"This ......"

Roger was able to advance to the middle rank, so he could naturally understand Reiner's meaning.

If imaginary numbers are used instead of longitudinal coordinate axes, then the numbers can be simply written in the form of X+Xi, and at the same time, the points expressed in this form can be directly applied to the conventional four-rule operation without the need to use complex coordinate calculations.

As we all know, the Cartesian coordinate system is closely related to the spell model, and the coordinate and vector calculation is a compulsory course for every mage.

More importantly, the introduction of imaginary numbers directly expands the level of the whole world, just like the number line on the blackboard and the whole blackboard, which one is more extensive, it is self-evident.

"But it's just a math game, and even if there are no imaginary numbers, the coordinate calculations can still be done, and it's really strange to use imaginary numbers to explain the equations of motion."

Hannah questioned that it was true that imaginary numbers were used to make it easier to model spells, but magic should avoid introducing unnecessary elements, and that imaginary numbers were superfluous concepts in this case.

"Guys, I'm sure you all know the Newington-Holland equations, right?"

Instead of answering Hannah's question, Reiner asked in reverse.

"Of course, you know, this is a system of four equations that describe the electromagnetic field, and your Excellency proves that light is an electromagnetic wave."

Roger replied, a little curious as to why Reiner had suddenly brought it up.

"What are you trying to say?"

"I mean, if we were to substitute the concept of imaginary numbers into these four equations, what would we get?"

Reiner then began to write formulas on the blackboard, which he skillfully translated into imaginary forms.

There is no doubt that the Newington-Holland equation with imaginary numbers is more concise and easier to understand.

"I think you've all seen the formula in the paper, and if we take this formula into the equation and calculate it, we can find that the sinusoidal electromagnetic field that changes with time can be directly transformed into exponential form, and at the same time, the exponential form of the equation can also be expanded into the form of trigonometric functions."

Reiner's explanation caused several jurors to ponder for a long time, because there seemed to be some surprising truth in the words.

“...... Wait, don't you say? ”

As a member of the Storm Councillor, Igor is often involved in discussions about the nature of light, and he is a staunch supporter of the wave theory, and Reiner's words make his mind quickly leap and think of many things.

"The Cialis formula and the Cialis transform mean that any exponential function can be transformed into the addition of an infinite number of trigonometric functions...... That is, the superposition of countless waves...... If it is reflected in the real world, that is, ......"

Muttering to himself, Igor's eyes widened, unable to imagine that the words were coming from his own mouth.

"All things can be expanded through progression and become the superposition of waves, and this world is the ?? of countless waves superimposed."

"How could it be ......"

Roger's mouth opened wide, he didn't expect that pure mathematical deduction could go straight to the essence of the world in a sense.

Of course, all Igor's conclusions are just speculation, and he has no way to prove it theoretically or experimentally, and naturally he can't get feedback from the world.

But it was a very innovative way of thinking, offering a new direction to mages who were committed to exploring the nature of the world.

"This is indeed a possibility, and it may have to be left to the High Council to explore."

Reiner shrugged and continued.

"But the value of this paper, I think it's enough to clarify it here."

Hearing Reiner's words, even Roger was silent.

It is inconceivable that imaginary numbers, such a purely mathematical, incomprehensible concept, can glimpse the tip of the iceberg of the essence of the world through it.

But all this is shown in front of everyone, and it is impossible to refute.

Seeing that the opposition gradually subsided, Reiner then said.

"Actually, this paper was completed ten years ago, when the Newington-Holland equations had not been proposed, and the paper, which was judged to be worthless, was written by an old man who did not even know a word, and I got it from the author's mother, an old man who didn't even know a word."

His words surprised everyone in the room, considering that ten years ago, the Newington-Holland equation had not been proposed at all, and the field of application of imaginary numbers was almost zero.

"At that time, the first reaction of those who read this paper was exactly the same as that of everyone here, that the content of the paper was worthless because it could not be of any help to the real world, and if you don't believe me, you can ask Director Percival, who was also one of the people who witnessed this paper back then."

Reiner said in a deep voice, looking at Percival, the mage's face was gloomy and he didn't say a word.

"Indeed, as a mage, there is nothing wrong with focusing your energy on improving your magical strength, efficiency and pragmatism are the principles of mages, and for this, it is indeed the act of a fool to spend time on seemingly meaningless mathematics."

In the huge conference room, pins could be heard, and only Reiner's voice echoed.

"The new spell results are like flowers blooming on the hillside, beautiful and attractive, but we must not forget that under the blooming flowers, in the soil, there are still roots."

He said, gradually increasing in volume and loudness.

"If the magic factions such as elemental, alchemy, and law are flowers, then mathematics is the foundation of all this, and we can't expect all theories to bloom beautiful flowers, because some things are the foundation in the first place! It is too short-sighted to simply evaluate something in terms of whether it makes sense and whether it can have an effect on the development of magic. ”

Reiner's words made Roger and the others' eyes widen, but on the other side of the long table, a person secretly clenched his fists.

It's Safros.

Isn't it a "meaningless" job that people call it "meaningless" when he spent a decade alone compiling a dictionary that might never come in handy?

A strong resonance pulsed through Safros's chest, and he felt a little sour in his nose and a little moist in his eyes.

"Ladies and gentlemen, we are mages, Your Excellency Braggs's definition of a mage is not a person who holds power, but a person who explores the truth, perhaps many people's original intention of learning magic has long since changed, they learn magic in order to pursue stronger power, higher status, and the pursuit of a perfect life, I don't mean to blame these people, after all, this is also one of the pursuits of human beings."

Reiner said, and then, the conversation shifted.

"But don't forget that there are people in this world who study magic just to find out that little doubt in their hearts, just to open the door to that truth, these people should be respected, but the reality is that many people who have gained power and status through magic will instead laugh at these 'fools' who are dedicated to research, and judge their achievements to the fullest, and even think that those theories are meaningless."

He walked from the blackboard to the long table and to Percival's side.

"I just want to say one thing about these people who wantonly ridicule the research results of others."

Reiner paused, then continued.

"He doesn't deserve it."