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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 bob_super on Friday June 16 2017, @05:56PM (7 children)

    by bob_super (1357) on Friday June 16 2017, @05:56PM (#526535)

    Primitive men wanted base 21, and women base 22.

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  • (Score: 2) by JNCF on Friday June 16 2017, @06:18PM (6 children)

    by JNCF (4317) on Friday June 16 2017, @06:18PM (#526547) Journal

    Neither fingers nor peni have 21 states; you can count higher with one hand of binary digits than you can with all 21 of your unary digits.

    • (Score: 2) by bob_super on Friday June 16 2017, @06:25PM (5 children)

      by bob_super (1357) on Friday June 16 2017, @06:25PM (#526550)

      I like counting in binary, but every time I get to 0b00100, someone punches me in the face.

      • (Score: 2) by JNCF on Friday June 16 2017, @06:39PM (4 children)

        by JNCF (4317) on Friday June 16 2017, @06:39PM (#526557) Journal

        Next time you should activate your web-shooters by quickly counting up to 18 (or 9, depending on which side you start from).

        To pick apart my original comment, I should have said that fingers and peni don't have 21 states that are easily discernable for the purposes of human counting. Even with just two states counting based on a boner could still prove difficult.

        • (Score: 2) by bob_super on Friday June 16 2017, @06:46PM (3 children)

          by bob_super (1357) on Friday June 16 2017, @06:46PM (#526562)

          Given that fingers can reliably attain three distinct states, but toes and other parts can't, it might be more efficient to count in base 3, hands-only.

          Still a problem when reaching 00100, 00200, or in the UK 00220

          • (Score: 2) by JNCF on Friday June 16 2017, @08:31PM (2 children)

            by JNCF (4317) on Friday June 16 2017, @08:31PM (#526610) Journal

            I'm assuming that knuckle joints aren't being used for state, since I have the most trouble moving those independantly. Given that state 0 is two curled joints, state 1 is the uncurling of the joint nearest the knuckle, and state 2 is the uncurling of both joints, can you hold your hand in the 02020 position? My middle finger can't move lower than 1 while its neighbors are both fully extended. I've considered a system that uses different bases for different fingers to allow for higher numbers, but that ruins all of the nice tidy rules we get from working in a consistent base. It's a trade-off.

            • (Score: 2) by bob_super on Friday June 16 2017, @08:58PM (1 child)

              by bob_super (1357) on Friday June 16 2017, @08:58PM (#526623)

              After all these political fights, it's nice to see an SN discussion reach peek geek.

              (Yes I can fold my 4th and 5th fingers independently).

              • (Score: 2) by JNCF on Friday June 16 2017, @09:27PM

                by JNCF (4317) on Friday June 16 2017, @09:27PM (#526639) Journal

                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.