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Polynesian people used a kind of binary number system 600 years ago (2013)
- protomyth 9y agoA couple of Native American tribes used octal because base 8 works for the number of things you can carry between the fingers. Would have made computing a bit simpler if that had been adopted instead of base 10.
- agumonkey 9y agoGotta say, I'd never have thought about space between fingers as the motivation for a base. We must investigate lobsters.
- kowdermeister 9y agoThat's also the explanation for base 60
- fishnchips 9y agoOh wow, I didn't know that. Reminds me of the Aborigines who looked for shapes and figures in the empty space between the stars as opposed to our own ancients who'd rather 'connect the dots'.
- cr0sh 9y agoNegative space astronomy - interesting...
- whatshisface 9y agoComputers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why the global human standard is base-eleven. Wait, what?
- subru 9y agoImagine you had two fingers and not ten. Try counting in binary. That should clear up the anomaly.
- whatshisface 9y agoYou can count from zero to two on two fingers, so two-fingered aliens may invent numerals for zero, one and two. If they develop that into a place value system, it will be (fingers+1)-ary, or in their case trinary.
- oculusthrift 9y agoyou can count from zero to three :)
- kazinator 9y agoI'm a Lisp programmer, damn it! I will use one of the fingers for one tag bit which indicates a pointer into the heap when zero, and from there I will boostrap bignums somehow, and the rest of the numeric tower.
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- kobeya 9y agoThere's a lot more possible states than eleven. 32 if you count just whether a finger is extended. More if you allow crossing fingers, interaction between hands, etc. And this isn't theoretical either: https://en.wikipedia.org/wiki/Chinese_number_gestures https://en.wikipedia.org/wiki/Chinese_number_gestures
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- mrout 9y agoThe problem I have with these sorts of articles is that they have a clear agenda behind them. Okay, so they used binary numbers 600 years ago. But why is that posted here? It's not because it's interesting. It's like a 'hey look they were ahead of us on one thing' sort of thing. Which isn't true, obviously.
- aaron-lebo 9y agoThe ability of the Polynesians to settle huge stretches of the Pacific might be one of the most impressive human achievements ever. Odds are they reached South America even if we never find direct evidence (there is some).
- doublec 9y agoThere's a study that found Polynesian DNA markers in indigenous Brazilian remains. It's probably what you are referring to by the some evidence. https://www.nature.com/news/dna-study-links-indigenous-brazilians-to-polynesians-1.12710 https://www.nature.com/news/dna-study-links-indigenous-brazi... I've visited Mangareva. It's a lovely island and a step in the journey to get to Pitcairn Island.
- rlander 9y agoDid your trip include Pitcairn Island? I'd be interested in your impressions of the place (population 50, boat every 3 months or so).
- doublec 9y agoYes it did. I visited in 2012. I put some photos online here http://cd.pn/pn2012/ http://cd.pn/pn2012/ That covers the trip from Mangareva to Pitcairn and back. I loved it on Pitcairn. The island is small but very hilly so there's more walking around and things to see than I expected. The people were friendly and welcoming. I went there via a yacht from Mangareva that was chartered through an island run travel agency. I stayed for about three weeks. There's definitely a feeling of isolation once the yacht left knowing that there's no way to leave until it comes back. I also had to adjust to no mobile phone and power only on half the day. I was constantly checking my pocket for the first few days to check mail and messages only to realise I didn't have a phone! I stayed with an island couple - accomodation fee covers food, etc. They were great. They have a shop on the island that gets stocked through the three monthly supply ship. Most of the food comes from island gardens, food growing wild and fishing. I fished a lot! There are artifacts from the Bounty and other shipwrecks around the island. Cannons, anchors, etc. There's a museum with more artifacts and island history. The church holds an original bible from the Bounty. There were a number of island events while I was there for birthdays and a market day where islanders sell there unwanted goods to other islanders or visitors. I was surprised at the number of visitors to the island. Lots of yachties ticking off their bucket list. And a surprising number of solo sailors visiting. I met a lot of interesting people. My perception may be coloured by the fact that I'm related to many people there through my grandmother who was born on the island in the early 1900s. I went there to learn about where she lived and my family ancestral history.
- jlebrech 9y agoOh well, no more computers for us then http://www.cbc.ca/news/canada/north/cultural-appropriation-make-it-illegal-worldwide-indigenous-advocates-say-1.4157943 http://www.cbc.ca/news/canada/north/cultural-appropriation-m...
- torrent-of-ions 9y agoA guy in an English suit asking for cultural appropriation to be made illegal. Oh the irony.
- jlebrech 9y agoI find that funny, but remember everyone else is allowed to appropriate white culture because reasons. This just seems like tribalism to me, yet the same people want open borders and freedom of movement, but not of ideas and culture.
- 1001101 9y agoWhile not intended to be used mathematically, the I Ching hexagrams developed around 1000AD represented the binary numbers from 0-63 (2^6), as discovered by Leibniz who was quite fond of binary himself.
- 19eightyfour 9y agoThat is weird, right? Where did the precise use of broken and unbroken lines, in all the combinations necessary to represent binary 0 to 63 originate? It's a compact representation to label 64 different things using 6 "sticks"...but why did they do it like this? Were they aware of binary numbers?
- MBCook 9y agoIt's not that hard. If you limit yourself to two symbols and try to think of ways to represent as many things as you can, you just have to keep adding additional columns/rows. As long as you realize that you can use different combinations of the "first" spots with each additional spot you quickly come up with what is effectively binary. I distinctly remember in early middle school trying to think of ways to enumerate things where you could never confuse one for the other based on the symbols. I was using base 10 because I wanted to store the combination of things in a variable in BASIC on a program I was trying to write on my calculator. As I was playing around on paper I came up with a great system. I would only use one and zero because you could always tell them apart, where as if you use the other numbers then you can't tell if you meant five or if that five was a combination of two and three. When you needed to make another thing and you were out of places you would just add a digit on the left. Then about five seconds later it hit me that what I had was just binary. All of a sudden the idea of using individual bits in masks to represent things (which I'd seen before) made a lot more sense.
- jes5199 9y agothe sticks are literal sticks, used in fortune telling. It's roughly equivalent to flipping a coin. If you had a game where you flipped six coins, and each combination had a different meaning, you would be close to inventing binary
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- petersjt014 9y agoOf course, we all know what they would have used if they were real pros: https://en.wikipedia.org/wiki/Factorial_number_system https://en.wikipedia.org/wiki/Factorial_number_system
- corysama 9y agoHi, Peter. Welcome to Hacker News! If you get downvoted, it's because HN community takes a somewhat strict approach when moderating comments that contribute noise to the conversation. "Nice article!" comments are routinely downvoted. As is sarcasm, witticisms, memes, references and other styles of comments that occur frequently but do not contribute to the discussion. It's a knowingly doomed attempt to hold back the flood of noise that covers Reddit.
- Others 9y agoThat last part feels a little aggressive in this case... The Wikipedia article he linked to is actually pretty interesting, relevant, and appropriate. Sure the presentation is tongue and cheek, but so are half of the comments on this site...
- corysama 9y ago> but so are half of the comments on this site... Yeah... There are a lot more jokes and sarcasm being voted up on HN these days. It's always been around, but it used to be voted down a lot more. Can't say I'm happy about that change. It seems the fate of all vote-based communities to eventually devolve into Digg 3.0...
- tray5 9y agoI agree that his comment didn't add all that much, but I think the snark on your end was a bit more distracting and irrelevant than his comment, and honestly his comment was kind of on topic. This site is thankfully strictly moderated and usually the discussion in the comments is very on topic, jumping at the chance to be smug like that degrades the quality of conversation much farther then being semi-relevant with a bit of a joke. Downvote and move on
- userbinator 9y agoThey 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. Interesting. Perhaps this is the very first use of binary-coded-decimal?
- janwillemb 9y agoThey 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. To my non-mathematically trained ears this doesn't sound like a binary system at all, but more like the highly inefficient Roman system. Am I missing something?
- MichaelBurge 9y agoIt's not at all like a Roman system except for the use of letters. You can separate a natural number n into two parts: n = 10 * q + k, where 0 <= k < 10 and q in N q = 1 * K? + 2 * P? + 4 * T? + 8 * V? where K?, P?, T?, and V? are 0 if the letter is absent and 1 if the letter is present. n is a textbook base 10 decomposition, and q is a sparse binary representation. Roman numerals didn't use quotient/remainder or a geometric expansion at all. Since the 'base' seems to switch between 2 and 5 each time, you can't cleanly decompose it. And there was that weird subtractive case.
- ajarmst 9y agoWhile the described system has some powers of 2, which is interesting, it is a far cry from positional binary. It most certainly does not prefigure the system described by Leibniz, nor the application of arithmetical operations to logic, which was the profound insight in question. This shares far more with things like the base-60 fractions used by Mesopotamians than anything recognizably similar to modern binary and logic systems. (Which of course derive a great deal from Aristotle, significantly more than 600 years ago).
- pfooti 9y agoIf this stuff is interesting to you, you should read about Geoff Saxe's work [0] with the Oksapmin people of Papua New Guinea. This book is newish (and I haven't read it, but I've read almost all of the studies the book is built on) and synthesizes a couple of decades of research into how these people count and talk about number and how that practice changed over time (there's some fascinating conclusions about how the base changed from base-27 to base-20 when western money, in particular the 1 pound : 20 shilling ratio, came to be more widely-used). And yeah, more or less base-27. They used body parts to refer to numbers 1-27, and often anything higher than that was just "a lot", but they could count more using the system if needed. How the Oksapmin people mingled both traditional counting and modern arithmetic is pretty fascinating (and says a lot about the underlying cognitive processes that make humans able to reason about number). 0: http://a.co/6gbRM1x http://a.co/6gbRM1x
- adrianratnapala 9y agoDid they use 27 as a radix when they went for bigger numbers? For example and Oksapmin might have say "four score and seven years ago", using their 27-numeral vocabulary to supply words for "four", "seven" and "twenty", but in this case the (closest thing to) a radix is 20, not 27.
- pfooti 9y agofor the most part, they didn't go for bigger than 27 very often. At the time Saxe started studying them in the late 1970s, they were living very close to nature, and often didn't have cause to need to accurately count higher than that (if you have one or two fish, the distinction is important - if you have 27 or 28, less so). But yes, the word fu (not foo, but enjoyably similar) which kind of means "a full amount", or enough, and was used as "one radix", so people do something like fu + another number word to mean 27 + that other number. I don't remember if there was evidence of treating it like a radix (like multiple fu + something), but I don't think that happened. Again, in this particular culture and economy, there wasn't much of a need to think about large numbers precisely. Which is part of what makes all this pretty fascinating - humans have some inbuilt capacity to reason about numbers (some studies of babies show that they can distinguish between two and three of things just as readily as two hundred to three hundred, sort of a visual field scale independence - I'd have to dig to find that study, I read it about eight years ago, I think it was in nature), but beyond a certain level it becomes intrinsically intertwined with our development of language and other conceptual frames.
- daxfohl 9y ago0b1001011000 years ago? Anybody?
- DrScump 9y agoI keep forgetting the New Year and write 0b1001010111 on all of my checks.
- vorg 9y ago> 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 Because base-10 seems to originate from two handfuls of fingers, I wonder why they didn't end up with a base-5 representation with a binary system? > takau (K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80 By using their numeral for five (say, F) to mean 5 in this scheme, they could have gotten rid of their numerals for 6 to 9. So 157 would be VTPKF2 instead of VTPK7.
- thinkingkong 9y agoIf you think this is cool you might also find the Marshall Island stick charts, and Polynesian navigation methods particularly intriguing. See https://en.wikipedia.org/wiki/Marshall_Islands_stick_chart https://en.wikipedia.org/wiki/Marshall_Islands_stick_chart https://en.wikipedia.org/wiki/Polynesian_navigation https://en.wikipedia.org/wiki/Polynesian_navigation
- erkose 9y agoBinary numbers have been in use since the balance scale was developed.
- contingencies 9y agoThis is not a bad point really. But taking that perspective, binary logic has existed since all forms of classification, ie. any form of recognition whatsoever, which all babies achieve innately (what is pain/hunger/warm/wet, who is mum, is that a voice I hear, etc.) In short, all structured thought requires binary logic, because otherwise classification wouldn't work, and thus neither communication, memory, etc. Full disclosure: I had a revelatory acid trip on this subject when a research mathematician first explained to me set theory as essentially a derivative matrix resulting from a boolean test.... the world as we perceive it is merely sets! This explains children learning! Mind. Blown. Bonus anecdote: If you like admiring early human achievements that have been unfairly obscured from popular history, check out the Polynesian crab claw sails. https://en.wikipedia.org/wiki/Crab_claw_sail#Performance https://en.wikipedia.org/wiki/Crab_claw_sail#Performance
- _Codemonkeyism 9y ago"Polynesian people used binary numbers 600 years ago" Disgrace to Nature for click bait. The number system might be clever but as described is not binary numbers. Especially the claim in the introduction "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." implying Leibnitz didn't invent binary and equate the existence of 4 numbers (10,20,40,80) which lack the simplicity of 2 states by representing it with KTPV with the invention of the binary number system is sensationalist. Interesting the quote “It’s puzzling that anybody would come up with such a solution, especially on a tiny island with a small population,” Bender and Beller say. It's only puzzling to scientists from "Department of Psychosocial Science" but would not be puzzling to scientists from the "Department of Mathematics".
- mrslave 9y agoAnd relevant to a classic contradiction in the startup community: idea vs (execution and capital). What you (say or think) matters a lot less than what you do.
- bobwaycott 9y agoThank you. This needed to be said.
- iamcurious 9y ago>implying Leibniz didn't invent binary Humanity is really old. At most, we can say that Leibniz was the last to invent it.
- protonfish 9y agoLeibniz recognized the concept of binary in the hexagrams of the I Ching and even published a paper on it. http://www.historyofinformation.com/expanded.php?id=454 http://www.historyofinformation.com/expanded.php?id=454
- siosonel 9y agoThe Polynesian people used binary numbers, but not only binary numbers. The article's title is correct. What's sensationalist about that? Is it an important finding? I think so. It helps shed light on the scientific and technical originality of other cultures. It matters a lot to acknowledge that knowledge does not always flow from west to east or north to south. It helps to rid of the notion of there being 'advanced' and 'primitive' cultures. Are the scientists from the "Department of Psychosocial Science" trying too hard to make that case? I don't think so. Some people like me thinks this is a newsworthy discovery. Apparently mathematicians would not agree but even so, should they dictate that I should be dismissive of this article as well? The way I see it, the article does not make outrageous or unfounded claims. I'm free to appreciate that numbers have a certain universality as an abstract concept or language that isolated people from different era and backgrounds naturally converge to.
- EddieSpeaks 9y agoThe article says "Arabic digits", They're not Arabic digits, they're Indian. The arabs just borrowed it when they started trading with us.
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- erpellan 9y agoThis reminds me of the story of ancient Ethiopians using binary maths. I read about it a while back and finally managed to track it down (the original link seems dead): https://web.archive.org/web/20170609082700/http://www.uh.edu/engines/epi504.htm https://web.archive.org/web/20170609082700/http://www.uh.edu...
- netcan 9y agoThe Polynesian history of the (european) middle ages keeps getting more interesting and mysterious. Evidence for polynesian contact with the Americas is mounting. Regardless, the medieval coonization of all the pacific islands is evidence of seamanship and navigation skills European mariners didn't achieve until well into the age of sail. European sailing was much more trade/cargo oriented & we know a lot less about "pre-contact" polynesian maritime cultre so it's hard to do put the technologies side-by-side. That said, it looks the polynesian ability to aim for and land on small remote islands circa 300CE was not surpassed by any other culture until the 18th century. Then there's the strange case of Easter Island with it's giant stone statues. Giant stone statues & "how-the-f%£$-did-they-do-this" megalithic monuments have existed for a long time (EG the sphinx), but these are usually produced by populous civic cultures. "High civilization" to use an out of date term. For a tiny island to produce this kind of an artistic culture without obvious predecessors or descendants is strange. As always in prehistory (in the literal, "before written records" sense), what we know is very little. But, it wouldn't be hard for me to believe that surprising numerical or mathematical systems existed there. It's a culture that has surprised us to the point of disbelief several times.
- openasocket 9y agoI'm having trouble imagining a society with mathematics (beyond just counting) but not writing. Are there other known examples?
- panglott 9y agoThose don't seem related to me at all. Quipu was an Incan record-keeping system that we don't understand well. Abaci are very ancient calculation devices that don't use writing. The oldest Mesopotamian and Roman versions were just a table with pebbles on it. And that's where we get the word for "calculate".
- openasocket 9y agoThey aren't required, it's certainly possible to have a number system and not a writing system. But for anything where you need to do non-trivial arithmetic or accounting you can't just do all that in your head and memorize the results. You need some way of recording the results in a persistent way, even if it's just tallies carved into a piece of wood. And I imagine any culture that figures out a recording system for numbers would pretty quickly (in historical terms, so like years or decades) develop a writing system. I could be wrong of course, I haven't really formally studied ancient history. Aside: Is Quipu not a writing system? I thought there was some evidence indicating it was.
- Eire_Banshee 9y agoMeh. Ancient babylonians used a base-16 number system. Does it really matter what number system they used?
- spraak 9y agoUm... apparently not to you but to many of the readers here (as we can roughly guess by the upvotes) it does matter.
- jloughry 9y agoRoger Bacon wrote about binary notation in the 13th century, although he called bits `fingers'. John Wilkins credited Bacon in his book Mercury, or the Silent and Swift Messenger published in 1641. Wilkins' book is basically a tutorial on communications security (COMSEC) that touches on channel coding, reliability, secrecy, key management, cryptanalysis, OPSEC, and data compression. ETA: Wilkins takes a clear position on the full disclosure debate but cautions of the hazard of experimenting with crypto technologies: `...the chiefe experiments are of such nature, that they cannot be frequently practised, without just cause of suspicion, when it is in the Magistrates power to prevent them.'