Base-2 system helped to simplify calculations centuries before Europeans rediscovered it.
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. A recent study shows 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.
Cognitive scientist Rafael Nuñez at the University of California, San Diego, points out that the idea of binary systems is actually older than Mangarevan culture. “It can be traced back to at least ancient China, around the 9th century bc”, he says, and it can be found in the I Ching, a millennia-old Chinese text that inspired Leibniz. Nuñez adds that “other ancient groups, such as the Maya, used sophisticated combinations of binary and decimal systems to keep track of time and astronomical phenomena. Thus, the cognitive advantages underlying the Mangarevan counting system may not be unique.”
All the same, say Bender and Beller, a ‘mixed’ system such as this is not easy, nor an obvious set-up to create. “It’s puzzling that anybody would come up with such a solution, especially on a tiny island with a small population,” Bender and Beller say. But they add: “This very fact also demonstrates just how important culture is for the development of numerical cognition — for example, how in this case dealing with big numbers can motivate inventive solutions.”
Nuñez agrees; he adds that the study shows “the primacy of cultural factors underlying the invention of number systems, and the diversity in human numerical cognition”.
Bender, A. & Beller, S. Proc. Natl Acad. Sci. USA http://dx.doi.org/10.1073/pnas.1309160110(2013).