Numberland

Chapter I · the number that is not there

Zero

For most of human history, nothing was not a number. Then a few daring scribes gave nothing the same rights as one, two and three — and arithmetic became a machine.

Counting begins at one. For thousands of years the world's number systems had no symbol for nothing: the Babylonians, writing in base sixty, simply left a blank gap where a digit was missing — a gap so fragile that one smudge could turn 62,000 into 6,200.

Then, in India, nothing got a personality. Brahmagupta's rules (628 CE) — a number plus zero is itself; zero times a number is zero — made arithmetic consistent. And zero's real magic is place value: the same 2 means two hundred or twenty, depending on the company it keeps. That trick turned calculation into an algorithm, the abacus into the computer.

Stones count in the units column. At ten, one carries over into the tens column — and the empty slot suddenly needs a name. Watch the gap become a ring.
Place value, animated: the same 2 rolls between the hundreds wheel and the tens wheel — two hundred here, twenty there.