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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!
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.
Wouldn't that be "Binesians"?
Table-ized A.I.
Leibniz freely admits that he took ideas from the I Ching: http://www.leibniz-translations.com/binary.htm
This uses binary math, though not quite explicitly: http://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication
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)
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.
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. 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.
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So, decades of stories containing obscure acronyms deemed unworthy of explanation, now the editors decide binary needs to be defined for the Slashdot audience.
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.
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