Tokens of plenty: how an ancient counting system evolved into writing and the concept of abstract numbers

Science News, Dec 24, 1988 by Ivars Peterson

Tokens of Plenty

One, two, three, four.... We learn to count at such an early age that we tend to take the notion of abstract numbers for granted. We know the word "two" and the symbol "2" express a quantity that can be attached to apples, oranges or any other object. We readily forget the mental leap required to go from counting specific things such as apples to the abstract concept of number as an expression of quantity.

Just such a leap may have occurred roughly 5,000 years ago among people living in ancient Mesopotamia, a fertile region watered by the Tigris and Euphrates rivers in the Middle East. Ten thousand years ago, counting was a concrete affair. Residents of small agricultural settlements kept track of their goods by maintaining stores of baked clay tokens--one token for each item, different shapes for different types of items. A marble-sized clay sphere would stand for a bushel of grain, a cylinder for an animal, an egg-shaped token for a jar of oil.

Thousans of years later, the growth of villages into cities and the increasing complexity of human activities forced a shift to more efficient means of data storage. The token system evolved into a kind of shorthand in which signs indicating standard measures of grain, impressed on a clay tablet, came to represent not grain or any other specific commodity but the concept of pure quantity. The coupling of signs for numbers with pictorial symbols for specific goods -- the beginning of writing -- provided ancient accountants with the tool they needed to record the multitudinous and varied activities of a city's citizens.

It was a revolution in both accounting and human communication, says archaelogist Denise Schmandt-Besserate of the University of Texas at Austin. For the first time, it provided a reckoning system applicable to any and every item under the sun. It put an end to a cumbersome scheme in which particular tokens were used for counting different goods. It also made taxation on a broad scale feasible.

For Schmandt-Besserat, this new picture of the origin of abstract numbers and the beginning of writing is the culmination of nearly two decades of study that began with a search for the earliest examples of the human use of clay. "I wanted to find out how clay was discovered, for what and when, so I went from museum to museum to review clay collections from the times between 10,000 and 6,000 B.C.," says Schmandt-Besserat. "I was looking for things like bricks and pots. Instead, I was surprised to find all these little clay objects. Nobody really knew what they were."

The objects, recovered from archaeological sites ranging from Turkey and Palestine to Syria and Iran, came in a variety of geometric shapes, including cones, spheres, disks, cylinders and pyramid-like tetrahedrons. Some appeared to be miniature models, an inch or less in size, of animals, tools and other natural or human-made items. Others bore markings such as incised lines. Sometimes excavators found only a few specimens; occasionally they encountered large collections of these mysterious objects.

Traditionally, archaelogists separated these objects into different categories according to shape and tried to guess the use of each particular class of objects. For instance, the disks, they thought, may have been lids for small jars and the spheres could have been marbles.

In contrast, Schmandt-Besserat tackled the problem from the point of view of what these objects had in common: They were all made of clay. They were similar in size and manufactured in roughly the same way.

"It was obvious to me they belonged together," Schmandt-Besserat says. Once these objects, or tokens, came to be considered as a group, their role in counting and record keeping gradually became more clear.

"Within a year, I realized that I was dealing with the precursors of writing," Schmandt-Besserat says. "But it took me a long time to see their connection with counting and numbers."

It was like working on a puzzle, she says. It meant tracking the development of writing on clay tablets backward in time, from what are known as cuneiform symbols back to pictographs and then to token shapes.

"Unfortunately, very few pictographic signs can be traced back and identified with tokens," Schmandt-Besserat. "There are many tokens for which there is no known translation."

The first appearance of clay tokens in the archaeological record coincides with the development of agriculture, especially grain cultivation, in the period from 8,000 to 7,500 B.C. People in Mesopotamia, once mainly hunters and gatherers, began settling in villages and relying on a farm economy based on grain consumption.

Archaeological studies of the period show evidence of grain cultivation in fields surrounding villages, the construction of communal silos for storing grain and a rapid increase in population. In such a setting, individual farmers needed a reliable way to keep track of their goods--especially the amount of grain stored in shared facilities. The answer they found was to fashion clay tokens, or counters, in the form of simple geometric shapes with plain, unmarked surfaces.