Chapter 16
Chapter 16
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Translator: Ace
Chapter: 16
Chapter Title: Achilles and the Tortoise
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"I've caught up! ...Huh?"
After Gwendolyn Everglow fell into the tortoise's trap.
The other students began to move as well.
"If speed's the problem, then I'll show you extreme speed!"
One senior mage condensed flames in both hands, then detonated them behind his back.
With a thunderous boom, his body shot forward like a rocket.
Another student tried to manipulate the track itself.
"Rise, O earth!"
At his shout, the marble floor bulged upward, surging forward like a wave and carrying him along.
Magic to reduce air resistance, spells to eliminate friction with the ground— all sorts of bizarre attempts flew around wildly.
But soon, they all realized the truth.
This wasn't a race of speed.
"What the...!"
"I can't pass it!"
Take one step closer, and the tortoise advances 1/10th as much.
Close that 1/10th, and it creeps forward another 1/100th.
This infinite chain of processes.
This was a prison woven from pure logic.
"Damn it! Why won't it work?"
A senior running beside me cried out in anguish.
But no one was there to answer his screams.
"Isaac Uphills."
At that moment, Gwendolyn gave up on the race and approached me.
"You know something about this, don't you?"
"...What makes you think that?"
"You're the only one not running."
"Aha."
So that's why she was paying attention to me.
I immediately started running.
No matter how fast I went, the tortoise ahead of me was always one step further.
One step.
Half a step.
Half of half a step...
It was a bizarre experience of time continually fragmenting.
I turned to her and said,
"How about this?"
"...It's already too late. I don't feel any sincerity at all."
"Damn..."
I came to an abrupt halt.
Crawl, crawl.
The tortoise ahead of us kept plodding along just fine.
Gwendolyn's mouth opened.
"Now that I think about it, during the first exam, you just stood there like this, then suddenly vanished and passed, didn't you?"
...Did I?
"If you're going to disappear, at least leave a hint."
"...Fine. I'll tell you."
At my words, the gazes of all the other students in the race snapped toward me.
"What? What did that guy just say?"
"Acting like he knows when he can't even escape himself..."
The senior who had rocketed into the air froze mid-flight and snorted derisively.
"Hey. Don't waste time. Just run."
I addressed that senior directly.
"This paradox happens because 'infinity' is defined ambiguously. It tricks you into thinking an infinite process equals infinite time."
"Trick? You say that looking at me like this? This is reality."
He was hurtling toward the tortoise as a flame-spewing rocket.
Crawl, crawl.
Of course, he couldn't overtake it.
'How should I explain this...?'
I'd probably need the most basic foundation of calculus: the epsilon-delta definition.
But even that "basic" was surprisingly hard to explain in words.
"...Explaining it verbally might be tough. I'll show you directly."
I gently closed my eyes.
In an instant, the space and time of the world receded into the distance, and my mind connected to the 'core of the magic'.
-Achilles can never catch the tortoise-
-Discontinuity of space,
-Discrete division of time,
-Errors in infinite sequences,
and more...
Preliminary analysis complete.
Now, overlay a new magic.
Through my fading consciousness, Gwendolyn's shout rang out.
"...You're modifying the magic directly? That's dangerous!"
At her words, the other students reacted too.
"What? Direct modification? Are you insane?"
"Stop that newbie quick! He'll die!"
"You crazy bastard!"
It was the same reason as when I'd modified Liam's magic tool.
Rebound. One mistake, and mana could backflow, killing me.
But there was no need to worry.
'I've done calculus for years. You think I'd mess this up?'
The students, including Gwendolyn, rushed toward me to stop me all at once.
But they couldn't reach me.
Shh. Shh.
The space between us began to divide infinitely.
One step closer left half a step remaining; closing that left half of half.
They had been trapped in the exact 'prison of logic' they'd just been struggling with.
"What the hell...!"
"No way... He already dominates the magic?"
At that moment, the crawling stone tortoise came to a sudden stop.
Then it turned its head and glanced at me for the first time.
Was it intrigued?
'A bit early for that...'
This alone wouldn't let me overtake the tortoise.
To pass it, I needed to establish a new law beyond mere understanding.
First.
"t → c"
Definition of the convergence point.
I defined the specific moment when I and the tortoise meet as the variable c.
Mana vibrated faintly, fixing a single solution—one the barrier had ignored—onto the logical void like coordinates.
Second.
"lim(t→c) f(t) = L"
Limit.
I declared that as time t approaches c 'infinitely closely', the distance function f(t) between me and the tortoise converges to the limit L = 0.
I overlaid the counter-logic of 'convergence' onto the barrier's concept of 'infinity'.
Then, with a sharp crackle, the tortoise glared at me.
"Not enough, huh?"
Vague phrases like 'infinitely close' wouldn't shatter this magic.
Then, third.