The Three-Body Problem (26 page)

“That’s why your empire must continue to develop, Great Emperor!” Von Neumann seized the opportunity. “If you can master the pattern of the suns’ movements, you will be able to make the most of each Stable Era, and also avoid the damage brought by each Chaotic Era. This way, your progress will be much faster than Europe’s. Believe us, we’re scholars. As long as we can use the three laws of motion and calculus to accurately forecast the movements of the suns, we do not care who conquers the world.”

“Of course I need to predict the suns’ movements. But if you want me to gather thirty million men, you must at least demonstrate for me how such calculations would be conducted.”

“Your Imperial Majesty, please give me three soldiers. I will demonstrate.” Von Neumann grew excited.

“Three? Only three? I can easily give you three thousand.” Qin Shi Huang glanced at Von Neumann, distrustful.

“Your Imperial Majesty, you mentioned just now the defect in the Eastern mind when it comes to scientific thinking. This is because you have not realized that even the complicated objects of the universe are made from the simplest elements. I only need three.”

Qin Shi Huang waved his hand and three soldiers came forward. They were all very young. Like other Qin soldiers, they moved like order-obeying machines.

“I don’t know your names,” Von Neumann said, tapping the shoulders of two of the soldiers. “The two of you will be responsible for signal input, so I’ll call you ‘Input 1’ and ‘Input 2.’” He pointed to the last soldier. “You will be responsible for signal output, so I’ll call you ‘Output.’” He shoved the soldiers to where he wanted them to stand. “Form a triangle. Like this. Output is the apex. Input 1 and Input 2 form the base.”

“You could have just told them to stand in the Wedge Attack Formation,” Qin Shi Huang said, glancing at Von Neumann contemptuously.

Newton took out six small flags: three white, three black. Von Neumann handed them out to the three soldiers so that each held a black flag and a white flag. “White represents 0; black represents 1. Good. Now, listen to me. Output, you turn around and look at Input 1 and Input 2. If they both raise black flags, you raise a black flag as well. Under all other circumstances, you raise the white flag.”

“I think you should use some other color,” Qin Shi Huang said. “White means surrender.”

The excited Von Neumann ignored him. He shouted orders at the three soldiers. “Begin operation! Input 1 and Input 2, you can raise whichever flag you want. Good. Raise! Good. Raise again! Raise!”

Input 1 and Input 2 raised their flags three times. The first time they were black-black, the second time white-black, and the third time black-white. Output reacted correctly each time, raising the black flag once and the white one twice.

“Very good. Your Imperial Majesty, your soldiers are very smart.”

“Even an idiot would be capable of that. Tell me, what are they really doing?” Qin Shi Huang looked baffled.

“The three soldiers form a computing component. It’s a type of gate, an AND gate.” Von Neumann paused to let the emperor digest this information.

Qin Shi Huang said impassively, “I’m not impressed. Continue.”

Von Neumann turned to the three soldiers again. “Let’s form another component. You, Output: if you see either Input 1 or Input 2 raise a black flag, you raise the black flag. There are three situations where that will be true: black-black, white-black, black-white. When it’s white-white, you raise the white flag. Understand? Good lad, you’re really clever. You’re the key to the correct functioning of the gate. Work hard, and the emperor will reward you! Let’s begin operation. Raise! Good, raise again! Raise again! Perfect. Your Imperial Majesty, this component is called an OR gate.”

Then, Von Neumann used the three soldiers to form a NAND gate, a NOR gate, an XOR-gate, an XNOR-gate, and a tristate gate. Finally, using only two soldiers, he made the simplest gate, a NOT gate, or an inverter: Output always raised the flag that was opposite in color from the one raised by Input.

Von Neumann bowed to the emperor. “Now, Your Imperial Majesty, all the gate components have been demonstrated. Aren’t they simple? Any three soldiers can master the skills after one hour of training.”

“Don’t they need to learn more?” Qin Shi Huang asked.

“No. We can form ten million of these gates, and then put the components together into a system. This system will then be able to carry out the calculations we need and work out those differential equations for predicting the suns’ movements. We could call the system … um…”

“A computer,” Wang said.

“Ah, good!” Von Neumann gave Wang a thumbs-up. “Computer—that’s a great name. The entire system is a large machine, the most complex machine in the history of the world.”

The passage of in-game time sped up. Three months went by.

Qin Shi Huang, Newton, Von Neumann, and Wang all stood on the platform at the apex of the pyramid. This platform was similar to the one where Wang had met Mozi. It was filled with astronomical instruments, some of which were of recent European design. Below them, a magnificent phalanx of thirty million Qin soldiers was arrayed on the ground. The entire formation fit inside a square six kilometers on each side. As the sun rose, the phalanx remained still like a giant carpet made of thirty million terra-cotta warriors. But when a flock of birds wandered above the phalanx, the birds immediately felt the potential for death from below and scattered anxiously in chaos.

Wang performed some computations in his head and realized that even if the entire population of Earth were arranged into such a phalanx, the whole formation would fit inside the Huangpu District of Shanghai. Though it was powerful, the phalanx also revealed the fragility of civilization.

Von Neumann said, “Your Imperial Majesty, your army is truly matchless. In an extremely short time, we have completed such complex training.”

Qin Shi Huang held on to the hilt of his long sword. “Even though the whole is complex, what each soldier must do is very simple. Compared to the training they went through to learn how to break the Macedonian Phalanx, this is nothing.”

Newton added, “And God blessed us with two consecutive Stable Eras to get them trained and ready.”

“Even in a Chaotic Era, my army continues to train. They will finish your calculations even if it’s a Chaotic Era.” Qin Shi Huang glanced over the phalanx with pride in his eyes.

“Then, Your Imperial Majesty, please give the great order!” Von Neumann’s voice trembled with excitement.

Qin Shi Huang nodded. A guard ran over, grabbed the hilt of the emperor’s sword, and stepped backwards. The bronze sword was so long that it was impossible for the emperor himself to pull it out of the scabbard. The guard knelt and handed the sword to the emperor. Qin Shi Huang lifted the sword to the sky, and shouted: “Computer Formation!”

Four giant bronze cauldrons at the corners of the platform came to life simultaneously with roaring flames. A group of soldiers standing on the sloping side of the pyramid facing the phalanx chanted in unison: “Computer Formation!”

On the ground below, colors in the phalanx began to shift and move. Complicated and detailed circuit patterns appeared and gradually filled the entire formation. Ten minutes later, the army had made a thirty-six kilometer square computer motherboard.

Von Neumann pointed to the gigantic human circuit below the pyramid and began to explain, “Your Imperial Majesty, we have named this computer Qin I. Look, there in the center is the CPU, the core computing component, formed from your five best divisions. By referencing this diagram, you can locate the adders, registers, and stack memory. The part around it that looks highly regular is the memory. When we built that part, we found that we didn’t have enough soldiers. But luckily, the work done by the elements in this component is the simplest, so we trained each soldier to hold more colored flags. Each man can now complete the work that initially required twenty men. This allowed us to increase the memory capacity to meet the minimum requirements for running the Qin 1.0 operating system. Observe also the open passage that runs through the entire formation, and the light cavalry waiting for orders in that passage: That’s the system bus, responsible for transmitting information between the components of the whole system.

“The bus architecture is a great invention. New plug-in components, which can be made from up to ten divisions, can quickly be added to the main operation bus. This allows Qin I’s hardware to be easily expanded and upgraded. Look further still—you might have to use the telescope for this—and there’s the external storage, which we call the ‘hard drive’ at Copernicus’s suggestion. It’s formed by three million soldiers with more education than most. When you buried all those scholars alive after you unified China, it’s a good thing you saved these ones! Each of them holds a pen and a notepad, and they’re responsible for recording the results of the calculations. Of course, the bulk of their work is to act as virtual memory and store intermediate calculation results. They’re the bottleneck for the speed of computation. And, finally, the part that’s closest to us is the display. It’s capable of showing us in real time the most important parameters of the computation.”

Von Neumann and Newton carried over a large scroll, tall as a man, and spread it open before Qin Shi Huang. When they reached the scroll’s end, Wang’s chest tightened, remembering the legend of the assassin who hid a dagger in a map scroll that he then displayed to the emperor. But the imaginary dagger did not appear. Before them was only a large sheet of paper filled with symbols, each the size of a fly’s head. Packed so densely, the symbols were as dazzling to behold as the computer formation on the ground below.

“Your Imperial Majesty, this is the Qin 1.0 operating system we developed. The software for doing the calculations will run on top of it. That below”—Von Neumann pointed to the human-formation computer—“is the hardware. What’s on this paper is the software. The relationship between hardware and software is like that between the
guqin
zither and sheet music.”

He and Newton then spread open another scroll, just as large. “Your Imperial Majesty, this is the software for using numerical methods to solve those differential equations. After entering the motion vectors of the three suns at a particular moment obtained by astronomical observation, the software’s operation will give us a prediction for the suns’ subsequent motion at any moment in the future. Our first computation will calculate all the suns’ positions for the next two years. Each set of output values will be one hundred and twenty hours apart.”

Qin Shi Huang nodded. “Good. Begin.”

Von Neumann lifted both hands above his head and solemnly chanted: “As ordered by the great emperor, turn on the computer! System self-test!”

A row of soldiers standing halfway down the face of the pyramid repeated the order using flag signals. In a moment, the motherboard made of thirty million men seemed to turn into a lake filled with sparkling lights. Tens of millions of tiny flags waved. In the display formation closest to the base of the pyramid, a progress bar made of numerous green flags slowly advanced, indicating the percentage of the self-test that had been completed. Ten minutes later, the progress bar reached its end.

“Self-test complete! Begin boot sequence! Load operating system!”

Below, the light cavalry on the main bus that passed through the entire human-formation computer began to move swiftly. The main bus soon turned into a turbulent river. Along the way, the river fed into numerous thin tributaries, infiltrating all the modular subformations. Soon, the ripple of black and white flags coalesced into surging waves that filled the entire motherboard. The central CPU area was the most tumultuous, like gunpowder on fire.

But suddenly, as though the powder had been exhausted, the movements in the CPU slackened and eventually stopped. Starting with the CPU in the center, the stillness spread in every direction, like a sea being frozen over. Finally, the entire motherboard came to a stop, with only a few scattered components flashing lifelessly in infinite loops. The center of the display formation blinked red.

“System lockup!” a signal officer called out. Shortly after, the reason for the malfunction was determined: There was an error with the operation of one of the gates in the CPU status register.

“Restart system!” Von Neumann ordered confidently.

“Wait!” Newton stopped the signal officer. He turned with an insidious expression and said to Qin Shi Huang, “Your Imperial Majesty, in order to improve system stability, you should take certain maintenance measures with respect to faulty components.”

Qin Shi Huang grasped his sword and said, “Replace the malfunctioning component and behead all the soldiers who made up that gate. In the future, any malfunctions will be dealt with the same way!”

Von Neumann glanced at Newton, disgusted. They watched as a few riders dashed into the motherboard with their swords unsheathed. After they “repaired” the faulty component, the order to restart was given. This time, the operation went very smoothly. Twenty minutes later,
Three Body
’s Von Neumann architecture human-formation computer had begun full operations under the Qin 1.0 operating system.

“Run solar orbit computation software ‘Three Body 1.0’!” Newton screamed at the top of his lungs. “Start the master computing module! Load the differential calculus module! Load the finite element analysis module! Load the spectral method module! Enter initial condition parameters … and begin calculation!”

The motherboard sparkled as the display formation flashed with indicators in every color. The human-formation computer began the long computation.

“This is really interesting,” Qin Shi Huang said, pointing to the spectacular sight. “Each individual’s behavior is so simple, yet together, they can produce such a complex, great whole! Europeans criticize me for my tyrannical rule, claiming that I suppress creativity. But in reality, a large number of men yoked by severe discipline can also produce great wisdom when bound together as one.”