Eclipse Three

A Practical Girl by Ellen Klages

Can I watch Howdy Doody when we get home?" Carolyn Sullivan asked. She pushed the cart down the canned foods aisle of the Shop-Rite while her mother added creamed corn and green beans to the basket.

"May I. And what's the magic word?"

"May I please watch Howdy Doody?"

"All right, if there's time after we make the beds. We have guests coming."

Carolyn sighed. The Institute for Advanced Study was holding a conference over the weekend, and they were expecting a visiting professor to arrive the next day. The house on Mercer Street had been in the family since the end of the Civil War. When Ensign William Sullivan's ship was torpedoed late in 1943, all hands lost, his widow transformed it into a guest house, to support herself and her baby daughter.

Einstein lived a block away.

Mrs. Sullivan wheeled the cart into a check-out line. "Would you like to play the register game?" she asked. "It'll be good practice. School starts next week."

Carolyn nodded. Her mother thought the game was a kind of homework-good for her-but she liked trying to add up all the groceries in her head as fast as the check-out girl could use the keys. She was the best in her class at arithmetic.

She put the cans of corn on the belt and watched as the white tabs jumped up at the back of the machine with a soft ka-ching, like ducks in a shooting gallery. Twelve cents, four times, which was easy. Then the beans. The first one was 13 cents, and she smiled, because there were four of them too, and that was 52 cents, which made the dollar rectangle in her head whole again. 48 + 52 = 100.

It made her happy when the numbers meshed together with nice, even edges.

The girl was fast, and Carolyn lost track, a little, when the roast went through-$2.37-because it was a big number and it ended with a seven. They were the hardest because they almost never made nice shapes. But when the girl hit TOTAL, Carolyn was only 68 cents off.

"Pretty good," her mother said as they loaded the bags into the back of the station wagon. She pulled a Tootsie Pop out of her purse. "I think that deserves a reward."

Carolyn made the candy last, sucking, not biting, and still had a tiny nub left when all the groceries had been put away. But by the time the last pillowcase had been fluffed and placed just-so, it was too late for Howdy Doody, so she went out to the backyard with her book. Newly cut grass clippings clung to her bare legs like jimmies on an ice cream cone, and her hair hung damp on the back of her neck in the August heat, but discomfort was the price of freedom. Next week it was back to plaid uniforms, memorizing and eagle-eyed nuns.

She sat against the stone wall that separated their yard from the woods, grateful for the shade of the elm. Four pages into Johnny Tremain, she heard the solid thwack of a bat hitting a baseball, and a second later a white missile whizzed over her head and landed in the underbrush beyond with a swishing of leaves and a soft thud.

Silence, for a moment, then a babble of boys' voices. She stood up and looked across the manicured lawn of the Taylors ' house next door. On the far side, she saw a trio of crew cut heads above the wooden fence. New kids, moved in last week.

"Do you have our baseball?" one of them yelled.

Carolyn cupped her hands around her mouth and called back. "It's in the woods."

"Okay."

He headed for the chain-link fence at the back of his own yard, and had one sneaker wedged a foot up before she could warn him, "You won't get through from there. Blackberry bushes. Big thorns."

She watched him shrug and leap the fence anyway.

"Ow! Shit!" came through loud and clear a moment later.

The urge to yell, "I told you so," was strong, but she hadn't met that boy yet. He swore, so he might try for payback. She watched him climb back into his yard, rubbing his knee, then made a bold decision.

"I'll get it."

Her mother always warned her about the woods. Besides the blackberries, it would be easy to get lost among the acres of trees. "You're all I have," she'd say. So Carolyn had never explored beyond the wall, mostly because, up until this summer, she hadn't been tall enough to climb over. But she was now.

She looked behind her to see if she was being watched, then scaled it and surveyed the ground on the other side. A soft verge of grass and dandelions grew at the base, and the blackberries seemed to peter out midway behind the Taylors '. She jumped down.

The ball had left a trail through the undergrowth, and she found it soon enough, too pale and too perfectly round to be part of the natural chaos. She recovered it from underneath a clump of damp leaves, disturbing a legion of rolly bugs and one fat salamander.

She'd planned to walk down the verge to the Wallers' house, on the corner, and return the ball from the sidewalk side. Then she saw three flat stones, piled one on the other, the topmost painted with a faded red crosshatch, like a tic-tac-toe game waiting to happen. That wasn't nature, either. She squatted down. The stones marked what looked like a path leading deeper into the trees. It might be nothing, and it might end in more blackberries, but, except for the market, she'd been cooped up inside all day. Chores and more chores. Everything had to be tidied up, "neat as a pin," when guests were coming.

Carolyn scuffed her feet in the leaves as she walked back to the stone wall, leaving her own trail, and threw the baseball as hard as she could across the Taylors ' yard, shouting, "Ball!" It landed next to the birdbath and knocked over a garden gnome. She headed away from the sudden clamor.

No one had used the path in a while. Saplings blocked her way and sprang back, hard, across her arms as she pushed through. Twigs snagged at her ankles, and her white socks were soon covered with a carpet of tiny green burrs that would take forever to pick out. But it was a path, and every hundred yards or so she found another pile of rocks. Some of them had tumbled over, but one stone always had the same mysterious crosshatch.

The woods were cool and shady. Carolyn could smell the earth, almost sweet from decomposing logs, with a bitter undertaste of autumn after autumn of fallen leaves. No breeze, and except for the sound of her feet crunching along, all she heard were birdcalls and the occasional rhythmic knock-knock-knock of an unseen woodpecker.

The path paralleled Stony Brook for a little while, then veered off to the left and ended at an old wooden fence with a narrow stile, its boards warped and moss-covered. Carolyn put one careful foot on the bottom step. It creaked, but held her weight, and she climbed up and sat at the top, looking into the ruins of what had once been a large and elaborate garden, not just a backyard.

Rosebushes taller than her surrounded stone benches and a sundial. The edges of a gravel walkway were blurred with weeds, and wildflowers grew knee-high. A dozen bees droned lazily in midair.

The walkway led to the back of an old barn. A huge maple tree, still thick-leafed with summer, blocked her view of all but one wing of the house-a single story with a bay window below a magnificent stained-glass peacock. She sat on the stile for a few minutes, savoring the discovery of a new place and debating about exploring further.

She had come this far, and didn't want to turn back now, but entering the garden wasn't just being in the woods. It was trespassing. If anyone still lived in the house-which didn't look too likely-she'd get caught. They'd call her mother and then she'd really be in trouble. She'd spend the last week of summer doing laundry and dishes and ironing. Inside.

After several go-rounds with herself, curiosity won and she clambered into the garden. Gravel skittered and the bees flew off to a safer distance, but nothing else happened.

The walkway continued around the barn. She turned the corner and barely stopped an out-loud gasp. The house on the other side of the wide drive was enormous, with gabled windows and a cupola, every inch covered in ornate Victorian gingerbread that needed painting.

She still thought the place was deserted-until she saw the round-fendered Buick, parked with its nose just inside the "barn," which turned out to be a four-car garage. The Buick had a Princeton sticker on its bumper, and New Jersey plates, 1952, just like her mother's car, all legal and up-to-date.

Carolyn stepped into the shadows and scrunched down. She eased around the corner of the house, planting each foot carefully so her Keds were almost silent. The wide porch held a line of peeling Adirondack chairs and wrapped all the way around to the front. That was even grander-stone pillars and more stained glass, green-limned copper letters over the entrance that said THE BRAMBLES.

It was a mansion, the biggest house she'd ever seen outside a magazine. But, except for the Buick, it would be easy to believe no one had been here for years.

"Hullo. Have you ever seen a giant turtle?"

Carolyn gave a little yelp and jumped back, whacking her elbow on a drainpipe. Cradling her arm, she looked around to see who had spoken.

It took her a moment to notice that the massive front door was open, just a crack, a foot in a leather oxford wedged into the gap.

"How giant?" she asked. Her brain was full of other questions, but that was the one that came out of her mouth.

The oxford moved and the door opened to reveal a boy about her age, sitting cross-legged on the floor. He made a circle with his arms, wider than his body. "Like this."

"Wow." Carolyn climbed the steps and stood on the porch.

"He's very old," the boy said. "Grandaddy sent him from China for my daddy's birthday. He's magic."

"Sure he is." Carolyn tried not to laugh, because the boy sounded serious, but she was a practical girl. She didn't believe in magic and fairy tales and all that baloney. Her family? Not so happily ever after.

The boy shook his head. "Not Daddy. Lotion."

"Lotion?" Was that what he'd said?

"My turtle."

"Funny name for a turtle." Even an imaginary one.

"He's Chinese." The boy stood up and pushed the door all the way open. He had short brown hair and was taller than Carolyn, by a couple of inches, but she could tell right away that there was something wrong with him. One side of his head was shaped funny, and his eyes didn't look straight at her, just a little beyond.

Real. Imaginary. Didn't look like it'd make much difference to him.

"Who're you?" he asked.

"I'm Carolyn. I live on Mercer Street, on the other side of the woods," she said, slowly, the way she talked to the little kids she babysat.

"I'm Bibber." He stopped and shook his head again. "No. The man from the bank says I'm too old. Now I have to be Robert." He looked from side to side, as if someone might be hiding on the porch, then whispered, "You can call me Bibber."

"How old are you?"

"Eleven. Last month."

"Oh. Me too. But not until December." She leaned against one of the pillars. "Do you live here?"

Bibber nodded.

"You must have a really big family."

"No. Just Higgins and Cook and Mrs. Addison, the housekeeper. But she's having a Day Off."

"How 'bout your mom and dad?"

"Mommy died having me and Daddy's in the war hospital. He's sleeping and he won't wake up."

"I'm sorry," Carolyn said. She wondered if it was Korea, or the last war.

"I know. That's why the bank man makes the rules for me." Bibber pointed at the doorway. "You wanna come in?"

"I guess so." He didn't look dangerous, and Carolyn felt sorry for him. Not just because he was-slow, but because she knew how it felt to have a war steal your father.

The inside of the house was cool and dark, darker than the woods. Heavy velvet curtains covered the windows, and massive furniture loomed around her. The walls were encrusted with big, gilt-framed paintings of dead birds and fruit.

"I don't play in here," Bibber said. "But Lotion sometimes hides under the sofa."

They walked through three rooms with high ceilings and fireplaces tall enough to stand up in. A long table with twelve chairs around it was bigger than her whole dining room at home; another eight chairs lined the walls. Twenty people could have dinner, she counted without really thinking.

The next room was one she didn't know a name for. Her house had a living room and a dining room, a kitchen and a utility porch, but this room was none of those. It had high-backed leather armchairs and small side tables and cabinets full of foreign-looking objects: curved knives, lacquered boxes, intricately carved figurines. On the walls were animal heads, stuffed and mounted, their glass eyes glinting in the dim light as she walked by.

"What did your grandfather do?" she asked.

"He went far away on boats. He bought things for museums." Bibber pointed to a cabinet. "He kept some of them."

"Yeah. I can see."

"I like this room," Bibber said, opening the double doors.

It was a library, floor-to-ceiling bookcases with rails that held two wooden ladders. At the far end, beneath the stained-glass window she had seen from the stile, was a bay window with a cushioned seat. The curtains were tied back, and in the sunlight, the leather spines of the books-brown, maroon, deep green-felt like an extension of the woods.

A table with two glass-shaded lamps sat in the center of the room, chairs on either side; a thick carpet with ornate dragons and flowers covered most of the parquet floor.

"I do too," Carolyn said. It was exactly the sort of room she had read about and always longed for, a place to sit and read for hours and hours. Cozy and enclosing, a world of its own, the perfect place to get lost in a story. "Have you read all these?" she asked. She looked around, wondering where she'd start, if it was hers.

Bibber didn't answer. He looked down at the carpet, staring at the head of a curled green dragon.

"Bibber?"

"I can't read by myself," he mumbled. "I know all my letters, but-"

"Oh." Carolyn couldn't imagine not being able to read. "Where do you go to school?"

"I don't. Nanny taught me lessons." Bibber sat down and wrapped his arms around his knees. "But she went away."

Carolyn hesitated, then sat down near him. "Well, I bet the bank man will get you another Nanny real soon."

"No." Bibber began to rock back and forth. "The bank man says I am too old. Mr. Winkle has hair now, and I have to go to Vineland."

"He can't send you there!" Carolyn blurted, before she could stop herself. Vineland was the state school for the feeble-minded. Going there was so bad that the nuns used it as their last-resort threat when someone didn't do their homework, or failed a test.

"He says I have to. And I can't take Lotion."

How could they forbid an imaginary animal? Carolyn traced a finger along the plush wool of the dragon's tail. "When do you go?"

"Next week," Bibber said. He wiped his eyes with the edge of his wrist. "I wanna stay here."

"I would too," said Carolyn.

They sat in silence for a few minutes before Bibber stood up. "Wanna see my picture book?"

"I guess."

He went over to a bookshelf, pulled out a pebbled black volume, opened it, shook his head, took out another. "There he is!" he said, suddenly sounding very happy.

Bibber laid the book on the long table and motioned for Carolyn to come see. When she stood up, she saw that it wasn't a real book, but a scrapbook, the pages filled with snapshots and postcards and ticket stubs. Someone had written names and dates and notes under each photo.

"That's my daddy, on his birthday." Bibber pointed to a photo of a boy kneeling with his hand on the edge of what really did look like a large turtle shell. The rest had been cut off by the camera. The caption underneath read: Bobby with a gift from Father, all the way from Nanking China! A card next to it said: A puzzler for you, son. Can you find the secret?

"Wanna see another one?"

"Sure."

Pinching the bottom corner between his fingers, Bibber carefully flipped the page to reveal a single, larger photo. Two boys in knickers sat cross-legged on either side of a huge tortoise, its shell painted with a complicated design, groups of connected dots.

"See. That's him and Lotion."

The caption read: Bobby and friend Bill admire the new addition.

Carolyn gasped, out loud this time.

The turtle was real.

And the other boy was her father.

Bibber wanted her to stay longer, but Carolyn needed to go home. She promised she'd return, then walked back through the woods, her mind racing with questions she doubted Bibber could answer. When she reached the stone wall at the edge of her own backyard, she felt like she'd been far away for a very long time. But next to the Taylors' a group of boys were still playing ball, and when she went in the back door, her burr-covered socks hidden in the pocket of her shorts, her mother had just begun peeling potatoes for supper.

"There you are," her mother said. "Where did you disappear to?"

"I was hot, so I took a walk," Carolyn said, which was true enough. She got a tumbler from the cupboard and drank a glass of water. "I'm going to go upstairs and read for a while, okay?"

"Dinner in an hour," her mother said.

Carolyn went upstairs, but not to her room. She opened the door to the attic-slowly, so it wouldn't squeak-and climbed the stairs in her bare feet. Way back under the eaves was a trunk with bits and pieces of her father's life before the war. She'd found it two summers ago, and had looked through most of the stuff, but she'd never mentioned it. She figured it wasn't against any rules-he was her father-but it made Mom sad to talk about him, so mostly they didn't.

The trunk was wood and brass with a rounded top. Carolyn had to move three cartons of winter clothes and Christmas ornaments before she could slide it out far enough to open the lid.

A flat box held wedding pictures, official papers and Navy medals. She set it aside, along with a Princeton High yearbook and pennant. She thought there was a folder from when he was her age-school essays and a science-fair project-and she was hoping that somewhere in it she'd find the answer to why Bibber had a picture of him. Because anything about her father was important, and Bibber would be lost to Vineland soon.

Carolyn opened a school composition book. Homework, math or science, with doodles and games of tic-tac-toe among the equations, some in pencil, some in blue or black ink. She leafed through a couple of pages and was about to throw it on the "other" pile when one of the doodles caught her eye-a sketch of a pile of rocks with a cross-hatch pattern. Below it, in a kid's handwriting, it said: Secret Passage of the Lo-Shu Club.

Excited, she turned a few more pages, but the attic was too hot to sit still, and sweat had begun to drip between her shoulders. She pulled out the next layer of papers in the trunk; they were crayon drawings-too young-so she carefully replaced everything except the composition book and shut the lid. She hid her find under the mattress in her bedroom and had her hand on the railing when "Honey? Supper," came from downstairs.

"Where did you go on your walk?" Her mother asked after a sip of iced tea. They were eating cold chicken and potato salad at the kitchen table, because there were no guests.

"Just down to the library." That was more or less true.

"Sounds lovely. It was too hot to bake anything, so I made an icebox cake for dinner tomorrow night. But if you want a snack, have an Oreo. The cake's for company. Don't cut into it."

"I won't." Carolyn was used to FHB-family hold back.

After dinner she washed their dishes and put them in the drainer, and only missed a few minutes of Mr. Wizard, her favorite show. When Arthur Godfrey came on, she left her mother knitting a new throw for the easy chair, and stole up to her room to find out more about the Lo-Shu Club.

Page after page of the composition book was covered with what looked like parts of tic-tac-toe games, some with the usual Xs and Os, and some with numbers in the squares instead. She could see that two people had written in it, because the 4s and 8s were different. The diagrams were surrounded by dozens of addition problems, like the drills Sister Li-guori gave for practice, but all really easy-just the counting numbers, in batches of three: 4+9+2, 3+5+7, 8+1+6, 4+5+6…

She liked puzzles and story problems because the answers made sense in real life. If Sister Liguori gave them one about cooking eggs, Carolyn could be sure the answer wasn't going to be a fraction, because who would take a third of an egg to a picnic? It was harder trying to figure out what the story was when all she had was numbers, but these were starting to make interesting patterns in her head. She was at her desk, chewing on the end of a pencil, deep in thought, when her mother called from the hall. "Lights out. Sweet dreams."

Rats. "'Night, Mom," she called back. She turned off her desk lamp, but took her flashlight under the covers and lay on her side. She had to use one hand to hold the light and the other to hold the notebook open flat, so she couldn't write anything down, but she was determined to get all the way to the end.

Half an hour later, her neck had a crick, and she was fighting back yawns. Uncle. She was too tired to think any more. She riffled through the remaining pages, about a dozen, then stopped and sat bolt upright, sheltering the book and the light in her lap.

Inside the back cover of the composition book, in capital letters and bright red ink, it said:

THE OATH OF THE LO-SHU CLUB.

ANY MEMBER IS MY BROTHER, AND I WILL RESCUE HIM

FROM DANGER, NO MATTER WHAT, NO MATTER WHERE.

I HEREBY SWEAR BY THE SIGN OF THE MAGIC TURTLE.

Underneath were two crosshatches and two signatures-William A. Sullivan and Robert M. Wilkins.

Bill and Bobby.

Carolyn woke up with her arms wrapped around the composition book, the flashlight down by her feet. She stashed both under her pillow and went down to breakfast, racing through corn flakes and orange juice so that she could return to her quest. Then her mother got out the vacuum cleaner.

"You can do the downstairs first," she said, as if it were some kind of treat. "I'll tackle the linens. I don't want to be ironing in the heat of the day. Holler when you've finished the living room and I'll carry the Hoover up so you can do the bedrooms-it's still a little heavy for you." She patted Carolyn on the arm.

So it wasn't until after lunch, when her mother went off to the cleaners and the bank and the drugstore, that Carolyn had a chance to get back to the notebook. She sat at the dining room table with a pile of scratch paper, going over her own sums for the third time, checking her work, when the doorbell rang.

The professor was early.

She put down her pencil and went to the screen door. An older lady with blond hair and glasses stood on the front porch in a plain blue dress, a cardigan sweater folded over one arm. Someone from the women's club, raising money for the March of Dimes again?

"Can I help you?" Carolyn asked.

"I'm Dr. Hopper. I believe I'm expected?"

Holy moley. Most of their guests were scientists. Only big brains got invited to the Institute's conferences. But none of them had ever been a lady before.

"Oh. Sure. Please come in," Carolyn said, in her most polite, talking-to-guests voice. "My mother will be home in a few minutes." She held the door open, saw a suitcase, and remembered to ask, "Do you need help with that?" Dr. Hopper was on the skinny side.

"No, thank you. I can manage." She picked up the small Samsonite case and walked into the front hall. "What a lovely home."

"Thanks." Carolyn thought hard. She'd watched her mother check guests in, but had never done it by herself. "Have a seat," she said, gesturing to the dining room table. "Would you like some iced tea?"

"I would. It's rather warm today."

Carolyn went into the kitchen and stood on a chair to get down one of the nice glasses. The lever on the ice-cube tray stuck, and the pieces came out broken, but she didn't think it would matter. She took the sweating glass and a napkin out to the table.

Dr. Hopper had a pencil in her hand, tapping it on the pile of scrap paper. She looked up when Carolyn came in. "I see you're working on the Lo-Shu problem."

Carolyn caught the glass before she dropped it all the way, but it splashed enough to soak the napkin. She set the tea onto the table. "How do you know about that?"

"I'm a mathematician." Dr. Hopper took a sip. "Legend says it was first discovered by a Chinese emperor who noticed the pattern on the shell of a divine turtle, and thought it was an omen."

"A turtle?" Lo-Shu. The light bulb finally went on. Lotion!

"That's the story." She smiled at Carolyn. "Mystical poppycock, of course. But it is the most common variation of an order-three magic square."

"Magic? It isn't math?"

"It's both." She laid the papers flat on the table. "Why don't you sit down, show me what you've found." She was a guest, but she sounded like a teacher.

"It's a square, three across, three up and down, with all the counting numbers, no repeats." Carolyn pointed to one of the diagrams.

4 9 2

3 5 7

8 1 6

"Do you see a pattern in the digits?" Dr. Hopper asked.

"I think so. The top row adds up to 15. So do the others."

"Very good. In this configuration, the sum of every row, column, and diagonal is the same 'magic' number-15."

"What can you do with it?" Sister Liguori was big on using math in real life.

"Not a thing. It has no practical application." Dr. Hopper laughed. "But that's a plus to many of my colleagues. Pure mathematics is about truth, unconnected to everyday life. They create their own perfect worlds, happily-" She turned. "Oh, hello."

"Hello. Welcome." Mrs. Sullivan stepped through the doorway from the kitchen and held out her hand. "I'm Eileen Sullivan. We spoke on the phone." She looked down at the stack of papers. "I see you've met my daughter, Carolyn."

"Oh yes. We've been discussing higher mathematics."

"Really?" Mrs. Sullivan raised an eyebrow. "I hope she hasn't been-"

"Not at all. I'm enjoying myself." Dr. Hopper stood up.

"Well, we try to make our guests feel at home here. Why don't I show you to your room?" Mrs. Sullivan headed toward the stairs. "You're at the back, on the right. A lovely view of the woods this time of year." She looked down at the suitcase. "May I take that for you?"

"No, thank you, I can manage."

Carolyn's mind kept wandering off to a place Sister Liguori had never mentioned-a perfect world where numbers could be magic. But her hands helped make dinner, set the table with the good china, and serve while her mother chatted with Dr. Hopper, who was one of the less boring guests they'd had. She'd been in the Navy during the war, a WAVE, but in a laboratory, not on a boat, working on something called a computer-a machine that could do arithmetic. Now she had a job with an important company, building an even bigger one.

"They're the first machines man has built to serve his brains, not his brawn," she said. "One day children will use something like UNIVAC for their homework, instead of memorizing multiplication tables."

Mrs. Sullivan frowned. "But then they won't learn anything."

"They will. They'll learn how to use numbers, see the patterns and connections. That's what mathematics is all about." She reached into the pocket of her sweater and took out a pack of Luckies. "Do you mind?"

"Not at all. Let me get you an ashtray." She went into the kitchen.

"What's your conference about?" Carolyn asked, leaning forward. She had never told her mother about the numbers making shapes, when they played the cash-register game, because it would sound kind of weird, but she thought Dr. Hopper probably understood.

"Let me see. Tomorrow morning's schedule has papers on combinatorics, twin primes, set theory, and imaginary numbers."

"What, like a make-believe one-fifty blibbity-blips?"

Her mother put the ashtray and a book of matches by Dr. Hopper's plate. "Carolyn! That's no way to-"

Their guest held up her hand. "It's a reasonable conjecture," she said, lighting her cigarette. "But no. Numbers like this." She took a mechanical pencil from the same pocket and drew a figure on the inside cover of the matchbook: √-1. "The square root of negative one."

Mrs. Sullivan stared. "I was an English major, and I only got through algebra, so forgive me, but if you multiply two negatives, isn't the answer always positive?"

"Yes. Every time."

"So the square root of negative one is impossible."

"No, only imaginary." Dr. Hopper smiled. "I know it sounds like mathematical fiction, but it's quite useful in understanding electromagnetics and quantum mechanics."

"I see," Mrs. Sullivan said.

Carolyn could tell that her mother was only being polite, but she wanted to know more about how numbers could be magic and how imaginary things could be useful. Because if the numbers in story problems were about real life, then-

"Is that your topic at the conference?" Mrs. Sullivan asked.

"No, Dr. von Neumann and I are part of a symposium on recent developments in electronic data coding. Among other things, we're going to be discussing one of your favorite games." She turned to Carolyn.

Huh? "Which one?"

"Tic-tac-toe." She tapped her ash into the small glass dish. "A bright young man at Cambridge – England -has programmed a computer called EDSAC to play. The Xs and Os are on a cathode ray display-like the picture tube in your TV."

"It's a pretty easy game," Carolyn said. Why would the brains talk about that?

"Exactly. It's finite, with perfect information."

"What?"

"Sorry. Mathematically, that means there's no luck involved. You can know every possible move, and there are only a limited number."

Carolyn nodded. "Yeah. Nine."

"Not even close. Try 362,880."

"Uh-uh!"

Dr. Hopper smiled again and drew a small tic-tac-toe board on the matchbook. "First move you have nine choices where to put an X, right?"

"Sure. That's what I said."

"Ah, but then the next player has eight choices of where to put an O. Seven choices for the second X, and so on until someone wins. Or ties." She stubbed out her cigarette. "That big number is nine times eight times seven times six-" She waved her hand in the air. "Etcetera, etcetera."

"Why on earth would anyone want to build a machine that plays games?" Mrs. Sullivan asked.

"Programming a computer to make logical decisions is the first step in replicating human intelligence. If all goes well, Tic-tac-toe is going to help create a better future." Dr. Hopper stood up. "May I use your phone? It's a local call. Dr. von Neumann."

Carolyn's mother seemed to be in a bit of a daze. Guests usually talked about the weather, or how the Phillies were doing that season. "Of course," she said after a moment. "On the table, in the hall. I'll get dessert. Coffee?"

"Please. Two sugars. I'll only be a minute." Dr. Hopper put her napkin down beside her plate and left the room. Carolyn heard her dial, then say, "Johnny? It's Grace. Are we still on for breakfast tomorrow?"

All night, Carolyn tossed and turned, thinking about numbers and Tic-tac-toe-and Vineland. Even though she had never met her father, only seen pictures, she felt like she almost knew the boy in the notebook, who had sworn to rescue his best friend if Bobby was ever in danger. Too late for that.

But now she could rescue Bibber.

The next morning, while her mother was getting ready for a Women's Club meeting and Dr. Hopper was waiting for her taxi, she filled the pockets of her shorts with chalk and pencils and a pen. She tucked a dozen sheets of scrap paper into the composition book that held the secrets of the Lo-Shu Club. She was ready.

By 9:30, the house was empty. Carolyn left a note-Gone to the library.-and headed into the woods. When she reached the stile, she slipped over into the garden. She crept along the far edge until she could see in through the library's bay window.

Good. Bibber was there. He lay on his stomach, moving a line of toy soldiers around a fort made of blocks. She duck-walked along the base of the porch to the front door and tiptoed through to the room of cabinets and animal heads, then quietly opened the double doors to the library.

Bibber looked up, and his whole face filled with a smile. Carolyn put her finger to her lips-Shh.

Bibber nodded. "Why are we being very quiet?" he whispered.

"I don't want your housekeeper to hear us."

"Oh. She won't," Bibber said. "Mrs. Addison is in the kitchen with Cook. She leaves me alone until my lunch." He shrugged. "Unless I make a big noise."

"What time do you eat?" Carolyn asked in her normal voice.

"Lunchtime."

That wasn't much help. But Carolyn figured it'd be at least noon, and that gave her plenty of time. "Do you know how to play Tic-tac-toe?" she asked.

"Uh-huh. I'm pretty good."

"Great." She laid the composition book and two pencils on the table. When she drew the grid on a piece of scratch paper she said, under her breath, "By the sign of the magic turtle."

Carolyn knew how to use numbers for a lot of useful things, but she hadn't known they could be magic until she met Dr. Hopper. If she said that was real, Carolyn believed it. She was at the Institute, with Einstein, the smartest man in the world, so she ought to know.

"You go first," she said.

Bibber drew a tiny X in the top right corner, and she followed with an O next to it. She wanted to put her O in the center-it was the best move-but she also wanted Bibber to win the first game. When he drew his third X in a row, he smiled in triumph. "I told you. I am good at this."

"Yep. So you get to draw the next one."

He did, his tongue in the corner of his mouth, concentrating on making the four lines as straight as he could.

There. They had both drawn the sign that made them members of the Lo-Shu Club. "You are my brother," Carolyn whispered. "I will rescue you from danger." She made an O in the center square, but let Bibber win again.

"Where do you keep Lotion?" she asked.

"He crawls all over the house. The downstairs part. Right now he's under the table."

"Here?" Carolyn moved one of the chairs and squatted down. On the carpet was the biggest tortoise she had ever seen-even bigger than the one in the Bronx Zoo. At her movement, he turned his head and looked at her with a yellow, reptilian eye. "How do you get him to come out?" They couldn't lift him, not even the two of them. He was the size of an ottoman.

"I wait until he's hungry," Bibber said. "We could try and feed him now."

"What does he eat?" He looked as prehistoric as a dinosaur, with scaly front feet the size of salad plates. He might eat anything.

"Fruit and stuff. Leftover salad. Watch." Bibber pulled a cluster of blue-black grapes from his pocket and lay them in a pile a foot away from the edge of the table.

In real-life slow motion, the tortoise rose up and lumbered forward, one leg at a time, until he stood over the grapes. He extended his surprisingly long neck, lowered his head, and mashed the grapes into his mouth in three pulpy bites.

"It's bad to feed him on the rug," Bibber said, pointing to a purple stain that was almost invisible against the elaborate floral design. "Mrs. Addison says."

"I can see why." Carolyn stared at Lotion's back. She'd planned to draw the Lo-Shu numbers onto the turtle with chalk, but she didn't need to. The pattern was carved into nine plates on his shell, the center square marked with five dots arranged like the pips on Monopoly dice, faint traces of red paint in the deepest grooves.

Lotion was already magic.

Now for the tricky part. Carolyn circled the room, chalking √-1 on the four walls, the window frame, the doors, and a side or shelf of each bookcase.

"What are you doing?" Bibber asked.

"Making things imaginary." It was pure math, and would be unconnected to the real world, where Vineland waited.

When she had marked all the openings, she made one more circuit, checking her work, then turned to Bibber. "Can you sit on Lotion?" The tortoise had eased back down to the floor, and lay with his eyes shut. He looked sturdy enough.

"Sure. I ride him around, sometimes." Bibber straddled the carved shell and scratched the tortoise on the top of his leathery head. "How long do I hafta sit here?"

"You'll know." Carolyn hoped that was true. She circled the room again, taking a few books from the shelves: Huckleberry Finn, Treasure Island, The Wind in the Willows, Peter Pan, The Jungle Book, The Wizard of Oz. She added a dictionary and the scrapbook with the picture of their fathers to the stack. Then, stepping around Bibber, she arranged the eight books in a square, three on a side, with Lotion at the center to make nine.

"What are those?"

"Books I think you'll like."

"I can't read." Bibber frowned. "I told you."

"You will. Pure math creates its own perfect world." She wrote nine blue numbers in ink on the soft skin on the back of Bibber's neck:

4 9 2

3 5 7

8 1 6

Magic turtle, magic boy.

"That tickles." Bibber laughed.

"Sorry." She patted his hair. "But now you can live happily ever after." She turned toward the door.

Bibber frowned. "Are you leaving?"

"Uh-huh."

"No. I want you to stay." He sounded sad.

Carolyn looked around at the room full of books and light and comfortable chairs, a room she'd always dreamed of. It was so tempting-a lifetime to sit and read, uninterrupted, no chores, no nuns-she bit her lip-no Mom. You're all I have, she heard in her mind, and shook her head. "I can't, Bibber. I have to go home."

"But you'll come visit?"

She opened the double doors. "I'll try." She stepped into the next room and closed them behind her, then marked each one with √-1.

"Keep Bibber away from Vineland," she said aloud, then added, "Please."

There. That was all the magic she knew.

She tiptoed back through the house, holding her hand tight on her pocket so the pen and pencils wouldn't make a noise. She was in the room with the paintings of fruit before she noticed that her other hand was empty. Her father's composition book, with all the notes and secrets of the Lo-Shu Club-she'd left it on the library table.

In a quiet hurry, she went back for it. Through the dining room, into the room she had no name for, to the double doors that-

Carolyn stared.

There were no doors.

Stuffed and mounted animal heads stared out glassily from above the wide rosewood cabinet that now filled the wall. And among them hung the empty shell of an enormous tortoise, its carved and polished surface glinting in the dim light.