The winter sun shone through the thick clouds and the bright glass, shining on the astrological diagrams hanging in the study, leaving a pale yellow halo, warm and beautiful.
Samantha, Neeshka's young female student, was still wearing the same expressionless face, as if Lucien owed her ten thousand arcana points. "Mr. Neeshka, are you going to attend the small meeting tomorrow morning?"
"Of course, why not? I'm going to refute Levski and Lucien Evans! I'm going to stop the committee from accepting such worthless papers! "Neeshka said angrily.
Samantha nodded slightly, not caring about her teacher's anger at all. "Then I'll tell your coachman to get ready tomorrow morning. Don't be late again."
After saying that, Samantha turned around and left with a pile of files in her arms, leaving Neeshka staring at the paper and Lucien's comment in anger.
… …
In the villa surrounded by flowers, Milina stood in front of the mirror and looked at herself, whose eyebrows and eyes were filled with anger. There were a few pieces of torn paper lying beside her feet. Milina lowered her voice and said angrily, "Lucien Evans …"
In her opinion, Tower Geometry was the only geometric system, and there was no new geometry that was fundamentally different from it. Levski's paper was full of obvious problems, because it was contrary to the real world. However, such a paper was highly praised by Lucien Evans. What revolution in calculus in geometry? What groundbreaking, groundbreaking, universal, highly discussed, and would play an important role in the future? What nonsense! Levski was trying to disguise a pile of cow dung as butter!
Undoubtedly, Lucien Evans's comment was a slap to her face, as well as to all the arcanists who studied mathematics in Tower. There were only a few papers in the field of mathematics that had such a high comment! Even Milina, who had obtained the Arcana Scepter, did not get such a high comment!
Milina left the mirror and walked to the bookshelf. She pulled out a few papers that she had published, combined the viewpoints in them, and wrote a new paper.
After she finished writing, she wrote the title at the front of the paper: "On Parallel Lines".
As a rigorous mathematician and astrologer, she would never fight an unprepared battle!
The other authorities in mathematics who received the paper and the evaluation result from the alchemical life all had the same reaction as Neeshka and Milina after reading the paper. They also contributed to the criticism of Levski's paper, but they still held a negative attitude towards the deduction that was contrary to their experience and intuition.
… …
In the morning, the haze disappeared, and the sky was clear.
In front of the mirror, Lucien tidied up his black double-breasted suit, white shirt, and light yellow vest. After dozens of seconds, he looked at himself carefully and made sure that he was well-dressed. Then he smiled and said to himself in the mirror, "I have to change my style today."
After saying that, Lucien took out the Holm Crown rings, Element, Electron, and Origin, and put them on his right thumb, middle finger, and little finger respectively. The light purple, blue, and translucent colors intertwined with each other, making the ring extremely eye-catching.
Then, Lucien took out the arcana badge with six silver stars on it and the badge of the board member holding a quill and put it on his left chest.
At the same time, on the right chest area of the black double-breasted suit that was transformed from the Immortal Throne robe, there was a clear mark. It was a magnificent throne supported by white bones.
Almost all the members of Arcana Review Board had won the highest honor in the field they were best at, but Lucien, who had won three awards and so many rings, was still very rare. Among all the members of Arcana Review Board, except for his teacher, Fernando, who had won two awards in two fields at most. Therefore, even without the Ice & Snow Medal, Lucien was still able to overwhelm them. The only problem was that Lucien did not have the Arcana Scepter, which represented the authority in the field of Mathematics.
Looking at himself in the mirror again, Lucien picked up the black top hat hanging on the clothes rack and put it on his head while walking out of the door.
Crossing the street quietly, Lucien entered the magic tower of the headquarter of the Congress. He stepped on the elevator and came to the fifteenth floor. Then he walked towards the meeting room that he had booked.
"Mr. Evans?" When Lucien was about to open the door of the meeting room, he heard a hoarse male voice.
Turning around, Lucien saw a middle-aged man whose magic robe was rather old, and whose style was more than a decade old, standing on a nearby balcony uneasily. There was a grayish-white ordinary cigarette in his hand, and a few wisps of smoke were rising in spirals.
"Mr. Levski?" Lucien guessed who he was. "Why didn't you go in?"
Levski slightly tidied up his yellow hair to make himself look less dispirited. Hearing Lucien's question, he smiled bitterly and said, "As soon as I go in, I'll be criticized and mocked by the six members, so I decided to wait outside for the meeting to start. Also, I'm a bit nervous, and I want to take a smoke to calm myself down."
Compared to the previous days, Levski seemed to be more relaxed after he got the approval. He could now express himself fluently.
Lucien understood his situation and smiled gently, "Are you ready? Are you ready to face their indifference, slander, and attack, and show them your new geometry? "
A trace of pain flashed across Levski's face, and he said unconfidently, "I'm ready, but they … I've presented my paper in front of all the arcanists who are good at mathematics. It was the first time I proposed the new geometry concept. Unfortunately, they didn't respond. They didn't discuss it, and they didn't believe it. There was only indifference, contempt, ridicule, and attack. I'm afraid that you'll be in trouble later, Mr. Evans."
"I'm very confident in your new geometry, so I'm not afraid of any attack." Lucien gave Levski confidence with his attitude.
Levski was excited again. The most difficult thing in life was to meet someone who understood him, his persistence, and his results. "Thank you, Mr. Evans. You're the first person who accepted my new geometry, and you gave it such a high evaluation. Even I didn't describe my paper in such a way. Thank you, thank you …"
As a sorcerer who was addicted to the world of arcana, Levski was not good at words. All he could say was "thank you" and a slight tremble.
At this time, Fernando, who was wearing a red magic robe, came to the meeting room and asked them to come in.
"Good morning, Mr. Fernando. You're finally here." After seeing Levski sit down, Lucien greeted Fernando at the door of the meeting room.
Fernando put on a serious face, as if they were discussing something serious. "I've read his paper. Although it's against my direct experience and knowledge, it's interesting and interesting."
As expected of the Lord of Storm who never praised anyone.
In the meeting room, except for Lucien, there were six committee members in total. Compared to the fifteen or sixteen people who held similar meetings in other fields, the number of committee members in the field of mathematics was much smaller.
Although many committee members were good at many fields and could attend different meetings, such as Lucien, who could attend the meetings on elements and thermodynamics, mathematics was just a tool. It could not directly change one's cognitive world or improve one's magic power. Therefore, there were not many committee members who were willing to study mathematics and become an authority in this field. Even including those who did not attend the meeting for various reasons, there were only nine committee members who were qualified to review mathematical papers.
"Mr. Evans, I'm Neeshka." Neeshka, who was wearing a grey top hat, greeted Lucien without a smile. However, when he saw the three rings on Lucien's right hand and the mark of the Immortal Throne on his right chest, his long white eyebrows slightly twitched. Subconsciously, he waved the black scepter in his hand, which seemed to contain countless mysteries.
Milina and the other committee members also stood up and greeted Lucien. Their attitude was not good, but not bad either. After all, the Lord of Storm, who was famous for his irascibility and mercilessness, was the special consultant who presided over and supervised the meeting today. More importantly, he was Lucien's teacher! No one wanted to be scolded for something that was not academic.
Lucien greeted them back one by one. He noticed that five of the six committee members were from Tower. They were all wearing grey pointy hats in a special style. Even Milina and Mabel were wearing the same hats, which gave him a weird feeling.
"This kind of hat is really not suitable for women." Lucien sighed and deliberately sat on the other side of the long table, directly facing the six committee members.
Fernando hated to talk nonsense, so he went straight to the point, "Regarding Levski's paper, Mr. Neeshka, Ms. Milina, and Mr. Evans have opposite opinions. Therefore, we're holding this small meeting to make the final decision on Levski's paper. Now, Levski will explain his paper first. You can raise your hand and ask questions at any time. "
Levski silently picked up the paper and walked to the magic platform in front of the meeting room. After a few steps, he suddenly tripped over a chair and almost fell down.
"Ha." "Humph." Neeshka, Milina, and the other committee members all sneered, which made Levski's face turn red.
Trying to calm himself down, Levski enlarged and projected the paper using the magic circle, and started to explain his postulates, inferences, and deductions.
"Mr. Neeshka, what's the problem?" When Levski came to a conclusion, Neeshka raised his hand and interrupted him.
Holding his dark arcana scepter, Neeshka said coldly and angrily, "Can you tell me why the sum of the three inner angles of a triangle is less than 180 degrees?"
"It's based on the previous axioms and postulates." Levski pointed at the deduction he had explained before.
Neeshka snorted, "Then find a triangle model like this one."
"But …" Levski was speechless. This was a pure mathematical deduction, which did not rely on real objects.
Neeshka spat out word by word, as if he was trying to express his anger, "Since you can't find it and it's against reality, then your paper is worthless! Completely wrong! "
After saying that, he sat down directly, not giving Levski any chance to explain.
Levski's head dropped, as if he was hit by a frost. But he still tried to raise his head and looked at the unfriendly eyes of the committee members. Then he was encouraged by Lucien's smile.
Fernando raised his hand, "Go on."
Levski took a deep breath and continued. After a while, Milina raised her hand.
"Ms. Milina, do you have any questions?" Levski found himself trembling. After so many years of experience, he knew what Milina wanted to ask.
Milina was holding an arcana scepter inlaid with many star-like gems. She sneered, "Levski, tell me why the perpendicular and oblique lines of the same line don't always intersect."
"It's based on the previous deduction …" Levski answered weakly. Lucien could not help shaking his head. At this moment, they needed to be imposing and overwhelming.
Milina picked up a stack of papers in front of her. Her smile disappeared and she said with a hint of anger, "Please find a line like this, or its model in reality!"
"I haven't found it yet …" Levski answered honestly, "But from the premise and logic, there's nothing wrong with it."
"That's your problem. You've forgotten that we're living in the real world, not in your imagination!" Milina scolded Levski mercilessly. Then she started to read her own paper, discussing the inconsistency between Levski's geometry and real experience and intuition.
Every statement of hers was like a dagger thrown at Levski, stabbing him until he was "bleeding", his face turned pale, and he was "on the verge of collapse".
"That's all," Milina said coldly. She no longer looked at Levski, as if he was just a clown who deliberately came up with an exaggerated paper to attract people's attention.
"Go on." Fernando hinted that Levski still had a lot to say.
Seeing Lucien's encouraging look, Levski lowered his voice and began the rest of the paper.
The committee members raised their hands and asked questions from time to time. Some twisted Levski's words to prove that he was wrong, and some refuted from the perspective of reality using Milina's method. Since this question had been going on for more than ten years, their tone was full of sarcasm and viciousness, which made Levski's face turn paler and paler.
However, Levski still insisted on finishing his paper in such a hostile atmosphere. He did not give up, nor did he get angry.
Back in his seat, Levski closed his eyes, as if he could foresee the final verdict. His paper still lacked a strong model to prove it. Thinking of this, he opened his eyes, looked at Lucien and gave him an apologetic look. Mr. Evans, I'm sorry for putting you in this trouble.
"When Levski was explaining, Neeshka, Milina, and other committee members have raised their doubts and expressed their opinions and arguments. Now, Mr. Evans, who hasn't spoken yet, will explain why he gave such a high evaluation." Fernando turned to Lucien and signaled him to go on stage.
Lucien adjusted his collar and walked to the podium with a stack of files in his hand. His steps were steady and calm.
"Mr. Evans, if I were you, I wouldn't insist. I understand your passion for revolutionary results, but we still have to respect the basic reality," Neeshka suddenly said. If Lucien's teacher was not the Lord of Storm, Neeshka would not have been so polite.
Lucien looked at him with a smile. "I only respect the truth."
Both Lucien's expression and tone could tell that Lucien was referring to Levski's paper. Milina chuckled, but her tone was as cold as the northern wind. "Mr. Evans, I'm sure you don't know that if a member of the review board makes an obvious, intentional, unjustified mistake during the review, he will be disqualified as a member of the review board." Lucien's face was as cold as the wind in the north.
"That's what I want to say to all of you." Lucien stood on the podium. His smile was calm, but his words were not soft at all.
Boom! As if something exploded in their hearts, all the committee members in the field of mathematics were filled with anger. Is he criticizing and attacking us?
Fernando blinked his eyes. He was a bit surprised that his student, who had always been polite and elegant, would say something so provocative. He thought to himself, This is strange. It seems that someone is in trouble …
"Mr. Evans, you'd better think about how to turn the geometry in your imagination into reality." Another female committee member, Mabel, sneered. She looked ordinary, old-fashioned and serious. Wearing a gray cap, she looked like an old nun in a church.
Salgueiro, a middle-aged man with messy black hair, pinched his face with his left thumb and forefinger and said in a low voice, "I'd like to know, Mr. Evans, why do you call Levski's paper the revolution of calculus in geometry? What's your reason? Can you prove that he's right? "
"You don't have any achievements in the field of mathematics. I seriously doubt your ability to review this paper." Neeshka, who spoke first, directly questioned Lucien's mathematics ability.
Enraged by Lucien's words, all the committee members became aggressive roosters.
Lucien raised his hand and said loudly, "If you have any doubts about my mathematics ability, please don't raise them to the committee until I finish my explanation."
Then he roared, "From now on, everything except the paper will disappear. You're the committee members, not kids!"
Shocked by the sudden roar, the meeting room suddenly became quiet.
Lucien looked around the meeting room and nodded slightly to Levski. Then he said loudly, "When I'm explaining, no questions or interruptions are allowed. All questions are to be asked at the same time. However, when I'm explaining, I'll ask you some questions. Please answer them honestly. Don't disappoint the committee member badge on your chest and the starry sky above your head!"
The committee members fell silent. They could not find any reason to refute Lucien's words. As a member of the Board of Auditors, a three-time winner of Holm Crown prize and a one-time winner of Immortal Throne prize, Lucien was qualified to make reasonable demands. Also, Lucien's aura was like a storm that was about to break out, ready to swallow anyone who dared to provoke him.
"Since no one disagrees, I'll take it as a yes." Lucien looked at his teacher, the Lord of Storm.
Fernando said with a straight face, "Then we'll do as Mr. Evans said."
Then Lucien turned around and manipulated the magic circle so that only the first axioms and postulates were shown on the projection.
"Mr. Neeshka, let me ask you, are these axioms and postulates wrong?"
Neeshka answered reflexively, "This is different from the real world."
"Mr. Neeshka, forget the sunshine outside, forget the outside world, and forget the content of the paper. Answer me honestly, are these axioms and postulates wrong?" Lucien shouted sternly.
Neeshka was suppressed by Lucien's imposing manner. He took a closer look and found that these were the five axioms and postulates of Tower Geometry, as well as the hypothesis proposed by Levski. So he nodded and answered, "The first axioms and postulates are not wrong, but the last one is ridiculous."
"This is proof by reductio ad absurdum. Don't you know proof by reductio ad absurdum?" Lucien shouted again.
Neeshka's white eyebrows twitched. He couldn't make himself look like an idiot who had never learned mathematics. "Then no problem."
"Do you think there's a mistake? Stand up if you have the courage! "Lucien was like a teacher in a magic school, facing the apprentices one after another, with an imposing manner.
How could there be a mistake? The other members shook their heads.
Then Lucien projected a few lines of content again. It was indeed Levski's paper.
"Ms. Milina, do you think there's anything wrong with the premise and logic?" Lucien looked at Milina with a serious expression.
Milina stood up and sneered, "This is different from the real world. You can't find …"
"Forget them! I said forget them! Only consider the premise and the logical deduction, only consider the pure mathematical problems! " "Tell me, is there anything wrong with this reasoning?" Lucien roared and interrupted Milina, "Is there anything wrong with this reasoning?"
Milina didn't know how to refute Lucien's roar. She deduced carefully and shook her head, "No, there's no mistake or loophole. It doesn't use other equivalent propositions as conditions."
"Good." Lucien gestured her to sit down and projected a few more lines. "Ms. Mabel, do you think there's a mistake in this reasoning?"
Just like this, Lucien asked one question after another, roaring again and again, making the members forget other factors and only consider the simple axioms, postulates, and logical deduction.
Hearing the roars, listening to the questions, and answering the questions, Neeshka and the other members' faces gradually turned pale, and cold sweat seemed to appear on their foreheads. Levski, on the other hand, was in high spirits, as if every roar from Lucien and every answer from the other members was injecting confidence and joy into him. Fernando, on the other hand, nodded thoughtfully.
When the last few lines of the paper were projected, Lucien turned to Neeshka and asked in a low voice, "Mr. Neeshka, is there a mistake in this reasoning? Is there a mistake in the premise?"
Neeshka clenched his fists, and he could vaguely feel the moisture in his palms. He swallowed a mouthful of saliva and did not dare to mention the truth again. He said in a trembling voice, "No. No mistake."
"Very good. No mistake." Lucien looked at the six members and seemed to be talking to himself.
Suddenly, he roared at the top of his voice, as if a storm was coming.
"If there's no mistake in this paper, then tell me, what's wrong with this paper?!"
"Tell me, what's wrong with it?!"
Milina was startled and answered subconsciously, "It's contrary to our intuition and experience …"
"Throw them out of your head!" Lucien interrupted her with a roar. "Tell me, from a purely mathematical point of view, what's wrong with it?"
"What's wrong with it?"
Neeshka, Milina, and the other members were silent, not knowing how to answer. If they did not mention the truth and experience, they would not be able to find the mistake in the premise and logic.
Levski clenched his fists, slightly raised his head, and closed his eyes. His face was full of mixed emotions, happiness, sadness, pain, and hope.
"Lucien Evans's roar is really like the Lord of Storm. No wonder he's his student."
"Another Lord of Storm?"
For some reason, Milina and the other members were not thinking about rebuttal, but these thoughts suddenly popped up in their heads.
Fernando shook his head and said to himself, "I don't have an illegitimate child."
Lucien saw that they could not organize a counterattack, so he took the opportunity to put the other paper in his hand into the magic circle. Then he adjusted the magic circle and displayed it together with Levski's paper.
"An Attempt to Explain Non-Tower Geometry …" Milina saw the title of the paper and continued reading.
The paper was displayed one page after another, but instead of replacing the previous pages, it was displayed side by side around the conference room.
Neeshka rubbed his eyebrows and said confusedly, "It's using differential geometry …"
Mabel, Salgueiro, and the other members also began to read the paper. As they read, their faces turned pale, cold sweat dripped down from their foreheads, and their hands almost dropped the quill.
"This is …" Levski jumped up, as if he saw the Goddess of Magic in front of him. This was the model of his new geometry! This was a hyperboloid model that was beyond imagination and intuition! This was the most powerful proof!
He cried silently, as he saw the sun rising, the darkness fading, and the arrival of hope.
Suddenly, another paper appeared. It was quite simple. Using the concept of projection, it proved that Levski's geometry was compatible with tower geometry on the unit circle. If tower geometry was true, then so was Levski's geometry!
Simple derivation, beautiful proof, full of mathematical beauty. There was no other evidence that could shock Neeshka and the other members more than this!
I'm not wrong! I've been on the right path! Levski screamed in his mind.
At this time, Lucien's gentle voice sounded in their ears, "As we all know, we can only see light within a certain frequency range. Beyond this range, we can't feel it directly. We have to rely on other tools to judge, but other tools also have their limits."
Since some of the preliminary mathematical results needed for the paper had not yet been published, Lucien gave the paper by himself. It was a bit more complicated than the original paper, but it didn't stop Milina and the other members from understanding it. As they read and listened to Lucien's words, they were very confused. Why was he talking about this now?
"So, in a specially arranged light scene, our eyes will be deceived by our own limits and thus produce hallucinations. This is part of the principle of illusions."
Although confused, Neeshka, Levski, and the other members all nodded. What Lucien said was right.
Lucien continued in a gentle voice, "It's the same for our ears. We can't hear sound waves beyond a certain range. Under certain conditions, our ears will be disturbed and thus produce auditory hallucinations."
"Our knowledge and experience are limited by the structure of our bodies and souls. I believe that we all know Shapeshifting. Is the world we feel when we shapeshift into different creatures the same as the world we feel now?"
"It's different." Levski answered affirmatively. Although many Shapeshifting spells relied on anatomical knowledge, such as the fact that bats used ultrasonic waves to find their way instead of their eyes, the Shapeshifting spells derived from the primitive magic patterns still allowed sorcerers to understand part of the world of different creatures.
Lucien smiled and looked at Milina and the other members who were confused, "So, are we right, or are they right? Obviously, we're looking at the same thing from different perspectives. We're all right, and we're all part of the truth. Therefore, our experience and knowledge are limited. "
"Our imagination is based on our experience. Our limited experience limits our imagination, so it's not omnipotent. The deeper we explore the world, the more we'll find that there are many things that we can't imagine at all, which are completely contrary to our intuition. "
Fernando nodded seriously. He roughly understood what Lucien meant.
Neeshka, Milina, and Levski were still a bit confused. They stared straight at Lucien.
Lucien raised his right hand and his face became serious.
"So, your eyes can deceive you, your ears can deceive you, your experience can deceive you, and your imagination can also deceive you."
Lucien paused and pointed at the paper projected on the wall with his right hand. He pointed at the logical deduction and conclusion and said in a low voice,
"But mathematics doesn't."
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