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  * * *

  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 massacre. 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 passage 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 impassively 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 assassin,” 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 pass through. It was my idea to use these tunnels to allow the allies to bypass 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 passing 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 assent. 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 massive 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 damn 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 massive 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 brass (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.”

  Caruso shifted uncomfortably in his wooden chair, making it squeak and groan as if it might collapse beneath his weight.

  “Then they started using protein enhancers, natural supplements that were undetectable by normal drug screenings. All of a sudden little shortstops from Nicaragua were hitting tape-measure home runs!”

  The commissioner, a grave-faced, white-haired man of great dignity, interrupted Bragg’s tirade. “We are all aware of the supplements. I believe attendance figures approximately doubled when batting averages climbed so steeply.”

  Undeterred, Bragg went on, “So the pitchers started taking stuff to prevent joint problems. No more rotator cuff injuries; no more Tommy John surgeries. When McGilmore went twenty-six and oh we—”

  “Wait a minute,” the National League president said. He was a round butterball, but his moon-shaped face somehow looked menacing because of the dark stubble across his jaw. Made him look like a Mafia enforcer. “Isn’t Tommy John surgery a form of artificial enhancement? The kind of thing you’re accusing Vic Caruso of?”

  Bragg shot back, “Surgery to correct an injury is one thing. Surgery and other treatments to turn a normal human body into a kind of superman—that’s unacceptable!”

  “But the fans seem to love it,” said the American League president, obviously thinking about the previous year’s record-break
ing attendance figures.

  “I’m talking about protecting the purity of the game,” Bragg insisted. “If we don’t act now, we’ll wind up with a bunch of half-robot freaks on the field instead of human beings!”

  The commissioner nodded. “We wouldn’t want that,” he said, looking directly at Caruso.

  “We’ve got to make an example of this … this … freak,” Bragg demanded. “Otherwise the game’s going to be warped beyond recognition!”

  The audience murmured. The cameras turned to Caruso, who looked uncomfortable, embarrassed, but not ashamed.

  The commissioner silenced the audience’s mutterings with a stern look.

  “I think we should hear Mr. Caruso’s story from his own lips,” he said. “After all, his career—his very livelihood—is at stake here.”

  “What’s at stake here,” Bragg countered, “is the future of Major League Baseball.”

  The commissioner nodded, but said, “Mr. Bragg, you are excused. Mr. Caruso, please take the witness chair.”

  Obviously uncertain of himself, Vic Caruso got slowly to his feet and stepped toward the witness chair. Despite his size he was light on his feet, almost like a dancer. He passed Bragg, who was on his way back to the front row of benches. I had to laugh: it looked like the Washington Monument going past a bowling ball.

  Vic settled himself gingerly into the wooden witness chair, off to one side of the judges, and stared at them, as if he was waiting for their verdict.

  “Well, Mr. Caruso,” said the commissioner, “what do you have to say for yourself?”

  “About what, sir?”

  The audience tittered. They thought they were watching a big, brainless ox who was going to make a fool of himself.