Passage II

SOCIAL SCIENCE: This passage is adapted from the book Lost Discoveries: The Ancient Roots of Modern Science—from the Babylonians to the Maya by Dick Teresi (@2002 by Dick Teresi).

"In the history of culture," wrote mathematician Tobias Dantzig in 1930, "the discovery of zero will always stand out as one of the greatest single achievements of the human race." Zero, he said, marked a "turning point" in math, science, and industry. He also noted that the zero was invented not in the West but by the Indians in the early centuries after Christ. Negative numbers followed soon thereafter. The Maya invented zero in the New World at approximately the same time. Europe, says Dantzig, did not accept zero as a number until the twelfth or thirteenth century.

There are many "biographies of zero," and Dantzig's concise and spirited account of the birth of a number is adequate for most of us. He sees zero's invention appearing on an Indian's counting board in, say, the first or second century A.D. The Indian counting board had columns for the ones, tens, hundreds, thousands, and so on. To "write" 302, for instance, a mathematician would put a 2 in the first (right) column and a 3 in the third, leaving the second column empty. On one fateful day, as Dantzig sees it, an unknown Indian drew an oval in the second column. He called it sunya, for "empty" or "blank." Sunyata, an important concept in Buddhism, is often translated as "emptiness" or "void."

The Arabs turned sunya into sifr ("empty" in Arabic), which became zephirum in Italy, and eventually zero. In Germany and elsewhere, sifr became cifra, and then, in English, cipher. In other words, it took over a thousand years for Western civilization to accept a number for "nothing." Dantzig blames the Greeks. "The concrete mind of the ancient Greeks could not conceive the void as a number, let alone endow the void with a symbol."

That's the short version, and not a bad one. You don't want to hear the long version, so let's suffice with a medium-sized tale.

Zero lay rustling in the weeds for many centuries before that Indian drew it on a counting board. It was an unnamed, unwritten force. It took many more centuries after the Indians and the Maya dared speak its name before zero was promoted to a full-fledged number.

The U.S. Library of Congress defends our calendar and its missing zero. "There has never been a system of recording reigns, dynasties, or eras," the library states, "that did not designate its first year as the year 1." In fact, the Maya had both years 0 and days 0.

The Babylonians had no zero, but they knew something was wrong. If they numbered the first year of each king's reign as year 1, then added up the number of years of each separate reign, they'd end up with too many years unless each king died just before midnight on New Year's Eve and his successor took the throne after midnight. Thus, the Babylonians called a king's first year the accession year. The following year was year 1. The accession year was a kind of year 0. The Babylonians, so far as we know, never articulated zero, but seemed aware that there was a missing number in their system.

The contemporary mathematician who has conducted the most rigorous research on nothing is Robert Kaplan, the author of The Nothing That Is: A Natural History of Zero. Zero turns up throughout history in different cultures as a series of dots and circles, and Kaplan writes of following "the swarm of dots we find in writings from a host of languages, across great spans of time, and on topics mathematical and otherwise."

Kaplan traces the roots of zero to Sumer and Babylonia. The Sumerians counted by tens and sixties, a system adopted by the Babylonians, who eclipsed them in Mesopotamia. The Babylonians, far ahead of the Romans and Greeks to come, imposed a positional notation on the old Sumerian sexagesimal system. Writing their numbers on clay, the Babylonians needed a symbol to put in the "empty" columns, just as we today use zero to differentiate between 302 and 32.

Somewhere between the sixth and third centuries B.C., the Babylonians began using two slanted tacklike symbols to insert in the empty columns. They borrowed the slanty tacks from their language, where they were used as periods, among other things. However, the Babylonians used their "zero" only in the middle of numbers, never at the end. Clearly, this was not a full-fledged zero.

Kaplan argues that when Alexander invaded the Babylonian empire in 331 B.C., he hauled off zero along with the gold. Shortly thereafter we find the symbol 0 for zero in the papyri of Greek astronomers, but the mathematicians never pursued the concept.