# Polynesians May Have Invented Binary Math

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tags: math, Polynesia

How old is the binary number system? Perhaps far older than the invention of computers or even the invention of binary math in the West. The residents of a tiny Polynesian island may have been doing calculations in binary—a number system with only two digits—centuries before it was described by Gottfried Leibniz, the co-inventor of calculus, in 1703....

But Leibniz may have been scooped centuries earlier by the people of Mangareva, a tiny island in French Polynesia about 5000 kilometers south of Hawaii. While studying their language and culture, Andrea Bender and Sieghard Beller, anthropologists at the University of Bergen in Norway, were astonished to find a mathematical system that seems to mix base-10 and base-2. “I was so thrilled that I couldn't sleep that night,” Bender says. It could be not only the first new indigenous arithmetic system discovered in decades, but also the first known example of binary arithmetic developed outside Eurasia.

Like all Polynesians, the people who first settled on Mangareva more than 1000 years ago had a decimal counting system. But, according to Bender and Beller, the islanders added a binary twist over the ensuing centuries. Just like English has a few special words like a dozen for 12 and a score for 20, the Mangarevan language has special words for large groups. But their special counting words are all decimal numbers multiplied by powers of two, which are 1, 2, 4, 8 … . Specifically, takau equals 10; paua equals 20; tataua, 40; and varu, 80. Those big numbers are useful for keeping track of collections of valuable items, such as coconuts, that come in large numbers. Bender and Beller realized that the Mangarevan counting system makes it possible to use binary arithmetic for calculations of large numbers, they report today in the Proceedings of the National Academy of Sciences in a paper that even nonexperts will enjoy reading....