Although the voice was soft, it was like a thunderbolt in the ears of Nesika, Milina and others, deafening and deafening.
They have studied mathematical knowledge and received the Arcane Scepter Award. They are always proud of mathematics. However, in reality, mathematics is only a tool for arcane exploration and spell analysis. It is their vassal, not much.
Arcanists are willing to devote their whole lives to this field full of unparalleled beauty. For most arcana, it is enough.
The arcane masters in the tower who like the field of mathematics and physics have more or less thoughts similar to what Lucien said, but this is just an occasional pride, an occasional flash of inspiration, and an occasional casual complaint.
No one has ever described the aspect of mathematics that is higher than intuitive understanding and real experience, and raised the importance of mathematics to the highest level like Lucien Evans.
A status they never expected.
Even though they knew very well that Lucien was adding weight to the accuracy of Levsky's thesis, it did not prevent them from being excited and excited for a long time.
Levsky was even more excited and trembling all over. Yes, mathematics will not deceive me, so there is "Strict Proof of the Principles of Geometry and the Theorem of Parallel Lines". In this seemingly boundless sea, in this violent storm, never
In the resting sea, it is precisely by firmly grasping mathematics, relying on it wholeheartedly, and not being "deceived" by the outside world, that you can survive the ups and downs, cross the vast sea, and not be blown over by the wind and waves.
Despair sinks!
Fernando still did not praise his students, but nodded slightly. The deeper meaning of these words was more worthy of exploration than the superficial content.
Lucien retracted his right hand, put away the papers that surrounded the entire conference room, and placed another thick pile of papers that he had just taken out of the storage bag in the magic circle. He smiled gently and said: "Next, let's try
Try starting on another road and see if you can use unusual scenery."
There are mathematical models and proof that Levsky geometry and tower geometry are compatible. Although Milina and other committee members are still extremely resistant, after all, no one likes to deny themselves and admit that they have made mistakes, and they have been wrong for more than ten years.
, but they had to initially agree with this new geometric system, to this point. If they want to overthrow Levsky geometry, they must correspondingly overthrow the tower geometry that is compatible with it, which is completely contrary to their original intention.
In addition, their hearts were struck by Lucien's words. Their emotions were complicated but relatively stable at this time, and they looked at the paper without any prejudice.
""Another Assumption of the Parallel Line Theorem"?" With her hair tied up, the elegant Myrina read the title in a low voice, vaguely guessing what it was.
"Another hypothesis..." Levsky seemed to feel that the fog in front of him was being dispelled, and he saw the problems that he had ignored in the past ten years of persistence.
As if he were in a magic school class, Lucien pointed his finger at the projected paper and let the content be displayed line by line: "Mr. Levsky hypothesized that 'by passing a point outside the straight line, at least two straight lines can be drawn parallel to the known straight line.'
Then together with the original axioms and postulates, a new geometric system that is logically rigorous and self-consistent is deduced. What if we don't make another hypothesis? Another hypothesis that forms a complete set with Levski geometry and tower geometry.
:'There is no straight line parallel to the known straight line through a point outside the straight line'."
"Next, let's do some deductive reasoning. Let's see what happens."
Levsky took a deep breath and became excited again, seeming to understand something, while Nesika, Milina and other committee members looked solemnly at the paper projected by Lucien.
Pages of papers were turned over. Paragraphs of explanations were given. Because he was facing authorities in the field of mathematics and physics. Lucien explained very quickly and briefly went through many places, but Nesika and others looked increasingly expressionless.
The more serious he became, the more doubtful he became. At some point, Mapel blurted out and whispered to himself: "I have actually deduced a proposition that is different from Levsky geometry but equally bizarre..."
"What the hell is going on..." her voice prompted Salguero's response.
"Is it another new geometric system that is essentially different from the geometry of the tower?" Milina was at a loss. Just a few hours ago, she still firmly believed that it was impossible to have a system that was essentially different from the geometry of the tower.
New geometric system, but in less than a day, this view seemed to have been ruthlessly shattered, and it was shattered twice in a row.
She was confused and grateful. Fortunately, this was a viewpoint in the field of mathematics and physics, which did not involve the structure of the cognitive world. Otherwise, her head would have exploded with a bang. She was worthy of being secretly known as the "Skull Crusher" and the "Brain Eater".
Sean Evans.
Levsky was not confused, but fell into deep contemplation. Why did this happen? Why did starting from the different negations of the fifth postulate and the fifth postulate itself, each of them was complete, independent, and logically rigorous?
Different geometric systems that are self-consistent? Why is this? Is this related to the real world?
Under the influence of Speaker Douglas, arcanists who grew up in the Magic Council inevitably like to ask why, but there are very few like Lucien.
"It's interesting..." Fernando nodded lightly.
Time passed quickly, and Lucien reached the last part of his paper, using a spherical-like model to prove the feasibility of the previous content.
Nesika sighed deeply and said: "Sure enough, it is a new geometric system, Evans geometry."
"Mathematics really doesn't lie..."
It was because of pride and prejudice that I missed the opportunity to name the entire geometric system after my own name. If I could accept Levsky's hypothesis, then Lucien Evans's hypothesis would be easy to come up with.
Lucien did not end, but showed the last few pages of the paper: "I defined the concept of curvature in the paper. From calculations, it can be concluded that when the curvature is zero, it is tower geometry. When the curvature is less than
When the curvature is greater than zero, it is the new geometry of Mr. Levsky. When the curvature is greater than zero, it is the geometry I just talked about. They have something in common in nature and are compatible."
Mirina exhaled softly and seemed to be a little more accepting now.
Levski suddenly understood and was about to applaud with joy when he saw Lucien pressing his hand to signal everyone to be quiet.
What else does he want to say?
The same question appeared in the minds of different committee members. It also appeared in Levsky's mind.
Lucien no longer roared as aggressively as before, but spoke in a soft and gentle voice:
"We can see that under certain circumstances, the mathematical knowledge we study exceeds our empirical knowledge and intuitive feelings. This makes us subject to many constraints, making the development of the mathematical field like an eagle with its wings restrained.
We can only move forward with difficulty."
"So, we can try to separate mathematical knowledge from reality, and temporarily ignore their physical models and practical significance. Simply start from the most primitive, fundamental, and simple concepts and axioms, and develop rigorous and self-consistent concepts through reasoning and deduction.
A mathematical system. As for the function of this system and what it represents, we will only consider it when we encounter new problems and need this system during specific arcane exploration."
"This is my personal opinion."
Lucien briefly mentioned the concept of the axiom system, but did not discuss it in depth. It is not too late to wait for the arcanists to slowly accept this concept and have the awareness to think in this aspect before developing anything.
It needs to be done step by step.
Bang bang, sparse applause sounded. Coming from Levsky, he felt that he and Commissioner Evans had too much in common. Every word he said was something he vaguely felt but could not express.
, at the same time, his understanding and support of his new geometric system proved to be no less than saving his own life, and his inspiring speech made him even more excited when he thought about it now.
In the applause of one person, Nesika's expression changed continuously, and all the previous events came to mind. She finally raised her hand hesitantly and applauded gently.
With the first person's response, Mirina, Mapel, Salguero and others also followed suit and applauded, gradually changing from hesitation and resistance to sincerity.
"Now, is there anyone who objects to Commissioner Evans's high evaluation of Levsky's paper?" Fernando asked after the applause stopped.
Nesika raised her long white eyebrows, stood up suddenly, looked at Levsky and said: "Please accept my apology, this is a paper worthy of winning the Arcane Scepter Award, my pride and prejudice
This prevented me from accepting the new geometric system, and I fully agree with Commissioner Evans’s assessment.”
"I also apologize to you for the indifference, slander and attack for more than ten years. Levsky, you are a genius, outstanding and great mathematician. My stubbornness and shallowness blinded my eyes.
, making me look ugly, Commissioner Evans’ evaluation results and the Arcane Scepter Award are the best compliments to you.” Milina also stood up with Nesika and bowed deeply with the mysterious forehead-holding ceremony.
It was expected that Nesika and Milina would not object again, but she did not expect that they would directly apologize in public. A surge of sour emotions rushed into Levsky's head, making his nose sore.
, making his eyes blurred, and he watched each committee member stand up to apologize, but he was speechless.
Are you aggrieved? Of course you are aggrieved!
Is it painful? Of course it’s painful!
But at this moment, it seems that all these have been rewarded with belated affirmation!
Nesika looked at Levsky, whose eyes were red and his lips were trembling, but could not speak. She sighed with understanding, and then looked at Lucien: "Commissioner Evans, I apologize for my previous doubts.
An undoubted mathematical genius, you are an undisputed authority in the field of mathematics. Your new geometric system and the proof of Mr. Levsky's geometric system will definitely win you the Arcane Scepter Award!"
"Thank you for your approval." Lucien replied in a very soft voice.
Myrina said doubtfully: "Commissioner Evans, what's wrong with you?"
Lucien smiled bitterly: "My voice is hoarse..."
Storm Lord is not that easy to learn!
ps:
Change first and then change.
In order to finish yesterday's chapter in one go, I wrote it until almost noon or three o'clock, without having lunch. In addition, I always skip breakfast during holidays, so I felt very bad. I didn't recover until eleven or twelve o'clock last night. This chapter is in the morning.