Throne of Magical Arcana

The winter sun passed through the thick clouds, crossed the bright glass, and shone on the astrological charts hanging in the study, leaving a light yellow halo, warm and bright.

Nessica's young female student, Samantha, still had the expressionless expression that you owed me 10,000 arcane points: "Teacher, do you want to participate in the small discussion meeting tomorrow morning?"

"Of course, why not? I'm going to refute Levsky and Lucian Evans severely, and I'm going to make the committee stop accepting such worthless papers!" Nesska said angrily and sharply.

Samantha nodded slightly, not caring about the teacher's anger at all: "Then I will tell your coachman to get ready tomorrow morning, so don't be late again."

After finishing speaking, she turned and left with a stack of documents in her arms, leaving Nessica to look at the paper and Lucien's assessment results and get angry.

…………

In the villa surrounded by flowers, Milina stood in front of the full-length mirror, looking at herself with sullen brows and eyes, with a few torn papers lying quietly under her feet, and said in a low voice, "Lucien Evans... ..."

In her view, tower geometry is the only geometric system, and there is no new geometry that is essentially different from it. Levsky's thesis is full of problems that can be seen at a glance because it violates the real world. However, such a paper has received such a high evaluation from Lucien Evans. What kind of calculus revolution in the field of geometry, what is groundbreaking, breakthrough, popular, highly discussable, and will play an important role is simply nonsense , Turning black and white, trying to disguise a pile of cow dung as cream.

This is undoubtedly a slap in the face of myself, and a slap in the face of all arcanists who study mathematics and science in the tower. There are only a handful of results in the field of mathematics that have such evaluations! Even if I got the result of the arcane scepter, I didn't get such a high evaluation!

Leaving the mirror, Milina walked to the bookshelf, took out several papers she had published, synthesized the viewpoints in them, and wrote a new paper eloquently.

After finishing writing, she wrote the title at the front of the thesis: "On Parallel Lines".

As a rigorous mathematician and astrologer, she never fights unprepared!

And other authorities in the field of mathematics who received the papers and evaluation results sent by Alchemy Life, after roughly reading them, all had emotions and reactions similar to those of Nessica and Milina. They were also responsible for criticizing Levsky's paper However, they still hold a negative attitude towards this reasoning and deduction that violates real experience and intuitive understanding.

…………

In the early morning, the haze that had lasted for several days dissipated, and the sky was rare and transparent.

Lucien leisurely arranged his black double-breasted long dress, white shirt, and light yellow vest in front of the full-length mirror. After a few tens of seconds, he looked carefully and made sure that he was well-dressed and meticulous. He said to himself, "Today we have to change our style of conduct."

After finishing speaking, Lucien took out Holm's crown rings "Element", "Electronics", and "Origin", and put them on the thumb, middle finger, and little finger of his right hand in an orderly manner. The lavender, azure, and clear brilliance They reflect each other, like a dream, very eye-catching.

Then, Lucien took out the arcane badge as deep as the night sky with six bright silver stars, and the review committee badge holding a quill, and put them on his left chest.

At the same time, the right chest position of the black double-breasted long dress transformed from the Immortal Throne's robe highlights a distinct imprint, a gorgeous throne supported by white bones.

Almost all the members of the Arcane Review Committee have won the highest honor in the field they are best at, but those who have won three field awards like Lucien, who have won so many rings, are still a minority of the minority. Except for the teacher Fernando, most of the participants in the meeting were awarded twice in two fields, so even if they didn't show the Ice and Snow Medal, they could overwhelm them in momentum. stick", seems a bit professional.

Looking at the mirror again, Lucien picked up the black top hat hanging on the coat rack next to him, put it on his head, and walked out the door.

Passing through the street quietly all the way, entering the magic tower of the parliament headquarters, boarding the elevator, and reaching the fifteenth floor, Lucien walked towards the reserved meeting room without haste.

"Committee Evans?" Just as he was about to push open the door of the meeting room, Lucien heard a hoarse male voice.

Turning his head to look, he saw a middle-aged man in a rather old magic robe, which was still in the style of more than ten years ago, standing a little nervously on a nearby balcony, holding a gray-white ordinary cigarette in his hand, a few strands of blue Smoke billowed out.

"Mr. Levsky?" Lucien probably guessed who he was, "Why didn't you go in?"

Levsky's withered and yellow bird's nest-like hair was slightly tidied up to make himself look less down and out. After hearing Lucien's question, he smiled wryly: "As soon as I go in, I will be accused of being sarcastic by the six committee members. , so I’m still waiting outside for the meeting to start, and I’m a little nervous, so I just smoked a cigarette to calm down.”

Compared with the dull autism some time ago, he seems to be a little more relaxed after getting the affirmation, and he can express himself fluently.

Lucien understood his situation and smiled gently: "Then are you ready? Are you ready to face their indifference, slander and attack, and show them your new geometry?"

There was a trace of pain on Levsky's face, and he said unconfidently: "I'm ready, but they... I once gave my thesis in front of all the arcanists who are good at mathematics and science in the tower, and that was the first time. When the new geometric concept was proposed for the first time, unfortunately, they did not respond, did not discuss, did not believe, in addition to indifference, contempt, ridicule and criticism, or indifference, contempt, ridicule and criticism, I am afraid that I will implicate you, Commissioner Evans. .”

"I'm very confident in your new geometry, so I'm not afraid of any attack." Lucien gave Levsky confidence with his own attitude.

Levsky became excited again. The most difficult thing to meet in life is someone who understands himself, understands his persistence, and understands his achievements: "Thank you, Commissioner Evans, you are the first person to accept my new geometry, and I gave such a high evaluation directly, even I have never described my thesis in this way, thank you, thank you..."

He is a magician obsessed with the arcane world, he is not good at words, only thank you and a slight trembling when he tosses and turns.

At this time, Fernando, whose red magic robe was dragged on the floor, came to the meeting room and motioned for the two to enter.

"Good morning, teacher, you are still here." After watching Levsky sit down, Lucien greeted Fernando at the door of the meeting room.

Fernando showed a serious expression discussing serious matters: "I read his thesis. Although it goes against intuitive experience and understanding, it is interesting and interesting."

Sure enough, he was still the master of the storm who never boasted.

In the conference room, except for Lucien, there were six committee members in total. Compared with the fifteen or sixteen people who held similar seminars in other large fields, the number of committee members in the field of mathematics and science seemed much less.

Although many committee members are good at multiple fields and can attend different discussion meetings. For example, Lucien can participate in elements and heat respectively, but mathematics and science are just tools, and they do not directly bring about changes in the cognitive world and the improvement of magic power. However, there are not many committee members who are willing to delve into this field and become an authority. Even if they did not come for various reasons, there are only nine members in the entire committee who are qualified to review mathematical papers.

"Commissioner Evans, I'm Nessica." Wearing a gray top hat, Nessica greeted Lucien without a smile, but when she saw the three rings on Lucien's right hand and the right breast After the imprint of the Immortal Throne, his long white eyebrows moved slightly, and subconsciously shook the black scepter in his hand, which was as deep as it contained countless mysteries.

Mirina and the others also got up to greet Lucien. Their attitude was not good, but it was not bad. After all, the special advisor who presided over and supervised the meeting today was Fernando the Storm Master. Most importantly, he is Lucien's teacher! No one wants to usher in a stormy roar due to issues other than academics!

Lucien returned the salute one by one, and noticed that five of the six committee members belonged to the high tower, and they all wore special-style pointed gray hats. feel.

"This kind of hat really isn't suitable for women." Lucien sighed and deliberately sat on the other side of the long table, directly facing the six committee members.

Fernando hated nonsense the most, and said bluntly: "For Levsky's "Strict Proof of the Principles of Geometry and the Theorem of Parallel Lines", Commissioner Nessica, Commissioner Milina and Commissioner Evans have opposite evaluation results, so we Convene this small panel to make the final verdict on Levsky's thesis. Next, Levsky will explain his thesis first, and members of the committee can raise their hands and ask questions at any time."

Levsky silently picked up the paper and walked towards the magic platform in front of the conference room. Just a few steps away, he suddenly tripped over a chair, made a loud noise, stumbled and almost fell.

"Heh." "Humph." Nesska, Mirina and others laughed and sneered one after another, making Levsky's face turn red quickly.

Trying to calm down his panic, Levsky used the magic circle to enlarge and project the thesis, and began to explain his postulates, reasoning and deduction.

"Mr. Nesska, what's the problem?" Levsky interrupted with a raised hand after Levsky talked about a deduced conclusion.

Nesska held his deep and dark arcane scepter, and said indifferently with hints of anger: "Tell me why the sum of the three interior angles of a triangle is less than 180 degrees?"

"This is derived from the previous axioms and postulates." Levsky pointed to the derivation mentioned earlier.

Nesska snorted coldly: "Then find a triangle model like this."

"This..." Levsky was at a loss for words for a moment. This is a logical derivation of pure mathematics and does not depend on real objects.

Nesska spit out word by word, as if wanting to express the anger in her heart: "Since you can't find it, and it goes against reality, it proves that your thesis is worthless! It's completely wrong!"

After speaking, he sat down directly without giving Levsky a chance to explain.

Levsky looked as if he had been hit by frost, his head shrugged, but he still tried his best to raise his head, met the unfriendly eyes below, and was encouraged by Lucien's smiling and approving eyes.

Fernando raised his hand: "Continue to explain."

So Levsky took a deep breath and continued on. After a while, Mirina raised her hand.

"Ms. Milina, what questions do you have?" Levsky found himself trembling. After so many years of experience, he could guess what Milina wanted to ask.

In Mirina's hand was an arcane scepter inlaid with many star-like gems. She sneered and said, "Levsky, tell me why the vertical and oblique lines of the same straight line do not necessarily intersect."

"This is derived from the previous deduction..." Levsky replied weakly, and Lucien couldn't help shaking his head. At this time, he needed momentum and overwhelmed the confidence of others.

Milina picked up the stack of papers in front of her, her smile restrained, and said with a touch of anger: "Please make such a line, or find its realistic model!"

"I haven't found it yet..." Levsky replied honestly and shocked, "But from the premise and logic, there is no problem with it."

"This is your problem, you forgot that we live in the real world, not in the imagination!" Milina accused mercilessly, and then read her thesis, discussing Levsky's geometry and real experience, The inconsistency of intuitive understanding.

Every passage of her discourse seems to be thrown at Levsky like a dagger, causing him to be "dripping with blood", turning pale and "shaky".

"My opinion is over." Milina said indifferently, without looking at Levsky again, as if he was a clown who deliberately made exaggerated and weird papers to attract others' attention.

"Continue to explain." Fernando indicated that Levsky's thesis still has a lot to explain.

Levsky received Lucien's encouraging gaze, and his voice weakened a bit to talk about the following content.

A committee member raised his hand to ask questions from time to time, some distorted Levsky’s meaning to prove his fallacy, and some followed the method of Milina and others to refute it from a realistic perspective. Since this problem has lasted for more than ten years, Their tone couldn't help being tinged with acrimony and a touch of malice, which made Levsky's face turn paler and paler.

However, in such a hostile atmosphere, Levsky still insisted on finishing his thesis, without giving up, and without getting angry and "exchanging words".

Back in his seat, Levsky closed his eyes, as if he could foresee the final verdict. His thesis still lacked a strong model proof. Thinking of this, he opened his eyes, looked at Lucien, and gave him a Sorry to bother you with that look, Commissioner Evans.

"During Levsky's explanation just now, members such as Nessica and Mirina have raised doubts and given their own opinions and arguments. Next, member Evans, who has not yet spoken, will explain the reasons for his high evaluation." Fernando His eyes turned to Lucien, motioning for him to come to the stage to explain.

Lucien straightened his neckline and walked up to the podium with a stack of documents, his steps were steady and unhurried.

"Commissioner Evans, if I were you, I wouldn't insist on it. I understand your love for subversive results, but it still needs to respect the basic reality." Nessica said suddenly, if Lucien's teacher Not the Lord of Storms, he would never be so polite.

Lucien smiled and looked at him: "I only respect the truth."

Regardless of the expression or tone, the committee members could tell that the truth in his mouth refers to Levsky's thesis, so Milina smiled lightly, but without the slightest smile, as cold as the cold in the depths of the North. Feng: "Member Evans, I don't think you know that if a review committee member makes an obvious, intentional, and unreasonable mistake when reviewing a paper, he will be disqualified as a committee member."

"This sentence is also what I want to say to everyone." Lucien stood on the podium with a flat smile, but his words were not soft.

Boom, as if something exploded in my heart, a committee member in the field of mathematics and physics is full of anger. Is this accusing and attacking us?

Fernando blinked his eyes, a little puzzled that his always elegant and polite student would say such provocative words, he thought to himself, it's a bit abnormal, it seems that some people are in trouble...

"Commissioner Evans, you should first think about how to turn the geometry of your imagination into reality." Another female committee member, Mapel, sneered. old nun.

The middle-aged man with messy black hair, who didn't seem to like to take care of himself, pinched his face with his left thumb and index finger, and said in a low voice, "I'd like to know why you called Levsky's paper, Commissioner Evans. What is your reason for the calculus revolution in geometry? Can you prove him right?"

"You don't have any achievements in the field of mathematics and science. I seriously doubt your ability to review this paper." Nessica, who spoke first, directly questioned Lucien's level of mathematics and science.

Enraged by Lucien's words, all the committee members turned into aggressive roosters.

Lucien raised his hand and suppressed it, and his voice was loud: "For any doubts about my mathematics and science level, please ask the committee after I have finished explaining."

Then he growled slightly: "From now on, everything other than the thesis will disappear. You are review committee members, not children!"

Shocked by the sudden roar, the meeting room suddenly became quiet.

Lucien looked around the meeting room, nodded slightly to Levsky, and then said loudly: "When I explain the reasons, I am not allowed to ask questions or interrupt. When telling the story, I will ask you questions, please answer honestly, worthy of the committee badge on your chest and the starry sky above your head!"

The committee members were silent, and couldn't find a reason to refute Lucien for a while. As an audit committee member, as the winner of the Holm Crown Award three times and the Immortal Throne Award once, he is qualified to make certain reasonable demands, and his momentum is Like a storm that is ready to go, it chooses to devour someone, making people subconsciously not want to provoke him on small issues.

"Since everyone has no objection, it is considered agreed." Lucien looked at the master of the storm.

Fernando said with a straight face: "Then follow what Commissioner Evans said."

So Lucien turned around and manipulated the magic circle so that only the original axioms and postulates were displayed on the projection:

"Commissioner Nessika, let me ask you, are these axioms and publics wrong?"

Nesska replied reflexively: "It's different from the real world."

"Commissioner Nessica, forget about the sunshine outside, forget about the outside world, and forget about the content behind this paper, and answer honestly, are there any mistakes in these axioms and axioms?" Lucien snapped.

Nesska was overwhelmed by Lucien's aura, and looked carefully. Isn't this the five axioms and four postulates of tower geometry, as well as the hypothesis put forward by Levsky, so she nodded and replied: "The previous axioms and postulates are not wrong, but the last one is absurd."

"This is the method of proof by contradiction, don't you know the method of proof by contradiction?" Lucien shouted again.

The white eyebrows twitched, and Nesska couldn't make herself look like an ignorant idiot, a fool who hadn't studied mathematics: "That's no problem."

"Do you think there is a mistake? If there is, stand up bravely!" Lucien was like attending a class in a magic school, facing the magic apprentices one by one, with an imposing manner.

How could there be a mistake in this, the other committee members shook their heads.

So Lucien projected a few lines again, which turned out to be Levsky's thesis.

"Commissioner Mirina, do you think there are premise and logical errors in this reasoning?" Lucien looked at Mirina sternly.

Milina got up and sneered: "This is different from reality, I can't find it..."

"Forget them! I said forget them! Only consider assumptions and logical deduction, and only purely mathematical problems!" Lucien snarled and interrupted Milina, "Tell me, there is a logical reasoning in this paragraph. Is it wrong?"

Milina was so confused by the rant that she didn't know how to refute, she deduced it carefully, shook her head and said: "There are no logical errors or loopholes, and no other equivalent propositions are used as conditions."

"Very good." Lucien motioned her to sit down, and then projected a few lines again, "Commander Mapel, do you think there are premise and logical errors in this reasoning?"

In this way, Lucien asked section by section, rant again and again, over and over again to make the committee members forget about other factors, and only consider simple axioms and logical deductions.

Under the yelling, listening to the questions, and asking if there were any mistakes in the answers, the faces of Nesska and other committee members gradually turned blue, and there seemed to be a little cold sweat on their foreheads, while Levsky was full of energy, as if every sound of Lucien Roaring, every answer from the committee members infused him with confidence and joy, while Fernando nodded thoughtfully.

As the last few lines of the thesis were projected, Lucien turned his gaze to Nessica, and said in a low voice: "Committee Nessica, is there any loophole in logical deduction in this paragraph, and is there any mistake in the premise."

Nesska clasped his hands tightly, and could vaguely feel the wetness in his palms. He swallowed a mouthful of saliva, did not dare to mention the reality, and said slightly tremblingly: "There are no loopholes, no mistakes."

"Very good, no loopholes, no mistakes." Lucien looked at the six committee members and seemed to be talking to himself.

Suddenly, he roared at the top of his voice, as if a storm were coming:

"Since there are no mistakes in every place, then tell me what is wrong with this paper?!"

"Tell me, what's wrong with it?!"

Mirina was taken aback, and subconsciously replied: "It goes against our intuitive understanding and real experience..."

"Throw them out of your mind!" Lucien snarled and interrupted, "Tell me, from the perspective of pure mathematics, from the perspective of assumptions and logical deduction, what is wrong with it?"

"What's wrong?"

Nesska, Milina and the others were silent, not knowing how to answer, without mentioning reality, without mentioning experience and understanding, and they really couldn't find any premise and logical errors.

Levsky clasped his hands tightly, raised his head slightly, closed his eyes, his face was full of complex emotions, joy and sorrow, pain and hope.

"Lucien Evans' roar really has the aura of a storm master, and he is indeed his student."

"Another storm master?"

For some reason, Milina and the others didn't think about rebuttal words in their heads, but these thoughts popped up suddenly.

Fernando shook his head and said to himself amusedly, "I don't have an illegitimate child."

Seeing that his aura made them unable to organize a counterattack for a while, Lucien took advantage of the victory to pursue, put another paper in his hand into the magic circle, adjusted the magic circle, and displayed it together with Levsky's paper.

"An Attempt to Interpret Non-Tower Geometry"..." Milina saw the title of the thesis and continued to read.

The papers are displayed page by page, but instead of replacing the previous content, they surround the conference room and display them side by side.

Nesska rubbed her brows, and said in doubt: "The knowledge of differential geometry used..."

Mapel, Salgueiro and other committee members also started reading. As they read, their faces turned pale, drops of cold sweat rolled down their foreheads, and they almost couldn't hold the quill steadily with their hands.

"This is..." Levsky jumped up, as if seeing the goddess of magic appearing in front of him. Here's a model of my own new geometry! This is a "hyperboloid" model that exceeds normal imagination and intuitive understanding! This is the most powerful proof!

He wept silently, seeing the rising of the sun, the receding of darkness, and the coming of hope.

Suddenly, another paper appeared, which was quite simple. Using the concept of projection, it proved the compatibility of Levsky geometry and tower geometry on the unit circle. If the tower geometry is true, then Levsky geometry is also true. !

Concise derivation, wonderful proof, full of mathematical beauty, there is no more proof than it that shocked Nesska and other committee members!

I am not wrong, I have been on the right path! Levsky screamed frantically in his heart.

At this time, Lucien's voice sounded softly in their ears: "As we all know, we can only see light within a certain frequency range. If it exceeds this range, we cannot directly feel it, and we can only rely on other tools to detect it." Judgment, and other tools also have limits."

Since some of the preliminary mathematical results required for the thesis have not come out, Lucien derived it by himself, which is a bit more complicated than the original thesis, but this does not prevent Milina and other committee members from understanding. With Sean's words, strong doubts arose in his heart, what is he talking about now?

"So, in a specially arranged light scene, our eyes will be deceived due to their own limitations, resulting in hallucinations, which is the principle of partial illusion."

Although puzzled, Nesska, Levsky and the others nodded, saying they were right.

Lucien continued to speak softly: "The same is true for our ears. Sound waves beyond a certain range cannot be heard. Under certain conditions, it will be disturbed and cause auditory hallucinations."

"Our understanding, our experience, is limited by the structure of our body and soul, and there will be a considerable degree of limitations. I believe that everyone will be transfigured, and the world we feel after being transformed into different types of creatures is the same as the world we feel now. Is it the same?"

"It's different." Levsky replied affirmatively, although many deformation techniques rely on the understanding of physiological anatomy, such as before knowing that bats use ultrasonic waves to find their way instead of eyes, the transformed bats have biases in this regard, However, the transformation technique obtained from the original magic pattern can still allow magicians to partially understand the world that different creatures feel.

Lucien smiled and looked at the confused Mirina and the others: "Are we right, or are they right? Obviously, this is looking at the same thing from different angles. Everyone is right, and they are all part of the truth. So our experience, our knowledge is limited."

"And our imagination is based on our experience, and limited experience constrains our imagination, making it not omnipotent. The deeper we explore the world, the more we will find many things that we can't imagine at all, It totally goes against our intuition."

Fernando nodded solemnly, probably understanding what Lucien meant.

Nesska, Mirina, Levsky and the others were still a little confused and looked straight at Lucien.

Lucien raised his right hand, his expression became serious:

"So your eyes can deceive you, your ears can deceive you, your experience can deceive you, and your imagination can deceive you."

Having said that, he paused, pointed his right hand to the thesis projected on the wall in the eyes of everyone, pointed to the logical deduction and conclusion, and said in a low voice:

"But math doesn't."

changed.

This chapter has more than 7,700 words, which is equivalent to adding a new chapter soon.

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