The Blinding Knife
Page 28
She raised her eyebrows and peered at them over her goggly lenses. They repeated it, louder. Kip joined them, lest he be even more different.
“Good. Now, the abacus. Any of you here from Tyrea?”
“No? Oh, the boy, of course,” she said as Kip raised his hand. She went on, “Tyrea was, despite all evidence to the contrary, once the seat of a great empire, long before Lucidonius came. Perhaps it was crumbling by the time he did come, or perhaps he hastened its demise. That is for another class. The Tyrean Empire gave us a few gifts and a few curses. The only one I care about for this class’s purposes is the base twelve number system. Tyrea is the reason our day is broken into twelve-hour halves, and sixty-minute hours. Some of you Aborneans and Tyreans may have been taught to use the base twelve system in counting and in arithmetic. If so, this class will be much, much harder for you. That number system is unholy, and you will not use it henceforth. Unholy? you ask. Yes, blasphemous. How can a number system be unholy? Well, how can a number system be based on twelves? What is our number system based on, anyone?”
“Ten,” a girl in the front row said.
“Correct. Why does ten make sense?”
No one answered. “Fingers,” Kip said, being a wiseass.
“You think you’re joking, but even fools can be right.”
Kip scowled.
“It’s true. Fingers and toes. So if fingers and toes are the easiest way for primitives and morons to count”—she glanced at Kip—“especially before parchment or vellum or paper, how does a society count based on twelves?”
Kip scowled harder.
A girl at the back raised her hand. Magister Hena called on her. “The Tyrean gods had six fingers and toes.”
“Exactly. That’s why you’ll hear stories of children who have six fingers and toes being venerated in certain superstitious corners of the world. You’ve heard of such things, right, boy?”
“It’s Kip, and no, I’ve never heard of any such thing.”
“Well, then perhaps your parents were particularly enlightened for Tyrea. Or ignorant even of the ignorance, I suppose.”
Kip opened his mouth, then shut it. Don’t, Kip. It doesn’t matter. He suddenly felt hungry.
The next hour was spent learning how to use an abacus. The four beads on the bottom row were called the earthly beads, and the one bead on the top row was the heavenly bead. And first they simply counted, up and down, adding by ones, subtracting by ones. Then adding by twos and subtracting by twos, then fives.
Some of the students clearly were bored, having learned this long ago. Others, like Kip, struggled to keep up with even basic arithmetic. But the children who did the worst were the few who had learned to use the abacus on the base twelve system. They seemed frozen; everything they’d learned was wrong.
The next lecture was better. It was Properties of Luxin, taught by a ferret-faced Ilytian magister who leaned on his cane in between making points. Kip was surprised to find that half of the auditors were non-drafters. And the non-drafters were all smart and driven. These were the future architects and builders of the Seven Satrapies. Like the drafters, these boys and girls had their tuitions paid for by the satraps. Some were connected—second and third sons of nobles who had to be given some way to support themselves. But even they had passed competency tests in order to be accepted.
Kip could tell right away that these children wouldn’t need any training on the abacus.
The tutorials were pretty basic today, though. Sheets of blue luxin one foot by one foot and one thumb thick were placed on supports, then weights added to the center until they shattered. The same was done with green, and superchromat-drafted yellow.
Magister Atagamo then had those students who were able to do so draft their own sheets of blue luxin. He tested each of those. They all failed at much lower weights—especially the boys’. “Later, I will have you memorize the theoretical weakest blue luxin that will still hold a solid so that you know the full range. For now, be aware that we are establishing maximum strengths. The luxins we have to work with are superchromat-drafted. Your own luxin will be weaker than this. Boys, yours will usually be substantially so.”
Then Magister Atagamo’s assistants put a cubit tub on a scale, showed how it measured one foot per side, zeroed the scale, and filled it with water. Kip noticed that all of the other students were writing everything down.
The weight of the water within that small tub was a seven, the basic unit of measuring weight. Of course, that was too big of a weight to be useful for a lot of things, so it was broken into sevs: one-seventh fractions of a seven. Kip weighed twenty-nine sevs, or four sevens and one sev, usually expressed as four sevens one.
But the magisters weren’t finished. They poured out the water and had three superviolet drafters fill the tub with superviolet luxin. That was when Kip knew he was in real trouble—they were measuring everything! When they unsealed the superviolet and it dissolved into feather-fine, nearly invisible dust, they swept that out into a tiny cup and measured it. Everything that could be quantified was.
For a while, with the rest of the students, Kip simply wrote down the numbers without knowing why. Then they asked them to add the weights of all the colors together. The students who were already proficient with their abacuses did so quickly. Kip barely got through adding the first two before those students were finished.
Magister Atagamo said, “Now, subtract the weight of the cube of green luxin from that total, and add the weight of a small woman, let’s say eleven sevs.”
Four girls—non-drafters all—had the total practically as soon as the magister was finished talking. Kip was aghast.
“Excellent,” the magister said. “Now, a practical example. You’re a blue drafter, manning the counterweights for the lift in one of the towers. One of the counterweights breaks in half. It is made of iron, and weighs thirty sevs six. How much blue luxin will you have to draft to replace the counterweight? If your counterweight is more than three sevens heavier than the original when combined with the weight of the delegation, the pulley will break, killing everyone. When you have your answer, come show it to me. For the sake of our example, we’ll pretend that the delegation is coming from your home satrapy, and if you don’t have the lift ready by the time they arrive, you will shame them and lose your sponsorship. So you have thirty minutes to get your solution. If you get the answer quickly, you can leave, take the rest of the morning off. If you can’t, there will be a mark against you for today. Go.”
The other students set to work immediately, and Kip saw that the easy answer was impossible. He couldn’t just add full-size blocks of blue luxin together, because that would make the counterweight too heavy. The arithmetic here was to find the exact fractional volume of blue luxin he would need to make a new counterweight.
The best girls and boys were already working their abacus beads back and forth. Kip wasn’t good enough with the abacus. He’d never make it in time. He didn’t know how to figure fractions. He could work the entire time and still not—Oh.
Got nothing to lose, do you, tubby?
Kip scribbled something on his paper, stood up, and walked to the magister’s desk.
The magister looked at him tolerantly, like he was a student who hadn’t understood the question and was about to ask for clarification. Kip held up the paper.
“Good. Now, the abacus. Any of you here from Tyrea?”
“No? Oh, the boy, of course,” she said as Kip raised his hand. She went on, “Tyrea was, despite all evidence to the contrary, once the seat of a great empire, long before Lucidonius came. Perhaps it was crumbling by the time he did come, or perhaps he hastened its demise. That is for another class. The Tyrean Empire gave us a few gifts and a few curses. The only one I care about for this class’s purposes is the base twelve number system. Tyrea is the reason our day is broken into twelve-hour halves, and sixty-minute hours. Some of you Aborneans and Tyreans may have been taught to use the base twelve system in counting and in arithmetic. If so, this class will be much, much harder for you. That number system is unholy, and you will not use it henceforth. Unholy? you ask. Yes, blasphemous. How can a number system be unholy? Well, how can a number system be based on twelves? What is our number system based on, anyone?”
“Ten,” a girl in the front row said.
“Correct. Why does ten make sense?”
No one answered. “Fingers,” Kip said, being a wiseass.
“You think you’re joking, but even fools can be right.”
Kip scowled.
“It’s true. Fingers and toes. So if fingers and toes are the easiest way for primitives and morons to count”—she glanced at Kip—“especially before parchment or vellum or paper, how does a society count based on twelves?”
Kip scowled harder.
A girl at the back raised her hand. Magister Hena called on her. “The Tyrean gods had six fingers and toes.”
“Exactly. That’s why you’ll hear stories of children who have six fingers and toes being venerated in certain superstitious corners of the world. You’ve heard of such things, right, boy?”
“It’s Kip, and no, I’ve never heard of any such thing.”
“Well, then perhaps your parents were particularly enlightened for Tyrea. Or ignorant even of the ignorance, I suppose.”
Kip opened his mouth, then shut it. Don’t, Kip. It doesn’t matter. He suddenly felt hungry.
The next hour was spent learning how to use an abacus. The four beads on the bottom row were called the earthly beads, and the one bead on the top row was the heavenly bead. And first they simply counted, up and down, adding by ones, subtracting by ones. Then adding by twos and subtracting by twos, then fives.
Some of the students clearly were bored, having learned this long ago. Others, like Kip, struggled to keep up with even basic arithmetic. But the children who did the worst were the few who had learned to use the abacus on the base twelve system. They seemed frozen; everything they’d learned was wrong.
The next lecture was better. It was Properties of Luxin, taught by a ferret-faced Ilytian magister who leaned on his cane in between making points. Kip was surprised to find that half of the auditors were non-drafters. And the non-drafters were all smart and driven. These were the future architects and builders of the Seven Satrapies. Like the drafters, these boys and girls had their tuitions paid for by the satraps. Some were connected—second and third sons of nobles who had to be given some way to support themselves. But even they had passed competency tests in order to be accepted.
Kip could tell right away that these children wouldn’t need any training on the abacus.
The tutorials were pretty basic today, though. Sheets of blue luxin one foot by one foot and one thumb thick were placed on supports, then weights added to the center until they shattered. The same was done with green, and superchromat-drafted yellow.
Magister Atagamo then had those students who were able to do so draft their own sheets of blue luxin. He tested each of those. They all failed at much lower weights—especially the boys’. “Later, I will have you memorize the theoretical weakest blue luxin that will still hold a solid so that you know the full range. For now, be aware that we are establishing maximum strengths. The luxins we have to work with are superchromat-drafted. Your own luxin will be weaker than this. Boys, yours will usually be substantially so.”
Then Magister Atagamo’s assistants put a cubit tub on a scale, showed how it measured one foot per side, zeroed the scale, and filled it with water. Kip noticed that all of the other students were writing everything down.
The weight of the water within that small tub was a seven, the basic unit of measuring weight. Of course, that was too big of a weight to be useful for a lot of things, so it was broken into sevs: one-seventh fractions of a seven. Kip weighed twenty-nine sevs, or four sevens and one sev, usually expressed as four sevens one.
But the magisters weren’t finished. They poured out the water and had three superviolet drafters fill the tub with superviolet luxin. That was when Kip knew he was in real trouble—they were measuring everything! When they unsealed the superviolet and it dissolved into feather-fine, nearly invisible dust, they swept that out into a tiny cup and measured it. Everything that could be quantified was.
For a while, with the rest of the students, Kip simply wrote down the numbers without knowing why. Then they asked them to add the weights of all the colors together. The students who were already proficient with their abacuses did so quickly. Kip barely got through adding the first two before those students were finished.
Magister Atagamo said, “Now, subtract the weight of the cube of green luxin from that total, and add the weight of a small woman, let’s say eleven sevs.”
Four girls—non-drafters all—had the total practically as soon as the magister was finished talking. Kip was aghast.
“Excellent,” the magister said. “Now, a practical example. You’re a blue drafter, manning the counterweights for the lift in one of the towers. One of the counterweights breaks in half. It is made of iron, and weighs thirty sevs six. How much blue luxin will you have to draft to replace the counterweight? If your counterweight is more than three sevens heavier than the original when combined with the weight of the delegation, the pulley will break, killing everyone. When you have your answer, come show it to me. For the sake of our example, we’ll pretend that the delegation is coming from your home satrapy, and if you don’t have the lift ready by the time they arrive, you will shame them and lose your sponsorship. So you have thirty minutes to get your solution. If you get the answer quickly, you can leave, take the rest of the morning off. If you can’t, there will be a mark against you for today. Go.”
The other students set to work immediately, and Kip saw that the easy answer was impossible. He couldn’t just add full-size blocks of blue luxin together, because that would make the counterweight too heavy. The arithmetic here was to find the exact fractional volume of blue luxin he would need to make a new counterweight.
The best girls and boys were already working their abacus beads back and forth. Kip wasn’t good enough with the abacus. He’d never make it in time. He didn’t know how to figure fractions. He could work the entire time and still not—Oh.
Got nothing to lose, do you, tubby?
Kip scribbled something on his paper, stood up, and walked to the magister’s desk.
The magister looked at him tolerantly, like he was a student who hadn’t understood the question and was about to ask for clarification. Kip held up the paper.
