"This paper ......"

Director Percival didn't finish reading it, in fact, when he saw the title and author of the paper, he had already guessed a lot.

Percival had carefully read this paper by Siris ten years earlier, at a symposium that was proposed by his mentor Portoardo.

Percival remembered that it was an afternoon, and when he read the paper, his whole body trembled like an electric current, and Parcival couldn't believe that Siris, who was about his own age, had reached such a level.

While his peers were still worried about dinner dishes and tomorrow's weather, Siris's eyes had drifted to the distant stars.

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

There is no doubt that in the real world, imaginary numbers do not exist, it is a purely virtual concept, which is not only difficult to understand, but also has no connection to reality.

At that symposium, Puerdo's same opinion was made, and although the formula in the paper was so concise and elegant, it didn't make sense.

At this moment, Percival could not believe that in front of him, this paper appeared again.

It was also at a seminar, also brought out by a young and gifted mage, and Percival felt a trance.

Just when Percival lost his mind, Roger had already finished reading the paper first.

He put it down, then spoke.

"Ridiculous, simply ridiculous!"

Obviously, he also disagrees with the existence of imaginary numbers, and finds it whimsical.

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

With Roger's words, several others gradually finished reading the papers.

Big Bear Bell was silent, he was not very good at math and did not dare to express his opinions at will.

Hannah glanced at Percival and continued.

"It's a purely mathematical treatise, and the concepts in it seem to be forced to solve problems only, and honestly, I can't think of any point in this imaginary number."

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

"Well, I think this paper might need to be reviewed by a mage who specializes in this area, and some of the mathematical tools are beyond my knowledge."

Safros shook his head, not saying what he thought.

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

Ten years ago, no one could accept the existence of imaginary numbers, and ten years later, how can it be so simple to change people's opinions.

He stood up and spoke.

"Guys, I'm sure you're all confused by the imaginary numbers in this paper, thinking that they are numbers that don't make sense in the real world."

"Isn't it?"

Roger asked rhetorically.

"If I have an apple, that's normal and reasonable, but if I have an apple, then what does the apple in my hand look like? Reiner, can you show me? ”

He used a very realistic example to make Hannah next to him nod his head again and again.

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

Reiner replied unhurriedly in the face of Roger's almost mocking question.

"Numbers that cannot exist in reality have no meaning of existence, even if a set of theories about imaginary numbers are complete, but they are just calculations on paper, what is the connection with the reality of our lives?"

Roger continued, not against Reiner, but at several others, hoping to seek approval.

"The reason why not too many people put the effort into mathematics is not only because they can't get feedback from the world, but because pure number games can easily become ethereal theories like imaginary numbers, and become a trap for mathematics for mathematics's sake."

His words made everyone ponder, indeed, if the theory cannot be applied to guide practice, then the most exquisite theory is useless, and the development of magic over the years has always been to find solutions after encountering problems, rather than wasting energy to explore knowledge that has no practical meaning.

This is precisely the principle of pragmatism, efficiency first.

Everyone in the room looked at Reiner, wondering what Reiner would explain.

"Lord Roger, I think I need to educate you about math."

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

"Y-What did you say?"

Roger was enraged by Reiner's attitude, and he tried to stand up, but reason restrained him.

Reiner smiled, drew a horizontal line on the board, and punched an arrow.

"This is the number line that we often use in mathematics, and now I'm marking three dots here.-1, 0 and 1, which are integers and negative numbers, the most basic content, even a six-year-old knows it."

Some of the unexplained judges watched Reiner continue to mark on the number line, taking half of the time between 0 and 1 and marking the word 0.5.

"Integers can't fill the entire axis because there are actually decimals on it, and there are countless decimal places between 0 and 1 alone, but in reality, the number line is still not filled up here."

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

"Root number two, this is an infinite non-cyclic decimal, that is, an irrational number, it also exists on the number line, in fact, at this point, the rational number and the irrational number have filled the entire number line."

After listening to Reiner's words, Roger spoke.

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

He wanted to tease Reiner, but he didn't expect Reiner to nod.

"The imaginary number certainly doesn't exist on this number line, but at least it exists on this blackboard."

"What?"

Even Percival couldn't help but question, he glanced at the number line again, the rational number and the irrational number had filled the whole number line, and any number on it should be included.

And that, of course, does not include imaginary numbers.

"Imaginary numbers, here."

Reiner picked up the chalk and hit a dot above the 0 of the number line.

"What are you kidding?"

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

"Hear him out, Roger."

Bear Bear sensed something and looked at Reiner.

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

Reiner's words sounded bizarre at first, but Igor's mind was racing, and soon, in his field of vision, the number line became extremely small, and the whole blackboard appeared before his eyes.

"Yes, a simple number line can't represent all the points on the plane, but if you add an axis, you can establish a coordinate system and represent all the points."

Igor had an epiphany that the Cartesian coordinate system had been deeply rooted in the hearts of the people, and people had long accepted the use of two numbers to represent the coordinates of a point, and the existence of imaginary numbers was a coordinate axis that was detached from all the actual numbers that existed in the past and expanded the world by a hundred times!

With such a simple and clear concept, I didn't expect that before Reiner's demonstration, none of the mid-level mages present would think of it.

Imagination limits their cognition!