Dozen

She lined up ten acorns, then a bundle of ten, then a bundle of ten bundles. "We bundle by ten, so ten ones make a ten, ten tens make a hundred, and each column to the left is worth ten times the one on its right. That's a positional system — a mark's value depends on which column it sits in. And why ten?" She spread her paws and wiggled her fingers. "Because we counted on these. Base ten isn't a law of the universe. It's the number of fingers on two hands, made permanent."

"But hands aren't the only counters people used," she went on, and this was her favourite part. "The Maya bundled by twenty — base twenty, fingers and toes together — and built a place-value system so powerful their astronomers tracked the years across centuries. That's vigesimal." She drew a fresh set of columns. "And in Babylon they bundled by sixty — base sixty, sexagesimal — which sounds enormous until you notice you still use it every single day. Sixty seconds in a minute. Sixty minutes in an hour. Three hundred sixty degrees in a circle. That's Babylon, four thousand years old, still ticking on your wrist."

A young rabbit frowned. "So the base is just... made up?"

"Chosen," Dozen corrected gently, "not made up — and every choice has to obey the same clever rule: each column is worth the base times the column before it, and you need exactly base-many digits to fill one column before it rolls over into the next. Ten digits for base ten, zero through nine. Twenty for the Maya. Sixty for Babylon. Change the bundle and the whole system reshapes around it — but the deep idea, bundling into place-value columns, stays exactly the same underneath."

She learned this without a book, the way she learned most things — by watching. Traders from far roads counted in bundles that weren't hers, and at first she thought them wrong, until she matched their answers to her own and found the same amount arriving by a different-sized road. "That was the lesson," she said. "Not that ten is right and twenty is wrong. That the amount is real, and the base is a costume we dress it in. A dozen eggs, a score of years, an hour of sixty minutes — three different bundles, all just counting."

The rabbit turned it over. "So even the computers—"