Meet the principal

"This paper..."

Director Percival did not finish reading it. In fact, when he saw the title and author of the paper, he had already guessed a lot.

Percival had read Siris's paper carefully ten years ago, when it was suggested by his mentor Bodordo at a seminar.

Percival still remembered that it was an afternoon. When he saw this paper, his whole body trembled as if electricity was spreading. Percival could not believe that Sirius, who was similar to himself, had reached such a level.

While his peers were still worrying about the dishes for dinner and the weather tomorrow, Sirius' eyes had already drifted to the distant stars.

But this paper has a fatal flaw, which is the imaginary number established by Sirius.

There is no doubt that in the real world, imaginary numbers do not exist. This is a purely virtual concept that is not only difficult to understand, but also cannot have any connection with reality.

At that seminar, Bordo also expressed the same opinion. Although the formula in the paper was so simple and elegant, it was meaningless.

At this moment, Percival couldn't believe that this paper appeared in front of him again.

It was also brought out by a young and talented mage at the same discussion, and Percival felt in a trance.

Just when Percival was lost in thought, Roger had already finished reading the paper first.

He put it down and spoke.

"Absurd, absolutely ridiculous!"

Obviously, he did not agree with the existence of imaginary numbers and thought it was fanciful.

"Imaginary numbers? Square equals -1? What on earth was the person who wrote this paper thinking?"

Following Roger's words, several others gradually completed reading the paper.

Big Bear Bear was silent. He was not very good at mathematics and did not dare to express his opinions at will.

Hannah glanced at Percival and continued.

"This is a purely mathematical paper, and the concepts in it seem to be forcibly established just to solve problems. To be honest, I can't think of the meaning of this imaginary number.

"

Igor heard the speeches of several people, glanced at Reiner, and then spoke slowly.

"Well, I think this paper may be better reviewed by a mage who specializes in this area. Some of the mathematical tools are beyond my knowledge."

Savros shook his head and did not express his thoughts.

Seeing the looks of everyone present, Reiner was naturally prepared.

Ten years ago, no one could accept the existence of imaginary numbers. Ten years later, how could it be so easy to change people's views.

He stood up and spoke.

"Everyone, I am sure you are all confused by the imaginary numbers in this paper, thinking they are numbers that have no meaning in the real world."

"Is not it?"

Roger asked rhetorically.

"If I have one apple, that is normal and reasonable, but if I have i apples, what does the apple in my hand look like? Reiner, can you show it to me?"

He used a very realistic example, which made Hannah nod beside him.

"Of course I can't show it to you, Lord Roger."

Faced with Roger's almost sarcastic question, Reiner answered unhurriedly.

"Numbers that cannot exist in reality have no meaning. Even if the theory about imaginary numbers is complete, it is just a calculation on paper. What connection does it have with the reality we live in?"

Roger continued, saying that he was not targeting Reiner, but several others, hoping to seek approval.

“The reason why not many people invest in the study of mathematics is not only because they cannot get feedback from the world, but also because pure digital games can easily become illusory theories like imaginary numbers, and become a trap of mathematics for the sake of mathematics. .”

His words made everyone think deeply. Indeed, if theory cannot be used to guide practice, then no matter how sophisticated the theory is, it will be useless. The development of magic over the years has always been to seek solutions after encountering problems, rather than wasting energy to explore. Practical knowledge.

This is exactly the pragmatism of the mage, the principle of efficiency first.

Everyone here looked at Reiner, wondering how Reiner would explain.

"Lord Roger, I think I need to educate you on mathematics."

Reiner walked to the blackboard on the side of the conference room and picked up the chalk.

"W-what did you say?"

Roger was irritated by Reiner's attitude. He wanted to stand up, but reason still restrained his behavior.

Reiner smiled, drew a horizontal line on the blackboard, and typed an arrow.

"This is the number line we often use in mathematics. Now I mark three points here. -1, 0 and 1. These are integers and negative numbers. The most basic content, even a six-year-old child knows it. "

The somewhat confused judges watched Reiner continue to mark on the number line. He took half the value between 0 and 1 and marked 0.5.

"Integers cannot fill the entire coordinate axis, because there are actually decimals on it. There are countless decimals between 0 and 1, but in fact, up to this point, the number axis is still not filled."

Reiner drew a square on the side, connecting its diagonals.

"The root number two is an infinite non-repeating decimal, that is, an irrational number. It also exists on the number axis. In fact, at this point, rational numbers and irrational numbers have filled the entire number axis."

After listening to Reiner's words, Roger spoke.

"Now that the entire number line is filled, where are the imaginary numbers? Isn't it on this blackboard?"

He wanted to tease Reiner, but unexpectedly Reiner nodded.

"Of course imaginary numbers do not exist on this number line, but at least they exist on this blackboard."

"What?"

Even Percival couldn't help but question. He glanced at the number line again. Rational numbers and irrational numbers had filled the entire number line. Any number on it should be included.

And that certainly doesn't include imaginary numbers.

"Imaginary numbers, here."

Reiner picked up the chalk and marked a dot above 0 on the number line.

"Are you kidding me?"

Roger stood up. He felt that Reiner was deliberately mocking him. He was about to step forward to drive the young mage off, but was stopped by Bear.

"Just hear him out, Roger."

Bear noticed something and looked at Reiner.

"The position of the imaginary number i is exactly above the number axis, one unit length away from the origin."

Reiner's words sounded a bit bizarre at first, but Igor's mind raced. Soon, in his field of vision, the number axis became extremely small, and the entire blackboard appeared in front of his eyes.

"Yes, a simple number axis cannot represent all points on the plane, but if you add an axis, you can establish a coordinate system to express all points."

Igor suddenly realized that the rectangular coordinate system has been deeply rooted in the hearts of the people. People have long accepted the use of two numbers to represent the coordinates of a point, and the existence of imaginary numbers is separated from all the actual numbers in the past, broadening the world a hundred times. A coordinate axis!

Such a simple and clear concept, I didn’t expect that none of the mid-level mages present had thought of it before Reiner’s demonstration.

Imagination limits their knowledge!