Your notoriety is known to everyone.

Rogers' tone was extremely calm, and his eyes were sharp and aggressive as he stared directly at Elena.

Dusk is the time when he sacrifices Kevin to the bottomless pit, and it is also the time when he completes the mission of saving the world and obtains the [Ignorance Bonus].

That is to say, before this, it was entirely possible for Elina to include him in her foresight, and as long as the special effect was not activated on him, the corresponding information would not pop up in the prompt box.

From that day on, he had been constantly sorting out the plot, constantly calculating Alice's growth progress, and constantly thinking about what benefits he could get.

Because his mind was filled with complicated plans like these, he subconsciously forgot about the "marginal character" who had been following him and was restricted by his [Contract Special].

Even though Elena could not predict Rogers's future development and achievements, as long as Rogers would often appear by her side in the future, she would be able to predict some things through their interactions.

Even though these future events are uncertain and even unlikely to happen again, they are still extremely important.

"It's there again, with a look similar to that day." Elina stood on tiptoe, leaned forward, put her face in front of Rogers, and whispered in a complicated tone:

"I don't know whether to say you are sharp or dull.

"A fool would never be able to notice this, but why did you wait until now to discover it when you are so smart...

"We are in the classroom right now and the class is about to start. Also, because of the contract, I can't tell anyone anything.

"And in the end, what I saw was only a few daily routines, without any secrets, and without the need for you to be so vigilant and worried."

Rogers felt his breath intertwined with Elena's, his eyelids slowly drooped to half-closed, carefully judging the girl's facial expression.

If the time limit for erasing the corresponding memory of [Ignorance Special] was not just a moment, he would have probably already started to activate it, trying to erase all the future related to him that Elena had foreseen.

This was an instinctive fear and worry, just like when he first faced Elena who could easily judge the truth or falsity of his words.

What has been will be again; what has been done will be done again…

Rogers pushed Elena's face away, then gently pinched his Jingming acupoint with one hand, and the famous saying in Ecclesiastes emerged in his mind.

He didn't like to believe in something like fate. At most, he believed in the idea that "everything within the light cone is fate" which was born out of Einstein.

But at this moment, he had an indescribable emotion surging, as if all the past from the awakening of his past life memories to this moment had not disappeared, or even had not really passed.

“You can trust Alice, why can’t you trust me?

“Aren’t those contract clauses you compiled just so you can use me in the future?

“Since there is no trust, how can you use it with confidence?

"Rogers, when you asked me to help deal with the Saint, I told you that all this has a price."

Elina reached out and grabbed Rogers' collar, pulling it close to her face. Her eyes narrowed slightly, and unknown emotions were reflected in her amber eyes.

Chapter 47: Magical Points-Adding Method

"Feel sorry."

Rogers couldn't help but say this. He didn't know why he was apologizing, but he always felt that he had a lot to apologize for.

Just as Elina said, because of the restriction of [Li Ke Special], she couldn't do anything that would harm herself, not to mention that she already knew a lot.

Thinking back to the night when she brought wine to talk, Rogers couldn't help but reflect on the uneasy feeling he had when he just awakened his past life memories. There was no need to make up for it by controlling Elena.

Treating her with the same attitude as when we first met would naturally make her angry.

“A philosopher once said that we should be cautious about things that can be controlled and optimistic about things that cannot be controlled. We can only do things within our own capabilities. We should accept this fact and deal with it with optimism.

"I think I should think about the meaning of this and change my bad habit of getting caught up in details and perfection."

Rogers looked into Elina's eyes and calmly said Epictetus' famous words. Then he asked in a rather relaxed tone:

"So, our relationship should be pretty good in the future, right?"

Elina listened to Rogers' apology and watched his expression change as fast as flipping a book. Her momentum froze for a moment. She replied in an inexplicable tone, "Probably."

"I will restrain myself, just like you haven't come to dig up things I don't want to talk about since that night."

As Rogers spoke his words like a promise, Elina's hand on the collar gradually loosened. She hesitated for a moment and apologized in the same way:

"Just like you said, I shouldn't be childish, whether in dealing with the Saint or in this matter..."

"So, our compatibility is really bad." Rogers sighed helplessly, then he turned his head to look at Lufia and smiled to reassure her: "We are fine, just like before."

He said so, but he knew that some things had changed, like he could really try and give a little trust.

He wanted to tell Elena that he had never trusted Alice, and he had only trusted himself from beginning to end.

But when the words came to my lips, I couldn't really say them, as if they were stuck in my throat.

"Then let's find a workbench first. It happens that there are three of us in a group!" Lufia breathed a sigh of relief when she saw this. She smiled and grabbed the arms of Rogers and Elena, pretending to look for a suitable place.

She could clearly feel that the atmosphere just now was very unusual. This argument was completely different from the usual ones, otherwise she would have stepped forward to persuade the two to leave instead of watching worriedly from the sidelines...

Because the number of students is far greater than the number of alchemy workbenches equipped in the classroom, at least three to four students must be assigned to each alchemy table.

It was also during the process of searching for the alchemy table that Rogers began to understand why so many of his classmates had been avoiding him before.

He immediately saw the shy and affected Caspar, who was constantly telling something to the Third Prince. The Third Prince's expression was still polite, but the twitching corners of his mouth clearly showed the mood of this royal noble.

Because of Caspar's change, I wonder what bad name they will make up for me next...

As Rogers pondered in his mind, he smoothed his wrinkled collar with his hand.

"That's right! Saint Herta's students should pay attention to their dignity! Rogers gets an extra 100 credits!"

The resounding announcement, as resounding as a bell, instantly spread throughout the huge classroom. Every word of the voice was so clear and powerful that it seemed to be able to pierce through one's eardrums.

Rogers looked down and saw Professor Kuli, a short and sturdy man with a thick beard, standing next to him. He didn't know when he appeared.

The other person was one of the deans who had invited him to the temporary dormitory, and was also the first professor who took the initiative to praise him and expressed his willingness to teach him privately.

Perhaps because he was going to give a lecture, Kuli was wearing a simple grey magic robe today and a pair of glasses with thick lenses on his rosacea.

This outfit should have belonged to an old scholar, but when it was forced on him, it couldn't help but reveal a strong sense of incongruity and weirdness.

"Professor, isn't it a bad idea to give credit for these little things?"

A student nearby couldn't help but speak out, which immediately attracted a wave of agreement.

If Professor Kuli can add 100 credits today because of Rogers’ decency, can he add 200 credits tomorrow just because Rogers stepped into the classroom with his left foot?

This bias is too obvious! It's too outrageous!

"You think it's not good either?" Kuli looked up at Rogers, as if he also realized that such blatant extra points might not be a little bit appropriate.

"As a student, my job is to follow the guidance of my instructor. If you think this is not good, then it is not good."

Rogers did not answer the question directly, but expressed sincerely that he would respect Kuli's authority as a mentor.

"Hahahaha! Good kid! I like what you said! Rogers will get another hundred credits!"

Kuli laughed heartily, and the high-pitched tone and deep bass seemed to cause the air around him to vibrate.

The students all fell silent after hearing this, and no one stood up to criticize this obviously unfair behavior, because they were afraid that for every extra word they said, Rogers might have to add another hundred credits.

"Okay, I see everyone is here. Please open the prologue of your textbook and I will tell you what you will learn from me in the future.

"Oh, by the way, my name is Kuli! It's a simple and powerful name, I hope you all remember it!"

Kuli's opening remarks were extremely casual, in stark contrast to Alana's style yesterday.

Thanks to his loud voice, students no matter how far away they were could hear his story word for word.

"The basic structure of a magic circle cannot be simply summarized as concentric circles. This is a misconception that many apprentices have when they first get started!

"But you must also know that a magic circle with a circular main body as a layered structure must be the most stable!

“And whether it’s a single or a compound circular structure, their energy supply, conduction, function and safety are basically the same!

"..."

Rogers spread out the textbook on the alchemy table. He didn't understand what the things Kuli said had to do with the prologue. But these empirical knowledge, which sounded very plain and simple, and a bit contradictory upon closer thought, might be the precious and essential summary of the great magician.

After listening carefully to a lot of knowledge about formation structure, he recalled the topological structure called "Mobius Strip" proposed by Mobius and John Listing in the 19th century in his previous life, and wondered whether it could be incorporated into the composition of the magic circle.

After Kuli finished speaking, Rogers tore a piece of manuscript paper on the alchemy table into long strips, and then quickly folded a Möbius strip: "Professor, if it is this structure, can it form the base of the array or other parts?"

If the Möbius strip works, then maybe I should give the Klein bottle a try in this fantasy world.

In addition to these two typical examples, there are a large number of topological structures that continue to emerge in Rogers' mind.

Kuli, who was standing next to Rogers, looked up at the Möbius strip. He was a little confused when he first saw it, but after a moment of realizing that it was a structure with only one face and one boundary, he was instantly immersed in deep thought.

Chapter 48 Don't say that anymore! (Two in one)

"Child... I don't know how to answer you. Of course, it doesn't mean that it can't form a magic circle.

"But I'm not sure what it can do, or, it... the structure is a bit complicated...

"I've thought a lot about it. It should be possible to participate in the construction, but this kind of construction..."

After a while, Kuli grabbed his beard tightly with his hands, and his two thick eyebrows were almost twisted together.

His words were intermittent, as if he was thinking and organizing his words, trying to give Rogers the clearest explanation:

“However, a structure with an infinite loop nature will definitely reduce the loss of magic power to a great extent, which is likely to enhance the effectiveness of magic.

"When the magic power can be continuously circulated in the formation without any pressure, it also means that there is no need to add the insurance process of magic power overflow, and at the same time, the threshold for use is greatly reduced...

"And the most important thing is its symbol. This symbol can easily connect time and space... I don't know how to express this to you..."

At this point, Kuli seemed to have completely given up. He stopped trying to explain anything and just said in summary:

"Anyway! The structure you proposed is great! So great that I don't know how to praise you! I still need to think and study it more! No matter what the result is, I will definitely let you know!

"As for the credits, I will have to discuss it with the vice-president. After all, your contribution will be of great benefit to the entire magic community!"

Kuli supported his thick glasses frame with his hand, then lightly hit Rogers' chest with his huge fist, his tone full of appreciation and admiration.

"Is it really possible?" After hearing Kuli's explanation, Rogers showed an interested look on his face. He pondered for a moment and then said, "Professor, I actually have an advanced structural hypothesis."

"Advanced version?" Kuli was stunned. He didn't quite understand how this could be advanced.

"That's it, professor." Rogers threw the note aside and began to try to make gestures with his hands:

“We can extend the concept of the ring structure just now and regard it as a closed surface. It looks similar to a ring, but its special feature is that the inside and the outside are actually connected.

"When you look inside, it looks like a bottle. You can't get to the other side of the bottle by going through it from the inside or the outside, but you have to extend or go around the central axis..."

The Klein bottle is a mathematical object; there is no actual three-dimensional entity that can truly take on its particular shape.

Rogers had to describe to Kuli this pure mathematical concept that only existed in imagination with brief narration and continuous metaphorical supplementation, with great effort.

"It can tend towards symbolic concepts such as infinity, continuity and self-reference. It can be called the Endless Bottle..."

Kuli was very confused at first. It was a little difficult for him to understand the abstract concepts that Rogers talked about, but as he continued to use metaphors and arguments, his expression gradually became extremely serious.

But as time passed, shock and dullness slowly emerged on his rough face, and it was unclear whether he understood or not.

"Professor, do you think this structure is possible to realize in magic? Can it be used to construct magic circles?"

Seeing that something seemed to be wrong with the other party, Rogers asked tentatively.

"Ah? Oh... should... be ok, right?"

Kuli's face showed a frozen expression at this moment, his eyes staring into some empty direction, as if he had completely lost perception of the surrounding world and was only responding instinctively.

"Is this actually possible?" Rogers pinched his chin, thought for a moment, and gestured in the air again:

"Professor, you should be very familiar with the concept of a cube. It is the three-dimensional extension of a flat square. So what if we try to extend the cube further? In addition to length, width, and height, we can add a line pointing to a fourth direction..."

What Rogers is describing now is the hypercube, whose basic concept is much easier to understand than the Klein bottle.

However, this abstract geometric structure is not limited to the imaginary four-dimensional space, but can also be extended to higher dimensions, just like a cube can be extended to a hypercube.

Because of this, it will gradually become more complex and abstract.

Kuli's pupils slowly dilated, his originally dull expression slowly became alert, his brows furrowed even tighter, and tiny beads of sweat appeared on his forehead.

He trembled as he grabbed Rogers's hands that were waving in the air. The muscles on his face began to twist inexplicably, and he growled with trembling lips:

"Stop talking!"

The low roar seemed to come from deep underground, and in an instant it echoed throughout the entire classroom.

The bodies of all the students became extremely stiff at this moment, as if they were facing the shock from a predator of a higher level, which was constantly oppressing their hearts and imprisoning their bodies.

"I'm sorry, I didn't mean to do that, but you absolutely cannot continue talking like that! Do you understand?"

Kuli released Rogers' hands and warned him softly but seriously.