Flat White

The Oldest Culture: Mathematics

15 July 2021

5:32 PM

15 July 2021

5:32 PM

A series of articles examining Dark Emu-style claims.

The study of mathematics has been in the news lately, with great concern being expressed by professional mathematicians over the new mathematics curriculum being proposed by the Australian Curriculum Assessment and Reporting Authority.  Most of the concern being expressed relates to the subjugation of basic mathematical fundamentals by a regime of ‘problem-solving’.  However, there is also concern over the intrusion of ‘cross-cultural priorities’ (notably indigenous ones) into the course content. 

These days we hear a lot about what a sophisticated society the pre-colonial Aboriginal people enjoyed and how, in many fields, they were the world’s first practitioners.  This meme is part of a wider narrative that Bruce Pascoe borrows from in his book Dark Emu. 

Pascoe is wont to claim a lot of ‘firsts’ for Aboriginal society – the first loaf of bread, the invention of democracy, the first engineered fisheries in the world. But he is not alone. We hear these claims repeatedly and they spring from the idea that Aboriginal culture is the oldest in the world.  As critics of Dark Emu emerge from the woodwork (claiming that they knew all along it was rubbish) now that it has been thoroughly discredited, the main criticism they level at Pascoe is not that he cynically and shamelessly corrupted his sources but that he demeaned Aboriginal society by suggesting that their traditional hunter/gatherer lifestyle was inferior to the European agricultural model.    

I wonder if they appreciate the irony that these claims of Aboriginal exceptionalism are equally demeaning to Aboriginal people in that they are so deeply patronising.  Recently I have been presenting a series of short articles, extracted from my book Bitter Harvest, which examine some of these claims. 

On Monday we began with Aboriginal astronomy. Today we take a look at Indigenous mathematics. 

Professor Chris Matthews, Chair of the Aboriginal and Torres Strait Islander Mathematics Alliance and also a member of ACARA, tells us: 

Indigenous cultures, for over 40,000 years, have developed deep philosophies and knowledges about the world. These philosophies categorise the world – people, animals, plants, land – into two groups called moieties.

The two moieties exist so that all things can be kept in balance, that is, one moiety cannot out number the other or be considered more important than the other. From these moieties, there are numerous sub-categories that are placed in a relational space to create an order and a structure. 

After being immersed in the western education system, I am only starting my education in our Indigenous philosophies and knowledges. However, from the outset, I immediately saw its mathematical nature and how it can be applied to teaching mathematics.

For example, numbers are either positive or negative and, in a sense, have their own moiety. Similarly, the operations (+, −, ×, ÷) sit in this binary relationship in the notion of ‘joining’ and ‘separating’. Each of these mathematical concepts allows us to define relationships and keep them in balance. The order and structure that are created from such mathematical relationships is encapsulated in algebra. It is no surprise then that Indigenous people of Australia have language for number and have base-five number systems.

Much of the last paragraph is just ‘feel good’ rhetoric. I would contend that the concept of moiety (which has its most useful application in the avoidance of inbreeding within small kinship groups) springs, not from some philosophical grasp of mathematical principles, but from the fact that nature is dominated by observable pairs: we have two sexes, two hands, day and night, sun and moon, wet season and dry season, and so on. Aborigines did have numbering systems of varying complexity and could count more competently than many anthropologists have given them credit for, but as to them having base-five number systems, that is something of an overreach.

There is evidence that the Yolngu people of East Arnhem Land had such a system but since this was first demonstrated by Galarrwuy Yunupingu to V.C. Sobek in 1981, there is some doubt as to whether or not it is a recent invention of Yunupingu, rather than a long-standing tradition. Even if it were traditional to the Yolngu, there is little evidence it even existed elsewhere. The fact is that the highest mathematical achievement of Aboriginal culture was counting. So it is hard to see how incorporating Aboriginal mathematical concepts in our teaching advances us very far. 

Matthews also contends: 

A common perception is that mathematics, as well as science, is objective (i.e. culture and value free). Objectivity is often seen as the foundation of mathematics and science because it is believed that it leads to absolute facts and truths. However, I would contend that all knowledge systems are bound by culture, including mathematics, and once its subjectivity is embraced there is a much richer, diverse knowledge system to engage with and understand.

I would also argue that embracing the diversity of mathematics will lead to an education that provides a much deeper understanding and allows students to personally connect with the subject area.  

Read that again, just to make sure you read it right.  Matthews is an indigenous man from Stradbroke Island and holds a PhD in mathematics. As a representative of his ‘people’, his view on mathematics and science probably explains why the pace of Aboriginal technological advancement prior to 1788 was so glacial. Science advances by divorcing itself from culture. One example? The longevity of the geocentric model of the universe was due in large part to the fact that theologians strongly resisted the idea that the Earth was not at the centre of the universe. Contrary to Mathews’ assertion, objectivity is not ‘often seen as the foundation of mathematics and science’. It is the foundation of mathematics and science. 

Matthews laments that many kids are not inclined to study mathematics because they can’t see its relevance in their lives beyond the most rudimentary needs. For those with the aptitude to study mathematics at a tertiary level, its main attraction is its inherent beauty. They love it for its own sake or because they see its application in their chosen career.  

If we regard ‘culture’ as a teaching aid to assist indigenous students in understanding mathematics, that is one thing. But embedding it as a fundamental part of the discipline is to continue down the path that has seen our education rankings plummet in comparison to the rest of the world. It is not the function of our education system – certainly not the STEM faculties, at any rate – to make Aboriginal people feel good about themselves. 

Whether the various education ministers at the federal and state level – and New South Wales Education Minister Sarah Mitchell, I am thinking particularly of you when I make the following observation – are prepared to stand up against this ACARA nonsense remains to be seen, but if their track record on transgender issues, or Bruce Pascoe’s fraudulent ‘history’ for that matter, are anything to go by, it will be a cold day in hell before we see the likes of Dr Matthews and his ilk sidelined.   

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