Scientific Method / Science & Exploration

Polynesians may have beat computers to using binary

A mixed binary/decimal system may have made some calculations easier.

The decimal system of counting is part of our language, math, and the measurement units used by all right-thinking nations. It's so deeply engrained in how we operate that it's often difficult to imagine using anything else. However, it's mostly a historic accident, based on the number of fingers we happen to have. Although the vast majority of societies used decimal numbers, some developed systems based on five or 20 digits instead. But there were also some rare exceptions. A new paper in PNAS performs an analysis of a Polynesian culture's language, and it concludes that its speakers developed a mixed decimal/binary system. The researchers then go on to argue that the inclusion of binary made certain math operations much easier.

There are some instances of binary systems being used. For example, the paper cites a language from Papua New Guinea that only includes words for one and two. But it's not a full binary system in that there's no concept of larger digits; these are simply represented by additive combinations of the two digits (so five is expressed as "2 + 2 + 1").

In contrast, the authors argue that the indigenous people of Mangareva performed full binary calculations but layered the results on top of a decimal counting system. The trick is that there is nobody left who actually uses the Mangarevan numerical system; instead, it has to be inferred from the language and cultural background of the people.

Mangareva was settled during the Polynesian expansion. It's a small group of islands at the eastern edge of French Polynesia where things start to thin out before remote outposts like Pitcairn Island and Easter Island. Nevertheless, it was fully incorporated into the Polynesian trade network, which meant that its residents had to be able to keep track of trade goods. In addition, many of these goods (like sea turtles and fish) were used by political figures as gestures of munificence during formal feasts with their subjects. Keeping track of just how generous these gifts were was an important part of the political culture.

So counting large numbers was a critical part of the Mangarevan culture. Polynesians as a whole used a decimal system of counting, but different island groups often had distinct terms for different groupings of 10. The researchers describe the Mangarevan language's specific terms for groups of 10 and then show how these could be used as a form of binary, allowing calculations to rapidly manipulate groups of 10 to conveniently perform addition, subtraction, multiplication, and division. The system, they argue, would allow large groups of trade goods to be rapidly inventoried with a relatively small cognitive load, essential for a culture without any writing.

(To complicate matters a bit further, different types of goods were handled in batches of different numbers. For example, you always counted individual sea turtles, but fish were handled in groups of two. If you said there were 40 fish, you actually had 80. But the math was all done by counting groups of two.)

The authors were able to make all these inferences by examining the Mangarevan language, which is still spoken by roughly 1,000 people in the islands. However, the actual math system has been lost, replaced by a full decimal system introduced by French missionaries. The best we can currently do is infer that it would have been easier to handle some things in binary; we can't confirm that this was the mental process used by the Mangarevans before the arrival of Europeans.

If right, however, the Polynesians were using a binary system for a few hundred years before Leibniz introduced it to European thought around 1700. And it was still a few centuries before electronics made binary a central part of most calculations.

PNAS, 2013. DOI: 10.1073/pnas.1309160110  (About DOIs).

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