King Zheng nodded. A guard ran over, grabbed the hilt of the king"s sword, and stepped backward. The bronze sword was so long that it was impossible for the king to pull it out of the scabbard without help. The guard knelt and presented the sword to the king, who lifted the sword to the sky and shouted: "Calculating Formation!"
Battle drums began to beat, and four giant bronze cauldrons at the corners of the stone dais came to life simultaneously with roaring flames. A group of soldiers standing at the edge of the dais facing the phalanx chanted in unison: "Calculating 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 rearranged itself into a nine-square-mile calculating formation.
Jing Ke pointed to the formation and began to explain. "Your Majesty, we have named this formation Qin I. Look, there in the center is the central processing formation, the core component of the calculating formation, made up of the best divisions of your army. By referencing this diagram, you can see within it the adding formation, quick storage formation, and stack memory formation. Around it, the part that looks highly regular is the memory formation. When we built this 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 pa.s.sage that runs through the entire formation and the light cavalry waiting for orders in the pa.s.sage: 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. As the scroll reached the 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-"the soldiers standing ready form 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 pa.s.sed through the entire calculating formation began to ride back and forth swiftly. The main pa.s.sage 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 formation area was the most tumultuous, like tinder set on fire.
Suddenly, as though the fuel had been exhausted, the movements in the central processing formation slackened and eventually stopped. Starting with the central processing formation 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 formation"s status storage unit.
"Restart system!" Jing Ke ordered confidently.
"Not yet," King Zheng said, still holding on to 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 formation.
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 ma.s.s calculating phalanx. "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 w.a.n.g Jian* stepped forward. "Your Majesty, I must urge caution. Even in regular military operations, it"s extremely dangerous to concentrate so much of our forces 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 w.a.n.g 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 zeroes; only with the addition of eternal life for yourself, a one, can all of those become meaningful.
"General w.a.n.g, 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.
The morning of the forty-fifth day after the start of the calculations was foggy. It was impossible to see the calculating formation, enveloped in mist, from the dais. Soldiers in the formation could see no farther than about five men.
But the calculating formation"s operation was designed to be unaffected by the fog and continued. Shouted orders and the hoofbeats of the light cavalry on the main communication line echoed in the haze.
But those soldiers in the north of the calculating formation heard something else. At first, the noise came intermittently and seemed illusory, but soon, the noise grew louder and formed a continuous boom, like thunder coming from the depths of the fog.
The noise came from the hoofs of thousands of horses. A powerful division of cavalry approached the calculating formation from the north, and the banner of the state of Yan flew at their head. The riders moved slowly, forcing their horses to maintain ranks. They knew that they had plenty of time.
Only when the riders were about a third of a mile from the edge of the calculating formation did they begin the charge. By the time the vanguard of the cavalry had torn into the calculating formation, the Qin soldiers didn"t even get a proper look at their enemies. In this initial charge, tens of thousands of Qin soldiers died just from being trampled under the hoofs of the attacking riders.
What followed was not a battle at all, but a ma.s.sacre. Before the battle, the Yan commanders already knew that they would not meet with meaningful resistance. In order to increase the efficiency of the slaughter, the riders abandoned the traditional cavalry weapons, long-handled lances and halberds, and instead equipped themselves with swords and morning stars. The several hundred thousand Yan heavy cavalry became a death-dealing cloud, and wherever they rode, the bodies of Qin soldiers carpeted the land.
In order to avoid giving warning to the core of the calculating formation, the Yan riders killed in silence, as though they were machines, not men. But the screams of the dying Qin soldiers, whether cut down or trampled, spread far and wide in the thick fog.
However, all of the Qin soldiers in the calculating formation had been trained under threat of death to ignore outside interference and to devote themselves single-mindedly to the simple task of acting as calculating components. Combined with the disguise provided by the thick fog, the result was that most of the calculating formation did not realize the northern edge of the formation was already under attack. As the death-dealing region slowly and orderly ate through the formation, turning it into piles of corpses strewn over blood-soaked, muddy ground, the rest of the formation continued to calculate as before, even though more and more errors began to plague the system.
Behind the first wave of cavalry, more than a hundred thousand Yan archers loosened volleys from their longbows, aimed at the heart of the calculating formation. In a few moments, millions of arrows fell like a thunderstorm, and almost every arrow found a target.
Only then did the calculating formation start to fall apart. At the same time, information of the enemy attack began to spread, increasing the chaos. The light cavalry on the main communication line carried reports of the sudden attack, but as the situation deteriorated, the main pa.s.sage became blocked, and the panicked riders began to trample through the densely packed phalanx. Countless Qin soldiers thus died under the hoofs of friendly forces.
On the eastern, southern, and western edges of the calculating formation, which weren"t under attack, Qin soldiers began to retreat without any semblance of order. Amidst the utter lack of information and broken chain of command, the retreat was slow and confused. The calculating formation, now purposeless, became like a thick, concentrated bubble of ink that refused to dissolve in water, with only wispy tendrils leaving at the edges.
Those Qin soldiers running toward the east were soon stopped by the disciplined ranks of the Qi army. Instead of charging, the Qi commanders ordered the infantry and cavalry to form impregnable defensive lines to wait for the escaping Qin soldiers to enter the trap before surrounding them and beginning the slaughter.
The only direction left for the remainder of the hopeless Qin army, now without any will to fight, was toward the southwest. Hundreds of thousands of unarmed men poured over the plains like a dirty flood. But they soon encountered a third enemy force: unlike the disciplined armies from Yan and Qi, this third force consisted of the ferocious riders of the Huns. They tore into a Qin army like wolves into a flock of sheep and quickly overwhelmed them.
The slaughter continued until noon, when the strong breeze from the west lifted the fog, and the wide expanse of the battlefield was exposed to the glare of the midday sun.
The Yan, Qi, and Hun armies had combined in multiple places, surrounding what remained of the Qin army in small pockets. The cavalry of the three armies continued to charge the Qin soldiers, leaving the wounded and the few escapees to be mopped up by the infantry. Oxen formations, urged on by fire, and catapults were also put into operation to kill the remaining Qin men even more efficiently.
By evening, the sorrowful notes of battle horns echoed over a field covered with bodies and crisscrossed by rivulets of blood. The final survivors of the Qin army were now surrounded in three shrinking pockets.
The night that followed had a full moon. The pure, cold moon floated impa.s.sively over the slaughter below, bathing the mountains of corpses and seas of blood in its calm, liquid light. The killing continued throughout the night and wasn"t over until the next morning.
The army of the Qin Empire was entirely eliminated.
One month later, the allied forces of Qi and Yan entered Xianyang and captured King Zheng. The Qin Empire was over.
The day selected for the execution of King Zheng was another day when the sun and the moon appeared together. The moon floated in the azure sky like a snowflake.
The monument that had been intended for Jing Ke still hung in the air. King Zheng sat below it, waiting for the Yan executioner to cut the ox hide rope.
Jing Ke walked out of the crowd observing the execution, still dressed all in white. He came before King Zheng and bowed. "Your Majesty."
"In your heart, you"ve always remained a Yan a.s.sa.s.sin," the king said. He did not look up at Jing Ke.
"Yes. But I didn"t want to just kill you. I also needed to eliminate your army. If I had succeeded a few years ago in killing you, Qin would have remained powerful. Advised by brilliant strategists and commanded by veteran commanders, the million-strong Qin army would still have posed an unstoppable threat to Yan."
"How could you have sent so many men so close to my army without my notice?" King Zheng asked the last question of his life.
"During the year when the calculating formation was being trained and operating, Yan and Qi focused on digging tunnels. Each tunnel was many miles long and wide enough to allow cavalry to pa.s.s through. It was my idea to use these tunnels to allow the allies to bypa.s.s your sentries and appear suddenly near the defenseless calculating formation."
King Zheng nodded and said nothing more. He closed his eyes to wait to die. The supervising official gave the order and an executioner began to climb up the platform, a knife held between his teeth.
King Zheng heard movements next to him. He opened his eyes and saw that Jing Ke was sitting next to him.
"Your Majesty, we"ll die together. When the heavy stone falls, it will become a monument to both of us. Our blood and flesh will mix together. Perhaps this will give you some comfort."
"What is the point of this?" King Zheng asked coldly.
"It"s not that I want to die. The King of Yan has ordered my execution."
A smile quickly appeared on King Zheng"s face and disappeared just as quickly, like a pa.s.sing breeze. "You have accomplished so much for Yan that your name is praised more than the king"s. He fears your ambition. This result is expected."
"That is indeed one reason, but not the main one. I also advised the King of Yan to build Yan"s own calculating formation. This gave him the excuse he needed to kill me."
King Zheng turned to gaze at Jing Ke. The surprise in the king"s eyes was genuine.
"I don"t care if you believe me. My advice was given with the hope of strengthening Yan. It"s true that the calculating formation was a stratagem I came up with to destroy Qin by taking advantage of your obsession with eternal life. But it"s also a genuinely great invention. Through its calculating power, we can understand the language of mathematics, to divine the mysteries of the universe. It could have opened a new era."
The executioner had reached the top of the platform and stood in front of the rope holding up the stone monument, waiting for the final order as he held the knife in his hand.
In the distance, under a bright baldachin, the King of Yan waved his hand in a.s.sent. The supervising official shouted the order to carry out the sentence.
Jing Ke suddenly opened his eyes wide as though awakening from a dream. "I"ve got it! The calculating formation doesn"t have to rely on the army, not even people. All those gates-AND, NOT, NAND, NOR, and so on-can be made from mechanical components. These components can be made very small, and when they"re put together they will be a mechanical calculating formation! No, it shouldn"t be called a calculating formation at all, but a calculating machine! Listen to me, King, wait! The calculating machine! The calculating machine!" Jing Ke shouted at the King of Yan in the distance.
The executioner cut the rope.
"The calculating machine!" Jing Ke shouted the three words with the last of this breath.
As the giant stone fell, in that moment when its ma.s.sive shadow blotted out everything in the world, King Zheng felt the end of his life. But in the eyes of Jing Ke, a faint ray of light heralding the beginning of a new era was extinguished.
OLD TIMER"S GAME Ben Bova
Mathematicians and statisticians love baseball. It has the most detailed numbers of any sport.
The nature of the game lends itself easily to record keeping and statistics: batting average, RBI, home runs, ERA, strikeouts, stolen bases. By some counts, there are well over a hundred statistics commonly and uncommonly used in baseball. The stats are diligently tracked by fans, pundits, and players alike, but for the players there is one number that many would rather not think about.
Their age.
America"s pastime has changed much since the early semipro baseball clubs of the 1860s. "Old Timer"s Game" takes us to a near future in which the players themselves may change as well.
"He"s making a travesty of the game!"
White-haired Alistair Bragg was quivering with righteous wrath as he leveled a trembling finger at Vic Caruso. I felt sorry for Vic despite his huge size, or maybe because of it. He was sitting all alone up there before the panel of judges. I thought of Gulliver, giant-sized compared to the puny little Lilliputians. But tied hand and foot, helpless.
This hearing was a reporter"s dream, the kind of news-making opportunity that comes along maybe once in a decade. Or less.
I sat at the news media table, elbow to elbow with the big, popular TV commentators and slick-haired pundits. The guys who talk like they know everything about baseball, while all they really know is what working stiffs like me put up on their teleprompters.
Old man Bragg was a shrimp, but a powerful figure in the baseball world. He owned the Cleveland Indians, who"d won the American League pennant, but then lost the World Series to the Dodgers in four straight.
Bragg wore a dark gray business suit and a bright red tie. To the unsophisticated eye he looked a little like an overweight one of Santa"s elves: short, round, his face a little bloated. But whereas an elf would be cheerful and dancing-eyed, Bragg radiated barely concealed fury.
"He"s turning baseball into a freak show!" Bragg accused, still jabbing his finger in Caruso"s direction. "A freak show!"
Vic Caruso had been the first-string catcher for the Oakland Athletics, one of the best d.a.m.n hitters in the league, and a solid rock behind the plate with a cannon for an arm. But now he looked like an oversized boy, kind of confused by all the fuss that was being made about him. He was wearing a tan sports jacket and a white shirt with a loosely knotted green tie that seemed six inches too short. In fact, his shirt, jacket, and brown slacks all appeared too small to contain his ma.s.sive frame; it looked as if he would burst out of his clothes any minute.
Aside from his ill-fitting ensemble, Vic didn"t look like a freak. He was a big man, true enough, tall and broad in the shoulders. His face was far from handsome: his nose was larger than it should have been, and the corners of his innocent blue eyes were crinkled from long years on sunny baseball diamonds.
He looked hurt, betrayed, as if he were the injured party instead of the accused.
The hearing wasn"t a trial, exactly. The three solemn-faced men sitting behind the long table up in the front of the room weren"t really judges. They were the commissioner of baseball and the heads of the National and American Leagues, about as much baseball bra.s.s (and ego) as you could fit into one room.
The issue before them would determine the future of America"s Pastime.
Bragg had worked himself into a fine, red-faced fury. He had opposed every change in the game he"d ever heard of, always complaining that any change in baseball would make a travesty of the game. If he had his way, there"d be no interleague play, no designated hitter, no night baseball, and no player"s union. Especially that last one. The word around the ballyard was that Bragg bled blood for every nickel he had to pay his players.
"It started with steroids, back in the nineties," he said, ostensibly to the commissioner and the two league presidents. But he was looking at the jam-packed rows of onlookers, and us news reporters, and especially at the banks of television cameras that were focused on his perspiring face.
"Steroids threatened to make a travesty of the game," said Bragg, repeating his favorite phrase. "We moved heaven and earth to drive them out of the game. Suspended players who used "em, expunged their records, prohibited them from entering the Hall of Fame."