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Mangareva - Binary System

Remote islanders invented binary number system before famous mathematician

Mangareva is home to just 2,000 inhabitants. The island is a tiny 18 square kilometres and is located halfway between Easter Island and Tahiti. Yet on this small, remote island, the ancient inhabitants were more mathematically advanced than the rest of Europe when they invented a numerical system for trading. 

Research conducted last year and published in the journal Proceedings of the National Academy of Sciences, revealed that the indigenous people of the Polynesian Island invented a binary number system , similar to the one used by computers to calculate, centuries before Western mathematicians did. Andrea Bender, a cognitive scientist at the University of Bergen in Norway, and her colleague Sieghard Beller, were studying the Mangarevans when they noticed that the inhabitants had words for the numbers 1 to 10, but for numbers 20 to 80 they used a binary system, with separate, one-word terms for 20, 40, and 80. For really large numbers, they used powers of 10 up to at least 10 million.

The remote island of Mangareva. Source: Wikipedia

"Those were probably the numbers that were most frequent in their trading and redistribution systems," said Bender. "For that specific range, it was helpful to have these binary steps that make mental arithmetic much easier — they didn't have a writing or notational system, so they had to do everything in their mind."

One of the most famous mathematicians of the 17 th century, Gottfried Wilhelm Leibniz, is known to have invented a binary numeral system. Nowadays, binary numbers – where each position is written as a 0 or 1 – form the foundation of all modern computing systems.  But the study showed that the Manareva islanders were using a combined decimal and binary system which had died out by the mid-1400s.

 

Gottfried Willhelm Leibniz

The Mangarevans traded across long distances for items such as turtles, octopuses, coconut and breadfruit with people on the Marquesas Islands, Hawaii and the islands around Tahiti. It is believed that the binary system helped ancient people to keep track of their trading activities. What is more surprising is that they were able to use a complex number system without needing notation.

The numbering scheme may be the only known example of an extensive binary numeral system that predates Leibniz.

By April Holloway

Comments

The information is interesting, but I'd like to point out that when we give importance to the fact that it is "before" the discovery in other places, we bring a lot of problematic notions. First, that there is a one-way evolution of time, that different people from different times and places would often get to the same conclusion, as if a culture that did not develop binary numbers were inferior to this one (or to ours). As if, given time, they would build skyscrapers and rockets. We must understand that these things do not come about arbitrarily, but because of a need. If a certain culture doesn't have the need of binary numbers, it won't and that's fine in itself. There is more than one way to do architecture, art, one way to develop science or religion, or even to think of development itself.

There is a bit of a trap there, because while we also like to treasure the culture and show off its intelligence, we do so by measuring it with our rulers. It's like a racist saying "that black man is beautiful, he is not even that dark", you see my point?

Before famous mathematician? Would it happen after the famous mathematician? Or even, given that they are completely unrelated, are they really any better or worse for being chronologically more distant to us?

That sort of way of thinking is poisonous to history and anthropology. To only look at other cultures through our lenses.

So strange to read a coherent and thoughtful comment. My faith in comment reading is momentarily restored.

I couldn't agree more ! Very well put !

There's no doubt that 1500 to 1000 years ago there was a very advanced civilization in Eastern Polynesia. From those islands they reached Hawaii, New Zealand, Easter Island and possibly South America. This involved journeys of thousands of miles upon the open ocean. They would've been away for months at a time. But they always returned to populate the islands they discovered and maintain trade - at least for a time.

i don't see then how they did all their figuring in their minds. They would have developed a type of heiroglyphic writing or symbols to use first in order to put down on stone tablet or clay; with necessity being the mother of invention. Where are these artifacts ? pics ? And why Suddenly come up with and use binary ? for mere numbers 20 thru 80 ?? How do the modern Norwegians discern this as, binary ? Provide some proof, I would love to be shown wrong, but till then, I must disagree with them and this article.

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