Convergent Series Read online

  They turned toward the beach. Janet asked, "Why would you want to kill me?"

  "The alimony's bleeding me white."

  "That's all?"

  "No. Personal reasons."

  She laughed. He had wondered before: was her laughter always scornful, or did it only sound that way?

  "My God, Murray! Surely you can tell me, your intended victim!" She sobered suddenly. "Never mind. I don't want to know why. Do you still plan to kill me?"

  "No. Not after that."

  "The accident."

  "Of course. I don't have the nerve. Suppose I did it, and then froze up? My car's in a police lot with a dog's body in the trunk. Well, that won't get me killed. But suppose it was you?"

  "Thafs almost funny," said Janet.

  "Want a real laugh? I may never drive the freeway again, either. I was so sure I was dying..."

  "I think I'd better tell someone else about this conversation, just in case."

  "Go ahead then," said Simpson. And he had an odd thought: this was his last chance to go through with it. Before she told someone.

  And then, an odder thought. Her tone: too light. She still didn't believe him. He was beginning to doubt it himself. Had he really intended to kill Janet?

  She'd hurt him badly. She'd hurt him by leaving him: she, the only woman for Murray Simpson. She might as well have taken his testicles along. And he wanted to hurt her, badly.

  They had reached the house. Janet pulled into the garage and shut off the ignition. "Do you always leave the door open?"

  "Sometimes I forget."

  Very uncomfortably, Janet asked, "Shall I come in and make you some coffee?"

  "No. No thanks." Simpson opened the door and got out.

  And felt it end.

  Deep peace. Massless body, without sensation. The darkness of the blind.

  Simpson said, "What happened?"

  "You didn't kill her," said the voice without character.

  "No, of course not. Am I dead again?"

  "You are dead, still."

  "How?"

  "Loss of blood through a ruptured spleen, symptoms masked by shock. Your most recent memories were a dry run. Simpson, you did not kill your wife."

  With abstracted logic, Simpson said, "But I would have, if there hadn't been an accident."

  "That is debatable. In any case, it was your own accident. You caused it without help."

  "Deliberately?" Simpson didn't know.

  "Your judge will decide. Shall we go?"

  "Yes."

  They went.

  Convergent Series

  ***

  I graduated college with a B.A. in mathematics and a minor in psychology. This peculiar combination is easy-to explain. I spent two years taking courses for fun. Then I looked for the quickest way to graduate, and that's what came out.

  The mathematics background has been useful, of course. But "Convergent Series" is my only story to have derived directly from mathematics.

  —LN

  ***

  It was a girl in my anthropology class who got me interested in magic. Her name was Ann, and she called herself a white witch, though I never saw her work an effective spell. She lost interest in me and married somebody, at which point I lost interest in her; but by that time magic had become the subject of my thesis in anthropology. I couldn't quit, and wouldn't if I could. Magic fascinated me.

  The thesis was due in a month. I had a hundred pages of notes on primitive, medieval, oriental, and modern magic. Modern magic meaning psionics devices and such. Did you know that certain African tribes don't believe in natural death? To them, every death is due to witchcraft, and in every case the witch must be found and killed. Some of these tribes are actually dying out due to the number of witchcraft trials and executions. Medieval Europe was just as bad in many ways, but they stopped in time...

  I'd tried several ways of conjuring Christian and other demons, purely in a spirit of research, and I'd put a Taoist curse on Professor Pauling. It hadn't worked. Mrs. Miller was letting me use the apartment-house basement for experiments.

  Notes I had, but somehow the thesis wouldn't move. I knew why. For all I'd learned, I had nothing original to say about anything. It wouldn't have stopped everyone (remember the guy who counted every I in Robinson Crusoe?) but it stopped me. Until one Thursday night—

  I get the damndest ideas in bars. This one was a beaut. The bartender got my untouched drink as a tip. I went straight home and typed for four solid hours. It was ten minutes to twelve when I quit, but I now had a complete outline for my thesis, based on a genuinely new idea in Christian witchcraft. All I'd needed was a hook to hang my knowledge on. I stood up and stretched...

  ... And knew I'd have to try it out.

  All my equipment was in Mrs. Miller's basement, most of it already set up. I'd left a pentagram on the floor two nights ago. I erased that with a wet rag, a former washcloth, wrapped around a wooden block.

  Robes, special candles, lists of spells, new pentagram... I worked quietly so as not to wake anyone. Mrs. Miller was sympathetic; her sense of humor was such that they'd have burned her three centuries ago.

  But the other residents needed their sleep. I started the incantations exactly at midnight.

  At fourteen past I got the shock of my young life. Suddenly there was a demon spread-eagled in the pentagram, with his hands and feet and head occupying all five points of the figure.

  I turned and ran.

  He roared, "Come back here!"

  I stopped halfway up the stairs, turned, and came back down. To leave a demon trapped in the basement of Mrs. Millet's apartment house was out of the question. With that amplified basso profundo voice he'd have wakened the whole block.

  He watched me come slowly down the stairs. Except for the horns he might have been a nude middle-aged man, shaved and painted bright red. But if he'd been human you wouldn't have wanted to know him. He seemed built for all of the Seven Deadly Sins. Avaricious green eyes. Enormous gluttonous tank of a belly. Muscles soft and drooping from sloth. A dissipated face that seemed permanently angry.

  Lecherous— never mind. His horns were small and sharp and polished to a glow.

  He waited until I reached bottom. "That's better. Now what kept you? It's been a good century since anyone called up a demon."

  "They've forgotten how," I told him. "Nowadays everyone thinks you're supposed to draw the pentagram on the floor."

  "The floor? They expect me to show up lying on my back?" His voice was thick with rage.

  I shivered. My bright idea. A pentagram was a prison for demons. Why? I'd thought of the five points of a pentagram, and the five points of a spread-eagled man...

  "Well?"

  "I know, it doesn't make sense. Would you go away now, please?"

  He stared. "You have forgotten a lot." Slowly and patiently, as to a child, he began to explain the implications of calling up a demon.

  I listened. Fear and sick hopelessness rose in me until the concrete walls seemed to blur. "I am in peril of my immortal soul—" This was something I'd never considered, except academically. Now it was worse than that. To hear the demon talk, my soul was already lost. It had been lost since the moment I used the correct spell. I tried to hide my fear, but that was hopeless. With those enormous nostrils he must have smelled it.

  He finished, and grinned as if inviting comment.

  I said, "Let's go over that again. I only get one wish."

  "Right."

  "If you don't like the wish I've got to choose another."

  "Right."

  "That doesn't seem fair."

  "Who said anything about fair?"

  "—Or traditional. Why hasn't anyone heard about this deal before?"

  "This is the standard deal, Jack. We used to give a better deal to some of the marks. The others didn't have time to talk because of that twenty-four-hour clause. If they wrote anything down we'd alter it. We have power over written things which mention us."

  "
That twenty-four-hour clause. If I haven't taken my wish in twenty-four hours, you'll leave the pentagram and take my soul anyway?"

  "That's right."

  "And if I do use the wish, you have to remain in the pentagram until my wish is granted, or until twenty-four hours are up. Then you teleport to Hell to report same, and come back for me immediately, reappearing in the pentagram."

  "I guess teleport's a good word. I vanish and reappear. Are you getting bright ideas?"

  "Like what?"

  "I'll make it easy on you. If you erase the pentagram I can appear anywhere. You can erase it and draw it again somewhere else, and I've got to appear inside it."

  A question hovered on my tongue. I swallowed it and asked another. "Suppose I wished for immortality?"

  "You'd be immortal for what's left of your twenty-four hours." He grinned. His teeth were coal black.

  "Better hurry. Time's running out."

  Time, I thought. Okay. All or nothing.

  "Here's my wish. Stop time from passing outside of me."

  "Easy enough. Look at your watch."

  I didn't want to take my eyes off him, but he just exposed his black teeth again. So I looked down.

  There was a red mark opposite the minute hand on my Rolex. And a black mark opposite the hour hand.

  The demon was still there when I looked up, still spread-eagled against the wall, still wearing that knowing grin. I moved around him, waved my hand before his face. When I touched him he felt like marble.

  Time had stopped, but the demon had remained. I felt sick with relief.

  The second hand on my watch was still moving. I had expected nothing less. Time had stopped for me for twenty-four hours of interior time. If it had been exterior time I'd have been safe— but of course that was too easy.

  I'd thought my way into this mess. I should be able to think my way out, shouldn't I?

  I erased the pentagram from the wall, scrubbing until every trace was gone. Then I drew a new one, using a flexible metal tape to get the lines as straight as possible, making it as large as I could get it in the confined space. It was still only two feet across.

  I left the basement.

  I knew where the nearby churches were, though I hadn't been to one in too long. My car wouldn't start.

  Neither would my roommate's motorcycle. The spell which enclosed me wasn't big enough. I walked to a Mormon temple three blocks away.

  The night was cool and balmy and lovely. City lights blanked out the stars, but there was a fine werewolf's moon hanging way above the empty lot where the Mormon temple should have been.

  I walked another eight blocks to find the B'nai B'rith Synagogue and the All Saints Church. All I got out of it was exercise. I found empty lots. For me, places of worship didn't exist.

  I prayed. I didn't believe it would work, but I prayed. If I wasn't heard was it because I didn't expect to be? But I was beginning to feel that the demon had thought of everything, long ago.

  What I did with the rest of that long night isn't important. Even to me it didn't feel important. Twenty-four hours, against eternity? I wrote a fast outline on my experiment in demon raising, then tore it up. The demons would only change it. Which meant that my thesis was shot to hell, whatever happened. I carried a real but rigid Scotch terrier into Professor Pauling's room and posed it on his desk. The old tyrant would get a surprise when he looked up. But I spent most of the night outside, walking, looking my last on the world. Once I reached into a police car and flipped the siren on, thought about it, and flipped it off again. Twice I dropped into restaurants and ate someone's order, leaving money which I wouldn't need, paperclipped to notes which read "The Shadow Strikes."

  The hour hand had circled my watch twice. I got back to the basement at twelve ten, with the long hand five minutes from brenschluss.

  That hand seemed painted to the face as I waited. My candles had left a peculiar odor in the basement, an odor overlaid with the stink of demon and the stink of fear. The demon hovered against the wall, no longer in a pentagram, trapped halfway through a wide-armed leap of triumph.

  I had an awful thought.

  Why had I believed the demon? Everything hed said might have been a lie. And probably was! I'd been tricked into accepting a gift from the devil! I stood up, thinking furiously— I'd already accepted the gift, but—

  The demon glanced to the side and grinned wider when he saw the chalk lines gone. He nodded at me, said, "Back in a flash," and was gone.

  I waited. I'd thought my way into this, but—

  A cheery bass voice spoke out of the air. "I knew you'd move the pentagram. Made it too small for me, didn't you? Tsk, tsk. Couldn't you guess I'd change my size?"

  There were rustlings, and a shimmering in the air. "I know it's here somewhere. I can feel it. Ah."

  He was, back, spread-eagled before me, two feet tall and three feet off the ground. His black know-it-all grin disappeared when he saw the pentagram wasn't there. Then— he was seven inches tall, eyes bugged in surprise, yelling in a contralto voice. "Whereinhell's the—" he squealed.

  He was two inches of bright red toy soldier.

  I'd won. Tomorrow I'd get to a church. If necessary, have somebody lead me in blindfold.

  He was a small red star.

  A buzzing red housefly.

  Gone.

  It's odd, how quickly you can get religion. Let one demon tell you you're damned... Could I really get into a church? Somehow I was sure I'd make it. I'd gotten this far; I'd outthought a demon.

  Eventually he'd look down and see the pentagram. Part of it was in plain sight. But it wouldn't help him.

  Spread-eagled like that, he couldn't reach it to wipe it away. He was trapped for eternity, shrinking toward the infinitesimal but doomed never to reach it, forever trying to appear inside a pentagram which was forever too small. I had drawn it on his bulging belly.

  The Deadlier Weapon

  He was standing just off Overland Drive, at the mouth of the on-ramp to the Santa Monica Freeway, eastbound. He waited with an air of ready confidence, and his thumbsmanship seemed practiced. His placement was perfect. A few yards further up the ramp, and no car could have stopped for him without being hit by the car behind. A few yards closer, and no driver would have known which route he wanted: the freeway, or the street going past the ramp.

  That was what caught my attention: the perfect placement, not too far, not too near. A traveler, for sure.

  I dropped my arm out the window to signal, hit the brakes, and pulled up an easy foot and a half beyond him.

  He was running before the car stopped. I pulled the lock knob and he threw the door open and was in, grinning, wasting no time. Good again. Nobody waits for a lazy hitchhiker; you trot or you don't ride. As soon as he was in I swung between two cars and headed up the ramp, accelerating.

  The traffic wasn't bad, not at three in the afternoon. Still, when you enter a freeway you concentrate on the traffic. Everything else gets ignored. I hardly knew what my passenger looked like; I'd seen only a poised silhouette with its thumb raised against the afternoon sky. But I gave him points again. He didn't speak until I was firmly settled in the middle-right lane and could afford to relax a little.

  I don't pick up riders often. When I do, I follow the whim of the moment. The ones who look chatty when I want peace and quiet, and the ones who look glum or taciturn when I'm after conversation— these get left standing. I like the unusual ones, the ones who seem to have a kind of salesmanship.

  Six months ago there'd been a college girl on Wilshire, carrying a bright red Christmas package almost as big as she was. She was homesick for Kansas. She'd told me what freezing rains are like, when water falls from the sky at night and freezes where it hits, so that in the morning all the trees and bushes are tinkling crystal, crackling in the wind. That would be something to see. But I expect I never will.

  Once there'd been a Negro on the freeway, carrying a gas can and smoking. As soon as he was in the car he'd
tipped the ash off his cigarette into the gas can. "Okay," I'd said, to prove I was alert. "So you didn't run out of gas. Where you heading?"

  "San Francisco," he'd told me. He'd started in Louisiana.

  There was the guy who did run out of gas, stranded on the left of the freeway with his wife and four kids.

  "Oh, the kids are no trouble on a trip," he'd told me. "We know how to keep them interested. We play a game. The first kid to spot an Edsel gets a double ice-cream cone, immediately."

  "Must make for frequent stops."

  "How long since you last saw an Edsel?"

  Right. I'd never seen two in the same day.

  The hitchhiker said, "Thanks for the lift."

  Traffic was fast and easy, the cars evenly spaced. I risked a look to the side.

  He was young, somewhere in his mid-twenties. His nose was a touch too large and a touch too pointed, and his brown hair a touch too long. Gray plastic sunglasses, dark blue windbreaker over a white shirt, serviceable gray slacks. Shoes which looked rugged enough but which were not hiking shoes. He'd shaved recently. Despite the long hair, he looked too neat to have been on the road long. Perhaps he was just starting a trip.

  "That's okay," I said. "You've used that thumb a lot, haven't you?"

  "That's true." I heard a click then, but it didn't register until later. His voice was college educated, with a little too much tenor.

  "How far you going this time?"

  "Just far enough."

  An odd answer. I glanced over at him and found the point of a knife just touching my larynx. "Watch the road," he said.

  I turned back. Now I remembered the click. The knife was a switchblade with a six-inch blade, not very clean, but sharp, with the marks of a whetstone along the edge. I'd caught all of that in one glance.

  "Neither of us is going to get hurt," the man with the knife said soothingly. He held the point at the side of my neck, just touching. "When you get the chance, you're going to pull over to the side, and I'm going to take your watch and the money in your wallet. Nothing else. I'll leave the wallet. I don't want your credit cards."

  The lane to my left was clear. "Imagine how relieved I must be to hear it," I said, and eased over.