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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?

 

Lewis Padgett

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"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.

 

Lewis Padgett

 

Logic has borrowed, perhaps, the rules of geometry, without comprehending their force... it does not thence follow that they have entered into the spirit of geometry, and I should be greatly averse... to placing them on a level with that science that teaches the true method of directing reason.

 

Blaise Pascal

 

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.

 

Lewis Padgett

 

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

 

Omar Khayyam

 

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.

 

Lewis Padgett