Chapter 379: 178th Void Realm

"Functional?"

Ilana repeated the unfamiliar term softly, her clear eyes filled with curiosity and a thirst for the unknown.

"That's right."

Luo Yan's voice was gentle and clear. To help his talented apprentice better understand the mysteries of functionals, he offered a simple, easy-to-understand analogy.

"Ilana, do you remember the 'calculus' we studied? What is its core purpose?"

Ilana answered without hesitation.

"It is to study the rate of change of functions and find their extrema. For example, finding the highest point of a mountain peak or the lowest point of a valley."

"Exactly right." Luo Yan nodded approvingly. "Calculus tells you at which 'point' you can stand the highest or lowest. However, 'functionals' aim to solve a completely different problem."

He took out his wand and waved it gently, drawing a gentle curve in the air, then a steep one.

With his mastery over magic, he no longer needed to rely on incantations, able to precisely control every flickering "light element" as it drifted along the trajectory of his wand.

"Our 'functionals' don't care which point is the highest; they care about this: if we want to walk from point A at the foot of a mountain to point B at the foot of the mountain, there are countless paths to choose from. Which 'path' has the shortest distance? Which 'path' is the least strenuous to walk?"

"Or, when a flickering ball of light slides from point A on the edge of a bowl to point B, which 'curve' will it follow to minimize the time spent?"

Luo Yan looked at Ilana's eyes, which had instantly brightened, and continued: "You see, what we are looking for is no longer an optimal 'point', but an optimal 'line'—that is, the optimal function itself that allows the 'total distance', 'total time', or 'total consumption' of the whole to reach a minimum value."

These words were like a key, unlocking the tightly sealed door in Ilana's mind, instantly straightening out her thoughts that had been as tangled as a ball of yarn.

"I understand... So, we are no longer seeking a numerical solution, but... a functional solution! A law that describes the very concept of 'optimal'!"

A rare excitement appeared on that cold face—it was the expression of a sailor who, after drifting for months on the vast, boundless ocean, finally catches sight of the coastline!

Having said this, she paused for a moment, struggling to control her slightly trembling voice, and continued.

"We are solving... a system!"

"Precisely! You summarized it very well."

Luo Yan smiled with satisfaction, then changed the subject and continued.

"The dilemma Mr. James Wali encountered must be this very problem... I am very happy that you were able to summarize his problem."

He pointed to the notebook and continued with a smile.

"This gentleman guessed with genius that when an object moves from one point to another, it will choose a path that minimizes a certain 'action.' But he lacked a key mathematical tool, a tool capable of finding that single 'optimal path' from among these infinite possibilities."

Watching Ilana, who was continuing to have an epiphany, Luo Yan's voice carried a hint of guidance, leading her to the door she was just one step away from opening.

"... And this tool is the calculus of variations, based on 'functionals'!"

"It can help us establish a brand-new equation, which I call the 'path optimization equation'. As long as every point on a path satisfies the equilibrium conditions described by this equation, then this path is the 'optimal solution' we are looking for."

"Do you know this equation?" Ilana blinked, her face full of admiration.

She felt he knew everything.

The problem she had been racking her brains over for days had been explained thoroughly by her respected mentor in just a few sentences.

Luo Yan wanted to say that, of course, he knew what it was.

Wasn't that just the Euler-Lagrange equation? He didn't need to ask the official website; he knew this thing, and he knew exactly how to use it.

However, doing so would undoubtedly stifle a soul with limitless potential.

The people of this world originally had the opportunity to walk this necessary path on their own, without relying on the wisdom from the other side of the void.

This is true for civilization, and it is the same for individuals.

As a true top student who could graduate with excellent grades even in hell, Luo Yan knew very well that for a genius like Ilana, pointing out the correct direction was far more meaningful than spoon-feeding.

Therefore, he told a lie and made a choice different from the one Lin Te Isaac had made back then.

"I, of course, do not know, but I believe that with your talent, you will definitely be able to discover its existence on your own."

Talent...

Ilana's face felt a bit hot.

The word "talent" is usually used to describe the potential for comprehending extraordinary power, so it is rarely used to describe ordinary people outside the nobility.

"Do I... have that ability?"

"Of course you do. Haven't you already walked along the path Mr. James Wali took, reaching a height he did not reach? I think his extraordinary power is certainly above yours, but that does not prevent you from also being able to 'stand on the shoulders of giants'."

Luo Yan smiled slightly, looked into those clear, transparent eyes, and continued in a gentle voice.

"Now, I want to teach you some basic techniques regarding the calculus of variations... Hmm, consider it preparing a lesson for me; I will talk about it in science class tomorrow."

"If you learn it, that would be even better; then you can teach it for me later."

Luo Yan stood beside Ilana, patiently explaining the basic concepts and core difficulties regarding "functionals". His voice was gentle and clear, peeling away the layers of those originally abstract and dry theories and presenting them before his most talented apprentice.

Ilana listened with rapt attention, nodding in sudden realization from time to time, and occasionally frowning to raise deeper questions.

The two were completely immersed in the exploration of knowledge, forming a pure academic aura that others could not easily step into.

And this conversation, falling into the ears of Oufiya, who was eavesdropping with her ears pricked up nearby, was no less than the most profound and difficult-to-understand magic tome.

"Variations?", "Path optimization equation?", "Principle of least action?"...

This... what is this?

Is this really arithmetic?

Why is it that she recognizes every word when taken apart, but when put together, it becomes the whispers of the devil?

Oufiya was dumbfounded.

Looking at the formulas and calculation steps written down rapidly like ghost symbols in Ilana's notebook, she only felt that the professors at the Imperial Royal Academy were teaching a pile of trash!

That might be a bit of an exaggeration, but this was her most intuitive feeling!

At the same time, she also felt for the first time, so intuitively, that there could be a chasm as wide as a natural moat between geniuses and geniuses.

This huge sense of disparity left her deeply struck.

Especially when she saw the genuine appreciation and approval in Prince Kelin's eyes, a faint sourness and grievance welled up in her heart.

This won't do... Oufiya, you are the daughter of Duke Kastelion, a recognized talented woman in the Shengcheng and even the Empire! How could you lose to a country girl who popped out of nowhere on a snowfield far from the Holy Light?

Although in the eyes of the Luo De people, Ilana was already an imperial girl beyond reach, in the eyes of the Shengcheng's young lady of the Duke, they were actually no different.

Oufiya did not mean to look down on Ilana; she was simply ignited by that thirst for knowledge and the look of approval in her eyes, fueling her competitive spirit!

How could a descendant of the Kastelion family lose to a commoner!

That lecture, which sounded like reading a heavenly book, finally ended. Luo Yan left with satisfaction, and Ilana continued her research with admiration and epiphany.

Oufiya took a deep breath, straightened her cuffs, and walked to Ilana's side with elegant steps.

Ilana noticed someone and looked up in confusion.

Seeing that it was the young lady of the Duke, she immediately showed a look of surprise, put down her quill, stood up from the desk, and said with cautious wording.

"May I ask what is the matter? Miss Kastelion..."

Looking at the polite and cautious Ilana, Oufiya showed an elegant and appropriate smile on her face and said politely.

"Please don't be nervous. I don't have any special purpose; I just noticed that Prince Kelin seems to value you highly, so I was a bit curious... May I know your name?"

"Ilana Ottavia... from the Pierce Province of the Empire." Ilana reported her family name in a low voice, looking at the young lady of the Duke in confusion.

She didn't feel that Prince Kelin valued her highly; on the contrary, she had caused the Prince quite a bit of trouble, always disturbing him because of some academic confusion.

Noticing the conversation between the two, Jiemi quietly poked Ram's arm.

"Hey, look over there."

Ram raised his head in confusion and looked in the direction Jiemi was pointing with his index finger.

"What's wrong?"

Jiemi said nervously.

"I always feel the atmosphere between them is a bit subtle."

"You mean... Ilana and Miss Kastelion?" A look of surprise appeared on Ram's face. "But why?"

"I don't know... I was counting on you to help me find out." Jiemi shook his head like a rattle, his face showing both nervousness and a hint of excitement.

Although he was a little worried that Ilana would be bullied by this noble girl, he was also looking forward to the fun that would follow.

Forget it...

Anyway, Prince Kelin definitely wouldn't sit idly by.

"Ilana Ottavia... That's a good name."

Staring intently at the confused Ilana, Oufiya coughed lightly and issued a declaration of challenge in an incomparably serious tone.

"I will not lose to you!"

"...?"

That sudden sentence left Ilana stunned on the spot.

Will not lose to... me?

The other party was already a noble and far superior to her in magic talent. She didn't know how this young lady could win. It seemed more appropriate for her to say "I will not lose to you"?

Of course, only a little more appropriate.

Everyone has a different mission when they come to this world. She had no interest in competing with anyone for anything; she just enjoyed the pure pleasure of being immersed in her own world.

Studying mathematics allowed her to temporarily forget the unhappiness in reality and not have to worry about complex and complicated interpersonal relationships.

Ilana's gaze shifted slightly downward and suddenly fell on the draft paper filled by Prince Kelin, and a hint of realization rose in her eyes.

So that's it...

It's mathematics.

She looked at this new companion who was full of fighting spirit and showed a gentle and encouraging smile from the bottom of her heart.

"Hmm, let's work hard together."

That smile, clear and bright like the afternoon sun, was like an arrow wrapped in honey, instantly piercing Oufiya's heart.

To, together?!

This, this is... how indecent!

She felt her cheeks turn completely red in a "whoosh", and all the fighting spirit and follow-up lines she had prepared were forgotten in an instant.

Damn it!

This person... why can she say such things so calmly?!

"I, I'll go over there and check the instruments..."

Oufiya let out a wail in her heart, dropped a sentence that didn't match the context, turned around in a panic, and fled in a near-disgraceful manner.

Jiemi and Ram, who were secretly watching, both showed expressions of surprise.

Although they didn't know what happened, the respected Miss Kastelion actually lost?

Expressions of admiration appeared on both of their faces simultaneously, and the way they looked at Ilana couldn't help but become filled with awe.

As expected of Miss Ilana, who received the "true teachings" of Prince Kelin!

Simply too strong!

Also not understanding what had just happened, Ilana showed a confused expression on her face and sat down gently.

Speaking of instruments, her next experiment did indeed require some instruments; relying solely on calculation could not solve everything.

I'll go to the Craftsman Street to have a set custom-made in a while...

The "Magical Science" laboratory was filled with a cheerful atmosphere, while in another lonely mage tower, the atmosphere was as oppressive as lead.

This is the 178th Void Realm Observation Laboratory.

Quite different from the vibrant pastoral scenery of the 440th Void Realm, behind the 178th Void Realm is a world wrapped in eternal smog.

Huge factory ruins are like tombstones of steel, paving the boundless wasteland. On the empty streets, apart from the whistling wind, there is not a single trace of human life.

Undoubtedly, this world is dying, like a whale stranded on a shoal.

However, fortunately, its death is an extremely long process, long enough that it might last for several centuries.

In this sufficiently long time, the Academy can follow the "wastelanders" living on this ruin and feast like carrion vultures.

Incidentally, the 178th Mage Tower can also find some clues from behind the Void Realm as to why this civilization, which once flourished, headed toward decline.

According to the archives left by the previous mentor, this world was once exceptionally prosperous, but it is suspected that it fell into a crisis of resource depletion when its civilization reached its peak.

Thanks to this resource crisis, their civilization stagnated in the steam age, and this is thought to be one of the reasons why the Academy was able to establish a stable connection with this world.

The closer the civilization levels of the two worlds, the deeper the consensus between the two worlds. And the higher this consensus, the more stable the Void Realm channel, which also means that the mages of the Academy can reap more benefits from behind the Void Realm.

For the Academy, the 178th Void Realm undoubtedly belongs to high-quality resources, and the "Wraith Coke" it produces in abundance is enough to make the mentors and lower-level professors of the entire Academy drool.

Due to its huge strategic value, Professor Alister has always regarded the 178th Void Realm as his own private property, firmly controlling this Void Realm through the power of the "Thorn" society and extracting resources from it.

However, perhaps because the professor's love was too deep, or perhaps because the professor's subordinates squeezed too hard, the long-term material transfer has severely weakened the width of the Void Realm channel, so much so that the output of the 178th Void Realm in recent years has been far inferior to before.

Alister's original plan was to squeeze the last drop of oil and water from this Void Realm, then find some unimportant small character to take the blame, and finally retreat with his core team after achieving success.

In the end, sustainable development of the Void Realm is just a slogan.

Truly powerful professors never lack Void Realm resources; what they want is for "outsiders" like Hector and Kelin to remain cautious and conduct sustainable research, so as to facilitate them, who are in the core of power, to continuously steal the trash that the people of the other world don't need...

This is true sustainable development of the Void Realm.

However, now, a new turning point has appeared in the situation.

A guy from the Shengcheng stumbled upon a way to "reinforce the Void Realm channel", undoubtedly giving the 178th Void Realm a chance to come back to life!

At this moment, a group of researchers is standing in front of the Void Realm lens, observing in battle array, and looking for any possible timing for interference.

"Mentor, there is still no change." A teaching assistant reported in a low voice, "The Gray People's harvest today is only half a rusted pipe and a few pieces of inferior coke."

"They are too stupid. We have accelerated five Void Realm cycles under the condition of exerting interference, but they haven't noticed any signs of us," the teaching assistant standing next to him also had a frustrated expression and complained, "And there is no totem of faith like the 440th Void Realm here. Source power is everywhere, but it is scattered everywhere, and it cannot be gathered at all!"

Listening to the complaints of the teaching assistants, Mentor Moke, who was in charge of the experiment, said nothing.

He stood with his hands behind his back, staring fixedly at the lifeless wasteland in the lens, his brows tightly locked, his heart filled with anxiety and irritability.

Professor Alister handed him the task of "reproducing the 440th Void Realm experiment", which is both trust in him and a fatal test.

He knows very well the current situation of the 178th Void Realm. This fragile channel may not last long, and this mage tower may lose its connection with the other world at any time.

And once they lose the connection, and have not made any valuable progress before that, his academic career will be about at an end.

Professor Alister will be completely disappointed in him, and he will also become that small character who is abandoned.

Of course.

This path is also one he chose himself.

Without Professor Alister's promotion, relying only on his own strength, it is absolutely impossible to reach the position of mentor.

In the Tower of the Great Sage, there are too many capable people.

"Continue to observe."

Looking at his dejected subordinates, Moke continued expressionlessly.

"The Gray People are by no means as stupid as you imagine! I think that since they can develop a highly prosperous civilization, it shows that they have the 'inspiration' to gain insight into the Void Realm."

"We should be more patient with them!"

Although Moke's palms were covered in sweat from nervousness, at the same time, his heart was filled with confidence.

He had repeatedly studied Prince Kelin's paper, and almost every word in the paper had been crushed and swallowed into his stomach.

At first, like most scholars who read the paper for the first time, he thought it was just nonsense from someone who got lucky. But when he saw the detailed, unquestionable observational data and the clear, logical theoretical model, his mentality instantly changed from disdain to shock, and finally turned into a heartfelt admiration mixed with jealousy.

This guy is simply a genius!

And the bravest kind!

A long time ago, mages in the Academy had also proposed similar conjectures, deepening the connection between the two worlds by actively guiding the civilization in the Void Realm, rather than just passively observing. However, this conjecture was just a conjecture, and no one had dared to try this bold behavior.

No one dared to take this risk at all!

However, this Prince Kelin not only dared to face the risk of the Void Realm collapsing, but even succeeded in one go!

Since Prince Kelin has already proven that this path is feasible, then they only need to walk the path he walked again!

Moke had no doubt that he had thoroughly understood the Prince's paper and had already distilled it into an "outline" for Void Realm exploration in his heart.

First, they must find a suitable spokesperson in the Void Realm. Then, they must bestow upon him absolute authority and power through "miracles". Then, establish a unified religion based on this. Finally, the entire civilization will inevitably become the shape they expect, and they will also be able to obtain more benefits from this newborn world!

Perhaps sensing his strong expectation, as the time behind the Void Realm accelerated, the opportunity he had been waiting for finally arrived.

It was a scavenger on the verge of death.

Perhaps due to exhaustion, or perhaps because he accidentally triggered some terrifying trap, he suddenly collapsed into a messy pile of trash. The gills, composed of countless fine folds, pulsed gently in the thick, toxic fog, just like a fish stranded on the shore.

The fate of an individual, when reaching the end of life, was strangely similar to the civilization behind him... as if this hunched figure was the epitome of the entire Gray People civilization.

He did not give up, still reaching out his hand, wanting to crawl toward the outside of the garbage dump.

Even that unyielding and stubbornness was exactly the same as the civilization that was heading toward decline. He did not let go of any possibility of living, struggling like countless scavengers struggling on this ruin.

At the last moment of his life, in severe pain and despair, he let out the most primitive roar toward the sky, venting his desire for survival.

And it was precisely this strong desire for survival that unexpectedly connected him to a "person" on the other side of the Void Realm who was also full of desire for survival!

That was a high-and-mighty existence, looking down on this declining world with wise eyes, just like the god of death who dominates all things.

"It's him!"

The moment his gaze met those low-hanging eyes, a fanatical light burst out in Moke's eyes, and he ordered the researchers to pause the acceleration of the Void Realm.

Undoubtedly—

This is the best interference object bestowed upon him by Saint Xisi!

On this land full of despair, is there any existence more suitable for spreading the gospel of the Holy Light than this poor wretch on the verge of death?

He almost immediately chose this guy, deciding to foster him as his own "divine messenger", establish an emerging religion worshiping the "savior from outside the domain" on the wasteland, and forcibly twist this civilization struggling in the material ruins onto the path of "spiritualism"!

Everything is just as Prince Kelin demonstrated to them!

Turning to face the teaching assistants who were also excited, he ordered loudly in an unquestionable, near-crazy tone.

"Heal him! No, tell him my name first!"

"Then, bestow upon him life—"

"And, the power he craves!"

(End of chapter) ===== CHAPTER 380 =====