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Math Science

Polynesians May Have Invented Binary Math 170

Posted by samzenpus
from the original-number dept.
sciencehabit writes "How old is the binary number system? Perhaps far older than 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."
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Polynesians May Have Invented Binary Math

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  • by Cryacin (657549) on Monday December 16, 2013 @06:49PM (#45708877)
    Those who understood binary, and those who didn't.
  • How is this news? (Score:2, Informative)

    by Anonymous Coward

    Different cultures have been counting in bases other than base-10 for all of human history. Of course a gentleman in the 18th century wasn't the first to use binary.... that's preposterous.

    The Mayans, for example, counted in based 20 (supposedly because they counted on both their fingers and, thanks to a warm climate, exposed toes).

    • by JustOK (667959) on Monday December 16, 2013 @07:10PM (#45709151) Journal

      There was a Mayan tribe that went around naked. The men used base 21 and the women base 22

    • Different cultures have been counting in bases other than base-10 for all of human history.

      Yes, the actual article discusses that.

      The article, however, is remarkably weak in support for the hypothesis that the people of Mangareva (the "tiny Pacific island" mentioned) actually used binary arithmetic, since in fact it doesn't give any evidence at all that they actually used binary arithmetic. What it says is they have number words for three binary powers of ten:paua for 20; tataua for 40; and varu for 80.

      The jump from there to "thus clearly they invented binary arithmetic" is speculation. They st

      • by icebike (68054) on Monday December 16, 2013 @09:26PM (#45710271)

        The article, however, is remarkably weak in support for the hypothesis that the people of Mangareva (the "tiny Pacific island" mentioned) actually used binary arithmetic, since in fact it doesn't give any evidence at all that they actually used binary arithmetic. What it says is they have number words for three binary powers of ten:paua for 20; tataua for 40; and varu for 80.

        The article wasn't so much weak, as it was in awe of an accident of hindsight. (It only looks "special" because we settled on binary for computers.)
        It explicitly made the point that base 10 was used except to refer to large groups.
        Their "special words" took hold only after they ran out of fingers.

        In fact, if you look at it as counting the number of "bodies worth of fingers and toes" it looks less like using binary and more like "We can't count that high, but there was one fish in the pond for every finger and toe of each person in our boat). After that they just counted boats.

        Its really not much different than westerners counting in dozens, and grosses (something that wiki unconvincingly attributes to the convenience of 12 having many divisors [wikipedia.org]. From the same article you learn there were Latin terms for groups of 15, 20, etc. It seems that special, extra ordinal counting numbers for baskets full of stuff are not that unusual.

        • by mcgrew (92797) *

          The article wasn't so much weak, as it was in awe of an accident of hindsight. (It only looks "special" because we settled on binary for computers.)

          Leibnitz discovered binary math in 1679. His ideas came from the I-Ching, and he believed that the ancient (9000 BC) Chinese knew binary calculus (according to wikipedia).

          Apparently, binary math isn't new.

      • You've got it nailed. There is nothing in the article to suggest that Polynesians used base two. Wild speculation based on a few words in an almost extinct language. Wow. There is more evidence to support the idea that ancient space men visited the earth at various times, and THAT evidence is exceedingly thin.

      • by danlip (737336)

        What it says is they have number words for three binary powers of ten:paua for 20; tataua for 40; and varu for 80.

        Which to me is clear evidence they did not use binary math, but base-10 or base-20.

    • Its not news, as indicated by the journalistic codeword "may" as in "there MAY not actually be a story here but its good for click-throughs, so we're going to run it anyways".

      Its very similar to Bettridge's Law of headlines: If a headline uses the word "may", you can generally assume that there will be little actual substance and a lot of overstatement in the article.

    • by Optali (809880)

      The Mayans also counted in base 13... go figure where they got the idea for this

    • by mcgrew (92797) *

      Wikipedia says Leibnitz got binary from a friend who had been to China and introduced him to the I-Ching, which was developed about 9000BC. Leibnitz also believed that the ancient Chinese had developed calculus (also because of the I-Ching).

      Amazing what I learn reading slashdot. It leads me to good wikipedia articles.

  • Binary mathematics was always there.

    Australian aborigines have been known to use the binary system as well.

    Being able to count to 512 on your fingers can be handy!

  • Bad News, Everyone!

    It turns out that we've been trying to figure out binary math for hundreds of years longer than previously believed, which means we humans are worse at math than we thought!

  • by Anonymous Coward

    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.

    There must be a Gilligan's Island joke in here somewhere...

  • by Anonymous Coward

    So this tribe had special numbers for 10, 20, 40, and 80, so that means they had a binary number system? That's a big stretch. That probably means they counted on two people's fingers and toes.

    BTW the French word for eighty is quatre-vingt (four twenties). Same idea, probably.

    • Going to make that point myself. There is 'four score' in English, and an old Northumbrian counting scheme that used to count in multiples of 20 ('chiggit'). Weirdly enough, 'quatre vingts' seems a compartively recent invention: I am told 'ottante' was used in Belgium around WW1. This counting style may not have been ancient.
      • by CastrTroy (595695)
        The interesting thing is that in French, they stopped making new numbers after sixty. Seventy is "soixante dix" which is sixty ten, which is followed by "soixante onze", "sixty eleven", and so on. Eight, like you said is quatre vingts, and ninety is "quatre vingts dix".
  • by newcastlejon (1483695) on Monday December 16, 2013 @07:02PM (#45709047)
    Either they did or they didn't.
    • Exactly! It's either 1 or 0 when talking about binary!
      • by bobbied (2522392)

        There is true, false and carry.. Unless you are out of fingers in which case the carry signal sets overflow.

    • "If God forks the Universe every time you roll a die, he'd better have a damned good memory."

      What's with this "if"? Either He does or He doesn't.

    • Studies of the Mangareva language in the 1930s recorded that it contained specific words for 10, 20, 40 and 80. Sort of like how English has special words "dozen" and "score" for specific quantities. Their culture and language has been nearly obliterated by external influences over the centuries, so all that remains is the fact that they had special words (beyond their normal numbers) for those values. That could be pure coincidence, or it could indicate that they worked with binary numbers and thus had

      • by fatphil (181876)
        There's a good chance it's just mensuration for trade. Things traded in bulk were traded in 10s, and things traded in small quantities were traded in units.

        Imperial units for fluid measure kinda did that either side of the gallon. Smaller, for domestic use, it's binary division, but then suddenly there's a factor of 9 (firkin) for the quantities likely in commercial use.
        • by Khashishi (775369)

          Aren't numbers mainly developed as a tool for trade?

          They probably used binary in the same way that the anglos used base 12, with words like dozen, gross, great gross. But the merchants weren't satisfied with sticking with a single number base and you see some base 2, base 4, base 10, base 12, base 20, and the imperial system of units is a big mess.

          Metric is a big improvement as a consistent standard, but in some ways, it's too bad we settled on the decimal system rather than another radix with better proper

      • I'm still waiting to hear why we have special words for eleven and twelve. Some remnant of divisibility by 6?

    • But that is a much more catchy headline than simply stating that they probably used binary math for some things.

    • Uncertain information, that's what's with it. Next question?
    • by antdude (79039)

      Because they don't know? LOL.

    • "May" does not describe what the Polynesians did, but confidence in the evidence obtained about and the existence of possible counter-evidence for what the Polynesians did.

    • by Khashishi (775369)

      The word "may" indicates uncertainty in this case.

  • Why are variables called "bool"s instead of "leib"s?
    • George Boole. He invented the formal mathematical system of boolean logic.

    • Because bool sounds cool.
  • Poly? (Score:4, Funny)

    by Tablizer (95088) on Monday December 16, 2013 @07:03PM (#45709067) Homepage Journal

    Wouldn't that be "Binesians"?

  • I always thought that mathematics would have progressed much faster if humans had either four or eight fingers on each hand instead of five.
  • by Anonymous Coward on Monday December 16, 2013 @07:13PM (#45709179)

    Leibniz freely admits that he took ideas from the I Ching: http://www.leibniz-translations.com/binary.htm

    What is amazing in this reckoning is that this arithmetic by 0 and 1 is found to contain the mystery of the lines of an ancient King and philosopher named Fuxi, who is believed to have lived more than 4000 years ago, and whom the Chinese regard as the founder of their empire and their sciences.2 There are several linear figures attributed to him, all of which come back to this arithmetic, but it is sufficient to give here the Figure of the Eight Cova, as it is called, which is said to be fundamental, and to join to them the explanation which is obvious, provided that one notices, firstly, that a whole line — means unity, or 1, and secondly, that a broken line -- means zero, or 0.

    The Chinese lost the meaning of the Cova or Lineations of Fuxi, perhaps more than a thousand years ago, and they have written commentaries on the subject in which they have sought I know not what far out meanings, so that their true explanation now has to come from Europeans. Here is how: It was scarcely more than two years ago that I sent to Reverend Father Bouvet,3 the celebrated French Jesuit who lives in Peking, my method of counting by 0 and 1, and nothing more was required to make him recognize that this was the key to the figures of Fuxi. Writing to me on 14 November 1701, he sent me this philosophical prince's grand figure, which goes up to 64, and leaves no further room to doubt the truth of our interpretation, such that it can be said that this Father has deciphered the enigma of Fuxi, with the help of what I had communicated to him. And as these figures are perhaps the most ancient monument of [GM VII, p227] science which exists in the world, this restitution of their meaning, after such a great interval of time, will seem all the more curious.

  • by Anonymous Coward

    This uses binary math, though not quite explicitly: http://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication

  • by nightcats (1114677) <nightmeow@gma[ ]com ['il.' in gap]> on Monday December 16, 2013 @07:26PM (#45709337) Homepage Journal
    Perhaps an apocryphal story, but it goes that Leibniz was introduced to the I Ching (Yijing) oracle by a Catholic missionary friend who had gotten it translated into Latin (must have been strange). Anyway, the story goes that Leibniz instantly recognized the binary system in the 64 hexagrams and 8 trigrams. The I Ching is somewhere between 2,500 and 4,000 yrs. old in the format and ordering it still has today.
    • 64 hexagrams and 8 trigrams

      How does that prove they used binary? The numbers I get out of that are 64, 6, 8, and 3. Heck, 2 isn't even a common factor of all of them.

      • Each trigram is 3 lines, each hexagram 6 lines. The lines are either full line or broken and represent one bit each (1 or 0).

  • Dear World (Score:4, Funny)

    by Arancaytar (966377) <arancaytar.ilyaran@gmail.com> on Monday December 16, 2013 @08:04PM (#45709655) Homepage

    You now owe us royalties on every digital computer built in the last century. Please pay the total of one gazillion dollars to the following bank account.

    -Signed, Polynesia

  • by Anonymous Coward on Monday December 16, 2013 @08:53PM (#45710047)

    Humans used binary long before Leibniz and long before the Polynesians mentioned in the article. For one example:

    2 tablespoons = 1 ounce
    2 ounces = 1 jack
    2 jacks = 1 gill
    2 gills = 1 cup
    2 cups = 1 pint
    2 pints = 1 quart
    2 quarts = 1 pottle
    2 pottles = 1 gallon
    2 gallons = 1 peck
    2 pecks = 1 kenning
    2 kennings = 1 bushel
    2 bushels = 1 strike
    2 strikes = 1 coomb
    2 coombs = 1 hogshead
    2 hogsheads = 1 butt

    • 2 cups = 1 pint

      Or, 1 pint = a rather nonsensical 20 oz. Which is true for the imperial pint. Goodness knows why. Then it holds, so an imperial gallon is still 8 imperial pints.

      The Scots had their own similar system too with another whole raft of funny names.

      A Scottish Pint (a Joug) is apparently 4 mutchkins or 2 chopins.

  • by TranquilVoid (2444228) on Monday December 16, 2013 @09:48PM (#45710439)

    So, decades of stories containing obscure acronyms deemed unworthy of explanation, now the editors decide binary needs to be defined for the Slashdot audience.

    • Binary - A Number (counting) System (way of doing) With Only Two (one more than one and one less than one more than one more than one) Digits (stick like things [above your waist] that are on your hands [digital things in your pants]).

  • One of the researchers describing the Polynesian binary system is named Bender.
  • Did they use 2's complements like we do? How did they handle their floating point operations? Alas, it's a cruel trick. If you read the article, you'll see some brainless twits are hyping this otherwise legitimate paper, and the Mangarevans didn't really use binary math. They just multiplied by 2.
  • Not a nit that I would pick on any other site, but Leibniz invented/discovered calculus independently.
    • Yeah, but slightly later right? That pattern seems to happen a lot in science.

      • by glwtta (532858)
        From what I remember, yes, his work was slightly later, but he also published it earlier. Stands to reason that this would happen a lot - the only alternative is that different people discover something at the exact same time.
  • From TFA: "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."

    So, when working with large quantities, they tended to double things. One heap, two heaps, four heaps. (A) That's not binary math, that's just groupings that they found convenient. The fact that ancient traders introduced 12 and 60 as convenient grouping (because they can be easily subdivided) doesn't mean that anyon

  • http://www.nature.com/news/polynesian-people-used-binary-numbers-600-years-ago-1.14380 [nature.com]
    >>Cognitive scientist Rafael Nuñez at the University of California, San Diego, points out that the idea of binary systems is actually older than Mangarevan culture. “It can be traced back to at least ancient China, around the 9th century bc”, he says, and it can be found in the I Ching, a millennia-old Chinese text that inspired Leibniz. Nuñez adds that “other ancient groups, such as the M

  • A binary counting system is infinitely extensible. English plus both other language have plenty of "two idioms" in them that reflect out bilateral bodies or interaction with just one other person. For example a pair of pants, shoes, glasses. These idioms make sense in the singular. I hear some Semetic languages have gramatical cases just for twoness. For example a word for "our" just for couples.
  • There are several algorithms using the binary number system, including left-to-right binary exponentiation, in Pingala's Chanda-sutra, before 200 BCE. Knuth's _The Art of Computer Programming, Volume 2: Seminumerical Algorithms_ cites B. Datta and A.N. Singh's 1935 _History of Hindu Mathematics 1_. Also al-Kashi described the right-to-left binary exponentiation algorithm in 1427 CE.

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