Throne of Magical Arcana

Layria pulled two of them out from the pile of journals. “Basics of Mathematics has been a heated discussion topic this month, and the barber paradox has been drawing the most attention. People call it the big crisis in mathematics.”

Although Layria was also good at mathematics, she was still an arcanist who was more into element and alchemy studies, and her interest in mathematics was more for its application. Therefore, she was not at all as anxious as those arcanists from Tower. Instead, she was quite excited.

Taking over Arcana and Nature, Lucien saw the papers written by the president, his teacher, and Hathaway on Basics of Mathematics. On the one hand, they had confirmed the significance of Basics of Mathematics as it helped promote the many studies in mathematics; on the other hand, they also believed that the solution to the barber paradox had to rely on the further development of set theory and its more strict definition.

Before the Basics of Mathematics was born, there was no solid concept of set theory in the Congress. Many mathematician arcanists had realized that set theory could help build the entire palace of mathematics, and thus, it was the foundation of all mathematical findings. Therefore, all the grand arcanists and other arcanists from Tower hoped that they could make the most of the value of set theory while strictly avoiding the possible paradoxes.

However, they did have different beliefs even though they agreed upon the significance of set theory. Some arcanists, for example, Douglas and Hathaway, believed that mathematics should also follow logic, while others, for example, Fernando and Lucien’s concept of the axiomatization of math, believed that mathematics consisted of pure symbols and carried no substantial content, and as long as two mathematical theories were not contradictory to each other, studies on both of them could always proceed. Meanwhile, there were still some other trends.

Of course, it was very hard to tell which was correct and which was wrong. All of them could facilitate the development of math, although to different degrees.

“It seems that we haven’t been frightened by the paradox. Arcanists are full of passion to solve the problem.” Lucien grinned.

His students were a bit speechless. The way their teacher was talking was like he wasn’t the one putting forward the paradox.

Lucien leafed through the journal and saw Bergner’s paper on “Goldbach’s conjecture”. Bergner admitted that the conjecture could not be proved at the moment, but it could be approached step by step. That could be done first by proving that even numbers could be written in the sum of the product of M prime numbers and the product of N prime numbers. In other words, they had to prove “M+N” first, and when they could reduce M and N to one, the problem would be solved.

“Sir, they’ve given your conjecture an interesting name, ‘1+1’. But Mr. Bergner is still on his way to prove ‘9+9’.” Heidi grinned. “But sir, you haven’t solved it, have you? Did you throw the conjecture at us on purpose?”

“I have not…” Lucien shook his head, feeling amused. He expected that Nature would publish many papers on proving “M+N” in the following years, and he hoped that a few decades later, someone could reach “1+2”.

After their discussion on the latest journals was done, when Lucien was about to go back to his own office, Heidi asked, “Sir, I heard that the kingdom is going to hold a Rentato Music Festival, and your opera The Valkyrie will be on the opening ceremony?”

“It should be, if everything goes well,” Lucien admitted.

These students’ eyes lit up as they looked forward to this opera. In the past years, Lucien had put much of his effort on studying magic and arcana, so he only produced some short piano pieces and light music pieces, which quite disappointed his fans. It was said that the opera was from Lucien’s years of effort, and thus, it must be perfect and would become a classic.

Sprint was not one of them. He curled his lip as he did not understand their passion. He did not have a specific preference for music.

Later, Lucien walked back to his own office and started staring at the parchment roll in front of him.

After a while, he finally picked up his quill-pen and dipped it into the ink bottle. He then wrote down a title—”Determinism, Free Will, and the Source of Magic”.

Although the title resembled Mr. Schrödinger’s famous paper named Indeterminism and Free Will, the contents were only similar to a very limited extent. After analyzing the inherent contradictoriness of determinism, Lucien introduced self-awareness and led the discussion to the relationship between the effect of the observer and the origin of magic. Like the model of the ocean in the vacuum, there was no theoretical evidence for this.

“Since awareness has its influence on microscopic particles, the material basis in our world seems to be less firm, so things around us change when we add spiritual power or corresponding magic patterns to them, and magic spells are thus produced. For example, some of our transformation spells work in the way that they reform our bodies on the microscopic particle level. Most magic spells that are not cast with permanent effects have limited lifespans. In the past, we believed that this was because magic effects were ‘rejected’ by nature, but now, I prefer to use the effect of an observer to explain it. Once the ‘observer’ appeared, the magic effect would collapse…

“The change in blood powers might come from the instability on the micro-level, for example, the transition of quanta…

“… Some magics require large quantities of energy, which exceeds our spiritual power. But the question is, where does the energy come from?

“… In some transformation spells, materials can be added or removed. As for reduction, we can understand it in the way that the reduced part of the material is temporarily stored in the time and space created by the magic and will resume after the spell’s time is up. While this reduction process is understandable, what about the addition of materials? Do those additional materials grow out of nothing? Even if they are formed in this way, according to the law of conservation of mass and energy, the energy required is great. Then where does the energy come from?

“So my assumption is that when casting a transformation spell, what we get from the surroundings is not energy, but basic substances. But where do these basic substances come from?

“…Maybe the existence of the ‘real world’ can solve our problem, but how does the ‘real world’ exist? Does it exist in every corner of the universe, which means that real vacuums never exist? What is the nature of the ‘real world’? Why can it provide basic substances?

“…Can meditation be described as a process of increasing self-awareness? In other words, the growth of a sorcerer is the process of a weaker observer to a stronger one…”

Lucien wrote the paper all the way to the end without a stop. Finally, Lucien picked it up and released a sigh of relief. He had to make sure that the paper was logically-sufficient, and thus, he had to make others believe that he was inspired by the model of the ocean in the vacuum.

Lucien then put down the paper and turned to ask himself, “Then how should I explain transformation spells… How do they actually work?”

In the afternoon, after submitting the paper to the Sorcerer Administrative Department, Lucien returned to the Atomic Universe and saw Natasha sitting on the couch, absent-minded.

Lucien wondered why both of them were in such an absentminded state today. He walked to Natasha and waved his hand in front of her eyes.

“What is it?”

Natasha, in her long, purple dress, was woken up from her thinking with a start.

She smiled. “It’s close to Rentato Music Festival now, so I think I’m missing Aalto.”

“I see. I sometimes do, too.” Lucien smiled and pulled Natasha up from the couch. “If you want to, let’s go and take a walk in Aalto right now.”

“What?” Natasha was a bit surprised. Since when did Lucien start taking actions without any plans?

But she still grinned and said, “Alright. We’ll enjoy dinner in Aalto.”

There was no need to plan for a casual walk!