Reilly 11 - Case of Lies (10 page)

“Nobody. My pop. He’s a Sanskrit scholar. What’s the square root of minus one?”

“You know what? I bet your father already told you the answer, told you it’s an imaginary number with its own number line.”

“Egg-zackly. So if you can set up a brand-new number line for negative square roots, why can’t you set up a new number line for one divided by zero?”

Mr. Pell looked down at him from the height of a mountain. He bent and picked up the chalk, and said in a low tone, close to Elliott’s ear, “Listen to me, kid. I’m going to tell you a secret. You’ll understand it better when you’re older. Do not tell the rest of the kids about this. You cause enough trouble already. They’ll get confused.”

Elliott raised his eyebrows. He tried to look nonchalant.

“You can divide by zero, if you invent another arithmetic. This arithmetic you’re learning-it’s just the one that works best for things like building houses. There are all kinds of arithmetics and geometries.”

Elliott understood immediately. His head swam. The relief was so overwhelming, he almost fell down. This arithmetic was a game, and
there were other games.

“Got it?” Mr. Pell said. “Satisfied? Now beat it, would you? Please?”

On his tenth birthday, his father gave Elliott an old edition of Euclid ’s
Elements
. Winter had brought its cold wind to sweep down on the island. Elliott stayed up in his room for two weeks. When he came down he said, “I don’t understand this at all.”

“Let’s have a look.” They opened the book to Euclid ’s assumptions, the logical statements that are self-evident and are the basis of plane geometry.

“Two points make a line,” the book said.

“Why?” Elliott said. “The line could stop halfway to the second point. Or the two points could be on top of each other, so it looks like one point. Or the line could be wavy.”

“Oh, I quite agree. But you have to think like Euclid,” his father said. He smoked Marlboros. The smell of math to Elliott forever more would be connected to the smell of burning tobacco. They were in Pop’s warm den, piles of papers and books everywhere, the TV on a football game as usual. Elliott’s mother was sitting on the chair under the window, reading a book, her brown hair lit by the lamp.

“ Euclid developed a system that hangs together, that’s the main thing. Let’s try to make his sentence about points more accurate. He’s saying that if you take any two points in the universe, the simplest relations between them is generally a directional arrow that we call a line.”

“Okay. That makes sense. But why triangles? Angles and sides and all that. Why is a right triangle so important?”

Pop stubbed out one cigarette and fired up another one. “Because the Greeks discovered that they could say beautiful, simple, elegant things about right triangles. And because they could build houses using right triangles.”

“Houses again! How come it’s always about houses? Why not start with a-a cloud? Why not invent a formula for finding the volume of a cloud?”

“Too messy,” his father said. “ Euclid started with something easy and useful. In all fairness, he was fond of squares and circles too.”

“Why did he get to make up his own rules? They’re wrong!”

“The one about parallel lines may not always work. The others have stood up pretty well,” Pop said mildly.

“But what about two points making a line? I could make a system where they don’t, couldn’t I?”

“Attack the system at your own risk. I’m going to tell you a story.” Commercials had taken the place of football on the TV in the wall unit across from his father’s desk. He muted the sound and said, “A long time ago there was a genius named Pythagoras. He was a genius because he made some discoveries about the integers that no one had ever made before. These discoveries were so elegant, so incredible, that numbers became a religion. The Pythagoreans believed, for instance, that the cosmos formed from a one. It split into the integers, which formed themselves into geometrical shapes, and finally became air, earth, fire, and water. All Nature, all Reality, grew from Number.”

“Is it true?”

“I’m a linguist,” Pop said, “so I wouldn’t turn to Number. I suppose I could found a religion that said that in the beginning was the Word. Wait a minute, I’m already Episcopalian.” Elliott’s mother laughed.

“So the Pythagoreans were an important cult. The most important belief they held was that all Nature came from whole numbers, by which I mean integers and ratios of integers, what we call fractions today.

“Then one day something terrible happened. One of the Pythagoreans, maybe the Master himself, made a new discovery.” The football game came back on, but Pop was rolling now and his eyes went to the screen but his voice stayed with the story.

“They had just discovered the formula for finding the hypotenuse of a right-angle triangle,” he said. “A squared plus B squared equals C squared. Can you imagine how they must have felt, sitting in the shade on a summer’s day, looking at each other when they found this wonderful formula?” Elliott thought of the bearded men in white robes, sitting on steps by white columns, clapping each other on the back. It must have felt like winning the Super Bowl.

“Then somebody said, ‘Let’s try that triangle out with a side that measures a single unit, a one,’ ” Pop said. “They tried it out. And a devil sprang out! Because one squared plus one squared equals two. Therefore the hypotenuse was the square root of two.” He leaned toward Elliott and said in a chilling theatrical whisper, “And that number couldn’t exist.”

“Wow!” Elliott said.

“That thing, that square root of two, couldn’t be described as an integer or as a ratio. It completely contradicted the beautiful universe the Pythagoreans had constructed. Now they had a choice-to accept this ugly thing into their system and work with it, or to try to suppress the fact that it existed. To lie about it, because the Pythagorean religion could not encompass something as ill-formed, as unlocatable as this.”

“So what did they do?” Elliott’s mother said.

“They swore the whole brotherhood to strict secrecy. This secret made a mockery of their beliefs. Now their religion was based on a lie.”

“What happened?” Elliott asked. He lay on the rug, his head propped in his hands, near the fireplace, the book forgotten. It was almost nine, but he wasn’t feeling sleepy, he was all fired up.

“A young man named Hippasus leaked the secret,” Pop said. “And you know what happened then?”

“What?”

“They killed him. Set fire to a ship he was on near Calabria. Sunk it.”

“The Pythagoreans did that?” Elliott gasped.

“Never underestimate the passion of a mathematician,” Pop said. “Of course, the secret was already out. Nowadays we call those ugly numbers the irrational numbers.”

“We let those numbers in?”

“And even uglier things. The imaginary numbers. The transcendents. The transfinites.”

“Poor Hippasus,” his mother said. She dog-eared her page and went into the kitchen.

“Those numbers aren’t real,” Elliott said. “Not like One and Two.”

“Prove they don’t exist and I’ll give you a canoe,” his father said.

In this way Elliott learned that what his intuition told him was only acceptable to other people if he could show them a proof. Elliott became obsessed with mathematical proofs. He had found his own language, a language his father couldn’t learn any more than Elliott could remember the conjugation of a Sanskrit verb.

The proofs of the main theorems of mathematics contained absolute certainty, a certainty that existed nowhere else in his universe of home and school.

A fever overtook him. The proofs burned into his eyes late at night.

Proofs were the rewards of playing this particular game of arithmetic, but he never forgot that other, more difficult games waited in the murk of the future for him to discover.

“El,” Pop called. Elliott put his memories aside, set his bowl into the stainless-steel sink, and went into the living room. Pop never went upstairs anymore; the muscles in his legs had become too weak. Pop was barefoot. His back had hunched in some indefinable way. How strange. He was growing old as well as sick.

As he looked at his father carefully taking out the ad supplements, then putting the newspaper back in order so he could read it in sequence, he felt again the burning pressure to work, to find, as quickly as possible. Pop was only fifty-five, but he had been ill for five years now and his sharp mind had changed in some way hard to describe. It was as though only small things mattered to him anymore, the Zeros, the Ones.

His mother’s clock ticked on the mantel, next to a picture of his father shaking hands with Noam Chomsky at a podium somewhere.

“I don’t know why, but I feel so cold,” Pop said.

“How about a bath?”

“I need a little push.” Elliott pushed his chair into the adjoining bedroom, pulled down the curtains, and got the water running in the tub. Pop had a special tub where you opened the waterproof door and stepped in and sat down on the bench. So far, he could manage.

“Think I’ll go upstairs and do some work,” Elliott said.

“You look tired. You haven’t told me about the conference at Lake Tahoe.”

“Well, lots of presentations that didn’t interest me much. Nothing new, really,” Elliott lied.

“Did you see any old friends?”

“I did see a couple of guys from MIT, but I didn’t know them well.”

“What are they doing these days?”

“One works at Lawrence Livermore Lab in California. The other one went to Los Alamos.” He was used to lying about his activities, so the words came out very naturally.

“Oh. Physicists. That’s nice.”

“By the way, I got paid on the consulting work I did last spring. It’ll keep us going until Christmas.”

His father said, “You have found such an interesting career, all this flitting about, doing your consulting. It’s wonderful that you can spend so much time with me.”

“It’s my home. I doubt I could work anywhere else. I wouldn’t want to leave you, Pop. We get along.”

“My good fortune, that you love it here so much.”

“I do have to go to town for a couple of hours in the morning. Gloria will be here, though. Do you want anything special at the store if I leave before you’re up?”

“How about some of those Paul Newman chocolate wafers. Those are so good.”

“Cookies it is,” Elliott said. He locked up, then went upstairs, to the scratched oak desk he had spread his papers over all his life, to the single bed with its heavy plaid comforter. The closet door was open; he pulled it shut, locked the bedroom door, and leaned out the window toward the gleam of Seattle across the sound. Cool air flowed in, and he breathed in deeply.

His thoughts went back to the man in the ski mask at Tahoe, doing something to his car. He couldn’t avoid thinking about it anymore. He went over the events of the night before again and tried to analyze them.

Two possibilities presented themselves: Either he was heading toward another psychotic break, or the Tahoe shooter had found him and still wanted something from him.

Both alternatives frightened him. It felt like his heart had turned to a sack of crushed ice. He slammed the window shut and checked the lock again, pulled the blinds.

Then peered through them one last time, but all he saw was darkness.

7

PLACERVILLE USED TO BE A GOLD town back in the mid-eighteen hundreds. Today, gold still can be gathered, especially in the summer, from tourists on their way up Highway 50 from the San Francisco Bay Area toward Tahoe, 250 miles of not much happening until the steep peaks of the Sierra take over. First there is the Bay Bridge to get across, then the long traffic jam of the East Bay, then the new Carquinez Bridge where the Delta country begins.

Then there is nothing much-fields, heat, truck stops, military bases, Sacramento, factory outlets-for a couple of hundred miles. Then the uplift of the Sierra succeeds the hot valley behind as the SUVs and sedans labor up seven thousand feet of altitude to Echo Summit and Lake Tahoe just beyond.

But first, where the foothills begin, still seventy miles from Tahoe, the highway goes through Placerville, with its historic courthouse, quaint streets full of shops, and endless forest all around, and the culture begins to change with the climate. The idea of working ten hours a day in a Silicon Valley cubicle begins to seem suspect. The men want to stop for a beer, DUI laws be damned. The women want to wander down the street looking for a tiny piece of history to take home with them. It is freedom they are looking for, as if the flatlands have imprisoned them, and Placerville is the first town on the road where they can let loose.

Nina turned left and went up a short hill. Most of the homes were small and old, well-settled in their arbors of firs.

She drove until she saw a metal mailbox reading “Hanna.” Cracked asphalt led to a red Ford 150 pickup, which took up a lot of the driveway, and another filthy old truck huddled in the carport. Nina parked behind the pickup and climbed out. The sun shone down; it was so quiet here she could hear the creak of the trees catching breezes high above.

Chelsi, in shorts and a shirt that showed her brown stomach, opened the screen door on the shady porch and came out to greet her. Behind her shambled a man who must have been her father, tall and athletic like her, big-handed and big-footed.

“Dad, this is Nina.”

“Roger Freeman.” He squeezed her hand and put his other hand lightly over the squeeze as if to apologize for the strength of the handshake. “Sarah’s brother. Come on in, Dave’s inside.” He shot a quick glance at Chelsi. “He’s not at his best this morning.”

Dave Hanna sat in a La-Z-Boy in front of a recorded ball game on TV, the sound turned off, his eyes glued to the screen. He didn’t get up and barely acknowledged Nina’s greeting.

The small living room still held traces of Sarah Hanna-a white-framed wedding picture on the mantel of a smiling young couple, she seated quietly, big blue eyes hopeful, flowers held in her lap, he with his hand on her shoulder, making it clear how the marital dynamics would work even then. Sarah’s auburn hair touched the shoulder of her ivory gown. Dave looked a lot younger in the picture. Nina knew from her notes they had been married for ten years before Sarah died. Dave had been thirty-two, Sarah twenty-eight when they married.