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MatheMUSEments
From
Counting to Writing?
By Ivars Peterson
Muse, May/June 2006, p. 40.
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.
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Examples of tokens. |
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 caly 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.
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