Elliott said very definitely. He had sat up straight and was now for some reason holding his glass so that he could see it in the mirror above Kurt’s fireplace.

“I think I’ll have a shot of that whiskey,” Nina said. She poured herself a shot of Jim Beam. Maybe it would help her understand.

“I went back to the basics. To the li line. Let me think how to say this. The prime number line drags along forever below the li line, unless you believe Littlewood, which I don’t. It’s not really a line. It’s a zigzag sequence. But”-he pointed his finger at her before continuing-“each prime point wants so much, so very much, to be in a close relationship with the li line.”

“What do you mean, wants?” Nina said.

“Can you imagine what it would feel like to be able to see where you belong, but not be able to move toward it? She-she-it’s too late. It is so sad. So-damn-sad.”

“You should have a glass of water.”

“I can have a glass of water when I’m dead.” But he accepted the glass Nina brought him. “I really ought to be dead, too, after today. I wonder what it feels like to be dead. No, I don’t wonder. It’s too awful. I don’t want to wonder. I don’t want to think about Silke right now. Let’s talk about math some more.”

“Okay. I’ll tell you how I see the li line. The li line is like law,” Nina said. “Primes are like individuals in a society, unruly and unpredictable on their own, but society as a whole does follow the law. QED.” She tipped her shot glass back.

“No.”

“No?”

“Well, sort of.” He waved his hand and went on. “I found a damping coefficient-that’s from quantum mechanics-that describes the amount of friction each prime has been subjected to. It’s like a relative error term. My damping coefficient is built into a function based around the natural logarithm, which explains a lot of patterns in nature. As soon as I had that, I could factor really large non-prime numbers, too, as a simple corollary. Are you understanding any of this?”

“I’m not sure. But you sound authoritative. That’s half the battle.”

“Maybe for lawyers. You only have to be convincing. Not in math. In math you have to be right.”

“So you know where the prime ought to be at any point on the li line and you know how far it has been pushed from the li line. It becomes simple to find where the prime actually is.”

Elliott blinked. “Egg-zackly,” he said. “The whole secret is that the continuum breaks into quanta as it passes through the quantum veil. It’s an artifact of the definition of primes, insisting that they have to be integers. Integers! There’s no such thing as integers! It’s time for math to blast out of that particular childish fantasy! Like I said before, what is not random looks random after it passes through. Get it?”

“I’m trying.”

“It’s One getting broken into little twigs. All of math is really found between Zero and One. Real part one-half is in there. But Riemann-”

Nina smiled. “Okay. I give up.”

Elliott said, “Oh, well.” He sighed heavily.

“How long ago did you come up with this function?”

“Mostly after my breakdown. Junior year. Three years ago.”

“Tell me the function,” Nina said coaxingly. “Put it in words for me. I won’t understand it or remember it. I’d just like to hear it.”

“Why?”

“Because the way you love numbers, I love words.”

“I’ll tell you what I start with. The difference between pi of
x
and li of
x
is Big Oh of the square root of
x
over log
x
.”

It sounded like a guy dancing in a pentagram naked and trying to invoke a spirit, magical and improbable.

“I like that. Big Oh,” Nina said. She was sitting in a firelit cave with the shaggy Shaman of the Primes, hearing his incantations. She wished she could follow Elliott into his theories, appreciate the connections as he did.

“Oh, it is gorgeous,” Elliott said. “That’s the part everybody knows. Then-my function.”

“Tell me the function. Just say it out loud, once. I bet you never have put it into words.”

“Why do you really want to hear this? Are you taping this or something?”

This moment of paranoia on his part snapped Nina back to reality. A lawyer again, she said, “It’s four o’clock in the morning, Elliott. The robbery might be based on your damping coefficient. People may have died because of it, I don’t know. I guess I just want to hear the information that might be the cause of all this.”

“Read it in the
Journal of Mathematics
in about a year.” His voice had taken on a ragged edge. He obviously wasn’t about to tell her his damping coefficient, not that she would have had a clue what it meant anyway. “So you think Silke and Raj died because of my discovery?”

Nina didn’t answer.

“Fuck,” Elliott said. “Maybe they did. You know the old Greek? Pythagoras?”

“The philosopher?”

“Yeah. The Pythagoreans worshiped integers. They killed Hippasus when he let out the secret of the irrationals, like the square root of two, that can’t be described using ratios of integers. I think they’re going to kill me, too.”

“Who?”

Elliott answered, “The Pythagoreans of Silicon Valley.” He laughed into his glass.

“And are these people who want to kill you real, or just abstract bits of information?” Nina asked.

“That’s a really stupid question.” He seemed affronted. Nina didn’t think it was so stupid, considering what he had been talking about.

“Okay, tell me about the Pythagoreans.”

“Now you’re just humoring me. But I’ll tell you anyway. These Palo Alto Pythagoreans take meetings. They have a lot of money and power. They can pick their noses. I’d say they’re real. The name of the company is XYC.” He then launched into a story about a meeting in Seattle in which Professor Braun had tried to buy Elliott so that the function would be suppressed.

He was talking faster and faster, like a sparkler that flares up one last time before it goes out. It sounded like raving, but Nina wasn’t going to challenge him on anything right now.

“But why try to rob you two years ago, and only a week ago try to buy you?” was all she said. “It’s backwards.”

“They offered me a lot of money. I bet I could have got them up to ten million,” Elliott told her.

Nina took this in, her mouth open. “Your notebook is worth that much?”

“Guess so. It would be a lot cheaper just to steal it. I don’t dare keep a copy, and I could never redo the work I have done on the proof.”

“But you’d still know your function, wouldn’t you?”

Elliott sloshed whiskey out of his glass as he sat up. “Now I get it! Now I get it! That’s right!”

“What’s right?”

“He was going to grab the notebook and then shoot me. I was supposed to die.”

“Where is it now? The notebook?”

“Right here with me.”

“Could I see it?”

Elliott said, “I don’t show it to anyone. I’m neurotic about that.”

“Is it real, Elliott?”

“Of course it’s real. What do you mean, is it real?”

“Then let me see it.”

“No.” He made a protective motion with his hand. He apparently was carrying the damn thing inside Kurt’s robe pocket.

“Put it into a safe-deposit box.”

“I’m still working on it. I thought about doing that, but I worry about it when it’s not on me.”

“Publish your results. That might make you safe.”

“Not until the proof is finished.” He drank the last of the whiskey and gathered the bedding around him. “It’s your fault. If you hadn’t talked Silke into doing this deposition here, they would have let her go. Oh, I shouldn’t say that, I know. Sorry.”

“Maybe you’re right,” Nina said. “Maybe I took it too far. But after my friend was killed, I was going to pursue it to the ends of the earth. Maybe I should have thought more about the human consequences.”

“Well,” Elliott said with a shrug, “you’re a lawyer. Maybe I should have thought more about human consequences too.”

“Well, you’re a mathematician.”

“Yeah. I’m going to sleep now. Here I go.” He laid his brain-heavy head onto Kurt’s couch pillow. And that was that.

24

A SOFT KNOCK AT THE BEDROOM DOOR. Kitchen smells.

“Happy Thanksgiving, Mom,” Bob’s voice said. “Dad’s cooking a turkey, and the police are here.”

“Guten Tag.”
Two uniformed police officers, both men, sat with Elliott around the coffee table, papers spread in front of them. Elliott, wrapped in his comforter, nursed a mug of coffee.

“Excuse me.” Nina went into the kitchen.

Bob chopped onions on a board on the counter. Kurt stood at the stove, stirring something, a white dishcloth tied around his waist over his jeans. The kitchen air was hot and moist, with an old-fashioned dishwasher sitting in the corner, all its hoses exposed. The stove had legs, as she had noticed while cooking the eggs. But the smells were familiar.

“Happy Thanksgiving. Sleep all right?” Kurt said.

“How long have they been questioning Elliott?”

“Just a few minutes. You haven’t missed anything. They had some more details to go over. Here. Have some coffee.”

“It is Thanksgiving, isn’t it? I’d forgotten.”

“And I had quite a time finding a big turkey. Had to get a friend to buy it for me at the Hainerberg PX. It’s already in the oven. Turkey, chestnut stuffing, pumpkin pie. Home food. Nice job there, bud.”

“How you doing, Mom?”

“Okay.”

“The kitchen’s taken care of.”

“I see that.” She made her coffee, letting her hair fall forward so they couldn’t see how emotional she felt this morning.

“It’s no big thing,” Kurt said. “I always celebrate Thanksgiving. My sister came over last year.”

“How did the police get your address?”

“They called,” Kurt said. “I already had your plane tickets out tonight. I thought it would be okay. Is it okay? I don’t think they’ll be staying long.”

“Sure.” Nina went back into the living room and Elliott made room for her on the couch. The detective was taking him through the same story as yesterday, and Elliott seemed quite coherent for a guy who in the middle of the night had just about convinced her that nothing was real. The detective spoke very passable English. Nina sipped her coffee and listened.

When they finished with Elliott, he went in for a shower and they started on her. She had to repeat everything she could remember about the shooting. They looked disappointed when she had nothing new to add. At length the lead detective, a pale man with a shock of blond hair, gathered up his papers and said, “I knew Silke and her family.”

“I’m sorry.”

“An old family in Heddesheim. Her father was killed in a car accident when she was a baby. Her mother is a baker. Silke’s brilliance was noticed from an early age. She will be greatly missed. She was the first person in her family to go to university, and such a university! You know how it is in a little town-we had a parade for her. A send-off, I think you say.”

“It’s so unfair,” Nina said. “Such a waste.” The full weight of Silke’s death had finally fallen on her shoulders.

“Is there anything you can add to your description of this man with a gun who is wanted in the U.S.? He limped, he spoke American English, he moves around freely, he shoots well, medium height, medium weight-anything?”

“No.”

“Do you have any questions for us?”

“Where did he shoot from?”

“Across the street. The upper floor of a furniture store, empty at the time.”

“What did you find up there?” Nina was just doing her job, asking. She didn’t expect an answer of any substance. The police are adept at not giving out information.

“A fresh fingerprint,” the detective said. “At the window.”

It struck like a brick in the face. Nina put down her mug. “You have a print?” She was covering her mouth, willing it not to cry out and willing her eyes not to water. Evidence! A print.

“We’re running it through Interpol and your IAFIS right now.”

“He’s been so careful. It’s hard to believe.”

“A full impression. A thumbprint.”

“A print.” She blinked and lowered her head.

“Here.” He handed her a handkerchief.