Suppose xlogic showed conclusions inconceivable to an adult mind?
It was the random element that baffled investigation…
The crystal cube was similarly cryptic. It showed a mad pattern of colors, which sometimes moved.
It's the way out, I think … I'm not sure yet. My magic toys told me.
The songmeant a great deal. It was the way. Presently she would do what it said, and then…
He looked at the crazypattern on the carpet. If he could follow it, as the kids had done — but he couldn't. The pattern was senseless. The random factor defeated him.
There's no use trying to describe either Unthahorsten or his surroundings, because, for one thing, a good many million years had passed since 1942 Anno Domini and, for another, Unthahorsten wasn't on Earth, technically speaking. He was doing the equivalent of standing in the equivalent of a laboratory. He was preparing to test his time machine.
There was little time to waste. The Box was beginning to glow and shiver. Unthahorsten stared around wildly, fled into the next gossatch, and groped in a storage bin there. He came up with an armful of peculiar-looking stuff. Uh-huh. Some of the discarded toys of his son Snowen, which the boy had brought with him when he had passed over from Earth, after mastering the necessary technique. Well, Snowen needed this junk no longer. He was conditioned, and put away childish things. Besides, though Unthahorsten's wife kept the toys for sentimental reasons, the experiment was more important. Unthahorsten left the glossatch and dumped the assortment into the Box, slamming the cover shut just before the warning signal flashed. The Box went away.
Having finished his supply of cheese, chocolate, and cookies, and having drained the soda-pop bottle to its dregs, Scott caught tadpoles and studied them with a certain amount of scientific curiosity. He did not persevere. Something tumbled down the bank, and thudded into the muddy ground near the water, so Scott, with a wary glance around, hurried to investigate. It was a box. It was, in fact, the Box. The gadgetry hitched to it meant little to Scott, though he wondered why it was so fused and burnt. He pondered. With his jackknife he pried and probed, his tongue sticking out from a corner of his mouth — Hm-m-m. Nobody was around. Where had the box come from? Somebody must have left it here, and sliding soil had dislodged it from its precarious perch.
Maybe it was a music box. Scott shouldn't have felt depressed. The gadgetry would have given Einstein a headache and driven Steinmetz raving mad. The trouble was, of course, that the box had not yet completely entered the space-time continuum where Scott existed and therefore it could not be opened. At any rate, not till Scott used a convenient rock to hammer the helical nonhelix into a more convenient position. He hammered it, in fact, from its contact point with the fourth dimension, releasing the space-time torsion it had been maintaining. There was a brittle snap. the box jarred slightly, and lay motionless, no longer only partially in existence. Scott opened it easily now.
The soft, woven helmet was the first thing that caught his eye, but he discarded that without much interest. It was just a cap. Next he lifted a square, transparent crystal block, small enough to cup in his palm — much too small to contain the maze of apparatus within it. In a moment Scott had solved that problem. The crystal was a sort of magnifying glass, vastly enlarging the things inside the block.
The tiny people were deftly building a house. Scott wished it would catch fire, so he could see the people put it out. Flames licked up from the half-completed structure. The automatons, with a great deal of odd apparatus, extinguished the blaze. It didn't take Scott long to catch on. But he was a little worried. The manikins would obey his thoughts. By the time he discovered that, he was frightened, and threw the cube from him. Halfway up the bank, he reconsidered and returned.
His find he hid at the back of the closet in his own room upstairs. The crystal cube he slipped into his pocket, which already bulged with string, a coil of wire, two pennies, a wad of tinfoil, a grimy defenses stamp, and a chunk of feldspar. Emma, Scott's two-year-old sister, waddled unsteadily in from the hall and said hello. "Hello, Slug," Scott nodded, from his altitude of seven years and some months. He patronized Emma shockingly, but she didn't know the difference. Small, plump, and wide-eyed, she flopped down on the carpet and stared dolefully at her shoes. "Tie 'em, Scotty, please?" "Sap," Scott told her kindly, but knotted the laces.
Candidly, I don't see the point of teaching those apes philosophy. They're all at the wrong age. Their habit-patterns, their methods of thinking, are already laid down. They're horribly conservative, not that they'd admit it. The only people who can understand philosophy are mature adults or kids like Emma and Scotty.
Dennis Paradine, to his wife Jane, the parents of Emma and Scotty
Only babies spilled food, Emma had been told. As a result, she took such painstaking care in conveying her spoon to her mouth that Paradine got the jitters whenever he watched.
He took from his pocket a gadget he had found in the box, and began to unfold it. The result resembled a tesseract, strung with beads. Paradine didn't see it at first, but Emma did. She wanted to play with it.
Paradine blinked. The "abacus," unfolded, was more than a foot square, composed of thing, rigid wires that interlocked here and there. On the wires colored beads were strung. They could be slid back and forth, and from one support to another, even at the points of juncture.
The framework itself — Paradine wasn't a mathematician. But the angles formed by the wires were vaguely shocking, in their ridiculous lack of Euclideanlogic. They were a maze. Perhaps that's what the gadget was — a puzzle.
Paradine found himself growing slightly confused as he attempted to manipulate the beads. The angles were vaguely illogical. It was like a puzzle. This red bead, if slid along this wire to that junction, should reach there — but it didn't. A maze, odd, but no doubt instructive. Paradine had a well-founded feeling that he'd have no patience with the thing himself. Scott did, however, retiring to a corner and sliding beads around with much fumbling and grunting. The beads did sting, when Scott chose the wrong ones or tried to slide them in the wrong direction. At last he crowed exultantly.
Scott puzzled over the framework again. He experimented. This time there were no shocks, even slight. The abacus had showed him the correct method. Now it was up to him to do it on his own. The bizarre angles of the wires seemed a little less confusing now, somehow. It was a most instructive toy — It worked, Scott thought, rather like the crystal cube.
This was fun. Like putting on a play, only more real. The little people did what Scott told them, inside of his head. If he made a mistake, they waited till he'd found the right way. They even posed new problems for him — The cube, too, was a most instructive toy. It was teaching Scott, with alarming rapidity and teaching him very entertainingly. But it gave him no really knowledge as yet. He wasn't ready. Later — later —
Emma was sliding the beads to and fro in the abacus. The motions didn't seem so strange now. Even when the beads vanished. She could almost follow that new direction — almost — Scott panted, staring into the crystal cube and mentally directing, with many false starts, the building of a structure somewhat more complicated than the one which had been destroyed by fire. He, too, was learning being conditioned —
Paradine's mistake, from a completely anthropomorphic standpoint, was that he didn't get rid of the toys instantly. He did not realize their significance, and, but the time he did, the progression of circumstances had got well under way.
Emma and Scott had free rein with the toys. "What," Scott asked his father one evening, "is a wabe, dad?" "Wave?" He hesitated. "I … don't think so. Isn't wabe right?" "Wab is Scot for web. That it?" "I don't see how," Scott muttered, and wandered off, scowling, to amuse himself with the abacus. He was able to handle it quite deftly now. But, with the instinct of children for avoiding interruptions, he and Emma usually played with the toys in private. Not obviously, of course but the more intricate experiments were never performed under the eye of an adult.
Scott was learning fast. What he now saw in the crystal cube had little relationship to the original simple problems. But they were fascinatingly technical. Had Scott realized that his education was being guided and supervised — though merely mechanically — he would probably have lost interest. As it was, his initiative was never quashed.
Neither Paradine nor Jane guessed how much of an effect the contents of the time machine were having on the kids. How could they? Youngsters are instinctive dramatists, for purposes of self-protection. They have not yet fitted themselves to the exigencies — to them partially inexplicable — of a mature world. Moreover, their lives are complicated by human variables. They are told by one person that playing in the mud is permissible, but that, in their excavations, they must not uproot flowers or small trees. Another adult vetoes mud per se. The Ten Commandments are not carved on stone; they vary, and children are helplessly dependent on the caprice of those who give them birth and feed and clothe them. And tyrannize. The young animal does not resent that benevolent tyranny, for it is an essential part of nature. He is, however, an individualist, and maintains his integrity by a subtle, passive fight. Under the eyes of an adult he changes. Like an actor on-stage, when he remembers, he strives to please, and also to attract attention to himself. Such attempts are not unknown to maturity. But adults are less obvious — to other adults.
It is difficult to admit that children lack subtlety. Children are different from the mature animal because they think in another way. We can more or less easily pierce the pretenses they set up — but they can do the same to us. Ruthlessly a child can destroy the pretenses of an adult. Iconoclasm is their prerogative. Foppishness, for example. The amenities of social intercourse, exaggerated not quite to absurdity.
"Such savoir faire! Such punctilious courtesy!" The dowager and the blond young thing are often impressed. Men have less pleasant comments to make. But the child goes to the root of the matter. "You're silly!" How can an immature human understand the complicated system of social relationships? He can't. To him, an exaggeration of natural courtesy is silly.
From the standpoint of logic, a child is rather horribly perfect. A baby may be even more perfect, but so alien to an adult that only superficial standards of comparison apply. The thought processes of an infant are completely unimaginable. But babies think, even before birth. In the womb they move and sleep, not entirely through instinct. We are conditioned to react rather peculiarly to the idea that a nearly-viable embryo may think. We are surprised, shocked into laughter, and repelled. Nothing human is alien. But a baby is not human. An embryo is far less human. That, perhaps, was why Emma learned more from the toys than did Scott. He could communicate his thoughts, of course; Emma could not, except in cryptic fragments. The matter of the scrawls, for example — Give a young child pencil and paper, and he will draw something which looks different to him than to an adult. The absurd scribbles have little resemblance to a fire engine, to a baby. Perhaps it is even three-dimensional. Babies think differently and see differently.
Scott was questioning his sister. Sometimes he did it in English. More often he had resource to gibberish and sign language. Emma tried to reply, but the handicap was too great. Finally Scott got pencil and paper. Emma liked that. Tongue in cheek, she laboriously wrote a message. Scott took the paper, examined it, and scowled. "That isn't right, Emma," he said. Emma nodded vigorously. She seized the pencil again and made more scrawls. Scott puzzled for a while, finally smiled rather hesitantly, and got up. He vanished into the hall. Emma returned to the abacus. Paradine rose and glanced down at the paper, with some mad thought that Emma might abruptly have mastered calligraphy. But she hadn't. The paper was covered with meaningless scrawls, of a type familiar to any parent. Paradine pursed his lips. It might be a graph showing the mental variations of a manic-depressive cockroach, but probably wasn't. Still, it no doubt had meaning to Emma. Perhaps the scribble represented Mr. Bear. Scott returned, looking pleased. He met Emma's gaze and nodded.
Paradine, recalling instance of babies who had babbled in unknown tongues and baffled linguists, made a note to pocket the paper when the kids had finished with it. The next day he showed the scrawl to Elkins at the university. Elkins had a sound working knowledge of many unlikely languages, but he chuckled over Emma's venture into literature. "Here's a free translation, Dennis. Quote. I don't know what this means, but I kid the hell out of my father with it. Unquote." The two men laughed and went off to their classes.
Perhaps Paradine and Jane had evinced too much interest in toys. Emma and Scott took to keeping them hidden, playing with them only in private. They never did it overtly, but with a certain unobtrusive caution. Nevertheless, Jane especially was somewhat troubled.
We are dealing with madness. … All children are mad, from an adult viewpoint.
Rex Holloway, child psychologist, upon being consulted about Scott and Emma
"'Babies of course are not human — they are animals, and have a very ancient and ramified culture, as cats have, and fishes, and even snakes; the same in kind as these, but much more complicated and vivid, since babies are, after all, one of the most developed species of the lower vertebrates. In short, babies have minds which work in terms and categories of their own which cannot be translated into the terms and categories of the human mind.'"
Possiby a case might be made that our children are not human either: but I should not accept it. Agreed that their minds are not just more ignorant and stupider than ours, but differ in kind of thinking (are mad, in fact): but one can, by an effort of will and imagination, think like a child, at least in a partial degree — and even if one's success is infinitesimal it invalidates the case: while one can no more think like a baby, in the smallest respect, than one can think like a bee.
All I say is that babies think in other ways than we do. Not necessarily better — that's a question of relative values. But with a different manner of extension—
The brain's a colloid, a very complicated machine. We don't know much about its potentialities. We don't even know how much it can grasp. But it is known that the mind becomes conditioned as the human animal matures. It follows certain familiar theorems, and all thought thereafter is pretty well based on patterns taken for granted.
"Your mind has been conditioned to Euclid," Holloway said. "So this — thing — bores us, and seems pointless. But a child knows nothing of Euclid. A different sort of geometry from ours wouldn't impress him as being illogical. He believe what he sees." "Are you trying to tell me that this gadget's got a fourth dimensional extension?" Paradine demanded. "Not visually, anyway," Holloway denied. "All I say is that our minds, conditioned to Euclid, can see nothing in this but an illogical tangle of wires. But a child especially a baby might see more. Not at first. It'd be a puzzle, of course. Only a child wouldn't be handicapped by too many preconceived ideas." "Hardening of the thought-arteries," Jane interjected.
Let's suppose there are two kinds of geometry — we'll limit it, for the sake of the example. Our kind, Euclidean, and another, which we'll call x. X hasn't much relationship to Euclid. It's based on different theorems. Two and two needn't equal four in it; they could equal y2, or they might not even equal. A baby's mind is not yet conditioned, except by certain questionable factors of heredity and environment.
Paradine poured himself a stiff shot of whiskey. "That's pretty awful. You're not limiting to math." "Right! I'm not limiting it at all. How can I? I'm not conditioned to x logic." "There's the answer," Jane said, with a sigh of relief. "Who is? It'd take such a person to make the sort of toys you apparently think these are." Holloway nodded, his eyes, behind the thick lenses, blinking. "Such people may exist." "Where?" "They might prefer to keep hidden." "Supermen?" "I wish I knew. You see, Paradine, we've got yardstick trouble again. By our standards these people might seem super-doopers in certain respects. In others they might seem moronic. It's not a quantitative difference; it's qualitative. They think different. And I'm sure we can do things they can't." "Maybe they wouldn't want to," Jane said.
Holloway picked up the crystal cube. "Did you question the children much?" Paradine said, "Yeah. Scott said there were people in that cube when he first looked. I asked him what was in it now." "What did he say?" The psychologist's eyes widened. "He said they were building a place. His exact words. I asked him who — people? But he couldn't explain."
It would be interesting to know the conditions of the place where these things came from.Induction doesn't help a great deal, though. Too many factors are missing. We can't visualize a world based on the x factor — environment adjusted to minds thinking in xpatterns. This luminous network inside the doll. It could be anything. It could exist inside us, though we haven't discovered it yet.
If the undeveloped minds have been turned into the x channel, it's necessary to divert them back. I'm not saying that's the wisest thing to do, but it probably is from our standards. After all, Emma and Scott will have to live in this world.
That night Paradine slept badly. Holloway's parallel had been ill-chosen. It led to disturbing theories. The x factor — The children were using the equivalent of algebraic reasoning, while adults used geometry. Fair enough. Only — Algebra can give you answers that geometry cannot, since there are certain terms and symbols which cannot be expressed geometrically. Suppose x logic showed conclusions inconceivable to an adult mind?
Scott stirred in his sleep. Without awakening, he called what was obviously a question, though it did not seem to be in any particular language. Emma gave a little mewling cry that changed pitch sharply. She had not awakened. The children lay without stirring. But Paradine thought, with a sudden sickness in his middle, it was exactly as though Scott had asked Emma something, and she had replied. Had their minds changed so that even — sleep — was different to them?
A little of Scott's thoughts could still be understood. But Emma had become conditioned to x much faster. She was thinking, too. Not like an adult or a child. Not even like a human. Except, perhaps, a human of a type shockingly unfamiliar to genus homo. Sometimes Scott himself had difficulty in following her thoughts.
If it had not been for Holloway, life might have settled back into an almost normal routine. The toys were no longer active reminders. Emma still enjoyed her dolls and sand pile, with a thoroughly explicable delight. Scott was satisfied with baseball and his chemical set. They did everything other children did, and evinced few, if any, flashes of abnormality. But Holloway seemed to be an alarmist. He was having the toys tested, with rather idiotic results. He drew endless charts and diagrams, corresponded with mathematicians, engineers, and other psychologists, and went quietly crazy trying to find rhyme or reason in the construction of the gadgets.
It was the random element that baffled investigation. Even that was a matter of semantics. For Holloway was convince that it wasn't really random. There just weren't enough known factors. No adult could work the abacus, for example. And Holloway thoughtfully refrained from letting a child play with the thing. The crystal cube was similarly cryptic. It showed a mad pattern of colors, which sometimes moved. In this it resembled a kaleidoscope. But the shifting of balance and gravity didn't affect it. Again the random factor. Or, rather, the unknown. The x pattern.
The children had missed their toys, but not for long. Emma recovered first, though Scott still moped. He held unintelligible conversations with his sister, and studied meaningless scrawls she drew on paper he supplied. It was almost as though he was consulting her, anent difficult problems beyond his grasp. If Emma understood more, Scott had more real intelligence, and manipulatory skill as well. He built a gadget with his Meccano set, but was dissatisfied. The apparent cause of his dissatisfaction was exactly why Paradine was relieved when he viewed the structure. It was the sort of thing a normal boy would make, vaguely reminiscent of a cubistic ship. It was a bit too normal to please Scott. He asked Emma more questions, though in private. She thought for a time, and then made more scrawls with an awkwardly clutched pencil. "Can you read that stuff?" Jane asked her son one morning. "Not read it, exactly. I can tell what she means. Not all the time, but mostly." "Is it writing?" "N-no. It doesn't mean what it looks like."
Her mind has been conditioned unusually. It may be that she breaks down what she sees into simple, obviouspatterns and realizes a significance to those patterns that we can't understand. Like the abacus. She saw a pattern in that, though to us it was completely random.
Scott's thought-patterns are building up to a sum that doesn't equal this world. Perhaps he's subconsciously expecting to see the world where those toys came from.
In the latter half of the nineteenth century and Englishman sat on a grassy bank near a stream. A very small girl lay near him, staring up at the sky. She had discarded a curious toy with which she had been playing, and now was murmuring a wordless little song, to which the man listened to with half an ear.
"Just what does it mean?" "It's the way out, I think," the girl said doubtfully. "I'm not sure yet. My magictoys told me."
She had found the toys in a box one day, as she played by the Thames. And they were indeed wonderful. Her little song — Uncle Charles thought it didn't mean anything. (He wasn't her real uncle, she parenthesized. But he was nice.) The song meant a great deal. It was the way. Presently she would do what it said, and then — But she was already too old. She never found the way.
Scott kept bringing gadgets to Emma for her approval. Usually she'd shake her head. Sometimes she would signify agreement. Then there would be an hour of laborious, crazy scribbling on scraps of note paper, and Scott, after studying the notations, would arrange and rearrange his rocks, bits of machinery, candle ends, and assorted junk. Each day the maid cleaned them away, and each day Scott began again. He condescended to explain a little to his puzzled father, who could see no rhyme or reason in the game.
It was, Paradine thought, like a Scout trail through the woods, markers in a labyrinth. But here again was the random factor. Logic halted — familiar logic — at Scott's motives in arranging the junk as he did. Paradine went out. Over his shoulder he saw Scott pull a crumpled piece of paper and a pencil from his pocket, and head for Emma, who was squatted in a corner thinking things over.
Paradine, his mouth working, his nerves ridiculously tense, forgot the phone and raced up the stairs. The door of Scott's room was open. The children were vanishing. They went in fragments, like thick smoke in a wind, or like movement in a distorting mirror. Hand in hand they went, in a direction Paradine could not understand, and as he blinked there on the threshold, they were gone.
On the carpet lay a pattern of markers, pebbles, an iron ring — junk. A random pattern. A crumpled sheet of paper blew towards Paradine. He picked it up automatically.
Paradine looked at the paper he held. It was a leaf torn from a book. There were interlineations and marginal notes, in Emma's meaningless scrawl. A stanza of verse had been so underlined and scribbled over that it was almost illegible, but Paradine was thoroughly familiar with Through the Looking Glass. His memory gave him the words —
'Twas brillig, and the slithy toves Did gyre and gimbel in the wabe. All mimsy were the borogoves, And the mome raths outgrabe.
Idiotically he thought: Humpty Dumpty explained it. A wabe is the plot of grass around a sundial. A sundial. Time — it has something to do with time. A long time ago Scotty asked me what a wabe was. Symbolism. 'Twas brillig — A perfect mathematical formula, giving all the conditions, in symbolism the children had finally understood. The junk on the floor. The toves had to be made slithy — vaseline? and they had to be placed in a certain relationship, so that they'd gyre and gimbel.
Lunacy! But it had not been lunacy to Emma and Scott. They thought differently. They used x logic. Those notes Emma had made on the page — she'd translated Carroll's words into symbols both she and Scott could understand. The random factor had made sense to the children. They had fulfilled the conditions of the time-space equation. And the mome raths outgrabe — Paradine made a rather ghastly little sound, deep in his throat. He looked at the crazy pattern on the carpet. If he could follow it, as the kids had done — but he couldn't. The pattern was senseless. The random factor defeated him. He was conditioned to Euclid. Even if he went insane, he still couldn't do it. It would be the wrong kind of lunacy.