13 – Discussing Change
Contrary to his promise of teaching magic once I mastered Frauovian, Benjamin had postponed formal magic training for three years.
The curriculum for his disciples, based on their ‘magic talents,’ was an unusual arrangement.
From Noble mtl dot com
There must be some reason.
Suppressing questions that had lingered until now.
He must have had his reasons to keep it at this level.
Today, I would finally get the answers.
Flipping through the first chapter of the calculus textbook, Benjamin asked me.
“Why didn’t I teach magic? Do you perhaps know?”
“…I’m not sure. Perhaps there’s a reason one shouldn’t hastily learn magic.”
“There’s no such bizarre restriction in magic. If there were, I would have confiscated your magic books from you.”
It was a valid point.
Now, I could fluently read Pravbyan as well. Over the past three years, I had been secretly deciphering magic books.
As a result, I could now handle a total of twenty-two spells.
They were all the spells contained in Benjamin’s Type 1 Magic Primer – the basics.
It wasn’t a restriction.
I pondered slowly.
What if knowledge of mathematics or natural philosophy was essential to casting magic?
“Benjamin, I only learned what was necessary for an apprentice.”
“Indeed.”
“Meaning, to study magic (受學), foundational knowledge is necessary… such as mathematics, natural philosophy, and the like.”
“Hmm.”
“One shouldn’t proceed to the next stage of magic without mastering those.”
Benjamin nodded.
“You’re mostly correct. It’s not about not learning hastily or straying onto the wrong path or anything like that.”
“Then?”
“You hit a dead end.”
Thud.
Benjamin roughly closed the slightly open window.
“No matter what tactics you use, if you’re blocked by the basics, you can’t go beyond the introductory level. No matter how hard you try, it’s incomprehensible, and there’s no progress in application either. You have to stop there. And those who reach that point mostly lack the courage to go back to the basics of scholarship.”
Thinking of it as regression.
Benjamin looked at me with his gaze sinking.
“Well, you don’t have to worry about that.”
“Really?”
“Yeah. But only if you learn this.”
Thock. He tapped the book.
Drawn by his gesture, I looked at the book.
It was thick and worn. Probably a book he wrote when he was young.
Sounds like a book that’s been around for at least a few decades.
“Now you’ll be able to discuss change.”
He declared.
*
“Quisda. How is scholarship created?”
Benjamin spread two fingers.
“First. A genius emerges and writes down a new theory at once. Second. Several geniuses come together and, through discussions, give birth to a new theory.”
Do I have to be a genius first?
I answered straight away.
“Well, isn’t it the latter?”
“Why did you think that way?”
“Theory needs to be strict by nature. No matter how much of a genius one is, they will make mistakes and have flaws if working alone. Creating academia by oneself seems impossible due to the limits of an individual.”
“That’s a good insight.”
After a long exposure to Benjamin’s language, his ‘good’ was a negation.
“Wrong?”
Nod, nod. It means he was wrong.
So, is the first option correct?
While contemplating this, Benjamin unfolded his third finger.
“Third. If a genius’s crumpled paper and a crumpled paper made by several geniuses are thrown in a corner, the necessary people will weave them into one.”
“…”
“That’s the answer.”
“But the answer isn’t among the choices?”
“That’s just how life is.”
“Huh.”
Whether I became cold-eyed or not, Benjamin steadfastly continued his explanation.
“Calculus is a representative example of that. Since the digression was long, let’s start slowly.”
Benjamin picked up my magic book.
For the purpose of using magic. As a magic teacher, he often utilized magic with textbooks.
Again―
1st Type Magic [Point].
The fundamental of fundamentals, creating a small point in the air.
A point formed by condensing water vapor in the air stood still in the empty space.
“Now. There’s a point in space. I used a point for the example, but you can also change it to a 2D or 3D shape.”
The point changed its shape into equilateral triangles, squares, cylinders, and then returned to a point.
“It’s geometry.”
“Yeah. But doesn’t it feel somewhat dull?”
Indeed.
What typically accompanies magic was absent in Benjamin’s [point].
“There’s no movement.”
“Then let’s make it move. Focus. Think about how to describe this movement.”
Swoosh― the point flew through the air. At a constant speed.
“What do you think?”
“Could we express it as a linear function? Setting time on the horizontal axis and position on the vertical axis.”
“That’s what we learned in natural philosophy. What about velocity?”
“The quantity obtained by dividing distance by time.”
A formula remembered clearly.
However, Benjamin chuckled mischievously.
That playful smile was also a gesture of denial.
“If velocity is as defined, then the slope of the function represents velocity. But that’s not how motion works in our world.”
In that moment.
Thump―!
Blue dots started bouncing in all directions.
Acceleration. Deceleration. Forward and backward.
Ascending and descending. Finally, forming a spiral.
In that state, Benjamin asked again.
“How should we describe the speed of the dot?”
“……”
“The slope looks good. But how do we calculate the slope of the curve?”
The movement of the dot slowed down.
We cannot calculate the slope of the curve. Then what?
“We can divide it.”
In that moment, three graphs appeared in the air.
Real-time graphs with time as the x-axis, updating their values synchronously.
One is the position graph synchronized with the dot’s position. Another is the velocity graph. And there was one more.
“The method of ‘endlessly dividing.’ The name for that revolutionary approach was diverse. Some called it the method of ratios, and there were differing opinions among the geniuses who invented it. But not anymore. It was proven eighty years ago.”
“The study that describes the movement of all things in the world. The first step.”
“It is a limit.”
Benjamin opened his eyes wide.
My mind became distant.
# April 11. Slightly cloudy.
Winter has come to an end. The weather has become pleasant enough to spend time outdoors.
On a holiday morning.
I went out to the yard at the time when Benjamin usually falls into a nap.
With Dorothy.
It was about a year ago.
I watched Dorothy swing her wooden sword, dripping with sweat. At that time, I was complaining about severe physical fatigue, longing to learn military exercises.
The exercise club, which started like that (resting in winter due to the cold), was now celebrating its third year.
I don’t know why the method of swordplay, amidst a world dominated by guns and battleships, was chosen. But since it actually helped improve physical fitness, there was nothing to say.
Breathe steadily, and swing.
Thwack!
A cheerful sound.
Dorothy easily blocked the swing of my sword.
Blade against blade. Even if they are made of wood, getting hit hurts a lot, so one had to approach it with a mindset comparable to a matter of life and death.
Lately, the fact that I couldn’t win against Dorothy in a match fueled my competitive spirit even more.
“I’m coming.”
Dorothy twisted her posture.
Swoosh!
A sharp uppercut cut through the air.
I intercepted the blade diagonally.
A flowing attack, unlike my forceful pushing.
It seemed like I could easily deflect it.
“Kreuk.”
No, that wasn’t the case.
With a sharp clank, our blades tangled and splinters of wood scattered.
I thought I had blocked it well, but my wrist felt numb.
The duel continued.
One strike. Another strike.
I glanced at Dorothy, who had her tongue sticking out.
She wore only a light outfit—a shirt over her underwear—and had a calm expression.
It was the same as always, but when she showed off these skills, it seemed like Dorothy had lived an extraordinary life.
After exchanging sword strikes several times, the duel finally came to an end.
“Ugh… Let’s take a break.”
“I’ll rest too. You’ve gotten stronger.”
We both lay down on the grass with nothing else to do.
In the first few months, Dorothy was still energetic after each duel, but now, due to my growing physique, she had started to expend some stamina.
“Phew…”
I opened a water flask and Dorothy unbuttoned her shirt. There was nothing to be embarrassed about after spending three years under the same roof.
At the corner of my vision, I saw Dorothy letting down her hair and wiping away the sweat.
There were numerous scars on her pale white skin, peeking through.
Affection and scars. And a change in skin color.
The masterpiece is the scar resembling an earthquake near the left collarbone. Dorothy favored conquering officers with minimal skin exposure.
Dorothy rarely spoke of herself and didn’t want to.
So, I had no way of knowing her past.
But it was clear that this leisurely life in the duplex was the life she desired.
As a member of the Oslo family, she was seeking her own happiness.
From Noble mtl dot com
I was the same.
If there was something to hope for, Benjamin wouldn’t spare his support.
The modest life of the Oslo family, from my perspective, was abundance itself. In practical terms, staying in this duplex was the best choice.
However, there was one problem.
People aren’t just beings evaluated practically.
“….”
Suddenly, I thought of the piggy bank placed in my corner.
A cast-iron piggy bank with eighty pounds.
Still.
I want to leave this land.
I want to set foot in the Federation, the magical homeland.
I’ll focus on receiving favors since there’s no justification, but if a justification arises…
Morality stopped there.
“Let’s go in.”
“Ah, yes.”
May 15th. Overcast.
At the end of spring, flipping through the pages of a calculus textbook.
It was a day when I pondered on how to apply the usefulness of derivatives to magic.
“Excuse me, is there a person named Eugene from the Empire residing here?”
Five soldiers from the Federal Army knocked on the door of the Oslo family, as if trying to prove that eternal secrets don’t exist.
