Chapter 37: The Genesis of Theory and a Journey to the Capital

The room remained still, save for the resonant clarity of Lia’s voice.

“…Therefore, in a system where only conservative forces perform work, the sum of kinetic energy and potential energy—that is, mechanical energy—is conserved. Ek₁+Ep₁=Ek₂+Ep₂.”

Klein leaned back against the sofa, his complexion still pale, yet his spirits had visibly lifted.

He listened in silence, showing no inclination to interrupt.

“The significance of this law lies in its offering an entirely new approach to problem-solving. We no longer need to analyze the forces acting upon an object at every single instant of its motion; instead, we merely focus on the energy states at the initial and final points.”

“Energy,” Klein echoed the word. “In magical theory, energy typically refers to mana. What is the relationship between your ‘energy’ here and mana?”

“Unrelated,” Lia responded without hesitation.

“Mechanical energy is a physical quantity possessed by macroscopic objects due to their motion and position. Mana is something else entirely; perhaps… we can consider it the ‘fuel’ that drives the alteration of rules, but it is not mechanical energy itself.”

Klein lapsed into silence for a moment, seemingly processing this profoundly novel concept.

“How would one calculate the gravitational potential energy of a stone upon which a ‘Floating Spell’ has been cast?”

“The Floating Spell counteracts gravity, effectively applying an upward supporting force.

Within the range of this spell’s effect, we can consider gravity to be ‘shielded,’ and thus its gravitational potential energy isn’t discussed.

Alternatively, we could consider the ‘force’ of the Floating Spell to perform negative work on the stone, its value precisely equaling the positive work done by gravity,” Lia explained with impeccable clarity.

“I understand.”

Unbeknownst to them, what began as a lecture intended for recuperation had swiftly evolved into an intense academic discourse. Time flew by amidst their questions and answers.

When Adèle cautiously ascended the stairs, carrying a tray of food, this was the scene that greeted her.

Lia sat in a chair, gesturing animatedly, her voice spilling forth a torrent of words Adèle found utterly incomprehensible.

Her mentor, the usually stern and aloof Klein, reclined on the sofa, eyes closed, as if listening to the most sacred scripture.

“…So, the work-energy theorem possesses a higher universality than the conservation of mechanical energy, because it encompasses situations where non-conservative forces perform work…”

Adèle listened for a while, feeling her mind turn to mush. She quietly placed the food on a small table, away from the two of them, then discreetly retreated, gently closing the door behind her.

The moment the door clicked shut, she felt the entire world grow peaceful.

The fourth floor had once again transformed into a realm beyond her comprehension.

The lecture continued until dusk. Only when Lia uttered the final word did she realize her throat was parched to the point of feeling as though it might emit smoke.

Klein opened his eyes and sat upright. Though his complexion still appeared somewhat poor, the precarious fragility that had clung to him had vanished.

“I require a period of adjustment,” he stated, looking at Lia. “I must fully digest this, then undertake a preliminary integration with my existing knowledge system.”

“Then you should rest well,” Lia said, standing up, feeling as though she had just fought a hard battle.

“Your strength is still somewhat lacking,” Klein suddenly remarked.

Lia froze.

“Retrieve the magic manual I gave you and begin studying it. Within two days, I expect to see you successfully cast an offensive spell,” he commanded.

***

Two days later, in the Mage Tower’s underground training ground.

Lia extended her hand, her mental energy converging in her palm, meticulously constructing the spell model according to the structure described in the manual. The magical elements in the air began to stir with renewed vigor.

“Focus, compress, then release,” Klein’s voice resonated beside her.

Fine beads of sweat broke out on Lia’s forehead. A fist-sized fireball coalesced above her palm, its color shifting from faint red to vibrant orange, radiating scorching heat.

She aimed at a target fifty meters away, then abruptly thrust the fireball forward.

Whoosh!

The fireball shrieked as it streaked through the air, carving a bright trajectory before precisely striking the bullseye.

Boom!

The target exploded, sending splinters of wood flying in all directions.

Lia gazed at her hand, a hint of elation sparking within her.

“Not bad,” Klein’s assessment was as concise as ever. “The structure is stable, and the energy conversion rate is approximately seventy percent, which is excellent for a novice.”

Lia retracted her hand, a newfound sense of confidence settling in her heart.

Though it was merely a first-tier spell, at least she was no longer defenseless.

“I intend to visit the Magic Association,” Klein announced, turning to walk out of the training ground. “Your thesis needs to be submitted to the council for final review.”

“May I come with you?” Lia blurted out almost instinctively.

She had been in the nation’s capital for so long, yet apart from Klein’s Mage Tower, she had seen no other places. She longed to witness firsthand what the heart of this nation looked like, to observe how the customs and characteristics of the capital differed from those she had experienced in her family’s domain.

Klein paused, turning back to look at her.

“The Association headquarters are dangerous.”

“Isn’t staying by your side the safest option?” Lia retorted.

Klein was taken aback for a moment, the corners of his lips curling into a faint smile, but he did not immediately reply.

He seemed to be weighing the pros and cons.

Lia’s heart fluttered with anticipation; she desperately wanted to go out and see the world.

“You may,” he conceded a few seconds later. “But there is one condition.”

“What condition?”

“Under no circumstances are you to leave my side by more than five hundred meters. Ideally, you should not leave my sight at all.”

“Deal!” Lia instantly agreed, fearing he might retract his offer.

Klein nodded, saying nothing further. He extended his hand.

“Give me the pendant.”

Lia, though puzzled, obediently removed the ‘Heart of the Guardian’ from her neck and handed it to him.

Klein took the pendant; the silver metal casing rested quietly in his palm. He covered it with his other hand, and a torrent of majestic mana began to surge into it.

Lia could feel the surrounding magical elements converging into Klein’s hands; the small pendant seemed to transform into a bottomless vortex. The runes on its surface glowed one by one, emitting a soft silver light, and its previously somewhat dim ornamentation regained its brilliant luster.

The entire process lasted for approximately one minute.

Klein released his hand, returning the pendant to her.

“There, put it on.”

Lia took the pendant, its feel entirely different from before. What was once cool metal now carried a gentle warmth, as if life itself resided within it.

She placed the pendant back around her neck, and that warmth seeped through her skin, permeating her body, bestowing upon her an unprecedented sense of security.

“Let’s go,” Klein said, turning towards the teleportation platform on the first floor.

Lia quickly followed. She knew this trip to the Association would be far from a simple sightseeing excursion.

Her theories were about to officially step onto the world’s stage.