May 15 2026 Seminar – by Rowena Ball
Title: Empirical mathematics in Australian Indigenous Smoke Telegraphy
Link: Preprint at https://arxiv.org/abs/2603.26037
Link: Recording of seminar
Link: Slides
Key words: Undergraduate mathematics, Indigenous mathematics, Smoke telegraphy
This study is part of a research and teaching program that I lead at ANU on mathematical knowledge of non-Western and Indigenous societies. All societies that we know of developed, communicated and practised mathematics, yet it is usually assumed that Australian mathematics began in the 19th century with a colonially transplanted British-European curriculum. Documenting the rich but neglected mathematical heritage of First Nations cultures of Australia has been one of the delights of my research life.
In the seminar I described some of the mathematics inherent in smoke telegraphy, a long-distance communications technology that was developed and practised from ancient to modern times by Aboriginal and Torres Strait Islander peoples of the Australian continent and islands. I juxtaposed aspects of that mathematics against analogous or cogent mathematical developments in European mathematics.
The research is based on numerous archival primary sources from the 19th century and early 20th century. White colonial society was absolutely fascinated with smoke telegraphy, because it was used to track white explorers and travellers with high precision, the codes were kept secret by the Aboriginal master signallers (and are classified knowledge to this day), and across much of the continent it was a more effective system than electrical telegraphy until well into the 20th century. The research also draws on several precious pre-colonial sources from the mid to late 1600s and from 1770.
Mathematical perception and know-how were intrinsic to smoke telegraphy. Beyond attributes such as quite complicated numerical coding, I described the use of chiral symmetry (or right- and left-handedness), which was understood and actively created by Indigenous smoke signallers, the use of frequency coding of the visible signals, and empirical knowledge of fluid dynamics.
Why have we never heard of smoke telegraphy? What became of it? was a question asked. In the far north of Australia, beyond the reach of poles and wires and the broadcast range of radio transmitters, smoke signalling and telegraphy was still used until the 1940s, but knowledge of the finer points declined. It seems that the very real Japanese threat in WWII caused the military to suppress it, presumably for national security reasons. For a decade or so after the war smoke signals became infantilized as a Scout-camp exercise that some people’s grandparents might remember, but as a sophisticated long-distance communications technology smoke telegraphy seemed to disappear from white public consciousness, from newspapers and books, and from the published white colonial histories.
How old might smoke-signalling technology be? is another question. Given the long cultural continuity of Australian Indigenous societies, smoke signalling as a method of long-distance communication may well be very ancient. Smoke is, of course, a natural signal, and humans would have exploited its potential very early in history. When sea levels were 80–150 m lower during a glacial maximum approximately 65,000 years ago, smoke from natural bush fires on the exposed Sahaul (Greater Australian) shelf would have been visible from several Indonesian islands and may have stimulated the original voyages to Australia. Did those voyagers who arrived safely perhaps send up smoke telegrams to be received by family and friends whom they left behind? “Arrived safely. Land of plenty. Build more outrigger canoes. Make sails. Come soon.” Was smoke signalling technology Australia’s first export to the world? Purely speculative, but not unreasonable, questions.
Another speculative but reasonable sequitur from this study is that development of mathematical ideation in the human brain may occur at similar rates and levels in all societies, and that expression of those ideas is cultural in actuation but always serves a social purpose. Humans are a social, mathematical species.
Australian Indigenous smoke telegraphy was a remarkable achievement on its own terms.
All the evidence supports that, prior to the roll-out of electrical telegraphy, it was the
most highly advanced, most effective, long-distance telecommunications technology in
the world. It also affirms the cultural universality of mathematics.
The materials and results of this study may be included in a cultural and historical introduction to first and second year tertiary mathematics and physical science courses where topics such as symmetries, groups, and the Fourier transform are studied. The systems properties of smoke telegraphy may inspire modelling and simulation problems to be set up and analyzed with modern mathematical, computational and machine learning tools. For Indigenous and minority students this study provides affirmation that mathematics is a valued part of their cultural heritage and identity and that Indigenous mathematical knowledge is rich and strong.
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