Nancy Kress - Feigenbaum Number.pdf - Nancy Kress - margozap

FEIGENBAUM NUMBER (v1.1)

NANCY KRESS

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

because 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."

"I'm not -- "

"You are. Just don't let the double vision stop you from trying anything you want to. I

don't." She glared belligerently. Behind her, the other Mia radiated determination tempered by

acceptance.

"Mia, I do try to do the things I want. Math. My dissertation. Teaching." Not that I wanted

to be doing that.

"Good," she snapped, and looked over my shoulder. "Double vision doesn't have to defeat

us if we don't let it."

I said, "Have you ever found any others like us?" What did my ideal self look like? What

strengths could she see on his face?

"No, you're the only one. I thought I was alone."

"Me, too. But if there's two of us, there could be more. Maybe we should -- "

"Damn it, Jack, at least look at me when you're talking to me!"

Slowly my gaze moved back to her face. Her physical face. Her mouth gaped in anger; her

eyes had narrowed to ugly slits. My gaze moved back.

"Stop it, you asshole! Stop it!"

"Don't call me names, Mia."

"Don't tell me what to do! You have no right to tell me what to do! You're no different from

-- "

I said, "Why would I look at you if I could look at her?"

She stood up so abruptly that her chair fell over. Then she was gone.

I put my hands over my eyes, blotting out all sight. Of everything.

"What was this system before it started to diverge?" Fran said.

She held in her hands a phase space diagram I hadn't seen before. Her eyes sparkled. Even

so, there was something heavy around her mouth, something that wasn't in the Fran behind

her, and for a minute I was so startled I couldn't concentrate on the printouts. The ideal Fran,

too, looked different from the day before. Her skin glowed from within, almost too strongly, as

if a flashlight burned behind its pale fine-grained surface.

"That was rhetorical, Jack. I know what the system was before it diverged-the equations

are there on the desk. But this one looks different. See ... here ... "

She pointed and explained. Nonlinear systems with points that start out very close

together tend to diverge from each other, into chaos. But there was something odd about

these particular diagrams: they were chaotic, as always around a strange attractor, but in

non-patterns I hadn't seen before. I couldn't quite grasp the difference. Almost, but not quite.

I said, "Where are those original equations?"

"There. On that paper -- no, that one."

"You're using Arnfelser's Constant? Why?"

"Look at the equations again."

I did, and this time I recognized them, even though subatomic particle physics is not my

field. James Arnfelser had won the Nobel two years ago for his work on the behavior of

electron/positron pairs during the first 30 seconds of the universe's life. Fran was mucking

around with the chaos of creation.

I looked at the phase space diagrams again.

She said, "You can almost see it, can't you? Almost ... see ... "

"Fran!"

She had her hand to her midriff. "It's nothing, Jack. Just indigestion on top of muscle

tension on top of sleeplessness. I was up all night on those equations."

"Sit down."

"No, I'm fine. Really I am." She smiled at me, and the skin around her eyes, a mass of fine

wrinkles, stretched tauter. And behind her, the other Fran didn't smile. At all. She looked at

me, and I had the insane idea that somehow, for the first time, she saw me.

It was the first time I'd ever seen them diverge.

Nancy Kress - Feigenbaum Number.pdf

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: