Didactylos Ring
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"She wandered over to one such desk which had, in the middle, a cylindrical ring. Or two. Or one-and-a-half. It was hard to tell. It seemed to glow, but only in that different parts of it were lit from different angles, despite a complete lack of lighting. It cast a shadow away from the nearest candle. And a few towards it...
“What’s this?”
“A Didactylos Ring,” Ponder explained, twiddling his cuffs. “If you were to put an ant on it so that it followed the contours of the face it was on without crossing any edges, given enough time, it would meet itself coming the other way. On the inside.”
“... Right...”
“Alternatively, if you were to try to draw a line along one face in the same way, thirty-five percent of people go mad before they run out of pencils.” He twiddled nervously with a cuff. “Within it, therefore, pi equals exactly infinity. For the most part. Or zero. Or minus six.”
“That’s silly,” Ann said, shaking her head. “Pi’s three point etcetera. That’s what pi is. You can’t change it.”
“Would you like a pencil?”
Ann thought again. “No, thanks. Minus six? Hm, yes... OK... What‘s it made of?”
Ponder hesitated. “The current theory is shadows.”
“Of what?”
“Itself.”"
"She wandered over to one such desk which had, in the middle, a cylindrical ring. Or two. Or one-and-a-half. It was hard to tell. It seemed to glow, but only in that different parts of it were lit from different angles, despite a complete lack of lighting. It cast a shadow away from the nearest candle. And a few towards it...
“What’s this?”
“A Didactylos Ring,” Ponder explained, twiddling his cuffs. “If you were to put an ant on it so that it followed the contours of the face it was on without crossing any edges, given enough time, it would meet itself coming the other way. On the inside.”
“... Right...”
“Alternatively, if you were to try to draw a line along one face in the same way, thirty-five percent of people go mad before they run out of pencils.” He twiddled nervously with a cuff. “Within it, therefore, pi equals exactly infinity. For the most part. Or zero. Or minus six.”
“That’s silly,” Ann said, shaking her head. “Pi’s three point etcetera. That’s what pi is. You can’t change it.”
“Would you like a pencil?”
Ann thought again. “No, thanks. Minus six? Hm, yes... OK... What‘s it made of?”
Ponder hesitated. “The current theory is shadows.”
“Of what?”
“Itself.”"