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posted by CoolHand on Friday June 16 2017, @05:02PM   Printer-friendly
from the ancient-computer dept.

Binary arithmetic, the basis of all virtually digital computation today, is usually said to have been invented at the start of the eighteenth century by the German mathematician Gottfried Leibniz. But a study now shows that a kind of binary system was already in use 300 years earlier among the people of the tiny Pacific island of Mangareva in French Polynesia.

The discovery, made by analysing historical records of the now almost wholly assimilated Mangarevan culture and language and reported in Proceedings of the National Academy of Sciences, suggests that some of the advantages of the binary system adduced by Leibniz might create a cognitive motivation for this system to arise spontaneously, even in a society without advanced science and technology.
...
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.


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  • (Score: 2) by tfried on Saturday June 17 2017, @07:34PM

    by tfried (5534) on Saturday June 17 2017, @07:34PM (#527119)

    This looks a lot more like Roman Numerals

    Not quite. The striking thing about Roman numerals is that they are clearly not based on an understanding of powers. They have "digits" for 1, 5, 10, 50, 100, 500, 1000, but each "digit" will typically have to be represented by a multitude of signs. Such as XLII for a mere 42, or inscrutable beasts like MCMXCVIII. It's not surprising that this system was replaced by the Arabic system, worldwide. (And still we see fascinating proofs of innumeracy in inconsistencies such as sixteen / twenty-six - or even the French soixante-dix-sept ("60+10+7")).

    The interesting bits about this are that a) the system probably developed independently, b) it is apparently based on an understanding of powers, and the representation of digits, c) it is unique in using two different bases (one of which happens to be 2).

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