Zero - Charles Seife [6]
Figure 1: Numerals of different cultures
As strange as this system seems to modern eyes, it made perfect sense to ancient peoples. It was the Bronze Age equivalent of computer code. The Babylonians, like many different cultures, had invented machines that helped them count. The most famous was the abacus. Known as the soroban in Japan, the suan-pan in China, the s’choty in Russia, the coulba in Turkey, the choreb in Armenia, and by a variety of other names in different cultures, the abacus relies upon sliding stones to keep track of amounts. (The words calculate, calculus, and calcium all come from the Latin word for pebble: calculus.)
Adding numbers on an abacus is as simple as moving the stones up and down. Stones in different columns have different values, and by manipulating them a skilled user can add large numbers with great speed. When a calculation is complete, all the user has to do is look at the final position of the stones and translate that into a number—a pretty straightforward operation.
The Babylonian system of numbering was like an abacus inscribed symbolically onto a clay tablet. Each grouping of symbols represented a certain number of stones that had been moved on the abacus, and like each column of the abacus, each grouping had a different value, depending on its position. In this way the Babylonian system was not so different from the system we use today. Each 1 in the number 111 stands for a different value; from right to left, they stand for “one,” “ten,” and “one hundred,” respectively. Similarly, the symbol in stood for “one,” “sixty,” or “thirty-six hundred” in the three different positions. It was just like an abacus, except for one problem. How would a Babylonian write the number 60? The number 1 was easy to write: . Unfortunately, 60 was also written as ; the only difference was that was in the second position rather than the first. With the abacus it’s easy to tell which number is represented. A single stone in the first column is easy to distinguish from a single stone in the second column. The same isn’t true for writing. The Babylonians had no way to denote which column a written symbol was in; could represent 1, 60, or 3,600. It got worse when they mixed numbers. The symbol could mean 61; 3,601; 3,660; or even greater values.
Zero was the solution to the problem. By around 300 BC the Babylonians had started using two slanted wedges, , to represent an empty space, an empty column on the abacus. This placeholder mark made it easy to tell which position a symbol was in. Before the advent of zero, could be interpreted as 61 or 3,601. But with zero, meant 61; 3,601 was written as (Figure 2). Zero was born out of the need to give any given sequence of Babylonian digits a unique, permanent meaning.
Though zero was useful, it was only a placeholder. It was merely a symbol for a blank place in the abacus, a column where all the stones were at the bottom. It did little more than make sure digits fell in the right places; it didn’t really have a numerical value of its own. After all, 000,002,148 means exactly the same thing as 2,148. A zero in a string of digits takes its meaning from some other digit to its left. On its own, it meant…nothing. Zero