title: Mangarevan invention of binary steps for easier calculation.
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.
authors.affiliation: Department of Psychosocial Science, University of Bergen, N-5020 Bergen, Norway.
authors.forename: Andrea
authors.initials: A
authors.lastname: Bender
authors.forename: Sieghard
authors.initials: S
authors.lastname: Beller
keywords: binary numeration systems; cognitive tools; cultural representations; mathematical cognition; mental arithmetic