Lewis Padgett

"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.

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.

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.

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.

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.

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.

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'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.

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.

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 —

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?

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."

The framework itself — Paradine wasn't a mathematician. But the angles formed by the wires were vaguely shocking, in their ridiculous lack of Euclidean logic. They were a maze. Perhaps that's what the gadget was — a puzzle.

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.

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.