by Various
And then it was a mad rush, because the policeman who wasn’t chafing the detective’s wrists was uncoiling his whip and putting his whistle to his lips. David knocked the man down and stepped on the clay whistle, and we went wild with cheers at the crunch it made beneath his boot. We rushed around the stranger like water around a rock, but then he wasn’t a rock but something lighter, something we could pick up and bear away with us as we boiled through the door and up the stairs and out into the streets, howling and calling and leaping, laughing at our pursuers in the oldest game we knew.
* * *
The policemen had numbers and the use of their call boxes at the major intersections to coordinate their work with one another. We had speed and our knowledge of the back alleys and cut-throughs and even rooftops in our flight to the park. None of us had ever been caught before, so why should it be any different that night?
But it was different. The numbers of the policemen were greater than we’d ever seen, and for the first time they dared the yards and alleys, for the first time they worked their way up the fire escapes to the roofs, spreading out and calling to one another in jargon we couldn’t decode. The last we ever saw of Justin was on the roofs, when he rounded a spinning vent and then screamed, hands to his throat where a whip wrapped around.
We had to keep running.
The stranger kept pace, no matter how fast we went or what twists our route took. He leaped with the strongest of us, ran with the swiftest, sneaked with the quietest. And when we stood looking down at the park, three stories up and a million miles away, he even laughed with us at the number of policemen who surrounded it.
“That’s what I meant by crowds,” he told us. “That’s what I meant by teeming.”
We were hidden from the view of those below, and had shaken off those behind, at least for the time being. The time being past time to separate ourselves from this man, at least to David’s way of thinking.
“That’s the park,” he spat. He’d been closer to Justin than most of us. “That’s where the detective said you came from and where Old Olivia said to take you back. We should never have been mixed up with any of this.”
The stranger nodded gravely. “You’re right. You should all go. But before you do, young lady…” He held out his hand, and Les put the blue and silver box in it.
He lifted the lid and set it aside, took the deck in one hand, and fanned the cards like a magician. It was a standard deck of playing cards, technically illegal but such as could be found in all the bars and most of the households of the Northside. We could see the four suits in the dim light of the gray dawn that was creeping up on us. Hearts and Ships, Clubs and Coins.
He turned his wrist and the faces of the cards were hidden from us. He held up the fanned deck to David. “Choose,” he said, and when David didn’t, the man didn’t argue when Les leaned forward and took a card from the precise middle of the deck.
She turned it over where we could see that it was the one we expected. The Jack of Coins. Our grandparents called that one the Rebel when they played behind drawn curtains.
“I see now,” said the stranger. “I remember why I came. I understand.”
We didn’t yet, and protested.
“It’s not me that’s lost,” he said. “It’s you.” Somehow, him pointing with his chin took in all of us, and all the Northside and its people, and all the other neighborhoods, and even the policemen. “Come on. I’ll show you the way.”
And we all followed him, even David, as he clambered down the fire escape to the street that ran alongside the park. By the time we reached the bottom, the crowd of policemen who waited for us numbered in the dozens.
The stranger paused before he put his foot on the topmost rung of the last ladder down. He took a card from the deck in his hand and his wrist flicked forward. The card sailed down and through the crowd, and stuck edge in to the asphalt like a razor. The policemen took a step back, then another as a second card sailed down. Then a third went, and a fourth, then the whole deck was flying through the air, pushing the policemen back and marking a path in two lines straight across the street to the north entrance of the park.
We trailed him across the way, and hesitated at the entrance. It had been closed all our lives.
“There’s everything to be afraid of,” he said.
All of us but David followed him in.
* * *
In, but not through.
The stranger cast one glance over his shoulder as we skirted a tree line and said, “Now you’re found.” He stepped sideways into the trees and out of this world as far as we could ever tell. Perhaps he will return. Perhaps he’s gone to yours.
We have lived in the park down through all the long years since, sortieing out across the Northside, chasing policemen, and reshaping the way of things. We were seditionists after all.
Not all of us lived from that night to this, but there are more of us now, and our ranks will ever grow, until we are as numberless as worlds.
Copyright (C) 2013 by Christopher Rowe
Art copyright (C) 2013 by Red Nose Studio
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Infinity in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.
—Georg Cantor, “On Various Standpoints Regarding the Actual Infinite,” 1885
Late one winter afternoon, lanky, gray-haired Jack Bohn lay on the living room couch with his legs propped on two stacked sofa cushions, typing into the worn laptop that rested on his thighs. He was a recently retired mathematics professor, trying to write one more big paper, this one relating to his notion that the natural world is filled with infinities of all sizes. The ultimate goal of his investigations was to reach a conclusion about how the different levels of infinity meshed.
“Alef arthritis,” he threw out to his wife Ulla, busy at her easel across the room, painting one of her glorious landscapes. Jack’s back ached all the time, each day more than before. “Alef arthritis is what ails you?” said Ulla, not overly concerned. “I’ve never heard of it.” She was a graceful woman with a warm, cheerful face.
“Well—I just invented the name. I see alef arthritis as being a stiffness that sets in when matter is cut off from infinity. I have alef arthritis in my back because I’ve lost touch with the transfinite. Stressing about the Planck length.”
“You’re fussing about quantum mechanics again?” said Ulla. She was using her palette knife to craft a spectrum of shades between two blues; a splatter of paint dropped to the floor. They’d learned to live with paint stains on the rug.
“My latest idea is that physical matter is transfinitely divisible,” said Jack. “When my head’s in the right place, I can see it and feel it: levels below levels, down past alef-null, alef-one, alef-two, on and on. But prim, stuffy quantum mechanics is getting in my face, saying that I should bail out at the Planck length scale, which is a piddling ten-to-the-minus-thirty-fifth meters. So lame. So puritanical. What they don’t understand is that the Planck length scale isn’t a wall. It’s a frontier. There’s a whole new subdimensional world below. And it’s intimately connected to the transfinite. That’s what my new paper is about. I’m hoping the physics angle can help solve the Generalized Continuum Problem.”
“That old shoe?” said Ulla with an experienced wife’s friendly mockery.
“The Generalized Continuum Problem is important,” said Jack, beginni
ng to frown. “It’s kind of sad that I’ve worked on it my whole life, and you don’t even know what it is.”
“Explain it to me again, Jack,” said Ulla, sweetening her voice. “Just one more time.”
“You always say that, and then you don’t listen.”
“But I know you love talking about it. And I do like the sound of the math words. They’re so exotic.”
“All right then. Here we go. The different levels of infinity are called alefs, and we number them with subscripts. We start the subscripts with zero, but it sounds cooler to call it null. So the sequence goes alef-null, alef-one, alef-two, alef-three, out through all the alef-k.” As he talked, he gestured in the air.
“My little professor,” said Ulla. She well knew how the alef symbols looked, and she liked their runic shapes. When Jack talked about the alefs, she saw the symbols instead of hearing the words. and She also remembered that Jack liked to use his crazy numbers as exponents, like and Whatever that meant.
Just as expected, he continued, “In 1873, Georg Cantor proved that for any k, is larger than So might be or it might be or something even bigger. Cantor’s guess was that the transfinite numbers are well-behaved, and that and that, in general, I myself think Cantor was a shade too cautious. I think and in general,
“And the Generalized Continuum Problem means deciding whose guess is right,” said Ulla, ready to end this discussion.
“Yeah,” said Jack slowly. “Of course both those guesses might be wrong. The general feeling is that the overall pattern ought to be something simple. But proving anything concrete is really hard.”
“I wonder if your back hurts because you won’t stop working on this thing,” said Ulla softly. “You’re retired now, Jack. Why another paper? Look out the window instead. A storm’s coming. Maybe we’ll get some lightning for once. I hope so. I love lightning.”
“I wish I could be more like you, Ulla,” said Jack, setting his laptop on the coffee table and rolling off the couch with an exaggerated grunt of pain. “You’re in touch with the higher infinities without even worrying about proofs. You sculpt smooth shapes from a continuous range of colors. I chop things into symbols and worry about proofs.” He stretched his arms, wincing at the pain in his back. “Dear infinity, please help me.”
The prayer—if prayer it was—echoed in the high-ceilinged room, just now lit by a sudden gleam of sunlight from amid the scudding storm clouds. Jack felt a twitch in his chest. And then he started choking.
He staggered backwards, holding his throat, seeing spots. He bent over and coughed with all his might. Something slid up from his throat. He spit it into his handkerchief. A preternaturally smooth and glassy figure eight. An infinity symbol.
“Are you okay?” asked Ulla, laying a hand on Jack’s shoulder.
“Look,” he whispered, not trusting his voice.
“Ick,” said Ulla, stepping back.
“It’s not gross,” said Jack, gaining confidence. He began polishing the loop with his hankie. “It’s like a crystal or a jewel.”
“You coughed up a tumor? How horrible!”
“Listen to me, Ulla. This is a miracle. I asked infinity for help and infinity came here.” He laid the amulet down on the coffee table; it made a reassuringly crisp click.
Brow furrowed, Ulla leaned closer, studying the crystalline lemniscate, its interior filled with reflections and bright caustic curves.
“I feel dizzy,” she said. “Like I’m leaning off a windy cliff.”
“I think there’s power in this thing,” said Jack.
“What if it’s some kind of bait?” said Ulla. “To draw us into a trap.”
“Wow, it just poked out a little stub,” said Jack obliviously. “A square plug! I bet I can jack it to my computer.”
Ulla wasn’t liking any of this. “Isn’t a computer the opposite of infinity?”
“I’ll let infinity show my computer where it’s at.”
Jack plugged the infinity symbol into his laptop and—the screen went into an endlessly regressing crash sequence of smaller and smaller windows, each one visible for half as long as the one before. Upon completing the series, the system gave a triumphant beep. The screen glowed white and displayed lines of black text.
CPU: Absolutely continuous matter.
Memory: Alef-null bytes activated.
Runspeed: Alef-null cycles per second.
“Score!” exulted Jack. “Can you believe this is happening, Ulla? I’ve thought about this for years. I know just what to do. I’ll—I’ll use my laptop as a Turing Evaluator. That way I can automatically generate my next paper, ‘Physical Applications of Transfinite Set Theory.’ I won’t have to write it at all.”
“And then we can finally take our vacation in the South Pacific,” said Ulla. “We’ll go diving. I’ll make paintings of the corals and the fish.”
“Yeah, baby. And I’ll have fun reading my new results! Here’s the way I’ll do it. I’ve got my other papers in files on my laptop, see. So I can use a simple little program to search through all the possible Turing machine text-generators to find one that generates files identical to my previous twenty-six papers—and then generates a brand-new twenty-seventh paper entitled ‘Physical Applications of Transfinite Set Theory’!”
“You’re doing monkeys on typewriters? That takes forever.”
“Not forever. Less than alef-null steps, if there’s a suitable program to be found.” Jack’s fingers danced across the keyboard. “Like I said, I’ve thought about this before.” As if energized by the presence of the infinity amulet, Jack was working very fast. “All set. Here we go.”
The search was successful. In less than a second, a new file had been saved on Jack’s hard drive. Not bothering to read it yet, Jack sent the paper to his printer in the next room. The machine hummed, pulsing out the pages.
But meanwhile the infinity symbol in the side of the laptop had grown dim. Reflections of the computer plug were filling the crystal’s interior with an ugly grid of orderly reflections.
“The amulet’s not happy,” said Ulla. “Unplug it.”
Jack pulled the crystal from the side of his machine. The shiny loop brightened. Writhing slowly in his hand, the lazy-eight smoothed away its plug, unknotted itself and became a zero.
Floating into the air, the circle grew to the size of a companionway door. And now a pair of figures stepped through, in the midst of a discussion. The heralds from the higher world resembled—
“A pencil stub and a toad?” exclaimed Ulla. “Are we going crazy?”
The pencil stub had white-gloved hands, legs with backwards knees, and eyes like a pair of glasses animated with black dots on white disks. He strutted across the floor, his point alertly aimed at the humans, his pupils tracking their every move.
The toad was taller; he walked on two legs and wore a baggy gray business suit. His bare chest-skin was pearly green with irregular spots of yellow. The slumped lump of his head sported eye bumps and a wide, downturned mouth.
“Hello Jack,” rasped the toad. “We were talking in the Szkocka cafe when we heard your call—and my overexcitable friend here tossed down an infinity-link. He has this crazy idea for getting you two to help with this problem we’ve been debating. The Generalized Continuum Problem.”
“You’re mathematicians?” exclaimed Jack happily. “The Generalized Continuum Problem?”
“Where did they come from?” demanded Ulla, walking around to peer at the back of the hoop.
“Alefville,” said the pencil stub in a clear tenor. “We’re transfinite beings; we call ourselves aktuals. And my full name is—” An intense, skritchy sound filled the room. It was like hearing someone handwrite an endless Library of Babel in a fraction of a second.
Ulla nodded her head appreciatively and fastened on a shard of the sound storm. “You said Stanley?”
“That’ll do,” said the bird-legged pencil stub. “And call my toad friend ‘Anton.’ For antagonistic.”
“S
tanley takes everything so personally,” said the toad, spreading the fingers of his webbed hands. “When I tell him he’s a self-deluding dreamer, he doesn’t appreciate that I’m trying to help. As for his plans for you, I’m not really sure that—”
“Oh shut up,” interrupted Stanley. “I’m offering them a free trip to Alefville.”
“We would grow?” said Ulla uneasily. “I don’t want to burst our house.”
“It’s more that you’ll be changing your focus of attention, ” said Stanley, narrowing the ovals of his cartoony eyes. “Basically, you’re already in Alefville. Infinity is everywhere. This portal is just a visualization tool.” He nudged the glowing ring with the sharpened tip of his nose. The ring rotated to a horizontal position and sank down to shin level, bobbing like a hula hoop.
“We’ll hold hands and hop through all together,” said Anton. “And, Stanley, I’m playing red again. I don’t believe you actually have a winning strategy. You’ve fooled yourself again.”
“I’ll keep on beating you forever,” said the cocky pencil stub. “Thanks to my absolute vision of the true class of all sets.”
“Absolute self-delusion,” croaked Anton, blinking his big golden eyes. “There is no great almighty One. Only the pullulating congeries of axiom models.”
“Wait!” said Ulla, looking suspicious. “You’re not taking us to some giant math seminar are you? My idea of hell, for sure.”
“You won’t be gone long,” said Stanley, not quite answering her question. He turned his pointed nose, gazing out their living room window. “You’ll be home for tea when the rain starts.”
In the next room, the printer had stopped. It gave Jack a good feeling, knowing that his new paper was done. Even if—worst case—he never came back at all, his masterwork was finished. “Let’s go for it,” he urged Ulla. “This might be just as interesting as diving in the tropics.”