The rise of complex mathematical systems is seen as one of the hallmarks of civilization, if not the pinnacle of human rationality, and yet, we haven’t really understood how our innate ability to appreciate quantity, something we share with other species, yields concepts of discrete quantity, counting sequences, and simple arithmetic. Human societies vary in the degree to which their number systems become elaborated—the Western tradition has become highly complex, while some of the systems of South America, Australia, and Africa contain relatively few numbers. In the 18th century, this phenomenon was seen as a difference between “abstract” and “concrete” thinking. Even today, such preconceptions linger. They include the two systems compared for the project: the numbers of Mesopotamia, the land between the Tigris and Euphrates, and the numbers of Oceania, the region encompassing Polynesia, Micronesia, Melanesia, Papua New Guinea, and Australia. Many of these count different types of objects with object-specific numbers, misunderstood as concrete thinking.
As a cognitive archaeologist, I am interested the artifacts and behaviors used in counting, as they influence how societies organize and structure their numbers and attest to how these things were done in the past. I want to understand how artifacts and behaviors interact with the number sense and language to produce the kinds of number systems found today. I am particularly interested in how artifacts influence societal-level change in behaviors and brains to produce numeracy and literacy. Accordingly, my goals were to provide insight into our human cognitive characteristics and capabilities over the last 50,000 years and challenge historical prejudices in cross-cultural comparisons.
During the project, I gathered numerical, linguistic, geographic, temporal, and cultural data on Oceanian number systems and compared them to a similar dataset on Ancient Near Eastern numbers compiled during my earlier doctoral work. The comparison allowed me to reconstruct traditional Oceanian counting methods from ethnographic observations, experimental recreations, and algorithm formulation and analyses. The reconstruction explained numerical structure and language throughout Polynesia and solved two mysteries of several centuries’ duration: what was meant when the New Zealand indigenes were described as “counting by elevens” and why the Hawaiian word for twenty means nine and two.
Insights into why and how counting creates object-specific numbers, in turn, let me reinterpret Mesopotamian numbers, a finding presently undergoing peer review that will significantly alter how ancient numeracy is viewed. It will help dispel the outdated idea these numbers were “concrete” and highlight the importance of material forms and behaviors in counting, countering the assumption that numbers are solely mental or linguistic constructs.
