Should we have learned indigenous mathematics or, more exactly, should we remember them – for we were all once indigenous peoples – the world would be different and probably better than it is today. For the ontology behind modern mathematics and, more broadly, modern science, is anything but neutral. Put differently, reality is not just there waiting passively for modern science to take possession of it with its apparently-inoffensive calculations. There is rather an ontology that modern science serves, and which it perpetuates, so that what there is can be represented in physical-mathematical terms alone. Heidegger calls this the modern “world picture.”(*) Yet in other ontologies mathematical calculations cannot be separated from a number of specifically-qualitative factors. As a result, the modern “world picture” does not picture reality in them.
Suppose, for instance, that you have 10 candies, and that you give 3 of those candies to your brother. How many candies will you still have? To find the answer you only need to make a rather simple calculation:
10 – 3 = 7
Hence the answer would be: 7 candies.
In the 2017 inaugural Lévi-Strauss lecture at the College de France,(**) Aparecida Vilaça reminded the audience that, for many indigenous peoples living nearby the Xingu river, in present-day Brasil, things are – how should we put it? – a little bit more complex. And the same can be applied to most extra-modern peoples.
When asked the aforementioned question (if you have 10 fishes, and you give 3 to your brother, how many fishes will keep?), they would likely respond: 13. 13, not 7.
Missionaries and, in their image, Western school teachers and official State educators, have repeatedly interpreted this and other similar answers to other similar questions as a proof of the inability of indigenous peoples to engage in mathematical reasoning. Interestingly, it was missionaries who first brought “numbers” to such peoples. For, on the one hand, it was paramount for the missionaries to teach them that there is “one” “god,” and that being “one” is nothing negative; for, in most indigenous worlds, to be “one” means to be “alone,” like e.g. widowers are, and, furthermore, we know that for them, normally, everything is “two.” On the other hand, missionaries historically paved the way to capitalism: teaching arithmetics to extra-modern people additionally served the purpose of making them familiar with economic accounting.
Yet, for the peoples of the Xingu river, 10 – 3 = 13. 13, not 7. And not because they cannot count, but because the count what we do not, or rather, they count what we do not see; put otherwise, in their counting, they count invisible magnitudes, as well.
Which invisible magnitudes? And why are they invisible to our eyes?
They are invisible to us because, in a commodity economy, like ours is, things are just what they are – or, shifting to an extra-modern perspective, they are less than what they can be. That is, a candy is a candy, a fish a fish, and an ax is an ax. Stop. And because they are only that, we can buy them and sell them: e.g. we can buy two fishes, paying for them, and sell three axes, being paid for them, while keeping all our candies, say, as an inversion. Money comes and money goes in proportion to the coming and going of commodities, and although prices can change, the number of commodities to be sold or bought does not: a candy is always a candy but not two, two fishes are always two fishes but not three, let alone one, and three axes are always three axes rather than four or one hundred and thirty eight.
In other words, we live in a world of discrete magnitudes. Even if a hundred hectares can also be viewed as a huge piece of land where you can plant crop that you can later sell to make money, that is, even if magnitudes can convert into one another, magnitudes are just magnitudes.
In contrast, extra-modern peoples live in words of relations, and a magnitude is always, above all, a relational index.
To understand this, let’s go back to our example.
What would happen if an indigenous person from the Xingu basin has 10 fishes and gives his brother 3? That his brother would give him back 6, i.e. twice the amount of fishes he would receive from her, as per the Xinguano law of reciprocity. Now,
10 – 3 + 6 = 13
Therefore, if an indigenous person from the Xingu basin has 10 fishes and gives 3 to his brother, he would end up having 13 instead of 7 fishes. For fishes (or axes, or whatever) are not only countable things, but occasions for relations to be put into practice, e.g. the relation of reciprocity between members of the same tribe or clan or extended family. And, more often than not, the same type of relation entails that one gives up everything one has so as to turn it into a gift by which new relations are thereby established.
This also means that Adam Smith and David Ricardo were wrong to surmise that non-European peoples’ “economies” where based on the very same principle the European economy they contributed to theorise was based on: the accumulation of commodities. But we will leave their criticism for another time. Suffice it to say that they made a major anthropological mistake whose identification casts doubts onto political economy’s main axiom, and thereby too onto the axiom of today’s neoliberal economy, namely, that, everywhere, people consist in exchanging and accumulating commodities, or, in other terms, that capitalism is natural and spontaneous.
Further reading: C. A. Gregory, Gifts and Commodities
(*) Martin Heidegger, Off the Beaten Track (edited and translated by Julian Young and Kenneth Haynes; Cambridge and New York: Cambridge University Press, 2002), pp. 57-85.
(**) Aparecida Vilaça, “The Devil and the Hidden Life of Numbers: Translations and Transformations in Amazonia – The Inaugural Claude Lévi-Strauss Lecture” (HAU: Journal of Ethnographic Theory 8, 1/2 [2018]: 6-19).
Missionaries have somehow succeeded in their endeavours. The calculative logic of capitalism determines how both humans and non-humans live – or perhaps it would be better to say, no longer live. Thus, for example, according to the Brazilian Instituto Socioambiental, in the Xingu basin 533 trees are cut every minute