History of Writing Ancient Numbers - Clay Tokens

Clay Tokens

The earliest known writing for record keeping evolved from a system of counting using small clay tokens. The earliest of these tokens were found in layer III of Mureybet by Jacques Cauvin. It coincided with a period of explosive rapid growth of the use of cereals in the Near East. This phase dates to the Pre-pottery Neolithic A / Pre-Pottery Neolithic B horizon with approximate c14 dates for this layer of between 9300 to 8600 BC.

To create a record that represented "two sheep", they selected two round clay tokens each having a + sign baked into it. Each token represented one sheep. Representing a hundred sheep with a hundred tokens would be impractical, so they invented different clay tokens to represent different numbers of each specific commodity, and by 4000 BC strung the tokens like beads on a string. There was a token for one sheep, a different token for ten sheep, a different token for ten goats, etc. Thirty-two sheep would be represented by three ten-sheep tokens followed on the string by two one-sheep tokens.

To ensure that nobody could alter the number and type of tokens, they invented a clay envelope shaped like a hollow ball into which the tokens on a string were placed, sealed, and baked. If anybody disputed the number, they could break open the clay envelope and do a recount. To avoid unnecessary damage to the record, they pressed archaic number signs and witness seals on the outside of the envelope before it was baked, each sign similar in shape to the tokens they represented. Since there was seldom any need to break open the envelope, the signs on the outside became the first written language for writing numbers in clay. An alternative method was to seal the knot in each string of tokens with a solid oblong bulla of clay having impressed symbols, while the string of tokens dangled outside of the bulla.

Beginning about 3500 BC the tokens and envelopes were replaced by numerals impressed with a round stylus at different angles in flat clay tablets which were then baked. A sharp stylus was used to carve pictographs representing various tokens. Each sign represented both the commodity being counted and the quantity or volume of that commodity.

About 3100 BC written numbers were dissociated from the things being counted and abstract numerals were invented. The things being counted were indicated by pictographs carved with a sharp stylus next to round-stylus numerals.

The Sumerians had a complex assortment of incompatible number systems and each city had their own local way of writing numerals. In the city of Uruk about 3100 BC, there were more than a dozen different numeric systems. One number system was used for counting discrete objects such as animals, tools, and containers. A different system was for counting cheese and grain products. Another system was used to count volumes of grain and included fractions. Another system counted beer ingredients. Another system counted weights. Another system counted land areas. Another system counted time units and calendar units. And these systems changed over the years. Numbers for counting volumes of grain changed whenever the size of the baskets changed. People who added and subtracted volumes of grain every day used their arithmetic skills to count other things that were unrelated to volume measurements.

The Sumerians invented arithmetic. Multiplication and division were done with multiplication tables baked in clay tablets.