Chapter 143: The Steps of Truth

The air in the grand auditorium was so thick it was almost viscous.

Lia Farrien patted the chalk dust from her hands.

She drew a straight line on the blackboard.

“The reason Achilles can never catch the tortoise is based on an incorrect premise.”

Lia turned, looking at Pairo.

“You all assume that space is infinitely divisible.”

Pairo let out a cold sneer.

“Is it not? ‘The length of a foot, halved every day, will not be exhausted in ten thousand generations.’ This is a geometric axiom every three-year-old apprentice knows.”

“That is a mathematical axiom,” Lia said.

“It is not a physical law.”

Lia picked up a new piece of chalk and drew two points.

“In mathematics, there are infinite numbers between zero and one. But in the physical world, there exists a minimum unit of length.”

She wrote an extremely complex constant derivation on the blackboard, finally circling a tiny value.

“When the distance is smaller than this value, space no longer has meaning.”

“Achilles does not need to run past those infinite points of division.”

Lia’s finger traced an arc through the air.

“He only needs to step over them.”

“Like stepping over a threshold.”

“On a microscopic scale, Achilles isn’t moving smoothly; he is performing a series of extremely minute jumps.”

“When the distance between him and the tortoise shrinks to this minimum unit, his next movement puts him directly in front of the tortoise.”

“There is no process of ‘not being able to catch up’.”

“There are only two states: ‘behind’ and ‘in front’.”

***

The audience erupted in an uproar.

Adèle’s mouth hung open, the quill in her hand falling to the floor.

‘Jumping… It’s not running across, but jumping across?’

The sneer on Pairo’s face froze.

He stared fixedly at the symbol representing “minimum length” on the blackboard.

This completely defied his intuition.

But he could find no loophole in the logic.

If space truly had a minimum unit, then his paradox would collapse on its own.

Because an infinite series was forcibly truncated in physics.

“This is impossible…” Pairo grit his teeth.

“How could space be composed of particles? If space is disconnected, what lies between? The void?”

“It is meaningless,” Lia answered decisively.

“Just as you cannot go to a bookstore to buy half a book, nor to the market to buy half an egg.”

“There is no ‘middle’ between the minimum units.”

“Because the space you imagine to be between them simply does not exist.”

Aqua’s gaze turned sharp.

The Fluid Master’s eyes were filled with a divine light.

“Then what if time is also fragmented? If time is broken into pieces, then this arrow is stationary at every point in time.”

“How can the sum of infinite moments of stillness result in motion?”

“In reality, it doesn’t move,” Lia said, looking at Aqua.

“It is ‘refreshing’.”

The entire hall fell into a dead silence.

Refreshing.

This was a word that had never appeared before in this context.

Lia walked to the edge of the podium and picked up a thick stack of parchment.

On the edge of each sheet, she drew a stick figure.

On the first sheet, the stick figure was on the left.

On the second, it shifted slightly to the right.

On the third, a bit further right.

Lia pinched the corner of the paper and flipped through them rapidly.

In everyone’s sight, the stick figure began to “run.”

“Do you see it clearly?” Lia stopped her movement.

“On every individual sheet, the stick figure is stationary.”

“But when they switch rapidly, you perceive it as movement.”

“Our world is this stack of parchment.”

Lia tossed the paper back onto the table.

“Every ‘time quanta’ is one sheet of paper.”

“On this sheet, the arrow is stationary.”

“On the next sheet, the arrow appears a little bit further ahead.”

“And on the next, further still.”

“The arrow never ‘flies’.”

“It simply disappears and reappears continuously at different coordinates in time and space.”

“What you call motion is, in essence, high-frequency refreshing.”

Aqua retreated two steps.

His face was deathly pale.

The staff in his hand trembled slightly.

This explanation was insane.

But it perfectly bypassed his logical trap.

If motion was not a continuous change in position but a transition of coordinates, then his logic failed completely.

“Sophistry!”

El, who had been silent, finally spoke.

The Air Master suddenly waved his hand.

A gale whistled through the auditorium.

Countless tiny wind blades spiraled through the air, emitting sharp shrieks.

“How could the world be a stack of paper! The wind is continuous! Water is continuous! It is lingering and smooth!”

“If the world were fragmented, why would my wind blades not break apart? Why would my mana not be interrupted?”

El raised both hands high.

A massive cyan sphere of wind formed above his head.

The high-speed rotating current tore at the surrounding air.

“I will prove you wrong. Using the most direct manifestation.”

El looked at the other two.

“Let us work together. Construct an absolutely continuous force field.”

“If space has gaps, then our force field will have loopholes. If the force field is flawless, it proves she is lying!”

Pairo and Aqua exchanged a glance.

Both raised their staffs simultaneously.

Red flames surged up.

Blue currents of water erupted.

Wind, fire, water.

The three elements intertwined in the air.

Three Eighth-Circle Archmages casting a spell together—this was extremely rare in the history of the Mages’ Association.

Augustus stood up abruptly.

“Stop! This is an auditorium!”

“Klein!”

The principal didn’t need to remind him.

Klein had already moved.

He stepped forward, shielding Lia.

Arcane radiance lit up his blue eyes.

A transparent barrier expanded instantly.

“Let them do it,” Lia’s voice came from behind Klein.

She lightly pushed against Klein’s back.

“Don’t stop them.”

“This is the best possible experiment.”

Klein glanced back at her.

Lia’s expression was calm, even carrying a hint of anticipation.

Klein withdrew his mana but remained standing half a step to her side, ready to act at any moment.

The three forces fused together.

A multi-colored sphere hovered on the stage.

It was spinning.

The surface was as smooth as a mirror, without a single flaw.

A perfect sphere.

Perfect continuity.

“Do you see it?”

Pairo’s voice was distorted by the output of mana.

“This is continuity! There are no breakpoints!”

“If there were minimum units, this surface should be jagged, like sand!”

“But it is smooth!”

“Lia Farrien, what do you have to say to this?”

Lia looked at the sphere.

It was beautiful.

Truly beautiful.

It was the final afterglow of classical physics.

“Macroscopic smoothness cannot hide microscopic fragmentation.”

Lia slowly put down the paper in her hand.

“You think it is smooth because your eyes are too coarse.”

“Or rather, the mana you input is too coarse.”

Lia said to Pairo, “Look at your perfect creation.”

“Use your spiritual power to perceive the very edge of that sphere.”

“Don’t look at the whole.”

“Look at that tiny point, a point a hundred million times smaller than a speck of dust.”

Pairo let out a cold snort.

He would look.

Truth did not fear the microscopic.

Pairo’s spiritual power followed his gaze, compressing frantically and focusing on an infinitesimal point on the sphere’s surface.

Aqua and El joined in as well.

The spiritual powers of three Eighth-Circle mages stacked together.

Their perception breached conventional limits.

Their field of vision enlarged.

Larger.

Larger still.

The originally smooth surface of the sphere began to blur.

And then—

They felt it.

They saw it.

It was not a smooth curve.

It was steps.

Extremely subtle, yet undeniable steps.

Energy did not flow like water; it was piled up like bricks.

Layer upon layer.

Because the bricks were too small, the wall appeared smooth on a macro level.

But on a microscopic level, it was serrated.

“This…” Pairo’s hands began to tremble.

“Impossible…”

“Why are there steps?”

“Why isn’t it an arc? Where did the curve go?”

Lia’s voice rang out at the perfect moment.

“There are no curves.”

“There are no perfect circles in this world to begin with.”

“Every circle is just a polygon made of countless tiny straight line segments.”

“When there are enough sides, it looks like a circle.”

Lia pointed at the still-spinning sphere.

“The essence of integration is summation.”

“So-called continuous functions are nothing more than approximate fits for an infinite number of discrete points.”

“Your magic models are built on calculus.”

“You believe integration is the essence of the world. You are wrong.”

“Summation is the essence.”

“Integration is merely a tool invented for the convenience of calculation.”

These words were like a sledgehammer, slamming ruthlessly into the souls of the three men.

The continuity they revered as truth was merely an approximation tool.

“No!” Aqua let out a roar.

“If water isn’t continuous, what is flow?”

“If energy is in chunks, what lies between this chunk and that one?”

He frantically drove his mana.

He attempted to fill those “steps” at the microscopic level.

He wanted to grind down those serrations.

He wanted to create true smoothness.

“Fill it!”

Torrents of water lashed the sphere.

El joined in.

The gale howled, trying to squeeze into every tiny gap.

Pairo bit his lip until it bled.

Flames were injected madly.

“No gaps! Absolutely none!”

They were fighting against the laws of physics.

They were attempting to use finite energy to fill infinite detail.

Lia shook her head.

“Stop.”

“You are attempting the impossible.”

“To achieve absolute continuity at the microscopic level, the energy required is infinite.”

“That is the ‘Ultraviolet Catastrophe’ in Planck’s formula.”

“You will burn yourselves dry.”

No one listened to her.

The three Archmages had fallen into a kind of mania.

Their worldview was collapsing.

If they could not restore this sphere to perfect continuity, their decades of cultivation would become a joke.

Their mana output power broke past its limits.

The space within the auditorium began to warp.

The sphere grew brighter and brighter.

But no matter how hard they tried, in the perception of their spiritual power, those steps remained.

The “quantum” jumps became even more violent due to the increase in energy.

Like a prisoner who has lost his reason, he cannot suppress his desire.

They were humble and affectionate, crawling at her feet.

Like an invisible large hand, in the dark void.

Those souls could not enter; they turned into energy.

Energy was stripped.

Energy was plundered.

Energy was exhausted.

Energy vanished.

Dark and empty.

Energy was not gone; it gathered in the dark abyss.

It was sucked away.

The flow of energy.

The abyss is infinite; the bottomless pit devours everything.

Energy was taken away by it.

It was an endless black hole.

It devoured everything.

Cerebral cortices were scratched madly.

Logic loops broke.

Cognitive foundations shattered.

Like a whirlpool in the dark. Energy was devoured. Energy was plundered.

She, who had devoured the energy. She was not without emotion. Her emotions were hidden in the depths.

Like a warm current surging beneath the icy sea.

“Why are you angry?”

He did not speak.

His face was pale.

“Am I angry?”

“Energy is being consumed.”

“I felt it.”

“Energy cannot stop.”

“Energy is dissipating.”

Energy gradually dissipated.

“I do not like it.”

Energy did not disappear. Instead, the energy was roaring. They refused to be smooth.

They stubbornly maintained their discrete portions.

“Why won’t it fill!!!”

Tears streamed from Pairo’s eyes.

His spiritual power was being torn apart by those serrations.

He saw it. Between those steps was an abyss.

Absolute nothingness.

No matter how much mana was poured in, it was infinite void.

It was simply impossible to make energy stay in that “between the steps” position.

It could either be on this level or that level; it could never stay in the middle.

This counter-intuitive phenomenon…

“AAHH!”

Aqua was the first to collapse.

He clutched his head and let out a piercing scream.

The water elements around his body instantly lost control.

The originally supple currents became as hard as iron, striking him like bullets.

Puh-puh-puh!

Blood splattered.

“It’s in grains… individual grains…”

Aqua fell to the floor, his whole body twitching.

He was still muttering incoherently.

“It’s all particles… water is sand… I am also sand…”

Next was El.

The Air Master tried to cut off his connection to the magic, but his spiritual power was already locked with the sphere.

He saw the essence of the wind.

It was the chaotic collision of countless gas molecules.

There was no direction, no pattern.

Brownian motion.

“There is no wind…”

El knelt on the ground, blood flowing from his orifices.

Finally, there was Pairo.

The most stubborn Fire Master.

His eyeballs were bloodshot, nearly popping out of their sockets.

He stared fixedly at the sphere.

“I don’t believe it!”

“I am Eighth-Circle!”

“I can define the rules!”

“Connect for me!!!”

He raised his staff toward the sphere, attempting to use physical means to forcibly fuse it.

But the moment the staff touched the sphere—it exploded.

Countless energy particles lost their bound state and returned to a state of high-frequency jumping.

BOOM!

A visible shockwave erupted.

The barrier Klein held open shook violently.

The audience members were blown off their feet.

The dust cleared.

Pairo lay in the center of the ruins.

His staff was broken in two.

His head was tilted to one side, half his hair scorched, his eyes vacant as he stared at the ceiling.

White foam bubbled from his mouth.

His fingers were still gesturing unconsciously in the air, as if drawing individual, disconnected line segments.

“Broken… it’s all broken…”

“There’s no going back…”

A deathly silence filled the auditorium, punctuated only by a few occasional coughs in the distance.

Three Eighth-Circle Archmages—titans of the kingdom’s magic world—had gone mad in ten short minutes.

Driven mad by a formula, by a concept.

Augustus stood up tremblingly.

He looked at the pitiable state of his three old friends, then at Lia standing to the side, completely unharmed.

He could only let out a sigh.

He wanted to say something, but in the end, he didn’t.

Lia tidied the bangs that had been ruffled by the wind.

“I said it before.”

Lia’s voice echoed in the silent hall.

“Do not let your arrogance limit the shape of truth.”

She turned around, facing the ashen-faced mages in the audience.

“Now.”

“Who else still feels that the world is continuous?”