Boolean Operations

"That doesn't seem right, does it?" Youji frowned. "Master, it doesn't seem to work like that. In board games... and driving too, computers are much better than biological brains."

Xiang Shan nodded. "That's right, but a computer that's good at chess can only play chess. It will never understand the question of why play chess? It might not even know that it is 'playing chess.' If its creator gives it no instructions, then it will never do a second thing for its entire life."

This must have happened... a very, very long time ago, right? Xiang Shan felt that this might have been history from before he was born. Back then, there had been a conductor. He had been a person with trisomy 21—what people called a "congenital idiot." Perhaps he had merely been born into a musical household and treated "imitating conducting gestures" as a game, but he had indeed taken the stage as a conductor. Did "music" exist within his brain?

Perhaps that poor man truly had known what music was in his heart.

But beyond "music," there had been many things he could not understand.

The intelligence nurtured within computers was even more extreme. After all, even someone with congenital intellectual disability knew hunger and thirst. When their body felt unwell, they cried. But even an AI whose chess skill could crush a chess saint would never develop thoughts such as "I need a power supply" or "I just want more computing resources."

"Actually, there has never been anything a computer could do that exceeded the human brain. Calculating with paper and pen... damn it, you probably don't even know what 'paper' is." Xiang Shan shook his head, casually picked up an iron rod, and wrote q and p on the ground.

Two values: 1 or 0, TRUE or FALSE.

Two gave rise to three, and three gave rise to all things.

Everything in a computer came from this.

"What I am going to teach you now is called 'Boolean operation.'" Xiang Shan said, "With an iron rod, humans can perform Boolean operations on the ground and thereby simulate any computer program—no, that should be put the other way around. Computers merely replace human hands in writing Boolean formulas on the ground. They are simply faster than writing by hand. Faster, and nothing more."

"This method of operation was born from the great George Boole. Before George Boole, Leibniz and Babbage had been doing the same thing—they tried to use machines for calculation. Babbage might once have come close to this realm, but in the end, he had not reached it. But Boole was unlike all those before him. Just as Isaac Newton had tried to describe the trajectory of matter in the dimensions of time and space, Boole had tried to describe the trajectory of mental activity. It was an earth-shattering achievement. Of course, the gap between Boolean algorithms and genuine human thought was like the gap between Newtonian mechanics and the real world. But this was already a beginning."

"After Boole, people realized that gears and levers could perform calculations, neural networks could perform calculations, circuits constantly opening and closing could perform calculations, and even a pile of chemical equipment could perform calculations—Boolean algorithms broke down a corner of human thought into something machines could understand."

The history of humans using circuits to simulate neural networks and perform Boolean calculations was even older than the von Neumann architecture—in 1943, neurobiologist Warren McCulloch and mathematician Walter Pitts created the first artificial neural network capable of performing Boolean calculations.

Before Boole's era, there had also been an inventor named Joseph Jacquard. He invented an entirely new kind of loom. This loom could use punched cards to control the needles and threads in the machine, weaving warp and weft. Similar things had independently appeared many times throughout history. Such "punched cards" could even be traced back to China's Eastern Han dynasty.

This was the ancestor of the Turing Machine's "punched paper tape," the most primitive memory, containing only a few bytes—the earliest "memory" of machines.

And Hilbert's plan, proposed for the study of pure mathematics, spurred the birth of the Turing Machine.

In the end, these results converged in the hands of another man named von Neumann.

Thus, an unprecedented tool in human history was born. Human society, life, politics, and military affairs were all changed by it.

"But a tool is still just a tool." Xiang Shan warned his disciple. "Its essence is still the creation of thousands, tens of thousands of arms to perform Boolean operations for you. Anything a computer can do, you can do yourself with Boolean operations. The computer is merely faster—though that kind of 'speed' has already become a qualitative change."

"For ordinary users, you only need to hand the task to those 'many arms' and wait for the result. But that will not cultivate inner power. Those who have mastered inner power are able to maximize the strength of these countless arms, even transmitting their will through them."

"Therefore, you must begin by learning Boolean operations."

In the field of inner power, mathematics was the "Tao," and Boolean operation was the "one."

The Tao gave rise to one, one gave rise to two, two gave rise to three, and three gave rise to all things.

Boolean algorithms themselves were not complicated, merely extensions of logic. Mathematics at roughly a high-school level was enough to get started.

The rest was simply a great deal of practice.

Xiang Shan spent some time explaining the essence of these matters to Youji, then directly compiled a workbook in his mind and transmitted it point-to-point into Youji's brain chip.

Youji's steps were extraordinarily heavy when he left the room.

Xiang Shan nodded in satisfaction. He had a feeling that he had wanted to try doing this for a long time.

He did not know why. Perhaps it was the influence of his past experiences?

In any case, he was quite happy.

Youji finally finished the exercises and returned to his room.

Then he discovered that the atmosphere in the room had completely changed.

Xiang Shan sat before the terminal with his eyes closed, as though meditating. Countless symbols appeared and vanished across the terminal screen as it refreshed. More code overlaid the code already there.

The canine prosthetic connected to that terminal was performing all kinds of movements.

Xiang Shan was comprehending the meaning of every line of code, then replacing the original code with his own.

He intended to try mastering this component he had never seen before.

"Youji, have you finished the exercises?" Xiang Shan maintained his original posture. "Is your brain chip the kind that can be removed at any time? Would it be convenient to let me take a look at one now?"

Youji nodded. "I can, but..."

He lowered his head, and the rear section of his skull opened. A backup chip then popped out.

A prosthetic's driver chips always came in pairs or more. When one encountered a BUG and crashed, the other would instantly take over the body. At the same time, the one with the BUG would rapidly watchdog and restart.

This was different from Xiang Shan's integrated skull. A modern artificial skull like Youji's was designed to be opened conveniently.

Youji handed his backup chip to Xiang Shan. "Master, what are you doing?"

"I'll be done soon. I'll tell you once I'm finished." Xiang Shan shook his head. He had indeed been too careless not to notice this at first. In this era, those above held even more severe power of life and death over those below than he had imagined. When he discovered that Doctor Schultz had invited him online, he had naively concluded that most cybernetic prosthetics were not connected to the network at all times.

When he accepted Youji as his disciple, he had only thought about avoiding the village's surveillance routes.

But what the mayor had said earlier reminded him.

No matter what society was like, never underestimate the plunder tyrants inflicted upon people.

There should, in fact, be a frequency band that ordinary people did not know about, or simply could not use. On that non-civilian frequency band, all prosthetics were connected to the network—their users simply did not know it.

The only thing worth being thankful for was that those "true ruling groups" now seemed to be short-handed, or faced some other objective difficulty, and were not monitoring every single person at every moment.

Tch... it probably hadn't been this severe in the past.

But I should have anticipated this extreme state.

"As the saying goes, 'Practice martial arts without cultivating inner power, and in the end it is all for nothing.'" The design of inner power had included ways to resist such a situation from the very beginning.

Therefore, after restoring a little of his own inner power, Xiang Shan began building Youji's defenses against external evils, clearing the backdoors within his chip.

Very quickly, Xiang Shan searched through the entire chip. Just as he had expected, it indeed contained several protocols he had never seen before, pointing toward certain ports with signal-transmission functions.

These ports used shortwave communication. Their signals were relatively weak, and their data transmission capacity was limited. They could probably only upload low-quality audio or images.

But this meant that the rulers truly could spy on any individual at any time.

"Very good. At least it is worth being thankful that this era has no military or police force, and the lords have far too much discretionary power... At most, they can only realize that I might be a knight-errant."

Xiang Shan quickly wrote a firewall into Youji's chip, making it reject remote access through that specific port and transmit fabricated images instead. He then erased several other protocols.

Of course, before doing these things, he had first made backups.

Xiang Shan returned the chip to Youji and said, "Try it yourself. Tell me if anything feels wrong. If there are no problems, help me with something later."

Xiang Shan himself was currently controlling his prosthetic through the cheap chip the mayor had given him. That driver chip might also contain a backdoor. Xiang Shan's artificial skull could not open and close freely like Youji's. Without special tools, he would need someone else's help to remove the chip inserted inside.

That was equivalent to exposing his own brain to someone else. Xiang Shan needed an assistant he could trust before he dared do such a thing.

Furthermore, he had to prevent a situation where, halfway through the process, the assistant was remotely brain-controlled and their finger twitched into his brain. That was why he had prioritized preparing an Empowerment for Youji.

While transmitting his mathematics homework to Xiang Shan for inspection, Youji followed Xiang Shan's instructions, running and jumping to test whether there were any BUGs in the driver chip.

Humans had learned long ago not to pursue programming without BUGs. As long as a program could run, it did not matter if BUGs existed.

According to type theory, high-level languages could roughly be divided into "type-unsafe languages," "type-safe languages," and "strongly normalizing languages." Strongly normalizing languages could guarantee that "nothing would go wrong." Such languages could give a unique result for any program and halt, never falling into an infinite loop. But precisely because strongly normalizing languages abandoned the concept of "loops," they lost Turing completeness, so any flawed system was simply not recognized and was forbidden from running.

Simply put, a strongly normalizing language meant, "Once the program runs, it absolutely will not go wrong—but if it contains even the slightest error, it cannot run at all."

The knights-errant, meanwhile, tended to use "type-unsafe languages." Users of such languages lived every day in confusion: My code won't run? Why is that? My code runs? Why is that? Such languages easily produced "unpredictable errors"—and that "unpredictability" could be said to be ordained by mathematics itself. Before a program ran, even its creator could not predict it.

Of course, this "difficulty in understanding" applied equally to enemies.

Xiang Shan would rather go to more trouble and conduct several tests before writing any program than choose a "type-unsafe language."

But Xiang Shan's skill really did seem fairly good. Youji's driver chip could still control his prosthetic normally.