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. 2014 Jan 28;111(4):1322-7.
doi: 10.1073/pnas.1309160110. Epub 2013 Dec 16.

Mangarevan invention of binary steps for easier calculation

Andrea Bender  1 , Sieghard Beller
Affiliations

Mangarevan invention of binary steps for easier calculation

Andrea Bender et al. Proc Natl Acad Sci U S A. .

Abstract

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.

Keywords: binary numeration systems; cognitive tools; cultural representations; mathematical cognition; mental arithmetic.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Two of Leibniz’s examples for binary notation and calculation (1).
Fig. 2.
Fig. 2.
Mangareva and some of its trading relations.
Fig. 3.
Fig. 3.
Calculating 70 + 50 (= TPK + TK) by joining, sorting, and regrouping of terms.
See this image and copyright information in PMC

Comment in

  • Cultural evolution and the way we count.
    Bell AV. Bell AV. Proc Natl Acad Sci U S A. 2014 Jan 28;111(4):1227-8. doi: 10.1073/pnas.1322267111. Epub 2014 Jan 7. Proc Natl Acad Sci U S A. 2014. PMID: 24398518 Free PMC article. No abstract available.

References

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