Chapter Third Semiperfect
Scene Three: Carry, the One
“It’s 2,348, not 2,338,” said a voice.“What?” said Denario. He looked around. For hours, the shopkeeper's back office in Ruin Thal had been empty except for him.
“I don’t know how you made that mistake.” It was a young girl with brown hair. She had crept in and sat down on the inventory bench behind him so quietly that he'd never heard a thing. Her stealth seemed aided by her size, which was tiny. She was so thin and short, Denario had no problem believing that she walked everywhere in silence. “You must have carried wrong.”
He gaped at her for a second or two. Her face was plain but with a nice nose, deep, dark brown eyes and an intense gaze. She wore a white blouse under a blue, sleeveless dress. It looked like the sort of functional arrangement chosen by mothers everywhere. She was as cute a child as there could be, elf-like in her proportions, but his instant impression was one of intelligence. Working under her stare felt like having his thoughts laid open to the point where she could see to the back of his skull.
He hadn't quite listened to her so he hesitated. In his mind's ear, he replayed her words.
“No, I didn’t,” he said automatically as he re-summed the figures in his head. He didn't bother to look at the chalk. There weren't that many rows. A moment later, he added, “Yes, I did. Damn. I put an eleven above the ten's place but I dropped the one.”
“You see?”
“I'm glad that wasn't the ink draft.” He cursed Melcurio. Then he covered his mouth. “My apologies. I meant to say 'thank you.'”
“I hear cursing all the time.”
“From customers?” Hadn't he seen this girl in the front of the shop? Yes, he was sure that he had. This must be the shop owner's daughter. She had been the one handling the money.
“Usually from my da after the customers leave.”
Her father, Udo Vogel, was a distant relative of Mayor Ilse Richter of North Ackerland. As a maiden, Ilse had been a Vogel, too, and had belonged to the Goat Clan. When Ilse had left the clan for marriage, she had deftly kept in touch with everyone, including Udo and his father, Addler.
Addler Vogel was still alive although he'd reached nearly sixty, ancient by almost any standard. He didn't write much and he couldn't travel the way he once had but he still liked getting letters from Ilse. He and his son Udo had been surprised to learn Ilse was now the mayor. Addler had remarked, though, that if any woman could do it, it was her.
This girl’s grandfather, in his youth, had been a mule driver for caravans. He'd been born to modest means, a middle son among many children, but he'd taken an understanding to mules as soon as he met them. By the age of twelve, he saw a way to escape his village. After he got himself hired by a desperate caravan manager, he mastered the previously-unruly animals and moved up the ranks. He saved up goods and money to trade for armor. The armor helped him live through several caravan raids. In a few years, he was a senior driver and the assistant chief of a caravan. Various clans had made him a member. He'd collected more tattoos. He'd traveled beyond the Mundredi lands.
Udo Vogel had hinted that there was more to his father's story than that but the family didn't like to talk about it. Denario knew that Addler's caravan jobs had made him a fortune. After amassing too much wealth to carry on three burros, he'd left his final caravan as he passed Ruin Thal. Here, he'd settled down to provide services the town had never seen before. Addler had a plan for his retirement and he stuck to it. To begin with, he married a woman from a prestigious family. He could afford the bride price. Hence, by luck or by Addler's design, Udo Vogel was second cousin to the mayor of Ruin Thal.
When the mayor, a thin and nervous man, had held a victory party for the arrival of Denario the Dramatic, Accountant of Oggli, Hero of the Mundredi Army, the shop keeper had been invited. He'd sat at the head table with Denario and the town leaders despite the fact that Udo had no official post. He was not a burgher. He simply ran his father's store, the most popular general store in town. Indeed, Udo and his father seemed to have cornered the market on most manufactured household goods in Ruin Thal by way of exclusive contracts with the craftsmen. It was a new idea to the area. Probably no one had understood what old Addler was up to when he built up his business.
The knight, Sir Fettertyr, was not happy with Addler's arrangements. But even Fettertyr didn't seem to know what to make of them because they were sworn to in every church, written, sealed, and testified to by priests and judges. The craftsmen weren't opposed to their contracts, either. Once Addler accepted their merchandise he promised them payment in pigs' ears, dried fish, coins, goats, knots, debtor sticks, or furs regardless of whether or not he could sell what they'd made. No other merchant in the area offered that bargain.
It was Udo to whom Denario had given the silver trinket of a goat entrusted to him by Ilse Richter. To his credit, Udo had known immediately what it meant. When he found out what Denario's profession was, he offered room and board in exchange for a review of his shop's records and inventory.
“Your father is smart to promote the use of money,” the accountant said. He'd tried to like Udo for Ilse Richter's sake but he hadn't been very successful. The man seemed obsessed with wealth. Here he was, promoting the use of coins but Denario couldn't root for him as a person. At least he was bright and energetic. Udo seemed open to new ideas.
His daughter shrugged.
“I like money better than dried fish. Yuck. But coins aren't as practical as furs,” she said. “Furs are easier to carry and you can wear them, too.”
“That's not right. Gold and silver ...” Denario prepared to launch into a speech about how money made everyone more wealthy by increasing the efficiency of trade. Her age made him re-think his strategy. After a moment spent rubbing his chin, he settled for, “You're not wearing furs right now.”
“It's almost summer.”
“Well, in the warm lands around the Complacent Sea, no one uses furs as money. They're not wanted for clothes so much. But coins are still valuable. Coins are good from one end of the old empire to the other.”
“Oh, I see. Metal is always useful, no matter how hot or how cold you are.”
“Yes!” he exclaimed, please that she'd seen the point so quickly.
“That's why we use it as money. But why do we use metals that are hard to find?”
Denario scratched his head. “We're not meant to, really. There's plenty of money that's made of copper, iron, lead, nickel, or tin. But the smithies say that gold is the easiest metal to work with and it doesn't rust. Silver tarnishes black. Copper turns green. Cheap iron and lead rust or break. That's why everyone wants gold. And it's hard to mine, too, so that makes it more prized. I suppose it's the smithies who set the price, more or less.”
“I don't know of any coins made of lead or nickel or tin.”
“Those metals are included in lesser coins. Brassers are a combination of copper, nickel, and tin. Munis are mostly lead.”
“Doesn't that spoil them for their worth as metals? If you mix them all up, you make more work for some smith or an alchemist when he has to melt them down to make something.”
“You're right. I think the idea is to make the coins themselves worth more in trade than they are for melting down.”
“But if they're really worth more, not just getting higher value because our knight says so, that worth needs to come from somewhere. Doesn't it? Does it come from the gods?”
“Um … the extra value of a coin is that you can use it instead of barter. That's about it. But that means more than you'd think. Say, what's your name?” Denario stopped himself from adding, 'little girl.' She was just old enough that it would be annoying. And Denario had heard plenty of 'little boy' comments when he was growing up.
“Carinde. My da calls me 'Cari.' He says it's because he had to carry me so much when I was little. I didn't walk until I was over a year old. One of my legs got broke when I was born.”
“You look fine now.”
“I'm not lame.” She stuck out her chin in a defiant way that reminded him of Valentina Ansel. Then she showed him her left leg and wiggled it. She had some kind of leggings on under her dress so she didn't have to bare her ankle. “But if I was, I wouldn't care. I can do my jobs just fine.”
“I'm sure you can.” He looked her over for signs of weakness. Plenty of peasants were deformed in some way or another. Carinde looked better than most. “It's funny. I think I would have called you Cari, too, because you're good at math.”
She tilted her head at him without a word.
“Cari? As in, 'Carry the one?',” he explained. “I mean, like I should have done just now and you noticed?”
She squealed. “Ha! That's so funny!”
Denario felt like a fraud. He'd never known anyone named Carry or Cari but he realized that Carinde would have heard the joke many times if she'd grown up in the vicinity of Oggli. She simply had gotten no chance at an education here in Ruin Thal. She must have picked up math from her father and grandfather.
“You understand money better than anyone I've met in a while. You know addition, too.” He hazarded a guess. “Do you know subtraction?”
“Of course!” she rolled her eyes. “You can't do business without it.”
“What about multiplication?”
“What's that?”
He spent less than a minute describing it. Carinde nodded at various points and told him what 6 x 6 was before he asked.
“So that's what it's called,” she said. “Multiplication. I thought it was memorizing the tables and I know that up to ten times ten. It makes my grandda laugh when I do it. Sometimes he adds in his head and I do my tables and beat him. It's a race. And then he laughs and laughs.”
“I really ought to talk with Herr Addler,” Denario mumbled. He'd barely spoken to the old fellow, partly because Udo didn't seem to like anyone to talk for long with his father but also because, like many old men, Addler at the first handshake had been full of complaints about his teeth, his back, his feet, his eyes and about everything else, really, including how Denario smelled.
The accountant had taken the hint about his odor and had accepted the offer of a bath, cold with gray, gritty soap. He only wished that he'd known he could talk with Addler about math, economics, travel, and other serious matters. The cloudy-eyed fellow had gone to bed before Denario was done drying himself and that was more than an hour before sunset. If he'd arisen yet this morning, he'd done so after Denario had walked down to the storeroom with Udo.
At least Addler had taught his grand-daughter well. Carinde seemed ready to advance to the next level of mathematics. Maybe she had grown beyond ready, advancing whether anyone intended it or not. She couldn't get enough attention from her parents nowadays with a toddler in the house and another on the way.
According to Udo's tale last night, his first wife, Carinde's mother, had died years ago. Carinde's younger brother had died a bit later, leaving her an only child. Naturally, Udo had taken a new wife and together they'd had another girl. Three years later, that wife was pregnant again. The poor woman cooked for the family, helped run the store, and did her household chores with the toddler by her side. By rights she should have put Carinde to work as her assistant. But that option had been denied to her because Carinde had, between the marriages, become essential to the store. Denario had seen that Cari negotiated and tracked all of the sales and purchases. He knew it had to be her handwriting in the log scrolls, too, because it wasn't her father's unreadable scribble and there weren't other folks who touched the scrolls. Cari's script was curlier than most men preferred. It was also neater than that of some professional scribes.
“Tell me, Cari,” he said, intending to test her, “if you got an order for forty of those place settings you offer to rich customers, the ones with a plate, a bowl, a knife and two spoons each, would you know how to calculate the spoons you need? Assume that you have twenty spoons on hand.”
“Forty is a lot.” She tapped her lips as she considered. “I need eighty of them total. I've got twenty spares in the bin. So I just subtract twenty to get the amount I need to fill the order. That's sixty.”
“Very nice.” She'd solved it easily.
“But I'd order more than that, you know. We always need a few spoons on hand.” She pointed to the front of the store. Then she clasped her hands together and placed them in her lap. At that moment, she looked like a young lady, not merely a girl.
“Naturally. But what about something harder?” He gestured to the corner of the warehouse. “What if a caravan came in and sold you two thousand brassers worth of furs?”
“We don't keep that many brassers around. No one does.”
“Banks do. You wouldn't know about banks, I suppose. Anyway, after you talk with the caravan leader a bit, he agrees to value your knives at twelve brass apiece, your copper bottomed pots at eight brass apiece, your oil lamps at three, and your white linens at a silver dollar per yard. He buys up all the linen, four bolts, and then he asks you to calculate the other amounts so that his account comes out exactly even. Could you do it?”
“That's too hard. I'd need the abacus. He's being too generous about the oil lamps, too, but I wouldn't say anything against it.”
So he'd managed to find a problem she couldn't simply do in her head. He told her to go get her father's abacus from the storefront. Carinde came back with a bare, wooden board with eight slots carved into it. In her other hand, she brought a small fist of white beans. Those were her counters. After they moved four baskets of store inventory, mostly wooden bowls, flax seeds, and scraps of cloth, they re-positioned themselves at a long table. Denario watched her manipulate the beads in various slots as she to tried to arrive at an answer to the problem. There were many possible answers and she was aware of that. Nevertheless, she couldn't couldn't come up with a single one that was right. After a while, she gave him a very suspicious, narrow-eyed look.
“Can you do this?” she asked.
“Let me show you.”
He had been using her father's slate earlier. It was a nice, flat one, bigger in all dimensions than he could afford to lug in his pack. Udo had hidden his chalk except for a nub the size of his pinky nail that Denario felt too proud to use. He drew with his own piece instead.
2000 = (4 bolts)(3 yards/bolt)(35 brassers per silver)(12)(n of knives)(3)(n of lamps)(8)(n of pots)
number of knives = K, number of lamps = L, number of pots = P
2000=(3)(4)(35)(12)(K)(3)(L)(8)(P)
Patiently, he stepped through the multi-variable equation, explaining each step and shortening his notation along the way. Carinde didn't get impatient as he erased and drew and erased and re-drew each simplified equation again. In fact, she seemed fascinated. She'd never encountered the idea of a variable before. She'd been solving single-variable equations for all of her remembered life but she'd never had a name for them.
At one point, she hopped up, ran to the front of the store and ran right back. Denario didn't ask why but he found out the reason when she did it again.
“That's three solutions in about ten minutes,” she announced as she returned. She must have gone to check the store clock, a huge, primitive thing with a wooden windup key they kept behind the front desk. The family wound it every morning and they reset it by the town sundial when the weather was good. “I'll bet you could move faster.”
“Yes, this is just a math lesson. I thought you might enjoy it.”
“It's amazing. Did you think of this all by yourself?” She clapped her hands just below her chin. It made Denario wish he could take credit for inventing algebra. He had to settle for explaining what history of algebra he knew, which wasn't much. It had been invented by foreigners and brought to the city of Muntar at the southern tip of the Complacent Sea many years ago. Master Molto Numat had brought the discovery from Muntar to Oggli along with other forms of advanced math when he revived the practice of accounting.
“What does the first problem you gave me look like in algebra?” she asked.
Denario erased the slate. It was big but only two equations could fit on it at the same time.
Number of spoons needed = (40 place settings)(2 spoons/setting) – 20 spoons on hand
N = (40)(2) - 20
“That's just so easy,” Carinde remarked. “I would solve it for 'n' before I finished writing it.”
“For one variable, yes. But even for one variable, it can help to write the problem out like this. It makes the solution more obvious. Even someone who isn't good at math can see it.”
“This would be perfect for Klara,” Carinde said. Klara was her step-mother. The girl didn't seem to intend any sort of insult to the woman. She got along decently with her step-mother or so it appeared. Nevertheless, Denario understood not to comment.
Carinde took over the slate. She spent half an hour working through permutations of the multi-variable equations with no sign of losing interest. She worked fast. If Denario hadn't already known some of the answers, he would have been hard pressed to keep up. The girl rendered her ninth solution before her father, Udo, barged into the inventory room.
“How's the ...” he began before his mind registered the situation. A moment later, he roared, “What's this?”
Denario was suddenly aware that Carinde was female. These locals had rules about men not being left alone with women. Udo didn't act like a Mundredi in most respects – he hadn't tattooed his wife or daughter with the goat sign, for one thing, and had only three tattoos himself, the minimum – but he sounded upset. The accountant was surprised when the man's next words were, “You're using my chalk?”
“No, father,” Carinde piped up. “These pieces belong to the accountant.”
“It's true.” Denario let out the breath he'd been holding in. “I travel with my own. Compass, rule, ink, paper, ropes, theodolite, pen, chalk … these things and a few others are tools of my trade.”
Udo's blue eyes darted between the accountant and his daughter. Something had been going on and the shopkeeper was coming to the decision that he didn't like it. But he didn't know how to put it into words. His fingers pulled at his blonde curls. Denario had time to think that the shopkeeper must have gotten many of his features from his mother. Except for his nose and perhaps his quick mind, he didn't take after Addler Vogel. He had a quicker mouth than Addler, too, and Denario could practically see rejoinders rise to his lips only to be discarded.
What Udo settled for was, “Well, I'm not paying for that chalk.”
“No need, Udo. I'm giving it.”
“What, giving it to my … I mean, giving it to me?”
“I hadn't thought of it as a present. But you know, your daughter is so good with her math lessons, I think I ought to give her a chalk when we're done.”
“I'm not paying for these lessons, am I?”
“The first one is free,” Denario countered. With that statement, he almost felt he could get a handle on talking with Udo. To the shopkeeper, everything was a negotiation. The accountant understood the type. He'd encountered the need to haggle in many places and Master Winkel had instructed him in how to bicker properly. If you didn't make shopkeepers pay, he'd warned, they thought you weren't worth anything. “You can sit in on the lesson, too, if you like, and then you and I can discuss the price for more.”
Denario's words calmed the man, as he'd been pretty sure they would. Now Udo didn't see Denario as a threat but as another tradesman. Udo knew how to deal with tradesmen. He took a slow, deep breath. He rubbed his blonde beard. His hands dropped to his waist.
“First one free, eh?” He smiled.
“That's right.” Denario tried to match the man's cunning expression. Winkel had told him this was a rule you were to follow when making bargains but Denario had never been good at it. His master had told him that bargaining was his weakest skill. Vir had said something similar to that. Denario didn't feel like he was getting better. “I can show you what I showed your daughter.”
“Not so fast,” countered Udo. “If you're any good as a teacher Cari will have learned something useful already. She's the one who should show me what she's learned. While using your chalk.”
“Cari, how confident to you feel about ....” He turned to find he was talking to a mop of brown hair, the back of the girl's head. She erased the slate with her right hand. The chalk had moved to the fingers on her left. That was an interesting thing he'd noticed about her. She seemed equally comfortable with either hand. She switched between them constantly.
“Okay, da,” she said. She pulled her long, brown hair behind her left ear. “I'm going to write down a problem so easy that you won't see the point. But it's just to get you used to this way of writing. It's called algebra.”
“And then we'll do something harder?”
“Yes, da.”
Carinde wrote the first line so confidently that Denario worried she might overreach herself. She didn't, though. She changed the constants in the equation on a whim. And she picked good constants.
Number of spoons needed = (30 place settings)(2 spoons/setting) – 5 spoons on hand
N = (30)(2) - 5
She paused, switched the chalk to her right hand, and wrote the solution. When her father complained there was no need for algebra, she talked over him and moved, with a snappy, left-fisted erasure, to a multi-variable example. This one proved to be her own concept, perhaps one pulled from her real experiences in running the store. Her father shut his mouth for a few minutes. He rubbed his silk-bearded chin.
It didn't take long for Udo to be convinced. Denario could tell. But the shopkeeper didn't care to say so yet. His bright eyes darted from the slate to his daughter and back. Sometimes he studied Denario when he thought the accountant wasn't looking at him. He kept relatively quiet through Carinde's third iteration of the solutions in which she made a variance in the caravan price for cloth, when her step-mother cried out, “Udo!”
The shopkeeper grunted and rose.
“Udo! Mister Kleincarver is here and says you promised him five pence per bowl on wooden bowls.” Although her voice was distant, it was growing closer.
“Coming,” Udo muttered. Out of the side of his mouth, he said to Denario, “This is an improvement on what we've done before, accountant. I'll discuss a price with you tomorrow morning at breakfast.”
The thin, little girl clapped her hands. She leapt to her father before and squeezed him in a hug before he could pass out through the doorway. He gave her a bewildered and slightly begrudged smile. Then, with another call to his wife, he was gone.
Carinde finished the exercise she'd begun for her father. There was no real reason. She just wanted to keep going and Denario didn't mind. It surprised him, though, when she next asked about geometry. She didn't know to ask for it by name. She had heard the town story about something he'd done the day before and she wanted the details.
“It was a star you made inside a circle?” she asked. “And you used your tools to make it perfect?”
“Something like that, yes. There were other shapes, too. I had to get out my compass and protractor.”
Carinde erased the slate. Denario chuckled and reached into his accounting bag. First, he spent some time showing the girl how to read a protractor. She'd never seen one before and the idea of angles was new to her. She wanted to know why a circle, according to the protractor, had 360 degrees of measurement rather than 10, 100, or 1000. Denario had no definite answer, only his own guesswork.
“Whoever figured out circles first had been accustomed to base twelve mathematics,” he said. She didn't know what that meant so he told her he'd explain in later lessons. “Why they used three hundred sixty instead of twelve or one hundred forty-four degrees, I've no idea.”
“Three hundred sixty divides in a bunch of different ways. Maybe it just turned out to be more practical,” Cari suggested.
“It is practical.” He nodded.
As he drew a simple cross, he let Cari measure the right angles. She chose the radius of the circle, too, and decided to let it go to the edge of the slate. From the center of the cross to the mark of the radius, he drew a circle with his compass. He told her she could trace it later. With his protractor, he pinpointed the 72 degree angle. Where the line of the angle intersected the edge of the circle would be one of the tips on his five-point star. He repeated the procedure several times and measured the distance between the points carefully to make sure the star would be symmetric. It was a tricky procedure but it was worth it because, in the end, Cari was impressed.
“That is enormously clever,” she said.
“It does look nice, doesn't it?” This one had turned out well.
“I've never met a real hero before,” she said. “I thought they were all supposed to be dumb.”
“That's what the guards at the back gate thought, too.” He tried not to roll his eyes at the idea. “Maybe I'm more dramatic than I am heroic.”
“It's modest of you to say that.” She touched a finger to her lips. He brow made a tiny knot of concern. “Is that the right word? Modest?”
“Maybe. What about your grandfather? He was a hero. And he was smart. It's allowed.”
“Grandda? I suppose he was a bit heroic. He says he was anyway. But that was a long time ago. There's no one to gainsay him. You killed those men just yesterday. Or was it the troll who helped you?”
“It was a troll.”
“And the troll didn't eat you? It ate the others?”
“Yes.”
“Why? No one told me why.”
“No one asked me why. Until you, just now. It's simple. I gave the troll some food. It was a lucky guess that trolls eat rocks. And she did. So she decided I was nice.”
“She? I thought all trolls were male. But I guess that doesn't make sense or else how would there be new trolls ...” Carinde trailed off. Denario could have sworn she was blushing. “Anyway, you have a sword.”
“Um, yes.” What did that have to do with anything? Denario scratched his nose.
“That's heroic. And you helped our shaman do his rain dance. We haven't had a good rain in the longest time.”
“Sorry about that.” He stopped scratching and sighed. “I know a lot of geometry. I know how to dance a few Ogglian dances. I thought I could fix his problem.”
“Geometry. That's your funny word for the math you use to make shapes.”
“I was sure the shaman was doing his geometry wrong. I made suggestions. He invited me to dance. We followed my geometry. I didn't know that we would end up with a rain of pickle relish.”
“Don't be sad.” Carinde patted his hand like she was a grandmother and he was a little boy. Then she rubbed her tummy. “I like pickles. And it was sweet relish, too. Yum.”
“Some citizens complained.”
“Poo on them.” She took on the demeanor of a little girl again. “Anyway, it made the highwaymen turn back.”
“So I hear.” When he put down his chalk shard, Carinde picked it back up. She put it into his cloth wrapper for him. To her, it was a precious thing. He definitely wanted to give her all that he could spare when he left. She was a great student. Chalk was cheap in Oggli. “That's strange, isn't it, Cari? The mercenaries marched away. Maybe they were frightened by the magic. Magical storms can be dangerous.”
“So you were a hero again!” She clapped for him in an endearing way.
“If so, the shaman must be one, too.”
“You're being modest. Again.” She gave him a stern look.
“They probably ran out of food.” He nodded to himself. That was the most likely explanation although he hoped his geometry had helped to speed them on their way.
“No, they were scared of you.” Carinde folded her arms. The child seemed sure of herself. Her jaw stuck out in that certain way, very like Ilse Richter and Valentina Ansel. Maybe it was a common gesture among Mundredi women.
“I don't think ...”
“They didn't run out of food. I saw them from the top of the west wall. They were filling their pockets with relish. I mean, they were doing it as they left. One of them had bread because he was making a green sandwich.”
Next: Chapter Eighteen, Scene Four
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