Misconceptions about Aboriginal cultures and their access to an understanding – and use – of mathematical concepts have had a powerful and enduring impact on beliefs about their level of sophistication. One widely held belief is that Aboriginal cultures had very limited language references to numbers, being associated with a belief that ‘numbers’ are essential for measuring and assessing things (mathematics tasks) this combination has created a perception that these cultures are, therefore primitive and ignorant of facts known to ‘more sophisticated’ cultures.
Were this to be a fact rather than merely a belief, much that is known about the achievements of Aboriginal cultural principles and practices – in regard to living with, and managing, the diversity of environments across the Australian continent – could not have been possible.
In other words perceptions of the ways that Aboriginal cultures built shelters, harvested food stuffs and travelled extensively (to name a few achievements) are seriously hobbled by mistaken beliefs, cultural misperceptions and misunderstandings about what was being observed and recorded by early Europeans.
Two recent books on the history of the development of mathematical concepts provide good examples of how the issue of ‘Aboriginal maths’ is treated in general texts about the present understanding of mathematical knowledge. Both books focus almost entirely on the development of Western/European concepts, giving less attention to knowledge from other cultures and even less to the practical uses and applications of maths. While this is an entirely reasonable approach, given their stated intentions as authors. However each addresses, in quite different ways, the state of current awareness of maths in cultural and social contexts beyond those addressed in their books.
Flaws and Inaccuracies
In his book on ‘From O to Infinity in 26 Centuries – the extraordinary story of Maths‘, Chris Waring (Michael O’Mara Books UK, 2012) displays a seriously flawed and limited understanding of the nature of Aboriginal occupation of this continent. He indicates no awareness of the complexity and diversity of cultures, differences among national identities as indicated by (for example) language differences, and dismisses their practical capabilities as evidenced a toss the landscape, when he writes that
Australian Aboriginal tribes were living in a hunter-gatherer society when they were first encountered during the eighteenth century. The tribes that possessed a concept of numbers generally had words for one, two and sometimes three. Any numbers larger than three they made by adding together a combination of the first three numbers. So a tribe with the numbers one, two, three would have been able to count to nine by saying one, two, three, three-one, three-two, three-three. The fact that these people had no word for numbers larger that three suggests that they very rarely, if ever, needed to use them.
So much is open to challenge in this bald assertion (no referencing is supplied) that two items will suffice to demonstrate its errors, and illustrate the damage to perceptions about Aboriginal culture, made by such an ill chosen set of words. First, there is no suggestion that the ‘tribes’ might differ greatly across the continent, implying that ‘these people’ were therefore all so similar that a single assertion about a ‘lack of need for numbers’ applied to all without differentiation. If this perspective were to be applied in reverse we can imagine that Dutch, Portuguese and English visitors to ‘Terra Australis’ from the 1600’s onwards were all regarded as members of ‘one tribe’ and whatever characteristics were ascribed to one set of visitors could accurately be ascribed to them all. We can readily see what a nonsense statement this is. Yet this is what Waring implies in his dismissive clumping of all ‘these people’ as members of a single undifferentiated entity.
The second challenge raises issues of even more concern. If, as Waring suggests, Aboriginal cultures ‘very rarely, if ever, needed to use’ numbers it indicates his ignorant acceptance of misleading information about those cultures and their achievements. For example an understanding of water flow, fish spawning cycles, weather patterns and food supply and distribution are all explicitly illustrated in the extensive fish trap arrays at Brewarrina, NSW. Similarly, knowledge about load-bearing limits of building materials, tensile strengths of materials and market locations and demands are on display at the Wilgie Mai ochre mine in Western Australia, where it is estimated around 40,000 tons of ochre were produced during approximately 8.000 years of mining. Finally (for now) an in-depth knowledge of numbers is displayed at the astrological site of Wurdi Youang in Victoria, where astrophysicists have demonstrated that the only viable explanation for a highly ordered patterning of stones demonstrates understanding of the concept of the seasons as marked by the arrival of the solstice – http://www.atnf.csiro.au/research/AboriginalAstronomy/Examples/WurdiYouang.htm
Waring’s dismissal of Aboriginal maths exemplifies a ‘Western/Eurocentric’ perspective that seems unable to see things that do not fit within its view of ‘how things are’, and, moreover, writes as though things could not any other way. We can only wonder how Waring imagined that Aboriginal people lived and thrived for all that time without numbers. Or whether such a thought occurred to him at all.
Appreciating the unknowns
On the other hand Ian Stewart in his book ‘Taming the Infinite – the story of mathematics from the first numbers to chaos theory‘ (Quercus, UK 2008) has a more speculative view on the relationships between culture and maths. While his work focuses on only the last four Millenia and is confined to the northern hemisphere, he does suggest that there is room to explore those relationships and that, perhaps, this need not be done through either a Western worldview or a conventional Mathematical one, when we writes that –
Whether you like maths or not, it is hard to deny the profound effects that numbers have had on the development of human civilisation. The evolution of culture, and that of mathematics , has gone hand in hand for the last four Millenia. It would be difficult to disentangle cause and effect – I would hesitate to argue that mathematical innovation drives cultural change, or that cultural needs determine the direction of mathematical progress. But both of those statements contain a grain of truth, because mathematics and culture co-evolve.
As this project is addressing issues of Aboriginal engineering, Sttewart’s perspective on the co-evolution of maths and culture opens up possibilities for exploring Aboriginal engineering without the need for a prior acceptance of maths as a prerequisite for engineering knowledge.
In the context of widespread evidence of Aboriginal engineering knowledge throughout the Australian landscape, it is important that anyone referring to Aboriginal knowledge and use of maths does not fall into the trap of perpetuating old myths. This is an important aspect of the wider work of this project.