Book 13 Chapter 10
3 years later (3)
For that reason, eleven years old was also a period when I frantically studied the Earth attribute among the four great elements.
Earth attribute magic is the most difficult of the eight attributes.
This is because it is based on geometry (幾何學), the study of the properties of space, and it really gets more interesting the deeper you dig.
“Archmage Zernix completely solidified the concepts of geometry. He deductively proved and then organized 'Elements of Geometry,' left behind by the first mage, Emitsa Page, and then left it to the world. That's why it was named 'Zernix Geometry'.”
“Was he a good mage?”
Like the dean?
Respect for Zernix had been vaguely growing since the time I first learned the elements.
“I believe that the passion he showed in researching geometry to this extent clearly stemmed from goodwill (善意).”
Anyway, what I was learning then was Zernix Geometry.
Zernix Geometry is also defined as axiomatic geometry, as mentioned earlier, because Zernix systematically organized the Elements of Geometry.
Zernix Geometry is also an important first step in learning the logical system of 'axioms-postulates-theorems'. The concepts of axioms, postulates, and theorems are as follows:
- Axiom (公理).
An axiom refers to providence.
- Postulate (公準).
A postulate does not belong to providence, but refers to a principle that is naturally accepted in everyday life and can be used as a logical proposition.
- Theorem (定理).
A theorem is something that can be asserted identically to a postulate by weaving and combining these postulates (providence cannot be transgressed by a postulate).
It was astonishing. I trembled with fear.
That the principles of this uncertain and vast world could be expressed so easily and clearly, I was deeply impressed and surprised by the clarity of mathematics every day.
“Let's continue with the explanation of Zernix's 5 axioms, 5 postulates, and 23 theorems tomorrow.”
Geometry, born to measure the dimensions of land through points, lines, curves, planes, and volumes, allowed for the systematic study of shapes.
While general mathematics deals with many 2D shapes, geometry can even visualize 3D, providing truly many research challenges.
If one mastered geometry, they could even dabble in hyperdimensional spatial transfer magic, but the dean firmly shook his head.
“Research into hyperdimensional magic is strictly forbidden by order of the Papal State.”
“Why?”
“I don't know the details. They said there's a high possibility of being eroded by the Abyss (深淵).”
“Why?”
“It happened 500 years ago. It was during the era of Lyuken Ludwig.”
“He's the 5th Archmage! The master of the 6th Archmage Zernix!”
“Yes, it's good to see Lin's excited eyes. Anyway, it seems something happened back then. Lyuken Ludwig advised the Mage's Alliance and the Papal State about the dangers of hyperdimensions, and it was accepted.”
Why on earth did Lyuken do such a thing? Was it breaking the ladder?
A slight sense of despair came over me.
As I aimed to become like the old Archmage Zernix, I wanted to learn spatial transfer magic, which was said to be his specialty.
- Lin, black magic is absolutely forbidden.
But I decided never to do anything the dean disliked, whatever it was. Anyway, I was glad to be able to learn so much from the dean, as he was an expert in the Earth attribute.
“There is no mathematics that can be as helpful to human life as geometry. Accurate surveying affects not only simple construction but also various other fields.”
“In what way?”
“Let's say a river floods and the boundary stones of the land are gone. How would you accurately divide the land between two farmers again? The method of measuring land area helps here.”
I was just… happy with the environment itself, sitting face to face with the dean in one space and being able to listen to his knowledge.
The dean's voice was just like the sound of rain.
There was sound, but it wasn't loud. It spread quietly and clearly, pleasantly leaving ripples deep in my heart.
“If land is damaged by various natural disasters, great lords request court mages, and minor lords request mages from the Mage's Alliance for investigation. This is to accurately calculate and restore the lost area.”
The dean's magical conviction was based on helping the powerless, in line with the school's tradition.
He taught me to do the same.
He didn't force me to, but all his teachings were simply founded on that principle. It seemed this was also why he had mastered the Earth attribute.
“Hmm, I've learned enough geometry; now it's time for practical application.”
And so, wandering alone outside the magic tower to test the newly learned geometric theories became a daily routine.
“Excuse me, sir, is there any village where rivers or streams flood frequently?”
I asked a peddler.
This was to find a research site where measurement methods would vary depending on the situation.
“There is, but it's a bit hard to get to. There's no proper road.”
“Why?”
“Because the road gets buried whenever anything happens, and road maintenance costs are higher.”
“Which direction?”
The peddler pointed northeast.
“If you go straight this way, you'll find it, but the forest is dense, the ground is muddy, and it's no path for a child. Let's go together to a nearby village. I'll roughly show you the map.”
“It's fine. Knowing the direction is enough.”
If there's no road, I'll just make one.
Through Zernix Geometry, my ability to define space by handling lines, planes, and points, in other words, my geometric knowledge, had greatly expanded.
I thought it wouldn't be bad to test the limits of that knowledge by pioneering a road.
“Uh, uh? A ma-mage? H-huh! I-I'm sorry. I didn't recognize you…!”
This is based on Zernix's fourth of 23 theorems: [A straight line is a line drawn directly along the points on it].
While it's difficult to find the coordinates of a straight line all at once, if you think of first setting points as axes and connecting them, finding the coordinate equation becomes extremely easy.
The characteristics to be carved into the magic, that is, the runes, were decided as Gan (墾; reclaiming land) and Cheok (拓; expanding).
Kugugugugugugugu…!
The road, which was being pioneered by gradually bringing out bedrock, stopped just before hanging at the edge of the horizon.
Ugh…
Is my magic power still insufficient?
I need to work harder on increasing my magic power.
If I set aside about a month, I could lay a road to the village.
“Oh, did you say the road gets submerged whenever anything happens?”
“Yes? Ah, yes! Because the ground here is low.”
“Then I'll need to dig furrows on both sides and make a few drains. Oh, and you don't have to use honorifics.”
“Uh, how could I do that, to a mage?”
“I'm not 'Mage-nim,' just a mage, you know.”
“But how much did you receive? I heard the cost of hiring a mage for road pioneering is enormous, and that village is quite poor…”
“Money? I didn't receive any of that.”
“What?”
I had never seen the dean receive money for doing such things. So, I had come to believe that it was common not to accept payment when using this kind of magic.
“It's just for my own satisfaction, why would I accept money?”
Laying the road took about two months, contrary to initial expectations.
The forest in the middle was the problem. Calculating the coordinates of the forest area was truly tricky.
It was because of various plants and animals; to find a way not to harm their reproduction, I had to study geometry in even more detail.
It's joyful…
It's so, so joyful…
How can I explain the process of that exploration and research, and the exhilaration when that exploration and research were actually proven?
When I didn't know something, I looked it up in a grimoire or asked the dean, and in that process, I keenly felt that I was alive.
It was a very important time for me to realize my lack of magic power and knowledge. I was happy about the fact that 'I was still lacking'. That meant, after all, that 'there was still much to fill'.
“Look, that's her.”
“So young, yet such an amazing mage?”
“Shh! Just be quiet and watch. Your jaw will drop.”
It seemed word had spread among the peddlers, as spectators gathered during the day, so I mainly worked at night.
When the road was about halfway done, it seemed word had spread to the village, and even residents came flocking.
It was fortunate that this was a remote place; if it had been a place with a little more traffic… just imagining it was dreadful.
“Oh, the road is…”
“This is magic…”
Then, whether day or night, as if they were taking turns on duty, they would come during my working hours, give me food, and leave.
This was, after all, purely for my own satisfaction and merely my magic experiment.
Therefore, hearing words of gratitude didn't feel very good.
But I felt good when I received food. Magic is a process that makes the brain work 12 times faster than usual, so sugar quickly becomes deficient.
The construction connecting the road and the village was finished around October. The villagers were so delighted that they toasted on the road that had become a crossroads.
“Thank you very much, young Mage-nim…”
“We couldn't lay a road at all, and though we thought about asking the Mage's Alliance, the cost was too high, so we couldn't even consider it…”
I adamantly refused their offer of recompense. It wasn't an excuse out of shyness.
What was I supposed to do when I really just did this on my own initiative to research Earth attribute magic? As I've said several times, this was nothing but self-satisfaction.
If the dean had been a very worldly person, he might have taken money, whether I had used magic on my own or not, but the dean had never done such a thing while teaching me magic.
“In that case, we will make this day a village festival day and remember it for a lifetime.”
“Ah, why again?”
“Also, when reporting to the lord, we would like to name this road after you, Mage-nim. What is your esteemed name?”
The village chief said. A road named after me? I'm too embarrassed to do such a thing.
But I thought the name of the school would be different.
It didn't seem bad for the school's name to be attached to a place like this.
“If anyone asks, just say a mage from the Osarius School did it.”
As I was about to leave the crossroads, the villagers bowed respectfully.
A village child, eyes sparkling like stars, looked alternately at the crossroads and me, then placed both hands on their navel and bowed 90 degrees. It was an angle perfectly suited to a right angle as defined in mathematics.
For a moment, in those eyes, in that posture, was it a hallucination brought on by fatigue that I saw myself, on that eight-year-old day, witnessing the dean's magic for the very first time?
Hmm.
It must have been a hallucination.
* * *
Later, that crossroads was named 'Osarius Crossroads'.
Even after hundreds of years, that road solidly connected the village to the outside world. It became a pathway for goods.
It is said that successors (後進) who praise the achievements of Archmage Lin and wish to emulate them always visit this crossroads.
In this Linnevoro (a compound of 'Lin' meaning spring breeze and 'Nevoro' meaning childhood) village, a statue of the young Archmage who built the road on that youthful day stands. It is said that the inscription reads:
"Remembering forever the Archmage who, receiving no reward, but with only a good heart, connected this village to the world."