Master Tongtian

House of Thrandis.

Bathroom on the second floor.

Thrandis lay in the tub, eyes closed comfortably, murmuring words in his mouth.

"My dearest apprentice, you must remember that imagination is always the basis of all magic. Concreteness and geometry are all to assist imagination, not imagination itself."

Beside the bathtub, Rosen's mentality has changed a lot.

Yesterday, he was full of longing, and the sheep in his heart desperately wanted to escape from the sheepfold.

Now, just thinking that the woman lying in front of him might be a cruel murderer made him feel cold in his heart.

Let alone Qinian, staying calm is already the limit.

But his pursuit of magic remained unchanged. When he heard Thrandis's words, his thoughts were involuntarily guided.

After thinking carefully, he said: "Teacher, what you mean is that the hand of the mage does not necessarily have to be imagined as a hand."

"correct."

Thrandis nodded in approval and turned over in the tub again. The snow-white mountains were looming among the rose petals.

"As a basic sleight of hand, the reason why the mage's hand is easy to master is because it uses the hand as a concrete representation that is deeply embedded in the soul."

"But if you think about it, to move an object from one place to another, do you really need to imagine an entire arm?"

As soon as these words came out, Rosen felt a bright light suddenly flash in his mind, which instantly split the preconceived notions in his mind into pieces.

‘Moving an object does not require hands. The essence is that an external force does work on the object! ’

‘To put it more fundamentally, it’s because of the transfer of energy! ’

‘Ah~~The evil teacher really does harm to people! That guy Cyrus said half of what he said, which got me stuck in the mud. ’

At this moment, Rosen even had an idea in his mind. Even if Thrandis was really a murderer, as long as she didn't harm him, she would still be his most respected magic teacher.

Feeling that the towel stopped rubbing, Thrandis turned his head and looked at Rosen with lazy eyes. He saw him standing there blankly, his eyes blank, and he didn't speak, waiting patiently.

After a long time, she felt the towel on her body move again, and then she asked: "My dear apprentice, tell me what you think, and let me see if I have gone astray."

The last sentence reminded Rosen and made him give up the idea of ​​hiding it.

Of course, he would not speak directly about geophysics.

After carefully organizing his words, he began to tell his thoughts.

"Teacher, I just thought, there are countless ways to move an object, far more than just using hands, strong wind, water flow, or even just moving the object in the air, it will move."

"I guess there must be a commonality among them. And this commonality is the most direct and effective way to imagine the hand of the mage."

Hearing this, the laziness on Thrandis's face disappeared, and his eyes stared directly at Rosen's face.

After looking at it for a long time, she suddenly sighed: "I never expected that I would hear the most outstanding words of wisdom in the world from a 15-year-old magic apprentice."

‘Wow~’

She stood up from the tub and took Rosen into her arms regardless of his resistance.

"My dearest apprentice, don't struggle, let the mentor feel your presence. After all, as you continue to grow, such opportunities will become less and less."

There was no desire at all in her tone, only sighs.

Rosen stopped struggling: "Mentor, I have to remind you that not everyone likes this almost crude way of expressing feelings."

"Hehe~ As long as you are still my apprentice, you have to endure this."

Thrandis let go of Rosen and lay back in the tub.

"The 'commonality' you just mentioned is the goal that all mages have been pursuing in the past hundred years."

"Unfortunately, we still haven't found a convincing statement so far. We can only try to get as close to this goal as possible."

Rosen was slightly startled and couldn't help but think to himself: "This commonality is the transfer of energy. Is it so difficult to discover?"

But when I thought about it again, I no longer found it strange.

Even on Earth, it took thousands of years for humans to evolve modern science since civilization began.

In this different world with magic, subjectivity and objectivity are extremely unclear, and idealism and materialism are mixed together.

Especially the observer effect is ridiculously strong.

As long as a mage with magic power observes the target intently, he will definitely cause great interference to the target.

Trying to extract the basic laws of the material world from chaos is just as difficult as it is on Earth.

"Teacher, where is the progress now?"

Thrandis smiled softly: "Didn't you see it?"

Rosen was startled, and then he thought: "You mean, precise geometry?"

"How clever."

Thrandis couldn't help but admire: "From ancient times to the present, mages have been pursuing the most efficient way to use mana."

"This process is also a process of gradually eliminating daily experience and entering a purely logical world of thinking."

"So, moving an object also changes into imagining the trajectory of the object's movement."

As he spoke, a rose petal floated up from the pool and drew a standard circle in the air.

"Do you understand, my dearest apprentice?"

Rosen nodded slowly, and at the same time his mind moved, and another petal floated up, drawing a standard equilateral triangle in the air.

Thrandis encouraged: "Can it be more complicated?"

Rosen thought for a moment and replaced the equilateral triangle with a parabola.

“From straight lines to curves is a huge progress, but can it get any more complicated?”

Rosen immediately replaced the parabola with the sinusoidal oscillator of a trigonometric function.

Thrandis's eyes lit up: "Aha~ Is it a water wave? It's more interesting now."

Rosen nodded, his thoughts moved slightly, and the amplitude and phase of the sine wave continued to change, just like water waves flowing forward.

Thrandis watched and became interested, trying to imitate water waves with petals.

But soon, she discovered that she could indeed imitate water waves, but they were far less stable than Rosen's, and the curve transition was far less natural and precise than his.

She stopped and tilted her head to look at Rosen, a trace of doubt flashing in her eyes.

"You discovered a mathematical tool for describing water waves, right?"

Only by describing geometry with numbers can imagination be truly standardized.

Because of this, Thrandis can draw a perfect circle, and because there is no mathematical method to describe water waves, she cannot do the same thing as Rosen.

Rosen didn't hold back because it wasn't difficult.

This world may not have appeared yet, but with the current mathematical foundation, the sinusoidal curve described by trigonometric functions is already ready to emerge, and it is only a matter of time before it is discovered.

"Teacher, when I was reading "Principles of Exact Geometry", I accidentally discovered that when a trigonometric number is expanded in a cross mark, it will become a water wave. By modifying some of the parameters, the intensity and phase of the water wave can be modified at will.

"Well, I came up with the word phase myself, which means the time when the wave peak appears."

Thrandis didn't speak. She fell into silence, her eyes blank, obviously thinking about Rosen's words.

After a while, she woke up and looked at Rosen with a hint of shock in her eyes.

"Rosen, I don't know what words to use to describe you. Please forgive me for my frivolity in the past."

"Oh, no, this is an important result and has very broad application prospects. I must write a magic paper right away!"

She no longer cared about bathing and floated out of the tub.

The newly bought bath towel quickly flew to her side, and she quickly wiped away the water stains on her body. At the same time, she stretched out her arms and slipped into the newly bought bathrobe. The bathrobe seemed to be alive, 'automatically' fitting her body, and 'automatically' The belt is tightened, and the quill and wood grain paper are already on the table.

After she sat down, the quill jumped up as if it were alive and wrote quickly on the paper.

At the same time, another towel flew over and rubbed her thick, fiery red hair that was still dripping with water.

The whole process was smooth and smooth. At the peak, more than 10 lines of operations were displayed at the same time.

Not to mention, in every line of operation, the use of the mage's hand has reached a natural level.

It's like she is the master of this world.

Seeing such a level, the little pride that just arose in Rosen's heart immediately disappeared.

He secretly warned: "Rosen, Rosen! Do you want to raise your tail after a small achievement?" You are still far away! ’

After writing for a while, she turned back and said, "Rosen, do you want to be the first author of the paper?"

Rosen shook his head without hesitation.

"No, no, no, mentor, my only contribution is to provide some inspiration, but my shallow knowledge of magic and narrow experience are not enough to write a formal magic paper. So, don't mention my name."

He already knows that mathematics is just a tool to assist in spell casting. The real value lies in how to apply mathematics in spells.

And about this, he was still in a state of partial knowledge.

Thrandis thought about it seriously and nodded in agreement: "Indeed, you are too young and too weak to bear this reputation."

After writing a few more sentences, she pointed to the tub: "Clean them up, then leave here, and don't make any noise that may affect my thoughts."

"Teacher, do you want to deliver food?"

"want!"

"Yes, mentor."

Rosen was doing the aftermath work silently. When everything was cleared, he was about to go downstairs when another voice came from behind him.

"My dear apprentice, your study plan for the evening remains unchanged, so don't forget it."

"Yes, mentor."

He was very happy and left the room on the second floor briskly.

As I closed the door, a thought crossed my mind.

"Can such a powerful mentor really be a perverted murderer?"

"Based on the information I have observed now, it is absolutely impossible."

"But in order to protect themselves, murderers are usually very good at disguising themselves. It is common for them to behave the same way in front of others but also behind others."

"In addition, the mentor is acting crazy. It seems that he has a dual personality at the moment, but maybe there is a third personality hidden?"

"However, the rabbit won't eat the grass near the nest, so I should be safe. Let's continue to observe."

Returning to his small room, he began to seriously experiment with his new knowledge.

For the rest of the time, the two masters and apprentices, one was busy writing on the second floor, and the other was studying spells on the first floor, without interfering with each other.