Empirical mathematics in Australian Indigenous Smoke Telegraphy

Mathematics curriculums at most universities tend to perpetuate a belief that higher mathematics is historically and culturally European. First Nations and minority students may not see their identities and cultures reflected in the discipline, yet university mathematics educators are keen to diversify and broaden the appeal of their courses. This article presents an investigation on the mathematics of smoke telegraphy, as a contribution to inlaying cross-cultural mathematical heritage in the curriculum. Across Indigenous societies of Australia the technology and practice of smoke telegraphy was developed to a sophisticated level over millennia to fill a need for long-distance communications. Through an original bibliographic and archival analysis, we show that smoke signalling and telegraphy used empirical mathematics of symmetries, frequency coding, and understanding of fluid dynamics. We juxtapose this applied mathematical knowledge, within context, against the timeline of Western understanding and development of these strands of mathematics.