The Three-Body Problem

by Liu Cixin

  “Shameless!” He bent down to pick up his wig. As he straightened up, he saw Wang. Pointing in the direction of the escapee, he said, “He dared to claim that he invented calculus!” He put on his wig, put a hand over his heart, and bowed courteously to Wang. “Isaac Newton, at your service.”

  “Then the one who ran away must be Leibniz?” Wang asked.

  “Indeed, an unscrupulous man. I don’t really care about this little claim to fame. Inventing the three laws of mechanics has already made me the greatest, God excepted. From planetary motion to cell division, everything follows the three great laws. Now, with the powerful mathematical tool that is calculus, it will only be a matter of time before we master the pattern of the motion of the three suns.”

  “It’s not that simple,” said the man who had tried to stop the fight. “Have you considered the amount of calculation that’s needed? I saw the differential equations you listed, and I don’t think an analytical solution is possible, only a numerical one. However, the calculating capacity required is such that even if all of the world’s mathematicians worked without pause, they’d still not be able to complete them by the time the world ended. Of course, if we can’t figure out the pattern of the suns’ movements soon, the end of the world will not be too far away.” He bowed at Wang as well, a more modern bow. “Von Neumann.”

  “Didn’t you bring us thousands of miles to the East specifically to solve the problem of calculating these equations?” Newton asked. Then he turned to Wang. “Norbert Wiener and that degenerate who just ran away also came with us. We encountered some pirates near Madagascar. Wiener fought the pirates by himself so that the rest of us could escape, and he died valiantly.”

  “Why did you have to come to the East to build a computer?” Wang asked Von Neumann.

  Von Neumann and Newton looked at each other, puzzled. “A computer? A computing machine! Such a thing exists?”

  “You don’t know about computers? Then what did you have in mind for completing the vast amount of calculations?”

  Von Neumann stared at Wang with wide-open eyes, as though his question made no sense. “Using people, of course. Other than people, what else in the world is capable of performing calculations?”

  “But you just said that all the mathematicians in the world wouldn’t be enough.”

  “Instead of mathematicians, we’ll use common laborers. But we need many of them, at least thirty million. We’ll do mathematics using human wave tactics.”

  “Common laborers? Thirty million?” Wang was amazed. “But if I recall correctly, this is an age when ninety percent of the population are illiterate. Yet you want to find thirty million people who understand calculus?”

  “Have you heard the joke about the Army of Sichuan?” Von Neumann took out a thick cigar, bit off the end, and lit it. “Some soldiers were being drilled, but because they had no education, they couldn’t even follow the drill instructor’s simple orders to march LEFT-RIGHT-LEFT. So the instructor came up with a solution: He had every soldier wear a straw shoe on the left foot and a cloth shoe on the right. When they marched, he shouted”—here he switched to a Sichuan accent—“STRAW-CLOTH-STRAW-CLOTH.… That’s the kind of soldier we need. Except we need thirty million of them.”

  Hearing this modern joke, Wang knew that the man before him wasn’t a program but a real person, and almost certainly Chinese.

  “It’s hard to imagine such a large army,” Wang said, shaking his head.

  “That’s why we’ve come to see Qin Shi Huang, the First Emperor.” Newton pointed at the pyramid.

  “He’s still in charge?” Wang looked around. He saw that the soldiers guarding the entrance to the pyramid really were equipped with the simple leather armor and ji-style halberds of the Qin Dynasty. The anachronistic mix of historical elements in Three Body no longer surprised him.

  “The whole world is going to be under his rule because he has an army of more than thirty million preparing to conquer Europe. All right, let’s go see him.” Von Neumann turned to Newton. “Drop the sword.” Newton obeyed.

  The three of them entered the pyramid, and just as they were about to emerge from the tunnel into the Great Hall, a guard insisted that they strip off all their clothes. Newton objected. “We’re famous scholars. No one of our stature would carry hidden weapons!”

  As the two sides explored this stalemate, a deep, male voice came from the Great Hall. “Is it the foreigner who discovered the three laws of motion? Let him and his companions in.”

  They entered the Great Hall. The First Emperor was pacing back and forth, his robe and his famous long sword both dragging along the ground. As he turned to gaze at the three scholars, Wang realized that his eyes were the same as the eyes of King Zhou of Shang and Pope Gregory.

  “I already know the purpose of your visit. You’re Europeans. Why not go find Caesar? His empire is vast. Surely he can find you thirty million men.”

  “But my most honored Emperor, do you know what kind of army he has? Do you know what shape his empire is in? In the magnificent eternal city of Rome, even the river that flows through the city has been heavily polluted. Do you know the cause?”

  “Military industrial production?”

  “No, Great Emperor, it’s the vomit from Romans after their binge and purge feasts. When the nobles attend the feasts, stretchers have already been prepared for them under the tables. When they’ve eaten so much that they can no longer move, the servants carry them home. The entire empire has sunk into a quagmire of extravagance from which they cannot extricate themselves. Even if Caesar could organize an army of thirty million, it would not have the quality and strength necessary to perform this great calculation.”

  “I am aware of that,” Qin Shi Huang said. “But Caesar is waking up and reinvigorating his army. The wisdom of Westerners is terrifying. You are not more intelligent than the men of the East, but you can see the right path. For example, Copernicus could figure out that there are three suns, and you could come up with your three laws. These are very impressive accomplishments. We here in the East cannot, for now, match them. I don’t possess the ability to conquer Europe. My ships are not good enough, and the supply lines cannot be maintained for long enough to go over land.”

  “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. Th
e 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.