Friday, 21 August 2009

The Origin of Zero

The number zero as we know it arrived in the West circa 1200, most famously delivered by Italian mathematician Fibonacci (aka Leonardo of Pisa), who brought it, along with the rest of the Arabic numerals, back from his travels to north Africa. But the history of zero, both as a concept and a number, stretches far deeper into history—so deep, in fact, that its provenance is difficult to nail down.

"There are at least two discoveries, or inventions, of zero," says Charles Seife, author of Zero: The Biography of a Dangerous Idea (Viking, 2000). "The one that we got the zero from came from the Fertile Crescent." It first came to be between 400 and 300 B.C. in Babylon, Seife says, before developing in India, wending its way through northern Africa and, in Fibonacci's hands, crossing into Europe via Italy.

Initially, zero functioned as a mere placeholder—a way to tell 1 from 10 from 100, to give an example using Arabic numerals. "That's not a full zero," Seife says. "A full zero is a number on its own; it's the average of –1 and 1."

It began to take shape as a number, rather than a punctuation mark between numbers, in India in the fifth century A.D., says Robert Kaplan, author of The Nothing That Is: A Natural History of Zero (Oxford University Press, 2000). "It isn't until then, and not even fully then, that zero gets full citizenship in the republic of numbers," Kaplan says. Some cultures were slow to accept the idea of zero, which for many carried darkly magical connotations.

The second appearance of zero occurred independently in the New World, in Mayan culture, likely in the first few centuries A.D. "That, I suppose, is the most striking example of the zero being devised wholly from scratch," Kaplan says.

Kaplan pinpoints an even earlier emergence of a placeholder zero, a pair of angled wedges used by the Sumerians to denote an empty number column some 4,000 to 5,000 years ago.

But Seife is not certain that even a placeholder zero was in use so early in history. "I'm not entirely convinced," he says, "but it just shows it's not a clear-cut answer." He notes that the history of zero is too nebulous to clearly identify a lone progenitor. "In all the references I've read, there's always kind of an assumption that zero is already there," Seife says. "They're delving into it a little bit and maybe explaining the properties of this number, but they never claim to say, 'This is a concept that I'm bringing forth.'"

Kaplan's exploration of zero's genesis turned up a similarly blurred web of discovery and improvement. "I think there's no question that one can't claim it had a single origin," Kaplan says. "Wherever you're going to get placeholder notation, it's inevitable that you're going to need some way to denote absence of a number."

This article is by John Matson and appeared in the Scientific American (August 21, 2009)