Chapter Fifth Triangular Number
Scene Seven: Too Much MagicHermann Ansel saved Denario with his axe, which he used that morning to make the boys crude spears and wooden swords. His good deed let the accountant off the hook for his hasty promise. Hermann held a training session, too. All together, it took them four hours to break camp but the Ansels didn't seem to be in a hurry to see their old town. Even Valentina got into the spirit of things. She joined the spear practice.
“You know your sword drills quite well,” Herman whispered to Denario at one point. “How is it that you're so bad with the everything else?”
“I have no idea.” Denario rubbed his brow. Maybe a spear took more balance and coordination than he had. He'd managed to bruise himself with the butt end of the pole while demonstrating a turn and thrust move. It had hurt so much that he'd sat down and let Hermann take over the teaching with the pointed stick he'd made.
“And what are you doing now?”
The accountant finished reattaching a pair of copper circles to the head of his spear. It was this arrangement, along with some rather delicate wires, that turned his weapon into a theodolite. Of course, it was a theodolite without a glass lens. He had to rely on his crude line of sight through the crosshairs made by the disks as they met.
Denario stood and gave each disk a spin to test them. Then he sighted along the vertical axis toward the closest landmark, a hillock to the southwest.
“I'm going back to being myself, an accountant and geometer,” he told Hermann. “I'm taking earth measurements.”
“Why?” the Mundredi man asked. Behind them, Valentina led the boys in a blood curdling spear thrust and scream.
“To find out where I am.”
“But you're right here!” Hermann threw up his arms, exasperated.
While Valentina led the boys on six spear charges, Denario tried to explain. The Mundredi peasants who had been exposed to West Ogglian ideas knew what maps were. They had lost the art of creating them but it was only a few generations gone. Denario talked about how Vir's grandfather had understood mapping as he pointed to the intersection of his two copper circles. He sighted the top ridge of the hillock and invited Hermann to look. It turned out that Hermann didn't know what angles were, though, so the he didn't understand how distances might be estimated with them. He didn't want to learn about inclines or declines of the ground, either. If two objects met, then they did, and that was enough.
The accountant tried to explain leveling. That, at least, interested Hermann a bit more. He thought the leveler was ingenious.
“A little bubble of water in the wax tells you if the ground is straight? Smart.” He shook the level for no apparent reason, perhaps just to see the bubbles move. “But it's still useless. I can stand on the ground and tell if it's level enough for what I want.”
“The floors in your churches and homes are dirt,” Denario pointed out.
“What of it?”
“Haven't you ever wanted wood floors? Stone floors, maybe?”
“People made floors like that in South Ackerland, yes. We had wood floors in most of the civic buildings. I've seen masons lay out pegs and ropes to do it.”
“Aha! So they used peg-and-chain surveying.”
“No, they used ropes.”
“Same thing. I mean they had a type of surveying that's good for planning a building. You can make quite large structures that way. You can even survey fields. Not many, though. For that method, you need to be able to make triangles. You would need ropes strung across every field, through trees and streams and everything.”
“No one's going to do that. Is that why our folk don't make maps?”
“I'm not sure. Your ancestors must have had better methods once. Some of your kinsmen are good at math. Superb, even. I feel that someone among them must understand angles and other geometry. For making a detailed map, what you mostly need to know about is distance measurements and angles.”
“And that's why you use your theo-thingy.”
“Yes. With the maps I've made,” Denario concluded, “I could find my way back to every town I've visited. In fact, I can find many towns that I haven't seen because you've told me where they are. I can find water for drinking. My maps show streams and ponds. I could hand them to any people who are able to read maps and they could find those things, too.”
“It's a sort of magic, then," said the boy Franzel as he walked up, winded from his exercise.
Valentina stood well back, fists on her hips. Sweat dripped from her brow. Behind her, Adalwolf took huge gasps of air, which he made more difficult by trying to hide his exhaustion. He seemed to have a keen desire to avoid looking weak in front of a woman.
“No, it's not magic, really,” Denario corrected with a wave of his finger. “It's just maps. It's marks on parchment or paper.”
“You mean you can find your way back home using a piece of paper?” Franzel looked like he'd forgotten that his father was probably dead and that he was on a forced march through a land of strangers.
“Exactly,” said Denario. “Would you like to learn to read maps?”
“No.” He surprised the accountant by putting up both hands as if trying to ward off a spell. “It's too much magic for me.”
“Me, too,” Hermann agreed.