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Mangarevan invention of binary steps for easier calculation.

Andrea Bender¹, Sieghard Beller

¹Department of Psychosocial Science, University of Bergen, N-5020 Bergen, Norway.

Proceedings of the National Academy of Sciences of the United States of America

|December 18, 2013

Summary

The Mangarevan number system uniquely combined binary steps with a decimal structure, facilitating arithmetic. This ancient system demonstrates advanced numerical cognition independent of written notation, highlighting cultural influences on mathematics.

Keywords:

binary numeration systems cognitive tools cultural representations mathematical cognition mental arithmetic

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Area of Science:

Cognitive Science
Anthropology
History of Mathematics

Background:

Gottfried Wilhelm Leibniz described the advantages of the binary system for computation in 1703.
The suitability of binary systems for human cognition remains an area of interest.
Traditional number systems offer insights into diverse cognitive approaches to mathematics.

Purpose of the Study:

To analyze the structure and function of the Mangarevan number system.
To investigate how this system facilitated arithmetic operations.
To understand the uniqueness of the Mangarevan approach to numeracy and its implications for cognitive diversity.

Main Methods:

Analysis of the superimposed binary steps within the Mangarevan decimal structure.
Examination of historical and anthropological data on Mangarevan arithmetic practices.
Comparative study with Leibniz's formal description of binary computation.

Main Results:

The Mangarevan system utilized three binary steps integrated into a decimal framework.
This unique structure simplified and enhanced arithmetic calculations for the Mangarevan people.
The system's development predates Leibniz's formalization of binary computation by centuries.

Conclusions:

The Mangarevan number system represents an independent invention of binary principles applied to cognition.
This demonstrates significant advancements in numeracy achievable without formal notation.
Cultural factors play a crucial role in shaping the evolution and diversity of numerical cognition.