where the overbars denote ‘average’ or ‘expected value.’ If N is large, we expect that N̄c will be close to Nc and N̄F will be close to NF. Given the above formulas for Nc and NF, we see that π may be estimated from the formula:
Note that if we take the ratio of Nc/NF we find:
This does not directly provide an estimate of π…
[Wentworth’s analysis goes on to ask, ‘Suppose we use 2N/NC to estimate π. How good an estimate can we expect this to provide? Or, equivalently, how close can we expect Nc to be to (2/π)N? The answer is worked out; and, with the aid of the formula for the mean square deviation from the mean, the answer already expressed in the letter is arrived at. Wentworth’s letter itself goes on:]
I am a great believer in the infallibility of mathematics—but mathematicians are fallible, so I performed an experiment to check my conclusions. I tossed a stick onto a page with ruled lines one stick-length apart 125 times. The stick landed across a line 84 times and between lines 41 times. Thus 2N/Nc is approximately equal to 2.98. This, as an estimate of π, is off by about minus 5%. For 125 tosses, my formula predicts an accuracy on the order of plus-or-minus 6.8%. Thus the experimental results are consistent with the theoretical ones.
End of nitpicking, I do enjoy your work, and I wish you the best of luck with future endeavors.
Sincerely yours,
Robert Wentworth
P.S.—Since writing this letter, I’ve stumbled across a description of the π-determining experiment in a probability text (Papoulis: Probability, Random Variables, and Stochastic Processes, p. 185); the answer for the probability of crossing a ruled line agrees with the result I calculated. Papoulis calls the experiment ‘Buffon’s Needle.’
Also, a friend who is usually right tells me that, my argument about its improbability not withstanding, some historical figure (whose name he didn’t remember) really did use the stick-tossing experiment to determine π to a high degree of accuracy. Very strange. Perhaps you already know all about this…
from:
Samuel R. Delany,
November 7, 1984
Dear Robert Wentworth,
Thanks so much for your letter of 21 September on the mathematics of Venn’s solution to Belham’s problem. It was extremely kind of you to forward me your analysis.
‘Buffon’s Needle,’ hey? I assume that’s the same Buffon who once said: ‘Le style, c’est l’homme même.’—His style, that’s the man himself. Well, Professor Kermit’s protestations to Charles Hoequist aside, I don’t want to fall into the style of those who go on perpetuating misinformation once they have the facts.
A science writer and friend named Monte Davis (co-author of Catastrophe Theory, Davis & Woodcock, Avon Books: New York, 1980) leveled some criticism at the other example of Venn’s ingenuity from Neveryóna’s Chapter 8, i.e., Venn’s machine model for demonstrating fluid-containment replication:
Though in principle (Monte explained one pleasant afternoon when I was signing books down at New York’s Science Fiction Shop) Venn’s demonstration is correct, for the real ‘demonstration machine’ to operate as I described it, water just won’t do for the communicating fluid between the upper and lower basins. Nor will ordinary sand—even very fine sand—suffice as the imprint material in the lower tub. Rather, the upper container would require flooding with some ideally non-turbulent liquid, possibly a very light but very dense polymer oil (if there were such a thing). With most real liquids, however, the entrance into the pipe, the trip down, and the exit from the spigot at the bottom would add so much ‘noise’ to the ‘message’ that, in practical terms, little or none of that ‘message’ would enter the bottom basin intact. Similarly, the imprint medium in the bottom tub would have to be almost weightless. Nor could it mix with the incoming liquid. Rather, it would have to be immediately and ideally displaced. It seems I was led astray by some impressive photographs in Rene Thorn’s Structural Stability and Morphogenesis (i.e., illustration ten following page 167) that were, indeed, photographs of prepared models—not of real experiments. The captions to the pictures, however (printed several pages later), left it very unclear; and to learn that they were, indeed, models, rather than actual experiments, you had to negotiate a particularly daunting stretch of text. And I, I’m afraid, blew it.
In the forth-coming Grafton edition I shall try to make whatever minuscule repairs I can.
But to claim Nevèrÿon is fantasy and try to excuse my blunders on such grounds is a kind of fudging I don’t think I should even flirt with. Thank you, rather, for taking the time to set me straight; and, along with Davis’s conversational comments about the fluid-replication model, I want to lay out these facts before my readers. Ideally, I should like to print some of this correspondence as an appendix, if you agree to it. At any rate, let me acknowledge, and apologize for, my errors. Thanks also for your kind words on my tale.
All best wishes,
Samuel R. Delany
Return to Nevèrÿon
For
John P. Mueller,
with thanks to
Susan Palwick,
Robert S. Bravard, &
R. Keith Courtney.
Publisher’s Note
A NOTE: The book-bound order of these stories reverses the chronology of many of their internal events, so that someone more concerned with plot than structure might be more comfortable reading the three tales here from last to first. Also there’s an appendix that might do as an introduction for those only intermittently acquainted with some of the series’ other stories. Then again one can simply open the book and start at the beginning …
But it’s my hope that Nevèrÿon can be explored from many directions.
—Samuel R. Delany, New York, 1987
Contents
The Game of Time and Pain
1
2
3
4
5
6
7
8
9
10
The Tale of Rumor and Desire
The Tale of Gorgik
1
2
3
Appendix: Closures and Openings
A Biography of Samuel R. Delany
The Game of Time and Pain
It is at this point, Lacan writes, that the analyst will do his work not by responding sympathetically, nor by failing to respond (the apathetic listener). He has to replace the mode of the voice and the ear with the image, becoming, as he puts it, a ‘pure unruffled mirror’. Coupled with his description of the ego as ‘opaque to reflection’, the use of the term ‘mirror’ cannot be overlooked. It is in the mirror that the ego is first born as an idea, and it is in the echo of the symbolic voice that it gains its identity: the analytic mirror must displace—‘subduce’—these ‘archaic imagos’.
JULIET FLOWER McCANNELL, Figuring Lacan
1
‘NO ONE IS IN the castle.’ Barefoot, the old woman squatted before her loom. (Someone had told the pig girl the pattern the woman wove was magic—though she didn’t remember who or when. Perhaps it was just a tale that went from yard to yard in the afternoon.) ‘Never has been. Never will be.’
‘I saw him,’ repeated the tall woman. With one hand she propped a full water jar on her shoulder. (Swinging by her knee, the jar hooked to her forefinger had to be empty.) ‘He was a big man. He rode a wonderfully high-stepping horse with trappings of beaten brass and braided leather. His armor was more elaborate than that of any soldier you’ve ever seen pass through this part of Nevèrÿon. He was no ordinary Imperial officer. His cloak was embroidered like the richest of lords’. He rode into the overgrown courtyard, dismounted, and went inside. I watched him from the trees.’ The jar’s shadow moved from the grass to the crumbled earth around the loom’s foot to the half-finished fabric and back. ‘You can be sure, he’s a great personage, who’ll stay up there overnight so that he can join Lord Krodar’s funeral cortege that passes here tomorrow. Why h
e’s not with a whole retinue, I don’t know. Someone who rides such a horse and dresses in such armor and stops at the local castle shouldn’t be traveling alone. He should have servants and guards and fine-fringed wagons—don’t you think? That’s what I’d expect—at least of someone like him, stopping there for the night.’
‘There’s no one in the castle.’ The old woman pulled up swinging shuttles, pushed one down among the threads, hooked another through with her forefinger, completing one line to start in on the next. ‘You played among those walls and corridors when you were a girl. It was empty then. I played there when I was a child, too. No one was there. Those rooms, those halls, those stairs, those towers …’ She wrapped two threads around each other and thrust one through the warp, then tamped it with the tamping stick. ‘And you say there’s someone living in the castle … Ridiculous!’
‘Not living there, just stopping there. For the night, no more. Why do I stand here arguing with you, old lady!’ (The pig girl saw the shuttles’ shadows dance off on the grass far faster than the swinging jar’s.) ‘There’s a man in the castle this evening—a strong, great, powerful man, who rides a fine horse and sports rich armor and wears a wonderfully worked cloak. Lord Krodar’s funeral procession will pass along the north-south highway before midday tomorrow. You just watch. The man will stay in the castle tonight, and in the morning he’ll ride down to join the procession and pay his respects to that greatest minister of Nevèrÿon. He’ll travel with them all the way to the High Court of Eagles at Kolhari. And when he rides down to meet them, he’ll pass along here. If you can look up from your work for a moment, you’ll see him!’
‘I played in the castle,’ the pig girl said. She was eleven, very serious, somewhat gawky, and held a cat in her dirty arms. ‘Castles are full of wonderful women in beautiful clothes who dance and dance with wonderful men. You give orders for impossible things to be done; and, in the castle, people run right off to do them. That’s what everybody plays in the castle. I bet that’s what he’ll play. When you play in the castle like that, it doesn’t feel empty.’ She looked at the old woman, then at the tall one. She wanted them to approve of her, but they seemed unaware she was there.
‘The castle’s empty.’ The old woman shifted her squat. ‘There’s never been anyone in it. There wasn’t anyone before. And there isn’t now.’
‘This is silly!’ The tall woman raised her chin beside the jar on her shoulder. I only came to tell you a bit of gossip—’ the one by her knee swung faster—‘and here you sit, arguing with me about something you didn’t see and I did. I mean it’s just too—’
‘The castle’s not empty!’ the pig girl blurted. ‘It’s full of lords and ladies and wet, dark dungeons where they lock their enemies up in chains and beat them and torture them and kill them horribly and they come back as monsters who run hooting through the upper halls, so that the children who followed you in all turn around and chase each other out, shrieking and scared to death!’ She giggled. ‘Look down over the banister, watch them run outside, and you can laugh yourself sick—then sneak around and hoot some more! The castle’s full of beautiful queens and handsome warriors and monsters and sorcerers—’ Here she must have squeezed the cat, for she was a strong, friendly, clumsy girl. It meowed hideously, twisting in her arms, dropped to the grass, ran from the yard and up the slope, stopped to stare back, then fled.
‘Of course it’s empty! That’s not what I mean.’ The tall woman frowned at the pig girl. ‘Really, you’re as bad as she is. I only said there’s a man there this evening. And I’m sure he’ll stay till the funeral procession passes the village tomorrow.’
‘And I say there’s no one.’ The old woman pushed her shuttles through the strings. ‘You know it as well as I do. I think it’s always been empty. Who would ever live in those drafty halls? Who would ever stay in those cramped little rooms? Think of the cleaning. Think of the furniture. Think of the work!’
‘And I have work to do!’ The tall woman shook her head. ‘I certainly haven’t time to stand here arguing with someone who can’t follow two words in a row (how do you keep your weaving straight!) and a dirty creature—’ this last was to the pig girl—‘who dreams of queens, when she has work to do too!’ But there was a smile in with it.
The old woman, however, looked up crossly. ‘I’m doing my work!’ she declared. Strings quivered. Shuttles swung. ‘You’re the ones standing about, with your silly lies and your chatter!’
The tall woman shook her head again and, with her full and her empty pitchers, started across the yard.
The pig girl wondered if she should go after the cat, who, for all its meowing and occasional scratches, was better company than grownups. But she lingered by the loom for minutes, watching the pattern, with its greens, its beiges, its blues, extend itself, fixed and stable, line after line, behind quivering strings, aged fingers, shaking shuttles …
2
HIS BREATH LOCKED ON what burned in his throat: the air he dragged in through the heat, past whatever scalding constriction, woke him, rasping, choking, roaring. He opened his eyes on blackness, while a clutch in his stomach muscles jerked him to sit—which hurt! He thrust a hand down, grasped wet fur. Astonishingly warm, the air slid so slowly into his loud lungs. Water dribbled his cheek, his back, his forearm.
It was incredibly hot in the dark. At his breath’s painful height, he tried to push the air out; it leaked loudly from his gaping mouth, only a little faster than it had come in; only a little quieter.
Seconds later (it seemed minutes), he began to drag in the next chestful, dreading it even as he felt the constriction loosen. In his sleep, he’d urped some little stomach juices that, rolling into the wrong pipe, had stung his throat to spasm.
He tasted the acids at the back of his tongue, felt them burning deep down.
What ran on him was sweat.
And the small stone room in which he’d chosen to sleep (there’d been a bed, for one thing) had grown hugely hot.
He moved one leg over the fur throw he’d spread on the boards: the fur was drenched. Momentarily he wondered whether, in his infernal sleep, he’d spilled his urine. But no. It was only perspiration. As he stood up, bare feet on stone, it trickled his flank, his buttock. He rasped out one more breath, got in another, loud as a dying man’s gargle: the air came a little more easily …
He took a lurching step in darkness toward where he remembered the window. Pushing out, he felt rock. He moved over, pushed again, felt rock again; moved and pushed once more; wood swung—
The sliver of moonlight at the plank’s edge became a slab of silver: the shutter banged back.
He blinked.
(When he’d gone to sleep, it had been open, the moon down. Some breeze at moonrise must have blown it to.)
The air—from what was probably the warmest summer night—hit like springwater. It made him cough. For moments, he thought he would choke again. But in another minute his breath, though still labored, made only the normal roar between his lips, the usual whisper in his nasal cave.
Leaning naked on beveled rock, he looked down.
From its greenery (olive under the moon) a tree thrust out a dead branch. Below it lay a pool, rimmed with bricks whose pattern had been obscured here and warped there by grass tufts and roots. Above scummed water, a single owl (or bat) darted down and up and down, so that ripples rilled among the leaves and algae. Sweat on his lashes tickled into his eyes: he blinked. And twigs, ripples, and the lines between bricks seemed a tangled loom, with the mad shuttle of a bat (or owl) swooping through.
He turned to the sweltering room. Either side of his shadow, moonlight dusted the stone. Heat again was against his face. Air from the window chilled his back. How had the room gotten so hot?
In the corner lay his pack (from which he’d taken the fur), open, spilling the funeral gifts. His sword in its sheath lay on the floor. There was his helmet, his gauntlets, his grieves.
On the rumpled fur was a black blotch wher
e his sweat, neck to knee, had soaked it.
Another drop trickled his calf.
Taking one more breath of stifling air, he crossed the chamber, stopping to feel the fur. To lie on that again would be like crawling into wet rags. Besides, though he was a vital man, he was no longer a young one: he was of an age when to interrupt a night’s sleep was to end it.
At the door, he lifted the locking plank and leaned it on the wall. The rock was hot—almost too hot to touch! As he pulled one and another doorplank free, again he wondered how the little tower room he’d picked to sleep in could, on a summer night, become such a furnace.
As the third came loose, a cross breeze started. He shivered, naked, leaning the board against the wall; the heat warmed his knuckles. Taking another long breath, he stepped into the hall.
Not cold, he tried to tell his body. Just a summer’s night in an abandoned ruin. He rubbed the heel of his hand down his temple: sweat came away oily on his palm. He ran his other hand over his head: his rough hair, thin on top, was usually braided in the club-like military manner at the side of his head. But it had come largely loose. His fingers, catching in it, pulled the rest free.
Starting down the steps, he put his fingers against the rock. Yes, the wall even here was warm, despite the stairwell’s cool.
He descended in darkness. Beneath his bare feet the steps were dusty and irregularly spaced. Under his hand the stones were gritty. Once he crossed a landing he vaguely remembered, before doubling around on more stairs. For the third, the fifth, the seventh time he wondered if he should return to the little room for a weapon—just a knife. Then he saw the flicker.
Something crackled.
He moved to the arch and looked around the wall.
Across the hall, in the long fireplace, flames lapped the logs. On the floor, ten feet from the hearth, a young man lay, stomach down, head on his bent arm. The hair was yellow. The face was hidden in sleep and shadow.