It felt strangely good, warm, to be lecturing again: ‘Take a particular case. You know the two-body problem in astronomy? Given two bodies of known mass, velocity, and distance from each other, and the laws of motion and gravitation, to find their position at any past or future time. It was solved long ago. But the three-body problem is quite another story. Right away, with three sets of interaction, it becomes so complex that as far as I know there’s never been any general solution, and only a few special ones. As for the n-body problem—

  ‘Now in the biological sciences, including psychology and sociology, you can’t simplify. You have to consider the whole. A living organism is an incredibly complex set of interactions, beginning, probably, on the subatomic level and going on up to the entire universe, from which the organism cannot be separated either. You can’t apply our single-track analytic methods to such a case. The result is, of course, that aside from a few statistical regularities, those sciences are almost purely empirical, sociology hardly deserving the name. If, to use an old illustration, I want to tackle the three-body problem, I can and will start with the special case where one of them has zero mass. But suppose I were making an analysis of the influence of Pan-Asiatic foreign policy on American domestic affairs before the war. I could certainly not ignore the converse case, or the existence of other countries. It’s a fluid web of interactions. I’d have to consider them all simultaneously – which no existing symbology can do. Any results I got would be qualitative, non-mathematical, non-predictive – you see?’

  ‘I think I do,’ nodded Boyd. ‘Of course, people can think of two or more things at once.’

  ‘That’s different,’ said Karen. ‘That’s a case of divided attention, each branch of the mind following its single track. It’s normal enough, though carried to extremes it becomes schizophrenia.’

  ‘You get what I’m driving at,’ went on Wayne. ‘Our subhuman and human ancestors didn’t need to see the world as a whole. They were only concerned with immediate surroundings and events. So we never evolved the ability to think of an entire entity. On a childish level, how many bricks can you visualize in your imagination, side by side and not quite touching? I believe the ordinary human limit is half a dozen. Alaric says he can see any number, and I believe him. He’s a mutant.’

  ‘Some different brain structure,’ said Karen. ‘The X-rays don’t show it, so it’s probably a very subtle matter of cells or … what-you-call-’ems … colloids, or of organization.’

  ‘Al didn’t have to think, in our ordinary sense of the world, to design that weapon,’ said Wayne. ‘His extensive knowledge of scientific principles and data coordinated in his mind to show him. Well, if my guess is right, then the cells of human bodies are resonant to a particular wave form. And at once he knew all the factors he’d need to generate that wave. It wasn’t reasoned, as we reason, though it was thought – to him, thought on a very elementary, almost primitive level. Yet he didn’t think of merely warning people.’

  ‘I get it,’ said Boyd. ‘Humans think in chains. He thinks in networks.’

  ‘Yes, that’s about the size of it.’

  ‘Do you think … we … can ever do it?’

  ‘Hmmm—’ Wayne rubbed his chin. ‘I don’t know. Since intelligence seems to depend on upbringing among normal humans, whereas genius and feeble-mindedness seem more nearly independent of training and are hereditary, one might argue that they are both mutations. Some people seem to have had a degree of the network-thinking ability – like Nikola Tesla, I read a biography of him once. The fact that Al is the son of a mathematician, who does deal with complexities, is suggestive. After all, no mutation ever created a totally new characteristic. It would have to create a whole new set of genes for that. A mutation is a greater or lesser modification of an existing trait.

  ‘The point I’m making is that humans naturally think in straight lines, but some sort of network, total-considering logic has been developed. The semanticists have their nonelementalistic principle. In math, we only add in special cases, the rest of the time we integrate; and we have our generalized calculi of vectors and tensors. But – it doesn’t come naturally. It’s been worked out slowly and painfully, through many centuries.

  ‘To Al, it’s the natural way to think; but since like most mutations, it involves a loss elsewhere, the simple straightforward logic of humans is unnatural to him. And he’s just a kid, and probably not a genius anyway – merely an ordinary network thinker – so he hasn’t seen the principles of that logic, any more than a human his age sees the principle of nonelementalism. I’d say, off hand, that each type of mind can learn the other type of thought, but not comprehend or apply it on its higher levels.’

  ‘There’s another thing,’ put in Karen. Her eyes held a light which hadn’t been there for a long time. ‘Rod just said it. With the proper training, Al should be able to learn logic, at least enough to understand and communicate. His kind of thought is not adapted to the simple problems of everyday life, but he can be taught to handle those, as we teach human children unnatural things like algebra and physics. Maybe … maybe, then, he can teach us something.’

  Boyd nodded again. ‘It’s certainly worth the attempt,’ he said. ‘We have psychiatrists and other specialists at the capital. If we’d known before that you were a mathematician, Dr. Wayne, we’d have asked you to join the new science center. Consider yourself invited as of now. And if we and Alaric can come to understand each other – why, you may even get your biological and sociological math. Then we may be able to build the first sane civilization in history.’

  ‘I hope so,’ murmured Wayne. ‘I certainly hope so. And thanks Boyd.’

  He smiled tiredly. ‘By the way, Karen, you have your superman there. The highest genius, in his way, that the world ever saw. If he hadn’t had some kind of protection to grow up in and, now. to teach him the elements of thought, he’d never have lived. I’m afraid this particular kind of superman isn’t much of a survivor type.’

  ‘No,’ whispered Karen. ‘Nor human.’ Her hand ruffled the boy’s hair, and he smiled shyly up at her. ‘But he’s our son.’

  THE CHILDREN OF FORTUNE

  Now are we come

  to the house of the king.

  Bad luck has made us

  thralls at the millstone.

  Gravel gnaws our feet,

  we freeze above,

  but have peace to work –

  and woe with Frodhi.

  Now hands shall hold

  the hardened spears

  and the reddened weapons.

  Waken, Frodhi!

  Waken, Frodhi! –

  if thou wilt listen

  to our songs of war

  and stories of old.

  Fire see I burning

  on eastern beaches,

  signs which watch and

  warn of battle.

  A host is coming,

  hither it hastens

  to burn the houses,

  the home of Frodhi.

  Thou shalt be thrust

  from Leidhra’s throne,

  from ruddy rings

  and the quern of riches.

  Grip harder, maiden,

  about the mill’s handle,

  for now we are grinding

  blood on the ground.

  – The Song of Grotte (Anon., ca. tenth century A.D.

  I

  THE arrow came from a screen of brush, so fast that Collie was not aware of it until it had gone by. Woodsman’s reflex sent him leaping from the thing as it flashed, and the steel head thudded home into a tree.

  His second movement was upward. Twenty feet overhead, a branch was a blur of leaves and sunlight. His hands caught it, clung, and he chinned himself and threw a leg over. Crouched there, he drew a long gasp and looked down.

  Two men came out of the thicket and stared wildly about them. They were clad in tattered old levis, roughly tanned buckskin shirts, and their feet were bare on the soft forest floor. One was an Indian, a big gray-haired man, too old to be a mutie; the other was younger, perhaps sixteen, and had only three fingers to his hands. He grasped the bow, the Indian held a spear, and both had knives.

  There was no other way out of this, and no time to be afraid. Collie sprang again, drawing his shortsword even as he fell. He hit with a force that jolted through his legs and rattled his teeth. Stabbing out, he caught the bowman in the stomach.

  The youth screamed, dropping his weapon and clutching blindly at his belly. His comrade roared and struck out with the spear. It tore Collie’s shirt and furrowed along his shoulder. He yanked the sword free and leaped back ten feet. The Indian’s eyes grew wide. He hefted the spear, holding it before him as if for defense. Collie danced around him, seeking a way in. The Indian snarled, braced himself, and threw the shaft. It was a viciously fast movement, the head almost nailed Collie before he could spring.

  ‘Ya-a-ah!’ He jumped closer, crouched low and stabbing the way he had been taught. The Indian drew his knife and thrust underhanded. Then Collie had beaten down his guard and gone to work. It was not pretty.

  Breathing hard, Collie withdrew his blade and stood bent over two dead men. His blood was loud in his ears. Looking around, straining, he could discern only the rustle of leaves and the far-off harsh laughter of a jay. Fragments of sky showed through the forest roof, incredibly blue against its green. The woods were all shadow, speckled with sun, full of murmurs and dimness. No one else – nothing.

  Slowly, Collie plunged his sword into the ground to clean it. A thoughtfulness grew within him. It was – how long? Three years? – since there’d been outlaw trouble. Were these only a pair of strays, or was there a larger band somewhere? No way of telling, now when they sprawled staring sightlessly and flies were already on their wounds.

  Collie shivered. He’d never killed men before. Never wanted to, either. He wondered if he ought to be sick or something.

  No. Why should he? They were dead meat, there on the ground. Soon the earth would claim them and only the white bones would be left. They were nothing to him – a danger, a pest, outlaws. What counted now was letting the town know.

  He picked up the weapons and studied them. Crude things, cold-forged out of steel scrap; the bow and arrows weren’t bad, but they had better in town. Well, the blacksmith could rework the metal, he’d pay a cent or two for it. Collie stuck the knives in his belt, alongside his own, threw the quiver across his back, and picked up the spear. His free hand clashed his sword back into its sheath.

  He’d only been out for a walk, with some vague notion of trying to find the catamount’s den. It had been raiding sheepfolds for the past month, eluding all attempts to catch or kill it. Too damn smart for an ordinary animal – it must be mutie. Well, that could wait now.

  Turning from the dead men, Collie broke into a rapid trot homeward. He had ten miles or so to cover – about an hour’s travel. The woods closed in around him and he was alone again.

  He went softly, senses alert. There might well be others skulking around. No great need to fear them: given any kind of warning, he could get away faster than pursuit.

  The forest was tall and old, reaching farther along the western slopes of the Wind River Range than Collie had ever gone. He followed the slanting ground northwesterly, toward home. The thick mould underfoot muffled his passage, the brush barely whispered as he parted it. Sunlight and shadow blent into confusion here, you couldn’t see far and yet it was like standing in the middle of forever. A vault of branches rustled high overhead.

  Collie loped without breathing hard. He was a tall young man, twenty-four years old – or maybe twenty-three or twenty-five, nobody was quite sure. From the outside he didn’t look like a mutie. The homespun clothes hid his otherness, and the thin brown face was human enough. But when you looked closer, you saw that he was a bit too short in the body, a little too broad and deep in the chest, and entirely too long in the leg. It wasn’t enough to be a misproportion, but it gave him a coltish look.

  A rabbit bolted from his path. Collie didn’t have time to see him well, but those weren’t rabbit ears: they were big and round, more like a mouse’s. And had there been a tail at all?

  Nothing important. Maybe half the animals and people you saw were mutie, though only among humans were you likely to find a really deformed one. The bad cases among animals didn’t live long enough. It did not occur to Collie that his standards of ‘real’ deformity were no older than his own generation.

  Emerging on a long slope that spilled down toward a distant river, Collie crossed three miles of open land. There’d been a forest fire here once. The oldtimers said there were some enormous fires in the years after the war, when there was no one to fight them. The forests had shrunk, though they were starting to come back now. They didn’t seem crowded, though – so few people around. The gray line of a highway showed halfway down the slope, crumbled, overgrown, pieces bitten out of it by avalanches. Collie wondered what it had been like before the war. He couldn’t imagine it as full of cars, like the oldtimers said.

  The burned area was covered with new growth. Collie noticed a sapling which had escaped his eyes before. It was a funny one, all long willowy fronds and ferny leaves. He went through a patch of clover without stopping to look for four-leaved ones as he’d often done in younger days; even if there’d been time, they were getting just too damn common.

  The farmlands started on the other side of the burned section. Collie struck out down the narrow trail between fields of grain. He had covered a good mile before he realized what was wrong. This was cultivating time, but nobody was out in the communal fields.

  Nobody!

  The outlaws—

  His heart stumbled within him, and then he burst into a run. The land slipped by him, sun-flooded, wind-whispering, his moccasins thudded softly on the dirt and somewhere a bird was singing. He breathed hard, not for air but because he was frightened.

  God in Heaven, suppose it was a real outlaw attack? Suppose they had fallen on the town? There were stories enough of that from the old days – pillaging, burning, a scream of children drowned by barking laughter, dead men staring at the sky, fire and smoke and ruin. No!

  He topped a ridge and looked wildly down toward the village. It lay quiet under the sun, a sprawl of paintless houses, a few horses hitched to posts and wagons. Collie’s breath sobbed back into his lungs.

  But where was everybody?

  Hurrying down, he entered the outskirts. The stockade had been removed years ago, but the outlying houses were still supposed to be defensive posts. There was no one in them, no one in the street beyond. A cat yawned at him as he went by. It had two tails.

  As he neared the center of town, he heard the noise, feet, voices, excitement, but not panic. So everybody was in the market square for some reason, and he’d come back in time for the fun. Collie smiled shakily and rounded the last building.

  The broad open plaza was jammed, all the town’s three or four hundred people were there. It was too familiar a sight to register on Collie’s mind – men in clothes like his own, mostly bearded, a few carrying guns but the rest armed with knives and shortswords; women in dresses and clumsily made hats; children in whatever clothes or lack of them there happened to be. It was on the thing they surrounded that Collie’s eyes focused.

  A big metal shape, blinding in hot sunlight – long vanes reaching out over the heads – a helicopter! By God, a helicopter!

  Collie grabbed the arm of a fifteen-year-old. ‘ What’s this, Joe?’ he asked. ‘What’s goin’ on?’

  Joe faced around to him. ‘Hi, Collie,’ he said breathlessly. ‘Where you been? Gee, they been lookin’ all over for you.’

  ‘For me?’ Collie drew back a little. ‘You’re kiddin’!’

  ‘Yeah, you, nobody else. It’s from Oregon, Collie, it’s a guv’mint copter, an’ they said they was lookin’ for the runner they’d heard tell of, an’—’

  Collie didn’t wait any longer, but began shoving through the crowd. Joe looked wistfully after him, and wheeled his primitive chair around in search of a better view. Joe had been born without legs.

  II

  There were two men in the copter. The pilot was a lean, quiet young fellow in uniform, an automatic holstered at his belt; the other was some forty years of age, though he looked older, and in civilian dress. It was not too strange that so many of the townspeople should admire and wonder at their clothes more than anything else – aircraft were not uncommon, flying far overhead. But stuff such as this, the denseness and fineness of it, the color and cut and invisible seams, that was wholly new to the young and like a dear buried memory to the older. Only tattered fragments of pre-war cloth were left hereabouts.

  The sun was sliding down under the mountains, and candles were beginning to glow in windows. A breeze wandered forth with the tall shadows, low and sad out of endless woods and ranges, bearing with it the faint hoot of an owl and the longdrawn wail of a wild dog. Night and quiet came swiftly up here.

  Boss Johnson’s home was, obviously, the only one for such distinguished visitors. A fire burned large in the dining room hearth, crackling and sputtering, throwing its restless light on a few pictures and skins and such furniture as there was. The older children scurried about, serving dinner – fish, soup, venison, potatoes, black bread, butter, and the town’s best hard cider. The Boss’ wife was a large pale woman, subdued in the burly, bearded presence of her husband. Collie felt too shy to say much either; he sat uncomfortably in his holiday clothes, on the edge of his chair, and listened to the Boss rumble on.

  ‘Yep, gents, we ain’t got it so bad. There was hard years right after the war, like everybody else had, I reckon. Not many was left in this village. Most of the folks livin’ here now drifted in later, from other places. There was a few enemy sojers, even, who’d been wanderin’ around f’ years. They turned out to be pretty good people, once you got to know ‘em. We or-gay-nized, fought the outlaws, rounded up wild stock, started plantin’ again, grazin’, huntin’ – you know. Had to make damn near all our own stuff, still make most of it, though we do some tradin’ with other sections too. There’s been troubles, crop failures, one year there was some sickness damn near wiped out our sheep – was that one o’ the war sicknesses, you think?’