## Polynesians May Have Invented Binary Math 170

Posted
by
samzenpus

from the original-number dept.

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."*
## There were 10 types of ancient societies (Score:5, Funny)

## Re:There were 10 types of ancient societies (Score:5, Funny)

## Re:There were 10 types of ancient societies (Score:5, Funny)

## Re: (Score:2)

Your theory is flawed. Had they developed polymorphism, surely they would have developed cars to explain it to everyone else?

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The urine from anybody else just wouldn't work as well.

## Re: (Score:2)

Polysilicates, yes.

## Re: (Score:2)

This thread wins the "Thread of the year" award.

only thing missing is that they defined their maps as polygons.

## Re: (Score:3)

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I thought they invented polynomials.

No polynomials were invented by the Bhinese.

## Re: (Score:2)

Actually, there are 10 types of people: Those who understand Arabic numerals and applied them to binary, and all the rest.

## Re:There were 10 types of ancient societies (Score:5, Funny)

Those that understand binary

Those that don't

And those that don't realize the joke is base-3.

## Re: (Score:2)

## How is this news? (Score:2, Informative)

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).

## Re:How is this news? (Score:5, Funny)

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

## Re: (Score:2)

Are you saying that nipples are not visible unless there is a significant amount of fat behind them?

## Re: (Score:2)

Are you saying that nipples are not visible unless there is a significant amount of fat behind them?

In order to use a digit for counting, you need to be able to move it. He is saying that Mayan women had articulated nipples.

## Re: (Score:2)

You sure males have only 2 testicles?

Mate, I need to talk to my doctor.

## Weak evidence indeed (Score:2)

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:

pauafor 20;tatauafor 40; andvarufor 80.The jump from there to "thus clearly they invented binary arithmetic" is speculation. They st

## Re:Weak evidence indeed (Score:4, Informative)

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.

## Re: (Score:2)

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.

## Re: (Score:3)

Transistors are just switches, and the simplest switching is between on and off. But later there were developed trinary (aka ternary) switches (off, positive, negative) but by then the binary computer was so entrenched there was no impetuous to change.

Much of that work was done in Russia. Google "Setun".

There were some BCD hardware that was (claimed to be) much better at decimal math (even if it was faking it with binary). CDC was big into this in the 70s.

## Re: (Score:2)

My impression is that this difficulty is what tends to keep greater-than-two-state components away, even from areas where they could be incorporated transparently, from the point of

## Re: (Score:2)

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.

## Re: (Score:2)

What it says is they have number words for three binary powers of ten:

pauafor 20;tatauafor 40; andvarufor 80.Which to me is clear evidence they did

notuse binary math, but base-10 or base-20.## Re: (Score:2)

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.

## Re: (Score:2)

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

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## Re: (Score:2)

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.

## "Discovered" would be more appropriate (Score:2)

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!

## Re:"Discovered" would be more appropriate (Score:5, Funny)

I'm sorry for you! If you had all of your fingers, you'd make it to 1023!

## Re:"Discovered" would be more appropriate (Score:4, Funny)

GP probably uses signed integers.

## Re:"Discovered" would be more appropriate (Score:5, Funny)

That's called thumb's-complement - still in IEEE committee, but quite handy.

## Re: (Score:3)

## Re: (Score:2)

I'm sorry for you! If you had all of your fingers, you'd make it to 1023!

Floating point will get you further, if you don't mind loosing some digits of precision.. Should work great for 4 digits at +- E16 - E-16.

## Re: (Score:2)

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## Re: (Score:3)

Not sure if one, two, many is a myth, but one to many is a database relationship.

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Either you're using a sign bit, or you are missing a finger. 10 bits gets you a range of 0-1023 or 1-1024.

## Re: (Score:1)

Lets not forget finger #11

## Re: (Score:3)

You have six fingers on your right hand.... Someone is looking for you.

## Re: (Score:2)

If you are holding a 6th finger in your right hand, the left hand must be taking the selfie.

## Re: (Score:2)

Maybe he has limp digits, and needs one as a parity bit . . . ?

## Re:"Discovered" would be more appropriate (Score:5, Funny)

So you are always negative when good looking women are around..... Sorry for you.

## Re: (Score:2)

3 3/4 barrels of beer to the freeholder? That'll be 1 puncheon, 1 barrel, 1 kilderkin, and 1 pin. Other binary scaling can be seen in gills, cups, pints, quarts, gallons, pecks, bushels, etc...

## Professor Farnsworth Says... (Score:2)

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!

## FTFA (Score:1)

But their special counting words are all decimal numbers multiplied by powers of two, which are 1, 2, 4, 8 . Specifically,

takauequals 10;pauaequals 20;tataua, 40; andvaru, 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 Islandjoke in here somewhere...## Sounds like they're trying to hard (Score:1)

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.

## Re: (Score:2)

## Re: (Score:2)

## What's with this "may"? (Score:5, Insightful)

## Re: (Score:3)

## Re: (Score:2)

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

## Re: (Score:2)

"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.

## Language (Score:3)

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

## Re: (Score:2)

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.

## Re: (Score:2)

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

## Re: (Score:2)

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

## Re: (Score:2)

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

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## Re: (Score:2)

Uncertain information, that's what's with it. Next question?

How many slashdotters does it take to spot a thinly-veilled binary gag?

## Re: (Score:2)

## Re: (Score:2)

Because they don't know? LOL.

## Re: (Score:2)

"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.

## Re: (Score:2)

The word "may" indicates uncertainty in this case.

## bool (Score:2)

bool"s instead of "leib"s?## Re: (Score:2)

George Boole. He invented the formal mathematical system of boolean logic.

## Re: (Score:2)

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## Poly? (Score:4, Funny)

Wouldn't that be "

Binesians"?## Re: (Score:2)

Right. And the Micronesians invented fractions.

## Re: (Score:2)

They're "Some O 1 s"

## If only we had eight fingers (Score:2)

## Binary is much older than Leibniz... (Score:5, Informative)

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

## "Ethiopian" or "Egyprian" multiplication (Score:2, Interesting)

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

## The Chinese (of course) (Score:5, Interesting)

## Re: (Score:2)

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.

## Re: (Score:2)

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)

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

## Re: (Score:2)

They are paid and clear; all that gold and treasure at the Vatican.

## Europeans used binary before Liebniz or Polynesia (Score:3, Interesting)

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

## Re: (Score:2)

2 cups = 1 pintOr, 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.

## Binary - A Number System With Only Two Digits (Score:5, Insightful)

So, decades of stories containing obscure acronyms deemed unworthy of explanation, now the editors decide

binaryneeds to be defined for the Slashdot audience.## Re: (Score:3)

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]).

## How fitting (Score:2)

## That would be cool! (Score:2)

## co-inventor? (Score:2)

## Re: (Score:2)

Yeah, but slightly later right? That pattern seems to happen a lot in science.

## Re: (Score:2)

exactsame time.## Humpf...so what? (Score:2)

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

## Polynesians DIDN'T invent binary (Score:2)

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

## twoness versus binary (Score:2)

## They were two millenia late to the party. (Score:2)

## Re: (Score:1)

Or how about Base 13 just to fsck with people and make math teachers rich. It would also make QWERTY look sane in comparison.

## Re: (Score:2)

## Re: (Score:2)

Decimals have nothing to do with it.

Base 12 is incredibly convenient for breaking up one thing into several parts in many ways. A dozen divided in half gives six each. Into thirds gives 4 each. Into fourths gives 3 each. Into sixths gives 2 each.

Easy.

But anyway, even duodecimal is somewhat easier than decimal, too.

Base 10

1/2 = 0.5

1/3 = 0.3333...

1/4 = 0.25

1/5 = 0.2

1/6 = 0.1666...

1/7 = 0.142857...

1/8 = 0.125

1/9 = 0.1111...

Base 12 (using A for 10 and B for 11)

1/2 = 0.6

1/3 = 0.4

1/4 = 0.3

1/5 = 0.2497...

1/6 = 0.2

## Re: (Score:2)

If

bandnare integers,n < bandb%n != 0, then1/ncan't be written exact in base-b.Have fun proving that...

Yeah that's going to be great fun...

n=4; b=10

4 10 - check.

10 % 4 != 0 - check (2 != 0)

1/4 = 0.25 in base-10 which is exact.

Provings things which aren't true is always fun.

## Re: (Score:2)

There is NOTHING inherently special in binary, base10

Oh but there is. Count your fingers. People normally have 10 fingers, so base 10 is how language defined the basic numbers. Once we started writing things down, place value creeps in and we have the decimal system.

Mathematically, there is no unique reason to use base 10 except that one has to invent new digits when you go above 9 (OK above F for you Hex types). Binary, Octal and Hex are all used for convenience because the devices we have use multiples of 4 bits (usually). We used base 10 when all we ha

## Re: (Score:2)

"Invented?"

Biscovered.