Genius Wizard Conceals His Origins

Usually, the answer to a question posed by a speaker contains some kind of metaphor.

Such metaphors are evident when responding to a question without a clear answer, for example, a metaphysical question asking about the essence of existence or similar abstract concepts.

This is because the purpose is not to get an answer to the question.

There’s no obvious answer to a question like ‘What is life?’

Yet, the reason speakers ask such questions is simple. Sometimes, asking a question mixed with metaphor helps to draw the audience’s attention more than a direct explanation.

“Magic is a vector.”

That’s what I thought. Until now.

I let out a small laugh as I looked at the writing on the blackboard.

[Vector]

Vector.

A strictly academic term referring to a physical quantity that has both magnitude and direction.

At first glance, one might consider its definition complex, but in fact, it’s very simple. [Only on Galaxy Translations! / Axiomatic]

Two physical quantities are needed to represent nature. One that simply represents the quantity or its magnitude, and one that represents both direction and magnitude simultaneously *1. For example, one example of the former is mass, and an example of the latter is force.

The latter quantity, which has both magnitude and direction, is called a vector.

Setting aside the detailed definition…

“……”

Why is this coming up now?

When asked what magic is, I was certain a metaphorical expression would appear.

I wasn’t the only one feeling bewildered; the classroom gradually began to fill with helpless laughter.

Soon, a student raised their hand.

It was the shrewd-looking student who was first called on and rebuked.

“Professor. I request a correction to your statement.”

“What do you mean?”

“We are new students at the Federal University of Magic, and we’ve already learned basic concepts like vectors.”

“Oh?”

“We couldn’t give a proper answer because the question was vague. I request a correction regarding the contempt you showed us with your earlier statement, but…”

The shrewd one smiled slyly.

It might sound like sound reasoning if you just listen casually. While most students remained silent, a few who seemed to be the shrewd one’s friends sided with him, raising one corner of their mouths.

However…

Even if it might be correct, it was by no means a student-like attitude.

Even after narrowing it down to 700 entrants, are there still people like this?

As I was inwardly sighing…

Professor Louise stood in front of the shrewd one with a puzzled expression, tilting her head.

“Are you perhaps an auditing student? Or a student here for an external observation?”

“N-No, I’m not.”

“Otherwise, there’s no way you could say something so foolish.”

“…Ugh!”

A calm rebuke.

Louise’s voice was truly professorlike, so all 70 students could clearly hear that self-mutter.

The shrewd one’s face turned red and blue, but regardless, Louise stood on the podium again.

“I’ll say two things. First, I don’t add false words or digressions in my lectures. And second, this is quite embarrassing to say with my own mouth, but…”

Louise rolled up her sleeves and opened her lips.

“Those who will stand before you from now on are university professors. It means they at least hold a Ph.D. Don’t confuse this with school.”

The area was enveloped in silence.

The excited atmosphere right after the entrance ceremony instantly subsided.

Now, it finally feels like we’ve become students of the Federal University of Magic.

“Now, it’s time for an exciting magic studies lesson. Don’t look so deflated.”

In that brisk silence, Louise laughed cheerfully.

The next moment, gripping the chalk anew, she began writing on the board, her red hair fluttering.

“It’s not a joke that magic is a vector. At least, in the classical magic studies you’ll learn in your first year.”

[Disc]

“Let me give you an example. I think you all know the Type I Magic spell [Disc].”

I nodded.

It was a spell that could be called my specialty and the basis for my unique spell, [Flowering].

Louise turned towards us and asked another question.

“What are the conditions needed to cast [Disc]?”

Silence fell over the classroom again, but this time, its nature was different.

All the students seemed to be thinking seriously.

I was the same.

The conditions for [Disc]…

If it were me from a few years ago, who only used magic by sensation and instinct, I wouldn’t have been able to answer this question, but now, having received Benjamin’s teachings, I could derive my own answer.

First, as with all magic, you need to set the amount of mana input.

Create the disc shape through rotation.

Up to here is easy. [Only on Galaxy Translations! / Axiomatic]

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

Since I’ve always done this part instinctively, I couldn’t conditionalize it.

Other students also couldn’t raise their hands to give an answer.

There’s a considerable gap between actually casting magic and explaining its theory coherently.

After a while, Louise opened her mouth.

“You should know well about setting the amount of mana input and rotation, as you’ve learned that in school. The remaining one element is this.”

Louise drew a long vertical line on the blackboard, then drew an arrow shape at its top.

“It’s a vector. More precisely, a normal vector.”

Direction and magnitude.

A line that has both.

I was puzzled.

What does that have to do with making the disc a plane?

If you use that vector, it might be easier to imagine the axis of rotation, but it wouldn’t help in forming the plane.

While pondering on that…

“There’s more than one way to define a plane. And in Type I and II magic, using vectors is most effective. Think about it.”

[Ax + By + Cz + D = 0] *2

The equation Louise wrote. It was the equation of a plane in 3D space.

I knew from experience that this couldn’t be used in practical spellcasting.

“It’s not intuitive, is it? You could say it contains the result, not the principle. But vectors are different.”

The next moment, Louise wrote a new equation.

Using bold font, that is, vector notation.

[n · (r – r₀) = 0] *3

“You don’t need to understand this equation at all right now. The important thing is that this concise equation corresponds to the principle of magic casting.”

“……”

As Louise said, it was a concept we hadn’t learned yet.

But I tried to imagine the principle this equation implied.

Starting point. Vector n extending from that starting point. The dot product being 0 means it’s perpendicular to vector n. And that equation must refer to all points that are perpendicular to n and free in both distance and direction… *3

Ah.

I’m getting a feeling.

This was a way of defining a plane that I didn’t know, one that’s very magic-friendly…

…to the point where I wanted to take out a grimoire and experiment right away!

As if representing my wish, Louise took out a grimoire.

It’s a professor’s grimoire, no less. [Only on Galaxy Translations! / Axiomatic]

Unlike students who use lecture materials as grimoires for convenience, professors at this level have freedom in the form of their grimoires. It doesn’t even matter if it’s not in book form.

The fountain pen in Louise’s hand glowed blue.

“[Disc].”

Whoosh!

A water droplet rotates.

The disc that spread out nimbly in about five seconds formed a sharp plane that was admirable.

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

The reason I opened my eyes wide was because its axis of rotation started rotating rapidly while tilted about 45 degrees.

The entire disc begins a precession movement. *4

“Wh-What?!”

“That was possible…?”

Exclamations burst out here and there.

Louise opened her lips.

“There may not be many occasions to apply direction in the Type II magic I’m in charge of this time. We’ll mainly deal with optics, heat, waves, and such. But whenever I’m in charge of the first class for new students, I tend to talk about direction.”

Louise slowly moved her steps, scanning the faces of the 70 students. Of course, the disc was still spinning in the middle of the classroom.

“The Federation’s education system is very well-established. You can receive high-quality education just by following the path.”

But.

“If the path you’ve walked so far was a single trail, the path that will unfold before you at the Federal University of Magic is a crossroads.”

The university is no longer kind.

Even the Federation’s top institution for magic studies is no exception.

They say that among new students, at best, only about 30% will walk the path of a magic scholar. No one guarantees the future.

All decisions depend on yourself.

What’s important is effort, luck, will…

“…And direction.”

As Louise grinned, the wildly rotating disc turned into a handful of water droplets.

They would have helplessly dirtied the floor if pulled by gravity.

“Type II magic. [Mist].”

Whoosh—!

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

This is Type II magic.

The formless miracle that was called by names like divine arts rather than magic until hundreds of years ago.

“Congratulations on your admission, and welcome to the world of Type II magic.”

When Louise declared this…

I was genuinely amazed.

A moment later, I found that almost all the students were sighing deeply and clutching their heads.

Why are they like this?

As I was wondering, a female student next to me muttered quietly.

“What the hell was all that… life.”

Only then did I realize.

The equations that abounded in the middle and the magic demonstrated before our eyes that transcends common sense…

In other words, we’ll learn all of that from now on, and it will appear on tests.

“Ah.”

Ding dong.

Just then, the bell signaling the end of the lecture rang. Why did it feel like a bell announcing the beginning of a new path of hardship?

Fortunately, it seemed that the future at the university wouldn’t be just a continuous hardship.

My second lecture class for today is…

[Understanding Literary Genres].

A liberal arts course that all new students must take. It had a reputation for being a comfort to students overwhelmed by the difficulty of magic studies.

The lecture is held in the grand hall, which I had visited once for the entrance exam.

I opened the classroom door with a somewhat lighter heart.

And.

Right after entering the classroom, I made eye contact with a chestnut-haired female student.

She was in a wheelchair.

T/N

As the latter is defined to be a vector, it should be known that the former is known as a scalar. Scalars are physical quantities only described by magnitude, such as time, length, mass, distance, and temperature, among others.
This equation is a common (and straightforward) way to define a plane in 3D space. This general form can be expressed in intercept form, x/a + y/b + z/c = 1, where a, b, and c, are the x-, y-, and z-intercepts of the plane.
This equation represents the vector equation of a plane. Algebraically, the dot product (or scalar product) of two vectors, say vectors A and B, is the product of their respective magnitudes, |A| and |B|, and the cosine of the angle between them. By definition, if the dot product of two vectors is 0, and neither one of the two vectors are 0 vectors themselves, this implies that they are perpendicular as the angle between them must be 90° to result in a product of 0, as shown here: A · B = |A| |B| cos(90°) = |A| |B| * 0 = 0. From the equation, [n · (r – r₀) = 0], some normal vector n is perpendicular to the vector r – r₀. The second vector is just a fancy way of saying the distance from one starting point r₀ to any point r. Thus, a plane can be defined by the set of all terminal points of vectors originating from a chosen “starting point,” which are all perpendicular to some normal vector originating from the same “starting point,” regardless of their distance from the “starting point.”
A precession movement refers to the change in the orientation of the rotational axis of a rotating body. Assuming that the disc is originally horizontally flat, parallel to the ground, changing its axis of rotation from a perpendicular 90° to a 45° angle implies that such a movement occurred.

Please feel free to correct me in the comments! I will edit the T/Ns accordingly and credit those who point out any errors if there are any corrections to be made.