Chapter 142: The Paradox of the Arrow

The morning sunlight pierced through the floor-to-ceiling windows of the Mage Tower, shining upon the finished thesis on the desk.

The ink had already dried.

Lia sat at the table, holding a cup of cold coffee in her hand.

She looked across the table.

Klein was holding those few sheets of thin parchment.

He had been maintaining that same posture, reading for a full twenty minutes.

He had not turned a page.

He had not spoken.

Even his breathing frequency had dropped to a minimum.

The air in the room felt somewhat stagnant.

Lia set down her cup.

The porcelain cup made a crisp clink as it touched the table.

Klein’s eyelids flickered.

He set down the thesis.

His blue eyes no longer held their usual calm; instead, they were bloodshot.

He looked at Lia.

“One portion by one portion.”

Klein’s voice was somewhat raspy.

“Yes,” Lia answered.

“Not flowing, but jumping.”

Klein raised his hand.

A cluster of blue arcane fire ignited in his palm.

The flames flickered, their light soft and appearing continuous.

“According to your theory…”

Klein stared at the flames in his hand.

“This fire is not burning continuously, but is undergoing countless extinguishing and re-igniting cycles at an extremely minute level, imperceptible to the naked eye.”

“It is a collection of countless energy packets.”

“There are breaks in between.”

Lia nodded.

“Correct.”

Klein’s palm snapped shut.

The fire was extinguished.

He closed his eyes.

His face was pale.

A layer of fine cold sweat broke out on his forehead.

The mana circuits within his body were undergoing a violent tremor.

The magical cognition he had built over so many years—those axioms regarding mana being as smooth and flowing as water—were being ruthlessly shredded by the formulas on these few sheets of paper.

Continuity was the cornerstone of magic.

If energy was discontinuous, what was the point of integrals?

Were those elegant curves, those grand magic arrays, all sandcastles built upon an illusion?

Lia did not speak.

She watched him quietly.

The Heart of the Guardian pendant in her hand felt slightly warm.

She was waiting.

If Klein couldn’t hold on, she would immediately use physical means to knock him out.

Several minutes passed.

Klein opened his eyes.

The bloodshot veins in his eyes receded slightly.

The restless mana fluctuations also calmed down.

He let out a long breath.

“It feels terrible,” Klein said.

“Like someone took a blunt knife and hacked my spiritual sea into countless fragments.”

He picked up the thesis on the table.

His finger traced over that constant.

“But.”

“He is right.”

Klein stood up.

He walked to the window, looking out at the rolling architecture of the kingdom.

“Though it is ugly, though it is fragmented…”

“It explains that damned experimental data.”

“And that is enough.”

He turned around and picked up his mage robe hanging on the rack.

“Let’s go.”

Lia jumped off her chair.

“Where to?”

“The Mages’ Association.”

Klein pushed open the door.

“Since someone has to go mad, let everyone go mad with us.”

***

The headquarters of the Kingdom Mages’ Association.

People were coming and going in the hall.

The recent controversy regarding blackbody radiation made this place even more bustling than usual.

Everywork, mages could be seen arguing until their faces were red while clutching scratch paper.

The light of the teleportation array flared.

Lia and Klein stepped out.

The originally noisy hall fell silent for an instant.

There was no one now who didn’t recognize these two.

One was the creator of calculus and an honorary professor of the Physics Department.

The other was the kingdom’s youngest Eighth-Circle Archmage, known as a legendary protective maniac.

Lia kept her eyes forward.

She walked straight to the counter of the Theory Review Committee.

The receptionist was the same young mage from last time.

Seeing Lia approach, he immediately stood up straight, his face piling on a professional smile.

“Professor Lia, Master Klein.”

“How can I be of service to you?”

Lia placed the thesis on the counter.

“Submission.”

“Certainly.”

The receptionist skillfully picked up a stamp.

“For Introduction to Magic or Physics Reports again?”

“No.”

Lia shook her head.

“Send it to Arcane.”

“Front page.”

“Urgent.”

The receptionist froze for a moment.

Arcane was a journal for the entire continent, usually only publishing major discoveries.

He looked down at the title of the thesis.

On the Theoretical Basis of the Law of Energy Distribution in the Normal Spectrum.

It looked very ordinary.

He scanned further down to the abstract.

The stamp in his hand fell onto the table with a clatter.

“Could I… trouble you to let me look at that again?”

The receptionist’s voice was trembling slightly.

He pointed at that line of text.

“Energy… discontinuous?”

“You didn’t misread it.”

Lia tapped the counter.

“Stamp it.”

The receptionist swallowed hard.

Trembling, he picked up the stamp and pressed it down.

That one stamp…

Stamped out a world of chaos.

***

Merely two hours passed.

The entire Mages’ Association exploded.

The urgent supplement of Arcane spread to every corner like a plague.

“Absurd!”

An angry roar erupted from the second-floor lounge.

Immediately following was a loud bang.

A wall was smashed by rampaging mana.

An old mage rushed out, waving that copy of the newspaper in his hand.

“Energy quanta? Individual portions?”

“This is a total denial of our thousands of years of heritage!”

“This is a desecration of the Goddess of Magic!”

“That little girl has gone insane!”

More people gathered around.

As they read the content on the paper, some turned pale and fainted on the spot.

Some calculated frantically, trying to find a loophole in the formula, only to start tearing their hair out while muttering “impossible.”

Others simply spat out a mouthful of blood, their spiritual power running wild because their worldviews could not accept this interruption.

The association hall was in complete turmoil.

Lia sat on a sofa in the lounge area, watching the chaos outside indifferently.

她手里捧着一杯热茶，

She held a cup of hot tea in her hand.

Klein sat beside her, a book in his hand.

He had opened an invisible barrier, keeping all the noise and flying debris out.

“It’s livelier than I imagined.”

Lia blew on the tea leaves.

“This is only the beginning,” Klein said, turning a page.

“This is just the cognitive shock.”

“Wait until they regain their senses; the real…”

Before he could finish his sentence, the massive crystal chandelier in the center of the hall shook violently.

The gravity field within the hall became turbulent without warning; even space itself emitted a groan of being overstrained.

The originally noisy crowd fell silent instantly.

Everyone looked up, watching the mid-air in awe.

Three figures hovered there.

On the left was one wearing red robes, his beard resembling burning flames—Fire Master, Pairo.

In the middle was one in blue robes, surrounded by flowing water—Fluid Master, Aqua.

On the right was one in cyan robes, his feet treading upon rotating air currents—Air Master, El.

Three Eighth-Circle Archmages.

They ignored the clamoring crowd and walked straight toward the lounge area.

The crowd automatically parted to create a path.

Pairo walked up to Lia.

His eyes, burning with fire, stared fixedly at Lia.

The temperature in the air instantly rose by a dozen degrees.

“Lia Farrien.”

Pairo’s voice boomed like thunder in everyone’s ears.

“Withdraw your thesis.”

“Admit that it is nonsense you fabricated just to explain the data.”

“Otherwise.”

He raised the staff in his hand, the tip pointing at Lia’s nose.

“We shall initiate a trial against you in the name of Truth.”

Lia set down her teacup.

She looked up at these three fierce-looking old men without showing any fear.

“Data doesn’t lie,” Lia said.

“If the theory doesn’t match the data, it is the theory that is wrong, not the data.”

“Even if you have used that theory for thousands of years.”

“Arrogance!”

Aqua let out a cold snort.

The surrounding water elements began to grow restless.

“Do you think because you invented calculus, you are qualified to dictate the essence of the world?”

“The foundation of calculus is continuity!”

“You are denying your own book!”

“I am merely correcting it.”

Lia stood up.

She was only as tall as their chests, yet her aura did not lose out in the slightest.

“Since you are not convinced…”

“Then let us debate.”

“Right here.”

The whole hall was in an uproar.

Another Debate of Truth.

Last time it was against Balthazar.

This time, it was against three Eighth-Circle mages.

And it concerned the very bottom-most logic of magic.

“Fine,” El spoke up.

His voice was very soft, but it carried a bone-chilling coldness.

“We will let you know that the continuity of the world is an unquestionable iron law.”

“We will use logic to completely crush your ridiculous quantum theory.”

***

Ten minutes later.

The Central Auditorium.

The place was once again packed to the brim.

Augustus hurried over and sat in the judges’ seats.

His expression was very solemn.

He looked at Lia on the stage, then at those three old fellows.

This matter had blown up.

If Lia lost, the Physics Department might be disbanded immediately.

If these three old men lost… Augustus didn’t dare to think about it.

That would mean the entire magical system would have to be rewritten.

The debate began.

Pairo was the first to step forward.

He did not use magic to demonstrate.

He used logic.

Pure, ancient logic derived from philosophy.

“Miss Lia claims that energy is in discrete portions, that it is discontinuous.”

Pairo looked at the audience below.

“Then, this means the world is composed of individual, broken ‘instants’.”

“Since that is the case…”

“I ask you.”

He turned, pointing at a pillar at the end of the hall.

“Suppose there is a runner skilled in divine speed, Achilles.”

“He wants to chase down a crawling tortoise ahead of him.”

“The tortoise is a hundred meters in front of Achilles.”

“Achilles’s speed is ten times that of the tortoise.”

Pairo’s voice was full of confidence.

“If the world is continuous, Achilles will catch the tortoise very quickly.”

“But if we follow Miss Lia’s theory, the world is discontinuous and composed of minimum units.”

“Then.”

“When Achilles finishes this hundred meters, the tortoise has already crawled forward ten meters.”

“When Achilles finishes these ten meters, the tortoise has crawled forward another meter.”

“When Achilles finishes this one meter, the tortoise has crawled forward zero point one meters.”

Pairo spread his hands.

“And so on.”

“No matter how fast Achilles runs, he must pass through an infinite number of such steps.”

“As long as the tortoise is moving, it will always be ahead of Achilles.”

“Without continuous time and smooth space, Achilles will never catch the tortoise!”

“This is the paradox of discontinuity!”

The hall fell into a dead silence.

Everyone followed Pairo’s train of thought.

It seemed… sounded like… the logic was impeccable?

‘If things are disconnected, then he truly will always be a tiny bit short.’

Al sat in the audience, sweating profusely.

‘How… how do you refute this?’

Before the crowd could react, Aqua stepped up.

He took over the topic.

“Not only that.”

“If energy and time are in discrete portions…”

“Then motion itself does not exist!”

Aqua pulled an arrow from his sleeve.

“This is a Windrunner’s arrow.”

“Look at this arrow.”

“At every instant, this arrow occupies a definite spatial position.”

“In this instant, it is stationary.”

“If time is composed of such ‘instants’, then the arrow is stationary at every instant.”

“Stationary plus stationary is still stationary.”

“Therefore, the arrow can never move.”

“This is the dead end of your theory!”

The three Great Mages stood on the stage, their momentum like a surging tide.

The audience below began to waver.

The whispering grew louder and louder.

“Yeah, how do you explain that?”

“If every instant is stationary, then it really can’t move.”

“Is Professor Lia really wrong?”

Lia’s face showed no hint of panic.

She looked at the three old men; a sharp light flashed in the depths of her eyes.

This was exactly the opportunity she was waiting for.

‘Using macro-logic to fit a micro-world?’

‘Using classical mathematics to explain quantum leaps?’

‘That’s the strength of Eighth-Circle Archmages?’

She took a step forward, her heels clicking clearly on the wooden floor.

“Are you finished?”

Lia asked, her voice not loud, yet its penetration was extremely strong.

Pairo frowned.

“What? You still want to argue?”

“It’s not an argument.”

Lia walked to the blackboard.

She picked up a piece of chalk and weighed it in her hand.

“I am here to tell you that your logic traps, which you take such pride in, exactly prove the absurdity of continuity.”

“And.”

“To tell you why your Achilles is a fool.”

“Why your arrow cannot fly in your minds.”

Lia turned around.

The chalk pressed against the blackboard. With a snap of her wrist, a crisp breaking sound echoed in the silent auditorium.

That broken piece of chalk rolled to the ground, appearing like a final mockery directed at the continuous world.

“Watch closely.”

“This is your chance to understand what true truth is.”