Chapter Pi Times Seven Approximate
“Are dwarfs invited to the Festival of the Children? Or did you invite yourselves? You haven't got any tattoos. I'll bet hardly anyone has noticed.”
“Probably not,” the fellow grumped. “Until you. You have no tattoos either, I see.”
“My name is Denario.” He stuck out his hand. The dwarfs eyed it suspiciously. “I'm pleased to meet you because I would like to talk with someone, anyone, about math. Or if not math itself, then geometry, maps, and surveying.”
“Surveying? That's a bit unusual for a riverman. Are you trying to chart the No Map Creek? I'm told it can't be done.”
“True, maybe. And yet ... I've got a few ideas about that. I'm running an experiment.”
“I don't think mapping lends itself to experiments, lad. Either the measurements are right or they're not.”
“You will, maybe. If you live.” The dwarf finished the first peach. He pocketed the second and hiked up his trousers. “Hmph. Is that some kind of human survey instrument I see on your deck?”
“The theodolite? Yes.”
“We'd never use anything like that in a mine. Too inaccurate.”
“Lines of sight wouldn't be very useful, I suppose. You'd use geometry, probably the stake and chain method. Did dwarfs invent that? I always wondered.”
“We claim that we did. It’s so long ago, though, it's stuff of legend.”
“This is how humans do it.” Denario used the wood in his hand to pantomine the action. His audience relaxed and gave advice. The dwarf started rubbing his beard, though, during the accountant's monologue on the perfection of triangles.
“We've learned something about triangles, living underground.” He waited patiently for Denario to pause rather than interrupt. “The way you humans use them is too straight. That's not good enough for the deep, deep dwarfs, the really low down ones. They've discovered that large triangles, especially when you think of joining a lot of triangles together, have curves in them. The whole world curves, they say.”
“You must mean that the triangles are curved in three dimensions, then.”
“You've lost me there, lad. What's a dimension? Something from a human religion? Dwarfs wouldn't know about those.”
That was a brilliant excuse to stay out of religious arguments, Denario realized. He'd claimed something like it himself, from time to time, but it had proved generally better to point out his devotion to Melcurio. He was human. His ignorance wasn't considered an excusable condition by the priests and priestesses who tried to convert him at every opportunity. For dwarfs, it might work.
“A dimension is a natural thing, a direction.” Denario drew in the sand with the tip of his punt. He explained the concepts of length, width, and depth and waited for the usual human argument that they were 'all the same thing.' Instead, the dwarf knelt to caress the accountant's drawing of a cube. He gestured to the shape four times in a stiff, ceremonial way and mumbled phrases in dwarfish.
“This is sacred knowledge,” he said. “I had no idea that humans knew this.”
“The masons understand.” Denario rubbed the crown of his head under his hat. “Probably some carpenters do. How could they not? We think the wizards came up with it independently. And there's the accountants, like me. That's probably the list of major human professions in the know.”
“I thought you were a boatman.”
“For a while. I signed on as crew for this trip. I needed a faster way to get home from my last job.”
“But if you're a human accountant, you should travel by coach.”
“My last employer didn't like the way I worked. He had the coach waylaid. I ended up traveling by horseback, then by foot. Now it's by boat, as you see.”
“Did you try to make off with his money?”
“No, I found that the mayor's brother was stealing from the tax collection.” Denario hesitated to tell the whole story, especially to a dwarf who hadn't revealed his name. But the fellow egged him on with questions. He even carved out a seat for himself in the sand. He planted himself down, hands on his knees, as if prepared to listen all day.
When it came to the point in the adventure when Denario discovered the dead coachman and passengers, the dwarf hissed. As the Mundredi army won a victory and were awarded with a song, he demanded to hear it. He chuckled at how the accountant fumbled through every blow and he applauded at the part added by the citizens of Pharts Bad for the saving of the town's mine accounts. He slapped his leg in time with the tune, a traditional one, apparently familiar even to folks who lived under hills and mountains.
He made Denario chant it a second time so he could sing along. He was still humming to himself when Clever Jack appeared from the alley next to the kiln house. The boat master barely paused. He didn't seem to mind that his assistant had chosen to entertain a guest. By the twinkle in his eye, Denario could tell that the the trading news was good.
“Den,” he said, ignoring what he assumed was a boy who'd turned his back on him. “Business is brisk. We've got a lot of produce to shift. Children are making their parents load up carts for us as we speak.”
“Let me guess. We're taking on high-value 'boring' items and we're unloading sweets.”
“You've got it.” Jack broke into an open-mouthed grin. “I'm going to miss you when you catch the coach from Oupenli. Are you sure you don't want to partner up?”
“Right. A pity. And who is this little fellow? Are you training up another already? It seems that I can't turn my back without you giving math lessons.”
“This,” Denario began. He swept his arm downward and considered how to continue without a name. “Is one of the dwarfs we've heard about.”
“Wonderful!” The boatman turned and noticed their guest as if for the first time, which it nearly was. He thrust out his right hand. “Jack Lasker, at your service.”
The dwarf responded to the gesture with the same suspicion he'd given to the accountant's offer earlier.
“Might you be Clever Jack?” he said after a moment. “The master boatman?”
“I might.” He lowered his hand. “Out of curiosity, may I know what you've heard about me? The character of the words, at least?”
“Mostly good things.” The dwarf touched his bare upper lip for a moment. Then he nodded to himself. “Yes, mostly good.”
The balding fellow adjusted his woolen cap. That had been one of the clues by which Denario had deduced that he was a dwarf. His skull cap, although not steel, looked much like the helmets worn by dwarfs in the epic poem illustrations published in Oggli. After he'd straightened his clothing, he let his eyes fall to the accountant and, behind him, to the partially laden rafts. The center one held a lot but there was room for more, at least by weight. With another nod to himself, he rose, admittedly not very far, to his feet. He took two steps toward Denario and, right hand across his stomach, bowed his head.
“Master accountant,” he said. “You may tell your master boatman that the Chief of the Lost Mines, Renegade of Water Mountain, and leader of the first families of the travelers, Boldor Sonsonson, is here.”
“Pleased, I'm sure.” Denario tipped his hat. There had to be some sort of dwarfish protocol involved here but he had no idea what it might be. He had to bluff through.
“Boldor Sonsonson …?” he began. There had to have been a question in his tone of voice. The name begged for an explanation.
“Traditional name,” Boldor offered. “There must have been a first name at the front of all of the 'sons,' eons ago. It has been forgotten.”
“Thank you.” Denario introduced the dwarf formally to the boat master, which he supposed allowed them to talk on some other level than the one they had previously occupied. Jack returned the favor by introducing himself, also with several titles, including Master Raft Maker. He duplicated the dwarf's bow.
“Water Mountain?” he asked the dwarf directly.
“That's what humans call the place. It's also how we name it in our own tongue. The river Rodovnak runs underneath, squeezed beneath boulders at the base. Humans know only the springs and streams on the surface. Those are offshoots. The forces producing them are vast. Someday that mountain will be a canyon. Even now, the place is a spiderwork of rivulets, pools, fissures splitting open with steam, and deadfalls buoyed by the pressure of the Rodovnak. Each part is a trap for the unwary. Every home that's carved out of the slag will crumble in time to mud and grit. Decades spent hollowing out an underground road can be wasted by one rockfall that exposes a trickle of water. The road will soon wash away. The place is impossible to mine. But the jumbled earth there is so full of jewels, we work it anyway.” He sighed for the home he'd left behind.
“What makes you a renegade?”
“I read from our library the maps of some ancient citadels, long deserted. Quite a few were never seen by dwarfs. They were the underground lairs of titans or humans, only crudely mined. Nevertheless someone, probably humans, mapped them and recorded their histories. We know which ones were abandoned due to disease, which ones from cave-ins, which ones ran out of copper, silver, or iron, and which ones still held low-grade ores. A few were taken over by monsters, like dragons. That was hundreds of years ago. I asked myself, how long do monsters live?”
“How long until a mine is clear of disease?” wondered Jack.
“What about those low-grade ores?” Denario asked. “That's the most suspicious circumstance. Or should I say auspicious? Smithies have improved their methods in the past generation, I'm told. For sure, ore that was once cast aside is now carted in from afar.” An image came to him of the rock heaps outside of Pharts Bad.
“Humans have no idea.” Boldor rubbed his hands. “It's been hundreds of years since these underground lands were laid fallow. And some of them were mined by humans, after all. They were probably worth the lives of dwarfs even then if we had only been able to find them.”
“Which you are trying to do.” Jack grimaced with understanding. “That's why you're a renegade.”
“Right. The king felt it was an impossible journey. But I and a few others thought it could be done. We'd planned to be safely underground by now, though. The problem is that we're not accustomed to traveling in the open lands for so long or so far.”
“We're between mountains, that's all. Any dwarf would be lost. There are no hills of any size and no place to burrow without water coming in. We need to learn to navigate on the surface.” Boldor gestured to the landscape that mystified him. He might as well be a novice sailor at sea.
“You don't know where you're going?” Denario interjected.
“We've got good choices. I thought we'd explore a little, try to understand which mines both are close and worthwhile and which are worthless or too far away.”
“So ya don't know.” Jack made a rude noise. “Boldor, ya can't go to six places at once. Ya need to pick a spot and march. And ya need to move like ya mean business. If ya don't look hard and act tough as anything, ya'll get robbed.”
“Already happened.” The dwarf closed his hands in front of him. He looked at his feet, then at the gunwhales of the raft only inches away. He helped himself to a seat next to Denario. Maybe it was the result of the formal introduction but he seemed less shy. “We weren't tough. We didn't think to act like it.”
“I can show ya how the caravans operate.” Jack rubbed his chin. “But for a price. I might even hook ya up with a caravan what I know can be trusted.”
“And I could explain how to navigate,” offered Denario. “I can teach you to read maps, human or not.”
“Why would you think you can do that?”
“Because I've figured out the dwarf mapping system. It starts from the center and goes out like a sphere, a round fruit inside a mountain.” The accountant demonstrated with his hands.
The dwarf's mouth fell open. He sputtered. Finally, he threw up his fists, got up, and stomped around the riverbank. After a while, he slumped to a halt. But that didn't last. He kicked the sand and pebbles for a while longer. He knelt and thumped his forehead against a rock. A few moments later, he stood. He staggered.
“What did I say?” he moaned.
The accountant put his head in his hands as he pondered how the secret had been revealed.
“There was nothing in your words exactly,” he concluded. “This relates to something I've been thinking about for a while. Obviously, you've got maps. Why can't humans read them? Why can't you read ours? The only answer I could come up with is that you use a different coordinate system.”
“You came up with it on your own?”
“Not the system. We call it a polar coordinate system, although I don't know why. A wizard in Baggi chose the name. He must be quite old now but he writes letters to the public on occasion to make his case. He argues that polar coordinates are more efficient than using multiple depths of flat maps, which is what we generally do.”
“I'm is more efficient. And more beautiful.”
“Probably. I think he said the same thing. But hardly anyone reads his maps. It's mostly him and his apprentices. And dwarfs, it seems. His maps are useless to human mine foremen.”
Boldor folded his arms.
“Anyway, the wizard sparked a debate between the cartographers and the wizards around the Complacent Sea. It turned out that several other wizards had their own systems that they wanted to propose. A cartographer did, too, but his method involved creating more layers of flat maps and the wizards found that idea dull. The debate has gone on for a dozen years. It doesn't seem to be coming to a conclusion. The only progress in my judgment is that there's finally a human mine using the polar coordinate system. But they need constant help from the wizard and his assistants.”
“All right.” The dwarf stuck out his bearded chin. “Maybe you understand maps. Maybe you can teach. But what makes you think we can pay you for lessons? Our deal with the humans in town isn't settled.”
“Yah've got skills and strong backs.” Jack strode across the corner of the middle raft and onto the last one, the craft he'd built from mallow. Many spars of light wood lay across its deck because it was, as yet, unfinished. “Ya must, to have gotten this far.”
“Master Lasker is my agent for this trip.” Denario turned his left hand in his partner's direction. “I'm sure you could work out a deal.”
“It'll be a deal for no money,” said Boldor. “We're out.”
Jack put his fingers to his forehead for a moment.
“Are you the leader, Boldor?” he asked.
“Yes. I'm Chief of the Lost Mines. I'll be the king of a living mine someday if I find one worth reopening. But I've got to get us back into a mountain range first.”
“Aren't you tempted to go back to Water Mountain?”
“No. I'm a renegade. I must make my own home or die. The others could return, perhaps, if they were willing to endure a lifetime of living in shame. Not me. I left in defiance of the king.”
“Do you think your friends might give up?”
“No. I've asked them three times. The last time was yesterday. They all swore themselves to my service again. Then my closest partner, Dodni, got the bright idea of making false beards and handing them out to the village children as gifts for today's festival.”
“Ah, brilliant! That's why you weren't noticed. I didn't see through the disguises myself. The children often wear fake beards during the festival. Of course, usually they're quite bad.”
“You made those beards in a single evening?” Denario rose from his seat on the gunwhales. “They're fantastic. That was fast work. So you can you work on other materials besides metals.”
Jack raised his hand. “I've already caught on to that.”
“The beards were so we could let off frustration.” The dwarf picked up the stick he'd been using on the burghers. He tapped the accountant on the shoulder with it. That was as high as he could reach. Through the leather hauberk, it didn't feel like much of anything. “Our real work for the village nearly broke us. We spent a week, cutting and hauling pieces of a cordierite altar out of a ruined church. That was what we used to repair the kilns here. I suppose the burghers and the potters had no idea how hard the job was. Or maybe they never intended to pay.”
“That's awful,” said Denario with the sincerity of a young man who's been cheated.
“How much did they promise?” The boatman was busy with pieces of his third raft. He didn't quite look at the dwarf as he waited for his response. Instead, he tested his caulking between mallow boards. When Boldor came out with the amount of cash, goods, and services he was owed, Jack whistled.
“That's a lot for a little place like this,” he said. “On the other hand, it seems fair. And they could pay.”
“Now they claim to charge us for food. And for rent while we worked, even when we weren't in town.”
“Ya didn't bargain on that part?”
“Everyone knows you have to feed and house workers as part of the job. Doing otherwise is criminal.”
“What ya need,” said Jack as he picked up a mallow board, “is an agent.”
There was a pause. Boldor closed his mouth and put his fists on his hips. The boatman never stopped working. He measured out a length of rope. Denario understood there was some sort of fresh urgency to the boat building. Jack moved with clear purpose. He tied his knots. Denario knelt down and used a plank to make a ramp against the gunwhales of the middle raft. Since he couldn't lift a barrel of pickles, it was the only safe way to offload.
“He's good, Boldor,” Denario said. He grunted as he shifted the barrel onto its side. “I've done well with him arranging my pay.”
“But that's easy for you. Who doesn't want a certified accountant? And one from Oggli, the most famous of human cities.”
“It hasn't been like that.”
“Have you negotiated with the children today?” Jack interrupted. He lashed rope around the mallow spar in his hands, ten loops in ten seconds.
“That would be immoral.” Boldor stood up straighter, chin lifted with indignation.
“You really need an agent.” Jack frowned at his work and, probably, at the dwarf's sense of business. Denario felt torn between the two. Boldor had a point about the children.
“Maybe it would be acceptable, this one day. We debated it.” The dwarf relaxed his fists. He gnawed on his lower lip. “Maybe we need human help. I'm chief. I can delegate. But at what price to all of us?”
“For this job, since I'm fixing a done deal, I take one tenth. But for any deal you make with me after, it's one quarter.”
“Does that include lessons on dealing with humans?”
“Hey!” It was Denario's turn to be outraged. “Why does he get a better rate than me?”
“Because he's got a troop of dwarfs. But mostly because you didn't drive a good bargain, my friend. That's lesson one, Boldor. The accountant doesn't understand how to value his services. Neither do you. I'll teach you. Even so, there's more to a good bargain than understanding. For instance, both of you talk like you'll never pass through here again.”
“Because we won't,” said the accountant and the dwarf more or less together.
“How do you know? Anyways, whether you're returning here or not, you need to act like you are. Folks will give you better deals if they think they're establishing a business relationship. If they think it's a one-time deal, they’ll worry that you'll take their money and run. Plus folks who have been cheated in the past, or who remember their fathers or grandfathers got cheated, will be tempted to cheat first.”
Boldor froze for a moment. “That might explain some things.”
“By the way, how many are in your troop?”
“That's a lot.” Jack grunted. “And how much do you weigh?”
“Me, personally? What an odd question.” The dwarf stiffened, a sign that Denario was learning to interpret as Boldor taking offense.
“I need to know for professional reasons.”
Denario looked closer at the next mallow beam in the boatman's left hand. He'd been lashing piece after piece onto the raft as fast as he could, which was faster than Denario had believed possible until now. At last he was sure of the connection between the expansion of the third raft and the question about weight.
“Can I know the reason?” Boldor asked. Denario felt tempted to jump in with the answer.
“If we're going to have a deal, yes,” said Jack. “Will I be your agent and get you paid? If so, you can know. And then we'll have to move quickly.”
The remark produced a lot of beard-wringing. For all of his talk about leadership, the dwarf had been chief of his tribe only briefly. He must have found it one thing to make his decisions underground, where he felt secure and where he could assess the correctness of mine roofs, picks, hammer, packs, food supplies, water, maps, checklists, and other tangible things. It was another, more alien thing to make judgments about human character in the daylight while feeling vulnerable. This was a decision that affected the fate of his expedition. The dwarf's sunburnt skin paled. He let go of his beard. His thin lips pressed hard together in a grim line.
“I don't like it,” he said. “But what better choice is there? The others will be afraid. I know it. But Dodni and I together can calm them.”
“Right, then. How much do you weigh with all of your equipment?”
“You mean all of it and all of us together? I suppose as much as ten men.”
Clever Jack glanced at the six remaining beams. He could extend the raft another two feet in width, no more.
“There's not enough sedge reed,” he said. “Still, with careful placement we can do it. Denario, finish shifting out the pickles. Move the dried fruit last. That stuff weighs next to nothing.”
The accountant nodded. He had pulled up the anchor pegs from around six of the pickle barrels. There were only two more left. Out of laziness, he hadn't done the work of rolling them yet. If the raft had been less firmly rooted in the sand, his boat master would have had something to say about it.
“What does this have to do with getting paid?” Boldor asked. He backed up a few steps to watch the action.
Jack set down his loops of rope. He set down his handful of sedge reed, too, with which he intended to caulk the planks in the raft. Unencumbered and therefore unarmed, he walked to the low gunwhales of the third raft and leaned over. He thrust out his right arm in a formal manner.
“It's traditional to shake on a deal,” he said. “One tenth on this deal and a quarter of future deals if you stay with me. If you come along, you'll be required to work. You’ll see that the accountant does so as well. If your folk are miserable workers, I may let you off at the next stop or I'll charge you extra.”
“We're excellent workers,” Boldor announced. “Better than any humans we've met.”
“Do you know anything about boats?”
“We sail in tall caverns underground. Rivers are part of our lives just as they are part of yours. But Clever Jack, why would we come with you? Sailing in the daylight on a craft open to the birds and to other humans is reckless.”
“You'll come because I'm going to get you all of that pay,” asserted Jack. “I'll see to it that the children hold the potters and the burghers to their deal. But at first dawn tomorrow, the children will be no longer in charge. When that happens, how will you hold onto what you've gained? Even if you march straight out of town with everything on a cart, the villagers will follow.”
“I see.” The small fellow's shoulders sagged for a moment. Then he straightened himself with pride and stepped forward. He raised his hand to shake. “It's all reckless then. Better to be with our pay. And you.”