by Nancy Kress
“Wrong, Robert,” I said. “Stuff it up your tantric control.”
If he made any response behind me, I didn’t see or hear it.
On the way back through the shit-filled living room, I planned. I’d take Maia to a hotel; she wasn’t ready yet for my place. Rent a two-bedroom suite. See some shows: comedies and musicals. Good restaurants. The Picasso exhibit. Remind her of the world beyond Robert. And then, eventually . . .
No ghost in a machine could match living flesh. Maia’s flesh, creamy and smooth, naked . . . No. Not naked. Dressed in the lingerie she’d bought for my brother. Who was irretrievably dead.
As soon as I opened her bedroom door, I heard it. A soft murmuring, silence, murmuring. She was in the bathroom, the door ajar. I shoved through so fast the door sprang into the wall, ricocheted back, smacked me in the arm.
It was a small portable television, the cable connections disappearing into the wall. Robert’s face smiled tenderly at her, murmuring, murmuring. Maia, kneeling on the bath mat, looked up guiltily.
“Oh, Cal, there you are . . . we were wrong, dear. I’m sorry. So wrong . . . You see, he knew I would do it. Destroy the computer. He understands me so well, and to be understood like that by another person, to be actually seen . . . I’m sorry. You’d better go.”
“Maia! Don’t you see? He’s still controlling you!”
She stood. “No, you’re wrong. I chose to destroy the ghost, and I choose to go back to him. But not forever. Just a little while longer. It can’t be too long, don’t you see? Robert is dead. But for a little while longer . . . I’ll know when it’s time to go, won’t I, Robert?”
“You’ll know when it’s time to go, darling,” my brother’s image said. “Trust your own erotic instincts.”
Maia said to me, “I’ll call you, Cal.”
I choked out, “I won’t be there when you call, Maia! I won’t! Damn it, I’m not a thing you can just . . . just set aside until you’re good and ready, and done fucking a ghost!”
She said, “Get out.”
“You can’t just . . . damn it . . .”
“Get out, Cal.”
“Yes, Cal, leave,” Robert said, and smiled beyond her, over her shoulder. At me.
“Maia . . . Maia, I didn’t mean it . . . I didn’t . . . oh, God, listen, I will call you soon, I will, please let me, Maia . . .”
“Suit yourself,” she said coldly. “But now—get out.”
I went, cursing myself. I’d almost blown it. I’d almost let him goad me into losing. But Maia was kind under her sickness, and her kindness would let me back in. I could still win.
Outside the building, I suddenly felt weak, and leaned for a minute against the brick facade before hailing a taxi. But it was only a temporary dizziness. I would not let it be more than that. Robert was not going to beat me. Nothing he did would keep me away permanently, would end the battle for Maia . . . he wanted me gone.
Or—did he?
“Are you listening, Cal? I knew you’d destroy the initial hardware. I knew she’d help you. I planned it. I’m still in control.”
Was it possible my brother wanted me to keep on fighting for Maia? But, then, the way to escape his control would be to give up
The erotic power, the fundamental Dionysian energy, is only fully available to us through the fundamental acts: love and war. An opponent as much as an orgasm makes the energy flow . . .
But . . . what if he was actually fighting me so I would really give up, so that he could have Maia to himself even from beyond the grave? Then the way to escape his control would be to . . .
Or did he . . .?
The dizziness was stronger now. I put my head in my hands and leaned against the brick building in the warm spring sunshine. I could smell the dank newly opened earth, and around me in the close darkness rose the ghostly holographic images, smiling and tanned, looking at me, but saying nothing.
FEIGENBAUM NUMBER
“Behold! Human beings living in an underground den . . . Like ourselves, they see only their own shadows, or the shadows of one another, which the fire throws on the opposite walls of the cave.” —Plato, The Republic
I rose from the bed, leaving Diane sprawled across the rumpled sheets, smiling, lipstick smeared and large belly sweaty.
She said, “Wow.”
“Wow yourself,” I said and turned to the mirror. Behind me, the other woman rose ghostly from the bed and crossed, smiling, to the window.
Diane said, “Come back to bed, Jack.”
“Can’t. I have to go. Student appointment.”
“So what’s new?”
In the mirror I saw her eyes narrow, her mouth tighten. The other woman turned from the window, laughing, one slim graceful arm pushing back a tendril of chestnut hair.
Diane skinned her brown hair back from her face. “Is it too much to ask, Jack, honey, that just once after we make love you don’t go rushing off like there’s a three-alarm fire? Just once?’
I didn’t answer.
“I mean, how do you think that makes me feel? Slambam-thank-you, ma’am. We have an actual relationship here, we’ve been going out for three months, it doesn’t seem a lot to ask that after we make love you don’t just—”
I didn’t interrupt. I couldn’t. The dizziness was strong this time; soon the nausea would follow. Sex did that. The intensity. Diane ranted, jerking herself to a kneeling position on the bed, framed by lumpy maroon window curtains opened a crack to a neighbor’s peeling frame house and weedy garden. Across the room the other Diane stood framed by crimson silk draperies opened a crack to a mellowed-wood cottage riotous with climbing roses. She blew me a light-hearted kiss. Her eyes glowed with understanding.
The nausea came.
“—can’t seem to understand how it makes me feel to be treated like—”
I clutched the edge of the dresser, which was both a scratched pressed-board “reproduction” and a polished cherrywood lowboy. Two perfume bottles floated in front of me: yellow plastic spraybottle and clean-lined blown glass. I squeezed my eyes shut. The ghostly Diane disappeared in the act of sauntering, slim and assured, toward the bathroom.
“—don’t even really look at me, not when we make love or—”
Eyes shut, I groped for the bedroom door.
“Jack!”
I slammed the doors, both of them, and left the apartment before Diane could follow. With her sloppy anger, her overweight nakedness, her completely justified weeping.
Outside was better. I drove my Escort to campus. The other car, the perfectly engineered driving machine with the sleek and balanced lines, shimmered in and out around me, but the vertigo didn’t return. I’d never gotten very intense about cars, and over the years I’d learned to handle the double state of anything that wasn’t too intense. The rest I avoided. Mostly.
The Aaron Fielding Faculty Office Building jutted boxlike three stories from the asphalt parking lot, and it blended its three floors harmoniously with a low hillside whose wooded lines were repeated in horizontal stretches of brick and wood. The poster-cluttered lobby was full of hurried students trying to see harried advisers, and it was a marble atrium where scholars talked eagerly about the mind of man. I walked down the corridor toward my cubicle, one of a row allotted to teaching assistants and post-docs.
But Dr. Frances Schraeder’s door was open, and I couldn’t resist.
She sat at her terminal, working, and when I knocked on the doorjamb (scarred metal, ghostly graceful molding), she looked up and smiled. “Jack! Come look at this!”
I came in, with so much relief my eyes prickled. The material Fran’s long, age-spotted fingers were held poised over her keyboard, and the ideal Fran’s long, age-spotted fingers echoed them. The ideal Fran’s white hair was fuller, but no whiter, and both were cut in simple short caps. The material Fran wore glasses, but both Frans’ bright blue eyes, a little sunken, shone with the same alert tranquility.
She was the only person I’d ever seen who came
close to matching what she should have been.
“This is the latest batch of phase space diagrams,” Fran said. “The computer just finished them—I haven’t even, printed them, yet.”
I crouched beside her to peer at the terminal.
“Don’t look any more disorganized to me than the last bunch.”
“Nor to me, either, unfortunately. Same old, same old.” She laughed: in chaos theory, there is no same old, same old. The phase space diagrams were infinitely complex, never repeating, without control.
But not completely. The control was there, not readily visible, a key we just didn’t recognize with the mathematics we had. Yet.
An ideal no one had seen.
“I keep thinking that your young mind will pick up something I’ve missed,” Fran said. “I’ll make you a copy of these. Plus, Pyotr Solenski has published some new work in Berlin that I think you should take a look at. I downloaded it from the net and e-mailed you.”
I nodded, but didn’t answer. For the first time today, calm flowed through me, soothing me.
Calm.
Rightness.
Numbers.
Fran had done good, if undistinguished, work in pure mathematics all her life. For the last few years she—and I, as her graduate student—had worked in the precise and austere world of iterated function theory, where the result of a given equation is recycled as the starting value of the next repetition of the same equation. If you do that, the results are predictable: the sequences will converge on a given set of numbers. No matter what initial value you plug into the equation, with enough iterations you end up at the same figures, called attractors. Every equation can generate a set of attractors, which iterations converge on like homing pigeons flying back to their nests.
Until you raise the value plugged into the equation past a point called the Feigenbaum number. Then the sequences produced lose all regularity. You can no longer find any pattern. Attractors disappear. The behavior of even fairly simple equations becomes chaotic. The pigeons fly randomly, blind and lost.
Or do they?
Fran—like dozens of other pure mathematicians around the world—looked at all that chaos, and sorted through it, and thought she glimpsed an order to the pigeons’ flight. A chaotic order, a controlled randomness. We’d been looking at nonlinear differential equations, and at their attractors, which cause iterated values not to converge but to diverge. States which start out only infinitesimally separated go on to diverge more and more and more . . . and more, moving toward some hidden values called, aptly enough, strange attractors. Pigeons from the same nest are drawn, through seeming chaos, to points we can identify but not prove the existence of.
Fran and I had a tentative set of equations for those idealized points.
Only tentative. Something wasn’t right. We’d overlooked something, something neither of us could see. It was there—I knew it—but we couldn’t see it. When we did, we’d have proof that any physical system showing an ultra dependence on initial conditions must have a strange attractor buried somewhere in its structure. The implications would be profound—for chaos mathematics, for fluid mechanics, for weather control.
For me.
I loved looking for that equation. Sometimes I thought I could glimpse it, behind the work we were doing, almost visible to me. But not often. And the truth I hadn’t told Fran, couldn’t tell her, was that I didn’t need to find it, not in the way she did. She was driven by the finest kind of intellectual hunger, a true scientist.
I just wanted the peace and calm of looking. The same calm I’d found over the years in simple addition, in algebra, in calculus, in Boolean logic. In numbers, which were not double state but just themselves, no other set of integers or constants or fractals lying behind these ones, better and fuller and more fulfilled, Mathematics had its own arbitrary assumptions -but no shadows on the cave wall.
So I spent as long with Fran in front of the terminal as I could, and printed out the last batch of phase space diagrams and spent time with those, and went over our work yet again, and read Pyotr Solenski’s work, and then I could no longer put off returning to the material world.
As soon as I walked into Introduction to Set Theory, my nausea returned.
Mid October. Two more months of teaching this class, twice a week, 90 minutes a session, to keep my fellowship. I didn’t know if I could do it. But without the fellowship, I couldn’t work with Fran.
Thirty-two faces bobbed in front of me, with 32 shimmering ghostly behind them. Different. So different. Jim Mulcahy: a sullen slouching 18-year-old with acned face and resentful eyes, flunking out—and behind him, the quiet assured Jim, unhamstrung by whatever had caused that terrible resentfulness, whatever kept him from listening to me or studying the text. Jessica Harris: straight As, thin face pinched by anxiety, thrown into panic whenever she didn’t instantly comprehend some point—and behind her, the confident Jessica who could wait a minute, study the logic, take pleasure in her eventual mastery of it. Sixty-four faces, and 64 pieces of furniture in two rooms, and sometimes when I turned away to the two blackboards (my writing firm on the pristine surface, and quavery over dust-filled scratches), even turning away wasn’t enough to clear my head.
“The students complain you don’t look at them when you talk,” my department chair had said. “And you don’t make yourself available after class to deal with their problems.”
He’d shimmered behind himself, a wise leader and an overworked bureaucrat.
Nobody had any questions. Nobody stayed after class. Nobody in the first 32 students had any comments on infinite sets, and the second 32 I couldn’t hear, couldn’t reach.
I left the classroom with a raging headache, and almost tripped over a student in the hall.
Chairs lined the corridor walls (water-stained plaster; lively-textured stucco) for students to wait for faculty, or each other, or enlightenment. One chair blocked fully a third of my doorway, apparently shifted there by the girl who sat, head down, drawing in a notebook. My headache was the awful kind that clouds vision. I banged my knee into a corner of the chair (graffiti on varnish on cheap pine; clean hand-stained hardwood). My vision cleared but my knee throbbed painfully.
“Do you mind not blocking the doorway, Miss?”
“Sorry.” She didn’t look up, or stop drawing.
“Please move the damned chair.”
She hitched it sideways, never raising her eyes from the paper. The chair banged along the hall floor, clanging onto my throbbing brain. Beside her, the other girl shrugged humorously, in charming self-deprecation.
I forced myself. “Are you waiting for me? To see about the class?”
“No.” Still she didn’t look up, rude even for a student. I pushed past her, and my eyes fell on her drawing paper.
It was full of numbers: a table for binomial distribution of coin-tossing probabilities, with x as the probability of throwing n heads, divided by the probability of throwing an equal number of heads and tails. The columns were neatly labeled. She was filling in the numbers as rapidly as her pen could write, to seven decimal places. From memory, or mental calculation?
I blurted, “Most people don’t do that.”
“Is that an observation, an insult, or a compliment?”
All I could see of both girls were the bent tops of their heads: lank dirty blonde, feathery golden waves.
She said, “Because if it’s an observation, then consider that I said, ‘I already know that.’ ”
The vertigo started to take me.
“If it’s an insult, then I said, ‘I’m not most people.’ ”
I put out one hand to steady myself against the wall.
“And if it’s a compliment, I said, ‘Thanks.’ I guess.”
The hallway pulsed. Students surged toward me, 64 of them, except that I was only supposed to teach 32 and they weren’t the ones who really wanted to learn, they were warped and deformed versions of what they should have been and I couldn’t teach them becau
se I hated them too much. For not being what they could have been. For throwing off my inner balance, the delicate metaphysical ear that coordinates reality with ideal with acceptance. For careening past the Feigenbaum number, into versions of themselves where attraction was replaced by turbulent chaos . . . I fell heavily against the wall, gulping air.
“Hey!” The girl looked up. She had a scrawny, bony face with a too-wide mouth, and a delicate, fine-boned face with rosy generous lips. But mostly I saw her eyes. They looked at me with conventional concern, and then at the wall behind me, and then back at me, and shock ran over me like gasoline fire. The girl reached out an arm to steady me, but her gaze had already gone again past me, as mine did everywhere but in the mirror, inexorably drawn to what I had never seen: the other Jack shimmering behind me, the ideal self I was not.
“It affects you differently than me,” Mia said over coffee in the student cafeteria. I’d agreed to go there only because it was nearly empty. “I don’t get nauseated or light-headed. I just get mad. It’s such a fucking waste.”
She sat across from me, and the other Mia sat behind her, green eyes hopeful in her lovely face. Hopeful that we could share this, that she was no longer alone, that I might be able to end her loneliness. The physical Mia didn’t look hopeful. She looked just as furious as she said she was.
“Nine times out of ten, Jack, people could become their ideal selves, or at least a whole lot fucking closer, if they just tried. They’re just too lazy or screwed up to put some backbone into it.”
I looked away from her. “For me,” I said hesitantly, “I guess it’s mostly the unfairness of it that’s such a burden. Seeing the ideal has interfered with every single thing I’ve ever wanted to do with my life.” Except mathematics.
She squinted at me. “Unfairness? So what? Just don’t give in to it.”
“I think it’s a little more complicated than—”
“It’s not. In fact, it’s real simple. Just do what you want, anyway. And don’t whine.”