What Is the Soul of The Three-Body Problem?

The man addressed as President Zhao wore a smile as he extended his hand. "Professor Wang, about the game's mathematical modeling I approached you about last time, I didn't explain myself clearly..."

"It's not that you didn't explain yourself clearly. It's that I made myself very clear." Old Wang didn't take his hand and cut him off. "If The Three-Body Problem is really going to be adapted into a game, a domestic team should be the one to do it. If the rights go to your foreign company, can what you make do the original justice?"

"The Three-Body Problem is a science fiction novel, after all. Some of its concepts need to be backed by science. This isn't Harry Potter, where you can just recite a spell, throw in some special effects, and the audience will buy it."

Zhao Li seemed to have known Old Wang would say this. Without the slightest sign of panic, he said, "Professor Wang, your concerns are very reasonable."

"You're an academic, so you might not know much about the market. What's the domestic game market like right now? Mobile games, browser games, all kinds of reskinned online games. Players have been fed garbage for over a decade, and paid gacha pulls are the mainstream in this market."

Old Wang said nothing, but displeasure was already plain in his eyes.

"If a world-class IP like The Three-Body Problem is going to be made into a game, it has to be a AAA production: a vast world, high quality, cinematic storytelling. This isn't something you can solve by throwing money at it. It takes a complete industrial production pipeline, a mature technical pipeline, and over ten years of AAA development experience."

He spread his hands. "To put it bluntly, what domestic company has that capability right now? Penguin, Pig Factory, and the others haven't even made a single true AAA game."

"Have you?" Old Wang asked coolly.

"We have eight studios around the world and over three thousand top developers. You can see how sincere we are-we even specifically invited someone like you to be our consultant. Wherever mathematical modeling is involved in the game, we definitely won't fob the players off."

Qi Hao stood beside them, listening to their conversation. He didn't know much about the game industry, but the condescending tone this man named Zhao Li used made him uncomfortable.

He's making a Three-Body Problem game, and that makes him so full of himself?

Qi Hao hoped Old Wang would just take a broom and sweep this guy out.

A vast world, cinematic storytelling, a top team-it all sounded impressive, but in Qi Hao's eyes, as a thoroughly straightforward math major, these people had their priorities completely upside down.

If players wanted to watch a movie, they might as well just watch one. Why play a game?

Although he hadn't read The Three-Body Problem, he knew what the soul of the three-body system was.

It was the despair brought on by the utterly unpredictable, chaotic motion of the three suns.

If the logic shown in the game was fake, cobbled together by arbitrarily writing a few lines of pseudorandom code and scripts, then the game was essentially mindless popcorn entertainment dressed in the skin of science fiction.

Qi Hao had recently developed a thinking habit, and he began letting his thoughts branch out to the mathematical problems in the three-body system.

Old Wang seemed unwilling to continue the conversation in the hallway. He glanced at Zhao Li, his tone softening a little.

"President Zhao, I really do have something to do today. How about this: if you insist, I can hear you out first, but I'm not promising anything."

Zhao Li's eyes lit up, but Old Wang turned to Qi Hao at that moment.

"And you are?"

"Hello, Teacher Wang. My name is Qi Hao, first-year applied mathematics, class one." Qi Hao came back to himself and hurriedly pulled the sheets of scratch paper out of his bag. "I'd like to ask you about a problem."

Old Wang took the scratch paper and looked down at it. "These problems... aren't the sort a first-year student usually asks about."

The sheets were densely covered with derivations concerning a partial-order coloring problem on directed acyclic graphs. The notation was precise, the logic clear, and they even cited two theorems beyond the reach of undergraduates.

"I've been studying some things on my own lately, but I've run into trouble."

"Studying on your own? Come in first, then." Somewhat surprised, Old Wang stepped aside to let him through the door.

Zhao Li took half a step forward. "What about me?"

Old Wang didn't even turn his head. "Wait!"

"Or you can leave first. I might not have time today."

Zhao Li's expression shifted.

He managed a portfolio worth over a billion yuan in the Asia-Pacific region. The last time he met with the VP of Sony China, the man had been waiting in the lobby ahead of time.

He hadn't expected a math professor to put on airs with him.

Zhao Li took a deep breath and stayed.

Chaotic simulation of three-body motion, the fluid mechanics of the droplet's attacks, and visualization of the Dual-Vector Foil's dimensional reduction all required solid mathematical modeling.

The person who recommended Old Wang had said he was a decent man who worked conscientiously once he took on a job. Most importantly, the price of working with him was much lower than that of professors at Tsinghua and Peking Universities!

At the thought, Zhao Li sat back down on a chair in the hallway and crossed his legs.

He had plenty of patience.

A first-year student couldn't stay in there long anyway.

He'd be out in five minutes, ten at most.

He waited.

Inside the office.

Old Wang sat behind his desk, with Qi Hao sitting opposite him.

The sheets of scratch paper lay spread out on the desk. Old Wang looked at Qi Hao.

"Qi Hao..." He repeated the name, then suddenly remembered something. "Wait, were you the one reading a mathematical analysis textbook in English class?"

Qi Hao admitted awkwardly, "...That was me."

How could a teacher expose someone to his face like that?

Didn't he have any face to save?

Looks like Teacher Qi told on me!

They're university teachers already. Why do they still like telling on people just like high school teachers?

Qi Hao sighed inwardly and prepared himself for a lecture.

But Old Wang suddenly smiled.

"Liking math is a good thing," he said. "But you need to work on your English too, or how will you read papers later? Good math papers are all written in English."

Qi Hao breathed a sigh of relief.

Apparently, Old Wang had no intention of criticizing him at all. Teacher Qi had probably told on him for nothing!

"I understand, Teacher Wang."

Seeing that Qi Hao had the right attitude, Old Wang didn't pursue the matter.

"All right, tell me about your problem." Old Wang pushed the scratch paper between them.

Qi Hao collected himself and pointed to a derivation on the paper. "Teacher Wang, I've recently been studying a coloring problem on directed acyclic graphs. It has to do with the structure of partially ordered sets. Simply put, I need a particular coloring scheme such that the number of colors is exactly equal to a certain partial-order parameter."

"I've checked it in several special cases, and the conclusion holds, but I can't write a rigorous proof for the general case."

He didn't say he was writing a paper.

A first-year student saying he was writing a paper would sound like bragging no matter how he put it.

"Where are you stuck?" Old Wang asked.

"On the estimates from the partially ordered set to the chromatic polynomial."

Qi Hao turned to the second page. "I need to prove that, for a DAG satisfying this compatibility condition, its chromatic number is exactly equal to the length of the longest chain in its corresponding partially ordered set. For the lower bound, I can use Dilworth's Theorem to show that the maximum antichain size equals the minimum number of chains in a partition, but I can't write a constructive proof for the upper bound."

"Wait." Old Wang interrupted him.

He picked up a pen from the desk. "What exactly does Dilworth's Theorem state?"

"The minimum number of chains in a partition equals the maximum antichain length," Qi Hao answered quickly.

"Correct." Old Wang glanced at him. "Then do you know Mirsky's Theorem?"

"On a finite partially ordered set, the minimum number of antichains in a partition equals the length of the longest chain. It's the dual of Dilworth's Theorem."

Old Wang was pleasantly surprised.

Qi Hao's store of knowledge, awareness of the problem, and precision of expression already surpassed those of most undergraduates. He seemed even better than some of Old Wang's less promising graduate students.

This kid is worth keeping an eye on.

"Very good. Your problem can be solved like this..."

He picked up the pen and began writing quickly on the scratch paper.

Qi Hao stared at the derivations, his eyes growing brighter and brighter.

"So that's how it works. Construct it using a topological ordering, and that proves it."

"You catch on quickly." Old Wang glanced at Qi Hao. "I haven't even started explaining, and you already understand?"

"Yeah, I understand. I don't think we need to partition the partially ordered set itself into antichains. We can go straight back to the original graph and construct the coloring using topological sorting."

Old Wang said nothing, merely giving a slight nod to signal for him to continue.

Encouraged, Qi Hao spoke faster. "My earlier approach got stuck at the partially ordered set. I kept thinking about how to use an antichain cover to approximate the chromatic number, but halfway down that road, I couldn't carry the proof any further. It didn't occur to me that I could go straight back to the graph structure itself."

Old Wang nodded repeatedly as he listened. He asked, "You've been studying on your own lately? What books have you read?"

Qi Hao named several textbooks. Old Wang offered no comment after hearing them. He simply picked up his pen, wrote several titles on the scratch paper spread out before him, and pushed it over to Qi Hao.

"You can take a look at these when you have time."

Qi Hao took the paper and saw a densely written list of six or seven titles, all advanced textbooks and monographs on graph theory and combinatorics. Some he had heard of but hadn't been able to find, while others he had never even heard of.

"The library might not have some of them," Old Wang said. "Go look for them first."

"What if I can't find them?"

"Hey! Think about it. Would I be short of books?" Old Wang said with a laugh.

Qi Hao realized he was right. He really had never heard of a teacher being short of books. It suddenly dawned on him that Old Wang meant for him to come borrow them!

You could've said so!

"Any other questions?"

"Not for now."

Old Wang stood up. "Then come find me anytime you have a question."

Qi Hao thanked him and got up to leave. As he pulled the door open, he saw Zhao Li still sitting on the chair in the hallway. He had been waiting for nearly an hour.

Zhao Li had crossed his legs the other way, and his expression was rather sour.

Qi Hao gave him a slight nod, then turned and left.

Behind him came the sound of Zhao Li getting up and entering the office. Then Old Wang's voice rang out. "President Zhao, I'm a little busy here. Ten minutes should be enough for you to say what you need, right?"