Alex's Adventures in Numberland - Alex Bellos [5]
The Munduruku are not alone in the sweep of history in not counting members of their community. When King David counted his own people he was punished with three days of pestilence and 77,000 deaths. Jews are meant to count Jews only indirectly, which is why in synagogues the way of making sure there are ten men present, a minyan, or sufficient community for prayers, is to say a ten-word prayer pointing at each person per word. Counting people with numbers is considered a way of singling people out, which makes them more vulnerable to malign influences. Ask an Orthodox rabbi to count his kids and you have as much chance of an answer as if you asked a Munduruku.
I once spoke to a Brazilian teacher who had spent a lot of time working in indigenous communities. She said that Indians thought that the constant questioning by outsiders of how many children they had was a peculiar compulsion, even though the visitors were simply asking the question to be polite. What is the purpose of counting children? It made the Indians very suspicious, she said.
The first written mention of the Munduruku dates from 1768, when a settler spotted some of them on the bank of a river. A century later, Franciscan missionaries set up a base on Munduruku land and more contact was made during the rubber boom of the late nineteenth century when rubber-tappers penetrated the region. Most Munduruku still live in relative isolation, but like many other Indian groups with a long history of contact, they tend to wear Western clothes like T-shirts and shorts. Inevitably, other features of modern life will eventually enter their world, such as electricity and television. And numbers. In fact, some Munduruku who live at the fringes of their territory have learned Portuguese, the national language of Brazil, and can count in Portuguese. ‘They can count um, dois, três, up until the hundreds,’ said Pica. ‘Then you ask them, “By the way, how much is five minus three?”’ He parodied a Gallic shrug. They have no idea.
In the rainforest Pica conducts his research using laptops powered by solar-charged batteries. Maintaining the hardware is a logistical nightmare because of the heat and the damp, although sometimes the trickiest challenge is assembling the participants. On one occasion the leader of a village demanded that Pica eat a large, red sauba ant in order to gain permission to interview a child. The ever-diligent linguist grimaced as he crunched the insect and swallowed it down.
The purpose of researching the mathematical abilities of people who have the capacity to count only on one hand is to discover the nature of our basic numerical intuitions. Pica wants to know what is universal to all humans, and what is shaped by culture. In one of his most fascinating experiments he examined the Indians’ spatial understanding of numbers. How did they visualize numbers when spread out on a line? In the modern world we do this all the time – on tape measures, rulers, graphs and houses along a street. Since the Munduruku don’t have numbers, Pica tested them using sets of dots on a screen. Each volunteer was presented with the figure overleaf, of an unmarked line. To the left side of the line was one dot; to the right, ten dots. Each volunteer was then shown random sets of between one and ten dots. For each set the subject had to point at where on the line he or she thought the number of dots should be located. Pica moved the cursor to this point and clicked. Through repeated clicks, he could see exactly how the Munduruku spaced numbers between one and ten.
When American adults were given this test, they placed the numbers at equal intervals along the line. They recreated the number line we learn at school, in which adjacent digits are the same distance apart as if measured by a ruler. The Munduruku, however, responded quite differently. They thought that intervals between the numbers started large and became progressively smaller as the numbers increased.