Polynesians traditionally counted by sorting, setting aside every tenth item to represent ten of the items being counted. Large items were counted singly and smaller items by pairs and fours, creating side-by-side counting sequences or “object-specified counting.” Counting-by-sorting minimized the physical effort of moving items to count them and the mental effort of keeping track of the count. The method explains why iwakalua, the Hawaiian word for twenty, means nine and two: in counting pairs, every nine pairs (18 items) are sorted and the tenth pair (two items) is set aside as a counter. Polynesians also had a collaborative method where one person counted the units, a second person counted the tens, a third person the hundreds, and so on. These methods created an ephemeral abacus, ephemeral because the abacus existed only while counting was performed and an abacus because the method represented exponential values. In Mangareva in eastern Polynesia, a unique binary variant of counting-by-sorting developed. This method leveraged the binary relations created by counting by singles, pairs, fours, and eights; the result anticipated Western binary computation by centuries.

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Numbers in Polynesia

  • Karenleigh A. Overmann

摘要

Polynesians traditionally counted by sorting, setting aside every tenth item to represent ten of the items being counted. Large items were counted singly and smaller items by pairs and fours, creating side-by-side counting sequences or “object-specified counting.” Counting-by-sorting minimized the physical effort of moving items to count them and the mental effort of keeping track of the count. The method explains why iwakalua, the Hawaiian word for twenty, means nine and two: in counting pairs, every nine pairs (18 items) are sorted and the tenth pair (two items) is set aside as a counter. Polynesians also had a collaborative method where one person counted the units, a second person counted the tens, a third person the hundreds, and so on. These methods created an ephemeral abacus, ephemeral because the abacus existed only while counting was performed and an abacus because the method represented exponential values. In Mangareva in eastern Polynesia, a unique binary variant of counting-by-sorting developed. This method leveraged the binary relations created by counting by singles, pairs, fours, and eights; the result anticipated Western binary computation by centuries.