Language and Mathematics

Willy was a little flustered. Only after seeing that little brat from Yulia's Household had truly gone far away did he start running.

When that little brat had bumped into him just now, he had been terrified. He had only managed to restrain himself with the greatest effort.

"This can't go on..."

Thinking that, Willy ran quickly. Before long, he had left the edge of the village and crouched beside the road. A cloud of dust came rolling toward him. Willy stood and waved both hands.

The whistle roared. Amid the screech of brakes and an explosive burst of dust, a dark figure stopped before Willy. Then came the sound of a camera adjusting its focus. After a while, a rough voice said, "Willy? Why are you here?"

"Enoch..." Willy's voice trembled. "I'm scared, Enoch."

Willy lived off the heavy workers, so he naturally knew their routines. He knew that Enoch was very likely to pass down this road at this time.

"Hey! What are you so scared of?" Enoch did not care in the slightest.

Willy shrieked, "You were the one who told me to shove that guy out yesterday! It was you! You can't just abandon me! Otherwise... otherwise..." As he spoke, Willy began to cry. "Brother Enoch! I..."

At first, he really had wanted to curry favor with Enoch, which was why he had agreed to "mess with Yawg." Enoch was the most generous among the heavy machinery workers. More importantly, Enoch was lazy and often hired other workers for loading and unloading. As long as he got on Enoch's good side, Willy would never have to worry about work again.

But Willy had truly never expected that "Yawg"... no, that "mountain" seemed to be genuinely formidable.

He had actually managed to defeat a martial artist!

Enoch sounded a little nervous as well. "Did he spot you? That can't be right. Everyone around us was one of ours at the time... They were all involved. They couldn't possibly report us."

"It was that little brat from Yulia's Household!" Willy shrieked.

"Youji? He saw it?" Enoch was troubled. He truly found Youji annoying. If it had not been for Youji, perhaps Yulia would have accepted him—even Xiang Shan had been dug up by Youji.

"He was walking down the street just now and bumped into me! He bumped into me!" Willy shrieked. "That little brat must have seen it! Otherwise... otherwise..."

"Damn, he just bumped into you?" Enoch did not know whether to laugh or cry. "And you're freaking out over that?"

"What do you mean, 'just that'? I shoved that monster!" Willy shouted. "Even that dog lost. There's no way I can beat him!"

"That was just luck!" Enoch said viciously. "The lord was just kindhearted, that's all! Bah, what do you mean he won? Wasn't he lying on the ground saying, 'I lost, I lost,' or something? What a coward... Bah!"

"You can't abandon me!" Willy shrieked. "Let's lure that kid out! We can crush him or take him apart and sell the parts..."

"Hey! Are you insane?" Enoch jumped in fright. He truly intended to be with Yulia. Enoch knew his own personality—he could not keep secrets. If he harmed Youji, he would never be able to be with Yulia.

Enoch had already grown a little irritated from being pestered by this guy. But he also felt that if he let this guy act on his own and something happened to Youji, it might implicate him. So Enoch said, "It's no big deal... How about this? I was planning to go have some fun in the city today anyway. I'll treat you to something good, all right?"

"Something good?" Willy was a little confused. "What is it? A tournament? Or a new game?"

"Way more exciting than that... Come on, get in!"

Enoch had no driver's seat on his body. He tilted the cargo bed slightly and let Willy climb aboard himself.

Dust flew everywhere.

"A real programmer starts programming from bare metal!"

"A real programmer knows no distinction between object-oriented and procedural programming, nor between strongly typed and type-unsafe systems. From machine language to assemblers to compilers to countless high-level applications, he knows them all!"

Certain memories glittered. Xiang Shan could no longer remember who had said that to him. Yet some fragments of "knowledge" reminded him that the person had been a famous programmer in history, someone who had once shaped the course of history.

Xiang Shan had been very close with "that person," so he had learned "everything" about programming.

The essence of this thing was mathematics.

Programming was linguistics, and it was also mathematics.

Or rather, linguistics itself was a kind of mathematics.

Around the end of World War II, mathematicians opened up a new field known as the "word problem." In this field, certain mathematical concepts were clothed in "words," and the forms generated by algebraic structures naturally expressed themselves. Mathematicians attempted to manipulate mathematics using the rules of linguistics.

In 1944, the American logician and artificial intelligence pioneer Emil Post proved that the word problem possessed undecidability.

Then, in 1947, Anatoly Markov, Son of Andrei Markov, independently arrived at the same proof without knowing of Post's work.

Within "language," there existed "undecidability problems." This was the first undecidability problem not posed by humanity and not appearing in the field of computer science.

At the same time, linguists reached the same realm by traveling in the opposite direction.

If modern linguistics originated with Ferdinand de Saussure, then Noam Chomsky was the towering peak after Saussure. Besides being widely known as a linguist, philosopher, and sociologist, Chomsky could also be considered a mathematician.

His research into linguistics had even been recorded in the history of mathematics.

The two fields Chomsky created—"the grammar of context-free languages" and "the grammar of regular languages"—also held considerable standing in theoretical computer science.

Geneticists likewise respected Chomsky. They believed that Chomsky's research into language might become the key to deciphering the genetic code—they could reverse-engineer the "language of the Creator" hidden within genetic information.

Or rather, the "program" followed by genetic chemistry.

As long as one had sufficiently deep mathematical knowledge in the relevant fields, creating a unique language was not especially difficult.

The truly difficult part was making a language obscure to humans while remaining simple and understandable to machines.

The more obscure the language, the greater its advantages in internal cultivation. Knights relied on internal cultivation to hide themselves within the network and within this world. "Language" was the root of all their defenses. Their brains' linguistic functions worked in close coordination with their internal cultivation.

The more obscure the language familiar to the brain, the more untraceable the internal force became.

If one sacrificed computer operating efficiency purely for the advantages of internal cultivation, that would be putting the cart before the horse.

Lisp could not achieve "obscurity." It was too close to mathematics. Once someone knew its fundamentals, a capable mathematician could understand how to use it.

C Language was a "high-level language with characteristics of natural language." Too many people used it, so the language had developed in a kind of "wild growth," even producing the phenomenon of "language drift" in a very short time—something quite close to the evolution of natural language. If two relatively isolated regions of the network emerged in the world, C Language might even evolve "dialects."

Xiang Shan was familiar with both sides.

In the realm of internal cultivation, that meant mastering one method and comprehending ten thousand.

Xiang Shan felt that he should have known someone else. That person might not have been so famous, but he had definitely stood at the boundary of human knowledge.

He had learned many things from his friends—or so it should have been.

But on closer thought, that seemed contrary to common sense. In Xiang Shan's understanding, a person could at most study one field in depth, while only sampling the surface of everything else. Human knowledge had long expanded beyond the point where an "individual" could grasp its entirety.

He should not have understood engineering, excelled at programming, and possessed such strong mathematical ability. Even if he truly had been good friends with such remarkable people, there was no reason he could have learned all their strengths.

Einstein's best friend in his later years had been the top-tier mathematician Gödel. But that friendship had not raised Einstein's mathematical ability to Gödel's level—at least, in the eyes of true mathematicians, Albert Einstein's mathematical ability remained only at the level of "sufficient for a physicist."

But... that was simply how strange things had happened.

Xiang Shan dismantled the terminal's operating system. He replaced the original compiler with his own.

Whether it was the lowbrow Java, the merely foundational C, Perl, as beautiful and lonely as ancient poetry, Ruby, as passionate as modern poetry, Python, easy to learn but hard to master and nearly divine once perfected, or Lips, closest to mathematics and creation itself—even their successors were unsuitable for sustaining the existence of internal cultivation.

There was no other reason. They had all been created so that "others could use them."

These languages had been born to be understood by people.

The only thing preventing others from understanding them was intelligence.

Even if C Language had developed "dialects," dialects were still insufficient for secrecy.

For knights, a good language could conceal their intentions and provide a final chance to strike back after firewalls had been dismantled, encryption cracked, encapsulation torn open, and the Lesser Celestial Circuit of the Ren and Du Meridians interrupted.

And you could not hope your enemy was an idiot—you had to find a way to ensure that even if the enemy was smart enough, without critical information, he could not use his consciousness to reach the endlessly flowing code inside your program in a short time.

Each school's internal cultivation corresponded to a special compiler, with its own syntactic conventions and naming methods. The high-level languages they compiled differed drastically in design philosophy from the high-level languages of the past.

These were languages created "to be difficult for people to understand."

If programmers of the past had tried to create "the best language," so good that everyone would want to use it, then the languages created by knights were the complete opposite: "the worst languages."

More importantly, one still had to ensure that machines could accept such "bad" languages.

And in this regard, Xiang Shan possessed absolute confidence. At first, he had not known where that confidence came from.

After spending two hours rewriting the compiler, he recalled more knowledge.

The foundation of his internal cultivation was an unnamed language passed down only within an extremely small circle.

Very few people knew this language. It had never spread widely. Only a handful had ever seen it, and even fewer could learn or use it. The effort required merely to learn the language exceeded that of learning a foreign language. Programming with it was as difficult as writing first-rate poetry in a foreign language—and that foreign language had to belong to a completely different language family from one's native tongue.

"Come to think of it, if it really is that difficult... how did I ever learn it?" Xiang Shan muttered. "Who exactly am I? How am I this amazing?"

After completing the compiler rewrite, Xiang Shan seemed to unlock even more knowledge. Data rapidly streamed from the chip directly connected to his brain. Code overwrote code. Irregular blocks of color appeared on the terminal screen, then it quickly shut down and restarted.

This was not a creation from nothing. Long ago, Xiang Shan seemed to have experienced a very similar scene.

Perhaps because his memories were incomplete, he could not completely reproduce the techniques of that time. But even so, he had probably gained the capital to survive.

This unnamed language was absolutely the most fucking difficult language to use in the world.

But from a knight's perspective, it was also one of the strongest languages.