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Monday, September 15, 2025

Abacus Conundrums for Hermann Hesse . . .

Filed under: General — Tags: , — m759 @ 11:07 pm

. . . and for Harlan Kane

From “Mimsy Were the Borogoves” (Padgett, 1943) —

…”Paradine looked up. He frowned, staring. What in—
…”Is that an abacus?” he asked. “Let’s see it, please.”
…Somewhat unwillingly Scott brought the gadget across to his father’s chair. Paradine blinked. The “abacus,” unfolded, was more than a foot square, composed of thin,  rigid wires that interlocked here and there. On the wires the colored beads were strung. They could be slid back and forth, and from one support to another, even at the points of jointure. But— a pierced bead couldn’t cross interlocking  wires—
…So, apparently, they weren’t pierced. Paradine looked closer. Each small sphere had a deep groove running around it, so that it could be revolved and slid along the wire at the same time. Paradine tried to pull one free. It clung as though magnetically. Iron? It looked more like plastic.
…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.

 

From City of Illusions  (Le Guin, 1967) —

All the top of the table, Falk now saw, was sunk several inches into a frame, and contained a network of gold and silver wires upon which beads were strung, so pierced that they could slip from wire to wire and, at certain points, from level to level. There were hundreds of beads, from the size of a baby’s fist to the size of an apple seed, made of clay and rock and wood and metal and bone and plastic and glass and amethyst, agate, topaz, turquoise, opal, amber, beryl, crystal, garnet, emerald, diamond. It was a patterning-frame, such as Zove and Buckeye and others of the House possessed. Thought to have come originally from the great culture of Davenant, though it was now very ancient on Earth, the thing was a fortune-teller, a computer, an implement of mystical discipline, a toy. In Falk’s short second life he had not had time to learn much about patterning-frames. Buckeye had once remarked that it took forty or fifty years to get handy with one; and hers, handed down from old in her family, had been only ten inches square, with twenty or thirty beads…

. . . .

A crystal prism struck an iron sphere with a clear, tiny clink. Turquoise shot to the left and a double link of polished bone set with garnets looped off to the right and down, while a fire-opal blazed for a moment in the dead center of the frame. Black, lean, strong hands flashed over the wires, playing with the jewels of life and death. “So,” said the Prince, “you want to go home. But look! Can you read the frame? Vastness. Ebony and diamond and crystal, all the jewels of fire: and the Opal-stone among them, going on, going out.

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