Alex's Adventures in Numberland - Alex Bellos [13]
An even more startling finding became apparent when the teenagers’ dot-comparing scores were then compared to their maths scores since kindergarten. Researchers had previously assumed that the intuitive ability to discriminate amounts does not contribute much to how good a student is at tasks such as solving equations and drawing triangles. Yet this study found a strong correlation between a talent at reckoning and success in formal maths. The better one’s approximate number sense, it seems, the higher one’s chance of getting good grades. This might have serious consequences for education. If a flair for estimation fosters mathematical aptitude, maybe maths classes should be less about times tables and more about honing skills at comparing sets of dots.
Stanislas Dehaene is perhaps the leading figure in the cross-disciplinary field of numerical cognition. He started off as a mathematician, and is now a neuroscientist, a professor at the Collège de France and one of the directors of NeuroSpin, a state-of-the-art research institute near Paris. Shortly after he published The Number Sense in 1997, he was having lunch in the canteen of Paris’s Science Museum with the Harvard development psychologist Elizabeth Spelke. There they sat down by chance next to Pierre Pica. Pica brought up his experiences with the Munduruku and, after excited discussions, the three decided to collaborate. The chance to study a community that doesn’t have counting was a wonderful opportunity for new research.
Dehaene devised experiments for Pica to take to the Amazon, one of which was very simple: he wanted to know just what they understood by their number words. Back in the rainforest Pica assembled a group of volunteers and showed them varying numbers of dots on a screen, asking them to say aloud the number of dots they saw.
The Munduruku numbers are:
one
pg
two
xep xep
three
ebapug
four
ebadipdip
five
pg pogbi
When there was one dot on the screen, the Munduruku said pg. When there were two, the said xep xep. But beyond two they were not precise. When three dots showed up, ebapug was said only about 80 percent of the time. The reaction to four dots was ebadipdip in only 70 percent of cases. When shown five dots, pg pogbi was the answer managed only 28 percent of the time, with ebadipdip being given instead in 15 percent of answers. In other words, for three and above the Munduruku’s number words were really just estimates. They were counting ‘one’, ‘two’, ‘threeish’, ‘fourish’, ‘fiveish’. Pica started to wonder whether pg pogbi, which literally means ‘handful’, even really qualified as a number. Maybe they could not count up to five, but only to fourish?
Pica also noticed an interesting linguistic feature of their number words. He pointed out to me that from one to four, the number of syllables of each word is equal to the number itself. This observation really excited him. ‘It is as if the syllables are an aural way of counting,’ he said. In the same way that the Romans counted I, II, III and IIII but switched to V at five, the Munduruku started with one syllable for one, added another for two, another for three, another for four but did not use five syllables for five. Even though the words for three and four were not used precisely, they contained precise numbers of syllables. When the number of syllables was no longer important, the word was maybe not a number word at all. ‘This is amazing since it seems to corroborate the idea that humans possess a number system that can only track up to four exact objects at a time,’ Pica said.
Pica also tested the Munduruku’s abilities to estimate large numbers. In one test, illustrated overleaf, the subjects were shown a computer animation of two sets of several dots falling into a can. They were then asked to say if these two sets added together in the can