%0 Journal Article
%A Bender, Andrea
%A Beller, Sieghard
%T Mangarevan invention of binary steps for easier calculation
%D 2013
%R 10.1073/pnas.1309160110
%J Proceedings of the National Academy of Sciences
%X The paper describes the mixed counting system in Mangarevan, which is unique in that it had three binary steps superposed onto a decimal structure. In showing how these steps affect calculation, our analysis yields important insights for theorizing on numerical cognition: counting systems serve as complex cultural tools for numerical cognition, apparently unwieldy systems may in fact be cognitively advantageous, and such advantageous systems can be—and have been—developed by nonindustrialized societies and in the absence of notational systems. These insights also help to dismiss simple notions of cultural complexity as a homogenous state and emphasize that investigating cultural diversity is not merely an optional extra, but a must.When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition.
%U http://www.pnas.org/content/pnas/early/2013/12/12/1309160110.full.pdf