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 rearranged itself into a nine-mile-square calculating formation.
Jing Ke pointed to the formation and began to explain. “Your Majesty, we have named this formation Qin One. Look, there in the center is the central processing subformation, the core calculating component, made up of the best divisions of your army. By referencing this diagram, you can locate the adding subformations, quick storage subformations, and stack memory subformation. The part around it that looks highly regular is the memory subformation. 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 calculating procedure for the circular ratio. Observe also the open passage that runs through the entire formation, and the light cavalry waiting for orders in the passage: that’s the system’s main communication line, responsible for transmitting information between the components of the whole system.”
Two soldiers brought over a large scroll, tall as a man, and spread it open before King Zheng. When they reached the scroll’s end, everyone present remembered the scene in the palace a few years ago, and they all held their breath. But the imaginary dagger did not appear. Before them was only a large sheet of thin silk filled with symbols, each the size of a fly’s head. Packed so densely, the symbols were as dazzling to behold as the calculating formation on the ground below.
“Your Majesty, these are the orders in the procedure I developed for calculating the circular ratio. Please look here”—Jing Ke pointed to the calculating formation below—“where the soldiers standing ready for what I call the ‘hardware.’ What’s on this cloth is what I call the ‘software,’ the soul of the calculating formation. The relationship between hardware and software is like that between the guqin zither and sheet music.”
King Zheng nodded. “Good. Begin.”
Jing Ke lifted both hands above his head and solemnly chanted, “As ordered by the Great King, initiate the calculating formation! System self-test!”
A row of soldiers standing halfway down the face of the stone dais repeated the order using flag signals. In a moment, the phalanx of three million men seemed to turn into a lake filled with sparkling lights as millions of tiny flags waved.
“Self-test complete! Begin initialization sequence! Load calculation procedure!”
Below, the light cavalry on the main communication line that passed through the entire calculating formation began to ride back and forth swiftly. The main passage soon turned into a turbulent river. Along the way, the river fed into numerous thin tributaries, infiltrating all the modular subformations. Soon the ripples of black and white flags coalesced into surging waves that filled the entire phalanx. The central processing subformation area was the most tumultuous, like tinder set on fire.
Suddenly, as though the fuel had been exhausted, the movements in the central processing subformation slackened and eventually stopped. Starting with the central processing subformation in the center, the stillness spread in every direction like a lake being frozen over. Finally the entire calculating formation came to a stop, with only a few scattered components flashing lifelessly in infinite loops.
“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 central processing subformation’s status storage unit.
“Restart system!” Jing Ke ordered confidently.
“Not yet,” King Zheng said as he grasped his sword. “Replace the malfunctioning gate and behead all the soldiers who made up that gate. In the future, any other malfunctions will be dealt with the same way.”
A few riders dashed into the phalanx with their swords drawn. They killed the three unfortunate soldiers and replaced them with new men. From the vantage point of the dais, three eye-catching pools of blood appeared in the middle of the central processing subformation.
Jing Ke gave the order to restart the system. This time, it went very smoothly. Ten minutes later, the soldiers were carrying out the circular-ratio-calculating procedure. As the phalanx rippled with flag signals, the calculating formation settled into the long computation.
“This is really interesting,” King Zheng said, pointing to the spectacular sight. “Each individual’s behavior is so simple, yet together, they can produce such complex intelligence.”
“Great King, this is just the mechanical operation of a machine, not intelligence. Each of these lowly individuals is just a zero. Only when someone like you is added to the front as a one is the whole endowed with meaning.” Jing Ke’s smile was ingratiating.
“How long would it take to calculate ten thousand digits of the circular ratio?” King Zheng asked.
“About ten months. Maybe even sooner if things go right.”
General Wang Jian[12] stepped forward. “Your Majesty, I must urge caution. Even in regular military operations, it’s extremely dangerous to concentrate so much of our force in an open area like this. Moreover, the three million soldiers in this phalanx are unarmed, carrying only signal flags. The calculating formation is not intended for battle and will be extremely vulnerable if attacked. Even under normal conditions, to effectuate an orderly retreat of this many men packed so tightly would take most of a day. If they were attacked, retreat would be impossible. Sire, this calculating formation will appear in the eyes of our enemies as meat placed on a cutting board.”
King Zheng did not reply, but turned his gaze to Jing Ke. The latter bowed and said, “General Wang is absolutely right. You must be cautious when deciding whether to pursue this calculation.”
Then Jing Ke did something bold and unprecedented: he lifted his eyes and locked gazes with King Zheng. The king immediately understood the meaning in that gaze: All your accomplishments so far are like zeros; only with the addition of eternal life for yourself, a one, can all of those become meaningful.
“General Wang, you’re overly concerned.” King Zheng whipped his sleeves contemptuously. “The states of Han, Wei, Zhao, and Chu have all been conquered. The only two remaining states, Yan and Qi, are led by foolish kings who have exhausted their people. They’re on the verge of total collapse and pose no threat. Given the way things are going, by the time the circular ratio calculation is complete, those two states may already have fallen apart on their own and surrendered to the Great State of Qin. Of course, I appreciate the general’s caution. I suggest that we form a line of scouts at some distance from the calculating formation and step up our surveillance of the movements of the Yan and Qi armies. This way, we will be secure.” He lifted his long sword toward the sky and solemnly declared, “The calculations must be finished. I have decided that it must be so.”
The calculating formation ran smoothly for a month, and the results were even better than expected. Already, more than two thousand digits of the circular ratio had been computed, and as the soldiers in the formation grew used to the work and Jing Ke further refined the calculating procedure, speed in the future would be even faster. The estimate was that only three more years would be needed to reach the target of a hundred thousand digits.
12
One of the four great generals of King Zheng’s campaigns against the other six states. The historical Wang Jian was responsible for the destruction of the states of Yan (where Jing Ke was from), Zhao, and Chu.