The Zanna Function

by Daniel Wheatley

  Zanna’s basement smelled of concrete and cardboard and rust. She sat cross-legged in an old armchair, watching as Owin inspected the I-beam that ran across the ceiling. “Is it okay if I watch?”

  “I don’t mind,” Owin said. He tapped on the beam and thought for a moment before climbing down from his shield, which he had turned into a stepladder. “In fact, let’s do this.”

  The stepladder transformed into a large drafting table. As Zanna leaned forward, theoretical squiggles began to appear beneath Owin’s hands, which he slid across the surface, as if setting a dinner table. Except instead of plates and saucers, he had piles and piles of mathematical functions.

  “That’s your I-beam,” he said when he was done. “That’s every­thing that’s going on with it right now. That’s its existence.”

  Zanna stared at it all. It looked like a mathematical textbook had sneezed all over the place. “Dr. Fitzie said something like this today,” she muttered. “About what the difference is between a real cube and a theoretical one.”

  “Oh, dear,” Owin said, putting his hands down on the table again. “Don’t tell her I told you this, then. She’ll get mad at me for ruining her fun.”

  “It’s so complicated,” Zanna said.

  “Everything’s complicated,” Owin said. “That’s the first thing you’re going to learn at St. Pommeroy’s. It’s just a question about what you can muddle through and what’s not worth figuring out. That’s why I wanted an I-beam. Because when you start looking through all this, it’s actually pretty straightforward.”

  The mess on the table looked about as far from straightforward as Zanna could imagine, but Owin seemed to understand it just fine as he started organizing bits and pieces. “Some of the other Primers swear by using the pipes, but I don’t get it. Then you’ve got pressure and thermodynamics and fluid dynamics and probably a little electromagnetism to deal with, and it’s just a mess. Nope, I-beams are the way to go. Look here.”

  With a sweep of his hand, he moved all the functions to the side except for one group, which he put square in the middle. “These are all the gravitational functions operating on your I-beam. Did you know that there’s no limit to gravitational pull? It’s not just Earth pulling on you but the moon and the sun and every black hole and galaxy in the entire universe.” As he spoke, he began to unpack the group of functions, keeping some in the center and sliding some farther away.

  Zanna began to see things she recognized, such as gravitational functions—the same functions Cedwick had been haranguing her about earlier. Except these weren’t the neat theoretical ones in her textbook. These were out in the wild.

  “But most of these are so faint we can just ignore them,” Owin continued. “Unless you’re a perfectionist, you don’t need to account for the gravitational pull of Alpha Centauri on your I-beam. Or any of the trillion other celestial bodies. You’d never get anything done.” With a whisk of his hand, most of the functions cleared, leaving only a few remaining. “Now Earth’s gravity, that’s pretty important. The moon, you can take or leave.”

  “What would happen if you didn’t account for Earth’s gravity?” Zanna asked.

  “An excellent question!” Owin said. He put his fists together, knuckles touching. “Every time you start tinkering with the universe, there are two forces at work. The first is all the natural functions of the object, which tell it to keep doing what it’s always been doing. The second is you. If you understand enough of the big functions—momentum, gravity, chemical composition, electromagnetism, coordinates, crystallography, thermodynamics, pressure, stress, and so on—and get them on your side, you can ignore the smaller functions. But leave out something like Earth’s gravity and—” He pushed his fists together to demonstrate. “You get nowhere. Or worse.”

  “Worse?”

  “A Splutter,” he said. “Imagine you’re driving a car and decide to make a turn. Except your engine and one of the wheels decide to keep going straight. That’s a Splutter. The natural functions of the object tell it to do one thing, and the functions you’re mucking around with tell it to do a different thing, and you push so hard it tries to split the difference. Nasty stuff.”

  He moved the function of Earth’s gravity to a corner of the table. “So we’ll just put that aside for later. Next up—forces!” Owin set a dense package of functions in the middle with a grin. “These are fun.” He stopped for a moment, caught up in an idea. “Actually, let’s do this. What sort of physical forces do you see working on your I-beam?”

  Zanna had never really thought about it before and scrunched up her face. “Well, there are those joists running across it,” she said, pointing at the planks that made up the first floor of the house. “They’re pushing down with the rest of the house. That gets transferred to the pillars.” Her finger traced the path through the I-beam to one of the two supporting concrete pillars. “And that goes into the Earth.”

  “And that’s it?” Owin had the same look on his face as the one Pops wore when Zanna was overlooking something obvious.

  “No,” she said, scrambling to think of what she had missed. “I bet those pillars aren’t perfectly level. So it’s probably being twisted a little.”

  “But we can ignore that,” Owin said, “because it’s so little.”

  “Well, there’s air pressure—”

  “That’s also small enough that we can ignore it,” Owin said.

  She frowned and let out an angry breath. “Give me a hint.”

  “Think about what you already told me,” Owin said. “If it all was pushing down into the Earth, what do you think would happen? Wouldn’t it move?”

  It clicked. “The Earth is pushing back.”

  “Which goes into the pillars, through the I-beam, and into the joists,” Owin finished. “Good job; you’ve figured out reactionary forces. Old Newton would be proud.”

  He put the forces over with the Earth’s gravity and slid a new conglomeration into view, one that looked completely different from the previous functions. Instead of mathematical numbers and signs, there were chemical notations and a strange mesh of clouds. “So that’s the physics. Well, that’s everything they call physics. When you really look at it, physics and chemistry are just different applications of the same thing. Same with math. It’s all science.” He cleared his throat and lifted the mesh up from the table, turning it into a three-dimensional model. “This is the metallurgical composition. Going by industry standards, your I-beam is a basic carbon steel, which means it’s mostly iron with about 0.26% carbon. That’s this mesh here.” He made it expand so Zanna could see the atoms clearly. “That’s a carbon atom among the iron atoms. Makes the alloy stronger and harder. But it also makes manipulating it more difficult, because you need to hold on to two elements, and you really don’t want to Splutter an alloy. Yanking this apart would be an ugly business.” He winked and dropped the mesh back down on the table. “But don’t worry. It’s not as difficult as it seems. Metal is pretty basic, actually, when it comes to the chemical composition.”

  “What’s the rest of this?” Zanna asked, pointing to the other chemical functions.

  “Rust, stains, corrosion, oil, dust, dirt—who knows whatever else,” Owin said. “Unless you’re dealing with handpicked atoms, there’s always going to be some junk clinging on. If you really wanted to, you could throw in the chemical composition for all of these. But really, it’s okay to just ignore them.” He knocked his fists together again. “As long as you get the big stuff, you should be fine.”

  “So that’s everything you need?” Zanna asked. Now that Owin had talked her through it, the table didn’t seem nearly as messy as before. “Just those functions?”

  “Just those functions for your I-beam,” Owin clarified. “There are far more complex things out there in the universe. One of them’s right in front of me.”

  She looked around the basement before s
he realized what he was referring to. “Me?”

  “Quite.” With a gesture, all the functions of the I-beam disappeared. “Humans are the most complicated things in the universe. Everything else, we’ve at least got a handle on, but humanity? Not a clue.”

  He reached into his pocket and took out something that looked like a handful of loose change. But the coins didn’t have the markings of regular money. There were just lines of text stamped into the metal on one side and a symbol stamped on the other.

  “What are those?”

  “Blanks,” Owin said. “Each of these carries a function drawn up by the Primer mathematicians back at the Society. It’s a lot of work, drawing and testing and defending a decent function that’ll work under all conditions. The really complex ones, they can take a lifetime to get right.” He selected three coins—one brass, one pewter, one gold—and put the rest back in his pocket. “Here we go.”

  He rubbed his thumb over the brass coin, and a function bubbled to the surface. Even before Owin spread it out on the table, Zanna knew this one was different. The functions in her I-beam had been natural and full of messy numbers, like a homework problem she had to show her work for. This function created by the Primers was as clean and ordered as a typewritten page, with more variables and Greek symbols than numbers.

  “Now we’re going to see just how clever you are, Zanna Mayfield. Here’s a puzzle. You want to keep people out of your house, but you and your grandfather need to be able to come and go as you please. And if someone comes over to visit, they should be able to come in, as well—as long as you let them in. How would you do it?”

  Zanna clenched her tongue between her teeth. “Well, you could just put up a whole bunch of cameras. That’s what businesses do.”

  “Businesses!” Owin let out a chuckle. “You’re not a business, you’re a Scientist. You’ve got all the laws of the universe at your disposal. Come on now!”

  Zanna scrunched up her nose. Even if Owin hadn’t meant anything by it, she had never taken well to being teased. “Then I’d put up a giant iron shield around the whole house. And it’d open only for me or my grandfather because we’d have a code.”

  “Better,” Owin said. “But pretty obvious. What would your neighbors say? And what if you forgot the code?”

  He laughed again, but Zanna just crossed her arms. Owin cut his laughter short and cleared his throat, continuing in a gentler tone. “It’s a bit of a trick question. Yes, it is a shield, but instead of iron, it’s air pressure—a thin shell of air pressure covering the entire house. And there is a code to get in. But it’s not anything you or your grandfather will have to remember. It’s already within you. You got registered by the Summation, correct?”

  Zanna lifted her head. The sting of not being able to figure out Owin’s puzzle still burned at her cheeks. “You mean that gold thing Dr. Mumble had?” she asked. “I remember. It stabbed me in the hand.”

  “Yes, it does that,” Owin chuckled. “You see, when you gave the Summation a bit of your blood, you gave it your Self function. All those things that make Zanna Mayfield who she is—your childhood, your hopes and dreams, your regrets, and so on—that’s what we call the Self function. It’s one big, impossible, and wondrous function, and it’s the most complicated thing in the universe. And since only you can be Zanna Mayfield, if we plug that function into the air-pressure shield, it’ll let you pass through without a complaint.”

  He grinned, looking rather satisfied with himself. Zanna just sighed.

  “Does that mean I have to get stabbed again?”

  Owin’s smile faded a little. “I’m afraid so. I can make some nitrous oxide if you like—it’s a pretty basic anesthetic, but it’ll help take the edge off.”

  “No,” she said. “I’ll manage.”

  He nodded and flipped the gold coin at her. “Put your thumb in the middle when you’re ready, say your name, and give it a good squeeze. Have your grandfather do the same. And while you’re up there, see if you can find a good piece of iron for a key. Something you can hold and won’t easily lose.”

  She turned the coin over, amazed by the weight and luster. Holding it made Zanna feel a bit like a pirate, and she immediately pictured herself cackling and biting the coin between her teeth. Then she got serious again and pressed her thumb to the coin. “Zanna Mayfield.”

  Pain shot through her thumb. When she let go, she saw her bloody thumbprint on the face of the coin for a moment, and then it sank into the metal. After a few seconds, the coin was as pristine as before.

  “See?” Owin said. “Not that bad at all.”

  She climbed the basement steps into the kitchen and savored the smell of meatballs and basil and slow-simmered tomato sauce. Pops had cleaned out his cast-iron frying pan and was wiping it with a towel. “Is Owin staying for dinner?” he asked.

  “I don’t know,” Zanna said. She held out the coin. “He says you need to hold this and say your name. It’s so you can get through the protective shell of air pressure he’s putting around the house. It’s going to stab you, though. It needs a drop of blood.”

  Pops set the frying pan on the counter. “Now you’re pulling my leg.”

  “I’m serious!”

  With a chuckle and a pat on her head, Pops picked up the coin. “I know you are. Impossible things, right?”

  “You didn’t even see the school,” Zanna muttered. “I’ll tell you all about it after dinner.”

  “I’m all ears,” Pops said. He put his thumb on the coin. “Marco Gentino Zinola.”

  There was a moment of silence. Pops looked around the kitchen, as if he had expected lightning to jump from the walls. “Is that it?”

  “Are you bleeding?”

  He lifted his thumb. “Yeah, it bit me good.”

  “That’s it, then.” As he handed the coin back, Zanna’s eyes fell on the frying pan he had set on the counter. “Can I borrow this too? Owin says he needs something metal to use for the key.”

  “Nana’s frying pan?” Pops laid a protective hand on it. “This belonged to your great-great-grandmother, you know. When my mother came over—”

  “You’ve told me, Pops,” Zanna said. “He’s not going to take it apart or anything. Promise.”

  With a bit of apprehension, Pops nodded. “Well, I did always mean to pass it on. But I didn’t think it would be so soon.”

  “I’ll give it back,” Zanna said, picking up the heavy pan. “I’m just borrowing it for now.”

  “That’s what they always say,” he said, turning back to the stove where a pot of water was beginning to boil. “Well, hurry up down there, because dinner’s almost ready. And ask that boy if he’s staying.”

  She stomped down the basement steps and tossed the coin to Owin. “Here. And will this do for a key?”

  He glanced at the frying pan. “Cast iron. 3% carbon content. Seasoned in animal fats and oils. Salt.” He paused. “That’s been in your family a long time, hasn’t it?”

  “How’d you know?”

  “Because it’s got a story.” As he talked, a small hatch in the I-beam opened, and Owin slipped the gold coin inside. The metal closed around it, and the coin was completely lost to sight. “Ever had a teddy bear or a doll with a personality of its own? A lucky pair of socks? A piece of jewelry from your grandmother? That personality is a function you gave it. Just like gravity and electromagnetism. It makes that object yours. It’s part of its existence.”

  The pewter coin was the last one left, and he pinched the function out of it, putting it on the table so Zanna could see. Like the other Primer function, it was meticulously organized. “This is the key. It’ll let you unlock the protective barrier. I made it analog so you don’t have to deal with the raw theory, since you’re still just a first year. Just hold out the frying pan and twist it, like you were unlocking a door. But you’re going to have to help me.”
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br />   “Me?” Zanna frowned. “Why can’t you do it?”

  “Because that’s your frying pan,” he said. “Here. Put it on the table.”

  She did, and he began unraveling all the different functions inside of it. Some looked familiar—the gravity, for instance, and the chemical composition, though it had a lot more carbon than the I-beam. The forces were simpler, which made sense, since it wasn’t holding up a house. But then Owin pulled out something enormous that Zanna didn’t recognize, and put it square in the middle of the table.

  Zanna peered into it. At first, it seemed like it was just one massive scribble, like someone had covered an entire page while trying to get a pen to work. But as she kept staring, it began to make sense. How it made sense was a mystery in its own right, but somehow the knot of function began to unravel into a collection of memories and stories.

  “This is the story of your frying pan,” Owin said quietly as Zanna stared, unblinking. “And it makes all the other functions in it look like simple arithmetic. All those years of people using it, carrying it with them, passing it down from one generation to the next—it adds up. And I don’t understand it. But I bet you do.”

  In the frying pan’s function, she saw how every time Pops saw it appear, he knew a delicious hot dinner would soon follow. How the first time his mother let him cook with it, he burned his hand so badly it blistered for a week. How he knew, on the day his mother gave it to him, that she didn’t think she would be around for much longer. The frying pan was dangerous, but always full of love.

  Zanna pulled herself out of it and saw that Owin was grinning. “You get it now,” he said.

  “Yeah,” she muttered. “Why didn’t the I-beam have anything like this?”

  “Because no one’s given it one,” Owin said. “People don’t pass building materials down to the next generation. They don’t give I-beams personalities and backstories. They barely even pay attention to them.”

  “That’s true,” Zanna said. “So that’s why you can’t use my frying pan?”