Chapter 157

Lessons 2

Within the dim darkness, a flicker of consciousness surfaced. Something seemed to fill the depths of my head, traveling along my cranial nerves and forcibly waking me.

"Ghurk—!"

My limbs trembled. My back spasmed, and as my stiff muscles loosened, sharp pain jolted me awake.

My heavy eyelids lifted, but my eyes wouldn't focus. The blurry ceiling looked quite familiar.

'... Am I in the county?'

My room in Whitewolf County 1.

I closed my eyes and opened them again. Only then did my vision focus.

When I tried to sit up—

"Ghh—!"

... It felt as though my head would split apart. As though the physical overload from Predator[M] had hit my head instead.

"Hah...! Hah...!"

As I panted, the scattered fragments of my memory began fitting back together, piece by piece.

* * *

"Limits?"

"I'd like to hear your thoughts again, Iliana, just as before."

"... Oh! You mentioned that in your letter, too, didn't you?"

Iliana nodded in understanding. Then, after taking a moment to gather her thoughts, she began.

"To help you understand limits clearly..."

She extended her fingers. Blue magical power rippled from her fingertips, inscribing something in midair.

0 x ∞

"What does this equal?"

"Isn't it zero?"

There was nothing to think about.

And yet—

"No."

My head tilted of its own accord. Anything multiplied by zero became zero. Wasn't that common knowledge?

"Would you try imagining a point?"

"By a point, you mean..."

"A zero-dimensional point."

A point with neither area nor length. A point was zero.

"What happens when those points come together?"

"They form a line."

"And a line has length."

0 x ∞

"Do you understand why this value might not be zero?"

... I understood a little. And the same question the speaker in the vision I'd seen while using Predation[S+] on the Memorier had asked came to mind.

"How can a point with nothing to it become a line 'with length'?"

"This is where an important concept comes in."

Iliana waved her fingers again, and her blue magical power inscribed a small symbol in the air.

ϵ

"Do you know what this is?"

"... I've never seen it before."

Not even in my previous life.

"It's called epsilon. It's a symbol that represents an 'infinitesimal.'"

Infinitesimal.

"It isn't actually the symbol for an infinitesimal, but scholars of magic borrowed it because there wasn't a suitable symbol to express one."

As she arranged the magical power she'd released, Iliana asked me,

"Have you ever heard of infinitesimals?"

"I have."

From none other than Seraphia.

◆Authority of Bitter Cold(Power of Cold)[P]

: The user generates a [Supernatural Thermal Energy Deficit], reducing [Entropy] and [Enthalpy] within the energy dynamics system to [Infinitesimal] levels. As a result, all thermal energy and molecular motion within a [Finite System] converge on [0], completely halting physical, chemical, and biological processes.

"But I've only heard of them."

I didn't understand any of that.

"You can simply think of it as something endlessly small. The opposite of infinity."

Infinity was endlessly large. An infinitesimal was endlessly small.

"To make it even simpler, imagine a number with zeros continuing infinitely. Like 0.0000..."

"Ah."

"But it's still greater than zero. And a point is an infinitesimal."

"You mean..."

I gathered my thoughts before speaking.

"Are you saying that a point's length and size aren't zero?"

"Yes. Tiny as it is, it has a value greater than zero."

"Then why do we say a point is zero?"

No matter how small it was, if it had any value, wasn't it nonzero?

"Because of the limitations of our perspective."

"...?"

"Here's what that means."

Iliana waved her fingers again, and another expression appeared.

1

1 + 0

"Which of these is larger?"

"Aren't they the same?"

"No."

"Pardon?"

"From the perspective of our finite world, they're the same. But from an 'infinitesimal perspective,' there's a difference."

Iliana waved her fingers. A number line appeared in midair, marking the position of '1 + 0.' It sat exactly at '1.'

"As you can see, +0 makes no difference on a number line in the finite world. But—"

With a wave of her hand, the mark for 1 + 0 began to magnify.

Larger, and larger, and larger...

... Larger, and larger, and larger...

As the magnification repeated endlessly—

1 + ϵ

A value ever so slightly different from 1 appeared on the number line.

"Viewed from the ultramicroscopic world of infinitesimals like this, zero has a value."

"..."

"It's just that, from our finite world, that value is no different from zero."

... I couldn't make sense of it at all.

"But you're saying it's greater than zero, regardless?"

"That's right."

"Then shouldn't you avoid calling it zero in the first place?"

"From our perspective, it's zero either way."

"So you call it zero for convenience?"

"No. It really is zero. Because infinitesimals don't exist."

... What was that supposed to mean now?

"What did I first say an infinitesimal was?"

"You said it was something endlessly small."

"That's right. And 'endlessly' small doesn't simply mean incredibly small."

Infinite.

"It means literally 'infinitely' small."

"..."

"The zeros never stop. Endlessly, infinitely, on and on—"

Zerozerozerozerozerozerozerozerozez Zezero...

Iliana kept repeating zero until she ran out of breath.

"Phew...! L-like that, it continues forever."

"But it's still greater than zero in the end."

"Yes."

"Then isn't it different from zero, which doesn't exist at all?"

"As you just said, Lord Adrian, zero is defined as 'a quantity that does not exist.'"

Iliana gave a small nod and continued.

"But when you say an infinitesimal isn't zero, you're saying that it's a 'quantity that exists,' regardless, aren't you?"

"That's right."

"Then would you try imagining something infinitely small?"

"..."

"Can such a thing exist?"

"Well—"

"In the finite world—in other words, this world—nothing can become smaller than an atom."

Iliana waved her fingers, inscribing words in the air.

[An existence can be defined because it stops at a point where it no longer becomes smaller.]

"But infinitesimals don't do that. They become endlessly, 'infinitely' smaller. Nothing like that exists in this world. Therefore, an infinitesimal is zero."

... My head was so confused that it was starting to hurt.

"In that sense, perfect zero doesn't exist. The zeros you know, Lord Adrian, and the zeros used in magical studies are all infinitesimals. Tiny numbers, but greater than zero."

"You're saying none of the zeros are zero?"

"Yes. They're all infinitesimals that merely look like zero."

... It felt as though everything I'd ever taken for granted was being smashed apart.

"Do you understand the concept of infinitesimals a little better now?"

... Not in the slightest.

But then, to my astonishment—

"Now we're ready to discuss limits properly."

"...?"

Iliana suddenly said something utterly insane.

"Weren't you explaining limits all this time?"

"Of course not. Infinitesimals and limits are different. They're concepts that must never be used together."

"Then why—"

"It's just that, in terms of understanding them, they aren't all that different. After all, infinitesimals were devised to understand limits."

And so Iliana's lesson continued.

"To explain limits in detail..."

... Anything beyond this was outside the scope of my intelligence.

* * *

"... And that is the concept of limits as I understand it."

Iliana's explanation was finally over.

I could say this with confidence.

... This was an all-time record.

She'd broken her own record yet again.

"It's hard to understand, isn't it...?"

Should I be honest? I hadn't understood a single part of her explanation of limits.

Still, there were some things I'd understood fairly well.

"I managed to get a vague understanding of infinitesimals."

"R-really?!?!"

Iliana jumped. Her blue eyes opened wide, filled with an emotion beyond surprise—astonishment.

"That's an advanced topic even in higher magical studies!!"

... No wonder my head had felt ready to split apart.

"Even fully qualified mages take years to understand it! And even at Langrid Mage Tower, you can count the mages who understand it perfectly on one hand!"

... Was she praising me? Or boasting about herself?

"But if you understood it in one go, you're a real, genuine genius!"

"... I didn't understand it perfectly. As I said, only vaguely—"

"Even so! You're neither a mage nor a scholar of magic!"

"That's true, but..."

I did have what I'd learned in my previous life to draw on. In other words, Iliana, I'd learned it all from you.

"A great genius among geniuses!"

... Did she realize that or not?

Of course she didn't, but anyway.

◆Your Understanding of the Concept Skill, Limit[M], increases.

I'd managed to raise my Understanding of Limits[M], just as I'd intended. Even now, Iliana kept praising me, calling me a genius and whatnot.

Letting her praise go in one ear and out the other, I tried integrating my improved Limit[M] with everything.

And then—

◆The Concept Skill, Limit[M], is integrated with Find Weakness[U].

Unexpectedly, it seemed to integrate with Find Weakness[U]—

◆You have acquired the fusion skill, 'Weakness Hunt[M].'

◆Weakness Hunt[M]

: When using this skill, the player can [Analyze] information obtained through Find Weakness[U] from an [Infinitesimal Perspective].

This allows the player to perceive an opponent at the [Atomic Level], instantly identify [All Vulnerabilities], and precisely [Track] the opponent's [Cellular Activity], [Muscle Fiber Arrangement], and even [Neural Transmission Processes].

<This is a fusion skill formed by merging Find Weakness[U] and Limit[M].>

... I'd acquired an insane skill.

Its assessed grade was Myth[M]. Its effects were truly worthy of that name.

I immediately used Weakness Hunt[M] on Iliana, who stood before me.

◆Using the fusion skill, Weakness Hunt[M].

First, her heart, brain, and the other weaknesses any human naturally possessed were identified in an instant.

Then came weaknesses detectable at the cellular level. In other words, Iliana's own 'unique genetic weaknesses,' rather than universal ones, were also clearly revealed.

Among them was Iliana's Peak Human Intelligence[A+], an ability that explosively increased the distribution of neurons and neural networks in her brain, allowing her intelligence to reach the very peak of its biological limits.

However, she took [+2,330%] additional damage from aging and blows directly associated with brain damage.

Certain sound waves, high frequencies, electrical shocks, and the like could overload her brain's neural networks and incapacitate her.

Rapidly changing attack patterns during combat could temporarily paralyze her information-processing ability.

There were also mental breakdown and fatigue. Information addiction and sensory hypersensitivity.

And, in particular, emotional agitation.

Iliana's intellectual senses were so extraordinarily sensitive that everything and everyone in this world placed mental stress on her. Weakness Hunt[M] told me that provoking emotional agitation in her would allow me to bring her down with certainty.

That wasn't all.

"... Infinitesimals are an extremely difficult concept even in magical studies—!"

The chemical neurotransmitters released from Iliana's synapses were identified in an instant, revealing that she was in an 'excited state.'

Then there were her outstretched arms. Electrical stimulation stirred through her neurons, and changes in potential difference were detected. The electrical signals flowing through those neurons were analyzed.

From that, I knew that in roughly 0.25 seconds, Iliana's muscle fibers would contract—

"... You really have incredible talent!"

—and her arms would move.

It was like looking into the future. Like Ian's Lumen Pax, it allowed me to 'predict' an opponent's movements.

'Holy shit.'

... This skill really was crazy. Not merely insane—utterly crazy.

It wasn't graded Myth[M] for nothing.

There was just one thing.

Like Predator[M], Weakness Hunt[M] had a very, very serious problem.

'Agh—!'

My head couldn't keep up with the excessive volume of information and analysis. Dizziness that felt ready to sever my cranial nerves blurred my vision. Nausea surged up from within, leaving me unable to think straight.

But Iliana—

"Have you ever considered learning magic?!"

Apparently she couldn't see the state I was in. Her eyes sparkled like a tamer who'd discovered a baby griffin.

"... Oh! Come to think of it, you asked about Anti-Mana too, didn't you?"

"Th-that can wait..."

... If I listened to that now, my head might go pop!

"Urp!"

My vision swam dizzily, and I staggered. But could Iliana really not see my condition at all?

"Anti-Mana is energy with properties opposite to mana. In other words—"

Dopamine was erupting from her synapses.

* * *

... That was the last thing I remembered before passing out.

So, to put the reason I'd passed out in a nutshell—

... I wasn't smart enough.

Not even remotely.

"Ugh—!"

... I really felt like I was going to lose my mind.

I spent a while clutching my head as it threatened to split apart. Only after a long time did I finally manage to settle down.

"... More importantly, how much time has passed?"

Since my brain had forcibly shut down from overload, it seemed likely that quite some time had passed.

I slowly sat up and looked out the window.

And right then—

—"My proud brothers!!!"

A loud shout suddenly rang out beyond the window. Judging by its booming volume, it seemed to belong to a dwarf...

—"Our kin who forged the mined runesteel have sent word!!"

... Oh, they'd already finished mining the runesteel?

—"The two great calamities threatening Feractrum are completely gone!!!"

... Oh, they'd even resolved Feractrum's problems?

'Hmm.'

... Should I just pass out again?

Maybe by then they'd have reeled in the empire for me, too?