Only about 600 Mangarevan speakers now remain on the island, and in any case its indigenous number system has long been superseded by Arabic digits because of the influence of French colonialism. But Bender and Beller have reconstructed it from descriptions written by (mostly European) authors in the nineteenth and early twentieth centuries.
They find that the former Mangarevans combined base-10 representation with a binary system. They had number words for 1 to 10, and then for 10 multiplied by several powers of 2. The word takau (which Bender and Beller denote as K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80. In this notation, for example, 70 is TPK and 57 is TK7.
Bender and Beller show that this system retains the key arithmetical simplifications of true binary, in that you don’t need to memorize lots of number facts but follow only a few simple rules, such as 2 × K = P and 2 × P = T.
Polynesian people used binary numbers 600 years ago
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