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Empirical mathematics in Australian Indigenous Smoke Telegraphy

Rowena Ball

Abstract

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.

Empirical mathematics in Australian Indigenous Smoke Telegraphy

Abstract

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.

Paper Structure

This paper contains 12 sections, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Overview of article:
  3. What is smoke telegraphy?
  4. Results
  5. Discussion
  6. Systems, networks, and graphs
  7. Codes, encryption, and secrecy
  8. Symmetry, chirality and fluid dynamics
  9. The frequency domain and the Fourier transform
  10. Who were the smoke telegraphers?
  11. Continuity and vitality of smoke knowledge
  12. Conclusions

Figures (2)

  • Figure 1: The vortical nature and natural structure-forming capabilities of smoke flows are evident in this pastiche of stills from several experimental home movies.
  • Figure 2: Geometry of smoke streams in terms of pasta (ever a cheap and tasty mathematical prop Hildebrand:2010). (a) The fusilli shape on the left of the plate is analogous to a primary vortex stream and the cavatappi shape on the right of the plate is analogous to the secondary smoke spirals. (b) The chiral asymmetry property is apparent in the mirror image of the plate of pasta---the shapes are non-superimposable on their enantiomorphs in (a).