The main road from Port Town to Lumber Town snaked its way out of higher hills in the south, met the road from the village of Fish, then crossed the river on an old bridge of crumbling stone. Though summer was at hand in the lowlands, the travelers could see on their map that the swift muddy water came directly from the mountains, still white with snow.
Within sight of the bridge, the road disappeared into the dark evergreen forest that cloaked the lower slopes of the mountains and the northwestern corner of the kingdom.
Even though the ocean had given them a good supply of mussels and clams, little else along the beach had been edible. As they lingered on the road just outside the eaves of the forest, berries of several kinds dangled within easy reach. Neti, in a burst of sympathy, handed Miko one dark, sweet, juicy berry, but made sure his bowl was mostly filled with small, sour, green ones.
The group had only been in the area for a few minutes when Ilika’s
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bracelet chimed its warning tone and they scrambled deeper into the bushes.
Five soldiers on horseback galloped by, heading north toward Lumber Town.
When the group retook the road and entered the forest, none could resist looking straight up at the towering giant trunks all around them. At first the trees were only about a hundred feet tall, and some light slipped in from the edge of the forest. Before long, the only light was filtering down from the tops of the trees, somewhere in the dizzying heights two hundred feet or more above their heads.
They knew from the map that this part of the forest formed a triangle bounded by the southern edge of the forest and two of the roads to Lumber Town. Ilika proposed they go cross-country, as he wanted to give the soldiers plenty of time to do their business in town and hopefully depart. Everyone agreed.
So little sunlight penetrated the green canopy that almost no undergrowth shared the forest floor with the huge trunks. The going, therefore, was easy, and the few bushes they passed bore tasty red berries. Even Tera seemed comfortable in the new environment, finding plenty of tender leaves and a little grass.
Miko and Toli had been on work crews in the forest, carrying tools, food, and water for loggers. The rest admitted they had no idea such trees existed.
“These trees are hundreds, maybe a thousand years old,” Ilika began to teach as they walked. “I don’t know if there are any in your kingdom, but the oldest living beings in the world are trees almost ten thousand years old.”
Kibi frowned. “It seems wrong to cut them down.”
“In my country, large or very old trees have more rights than slaves in your kingdom.”
“Now
I
know I’m going to your country,” Kibi announced, “even if I have to walk the whole way.”
Ilika smiled. “I haven’t explained photosynthesis yet, have I?”
Their blank faces answered his question.
“Plants are the original magicians. They can do something that no animal can do, including people. They can make food out of sunshine.”
Several mouths opened in surprise. Rini looked fascinated, but not surprised.
Ilika continued. “Most plants need to put roots into the ground so they can also get to rocks and water, but some just need air. It’s the green stuff in the leaves that does the magic, a complex, wonderful organic molecule, with a hundred and thirty-six atoms, called chlorophyll.”
“Can you draw it for us?” Toli asked with excitement.
Ilika thought about the request. “It would take a long time, and not really do you any good. It’s mostly carbon, hydrogen, oxygen, and nitrogen, like other organic molecules, plus one little atom of magnesium.”
“Isn’t that a metal?” Sata asked.
“Yes. Remember what makes your blood red?”
Her face twisted as she tried to remember.
“Iron,” Boro said after Sata shook her head in surrender.
“Yes, another metal. In the process of photosynthesis, plants leave behind millions of different organic molecules that only they can create. That’s why most medicines come from plants, and that’s how animals live, by eating plants. No animal, anywhere, including people, can live without plants to eat.”
“But what about people who eat nothing but meat?” Miko asked.
“What do the animals eat who provide the meat?”
Miko slowly nodded.
“Any food chain can be traced back to plants. Animals cannot make food from rocks, water, and sunshine, like plants can. Entire kingdoms of people have died because they cut down all their forests, and their lands became deserts with almost no life.”
“Like the desert east of our kingdom?” Kibi asked, remembering the map.
“That one’s natural, caused by the hills and mountains of your kingdom catching the rain. We’ll see it after crossing the mountains.”
Kibi’s eyes sparkled at the prospect.
“A man-made desert is much uglier.”
Her eyes lost their sparkle.
They walked for another hour, then made an early camp on a gentle rise of land, clear of overhanging tree branches, and soft with needles. A trickle of a stream, just a short walk down the hill, provided water and rocks for a campfire circle. Parties spread out in twos and threes for firewood, berries, fresh greens, and to their delight, mushrooms in the moist places near the stream. Toli took the shovel, but had no luck finding edible roots, so he brought back some firewood.
All of them, as they worked or played, often stopped to look up at the giant trees all around. Sometimes they became dizzy and found themselves falling to the ground, or being caught by a friend.
Once they all gathered back at the camp, Ilika introduced their next topic of study. “You are ready to learn a new kind of number system for the measurement and calculation of angles. This will give you the basic tools you need for navigation.”
As they cooked dinner, Ilika laid out a large compass rose on the ground with their campfire in the center, true north correctly placed, pine cones every ten degrees, and rocks every forty-five. When everyone had eaten, they followed him around, discussed the major divisions of the compass, and learned the difference between the direction a ship was pointing, the direction it was going because of currents and winds, and the direction they might be looking.
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Faces aglow from learning actual seafaring skills, they absorbed modulus arithmetic in mere minutes, allowing them to pass over due north in either direction.
As evening descended upon the forest, they gathered back at the fire, and with many drawings, Ilika described how the compass was projected onto the planet from two different directions, allowing any point on the globe to be identified with numbers.
The longitude lines, with the compass projected down from the poles, were fairly easy for them to grasp. The latitude lines, projected onto a constantly moving surface, gave a little more trouble.
The lesson over, they became quiet and thoughtful. Ilika started massaging Kibi’s shoulders, and others got out combs or ointment. Bowls of
berries came around, and everyone started feeling that their visit to the great forest was going to be wonderfully pleasant and uneventful.
Deep Learning Notes
Why is Miko being fed acidic berries again?
Under a forest canopy, competition for sunlight become critical. The tallest trees get the most, of course, and the more completely they block the sunlight, the fewer bushes can grow on the forest floor.
Although there are some self-cloning plants whose clonal communities are even older, the oldest known individuals on Earth are the Norway Spruce on the Norway/Sweden border (8000-10000 years old) and the Bristlecone Pines of eastern California and Nevada (almost 5000 years old).
Ilika refers to plants as “the original magicians” because of photosynthesis.
What do chlorophyll molecules and Ilika’s bracelet have in common?
The direction a ship points is its “heading,” the course it actually takes (not necessarily a straight line) is its “track,” and the direction to anything else is a
“bearing.”
Modulus arithmetic is done by adding or subtracting whole cycles (360 in the case of compass degrees) until the result is between zero and the cycle size.
With compass directions, both zero degrees and 360 degrees are valid, and equivalent.
Although longitude lines radiate from the north and south axial poles, which are natural and fixed, they require us to select an arbitrary zero point from which to begin counting. That point, on our world, is in the Royal Observatory at Greenwich, England. The latitude lines are completely based on the natural north and south axial poles, with zero placed halfway between
(at the equator).
Chapter 31: Gleaming Eyes in the Dark
At least, they thought their visit to the great forest was going to be uneventful — until Rini spoke.
“We’re being watched.”
“Report,” Ilika said in a soft voice.
“It comes and goes, about dog size. Sometimes on one side, sometimes another. Never gets close enough to see more than gleaming eyes, about fifty feet away.”
“I think I’ve seen it,” Buna whispered.
“This is a forest,” Boro pointed out. “We’re the visitors.”
“Yes,” Ilika agreed. “Looks like we need to set a watch. Wood supply?”
They looked, and agreed it was enough for the night.
“Magic bracelet to chime the hours?” Buna inquired with a smirk.
Ilika smiled. “I’ll get it ready now.”
Sata helped Mati tie the donkey to a little tree within the light of the campfire. Boro collected a small pile of fist-size rocks.
When Buna shook Boro awake for his watch, dawn light was already in the sky. She whispered that the watcher had disappeared at first light, but she had caught a glimpse of its shape and size, too small to be a wolf.
Boro nodded as he put up his hood against the cool morning air. As Buna disappeared into her bedroll, he strolled around the perimeter of the campsite, rock in hand, but saw nothing.
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As soon as Kibi awoke in the morning light, she and Boro went to look for tracks, especially on the soft ground near the stream. They soon found what they were looking for, and both spoke the same word at once.
“Fox.”
At breakfast, Neti proposed they try to make friends with the fox, and give it something to eat from the stew pot each night. The other students liked the idea, but Boro felt a watch was still needed.
Ilika remained neutral about the idea, and plunged ahead into the measurement of angles, especially as they applied to common shapes.
During mid-day free time, when not gazing up at the towering trees, those who were weak at math made sure they reviewed with someone who was stronger. Buna was always mixing up equilateral and right triangles, and Toli tried hard to straighten her out. Kibi and Mati wouldn’t let Rini out of their sight until they had the difference between heading, track, and bearing firmly in mind. None of them wanted to let a bit of it slip past them if it applied to navigation.
“I was stopped by the fiery breath of the dragon,” Ilika read from his sheet of paper that afternoon. “See how the passive voice gives power to the dragon, and makes the fact that I stopped seem unavoidable, instead of a choice I made?”
Most of them nodded.
“You try it. First an active verb, then passive.”
They started writing. After a minute, Mati burst out laughing. All eyes
turned to her.
“Please, share!” Ilika begged with a grin.
She cleared her throat. “I ate the tart. I was eaten by the . . .” She doubled up with hysterical laughter.
Ilika smiled.
Sata’s hand shot up. “The tart was eaten . . . when I smelled its delicious fruit filling!”
“That works a little better. But thank you for sharing the funny one, Mati.”
After another hour, they were getting the idea, and their sentences became much more interesting. Ilika ended by having them write a paragraph about something they saw, heard, or felt during their watch shift the night before.
Most of them wrote about the gleaming fox eyes that had observed them from the darkness.
That evening, a little way from camp, Ilika came upon Miko looking at his scabby knees, crying softly from the burning itch and the shame. Ilika sat quietly with the lad for a few minutes, until Neti arrived with ointment and a bowl of sour berries.
Ilika didn’t see any signs of infection, but kept that fact to himself.
The students and their teacher stayed at that campsite for two more days, taking their first steps into the world of trigonometry. Ilika started with the simplest and most useful function, the tangent of forty-five degrees. As soon as they discovered that a triangle made from paper would allow them to pace off the heights of the trees, no bush or tree anywhere near the camp went unmeasured.
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In the afternoons, Ilika taught more of the tricks of writing, starting with personification, then moving into exaggeration and irony. Kibi and Sata were in their favorite element, and Mati and Rini also enjoyed themselves. Boro, Neti, and Buna tried hard, but it didn’t come easily. Miko and Toli would rather collect firewood.
Also during those two days, everyone became excited about the possibility of taming the fox. They all agreed not to throw rocks at it as long as it wasn’t hurting them, and they left a portion of their stew on a piece of bark each night.
The fox never ate the stew, which by morning was covered with ants. On the second morning, it waited through dawn and disappeared just before sunrise. On the morning of their departure, it sat in plain sight and watched them as they ate breakfast.
Deep Learning Notes
What are the differences in power and temperament between the different animals that made the students switch from fear and watchfulness, to sharing food, when they realized they were being observed by a fox instead of a wolf or mountain lion?
The illustration about angles shows three examples of both 3-sided and 4-sided figures. In both cases, the one on the left is the most regular, the one in the middle is partially regular, and the one on the right is the most general.
In what ways are the figures in the middle of each row regular, and in what ways are they not regular?
For those who attempt to write your own stories, be aware that passive voice is usually a bad writing habit. Compare “There were three apples in the basket,” to “Three apples nestled in the basket.” Occasionally, however, passive voice can be used to advantage, as in Ilika’s example. An active verb, with the dragon’s fiery breath as the subject, might be even better. Can you rewrite Ilika’s example using an active verb?
Why do you think Ilika did NOT tell Miko that he saw no signs of infection?
If you remember nothing else about trigonometry (and few adults do), the tangent of 45 degrees can help you with many difficult puzzles. Tan(45) = 1 =
far side / near side. This refers to the two sides surrounding the right angle, not the hypotenuse (the “sloping” side).
