Chapter 13
T/N: Edited 10/28/24.
It was a strange thing to do for the curriculum of a disciple taken in for his ‘magical talent.’
He must have his reasons.
It’s a question I had been suppressing for long.
I thought I would find the answer to the question after starting the magic lessons, so I focused on building a basic foundation.
Little did I know I would hear that answer today.
Benjamin, while turning the first page of the calculus textbook, asked me:
“Do you know the reason I didn’t teach you magic studies, by any chance?”
“…I’m not sure. There must be a reason why one shouldn’t learn magic hastily.”
“Magic doesn’t have such bizarre restrictions. If that were the case, I would have taken the grimoire from you first.”
He was right.
Now that I can read Frauvian fluently, I secretly studied the grimoire thoroughly over the past three years.
As a result, the number of magic spells I can currently handle is 22.
I can now recite all the magic spells contained in Benjamin’s Type I Beginner’s Magic Textbook.
It’s not a restriction.
I slowly continued my thoughts.
Could it be that knowledge of mathematics or natural philosophy is absolutely necessary to use magic?
“Benjamin. As a disciple, I was only learning the necessary content in an accelerated manner.”
“That’s right.”
“In other words, to learn magic studies, one needs foundational knowledge… such as mathematics and natural philosophy.”
“Hmm.”
“One shouldn’t move on to the next stage of magic without mastering those.”
Benjamin nodded.
“You got it somewhat right. It’s not for reasons like you shouldn’t learn it hastily or you’ll go down the wrong path.”
“Then why?”
“You get stuck.”
Slam.
Benjamin harshly closed the slightly open window.
“You hit a wall, and no matter what you do, you can’t go beyond the basics. No matter how hard you try, you can’t understand, and application and development are impossible. You have no choice but to stop there. Most of the people who reach that point don’t have the courage to rebuild the foundation of their studies from the beginning.”
Because they think it’s regression.
Benjamin lowered his gaze and looked at me.
“Well, you don’t have to worry about that.”
“Really?”
“Yeah. But only if you learn this as well.”
Tap.
He tapped the book.
Led by his hand gestures, I looked at the book.
It was very thick and worn out. It seemed to be a book he used when he was young.
In other words, it was a book that was at least several decades old.
“You will now be able to discuss change.”
He declared.
“Time for a quiz. How is scholarship created?”
Benjamin held out two fingers.
“First. A genius appears and writes down a new theory all at once. Second. Several geniuses put their heads together and give birth to a new theory.”
So, a genius has to appear first?
I immediately answered:
“Hmm. Wouldn’t it be the latter?”
“Why did you think that?”
“Because theories fundamentally need to be rigorous. No matter how much of a genius one is, they’ll make mistakes and have loopholes if they do it alone. Because there are individual limitations, I think it’s impossible for one person to create a discipline on their own.”
“That’s a good intuition.”
Having heard Benjamin-style language for a long time, his ‘good’ was a negation.
“Was I wrong?”
Nod, nod.
That means I was wrong.
Then, is the former correct?
It didn’t seem like the golden tower of scholarship was built by the hands of a few geniuses.
While I was thinking that, Benjamin held out a third finger.
“Third. When a pile of papers that a genius wrote down arbitrarily and a pile of papers that several geniuses made while wracking their brains are thrown into a corner, people who need them weave them into one.”
“……”
“This is the answer.”
“But the answer isn’t among the choices?”
“That’s how life is.”
“Heh.”
Whether I gave him a cold look or not, Benjamin steadfastly continued his explanation.
“Calculus is a typical example of that. The digression was long, so let’s get started.”
Benjamin picked up my grimoire to use magic.
As befits a magic scholar and professor, he often utilized magic as a teaching aid.
Snap.
Type I Magic Spell [Point].
The most basic of the basic magic that floats a small point in mid-air.
The point is created by condensing water vapor in the air standing still in the void.
“Now, there is a point in space. I used a point as an example, but you can also change this to a 2D or 3D figure.”
The point changed its shape to an equilateral triangle, a square, a cylinder, etc., and then returned to a point.
“It’s geometry.”
“Yes. But doesn’t it feel a bit dull?”
That’s right.
Benjamin’s [Point] lacked that which is usually included in magic.
“There’s no movement.”
“Then, let’s try moving it. Concentrate. Think about how you would describe this movement.”
Swoosh—
The point flew through the air. At a constant speed.
“What do you think?”
“Couldn’t it be represented as a linear function? With the horizontal axis as time and the vertical axis as distance?”
“It was something you learned in natural philosophy. What about velocity?”
“The quantity obtained by dividing distance by time.”
It’s a formula I clearly remember.
However, Benjamin grinned.
That playful smile was also an expression of negation.
“According to that definition, the slope of the function is the velocity. But the movements in the world we live in are not like this.”
At that moment…
Swoosh—!
The blue point began to fly around in all directions.
Acceleration. Deceleration. Forward and backward.
Rising and falling. Even drawing a spiral.
In that state, Benjamin asked again:
“How should we describe the velocity of the point now?”
“……”
“The slope is good. But how do we find the slope of a curve?”
The movement of the point becomes slow motion.
We can’t find the slope of a curve. Then?
“We divide it.”
At that moment, three graphs appeared in mid-air.
Graphs that are updated in real-time with time as the horizontal axis.
The first is a position vs. time graph synchronized with the point’s position. The second is a velocity vs. time graph. And there was one more.
“The ‘method of endlessly dividing.’ The names for that groundbreaking method were diverse. The limit method or whatever, even the geniuses who invented it had differing opinions. It’s different now. The proof was completed about 80 years ago.
The discipline that describes the movement of all things in the world. To understand it, the first step…
…is the limit.”
Benjamin widened his eyes.
And my mind became distant.
#April 11th. Slightly cloudy.
Winter has ended. It has become warm enough to wander around outside.
On a holiday morning…
At the time when Benjamin would usually be taking a nap, I went out to the yard.
Together with Dorothy.
It must have been about two years ago.
I saw Dorothy swinging a wooden sword while sweating profusely. Around that time, I was complaining of a severe lack of stamina, so I wanted to learn the military’s exercise methods.
That’s how the exercise club started (we take a break in winter because it’s cold), and it was already in its third year.
I’m not sure why we use wooden sword sparring in an era where guns and battleships dominate the world, but it actually helps improve physical strength, so I had nothing to say.
Catch your breath and swing.
Thwack!
A lively sound.
Dorothy easily blocked the wooden sword I swung.
Blade against blade. Even if it’s wood, getting hit hurts a lot, so we had to approach it with a mindset akin to a life-or-death match.
The fact that I haven’t been able to win a single match against Dorothy recently further stimulated my competitiveness.
“I’m coming.”
Dorothy twisted her stance.
Swoosh!
A fierce overhead strike flew through the air.
I raised my blade diagonally to counter it.
An attack with a flow, unlike me, who pushes with force.
It seemed like I could deflect it sufficiently.
“Ugh.”
But I was wrong.
Crack.
The blades entangled, scattering wood dust.
Even though I thought I blocked it well, my wrist felt numb.
The sparring continued.
One round. Another round.
I stuck my tongue out and looked at Dorothy.
A light outfit with just a shirt over her underwear and a peaceful expression.
She always has the same appearance, but when she displays such skills, it seems like Dorothy has also lived an extraordinary life.
The sparring finally ended after exchanging sword strikes several more times.
“Ugh… I’ll rest for a bit.”
“I’ll rest, too. You’ve improved a lot.”
We sprawled out on the lawn without regard for each other.
For the first few months, Dorothy was energetic even after sparring, but now she expends quite a bit of stamina due to my growing physique.
“Phew……”
I took off my top, and Dorothy also unbuttoned her shirt. There was nothing to be embarrassed about after living under the same roof for three years.
At the end of my gaze was Dorothy, who untied her hair and wiped away sweat.
On her slightly exposed white skin were numerous scars.
There were also lacerations and burns. And discoloration.
The most notable thing I noticed was a scar on her left trapezius that looked like it was branded with fire. It was the reason Dorothy favored officer uniforms with minimal skin exposure.
Dorothy rarely talks about herself and dislikes doing so.
So, I had no way of knowing about her past.
However, it was clear that this leisurely life in the duplex house was the life she had longed for.
She must be enjoying her own happiness as a member of the Oslo family.
The same goes for me.
If there is something I desire, I now know that Benjamin will not spare his support for it.
The frugal life of the Oslo family is abundant by my standards. Realistically speaking, continuing to stay in this duplex house would be the best choice.
However, there was one problem.
Humans are not beings who only consider practicality.
“……”
Suddenly, the piggy bank that I had carefully placed in the corner of my room came to mind.
The tin can now contains 80 pounds.
Still.
I want to leave this land.
I want to set foot in the Federation, the home of magic.
Because there is no justification, I only focus on gratefully accepting the kindness, but if a justification were to arise…
My thoughts were cut off there.
“Let’s go inside.”
“Ah. Yes.”
#May 15th. Cloudy.
At the end of spring, when I was flipping through about half of the calculus textbook…
…while pondering ways to apply the usefulness of differentiation to magic…
“Is there an Imperial named Eugene residing in your house by any chance?”
As if to prove that there are no eternal secrets, five Federal Army soldiers knocked on the door of the Oslo family.