MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

June 29, 2007

From Counting to Writing?

We learn to count at such an early age that we tend to take the notion of numbers for granted. We know that two can stand for two apples, two oranges, or two argyle socks. But abstract numbers are the product of a long cultural evolution. They may even have played a role in the invention of writing, or so archaeologist Denise Schmandt-Besserat argues.

Schmandt-Besserat has studied mysterious clay objects found in large quantities at sites all over the Middle East, particularly in Mesopotamia. These objects, or tokens, first appeared around 8000 B.C., when people who had been hunters and gatherers began settling in villages and growing grain. Schmandt-Besserat suggests that farmers needed a reliable way to keep track of their goods, especially the amount of grain stored in village silos. They kept a stock of tokens—one token for each item they owned, with different shapes for different types of items. For example, a marble-sized clay ball stood for a bushel of grain, a certain cylinder for an animal, an egg-shaped token for a jar of oil. All in all, it was a kind of data-storage system.

As life grew more complex, the tokens became more elaborate. A cone with markings, for example, represented not an amount of grain but a loaf of bread.

Excavations of temples have revealed that the people of Mesopotamia sometimes kept sets of tokens encased in clay globes. Because the tokens were no longer visible, they marked the globes by pressing the tokens into the soft clay before sealing and baking the globes. From the imprints, you could tell what was inside.

It didn't take long for people to realize that once the clay globes were marked, it wasn't necessary to enclose the tokens. The marks by themselves, impressed on a clay tablet, were enough.

The final step came around 3100 B.C., when someone realized that instead of representing, say, 33 jars of oil by repeating the symbol for one jar 33 times, it would be simpler to precede the symbol for a jar of oil by special signs expressing numbers. And the same signs could be used to represent the same quantity of any item.

This much is certain. But Schmandt-Besserat makes an additional intriguing suggestion: that the token system led to pictographic writing, which in turn developed into the writing system called cuneiform. Other scholars agree that Sumerian tokens were devices for keeping track of goods, but argue that writing developed independently. They say there is little evidence that cuneiform arose directly out of a token-based accounting system.

However this scholarly argument comes out, the clay globes with their strange contents bear silent witness to a world without numbers or an alphabet, a world so remote from our own that it is hard to imagine what it must have been like.

Muse, May/June 2006, p. 40.