Chapter 28: The Voice in the Mind

Lia was hunched over her desk the next day, thick sheets of parchment spread before her.

A paper densely covered with text, detailing various formulations of the theory of universal gravitation, lay positioned where Lia could easily see it, aiding her in organizing her thoughts.

The derivation of universal gravitation proved more intricate than she had anticipated.

The complexity wasn’t purely mathematical; rather, it lay in repackaging knowledge from another world into a language comprehensible to this one.

She bit the end of her quill, sketching elliptical orbits across the page.

“Kepler’s Third Law… no, here it’s called the Third Law of Stellar Motion,” she murmured to herself. “The square of a planet’s orbital period is directly proportional to the cube of its semi-major axis…”

Her quill glided swiftly across the paper, formulas appearing in neat rows on the parchment.

Soon, however, she encountered an obstacle.

To rigorously derive the law of universal gravitation, she would need the concept of limits from calculus and the notion of centripetal force.

Yet, in this world, centripetal force had never even been defined.

“Damn it,” Lia muttered, rubbing her temples. “I can’t possibly rebuild the entire system of physics from scratch.”

As she wrestled with her frustration, a knock echoed at her door.

“Come in.”

Klein pushed the door open, a magic scroll clutched in his hand.

His expression was graver than usual, and a sharpness Lia had never witnessed before gleamed in his blue eyes.

“Mentor?” Lia questioned, setting down her quill.

“The Association just issued an emergency summons,” Klein stated, placing the scroll on the table. “A large-scale beast riot has erupted at the border, requiring mages of the Eighth Ring and above for support.”

Lia blinked.

“You’re going?”

“I must,” Klein affirmed with a nod. “A summons of this magnitude cannot be refused by anyone.”

He approached Lia, his gaze falling upon the pendant at her chest.

“Remember my words,” he instructed. “Wear this, no matter when or where.”

“I will,” Lia promised, feeling the chill around her neck intensify slightly. “When will you return?”

“Three days, at the earliest,” Klein replied, withdrawing his hand. “While I am gone, see no one except Adèle.

Should anyone attempt to force their way into the tower, activate the Guardian’s Heart immediately.”

Lia nodded, discerning the worry in Klein’s tone, which in turn tightened a knot of apprehension within her.

“That derivation…” Klein murmured, glancing at the parchment on the table.

“I’ll continue working on it,” Lia assured him. “Please, go without worry.”

Klein stood in the room for a few moments, then finally turned and departed.

“Lia,” he paused at the doorway. “Protect yourself.”

After the door closed, the tower settled back into silence.

Lia heard the faint hum of a magic circle activating downstairs, followed by a profound, deathlike stillness.

She touched the pendant at her chest, then picked up her quill once more.

The derivation of universal gravitation had to continue.

Regardless of what transpired outside, this theory simply had to be completed.

***

Time ticked by.

The formulas on the parchment proliferated, and Lia’s brow furrowed ever deeper.

It seemed that for universal gravitation to manifest in this world with irrefutable certainty, many properties would first need precise definitions.

Just as she was agonizing over the precise articulation of a definition, the temperature in the room abruptly dropped several degrees.

Lia paused her writing, lifting her head to gaze around.

Nothing seemed amiss.

The windows were tightly shut, and the fire in the hearth still burned steadily.

Yet, the chill was undeniably real, a cold that seeped deep into her very bones.

She rose, walking to the window to peer outside.

The garden outside the tall tower lay serene.

Twilight sunlight spilled onto the stone path, revealing no unusual shadows or movements.

“Strange…”

Just as Lia was about to turn back to her desk, a voice suddenly resonated within her mind.

It wasn’t a sound she heard with her ears, but rather one that manifested directly within her consciousness.

“Calculus is flawed.”

Lia froze.

“What?” she instinctively uttered.

“The fundamental premise of calculus is erroneous,” the voice continued. “The very concept of the infinitesimal is self-contradictory.

A quantity is either zero or it isn’t.

How can it be both infinitely close to zero and yet not equal to zero?”

A chill ran down Lia’s spine.

The voice was not her own, yet it spoke within her mind.

“You… who are you?”

“I am here to help you discern the truth,” the voice replied. “You have been blinded by complex symbols.

The definition of limits is merely a word game.

Derivatives and integrals are nothing more than clever illusions.”

“Nonsense!” Lia retorted loudly. “Calculus has a rigorous mathematical foundation; the ε-δ definition is entirely self-consistent!”

“The ε-δ definition?” the voice scoffed, a mocking tone evident. “That is simply using more complex concepts to obscure a fundamental contradiction.

You say δ can be arbitrarily small, but how small is it, truly?

If it isn’t zero, then it isn’t truly infinitesimal.

If it is zero, then the entire definition loses its meaning.”

Lia felt as though a pedantic contrarian had taken up residence in her brain.

“You don’t understand mathematics at all!” she exclaimed, exasperated. “The definition of a limit is…”

“Is what?” the voice interrupted her. “A state that can never be truly reached?

Why, then, build an entire mathematical system upon a state that is eternally unattainable?”

Lia opened her mouth, only to find herself momentarily speechless, unsure how to retort.

It wasn’t because her interlocutor was correct, but because the sophistry of the argument sickened her.

It was akin to someone asserting, “Since you cannot prove the sun will rise tomorrow, prove the Earth is flat instead.”

“And universal gravitation,” the voice continued. “The gravitational force between two objects is inversely proportional to the square of the distance between them?

Then, as the distance approaches zero, the gravitational force would become infinitely large.

This is physically impossible.

Therefore, the formula itself is flawed.”

Lia’s temples began to throb.

“You’re twisting the concept!” she countered. “When the distance approaches zero, the scope of classical mechanics ends, and other theories take over…”

“Other theories?” the voice chuckled. “Are you suggesting that when one theory runs into trouble, you simply invent another to patch things up?”

Lia felt her blood pressure soaring.

The voice’s method of argumentation was a textbook example of sophistry.

It deliberately ignored the scope of the concepts, conflated the distinction between mathematical abstraction and physical reality, and then used this confusion to negate an entire theoretical framework.

“Your argument holds no water!” Lia declared loudly. “Mathematical abstraction itself is meant to handle ideal scenarios, and physical theories have their domains of applicability—that’s common sense!”

“Common sense?” the voice’s tone grew even more contemptuous. “Then why do mages in this world die from exploding heads when they study your theories?

If these theories are correct, why do they clash so violently with their existing understanding?”

Lia was stunned.

“What does this indicate?” the voice pressed on. “It indicates that your theories conflict with the fundamental laws of this world.

You are using a flawed logic to overturn a correct system.”

The deduction sounded plausible, yet Lia swiftly realized it was merely another piece of sophistry.

“Cognitive conflict does not equate to theoretical error!” she countered. “When the ancients proposed the heliocentric model, it too sparked immense controversy, but time proved them correct!”

“Then, what evidence do you possess to prove you are correct?” the voice questioned. “Beyond those intricate mathematical derivations, can you offer any experimental verification?”

Lia’s mouth opened, then closed again.

In this world, she truly could not provide experimental verification.

Lacking precise measuring instruments and modern experimental conditions, she could only rely on mathematical derivations.

“See? You have no evidence either,” the voice declared triumphantly. “You are merely using a mathematical language of your own invention to describe a world that fundamentally does not exist.

And those who believe you are paying the ultimate price for this erroneous belief.”

Lia felt her brain on the verge of exploding.

It wasn’t because her antagonist was right, but because this logic, which twisted black into white, infuriated her beyond measure.