Once upon a time there was a strange little species—that might have been biological, or might have been synthetic, and perhaps were only a dream—whose passion was sorting pebbles into correct heaps.

They couldn't tell you why some heaps were correct, and some incorrect. But all of them agreed that the most important thing in the world was to create correct heaps, and scatter incorrect ones.

Why the Pebblesorting People cared so much, is lost to this history—maybe a Fisherian runaway sexual selection, started by sheer accident a million years ago? Or maybe a strange work of sentient art, created by more powerful minds and abandoned?

But it mattered so drastically to them, this sorting of pebbles, that all the Pebblesorting philosophers said in unison that pebble-heap-sorting was the very meaning of their lives: and held that the only justified reason to eat was to sort pebbles, the only justified reason to mate was to sort pebbles, the only justified reason to participate in their world economy was to efficiently sort pebbles.

The Pebblesorting People all agreed on that, but they didn't always agree on which heaps were correct or incorrect.

In the early days of Pebblesorting civilization, the heaps they made were mostly small, with counts like 23 or 29; they couldn't tell if larger heaps were correct or not. Three millennia ago, the Great Leader Biko made a heap of 91 pebbles and proclaimed it correct, and his legions of admiring followers made more heaps likewise. But over a handful of centuries, as the power of the Bikonians faded, an intuition began to accumulate among the smartest and most educated that a heap of 91 pebbles was incorrect. Until finally they came to know what they had done: and they scattered all the heaps of 91 pebbles. Not without flashes of regret, for some of those heaps were great works of art, but incorrect. They even scattered Biko's original heap, made of 91 precious gemstones each of a different type and color.

And no civilization since has seriously doubted that a heap of 91 is incorrect.

Today, in these wiser times, the size of the heaps that Pebblesorters dare attempt, has grown very much larger—which all agree would be a most great and excellent thing, if only they could ensure the heaps were really correct. Wars have been fought between countries that disagree o...

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