Convergent Series Read online

  She ate as she walked: nuts and sugar-coated puffed wheat, an adequate trail snack. Dry gray bushes gave off a spicy smell as she brushed by them. She passed spear trees, slender vertical shafts of red wood, each with an artificial-looking ball of green leaves at the point. Sometimes she angled her path to cross a patch of mattress plant. Mattress plant was like thick-piled green cotton with roots, one plant sometimes covering an acre of ground, delightful to walk on. It was all familiar, part of her world.

  She kept a rhythmic pace, placing her feet almost heel-to-toe in a walk that moved the mass of her backpack straight forward instead of bouncing it up and down. In an hour she'd be in sight of the Burns' house, and no trouble finding it. People who lived this far from Starbase Town usually preferred hilltops.

  The nonesuch paused at the crest of the hill. He looked; he sniffed. Sight and smell were none too sharp in a nonesuch, and the girl was too far downslope. But her thoughts were clear and bright. Her brain was larger and more intelligent than any native to this world, excepting that of another nonesuch. Intelligence was a liability on Haven. A large brain, clear thoughts, made it easy for a nonesuch to follow.

  The nonesuch was not a local. He had wandered into this area, following a rich concentration of the thoughts of meat. The locals were few, and none had challenged him for territory. He was big, his claws were sharp, he could fight.

  The locals were few. That was peculiar, with thousands of human minds clustered a few miles distant, and thousands more scattered throughout the region, all broadcasting clear, bright thoughts. The locals left the humans strictly alone. They were numerous and easy to follow, but a local nonesuch would not prey on them. Why not?

  He would learn.

  The nonesuch knew from her thoughts that the girl had not seen him, was not looking toward him. He started down the hill.

  ***

  Slender spear trees, low gray bushes, patches of mattress plant. Nothing big could hide in such cover.

  Then what was it Doris had seen moving on the side of that big hill? There were no big animals in this region of Haven, except for domestic sheep and cattle and perhaps a nonesuch or two, Doris thought, smiling at herself.

  Motion near the hill's green crest. She'd looked again and it hadn't been there. A cloud shadow? Or another hiker? Perhaps she'd have company when she finished her walk.

  Pity Mark hadn't been able to join her. She toyed with a daydream: he'd finished early— the computer he had to fix had been unplugged or something— and he had followed her. Without a backpack he could double her pace.

  Or it was a nonesuch. But no, she could do without such company!

  The nonesuch: she'd heard about it as a child. Don't go outside the city without an adult, Little Doris. The nonesuch will get you. You'll never know it's there, because it's always behind you.

  Why, Dad?

  Because it's so ugly, Little Doris. It won't let you see it. It's ashamed of the way it looks.

  She smiled, remembering how solemnly she'd listened. And there had been stories of bad little girls eaten by the nonesuch ... Of course that had been a long time ago ...

  ***

  The nonesuch had fallen flat and frozen when he sensed the girl looking toward him. Now, as she resumed her rhythmic stride, he began moving again. But he was disturbed.

  The picture in the girl's mind was very like a nonesuch.

  It stood upright on its hind legs, on broad flat feet. Its head was round, its neck virtually nonexistent. Its eyes were tiny and close-set. Its teeth were large and triangular, and two large fangs protruded over the lower lip in front. Its skin was smooth, mottled in two shades of greenish brown. Brown hair flopped forward from the crown of its head. Its hands were big, like a man's with both thumbs missing, and each finger was tipped with a crescent claw.

  It was not quite a nonesuch, this picture in the girl's mind; some of the features were humanized. But it was close. She should have been frightened, but what he felt in her was certainly not fright.

  The nonesuch was wary. He would follow his habit. He would not let himself be seen.

  ***

  ... a long time ago. Dad and his nonesuch! And her uncles were in on it too. She was six before she caught on.

  It's always behind me, is it, Dad? Then I'll never know if it's real or not, will I? But how do you know what it looks like, Dad, if nobody's ever seen one?

  And finally Dad and Uncle Ray had laughed and given in. The nonesuch was like Santa Claus: a story.

  Adults thought it was fun to tell stories to kids. For a year or so afterward she'd wondered if Earth was another such tall story. But Earth was real; there were pictures, there were infrequent starships...

  ***

  The nonesuch had a problem. It had run across a grazer.

  The small quick beast was closer than the girl. It was moving round and round the borders of a mattress plant, trimming the borders with blunt teeth. The nonesuch sensed its placid thoughts, its continuous dull hunger and its continuous chewing. It hadn't seen him yet.

  The nonesuch was torn. He could have been on the grazer in a few minutes. The grazer would make a full meal... but at the last moment it was bound to make some disturbance, and the girl would turn and see him.

  With some regret the nonesuch moved on. He sensed the animal's sudden start as it saw him, then fear and frantic haste, dwindling with distance.

  It was curiosity that moved the nonesuch after the more difficult prize. Partly it was: how will human meat taste? and partly: why do the others leave these beasts alone? One question might answer another.

  Human meat might be poisonous, or merely unpalatable. But no local nonesuch had told him so. In fact, they would not answer him at all on this subject.

  And partly it was: She knows of me, but she doesn't believe in me. Incomprehension. Something alien here, something that went with the girl's quiet conviction that she had come from a different world.

  She was thinking of a man now... a man somewhat older than she, who had not proposed sex to her but who might... and her imagination was working in all her senses. The nonesuch savored sensations sharper than his own even in imagination: sight and touch and somasthesia. He liked the girl's mind.

  He would have liked to talk to her.

  Why not? She was not a nonesuch... she was very alien... but surely there must be concepts basic to all life. The nonesuch thought it through, then projected the most universal message he knew: I'M GOING TO EAT YOU

  There! She had reacted, a tensing of viscera, her head turning to look behind her, a shiver... but now she had forgotten. He had not truly reached her mind. She lacked that sense entirely, like an animal. Pity.

  Instead he savored in anticipation her sudden sharp knowledge, there at the end, when she would realize the reality of the nonesuch. How would it feel to her? To him? He increased his pace.

  ***

  She looked back as she passed a barrel tree. For an instant she was sure there was something behind her. She almost went back to look. Then one of the pigsized grazing beasts went bounding past her as if death itself were at its heels, and she went on, laughing. When they put those oversized hind legs to the test the bounders always looked like they were trying to do somersaults.

  She ought to be getting close to Great-Aunt Hildegarde's house. The pack was getting heavy.

  And there was still that feeling of something behind her.

  ***

  The barrel tree was a piece of luck. A nonesuch was big. He could never have fed himself had he not been unusually good at the predator business. A barrel tree was about the only growing thing big enough to hide a nonesuch. He kept the thick trunk and dark green crown between himself and the girl as he moved in for the kill.

  When he reached the barrel tree the girl was twenty meters beyond. Close enough. A nonesuch was no good for a long chase, but for short sprints he could move like light itself.

  Her back was to him.

  He charged.

  She heard
something. She turned, awkwardly because of the pack.

  She saw him.

  It was just as Dad and Uncle Ray had described it. Tiny, close-set eyes; wide mouth with triangular buck teeth; floppy mop of brown hair; big hands with long nails; short legs and big clumsy feet. A vicious caricature of some yokel farmhand, and it was gallumping toward her with clawed hands outstretched in moronic lust.

  Doris's eyes bugged. A giggle bubbled up into her throat and hung there. There wasn't any such thing.

  She knew that. Was she losing her mind? She closed her eyes hard, so tight it hurt, then opened them fast.

  Sure enough, there was nothing there.

  She looked about her, searching for the pattern of shadows that must have sparked that ridiculous illusion. A passing cloud shadow, perhaps? Nothing.

  She'd been stupid; she'd gone too long without a rest break. Doris walked back to the only shade in sight— the barrel tree— dropped her pack against its trunk and sat down under the crown of dark green leaves.

  ***

  It was the dull gnawing of hunger that brought him back to himself. Had he been asleep? Asleep, standing up?

  Memory came joltingly. The nonesuch mewled and began patting himself with his hands. Yes, he could feel that. That was real.

  He had not been asleep. The nonesuch knew what sleep felt like. He had been— gone. Now he was back (he felt his face; the claws pricked his skin), he was back, yes. From where?

  From nothing.

  She'd looked at him and not believed. Looked at him and seen— illusion, a trick of the mind, a trick of light and shadow. She'd convinced him in that moment, and there had been telepathic feedback, and— he was gone. Gone, until hunger made him real again.

  There was a grazer nearby, wandering toward him around the curve of a mattress plant. He plodded toward it, reluctantly, prodded by sharp hunger. The girl was nowhere near. He must have been gone for a long time.

  The grazer hadn't seen him yet.

  Suppose it refused to believe in him?

  Singularities Make Me Nervous

  Homecoming. The vast interstellar spaces have brought me back to my starting point, there below me, at the top of Rand's Needle. Three hundred stories of glass windows flash sunset fire at me, and the taxi slants down toward the landing roof.

  Homecoming. I should be feeling safe and warm. I do not.

  A broad flight of black marble steps leads me down into the lobby. I hail the guard before he notices me.

  "Hello, Emilio."

  He smiles. "Good morning, Mister Cox." He waits while I use the key— he doesn't have one himself— then holds the elevator door for me. He's noticed nothing unusual.

  I hold my apartment key ready. Will he have visitors? But that's silly. I didn't have visitors that night.

  Twelve floors down. I stand squarely in front of the peephole and ring the bell. A voice I know asks, "Who is it?"

  "Can you see me?"

  "Yes."

  I grin. My face feels tight. My breathing is funny. "Who am I, then?"

  Hesitation. "I wish I could take your retina prints."

  "They'd match, George. I'm you."

  "Sure you are."

  He's skeptical. I am not offended. "I'm you. And I've got a key to my own apartment. Shall I prove it?"

  "Go ahead."

  I unlock the door and walk in. The shock of recognition gets me in the pit of the stomach. Tables, chairs, favorite recline chair, couch showing the barely visible stain of a spilled eggnog. The Eddie Jones originals. The gallon brandy bottle on the wet bar. Twenty-six years in space, most of it in frozen sleep, but now it's over. I'm home.

  It's all here, all in place, right down to the tenant, George Cox, who is standing well back from me, taking no chances. He's holding an enormous folding knife with an engraved blade like a broad silver leaf.

  I say, "I can tell you where you got that."

  "So can a lot of my friends." He doesn't relax.

  "I didn't expect this to be easy. George, do you remember when you were, oh, eighteen or so? Going to Cal Tech. One night you got so lonely and so horny you called a girl you'd only met once in your life, at one of Glenda's birthday parties. She was a little plump and very sexy, remember? You called her but you got her parents. You were so nervous and embarrassed that—"

  "Shut up. All right, I remember. What was her name?"

  I can't remember. I tell him so.

  "Right again," he says.

  "Okay. Remember that Kansas sunset where the whole sky was split down the middle by one dark blue beam? You could follow it up across the sky and down into the east, almost to the horizon."

  "Yeah. Unbelievable. I never saw it happen again." He considers, then folds the knife and drops it in a drawer. "You're me. How about a drink?"

  "What do you think? Shall I mix?"

  "I'll do it," he says.

  I let him. I don't want to infringe on his territorial instincts. He goes to the trouble of mixing Navy Grogs, a compliment: he's decided it's a special occasion. I don't remember that detail from the night that I was him. I cut the straws while he's at work, and he gives me a sharp look. Nobody else would have known to do that.

  "You're me," he says, when we've settled in chairs and have imbibed some of the life-giving fluid.

  "How?"

  "The black hole. Bauerhaus Four."

  "Ah." He was expecting that. "So I made it back. They haven't even picked me to go yet."

  "They will."

  He sips at his drink and waits.

  "Black holes," I say. "Singularities. Stars that have collapsed all the way to a point. They've been there in the general theory of relativity for a hundred years or more. The first black hole was found in nineteen seventy-two, in Cygnus, circling a puffy yellow-giant star. But Bauerhaus Four is a lot closer."

  He nods. He's heard it before, a couple of weeks ago by his own reckoning, when Doctor Kurt Bauerhaus himself came to lecture us at the Spacebranch Authority Training Center.

  "But," I tell him, "not even Doctor Bauerhaus wants to talk about what goes on inside the Schwarzschild radius of a black hole. Singularities upset people like Bauerhaus."

  "It's time travel that does that."

  "I don't think so. Forget the time travel aspect and look at a black hole. A mass so big that when it collapses it goes all the way to a point. Even light redshifts to zero before it can get out. Would you believe it?"

  He shrugs. "It's in the equations. Bauerhaus said so. Relativity's peculiar from square one, and it's checked out every time it's been tested."

  "A hole into another universe, maybe, or into another part of this one, maybe. That's in the equations too. And there's a path around a rotating black hole that brings you back to your starting point without even going through the singularity. Which sounds harmless enough until you realize you're talking about event-points— points in space time."

  He raises his glass. "Skoal."

  I raise mine. "Right. I'm back before I started the trip Most astrophysicists would rather believe there's a hole in the theory. Singularities make them nervous.

  "Time travel makes me nervous."

  "You can see for yourself." I rap my chest. "It's safe."

  He doesn't look nervous. We're both relaxing now under the influence of the drinks. It's been a long, weary time since I tasted the cold brown sweet power of a Navy Grog.

  He says, "I'm only supposed to circle it, you know. And drop the probes."

  "I know. But Ulysses's autopilot is built to send one of the probes on a round trip through the Schwarzschild radius of the star and back to its starting event-point. You just take Ulysses through that path instead of sending the probe. You can't go wrong. You go back in time about twenty-six years, which brings you back to the Moon six months early."

  He shifts in his chair. "The Moon? Not Earth orbit?"

  "Not yet. I've got Ulysses hidden on the back side of the Moon. From there I took a jet platform to within sight of Ley Crater,
then hid that. I came back to Miami on a tourist shuttle. A year from now I'll go back to the Moon, pick up Ulysses and come home to a cheering mob."

  "Six months after takeoff. That'll tell them you did go through the Schwarzschild radius. Bauerhaus Four is eleven light-years away."

  "Well, you can make your own decision on that—"

  "The hell. You're me, and you've already decided!"

  "I've got a year to change my mind. But look at it this way. NASA is entitled to know you can use a black hole this way. They're paying for the trip. And what can they do to me?"

  "Yeah—"

  "And I'll be damned if I'll hide out for twenty-six years."

  He nods. "Right. G— George—" He stumbles over our name. "Just what's the point of all this?"

  He's guessed that already, I think. "Stocks. Luckily you're already playing the stock market a little. I've memorized the behavior of several stocks for the next six months. In six months we'll be a millionaire. Then we'll go through a stack of newspapers and you'll do the memorizing."

  He grins. "What for? We'll already have the money."

  "I hope you're putting me on," I say uneasily.

  He nods. I'm reassured, partly. But I'm the vulnerable one. If we make one mistake in the program, if the Typewriter of Time writes a different history this time around, I'm the one who'll disappear in a puff of smoke. Or will I? The paradoxes are all new, and we have to guess at how they'll work out.

  I came back from the Moon under an assumed name: C. Cretemaster. As C. Cretemaster I now rent an apartment across town from the younger George Cox. I don't want to bug him overmuch with my presence.

  I certainly bugged me, back when I was him. I was afraid the older George Cox would try to take over my life. He didn't... and yet he did. His very existence hemmed me in more than prison bars. I would make these choices, not those; where the road of life forked I would turn this way; all others were barred to me.