Mathematics, often romanticized as human intuition, may not be as natural to the human race after all. In a new study conducted by the a team of scientists, led by Rafael Nunez, director of Embodied Cognition Lab, it appears that abstract mathematical concepts like the number line, which involves the mapping of numbers onto space, need to be taught and aren’t ‘hard-wired’.
Nunez et al studied an indigenous tribal group from Papua New Guinea called the Yupno. The group lives in a remote part of the upper Yupno Valley in Papua New Guinea. The place has no roads. The team used a small plane and then hiked, carrying heavy equipment like solar panels, since the valley has no electricity.
The main study was conducted with three groups – one comprised 14 illiterate adults, another comprising 6 adults who had received very basic schooling from within the tribal community and another control group in California, comprising adults with formal schooling. All the three groups were given several objects and a long line. Then they were asked to arrange these objects on the number line.
The Yupno were given oranges. The first group (of unschooled adults) arranged the oranges, but stacked them up at the two endpoints and a put a few in the middle, totally ignoring the extension of the line in between, which is one of the most important properties of the number line. The second group did a little better, using the extension a bit more, but not quite as evenly as it should be. The control group in California treated the number line as it should be. All this suggests only one thing – that the concept of numbers, especially their mapping onto space, is a concept that has to be taught and is not ingrained in the human brain. The ability to build this intuition might be evolutionary, but not the intuition itself!
What about time?
The team also analysed the crucial concept of time. We tend to associate the flow of time with spatial position, associating ‘forward’ for future and ‘backward’ for past. Interestingly, the Aymara of the Andes, a previously studied group of Nunez et al., does the reverse. The Yupno uses ‘uphill’ and ‘downhill’, says Nunez. They even use the three-dimensional topography of the valley to describe time, obviously conflicting with just the forward and backward 2-D notions of time.
Cooperrider, a co-author in the study, says:
When confronted with radically different ways of construing experience, we can no longer take for granted our own. Ultimately, no way is more or less ‘natural’ than the Yupno way.
There you go – Mathematics, or even time, is not as universal as we thought. If some definition or notion of mathematics seems obvious, it may be because we lack imagination.