Wednesday, December 18, 2013

Polynesians May Have Invented Binary Math

Powers of two. The people of Mangareva may have invented binary arithmetic independently of the West.

Powers of two. The people of Mangareva may have invented binary arithmetic independently of the West.

How old is the binary number system? Perhaps far older than the invention of computers or even 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.

If you’re reading this article, you are almost certainly a user of the decimal system. That system is also known as base-10 because of its repeating pattern of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is followed by 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and so forth. But the decimal system is not the only counting system available. The Babylonians used base-60. The Mayas used base-20. Some Australian aboriginal groups may have used base-5. And of course, today most counting and calculation is done by computers not in decimal but binary, the base-2 system of zeros and ones.

Each system has subtle advantages depending on what sort of counting and calculations are needed. The decimal system is handy considering that people have 10 fingers. But when it comes to division, other systems are better. Because 10 has only two prime factors (2 and 5), dividing by thirds results in an annoyingly infinite approximation (0.3333 … ) whereas the base-12 counting system produces a nice finite solution. (Indeed, some mathematicians have advocated for a worldwide switch to base-12.) Binary, meanwhile, has a leg up on decimal when it comes to calculation, as Leibniz discovered 300 years ago. For example, although numbers in binary become much longer, multiplying them is easier because the only basic facts one must remember are 1 x 1 = 1 and 0 x 0= 1 x 0 = 0 x 1 = 0.

For the rest of the story: http://news.sciencemag.org/archaeology/2013/12/polynesians-may-have-invented-binary-math

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