Convergent Series

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by Larry Niven


  He's going through that now. I stay out of his way.

  And I'm still going through it. I'm the older George Cox now, but it doesn't help. My life is planned out in the minutest detail. My free will— my illusion of free will— will not return to me until Ulysses disappears among the stars. I didn't expect this.

  We meet rarely during the next five months. He and Frank Curey and Yoki Lee are deeply involved in astronaut training. I'm living off his salary, but that's okay with both of us, because the value of his stocks is building and building. I'm doing all the manipulating, in our name. He doesn't have time.

  It's like playing poker with reader cards! I feel no guilt: only a vast elation. The stocks move as I command them... or vice versa. Last time through this I wondered why the money didn't increase even faster. Now that I'm handling it myself, I know. There's a limit to how fast you can move money around, even when you know exactly where it ought to go.

  "I feel sorry for Yoki and Frank," he tells me. "They're working just as hard as I am, and for what?"

  "Think of it as predestination," I tell him. I wish I could think of a better answer. I remember how disappointed they will be, and how bravely they will try to hide it.

  The three of them spend two months in Ulysses itself. The ship is complete now; only the trainee pilots are not ready. I can see it up there at night, a splinter of light cruising slowly across the stars.

  And I remember:

  Passing the planets, passing through the cometary belt. Months of fiddling with the ram fields, adjusting the flow of interstellar hydrogen into the fusion region, until finally I was in clear space. Climbing into the cold-sleep tank.

  Waking at midpoint, staring in awe at the way the stars had changed, blazing blue-white before me, glowing dull red behind; then turning to the tricky task of reversing the fields to channel the fusion blast forward.

  Waking again to find that the stars were back to normal. Using the Forward Mass Indicator to seek out Bauerhaus Four. There. Searching that point with the telescope— and nothing.

  Dropping Probes One and Two. Into the ergosphere, the elliptical region of spin around the Schwarzschild radius. The size of the ergosphere would tell me how much of the star's spin the black hole had carried into itself: the dimensions of the path through the singularity.

  One was circling the black hole hundreds of times a second before it disappeared. Two followed the same path, fired a jet before it reached the Schwarzschild radius, and shot away at just less than lightspeed.

  I remember plotting the course for Probe Three.

  Following it down.

  Am I really going to do this foolish thing?

  Hell, I've already done it.

  I remember the way the stars bluffed near that empty point. Once a star passed directly behind it and for a moment it was a ring of light. There was no bump as I went through the Schwarzschild radius— only the gradually increasing pull of tidal force— but somehow I knew I had left the universe.

  Free at last. Free of the older George Cox.

  Sure I was.

  ***

  "We've been moving money around for five months now," I tell him on his return, "and we've passed the million mark. How's it feel to be a millionaire?"

  "Pretty good." He smiles in triumph as he looks through the books, but the smile is a bit forced when he turns to face me. He's not used to me yet.

  "Okay. Now, your job." I hand him a stack of newspapers. "Memorize these stocks."

  "All of them?"

  "No, just the ones that're going to go up, and when. But I haven't marked them, George. You'll have to find and mark them and then memorize them."

  He grumbles, as I did once. "You've had more free time than me."

  "Haven't we got cause and effect screwed up enough? I get this nightmare feeling that if we louse up the natural laws any worse, I'll go out like a candle flame. Will you do this for the best friend you ever had?

  Please?"

  He takes the newspapers.

  I don't see him for a week.

  ***

  One afternoon I answer a ringing telephone. It's him. His eyes are wide, his face is white. Before I can speak he blurts it out. "They picked Frank!"

  "What? The hell they did. They picked me."

  "They picked Frank! George, what'll we do?"

  His voice is fading. There's a singing in my head. The room is fading, going blurry. My knees buckle, and I drift toward the floor. I want to scream, but I can't.

  I'm cold. There is rough-textured rug under my chin. I feel it with my hands, and it's real, it's really there.

  I must have fainted.

  The other George is yelling out of the phone. "George! George!" I manage to get my face in front of the camera. I tell him, "Sit tight. I'll be right over."

  This time we aren't sitting. We're pacing, passing each other, talking in random directions... it would look like low comedy if anyone could see us.

  He's saying, "We could just forget it. Share the money. Ignore the paradox."

  "I hate that thought. George, get it through your head that the paradox is me. If this time track doesn't go as it went, I'm gone! We've got to do something."

  "Like what? Steal the ship?"

  "Hum. That's—"

  "If I steal Ulysses, you get court-martialed! You!"

  "Hah! They wouldn't even look for me."

  "And how are you going to spend our million dollars in my name?"

  Dammit. He's right. The effort I've spent, the risks I've taken, all for nothing.

  I stop in midstride. "Maybe they won't suspect me."

  "Hah. You couldn't get onto the shuttle field without showing your face."

  "Hah yourself. Someone must have been impersonating me. I've got an alibi."

  "Alibi?" He suddenly starts to laugh. "Hey, I'm going to make drinks. This won't make any sense at all to a sober man."

  ***

  A month to wait. A month to make plans. But it isn't: they've moved the take off date up two weeks. I'm starting to lose faith in any kind of consistent universe. At night I'm afraid to fall asleep. Every morning comes as a joyful surprise. I'm still here.

  I wish I could talk to Bauerhaus.

  We braced him after the lecture. A small, round, voluble man, he was willing to talk at any length about cosmology in general. The Big Bang that may or may not have started the universe, that may have sown the universe with quantum black holes smaller than an atomic nucleus and weighing more than a large asteroid... the possibility that the universe itself is inside somebody else's black hole... white holes spewing matter from nowhere.

  But they fought clear of one subject. "Gentlemen, we simply do not know what goes on inside the Schwarzschild radius of a black hole. We do not know that the matter actually goes to a point. It may be stopped by a force stronger than any we know of."

  What of the paths through a rotating black hole?

  He smiled like one sharing a joke. "We expect to find a hole in the theory here. We postulate a Law of Cosmic Censorship, a process that would prevent anything from ever leaving a black hole. Otherwise we could get black holes with so much spin to them that there is no Schwarzschild radius around the singularity. A naked singularity would be very messy. The mathematics is inconsistent— like dividing zero by zero."

  If he could see me now, both of me together, surely it would be singularity enough. We do not risk being seen together. The younger George Cox continues his training. Newsmen interview him and Yuri on the need for more Bussard ramjets, scout ships to seek out Earthlike worlds circling other stars. The older George Cox plays the stock market, and waits.

  Frank Curey has spent as much time in space as I have until the Ulysses flight, which hasn't happened yet. He stands about five feet zero, stocky and well muscled. His big square jaw gives him a bulldog look. He masses less than me or Yuri. So do the food and oxygen required to keep him alive for the year and a half he'll be awake.

  There's no reason Spacebranc
h shouldn't have picked him over me; yet I keep wondering. What was different this time? Did the younger George concentrate too much on his stocks, too little on training? Did he stop trying, because I was the proof that he would succeed anyway?

  Too late now. We've had one break. They picked me to pilot the ferry ship up and to help Frank with the final checkout of Ulysses.

  Frank and I got through the check points together. The guards pass us through with no fuss. The shuttle field is bright with artificial lights beneath a gray-blick sky.

  Frank is nervous, excited. He's talking too much. Muscles flex at the edges of his jaw'. "Twenty-six years. What can happen in twenty-six years? They could have immortality by then. Or a world dictatorship. Teleportation. Faster-than-light travel."

  "They could get that from you, if Probe Three works out."

  "Yeah. Yeah. If Probe Three comes back about the time I leave... but that's not too useful for space travel, George. There aren't enough black holes. No kidding, George, what d'you think I'll find when I come back?"

  Yourself. It's on the tip of my tongue, but I swallow it. "Me, waiting at the shuttle field to tell you all about it. Unless you go too far in. Then you might not come out until every star is dead."

  He clears his throat. "I know."

  I say, "Care to change your mind?" Thinking theres a chance...

  "Oh, come on," he snaps. That settles that.

  We've almost reached the shuttle. It's a lifting body, not large, with a radiation shield around the tailpipe and an escalator ramp leading up into the nose. I'm talking too much myself; I'm as nervous as Frank.

  Lucky there were two gates. I half-expected the guards to stop us, on grounds that one of us was already inside... but apparently he got through without a hitch. Or else he didn't make it.

  Frank is stepping onto the ramp when the other George Cox slides like a shadow from behind it. He's holding a heavy spanner.

  And wiry Frank whips around and plants his fist in George's belly, crosses instantly with the right, plenty of class that boy shows. George goes down like a consignment of cooked spaghetti, flat on his back, his face turned up to the harsh lights.

  Frank sees his face. He freezes.

  I don't have a spanner. I use the stiff edge of my palm against Frank's neck. Frank turns, looking bewildered, and I hit him on the point of the jaw. He goes down.

  I take his pulse. It hasn't stopped.

  George Cox's heart is beating too, but he's showing no other sign of life. I don't need to take my own pulse; it's thundering in my ears. The other George Cox may need a hospital. He's in poor shape to pilot an interstellar spacecraft.

  Which leaves...?

  Ulysses hovers before me, enormous. There are attitude jets like nostrils, but no sign of a main thruster: only the hydrogen fusion booster, as big as Ulysses itself, that will run me up to Bussard ramjet speed.

  From that point on I'll be running on interstellar hydrogen, sweeping it in and compressing it in magnetic pinch fields until it undergoes fusion. I've been through this before. I'm not even nervous.

  As the metaphysical complexities grow ever more hideously tangled, my choices grow simpler. I'm going to steal Ulysses because I can't possibly turn back. I'll follow the return path again, because it's my only hope of straightening this out.

  I could have been killed, that last trip through the singularity. I could be killed this time. But the ghost of the older George Cox is no longer with me.

  And the younger George Cox, the man I left tied back to back with Frank Curey, for verisimilitude... has become the real George Cox. There's been no break in his timeline, and no part of his timeline is me. I am fatherless, motherless, a ghost without origin.

  If George keeps his head, he'll stay out of prison. He spotted an impostor, his own double, walking toward the shuttle with Frank. He was about to do something about it, with the aid of a handy spanner, when Frank exploded in his face. That's all he knows.

  Docking. The whole ship goes Clunk, thot. Up to now they could have stopped me. Now it's too late.

  As I cross to Ulysses's manlock I feel a prickly awareness of the second Ulysses hidden on the back side of the Moon. I've found a way to breed very expensive spacecraft. I ought to patent it.

  How did it all get started, anyway? Was there ever a George Cox who followed the flight plan exactly?

  Yeah... and then a second George Cox watched Probe Three return even before Ulysses took off. That plan gave him an idea. If Probe Three could return before it started, so could he...

  Was he the older George Cox who knocked on my apartment door a lifetime ago? Or was he already several cycles gone?

  And what will happen if I just follow the flight plan this time? No, I don't dare. It would start the whole thing over again. Or would it?

  I wish I could ask Dauerhaus. But people like Bauerhaus don't like singularities in the first place.

  I don't blame them.

  ***

  The educated reader will have realized that you can't do that trick with a black hole of smaller than galactic mass. The tides would rip the ship atom from atom, then tear up the atoms. For story purposes it was necessary to fudge a little!

  ***

  The Schumann Computer

  Either the chirpsithtra are the ancient and present rulers of all the stars in the galaxy, or they are very great braggarts. It is difficult to refute what they say about themselves. We came to the stars in ships designed for us by chirpsithtra, and wherever we have gone the chirpsithtra have been powerful.

  But they are not conquerors— not of Earth, anyway; they prefer the red dwarf suns— and they appear to like the company of other species. In a mellow mood a chirpsithtra will answer any question, at length.

  An intelligent question can make a man a millionaire. A stupid question can cost several fortunes. Sometimes only the chirpsithtra can tell which is which.

  I asked a question once, and grew rich.

  Afterward I built the Draco Tavern at Mount Forel Spaceport. I served chirpsithtra at no charge. The place paid for itself, because humans who like chirpsithtra company will pay more for their drinks. The electric current that gets a chirpsithtra bombed costs almost nothing, though the current delivery systems were expensive and took some fiddling before I got them working right.

  And some day, I thought, a chirpsithtra would drop a hint that would make me a fortune akin to the first.

  ***

  One slow afternoon I asked a pair of chirpsithtra about intelligent computers.

  "Oh, yes, we built them," one said. "Long ago."

  "You gave it up? Why?"

  One of the salmon-colored aliens made a chittering sound. The other said, "Reason enough. Machines should be proper servants. They should not talk back. Especially they should not presume to instruct their masters. Still, we did not throw away the knowledge we gained from the machines."

  "How intelligent were they? More intelligent than chirpsithtra?"

  More chittering from the silent one, who was now half drunk on current. The other said, "Yes. Why else build them?" She looked me in the face. "Are you serious? I cannot read human expression. If you are seriously interested in this subject I can give you designs for the most intelligent computer ever made."

  "I'd like that," I said.

  She came back the next morning without her companion. She carried a stack of paper that looked like the page proofs for The Brothers Karamazov, and turned out to be the blueprints for a chirpsithtra supercomputer. She stayed to chat for a couple of hours, during which she took ghoulish pleasure in pointing out the trouble I'd have building the thing.

  Her ship left shortly after she did. I don't know where in the universe she went. But she had given me her name: Sthochtil.

  I went looking for backing.

  We built it on the Moon.

  It added about fifty percent to our already respectable costs. But... we were trying to build something more intelligent than ourselves. If the machine turned
out to be a Frankenstein's monster, we wanted it isolated. If all else failed we could always pull the plug. On the Moon there would be no government to stop us.

  We had our problems. There were no standardized parts, not even machinery presently available from chirpsithtra merchants. According to Sthochtil— and I couldn't know how seriously to take her— no such computer had been built in half a billion years. We had to build everything from scratch. But in two years we had a brain.

  It looked less like a machine or building than like the St. Louis Arch, or like the sculpture called Bird in Flight. The design dated (I learned later) from a time in which every chirpsithtra tool had to have artistic merit. They never gave that up entirely. You can see it in the flowing lines of their ships.

  So: we had the world's prettiest computer. Officially it was the Schumann Brain, named after the major stockholder, me. Unofficially we called it Baby. We didn't turn it on until we finished the voice linkup.

  Most of the basic sensory equipment was still under construction.

  Baby learned English rapidly. It— she— learned other languages even faster. We fed her the knowledge of the world's libraries. Then we started asking questions.

  Big questions: the nature of God, the destinies of Earth and Man and the Universe. Little questions: earthquake prediction, origin of the Easter Island statues, true author of Shakespeare's plays, Fermat's Last Theorem.

  She solved Fermat's Last Theorem. She did other mathematical work for us. To everything else she replied, "Insufficient data. Your sources are mutually inconsistent. I must supplement them with direct observation."

  Which is not to say she was idle.

  She designed new senses for herself, using hardware readily available on Earth: a mass detector, an instantaneous radio, a new kind of microscope. We could patent these and mass-produce them. But we still spent money faster than it was coming in.

  And she studied us.

  It took us some time to realize how thoroughly she knew us. For James Corey she spread marvelous dreams of the money and power he would hold, once Baby knew enough to give answers. She kept Tricia Cox happy with work in number theory. I have to guess at why E. Eric Howards kept plowing money into the project, but I think she played on his fears: on a billionaire's natural fear that society will change the rules to take it away from him. Howards spoke to us of Baby's plans— tentative, requiring always more data— to design a perfect society, one in which the creators of society's wealth would find their contribution recognized at last.

 

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