Chương 46: Chapter 45 Counting Beyond Twenty

"Here are ten stones. Count them." Karath arranged ten small stones across the ground.

"One."

"Two."

"Three." Krog stepped forward as the group's representative and picked up the stones one at a time while counting aloud. The seated orcs folded their fingers along with him and nodded. Their astonishing weakness with numbers had made Karath consider abandoning the map entirely. However, mathematics was a problem they would continue encountering as their civilization developed. He needed to teach them eventually. Karath did not expect much. He only wanted them to understand the four basic operations.

He therefore approached the matter as though teaching first graders and began from the very beginning.

"Now count the next ten."

"Eleven."

"Twelve."

"Thirteen." Krog began counting the second group of stones. The other orcs raised their feet and curled their toes as they followed along.

"Now another ten. You count them the same way as before. There are twenty stones, and one more makes twenty-one. The next is twenty-two." This time, Karath demonstrated personally.

"Hmm?"

"Oh! We can count with stones!"

"Then we should carry stones whenever we go hunting!" The orcs shouted as though they had achieved enlightenment. Their fingers and toes had been insufficient, but stones allowed them to continue counting. Kurdan raised another problem.

"Then how many stones are we supposed to carry?" Everyone fell silent.

"Hmm. We would need far more than thirty."

"What do we do? We cannot carry that many stones."

"Wait. Be quiet and keep listening." They appeared ready to fall into another collective panic, so Karath stopped them before it began.

"If one stone is placed beside another stone, how many are there?"

"Two!"

"Is Karath stupid? How can he not know that?"

"Krahahaha!"

"Karath is an idiot!" Karath's fist trembled. Perhaps he should beat them all again before continuing. How did elementary-school and kindergarten teachers manage children every day? Karath felt profound admiration for every teacher who had ever patiently explained basic arithmetic.

"Haa." He calmed himself by imagining that the massive orcs before him were ordinary children rather than warriors built like professional bodybuilders.

"Yes. One plus one is two. Then what happens if we add ten stones to another ten stones?"

"Huh?"

"Wait. We need to count with our fingers." The orcs tilted their heads.

"You idiots! The stones are right there. Count those!"

"I am first!"

"Move aside, fools!" At Kurdan's shout, every orc charged toward the stones. Thud! Unauthorized use: this story is on Amazon without permission from the author. Report any sightings.

"You bastard! Karath told us to count with the stones, not hit each other with them!" Thud!

"Should I smash your face with one instead?" The warriors fought viciously for possession of the counting stones. Amid the chaos, someone suddenly shouted.

"Twenty!"

"That is correct!" Karath cried out with genuine emotion.

"Krog, how did you understand it?" Krog answered while Karath stared at him with shining eyes.

"We already did it earlier. We counted ten stones, then another ten, and that made twenty."

"Then what happens if you add another ten to twenty?"

"It should become thirty."

"Oooooh!" Karath could not suppress his amazement. At least one of them understood his lesson.

"Oh! That is right. When we counted ten more after ten, it became twenty." Several others began understanding after listening to their exchange.

"What are you talking about?"

"What does counting ten more have to do with there being another ten?" Others still failed completely.

"Fine. Let us try again." Karath gathered the stones and resumed the lesson, changing the numbers one at a time. Led by Krog, more orcs gradually began understanding. Some remained hopelessly confused.

"You idiot! How can you not understand this?"

"Look carefully! There are five stones here. If we add five more, how many are there?" The warriors who understood first began teaching the slower ones beside them. More accurately, they began berating them while explaining what they had learned. A natural system of mentors and students formed between those who understood quickly and those who did not. Karath could divide his work and assign parts of it to the tribespeople beneath him. Those orcs could then divide the same task and pass it farther down.

It was a beautiful divide-and-conquer algorithm.

"Why can you not understand this?" Thud!

"You stone-headed fool!" Thud!

"Replace that useless skull with one of these rocks! It would probably work better!" Thud! Perhaps it was simply a chain of abuse. The mathematical education that began because of the map eventually became part of the tribe's daily routine. Karath did not teach anything particularly advanced. They merely spent around thirty minutes each day practicing numbers and simple addition. After approximately a week, most of the warriors began understanding addition. Karath then taught them Arabic numerals.

Soon, every young warrior could add three-digit numbers. Krog and several others who learned more quickly also began studying subtraction and four-digit numbers. At the same time, the mapping project began progressing properly. Once the orcs could count into the hundreds, they became capable of drawing reasonably detailed maps. Accurate distance was important, but maintaining the correct direction mattered just as much. Fortunately, direction caused almost no difficulty.

Every orc possessed an unnaturally strong sense of orientation. Perhaps that was one of the unwanted gifts bestowed by the monster-infested forest. An orc who became lost in this wilderness was practically dead. After generations of surviving in such an environment, the tribe might have naturally developed an excellent sense of direction. It was also possible that only orcs born with that ability survived long enough to pass on their traits.

"When Karath thinks about it, that is strange." He muttered while organizing his thoughts.

"What is?" Krog looked up from the map he was working on beside him.

"The tribe counts days, so why did everyone know numbers only up to twenty?" Orc knowledge was extremely unbalanced. Everything centered upon survival and hunting. Even so, they tracked days by observing the sun and moon. As on Earth, they considered one full cycle of the moon growing and shrinking to be a month. They did not describe dates numerically, such as the fifteenth day of the third month. Instead, they used expressions based upon the moon's appearance, such as the day of the third round moon.

"Do we really need numbers?" Krog asked with a tusked smile.

"They are useful for maps, but what else would we use them for?"

"It might not matter greatly, but it is strange that we cannot even count how many tribespeople live here." Karath was not entirely certain how necessary numbers were in a primitive society. The tribe had no currency. The orcs did not even trade goods among themselves. Still, being unable to count the people living beside them seemed absurd to someone with a modern perspective. Karath smiled lightly at the irony. Krog's expression, however, became bitter.

"I know numbers now, but in the past, Krog probably would not have wanted to count."

"Why?"

"Because the number changed too often." Karath immediately understood. His own expression became equally bitter. Knowing the tribe's exact population would also mean knowing exactly how many people died each day. Before Karath was born, the tribe's living conditions had been terrible. Death had been an ordinary part of daily life. People on Earth sometimes claimed that leaders of large organizations viewed those beneath them as nothing more than numbers.

Karath had briefly managed a small company and understood something else. Few things made reality more immediate than a number. Knowing exactly how many orcs died every day would have been horrifying, especially under conditions as brutal as these.

"But perhaps it is safe to count now." Karath deliberately spoke in a brighter voice. There was no reason for both of them to remain trapped in gloomy thoughts. He lifted the map they had been drawing together. Approximately one month had passed since Karath began teaching the warriors numbers. Naturally, any map created with primitive tools became less accurate as it extended farther from its original reference point. The farther they traveled from the settlement, the greater the distortion became.

That also meant the land directly surrounding the village had been mapped with considerable accuracy. The tribe could now place large numbers of traps near the settlement without worry. Every trap was marked upon the shared map. As long as the warriors consulted it, the chance of a hunter or scout falling into one decreased dramatically. A detailed map covering approximately five hundred meters around the settlement had become the common reference used by every warrior.

At first, they displayed it inside the chief's house. However, Grild was growing older and apparently desired some privacy. The tribe eventually constructed another earthen building. Every warrior assigned to hunt or patrol visited it daily to inspect or modify the map. It had become something resembling an operations center. The patrol system changed naturally alongside it. Rather than wandering through the area without a plan, scouts designed routes based upon the locations of the traps.

If they discovered an animal or monster caught inside one, they killed it. If a trap had been damaged, they repaired it. Karath hoped to eventually create scheduled shifts divided by time of day and establish a far more efficient patrol system. To accomplish that, however, he would first need to create units of time. The warriors would also need to learn writing before they could read a duty schedule. The thought alone was exhausting. He would proceed one step at a time.

If he continued building each part slowly, a solution would eventually appear. Programming had worked that way. Managing a company had been the same.

"That is true," Krog said. His tusked smile returned.

"Everything has become much better because of Karath." Krog's words caused Karath to remember everything he had accomplished. The settlement had already changed greatly since the day he was born. If he continued moving forward as he had until now, perhaps he would eventually create the environment he dreamed of. For the moment, Karath chose to believe that.