The world’s earliest unambiguous numbers come from Mesopotamia, the ancient civilization that once flourished between the Tigris and Euphrates Rivers. These numbers are usually assigned to the Sumerians, an early cultural group. The Sumerian number system was sexagesimal, organized on the number sixty. While we may never know why the Sumerians chose sixty instead ten, they counted on their fingers in the typical manner: five on each hand, as revealed by their words for numbers. These words were not recorded until long after writing had been invented because numerical notations work better when they aren’t cluttered with phonetic clues. The Sumerians also counted different kinds of objects differently—sheep were counted one way, food rations in another, containers of grain in a third way. Such object-specified counting is not uncommon, as it is also found in places like Polynesia. Unlike Polynesia, where object-specified counting involved the goods being enumerated, the Sumerians used tokens and numerical notations to represent their numbers, and these technologies enabled the elaboration of numbers into one of the ancient world’s greatest mathematical traditions.

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Sumerian Numbers

  • Karenleigh A. Overmann

摘要

The world’s earliest unambiguous numbers come from Mesopotamia, the ancient civilization that once flourished between the Tigris and Euphrates Rivers. These numbers are usually assigned to the Sumerians, an early cultural group. The Sumerian number system was sexagesimal, organized on the number sixty. While we may never know why the Sumerians chose sixty instead ten, they counted on their fingers in the typical manner: five on each hand, as revealed by their words for numbers. These words were not recorded until long after writing had been invented because numerical notations work better when they aren’t cluttered with phonetic clues. The Sumerians also counted different kinds of objects differently—sheep were counted one way, food rations in another, containers of grain in a third way. Such object-specified counting is not uncommon, as it is also found in places like Polynesia. Unlike Polynesia, where object-specified counting involved the goods being enumerated, the Sumerians used tokens and numerical notations to represent their numbers, and these technologies enabled the elaboration of numbers into one of the ancient world’s greatest mathematical traditions.