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Polynesians May Have Invented Binary Math
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."
Those who understood binary, and those who didn't.
Science advances one funeral at a time- Max Planck
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).
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!
An enigma, wrapped in a riddle, shrouded in bacon and cheese
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...
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.
Either they did or they didn't.
If God forks the Universe every time you roll a die, he'd better have a damned good memory.
So many easy divisors.
Why are variables called "bool"s instead of "leib"s?
Wouldn't that be "Binesians"?
Table-ized A.I.
I always thought that mathematics would have progressed much faster if humans had either four or eight fingers on each hand instead of five.
Leibniz freely admits that he took ideas from the I Ching: http://www.leibniz-translations.com/binary.htm
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 state that none of the islanders use binary arithmetic now, and there's no record they once did-- just those words for binary-multiples-of-ten.
Of course a gentleman in the 18th century wasn't the first to use binary.... that's preposterous.
I don't know what is "of course" about that statement. There doesn't seem to be any evidence of anybody using binary before then. Maybe somebody did, but it seen they didn't tell anybody.
http://www.geoffreylandis.com
This uses binary math, though not quite explicitly: http://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication
Why is it that people who are actually terrible at understanding the basics of maths think that because they express an interest, they are some kind of mathematical genius.
There is NOTHING inherently special in binary, base10 or whatever. What ***IS*** special is the realisation of using ANY form of number-base system to handle calculations. The same garbage about a particular base choice being 'magic' led the French morons experimenting with so-called decimal systems for times and dates- fundamentally ignoring why we have 12 hours to a half-day, and 60 minutes to an hour (here's a clue- how many ways can you divided these numbers, and get whole number results?).
Base2 is the WORST possible base choice for a general counting and calculation system for people. Morons dribble "it's used in 'computing' so it must be clever". As soon as base arithmetic was invented, mathematicians KNEW about base2 as a special case of base-n. How can people here be so thick they do not get this? Was high-school maths really this hard for you to understand.
Knowing you can use base2 (binary) is NOT having a practical reason to deploy base2. Only when binary state computing was developed did the use of Base2 (or base8, or base16) make sense. Any society using base2 in a pre-computer age can be labelled as seriously retarded.
AGAIN. All base arithmetic follows the same principles. Therefore an awareness of base-x, where x is a specific integer, gives awareness of any base-n, where n is any positive integer greater or equal to 2.
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.
Development is programmable; Discovery is not programmable. (Fuller)
"Invented?"
Because when you only have one digit left ... yes, ONE!
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
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
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 special words for 0b0001, 0b0010, 0b0100 and 0b1000.
The thing that doesn't make much sense to me is why they would have multiplied their binary digits by decimal 10. Instead of special words for 1, 2, 4 and 8 they have special words for 10, 20, 40 and 80, and that doesn't make any sense mathematically. Unless originally they used binary and had special words for 1, 2, 4 and 8, then gradually adopted decimal. The special words for such small numbers wouldn't have been useful, so the meaning switched to indicate 10 times that value. 10, 20, 40 and 80 would be useful quantities to have special words for when it comes to trading, buying and selling, and even talking about a person's age.
Either way, it sure seems to hint that they used binary math at some point in the past.
Better known as 318230.
Did they "invent" it or "become aware of" binary math?
God wills it, save the queen!
So, decades of stories containing obscure acronyms deemed unworthy of explanation, now the editors decide binary needs to be defined for the Slashdot audience.
Without electricity or plumbing, binary is just a waste of numerals.
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.
That's not binary, it's BCD.
#naabhaprzrag, #sverubfr-000, #agi-fcbafberq, negvpyr[pynff*=' negvpyr-ary-'] { qvfcynl: abar !vzcbegnag; }
One of the researchers describing the Polynesian binary system is named Bender.
Contribute to civilization: ari.aynrand.org/donate
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.
sic transit gloria mundi
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 anyone ever did base-12 or base-60 arithmetic.
Another sociologist looking for a quick paper to boost the all-important publication count.
Enjoy life! This is not a dress rehearsal.
I once read us average Polynesian islander males worked less than five hours a week while the average European male works over 80 hours per week between work and work at home including shopping. We are superior to you Europeans by a factor of 16.
Link to the website of the game, which was made by the group for computer-oriented theretical physics at the university of Oldenburg:
http://www.compphys.uni-oldenburg.de/61306.html
Philipp
That it's at least 1,000,000,000 years old.
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.
SJW n. One who posts facts.
http://www.nature.com/news/polynesian-people-used-binary-numbers-600-years-ago-1.14380
>>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 Maya, used sophisticated combinations of binary and decimal systems to keep track of time and astronomical phenomena. Thus, the cognitive advantages underlying the Mangarevan counting system may not be unique.”
Leibniz can't get a break, can he? First that rat bastard Newton climbs up on the shoulders of giants and steals his thunder on the discovery of Calculus, and now the Polynesians come along and claim the invention of binary math for themselves!
They "may have" traveled to other galaxies and used telepathy, too. If you use weasel words you can say anything.
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.
2 cups = 1 girl
It's really not that remarkable that my ancesters invented binary...to this day, we can only count to 1.
that a-rabs invented numbers
actually its girl(s) not gill(s)
It's still Binary, with the addition of SQL-like NULLS.
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.