This winter, the king and the witch lived a strange yet regular secluded life in an inn in the city of Lunda.

During the day, Loki would go out wrapped in a thick cloak, searching for suitable craftsmen at the guild for the dragon wing membranes, posting commissions, and then sending out the materials. The rest of the time she would take on simple commissions to earn some money. At night, she would return to the inn and begin crafting staffs using magic stones.

Wang would spend all day holed up in his room, either writing and drawing on the table or sitting cross-legged on the bed with his eyes closed, entering a world of imagination, sometimes for most of the day.

"Honestly, why do all that thankless work? Are you short of money?" One night, the king finally couldn't help but speak up, "I can be your personal hand warmer to support you."

Luo Qixi was polishing the edge of a magic stone when she heard this, so she looked up and blinked.

"It's not that I'm short of money," she said. "I'm just... used to earning it myself."

The king looked at her. The firelight from the fireplace danced on her profile, making her light blue eyes appear and disappear.

"...Whatever you want." Wang turned his face away. "But I still need to make the hand warmers. I'm out and about all day..."

Luo Qixi smiled slightly and did not refuse.

Because the king didn't want his witch sister to get cold, he first developed a hand warmer magic circle.

Larger cities in the northern countries have large snow-melting magic arrays. The principle is actually very simple; I just need to miniaturize them.

The only expensive expense is magic stone powder, the material used to draw the magic circle.

The magic circle is drawn on the material, and then magic power is injected into it to generate continuous heat. It doesn't use much magic power, so it's a very practical little thing.

It's just that it's too practical. Once it cools down, you can re-inject magic and use it again. How can I, the king, resell it to make money?

Therefore, in order to live a wealthy life in the future, Wang had no choice but to become a ruthless businessman.

Wang lay on the table, drawing product lines on parchment with a quill pen.

Three levels

"The cheapest ones are disposable; you just throw them away after use, and you make small profits but sell a lot."

The mid-range version allows you to replace magic stones as a magic source, making it last longer; buy as needed.

The most expensive is the custom edition—inlaid with high-quality magic stones (for showing off), with magic circles engraved on exquisite silk fabric, and includes a family crest customization service.

"Is the last one specifically for nobles?"

Luo Qixi leaned over to take a look.

"That's right. The finest steel is used on the hilt; that's the aesthetics of the nobility." Wang sneered. "Hmph, they don't care about practicality; they only care about 'I have what you don't.' When we hand it over to Philip, he'll definitely be able to sell it for an astronomical price."

Luo Qixi stared at the densely written "profiteering business plan" and remained silent for a long while.

The witch then praised the king's unscrupulous business practices.

The king rejoiced at the witch's praise.

I'll give the witch a share of the profits later. I don't plan to put the developer's name on my head now. What if the Dragon God smells it and comes looking for me?

Overall, this is a joyful occasion.

But this is one of the few things that brings joy this winter.

Wang soon encountered two problems.

The first was the writing of "Shadow Heroes: Origins".

Wang's literary skills were not particularly high.

Although I read many novels and watched many anime in my previous life, "reading" and "being able to write" are two different things.

Moreover, this book is nominally an "epic of heroism," but it is actually an "educational book written for my younger brother"—it needs to be passionate, a bit childish, educational, and not too fake.

Difficult! As difficult as climbing to the heavens!

"Witch sister, which title do you think is cooler: 'Partner of Justice' or 'Guardian of the Night'?"

"None of them are cool."

"...And what about the 'Watcher of the Abyss'?"

"When you gaze into the abyss, the abyss also gazes into you. And then you stare at each other for an entire afternoon, until finally the abyss blinks first?"

Witches can be cute now!

"That's right, it's not that scary, but the logic still makes sense."

Luo Qixi put down the magic stone in her hand, tilted her head and thought for a moment: "I think that instead of thinking of these fancy titles, we should write some real stories. For example, the people we met on the road—Emily, the villagers of Green Village, and even that Uncle Beishenliu."

"The real story isn't cool enough."

"But true stories can touch people's hearts," Loki said. "You want to educate Rudy, right? Then let him see that the real hero is not someone who stands in the light, but someone who chooses to do the right thing even in the darkness."

Wang remained silent for a while.

"...Witch sister, that's a really cool line. Can I write it into my book?"

"Whatever."

The second problem is far more difficult than the first.

Unlimited techniques.

Wang was not unaware of its underlying principles.

The Achilles paradox—one of the most famous paradoxes in the history of mathematics.

Achilles was the fastest runner in Greek mythology, while the tortoise was notoriously slow. Zeno said: If the tortoise were given a head start, Achilles would never catch it.

The tortoise started crawling 100 meters ahead of Achilles, who was ten times faster. Intuitively, Achilles knew he would catch up with the tortoise quickly.

Zeno's argument is that for Achilles to catch up with the tortoise, he must first reach the tortoise's starting point. This takes 10 seconds. In those 10 seconds, the tortoise crawls forward 10 meters.

现在阿基里斯与乌龟相距10米。他要再跑到乌龟的新位置110米处,需要1秒。这1秒内,乌龟又向前爬了1米。

This process repeats itself endlessly. Each time Achilles reaches the position the tortoise was in, the tortoise has moved forward a little further. This process can continue indefinitely; Achilles can only ever get infinitely close to the tortoise, but he can never catch up.

This paradox is mathematically valid; it is essentially an infinite series.

The truth of the paradox is that an infinite number of increasingly smaller intervals can be added together to obtain a finite sum. This is the dialectical relationship between "infinite subdivision" and "finite sum".

The king's idea was simple—to unleash a spell around his body, trapping any approaching object in the "Achilles' dilemma." Their distance from the king was infinitely subdivided, allowing them to only get infinitely close, never truly touching him.

Sounds perfect, doesn't it?

But the problem is—I live in reality, not in a math scratch paper.

In the world of mathematics, infinite subdivision is perfect. But in the real world, Achilles did indeed catch up with the tortoise.

Why?

Because the real world is not composed of abstract concepts. The real world has a minimum scale.

The virtual world can be simulated with infinite subdivisions, but the real world cannot.

There exists a lower limit in physics in the real world—the Planck length.

Spatial distances smaller than this scale are meaningless in reality.

This is only the first hurdle.

There is an even more pressing and practical problem—the magnitude of the magic itself.

Magic is a "universal particle"; it can be very small, but it cannot be infinitely small.

Each division of space requires me to use magic to create a boundary point in space that prevents objects from moving forward.

The dividing line between infinity requires infinite magic.

Although my magic power far exceeds the norm, it is ultimately finite and far from reaching the concept of infinity.

It consumed a lot of magic power, but the defensive effect only lasted a little longer.

Achilles will catch up with the tortoise in no time.

Moreover, the density of the dividing points is also limited. When the distance between the dividing points is less than the minimum radius of the magic's effect, the force field wall will fail and the entire defense will collapse.

Beyond that, there are many more difficulties, such as: what frame of reference should I use? What constitutes an encounter? Where did the attacker's kinetic energy go...?

Most importantly, it is the paradox itself.

It's not because of insufficient magic power or insufficient computing power, but because—the theoretical premise of this technique is in fundamental conflict with the basic laws of the real world.

All the magic I have improved and developed has been based on the physical rules of the real world.

The deeper you delve into the concept of no limits, the further you stray from it.

I realized with despair that magic is not omnipotent, and neither am I.

After realizing this problem, I was discouraged...

I may have already found the upper limit of magic, and perhaps I can develop other spells to increase their power, shorten their casting animation, and speed up their execution, but this upper limit...

You can see the end of it at a glance.

Of course, it's also possible that I've temporarily encountered a bottleneck, and bottlenecks can't be overcome in a short time by working in isolation.

Although I have the so-called cheat code, it can't help me solve my current predicament, nor can it make me the strongest in the world.

...If only there were a system where you could become stronger just by signing in.

Or... let me become stronger through dating.

What's wrong with this damn system of mine?

What a useless thing...

Wang spread his hands and buried his face in the table, lost in his own EMO.

Winter is almost over, and it will soon be time to go back. The plan to make up for the shortcomings with magic has failed. Although two more super-powerful attack spells have been developed, I am still a shameful glass cannon.

The next breakthrough seems a long way off...

Should I learn swordsmanship?

To be honest, Wang doesn't like running and jumping around, and exercising is really tiring.

Although I have special methods for adjusting my mindset, I simply don't want to do things I don't want to do.

Is it really necessary to waste time like this?

The door was pushed open.

Luo Qixi walked in, bringing with her a chill, her scarf covered in fine snowflakes. She took off her scarf and hung it on the hook by the door, then turned and saw Wang slumped on the table, pausing for a moment.

Although it's embarrassing for Luo Qixi to see me in such a shameful state...

But I simply don't have the energy to get back on my feet right now.

She didn't speak immediately, but gently closed the door, walked to the table, and gathered up the scattered scraps of paper.

Then he poured two cups of tea, presenting one to me and keeping the other for himself. Then he sat down beside me.

The fire in the fireplace crackled.

"Didn't work?"

"......Um."

Luo Qixi didn't ask any further questions. She held the teacup, watched the steam rising from the rim, and waited for a while.

"I've encountered bottlenecks before," she said. "Back in the Demon Continent, I just couldn't learn a high-level spell no matter what I tried. I practiced in front of stones every day until I couldn't even lift my hands."

"......Then what?"

Luo Qixi suddenly hugged my neck: "And then you stopped studying."

"Not learning anymore?"

"Yeah. Go out and be an adventurer, hunt big monsters, and earn money for the journey. I don't know when, but suddenly I just learned how."

The hand that was on my body started to ruffle my hair again.

"Later I thought, is it that sometimes something is missing? Is something lacking?"

"Is something missing?" The king paused briefly. "What is it that I'm lacking? It seems that while the path of magic hasn't reached its end yet, the wall is already visibly close at hand..."

"You're more authoritative than me in magic now, but are you sure?"

"I'm not sure." The king's voice lowered. "But I've tried every method I could think of. Limitless spells... they're theoretically correct, but the real world doesn't recognize them. Insufficient magic, insufficient scale, insufficient frame of reference—it's all a dead end."

Luo Qixi put down her teacup, cupped my face in her hands, and began to rub it.

"Then let's not take this route for now."

Looking into the witch's eyes, which were so close to his, the king instinctively looked away.

"You said before that I could always find a way. Sorry, I'm not as capable as you think."

"There's more than one way than magic. If one path doesn't work, let's try another. Besides... don't you already have the answer in your heart?"

Wang turned to look at the scrap paper under the ink bottle, which read "Sword God Style," "Northern God Style," and "Water God Style," followed by a bunch of question marks and doodles.

"Maybe we can give it a try..."

"Then give it a try. Isn't Gilead your aunt? Go study there for a few years."

"several years?"

You're not even seven years old yet.

Luo Qixi stretched out her finger and placed it on my forehead.

"Since magic can't break through the bottleneck in the short term, let's improve our weaknesses first. One is a long-term goal, to be achieved gradually. The other is a short-term goal, so don't waste time. Isn't that what you taught me?"

Yeah, even if we're here, being an EMO won't do any good. Since there are other paths, we can't waste time stuck in a dead end. As for wasting time, I can do that slowly until I die after I've killed the god.

The king, having regained his composure, met the witch's gaze.

The fireplace glowed her face with a warm orange hue. Her light blue hair fell over her shoulders, a few stray strands clinging to her cheeks, still damp from the snow.

Her eyes reflected the dancing flames, like the warmest cloud on a summer evening in Buena village.

Looking at the beauty before him, the king suddenly kissed the witch on the cheek.

Outside the window, the snow had long since stopped. In the distance, a sliver of gray light peeked through the sky.

Winter is almost over.

[Information Now Available - Magic Circle]

Most magic tricks can be performed by drawing a magic circle using materials.

Although it seems very inconvenient, this only applies to low-level magic.

For more advanced and complex magic, a magic circle can be drawn in advance, and it can be released directly by simply injecting magic power at the crucial moment.

Typical examples are divine-level healing and detoxification magic. Their incantations are ridiculously long.

However, if it is made into a roll in advance, it can be used at any time.

In some ways, magic circles can do even more.

Most portable magic circles are disposable items because the magic powder used as a magic circuit runs out of magic power after it has been used once.

There are also higher-grade materials that can be used to create magic circles that can be used multiple times, but those are extremely expensive.

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