Convergent Series

by Larry Niven

  "Ah. A functioning time machine, then. Done with relativity, I expect. But must the cylinder be infinitely long?"

  "I wouldn't think so. A long but finite cylinder ought to show the same behavior, except near the endpoints."

  "And when you say you can demonstrate this..."

  "To another mathematician. Otherwise I would not have been allowed to meet Your Splendor. In addition, there are historical reasons to think that the cylinder need not be infinite."

  Now the emperor was jolted. "Historical? Really?"

  "That's surprising, isn't it? But it's easy to design a time machine, given the Terching Effect. You know about the Terching Effect?"

  "It's what makes a warship's hull so rigid," confirmed the emperor.

  "Yes. The cylinder must be very strong to take the rotation without flying apart. Of course it would be enormously expensive to build. But others have tried it. The Six Worlds Alliance started one during the Free Trade period."

  "Really?"

  "We have the records. Archeology had them fifty years ago, but they had no idea what the construct was intended to do. Idiots." Quifting's scowl was brief. "Never mind. A thousand years later, during the One Race Wars, the Mao Buddhists started to build such a time machine out in Sol's cometary halo.

  Again, behind the Coal Sack is a long, massive cylinder, a quasi-Terching-Effect shell enclosing a neutronium core. We think an alien race called the Kchipreesee built it. The ends are flared, possibly to compensate for edge effects, and there are fusion rocket motors in orbit around it, ready for attachment to spin it up to speed."

  "Did nobody ever finish one of these, ah, time machines?"

  Ouifting pounced on the word. "Nobody!" and he leaned forward, grinning savagely at the emperor. No, he was not awed. A mathematician rules his empire absolutely, and it is more predictable, easier to manipulate, than any universe an emperor would dare believe in. "The Six Worlds Alliance fell apart before their project was barely started. The Mao Buddhist attempt— well, you know what happened to Sol system during the One Race Wars. As for the Kchipreesee, I'm told that many generations of space travel killed them off through biorhythm upset."

  "That's ridiculous."

  "It may be, but they are certainly extinct, and they certainly left their artifact half-finished."

  "I don't understand," the emperor admitted. He was tall, muscular, built like a middleweight boxer.

  Health was the mark of aristocracy in this age. "You seem to be saying that building a time machine is simple but expensive, that it would handle any number of ships. It would, wouldn't it?"

  "Oh, yes."

  "And send them back in time to exterminate one's enemies' ancestors. Others have tried it. But in practice, the project is always interrupted or abandoned."

  "Exactly."

  "Why?"

  "Do you believe in cause and effect?"

  "Of course. I... suppose that means I don't believe in time travel, doesn't it?"

  "A working time machine would destroy the cause and effect relationship of the universe. It seems the universe resists such meddling. No time machine had ever been put into working condition. If the Hallane Regency tries it something will stop them. The Coal Sack is in Hallane space. They need only attach motors to the Kchipreesee device and spin it up."

  "Bringing bad luck down upon their foolish heads. Hubris. The pride that challenges the gods. I like it.

  Yes. Let me see..." The emperor generally left war to his generals, but he took a high interest in espionage. He tapped at a pocket computer and said, "Get me Director Chilbreez."

  To Quifting he said, "The director doesn't always arrest enemy spies. Sometimes he just watches 'em. I'll have him pick one and give him a lucky break. Let him stumble on a vital secret, as it were."

  "You'd have to back it up—"

  "Ah, but we're already trying to recapture Coal Sack space. We'll step up the attacks a little. We should be able to convince the Hallanes that we're trying to take away their time machine. Even if you're completely wrong— which I suspect is true— we'll have them wasting some of their industrial capacity.

  Maybe start some factional disputes, too. Pro- and anti-time-machine. Hah!" The emperor's smile suddenly left him. "Suppose they actually build a time machine?"

  "They won't."

  "But a time machine is possible? The mathematics works?"

  "But that's the point, Your Splendor. The universe itself resists such things." Quifting smiled confidently.

  "Don't you believe in cause and effect?"

  "Yes."

  Violet-white light blazed through the windows behind the mathematician making of him a sharp-edged black shadow. Quifting ran forward and smashed into the holograph wall. His eyes were shut tight, his clothes were afire. "What is it?" he screamed. "What's happening?"

  "I imagine the sun has gone nova," said the emperor.

  The wall went black.

  A dulcet voice spoke. "Director Chilbreez on the line."

  "Never mind." There was no point now in telling the director how to get an enemy to build a time machine. The universe protected its cause-and-effect basis with humorless ferocity. Director Chilbreez was doomed; and perhaps Quifting had ended the war after all. The emperor went to the window. A churning aurora blazed bright as day, and grew brighter still.

  Plaything

  The children were playing six-point Overlord, hopping from point to point over a hexagonal diagram drawn in the sand, when the probe broke atmosphere over their heads. They might have sensed it then, for it was heating fast as it entered atmosphere; but nobody happened to look up.

  Seconds later the retrorocket fired.

  A gentle rain of infrared light bathed the limonite sands. Over hundreds of square miles of orange martian desert, wide-spaced clumps of black grass uncurled their leaves to catch and hoard the heat. Tiny sessile things buried beneath the sand raised fanshaped probes.

  The children hadn't noticed yet, but their ears were stirring. Their ears sensed heat rather than sound; and unless they were listening to some heat source, they usually remained folded against the children's heads, like silver flowers. Now they uncurled, flowers blooming, showing black centers; now they twitched and turned, seeking. One turned and saw it.

  A point of white light high in the east, slowly setting.

  The children talked to each other in coded pulses of beat, opening and closing their mouths to show the warm interiors.

  *Hey!*

  *What is it?*

  *Let's go see!*

  They hopped off across the limonite sand, forgetting the Overlord game, racing to meet the falling thing.

  It was down when they got there, and still shouting hot. The probe was big, as big as a dwelling, a fat cylinder with a rounded roof above and a great hot mouth beneath. Black and white paint in a checkerboard pattern made, it look like a giant's toy. It rested on three comically splayed metal legs with wide circular feet.

  The children began rubbing against the metal skin, flashing pulses of contentment as they felt the heat.

  The probe trembled. Motion inside. The children jumped back, stood looking at each other, each ready to run if the others did. None wanted to be first. Suddenly it was too late. One whole curved wall of the probe dropped outward and thudded to the sand.

  A child crawled out from underneath, rubbing his head and flashing heat from his mouth: words he shouldn't have learned yet. The wound in his scalp steamed briefly before the edges pulled shut.

  The small, intense white sun, halfway down the sky, cast opaque black shadow across the opening in the probe. In the shadow something stirred.

  The children watched, awed.

  ABEL paused in the opening, then rolled out, using the slab of reentry shielding as a ramp. ABEL was a cluster of plastic and metal widgetry mounted on a low platform slung between six balloon tires. When it reached the sand it hesitated as if uncertain, then rolled out onto Mars, jerkily, feeling its way.

  The child
who'd been bumped by the ramp hopped over to kick the moving thing. ABEL stopped at once. The child shied back.

  Suddenly an adult stood among them.

  WHAT ARE YOU DOING?

  Nothing, one answered.

  *Just playing,* said another.

  WELL, BE CAREFUL WITH IT. The adult looked like a twin to any of the six children. The roof of his mouth was warmer than theirs, but the authority in his voice was due to more than mere loudness.

  SOMEONE MAY HAVE GONE TO GREAT TROUBLE TO BUILD THIS OBJECT.

  *Yes sir.*

  Somewhat subdued, the children gathered, around the Automated Biological Laboratory. They watched a door open in the side of the drum-shaped container that made up half of ABEL's body. A gun inside the door fired a weighted line high into the air.

  *That thing almost hit me.*

  *Serves you right.*

  The line, coated with sand dust, came slithering back into ABEL's side. One of the children licked it and found it covered with something sticky and tasteless.

  Two children climbed onto the slow-moving platform, then up onto the cylinder. They stood up and waved their arms, balancing precariously on flat triangular feet. ABEL swerved toward a clump of black grass, and both children toppled to the sand. One picked himself up and ran to climb on again.

  The adult watched it all dubiously.

  A second adult appeared beside him.

  YOU ARE LATE. WE HAD AN APPOINTMENT TO XAT BNORNEN CHIP. HAD YOU FORGOTTEN?

  I HAD. THE CHILDREN HAVE FOUND SOMETHING.

  SO THEY HAVE. WHAT IS IT DOING?

  IT WAS TAKING SOIL SAMPLES AND PERHAPS TRYING TO COLLECT SPORES. NOW IT SHOWS AN INTEREST IN GRASS. I WONDER HOW ACCURATE ARE ITS INSTRUMENTS.

  IF IT WERE SENTIENT IT WOULD SHOW INTEREST IN THE CHILDREN.

  PERHAPS.

  ABEL stopped. A box at the front lifted on a telescoping leg and began a slow pan of the landscape.

  From the low dark line of the Mare Acidalium highlands on the northeastern horizon, it swung around until its lens faced straight backward, at the empty orange desert of Tractus Albus. At this point the lens was eye to eye with the hitchhiking child. The child flapped his ears, made idiot faces, shouted nonsense words, and flicked at the lens with his long tongue.

  THAT SHOULD GIVE THEM SOMETHING TO THINK ABOUT.

  WHO WOULD YOU SAY SENT IT?

  EARTH, I WOULD THINK. NOTICE THE SILICATE DISC IN THE CAMERA, TRANSPARENT TO THE FREQUENCIES OF LIGHT MOST LIKELY TO PENETRATE THE PLANET'S THICK ATMOSPHERE.

  AGREEMENT.

  The gun fired again, into the black grass, and the line began to reel back. Another box retracted its curved lid. The hitchhiker peered into it, while the other children watched admiringly from below.

  One of the adults shouted, GET BACK, YOU YOUNG PLANTBRAIN!

  The child turned to flap his ears at him. At that moment ABEL flashed a tight ruby beam of laser light just past his ear. For an instant it showed, an infinite length of neon tubing against the navy blue sky.

  The child scrambled down and ran for his life.

  EARTH IS NOT IN THAT DIRECTION, an adullt observed.

  YET THE BEAM MUST HAVE BEEN A MESSAGE. SOMETHING IN ORBIT, PERHAPS?

  The adults looked skyward. Presently their eyes adjusted.

  ON THE INNER MOON. DO YOU SEE IT?

  YES. QUITE LARGE... AND WHAT ARE THOSE MIDGES IN MOTION ABOUT IT? THAT IS NO AUTOMATED PROBE. BUT A VEHICLE. I THINK WE MUST EXPECT VISITORS SOON.

  WE SHOULD HAVE INFORMED THEM OF OUR PRESENCE LONG AGO. A LARGE RADIO FREQUENCY LASER WOULD HAVE DONE IT.

  WHY SHOULD WE DO ALL THE WORK WHEN THEY HAVE ALL THE METALS, THE SUNLIGHT, THE RESOURCES?

  Having finished with the clump of grass, ABEL lurched into motion and rolled toward a dark line of eroded ring wall. The children swarmed after it. The lab fired off another sticky string, let it fall, and started to reel it back. A child picked it up and pulled. Lab and martian engaged in a tug of war which ended when the string broke. Another child poked a long, fragile finger into the cavity and withdrew it covered with something wet. Before it could boil away, he put the finger in his mouth. He sent out a pulse of pleasure and stuck his tongue in the hole, into the broth intended for growing martian microorganisms.

  STOP THAT! THAT IS NOT YOUR PROPERTY!

  The adult voice was ignored. The child left his tongue in the broth, running alongside the lab to keep up.

  Presently the others discovered that if they stood in front of ABEL, it would change course to crawl around the "obstruction."

  PERHAPS THE ALIENS WILL BE SATISFIED TO RETURN HOME WITH THE INFORMATION GATHERED BY THE PROBE.

  NONSENSE. THE CAMERAS HAVE SEEN THE CHILDREN. NOW THEY KNOW THAT WE EXIST.

  WOULD THEY RISK THEIR LIVES TO LAND, MERELY BECAUSE THEY HAVE SEEN DITHTA? DITHTA IS A HOMELY CHILD, EVEN TO MY OWN EYE, AND I AM PERHAPS HIS PARENT.

  LOOK WHAT THEY ARE DOING NOW.

  By moving to left and right of the lab, by forming moving "obstructions," the children were steering ABEL toward a cliff. One still rode high on top, protending to steer by kicking the metal flanks.

  WE MUST STOP THEM. THEY WILL BREAK IT.

  YES... DO YOU REALLY EXPECT THAT THE ALIENS WILL LAND A MANNED VEHICLE?

  IT IS THE OBVIOUS NEXT STEP.

  WE MUST HOPE THAT THE CHILDREN WILL NOT GET HOLD OF IT.

  Mistake

  In a cargo craft between Earth and Ganymede, Commander Elroy Barnes lolled in his crash couch with a silly smile on his face. The shovel-blade re-entry shield was swung down from the ship's nose, exposing the cabin's great curved window. Barnes watched the unwinking stars. It was a few minutes before he noticed the alien staring in at him.

  He studied it. Eight feet tall, roughly reptilian, with a scaly, domed head and a mouth furnished with several dozen polished stiletto-blade teeth. Its hands were four-fingered claws, and one held a wide-baffeled pistol-like tool.

  Barnes lifted a languid hand and waved.

  Kthistlmup was puzzled. The human's mind was muzzy, almost unreadable. The alien probed the ship for other minds, but the ship was empty save for Barnes.

  Kthistlmup stepped through the glass into the cabin.

  Barnes showed surprise for the first time. "Hey, that was neat! Do it again."

  "There's something wrong with you," Kthistlmup projected.

  Barnes grinned. "Certain measures are necessary to combat the boredom of space, to s-safeguard the sanity of our pilots." He lifted a green plastic pill bottle. "NST-24. Makes for a good trip. Nothing to do out here till I have to guide the beast into the Jupiter system. So why not?"

  "Why not what?"

  "Why not take a little trip while I take the big one?"

  Kthistlmup understood at last. "You've done something to your mind. Chemicals? We use direct-current stimulus on Mars."

  "Mars? Are you really—?"

  "Barnes, I must ask you questions."

  Barnes waved expansively. "Shoot."

  "How well is Earth prepared against an attack from space?"

  "That's a secret. Besides, I don't have the vaguest notion."

  "You must have some notion. What's the most powerful weapon you ever heard of?"

  Barnes folded his arms. "Won't say." His mind showed only a blaze of white light, which might not have anything to do with the question.

  Kthistlmup tried again. "Has Earth colonized other planets?"

  "Sure. Trantor, Mesklin, Barsoom, Perelandra..."

  Barnes' mind showed only that be was lying, and Kthisthnup had lost patience. "You will answer," he said, and reached forward to take Barnes' throat delicately between four needle-sharp claws.

  Barnes' eyes grew large. "Oh, oh, bad trip! Gimme, gimme the bottle of Ends! Quick!"

  Kthistlmup let go. "Tell me about Earth's defenses."

  "I got to have an End. Big blue bottle, it should be in the medicine chest." Barnes reached to the side. He had the wall cabinet open before Kthistlmup caught
his wrist.

  "This 'End.' What will it do?"

  "End the trip. Fix me up."

  "It will clear your mind?"

  "Right."

  Kthistlmup released him. He watched as Barnes swallowed an oval pill, dry.

  "It's for in case we're going to run across an asteroid, so I can recompute the course fast," Barnes explained.

  Kthistlmup watched as Barnes' mind began to clear. In a minute Barnes would be unable to hide his thoughts. It wouldn't matter if he answered or not. Kthistlmup need only read the pictures his questions produced.

  Barnes' mind cleared further... and Kthistlmup found himself fading out of existence. His last thought was that it had been a perfectly natural mistake.

  Night on Mispec Moor

  In predawn darkness the battle began to take shape. Helicopters circled, carrying newstapers and monitors. Below, the two armies jockeyed for position. They dared not meet before dawn. The monitors would declare a mistrial and fine both sides heavily.

  In the red dawn the battle began. Scout groups probed each other's skills. The weapons were identical on both sides: heavy swords with big basket hilts. Only the men themselves differed in skill and strength.

  By noon the battle had concentrated on a bare plain strewn with white boulders and a few tight circles of green Seredan vegetation. The warriors moved in little clumps. Where they met, the yellow dirt was stained red, and cameras in the helicopters caught it all for public viewing.

  Days were short on Sereda. For some, today was not short enough.

  As Sereda's orange dwarf sun dropped toward the horizon, the battle had become a massacre with the Greys at the wrong end. When Tomas Vatch could no longer hold a sword, he ran. Other Greys had fled, and Amber soldiers streamed after them, yelling. Vatch ran with blood flowing down his sword arm and dripping from his fingertips. He was falling behind, and the Ambers were coming close.

  He turned sharp left and kept running. The swarm moved north, toward the edge of Mispec Moor, toward civilization. Alone, he had a chance. The Ambers would not concern themselves with a single fleeing man.