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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.
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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.
(Score: 2) by JNCF on Friday June 16 2017, @09:27PM
I can fold my 4th and 5th independently enough to count on, it's the combination of my index and ring fingers both being simultaneously fully extended that prevents me from fully folding my middle finger. I wouldn't be surprised if some, or even most, people are capable of the task. Given that binary takes us all the way to 1023 on ten fingers, I could see arguing that it's a good enough standard for visually conveying numbers if even just 20% of the population possesses my inferior knuckle architecture.
We should really start CRISPRing people into having hands that are conducive to counting in a dozenal system, obviously.