Meet the principal

"this......"

Roger was able to advance to the middle level, so he could naturally understand what Reiner meant.

If imaginary numbers are used to replace the vertical coordinate axis, then the numbers can simply be written in the form of Complex coordinate calculations are required.

As we all know, the rectangular coordinate system is closely related to the spell model, and coordinate and vector calculations are compulsory courses for every mage. If the imaginary number system is introduced, the efficiency of constructing the spell model will be greatly improved.

More importantly, the introduction of imaginary numbers directly expands the level of the entire world, just like the number axis on the blackboard or the entire blackboard. It is self-evident which one is broader.

"But this is just a mathematical game. Even without imaginary numbers, coordinate calculations can still be carried out. It is too strange to use imaginary numbers to explain the equations of motion."

Hannah questioned that it was indeed the role of imaginary numbers to make it easier to construct spell models, but magic should avoid introducing unnecessary factors. Imaginary numbers here are a redundant concept.

"Everyone, I believe you all know the Newington-Holland equations, right?"

Reiner did not answer Hannah's question, but asked instead.

"Of course I know. This is a system of four equations describing the electromagnetic field. You two have used this to prove that light is an electromagnetic wave."

Roger replied, a little curious as to why Reiner suddenly mentioned this.

"What do you want to express by saying this?"

"I mean, if we plug the concept of imaginary numbers into these four equations, what conclusions will we get?"

Reiner immediately began to write the formula on the blackboard, and skillfully converted it into a form with imaginary numbers.

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

"I think you have all seen the formula in the paper. If we bring this formula into the system of equations and perform calculations, we can find that the sinusoidal electromagnetic field that changes with time can be directly converted into an exponential form, and at the same time, the exponential form Formulas in the form can also be expanded into the form of trigonometric functions.”

Reiner's explanation caused several judges to think for a long time, because there seemed to be some surprising fact contained in these words.

"...Wait, can you tell me?"

As a member of the Storm Councilors, Igor often participated in discussions about the nature of light. He was a staunch supporter of the wave theory, and Reiner's words made his mind race rapidly and he thought of many things.

"The meaning of Sirius's formula and Sirius' transformation is that any exponential function can be transformed into the form of the addition of countless trigonometric functions...that is, the superposition of countless waves...if it is reacted In the real world, that is..."

As he muttered to himself, Igor's eyes widened, and it was hard to imagine that these words came from his own mouth.

"All things can be expanded through series and become the superposition of waves. This world is formed by the superposition of countless waves!??"

"How can it be......"

Roger opened his mouth wide. He did not expect that pure mathematical inference could directly reach the essence of the world in a certain sense.

Of course, all of Igor's conclusions are just guesses. He has no way to prove them theoretically or experimentally, and naturally there is no way to get feedback from the world.

But this is an extremely innovative idea, providing a new direction for mages who are committed to exploring the nature of the world.

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

Reiner shrugged and continued to speak.

"But I think the value of this paper has been sufficiently explained here."

Even Roger fell silent after hearing Reiner's words.

Imaginary numbers, such a purely mathematical and difficult-to-understand concept, can actually glimpse the tip of the iceberg of the nature of the world. This is really unimaginable.

But all this was shown in front of everyone, making it impossible to refute.

Reiner said after seeing the opposition gradually subsided.

"In fact, this paper was completed ten years ago. At that time, the Newington-Holland equations were not proposed, and this paper was also judged to be worthless. Its author had already died of illness. I I got this paper from the author’s mother, an old man who didn’t even recognize the word.”

His words surprised everyone present. You must know that ten years ago, the Newington-Holland equations had not been proposed at all, and the application field of imaginary numbers was almost zero.

"At that time, people who read this paper had the same first reaction as everyone here. They all thought that the content of the paper was worthless because it could not be of any help to the real world. If you don't believe it, you can ask Director Percival , he was also one of the people who witnessed this paper that year."

Reiner said in a deep voice and looked at Percival. The mage had a gloomy face and said nothing.

"Indeed, as a mage, there is no problem in focusing on improving one's magical strength. Efficiency and pragmatism are the principles of mages. For this reason, spending time on seemingly meaningless mathematics is indeed the fault of a fool. Behavior."

In the huge conference room, the drop of a needle could be heard, and only Reiner's voice echoed.

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

He said, the volume gradually getting louder and louder.

"If elements, alchemy, laws and other magic factions are flowers, then mathematics is the foundation of all of them. We cannot require all theories to bloom beautiful flowers, because some things are inherently the foundation! Does it make sense to use it? It is too short-sighted to simply evaluate something that can have an impact on the development of magic."

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

It's Savros.

He spent ten years alone compiling a dictionary that may never be put to use. Isn't this a "meaningless" job as people say?

A strong resonance pulsed in Savros' chest, and he felt his nose was a little sore and his eyes were a little moist.

"Everyone, we are mages. Mr. Braggs' definition of a mage is not a person who controls power, but a person who explores the truth. Perhaps many people's original intention of learning magic has already changed. In order to pursue stronger power, A higher status, learning magic in order to pursue a perfect life, I don’t mean to blame these people, after all, this is also one of human pursuits.”

Reiner said, and then changed the subject.

"But don't forget that there are still people in this world who study magic just to explore the questions in their hearts, just to open the door to truth. These people should be respected, but the reality is that many people have obtained magic through magic. People with power and status will instead laugh at these 'fools' who are dedicated to research, and judge their results, and even think that those theories are meaningless."

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

"I just want to say one thing to those who wantonly ridicule other people's research results."

Reiner paused and continued.

"He doesn't deserve it."