A Genius Mage Hides His Origins

39 – Direction

The answer to the questions thrown by the speaker at lectures often contains some form of metaphor.

Especially when it is a question without a clear answer, such as a metaphysical question about the essence of existence or concepts.

Because the purpose is not to obtain an answer to the question.

There is no obvious answer to the question, “What is life?”

Yet the reason the speaker poses such questions is simple. Sometimes, posing questions with metaphors mixed in helps gather the audience’s attention more than straightforward explanations.

“Magic is a vector.”

That’s what I thought. Until now.

I chuckled as I looked at the words on the blackboard.

[ Vector ]

Vector.

A thoroughly academic term that refers to a physical quantity that has both magnitude and direction.

At first glance, one might consider that definition to be complex, but in reality, it is very simple.

To represent nature, two physical quantities are needed. One that simply represents the quantity and one that represents both direction and magnitude simultaneously. For example, the former is mass and the latter is force.

And the quantity that has both direction and magnitude is called a vector.

Let’s leave the detailed definition aside.

“…….”

Why is that coming up now?

I thought there would be metaphorical expressions like solid iron when asking about magic.

It seemed that I wasn’t the only one who felt bewildered, as the classroom gradually filled with a hollow laughter.

One student stood out immediately.

He was a quick-witted student who was chosen first and received a round of applause.

“Professor, I would like to request a correction to your statement.”

“What do you mean?”

“We are freshmen at the Federal College of Magic, and we have already learned basic concepts like vectors.”

“Oh.”

“The reason we couldn’t give a satisfactory answer is that the question was ambiguous. We would like you to correct the fact that your previous statement made us feel humiliated, but…”

The professor smirked.

At first listen, it sounded like a well-reasoned argument. Most of the students remained silent, but a few who seemed to be friends with the professor nodded in agreement.

However.

Even if it was true, it was not a student-like attitude.

We had selected up to seven hundred students for admission, but were there still people like him?

I let out a sigh inwardly.

Louise, with a look of incomprehension, stood in front of the professor, tilting her head.

“Excuse me, are you an auditor? Or a student who came for an external field trip?”

“Uh, no.”

“Otherwise, you wouldn’t be saying such foolish things.”

“……Ugh!”

A calm rebuke.

Louise’s tone was truly professor-like, and all seventy students could hear her muttered words clearly.

The color of Yabsap’s face turned a mix of red and blue, but whether because of that or not, Louise once again stood at the podium.

“I’ll say only two things. First, I don’t include lies or digressions in my lectures. And second, although it’s quite embarrassing to say this with my own mouth.”

Louise lifted her sleeves and opened her lips.

“From now on, those standing before you are university professors. It means they’ve at least obtained a doctoral degree. Don’t mistake them for your school days.”

A silence enveloped the hall.

The excitement that followed the entrance ceremony quickly subsided.

Now, finally feeling like enrolled students of the Federal Magic University.

“Well, enjoy your magical studies. Don’t be too tense.”

In that cheerful silence, Louise laughed refreshingly.

In the next moment, holding a piece of chalk, she began writing on the board, her red hair fluttering.

“The fact that magic is essentially a vector is no joke. At least in classical magic that you’ll learn in your first year.”

[disc]

“For example, the first type of magic, [Disc], I think everyone knows.”

I nodded.

It was the magic that could be considered my specialty, and the foundation of the unique magic [Flowering].

Turning back to us, Louise asked another question.

“What are the conditions for casting [Disc]?”

Silence once again filled the classroom, but this time, its nature was different.

All the students seemed to be seriously contemplating.

I was no exception.

[Disc] conditions.

If it had been me from a few years ago, who only used magic with senses and instincts, I wouldn’t have been able to answer this question. However, now, having received Benjamin’s teachings, I could come up with my own answer.

First, like all magic, you need to set the amount of magical power.

Create the shape of the disc through rotation.

So far, it’s easy.

The problem is how to make the disc into a perfect plane.

I’ve always done this instinctively, so I couldn’t condition it.

Other students also found it challenging and couldn’t articulate an answer.

There is a considerable disparity between actually casting magic and logically explaining its theory.

After a while, Louise spoke up.

“Setting the amount of magical power. And you should know about rotation since you learned it in school. The other element is this.”

Louise drew a slender vertical line on the blackboard and then drew an arrow at the top.

“A vector. To be precise, a normal vector.”

Direction and magnitude.

A line that has both.

I was puzzled.

What does that have to do with making the disc flat?

If you use that vector, you might more easily imagine the axis of rotation, but it won’t help with forming a plane.

It was when I was thinking like that.

“There isn’t just one way to define a plane. And in Type 1 and Type 2 magic, using vectors is the most effective. Think about it.”

[ Ax + By + Cz + D = 0 ]

The equation Louis wrote. It was the equation of a plane in three-dimensional space.

And I knew from experience. That one isn’t useful for actual spellcasting.

“Not intuitive. Perhaps it contains results rather than principles. But vectors are different.”

The next moment, Louis wrote a new equation.

In bold. Using vector notation.

[ n · (r – r₀) = 0 ]

“You don’t need to understand this equation right now. What’s important is that this concise formula is consistent with the principles of spellcasting.”

“…”

Although it was a concept I hadn’t learned yet, as Louis said.

I somehow tried to imagine the principles implied by that equation.

Starting point. The vector n extending from that starting point. The dot product being 0 means the vector n is perpendicular. And that equation refers to all points perpendicular to n, free in both distance and direction…

Ah.

I get it.

That was a definition of a plane, highly friendly to magic, that I didn’t know.

I felt like experimenting with it right away, pulling out my magic book.

Representing my desire, Louis pulled out a magic book.

A professor’s magic book, to be precise.

While students often use lecture materials as magic books for convenience, professors have more freedom in the form of their magic books. It doesn’t even have to be in the form of a book.

The fountain pen in Louis’s hand glowed with a blue light.

“[Disc].”

Shwaaak!

Droplets spin.

The disc, swiftly unfolding within a few seconds, forms a sharp plane that elicits admiration.

Of course, if it had stopped there, it wouldn’t have been too surprising.

The reason my eyes widened was because it started rotating rapidly with its axis tilted at about 45 degrees.

The entire disc begins a choreographed movement.

“Huh, huh?!”

“It can do that…?”

Sighs of amazement can be heard all around.

Louise releases her lips.

“I might not have many opportunities to apply the direction in the Type 2 magic I’m in charge of this time. Mainly dealing with optics, heat, and waves. But I tend to talk about direction in my first class with new students.”

Louise slowly moves her steps, scanning the faces of seventy students. Of course, the disc was still swirling in the middle of the classroom.

“The Federal education system is very well-polished. If you follow the path, you can receive a high-level education.”

However.

“If the path you’ve walked so far has been a single trail, then the path that will unfold before you at the Federal Magic Academy is a crossroad.”

The university is no longer kind.

Even if it is the foremost magical education institution in the Federation, it is not an exception.

They say that only about three out of ten newcomers who walk the path of a magician are successful. No one guarantees the future.

All decisions lie with oneself.

The important things are effort, luck, and will.

“And direction.”

As Louis grinned, the spinning wheel erupted in a handful of water droplets.

Originally, it would have mercilessly dirtied the floor, pulled by gravity.

“Type 2 magic. [Mist].”

Paaak―!

In an instant, it split into thousands, tens of thousands of tiny water droplets, dispersing into the air.

This is Type 2 magic.

Until a few hundred years ago, it was called by names like sacred arts rather than magic, a formless transformation.

“Congratulations on your enrollment. Welcome to the world of Type 2 magic.”

When Louis declared that,

I was genuinely amazed.

And shortly after, I found that almost all students were sighing heavily and wrapping their heads.

Why are they reacting like this?

At the moment I was wondering, a girl next to me mumbled.

“What the hell is that nonsense… life.”

Only then did I realize.

Magic that transcends the complex formulas in the middle and common sense demonstrated before our eyes.

In other words, I’ll learn all of that from now on, and it means they’ll appear in exams.

“Ah.”

Deeeng―

At that moment, the bell rang, signaling the end of the lecture. Why did it feel like the sound was announcing the beginning of a new path of good deeds?

*

Fortunately, the future at the Magic University didn’t seem to be just a series of good deeds.

Today was the second lecture.

[“Understanding Literary Genres.”]

It was a required course for freshmen, said to be a consolation for students overwhelmed by the difficulty of magic studies.

The lecture was held in the auditorium, a place I had visited once before for an exam.

I opened the classroom door with a somewhat lighthearted feeling.

And.

Right after I opened the door and stepped into the classroom, my eyes met with a brown-haired female student.

She was in a wheelchair.