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Mangareva - Binary System

Remote Islanders Invented Binary Number System Before Famed Mathematician

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Mangareva is home to just 2,000 inhabitants. The island is a tiny 18 square kilometres (6.94 sq mi) 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.  

Uncovering Mangarevan Mathematics: A Cognitive Perspective 

Research conducted and published in the journal Proceedings of the National Academy of Sciences in 2013, 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: (Public Domain)

"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

Early Binary Systems: Mangarevan vs. Leibniz's Contributions 

One of the most famous mathematicians of the 17th 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. 

Portrait of Gottfried Willhelm Leibniz. (Public Domain) 

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. 

Top image: Aerial View of Mangareva (Gambier Islands), French PolynesiaSource: FRED/CC BY-SA 3.0 

By Joanna Gillan  




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.

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 couldn't agree more ! Very well put !

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

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.

Frequently Asked Questions

Mangareva is part of the Gambier Islands in French Polynesia. It was settled around the 9th century AD by Polynesians. In the 19th century, it became a center for Catholic missionaries. Today, it's known for its historical sites, including ancient stone temples and churches built during the missionary period. 

Evidence suggests that long-distance trade involving Mangareva dates back several centuries before European contact. Archaeological findings indicate that the Mangarevans were part of a widespread Polynesian trade network, with artifacts and materials from Mangareva found in other islands and vice versa. This trade network was well established by at least the 13th century, but it likely has even earlier origins, possibly dating back to the initial settlement of the islands around the 9th century AD. 

The binary number system was invented independently by various cultures throughout history. However, the most famous early proponent of the binary system was the German mathematician Gottfried Wilhelm Leibniz in the 17th century. 

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April Holloway is a Co-Owner, Editor and Writer of Ancient Origins. For privacy reasons, she has previously written on Ancient Origins under the pen name April Holloway, but is now choosing to use her real name, Joanna Gillan.

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