I used to think that the “decolonization” of STEM was strongest in New Zealand and South Africa, which of course is a movement to dethrone so-called “Western” science in favor of indigenous science. But now I’m beginning to wonder if the “indigenization/decolonization of science” isn’t making its way deep into Australia as well. I have followed developments in New Zealand far more closely than these other places, because I hear often from Kiwi scientists who beef about the dethroning of modern science (which hasn’t been “Western” in a while) in favor of Mātauranga Māori (MM), the “way of knowing” of the indigenous Māori people. Also, I have visited New Zealand, love the place, and would be devastated if science were watered down with superstition, myth, legend, and morality.
And that’s the first issue with “decolonizing” science. Usually those movements intend to either defenestrate modern science or at least teach “indigenous science” alongside it as an equally valid “way of knowing”. Yet indigenous science, like MM, is a grab-bag of empirical knowledge based on trial and error (the premier example is the navigation of Polynesians, the ancestors of Māori; another is how to catch eels), but is also imbued with superstitions, myths, legends, word-of-mouth tales, and “rules for living”, including morality. And rarely is indigenous science vetted with the same rigor as is modern science, because modern science has many features missing in indigenous “ways of knowing” (double-blind testing, deliberate replication, hypothesis testing, and so on). One result is that “indigenous science” can be wrong more often. One example is the insistence of some New Zealand researchers that Polynesians discovered Antarctica in the early seventh century. This is based on oral legend combined with mistranslation; in fact, the Russians were the first to glimpse the continent—in 1820.
Now trial and error methods can indeed produce empirical knowledge in the sense of “justified true belief”, but that is practical knowledge, designed to help people where to find things to eat, how to navigate, how to herd bison, when to plant food, and the like. Its ambit is far narrower than that of modern science, and examples of “indigenous science” that have made valuable contributions to modern science are thin on the ground.
Which brings us to the second issue with indigenous science. Although it’s touted loudly and passionately, examples of indigenous knowledge making substantial contributions to modern science are either scant or missing. Most of the written defenses of enthroning indigenous science I’ve seen are based on a need to pay attention to marginalized people as oppressed victims, whose knowledge must be elevated precisely because they were victims. But that’s no way to judge science.
And that is precisely the content of this puff piec, coming from Australian National University (ANU) in Canberra, touting the dethroning of “mainstream European-based mathematics” in favor of mathematics produced and used by “Indigenous and First Nations peoples around the world.” The article highlights Professor Rowena Ball of ANU’s College of Science, who lists these as her research interests:
Mathematics Without Borders, Truth-Telling in Mathematics History, Decolonisation of STEM, Indigenous and Non-Western Mathematics, Emergence of life, Nonlinear and complex dynamical systems, Thermochemical instabilities and oscillators, Thermodynamic analysis, Railways and trains, Country pub lunches
What is mathematics? What is included in mathematics? Who gets to say? How and why did Western mathematics exclusively colonise minds and curriculums over the whole world? Should that situation continue unabated?
It will not escape your notice if you read the piece, heavy with quotes from Dr. Ball, that she neglects the contributions of anything other than “mainstream European-based mathematics” to modern mathematics, leaving out the contributions of the Egyptians, Greeks, Arabs, Romans, and Babylonians to modern mathematics. Those people were apparently not “indigenous” and at any rate were not “colonized”. But Ball goes on and on, proffering only one tepid example of how a group of Australian aboriginals in Mithaka Country (an area of east-central Australia) had a form of mathematics that was useful. It turns out that it wasn’t mathematics at all, but practical knowledge that we wouldn’t recognize today as “math” at all.
Click the screenshot to read this short piece (h/t Peter Forsythe):
First I’ll give some of her quotes from the ANU piece (indented) and then her holotype specimen of indigenous math.
What constitutes mathematical knowledge? What is included in mathematics? Who gets to decide? These are some of the questions being asked in a growing decolonisation movement.
“Mathematics is a universal human phenomenon, and students of under-represented and minority groups and colonised peoples are starting to be more critical about accepting unquestioningly the cultural hegemony of mainstream European-based mathematics,” says Professor Rowena Ball from the ANU Mathematical Sciences Institute.
Professor Ball leads a research and teaching initiative called Mathematics Without Borders, aimed at broadening and diversifying the cultural base and content of mathematics.
“Mathematics has been gatekept by the West and defined to exclude entire cultures. Almost all mathematics that students have ever come across is European-based,” she explains. “We would like to enrich the discipline through the inclusion of cross-cultural mathematics.”
“Indigenous and First Nations peoples around the world are standing up and saying: ‘Our knowledge is just as good as anybody else’s − why can’t we teach it to our children in our schools, and in our own way?’
“And this is happening in New Zealand, North and South America, and Africa, and also in a great movement in India to revive traditional Indian mathematics.”
But wait! There’s more:
. . .“There is a lot of gatekeeping going on,” Professor Ball says of having to justify Indigenous maths. “One effect of colonisation of the curriculum is defensive protection of what is thought to be an exclusively European and British provenance of mathematics.”
“Like most mathematicians I was educated in European and British mathematics,” says Professor Ball, “and it’s fine stuff – I still love my original research field in dynamical systems.” But that mathematics did not develop in isolation, she says, and now there’s even more to learn about how non-Western societies have been seeing the world mathematically that many of us haven’t yet tuned into.
“What the general public think of as mathematics tends to be whatever they learned (or, more likely, did not learn) at school. But in many Indigenous societies, mathematics is lived from when you are born to when you rejoin your ancestors,” Professor Ball says.
Rejoin your ancestors? Does she mean as underground worm food? I don’t think so. But I digress. Ball argues that indigenous math is largely non-numerical, though in her one unpublished paper that is mentioned in the article (see below), numbers and counting figure largely.
At any rate, here is the single example Ball gives of valuable indigenous mathematics. I am not making this up: it involves the direction of smoke signals.
“One interesting example that we are currently investigating is the use of chiral symmetry to engineer a long-distance smoke signalling technology in real time,” Professor Ball says. “If you light an incense stick you will see the twin counter-rotating vortices that emanate − these are a chiral pair, meaning they are non-superimposable mirror images of each other.”
A memoir by Alice Duncan Kemp, who grew up on a cattle station on Mithaka country in the early 1900s, vividly describes the signalling procedure, in which husband-and-wife expert team Bogie and Mary-Anne selected and pulsed the smoke waves with a left to right curl, to signal “white men”, instead of the more usual right to left spiral.
Mithaka country is southwest Queensland − Kurrawoolben and Kirrenderri (Diamantina) and Nooroondinna (Georgina) river channel country − and for thousands of years this region was a rich, well-populated cultural and trade crossroads of the Australian continent.
To create and understand these signals, you have to be a skilled practical mathematician, Professor Ball says.
“Theory and mathematics in Mithaka society were systematised and taught intergenerationally. You don’t just somehow pop up and suddenly start a chiral signalling technology. It has been taught and developed and practised by many people through the generations.”
At that time in the early twentieth century, British meteorologists were just beginning to understand the essential vortical nature of atmospheric flows.
“Imagine if the existing Indigenous Mithaka knowledge of vorticity had been recognised, nurtured and protected? In what ways may it have fed into the high performance, numerical weather forecasting capabilities that we all rely on now?” she asks.
I don’t find this at all convincing. First, Bogie and Mary-Anne sound like white oppressors to me. But even if they weren’t, is the “reverse curl” something the locals actually used to signal “white people around”? It couldn’t have been going on for thousands of years because the first European people arrived in Australia in the early 17th century. So was there an elaborate system of smoke signals before that? Perhaps, but how are they based on mathematics? Patterns of smoke, like drumbeats, is a kind of language, and how to make the patterns and get them understood correctly is based on trial and error. Where does the math come in?
Further, the claim that the Mithaka knowledge of vorticity—I’m not sure what that knowledge is beyond empirical ways to make smoke signals—would have revolutionized “high performance numerical weather forecasting” long before now is simply risible.
Well, that’s enough. But I’d be remiss not to at least mention a paper by Xu and Ball that defends the thesis above. It’s called “Is the study of Indigenous mathematics ill-directed or beneficial?“, and appears at Arχiv.org, which means it hasn’t been published or peer-reviewed. There are a few examples of indigenous mathematics, which I put below. In some cases you’ll have to look up the references given to check on which people they’re referring to:
Much of ordinary day-to-day arithmetic and geometry performed by ‘illiterate’ women, artisans, carpenters and many other workers are unwritten and even unspoken (Wood, 2000). The apprentice learns by watching carefully then doing the mathematics themselves. The use of tools–an unwritten approach–to support arithmetic has a long history; there are different media for recording and computing with numbers, including stones, twigs, knots and notches (Hansson, 2018). People of many Indigenous Pacific and Australian nations can use parts of the body to count quickly and accurately (Goetzfridt, 2007; Owens & Lean, 2018; Wood, 2000), communicating methods, operations and results through speaking, listening and gesture. Weaving skills were taught unwritten to next generations to construct the numerical relationships that give rise to the desired complex geometrical designs with symmetries (Hansson, 2018). Knotted quipus were used by ‘illiterate’ Inca people of South American
Andes regions to allot land and levy taxes (Ascher & Ascher, 2013). The quipu (Figure 1), with its columns of base-10 numerical data encoded as knots, can be thought of as a spreadsheet, and it seems likely that the Inca knew and applied some array and matrix operations.Dan, an Indigenous language of central Liberia, is non-written but Dan speakers can carry out arithmetic operations orally, including addition, subtraction and division, play games that require fast counting, tracking and calculating skills, and practice geometric principles in constructing buildings (Sternstein, 2008). Fractal geometry, developed to a high art in Western mathematics from the late 1960s and executed in silico, has non-Western antecedents that were implemented in the built environment in Africa (Eglash, 1998). Chaology and fractal geometry have also been a part of traditional Chinese architectural and garden design for thousands of years (Li & Liao, 1998).
Clearly some indigenous people could count and calculate, though the calculating seems to fall largely to the Chinese, not usually considered indigenous. At any rate, what’s above doesn’t jibe with the claim and quote in the article:
Numbers and arithmetic and accounting often are of secondary importance in Indigenous mathematics.
“In fact, as most mathematicians know, mathematics is primarily the science of patterns and periodicities and symmetries − and recognising and classifying those patterns.”
A lot of the above sounds like counting and accounting to me. Regardless, it’s clear that some indigenous people could count and figure out patterns that involved counting. I’m not so sure about the Inca “matrix” operations, but one can hardly carry out some kind of commerce or taxation without being able to count. At any rate, yes, indigenous people had a form of “counting and pattern mathematics,” but to put them on a par even with what the ancient Egyptians and Greeks accomplished mathematically is to give indigenous people too much credit.
The mathematical and calendrical accomplishments of the Maya never seem to come up in discussions of this sort. We can thank Diego de Landa for destroying almost all of the Mayan written records that had survived until the Spanish conquest of Mexico, but what remains indicates a non-trivial understanding of celestial cycles (purely observational, but still requiring precise observation over long periods of time) and a mathematical system that was probably as good as any used elsewhere in the world at the time. They came up with the concept of the zero independently, and their notation could be used in multiplication and division (although, admittedly, there’s no evidence that they did use these operations).
None of this contributed to modern science, but the Mayans never really had a chance – the Spanish steamrollered over their civilization before examining its intellectual accomplishments.
A local climate change contributed.
I would have thought that mathematics would be one of the last areas to suffer the criticisms and revisions of Critical Social Justice. Perhaps attacking it directly is a strategy similar to placing violent transwomen in women’s prisons: do this early, because if you can get away with it the general public will simply have be more open to anything else you throw at them.
Very interesting, thanks. The indigenous “ways of counting” appear to be useful and clever, and made me think of the abacus. But I guess I don’t get the “defensive protection” of Western maths. By all means, if there are practical mathematical applications we can derive from indigenous cultures, let’s see them and use them if we can.
Time and again, scientifical and technological ideas have a simple litmus test: do they work? Would Ball want to fly in a plane based upon the science of these indigenous cultures? Why or why not?
It’s such an odd article. Professor Ball does seem to know some actual maths, unlike most of the people who spout this sort of thing in NZ. BTW, Bogie and Mary Ann were aborigines, not white saviours. The books of Alice Duncan-Kemp, from which the smoke signal story comes, and the reliability thereof have been discussed of late.
https://howlinginfinite.com/2024/02/11/a-bridge-from-past-to-present-the-forgotten-memoirs-of-alice-duncan-kemp/
I’m commenting as a retired mathematician.
What professor Ball means by “mathematics” is very different from what most mathematicians mean. We’ve seen this before. I remember a time when there were arguments about making mathematics more relevant. And that relevance movement fizzled out. I expect that this “decolonization” movement will also fizzle out.
If there is gatekeeping to limit us to European mathematics, why do we teach the “Chinese remainder theorem”? Mathematics is already very international.
I trust my mathematical colleagues to continue doing real mathematics. Perhaps some will pay lip service to this new movement, as a way of avoiding controversy. But I do not expect it to have any long lasting impact on serious research in mathematics.
There’s a Numberphile video – I think Babylonian multiplication with Johnny Ball – very charismatic and entertaining.
So many other famous puzzles too come to mind – Bridges of Köenigsburg, … etc.
“Mathematics has been gatekept by the West”
In my understanding, mathematics is not gatekept by any culture or any person. If there is a gatekeeper, it’s reality. And that’s why math is universal – because every human inhabits the same reality.
When I announced back in the 1980’s that I was off to University to do a degree in mathematics, the mother of one of my friends asked, in all seriousness, “so what do you do in a maths degree? Is it just really complicated sums?” I thought for a moment about the difference between mathematics and arithmetic and whether I could explain it, and then answered “yes”.
There is no gatekeeping in mathematics that I am aware of. It’s just that Europeans invented (or discovered) some really effective techniques and notation before anybody else and were thus able to get to many of the important discoveries first.
And even that is not necessarily true of everything. Algebra is famously of Arabic origin and our system for representing numbers was invented in India. Embracing these ideas made our mathematics better. If we had taken the “not invented here” approach that the decolonizers advocate, it would have been bad for mathematics. Conversely, really good ideas from other cultures will be assimilated into and will strengthen mathematics.
And underappreciated area of math (at least underappreciated by me) is synchronicity. While reading Jerry’s post on my phone I bumped into the Associate Dean for Learning in my Faculty of Science, a very kind person who is herself a physicist and part of a team of folx in the Dean’s office who are very keen on decolonizing the university and indigenizing our curriculum. Ironic!
Wrt whether smoke curling requires mathematical knowledge, my dog can catch a ball in flight (like a little four-legged shortstop, I’ll send Jerry a video, he could start a “Stupid Pet Tricks” section) but that doesn’t mean she’s solving the system of equations that describe the arc of the ball’s trajectory. She’s just got a very good cerebellum and lots of practice.
And that says nothing about whether curling the smoke or catching the ball is or isn’t an admirable ability. It’s just not math.
In fact, curling follows Canadian physical laws and therefore real curling can only be played in Canada…
Kidding 😉😂
Scotland says “Hello!”
Rowena Ball should be able to use Fourier Transforms to switch between Indigenous and Western maths – I tried it myself and it works!
It’d be interesting to look into how the superstitious stuff segregated from the scientific stuff.
I’m reading
The Scientific Revolution – A Very Short Introduction
Lawrence M. Principe
Oxford, 2011
… and the kooky stuff like astrology and alchemy (Newton) developed and was practiced alongside and by the same figures sometimes as the stuff that built modern science and math. It’s fascinating to learn and that book is essential (IMHO).
I’ll have to look again to see how it went.
I read the linked preprint by Xu & Ball ( https://arxiv.org/abs/2212.02778 ) and found this paragraph astonishing:
“But Deakin (2010, p. 236) has devised an infallible test for the existence of Indigenous mathematics! This is that there must be ‘an Aboriginal method of predicting eclipse’. To predict an eclipse, one needs clear and accurate understanding of the relationships between the motions of the Sun and Moon. In spite of the challenge, the answer is yes. Hamacher & Norris (2011) report a prediction by Aboriginal people of a solar eclipse that occurred on 22 November 1900, which was described in a letter dated in December 1899.”
Following up the Hamacher & Norris reference (it seems the wrong Hamacher & Norris paper is cited by Xu & Ball, and they appear to mean this one: https://ui.adsabs.harvard.edu/abs/2011JAHH…14..103H/abstract ), one finds the following discussion:
“Given that the letter was dated December 1899, we searched for any solar eclipses during this period. Between 1891 and 1900, only one solar eclipse was visible from this region, a partial eclipse that covered 73% of the Sun’s disk, which occurred on 22 November 1900 (Event #10).
“Reasons for doubting the veracity of this story include (a) the inconsistency in the dates [the prediction was actually for the following month of Jan 1900], (b) the lack of evidence that Aboriginal people made sub-arcminute
precision measurements required for eclipse prediction, despite evidence elsewhere for Aboriginal astronomical alignments accurate to a few degrees (e.g. Wurdi Youang, see Norris and Hamacher, 2011b; stone rows, Hamacher and Norris, 2011); and (c) a reaction of fear to something they would have anticipated seems counterintuitive. Once again this example raises the issue of the credibility of some of the sources at our disposal.” [One could also speculate that this community had learned of an upcoming eclipse directly or indirectly from other Europeans.]
This seems like pretty shoddy scholarship in my opinion. Maybe that’s why, as far as I can tell, the Xu & Ball paper hasn’t yet made it through peer review after over a year on arXiv 😉
The Navier-Stokes equation could have been derived many years before if we watched very carefully the way indigenous people pour water from the bottle to the glass…
Kidding 😂
The joke goes, “I don’t believe in superstition because it brings bad luck.” The Maori believe that when you die, your soul travels up to the northern end of New Zealand’s far north beyond Cape Reinga, where it settles over the islands visible from the cape. This form of spiritually based belief is part and parcel of their overall view of the world, so it’s not surprising that they incorporate it in their view of what makes up (pun intended) science.
How can you tell the direction a three-dimensional helical vortex is curling from a far distance (as a smoke signal? And a smoke vortex rapidly becomes chaotic.) From a distance, a helix looks like a flat sine wave with no chirality because it maps onto the flat plane. This was one of the challenges in figuring out how bacterial flagella work. They were long known to spin but how something that looked like a rigid flat sine wave could provide directional propulsion was a mystery. Eventually through electron microscopy they were shown to be gentle helices and so they screw the bacterium through the medium in a direction predictable by the “hand” of the helix and the direction of rotation. (This was the article that got me hooked on Scientific American in the early 1970s, which explained it all. With math.)
So I consider this vortex story a bush-land myth. Like the idea that water goes down a drain clockwise south of the equator and counter-clockwise north of it.
That is true though. As a Northern hemisphere inhabitant, I discovered as a child that water goes anticlockwise down the drain by doing experiments with my bathwater.
Of course, I found I could make it go clockwise too just by swirling my hand around in the water in a clockwise direction.
So where’s the Abo abacus?
I did enjoy Ball’s loose cannon on ‘reviving trad Indian maths’. Where did the concept of ‘zero’ emerge?
Was Srinivasa Ramanujan an indigenous mathematician? He grew in a British colony.
I think Ramanujan was Indian in every sense; he sent his work from India to Hardy, who was amazed and brought him to England. And he was pretty much a sui generis genius. However, I have never heard of people from India described as “indigenous”, though of course they were colonized. But his math wasn’t really any different from English math; otherwise Hardy couldn’t have understood it as pathbreaking.
Ramanujan is a hero in his home province of Tamil Nadu.
Those who might be termed ‘indigenous’ in peninsula India would commonly be termed ‘tribal’ peoples. Largely, they can be characterised as not usually speaking one of the Indo-European/ Indo-Iranian languages of Northern India, and not speaking one of the older Dravidian languages that are representative of South India. More piquantly, the Indian Civil Service classified them as ‘OBC’s ie members of the Other Backward Classes [ to distinguish them from Untouchables ].
However, wokerati eg the art world would preferentially use the term ‘Indigenous’ Indians for these ‘tribals’.
Thank you.
I believe that many of the aboriginal languages did not have the need to express large numbers ie they did not have a decimal system. Just a 1,2,3,4,5 and many approach.
https://www.slq.qld.gov.au/blog/indigenous-number-systems
How this could enhance any understanding of mathematics could be problematic.
It’s something of a tangent but the word “indigenous” as it’s now used has always struck me as odd. As JC notes the Chinese don’t seem to count. But they are indigenous to China!
In the UK, “indigenous” until very recently was a term only the BNP – an explicitly racist far-right party – would use. It meant “White British”, so it was (and still is for many people) coded precisely opposite to how it’s now used in the States.
You occasionally see “BIPOC” crossing the Atlantic in things like job applications. As a blonde-haired blue-eyed white person I’m sometimes tempted to apply under the “indigenous” category merely to enjoy the inevitable squirming.
Taken to its logical conclusion, it’s not clear who the “indigenous” inhabitants of Britain even were. Not the Angles, or Saxons, or Jutes, or Danes, or Romans. They’re all immigrants. So are the Celts and the Picts. It might be the Neanderthals, assuming other species of hominid can get a place on the Oppression Ladder.