Layria picked out two journals from the thick stack in her hands. "The hot topic this month is your 'Basics of Mathematics', and the barber's paradox has attracted the most attention. It's known as the great crisis in mathematics."
Although she was good at mathematics under Lucien's tutelage, she was essentially an arcanist in the field of elements and alchemy, and she was more interested in mathematics than in research. Therefore, when it came to the great crisis in mathematics, she was not as anxious and confused as the arcanists of Tower. Instead, she was more excited to watch the fun.
Lucien took over 'Arcana' and 'Nature', only to discover that Mr. President, his teacher, Granny Hathaway and other grand arcanists had all written papers on 'Basics of Mathematics'. On one hand, they fully affirmed the importance of 'Basics of Mathematics' in the development of mathematics, and on the other hand, they all pointed out that the solution of the barber's paradox depended on the development of set theory itself and its strict definition.
Although the Congress of Magic did not have a complete set theory system before Lucien wrote 'Basics of Mathematics', many arcanists who were good at mathematics had realized that the whole palace of mathematics could be established by combining set theory with other concepts. It was the cornerstone of all mathematical achievements. Therefore, not only did the grand arcanists want to avoid the paradox by strictly defining it, but also preserve all the valuable content in the current set theory. The papers of the arcanists of Tower also reflected the same opinion.
However, their papers showed different tendencies. Some of the arcanists started from the point that mathematics was equivalent to logic, represented by Douglas and Hathaway. Some of the arcanists believed that mathematics could be a completely formalized symbol system without any real content. As long as they did not contradict themselves, they could continue to study it. This radical view was represented by Fernando, and Lucien's axiomatic system also belonged to this group. Other than them, there were also other tendencies.
Of course, those tendencies belonged to their own worldviews and values, and it was hard to tell who was right and who was wrong. They could all promote the development of mathematics, although the extent of the promotion was different.
"It seems that the arcanists are not intimidated by the Barber's Paradox. Instead, they are very motivated to find a solution to this problem." Lucien chuckled.
Heidi, Chelly, and the rest of them secretly rolled their eyes at their teacher, as if he was not the one who proposed the barber paradox.
Lucien flipped through the pages and saw Bergner's paper on "Goldbach's conjecture". He admitted that there was no way to prove it for the time being, but he believed that he could take one step at a time. First, he would prove that even numbers could be expressed as the product of M prime numbers plus N prime numbers. In other words, he would first prove "M + N". When both M and N were reduced to 1, the problem would be solved.
"Master, your conjecture is jokingly called the proof of '1 + 1'. It feels very interesting, but Mr. Bergner hasn't even proved '9 + 9' yet. He's still far from solving it." Heidi said with a smile, "Master, you haven't solved the conjecture, and you're just throwing it out to see us pondering over it, have you?"
"I really haven't solved it …" Lucien shook his head in amusement. He could almost imagine that there would be many papers on "M + N" on 'Nature' in the future. Perhaps, somebody would be able to reach "1 + 2" in decades …
After the exchange of the latest journals, Lucien was about to enter his office, when Heidi suddenly smiled. "Master, I'm told that the kingdom is going to hold a Renstadt Music Festival, and the opening ceremony will be your opera 'Valkyrie'?"
"If my guess is correct, that should be the case." Lucien did not deny it.
"Oh, I'm looking forward to it!" Heidi, Layria, and the other students and assistants said with glittering eyes. Over the years, their teacher had devoted most of his attention to the studies of arcana and magic. In the field of music, except for the classic violin concerto, there were only some simple piano pieces and light music, which was quite disappointing for them who also liked great musicians. Their teacher, on the other hand, was said to have worked on the opera for years. It must be perfect and boasted many classic melodies and arias.
Sprint secretly sniffed, unable to understand their attitude. He would listen to music if it was available. Did they have to be so excited?
While Layria, Heidi, and the other students were whispering, Lucien walked into his office and stared at the paper before him in a daze.
After a while, he picked up his quill, dipped it in some magic ink, and wrote a title: "Determinism, Self-Consciousness, and the Origin of Magic".
Although the title of the paper was similar to Mr. Schrodinger's famous "Determinism and Free Will", the content was only partly the same. After analyzing the contradictions of determinism itself, Lucien elicited self-consciousness and then brought the question to the relationship between the "observer effect" and the "origin of magic". It was also not supported by any theory. It was a possible model like the ocean of negative energy.
"… It is exactly because of the effect of self-consciousness on microscopic particles that our material foundation is not 'solid' enough. That's why all kinds of changes can occur under the influence of spiritual power and the corresponding magic patterns, resulting in weird and changeable spells. For example, part of our transfiguration spells can be described as the body recombination on the microscopic particle level … Therefore, the spells that do not have permanent effects all have a duration. We used to explain the phenomenon as being rejected by 'nature', but now it seems that it is more accurate to describe it as being affected by other 'observers', resulting in the collapse …"
"The mutations of blood power may come from the 'instability' on the microscopic level, such as the quantum leap …"
"… Of course, many spells require enormous energy that our spiritual power cannot bear. So, the question is, where does the energy come from?"
"… In some transfiguration spells, there is a reduction and an increase of matter before and after the transformation. The reduction is understandable because part of the matter does not disappear but is stored in the temporary time and space created by magic. When the duration of the spell is over, it will naturally return to itself. But what about the increase of matter? Can matter be generated out of nothing? Also, according to the conservation of mass and energy, the energy required is extremely terrifying. Then, where does it come from? "
"I speculate that when we use such transfiguration spells, what we obtain from the outside world is not energy but basic matter. But where does it come from?"
"… Perhaps the existence of the 'real world' can solve our questions, but in what form does it exist? Does it exist in every corner of the universe so that the absolute vacuum does not hold? What is its nature? Why can it provide the basic matter of elements? "
"Can meditation be described as a process to strengthen self-consciousness? The growth of a sorcerer is the process from a weak observer to a strong observer … "
After writing the paper at great length, Lucien picked up the paper and blew at it. "As long as it can be seen that I got the inspiration from the 'vacuum ocean of negative energy', it will be enough. Well, the paper itself has to be logically consistent …"
After mumbling to himself, Lucien put down the pen and paper and stared at the paper in a daze again. "How should I explain transfiguration? What is its real mechanism …"
In the afternoon, after submitting the paper to the Sorcerer Administrative Department, Lucien returned to the Atomic Universe, only to see that Natasha was sitting on the couch in a daze.
Was it the couple's day to be in a daze? Lucien secretly smiled and waved his hands. "What's up?"
Natasha, who was wearing a purple court dress, was suddenly back to herself. She smiled awkwardly. "The Renstadt Music Festival is getting closer and closer, so I kind of miss Aalto."
"I can tell that sometimes, I think about my life in Aalto too." Lucien pulled Natasha to her feet with a smile. "In that case, let's go to Aalto right now."
"Huh?" Natasha was stunned at first. Since when was Lucien a man of action who did not plan in advance?
But she soon came back to herself and said with a brilliant smile, "Okay, let's have dinner in Aalto."
Such a "walk" did not seem to require any planning!
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