424 The Roaring Lucien Almost twice the regular length, thank you all (2/2)
He was being this polite to Lucien only because Lucien was the student of the Lord of Storm.
Lucien smiled and looked at him. ”Truth is the only thing that I respect.”
Judging his expression and tone, it was obvious that Lucien was referring to Levski's paper.
Milina chuckled, however, the look on her face was as cold as a winter blow. ”Mr. Evans, I'd like to remind you that you might be expelled from the board if you make a mistake too obvious on purpose.”
”This is what I'd like to remind you all as well.” Lucien's smile was gentle, yet his tone was firm and sharp.
All the board members present felt like something exploded in their mind.
— Was this young man accusing them?
Fernando blinked his eyes, feeling a bit surprised that his student, who was always elegant and polite, would say something so aggressive. It's so abnormal, and it looked like that someone's in trouble…
”Mr. Evans, you better first think about how to bring an imagined geometry into reality.” said another member, Mabel, who was a serious, ordinary-looking woman. Wearing the grey, pointy hat, she looked like an old nun.
Pinching his face, the middle-aged man with messy black hair named Salgueiro asked in a low voice, ”Mr. Evans, I'd really like to know why you think his paper will bring a revolution to geometry like how calculus changed maths. How can you prove it?”
”You never made any achievements in math. I doubt that you're qualified for reviewing this paper,” Neeshka said rather straightforward.
Pissed off by Lucien's words, the members had become as aggressive as a rooster.
Lucien raised his hand to quiet them down. His voice was loud and clear. ”If any of you doubt my capability in maths, please go and talk to the Board after this meeting.”
Lucien paused a bit and then raised his voice even higher. ”From now on, all things that are not related to this paper shall disappear. You are all board members, not kids!”
Lucien's sudden roaring made the meeting room silent.
Lucien looked around and nodded to Levski slightly. Then he said in the same volume, ”When I speak, no questions, no interruptions. All the questions should be raised after I finish. But during my speech,I am going to ask you questions. Please answer my questions honestly, for the sake of the board member badge you're wearing and for the starlit sky above you!”
The board members were silent and were at a sudden loss of any excuses to reject Lucien. As a board member, three-time winner of Holm Crown prize, and winner of Immortal Throne, Lucien was qualified to make some reasonable requests. Also, Lucien's imposing and aggressive manner made them wanted to avoid getting into trouble with him.
”If no one says no, then I'll take it as a yes.” Lucien looked at his teacher.
Fernando said with a straight face, ”then do as Mr. Evans asked.”
Lucien turned around and operated on the magic circle, so that now only the most basic axioms and postulates were shown.
”Mr. Neeshka, let me ask you. Are these axioms and postulates wrong?” Lucien asked.
Neeshka answered subconsciously, ”this is different from the real world.”
”Mr. Neeshka, forget about the sunlight outside, forget about the world outside, forget the contents of that paper. Tell me, honestly, are these wrong?” Lucien further raised his volume and demanded harshly.
Shocked by Lucien's manner, Neeshka took a closer look and found out these were the five postulates from Tower Geometry, the four axioms, and the hypothesis put forward by Levski. So he nodded. ”These are correct, but the last one is ridiculous.”
”It is proof by contradiction. Don't you know proof by contradiction?” Lucien asked, his voice full of reproach.
Neeshka's white brow twitched a bit. Obviously, he just could not say he had no idea what it was. So he nodded. ”Then…”
”So anyone? Anyone here thinks proof by contradiction is problematic? Raise your hand!” As if he had been teaching in a magic school facing rows of pupils, Lucien maintained his imposing manner.
The rest of the members all shook their heads.
Lucien then projected a few more lines of Levski's paper.
”Ms. Milina, following the logic, do you think this part of the reasoning is problematic, based on the premise?” Lucien cast a rigorous look at her.
Milina sneered. ”It's different. You can't find…”
”Forget those! I said forget them! Only think about the premise and the deductive reasoning! Think about math!” Lucien interrupted Milina, roaring. ”Tell me! Is it logically problematic?!”
Faced against Lucien's roaring, Milina was unsure how to refute him. She carefully deduced from the given premises and then shook her head. ”No… Logically speaking, it is correct. No equivalent proposition is used as a condition here.”
”Good.” Lucien gestured Milina to sit down, and then showed a few more lines.
”Ms. Mabel, following the logic, do you think this part is problematic, based on the premise?”
Lucien kept asking and roaring, over and over again. He kept pushing the board members to only think of the axioms and postulates and logical reasoning.
Answering ”No” to Lucien's questions again and again, the board members faces gradually paled. While the board members had sweat on their foreheads, Levski felt more and more encouraged. Every time when Lucien roared, he became a bit more confident. Meanwhile, Fernando nodded thoughtfully.
With the last a few lines of the paper projected on the wall, Lucien turned to Neeshka and asked in a low voice, ”So, Mr. Neeshka, following the logic, do you think this part is problematic, based on the premise?”
His hands clenching tightly, Neeshka could feel himself sweating. He gulped and did not dare to mention the real world again. ”No…”
”Good. No.” Staring at the six members, Lucien murmured.
Then, suddenly, he roared at the top of his lungs like a violent storm.
”No problem with every single line! Then tell me why this paper is wrong!
”Tell me!”
Startled, Milina burst out, ”It conflicts with the reality and what we know…”
”Throw them out of your brain!” Lucien roared, ”Tell me, in the sense of pure math, following the logic, based on the premise, where is it wrong?!
”Tell me!”
Neeshka, Milina, and the members all remained silent, having no idea what to say. If, as Lucien said, only in the sense of pure math, the paper was indeed correct.
Levski held his fists tight, his head slightly raising. Closing his eyes, his face was written with complex looks, a mixture of elation, sorrow, pain, and hope.
Somehow, the members started thinking to themselves:
Lucien's roaring resembled Fernando a lot. He was indeed the student of the Lord of Storm. Maybe… this was another the Lord of Storm…
That was what all the members were thinking right now.
Fernando shook his head and murmured to himself amusingly, ”I don't remember I've got a love child.”
Seeing that the members were all shocked, seizing the momentum, Lucien put another paper in the magic circle and projected it on the wall together with that of Levski.
”An Attempt to Explain Non-Tower Geometry…” Milina silently read the title of the paper, and then she went on reading further.
One by one, the pages of Lucien's paper were cast on the walls surrounding the board members.
Neeshka rubbed his brows and said confusedly, ”So this is differential geometry that he's using…”
Mabel and Salgueiro started reading as well. A while later, their faces lost colors. Beads of cold sweat rolled down from their foreheads. They could barely hold their quill-pen.
”This is…!” Levski sprang up from his seat, as if he saw the Goddess of Magic standing right in front of him. Because what was in front of him was the very geometry model he had been looking for! This is the Hyperbolic Geometry model that went beyond normal imagination and experience. This was the most powerful proof!
He cried out silently. After so many years, he finally saw the sun rising in this world, driving away all the darkness. After so many years, he finally saw hope!
Lucien's paper was not complex. To be more specific, it was in fact very simple. Using stereographic projection on the unit circle, Lucien proved that Levski Geometry was compatible with Tower Geometry. Thus, if Tower Geometry was tenable, so was Levski Geometry!
Lucien's concise derivation and wonderful proof were full of the beauty of math. This was the most shocking as well as the most solid proof to persuade the members!
Levski cried out loud in his mind: He was not wrong! He was the one who had been right all the time!
At this time, Lucien started speaking again, but his voice had softened. ”As is known to all, we are only able to see light within part of the spectrum. To see more, we have to use tools, but the tools also have their limitations.”
Since some prerequisites that the paper was based on were not available beforehand, Lucien had to prove them in his paper, which made the paper to some degree more complicated than Levski's, but the members could still understand. Hearing Lucien's words, the board members wondered what Lucien was trying to say.
”… So, when light plays tricks in some scenarios, our eyes can deceive us, thus we have illusions. Some illusion spells were created based on this.”
The board members nodded, agreeing with Lucien's words.
Lucien kept going in the soft voice. ”Similarly, our ears can also deceive us. We can't hear when sounds exceed a certain frequency. And under some circumstances, we hear things that do not exist.
”So, our knowledge and experience are limited to the design of our body and soul. We all know how to transform. When we transform into other creatures, do we still feel the same way in this world as we do right now?”
”No,” said Levski firmly. Although many transformation spells came from the advancement of anatomy — before the discovery that bats used echolocation, the bat transformation spells all had similar errors — ancient sorcerers still managed to see the world in the eyes of other creatures with the transformation spells obtained from those creatures' magic patterns.
Looking at the confused board members in front of him, Lucien smiled. ”So are we correct? Or are those animals and creatures correct? Obviously, we are all correct. We just have different perspectives. The truth we see is part of the bigger truth. Therefore, our knowledge and our experience are always limited.
”Our imagination is based on our experience, thus our limited experience can easily put constraints on our imagination. As we explore this world further, we'll see more and more things that go beyond our perception and understanding.”
Fernando nodded seriously. He knew what Lucien was trying to say.
Neeshka, Milina, Levski, and the rest of the members were still feeling a little confused. They stared at Lucien, waiting for further clarification.
Lucien raised his right hand and his look became serious.
”So, your eyes can lie to you; your ears can deceive you; your experience can mislead you; your imagination can restrain you.”
Lucien paused a bit. Under the board member's gaze, Lucien pointed at the paper projected on the walls and said in low voice,
”But maths won't.”