Recently, an American researcher from the University of California was conducting research on the Suya Indians of Mato Grosso, Brazil, attempting to determine how they count. This group of Amazonian Indians are largely famous for their music; Anthony Seeger, a Professor of Ethnomusicology at the University of California, Los Angeles, who has produced a book called Why Suya Sing, says that their singing is used to create community, establish relationships and social identity and also formulate ideas about time and space.
Singing, to a Suya, is hard and soft science.
This particular researcher was investigating the level of sophistication of the Suya concerning mathematics. Many scientists examining cultural differences over number systems operate on the assumption that many native cultures basically don’t have language to describe quantities of things; for instance, the Piraha people use the same word ‘hoi’ to describe ‘about one’ and ‘about two’; the only difference is a subtle alteration in inflection of pronunciation. The much-studied Munduruku in the Amazon have words for numbers only up to 5.
This has led many scientists to examine whether human beings have innate numerical skills or whether it is simply a part of cultural conditioning. Is it possible to operate entirely without numbers?
So this particular researcher asked a member of the Suya tribe what was the correct answer to the following numerical problems: If you had 10 fish and gave away three fish, how many would you have?
The Suya answered without hesitation and as though the researcher were a bit dull-witted to have even asked the question.
As anybody in the village could tell you, the answer, of course, is 13.
Minus equals plus
This was how he worked it out. In the Suya tradition, whenever you give something away to someone else, the recipient pays you back double. So if he gave three fish to his brother, he said, his brother would have to give him back two times three fish, or six. So added to his 10 original fish he would first have 16 fish.
Once he deducted the three fish he originally gave his brother, he would have a net increase of three, or 13.
So, 10-3 = 7 in Western mathematics transforms into 10 + (2x3) - 3 = 13 in Suya mathematics.
In fact, the native was dismayed at the American version of the equation. He does not view giving away as equivalent to subtraction. He finds the entire notion of it abhorrent.
“Why is it that ‘giving’ is always seen as a ‘minus’ for white people?’ another member of the tribe asked. “I know that you want me to use the minus sign instead of the plus sign, but I don’t understand why.”
This was a little shocking to Alex Bellos, the author of the recently published Alex’s Adventures in Numberland (Bloomsbury, 2010), a study of cultural differences in mathematics. He began the study of his fascinating book with the belief that numbers are a universal language – the way in which we could, say, communicate with extra terrestrials — only to find that our basic understanding of arithmetical relationships depends upon cultural context.
Relationships in the numbers
I find the story delightful for several reasons.
It reveals something very profound not simply about mathematics but about how different cultures view relationships in general, particularly how we view ourselves in relation to other things.
Our sense of mathematics very much depends upon how we define our world, and whether we view ourselves and all the things around us as individual entities separate from each other or inherently intertwined.
Many non-Western societies — pre-literate cultures such as the Aborigines, the ancient Greeks and the Egyptians, the adherents of Eastern religions such as Buddhism, Zen and Taoism, and a number of modern indigenous cultures — conceive of the universe as inseparable, connected by some universal energy ‘life force’. The beliefs of many tribal societies about this central energy force have many similarities, suggesting that an intuitive understanding of the interconnectedness of all things is fundamental to human experience.
This central belief breeds an extraordinarily different way of seeing and interacting with the world. These traditional cultures believe that we are in relationship with all of life – even with the earth itself. They hold a very different notion of time and space as one vast continuum of ‘now’ and ‘here’.
They even perceive the world out there very differently. We see the thing; they see the totality, the relationship between the things. To an indigenous native, math and the song are equivalent — all about the plus sign, the connection, in this instance, between the man with the fish and his brother.
We would do well to take a few math lessons from the Amazon.