BY BBC http://www.bbc.co.uk/news/science-environment-13469925
Tests given to an Amazonian tribe called the Mundurucu suggest that our intuitions about geometry are innate.
Researchers examined how the Mundurucu think about lines, points and angles, comparing the results with equivalent tests on French and US schoolchildren.
The Mundurucu showed comparable understanding, and even outperformed the students on tasks that asked about forms on spherical surfaces.
The study is published in Proceedings of the National Academy of Sciences.
The basic tenets of geometry as most people know them were laid out first by the Greek mathematician Euclid about 2,300 years ago.
This "Euclidean geometry" includes familiar propositions such as the fact that a line can connect two points, that the angles of a triangle always add up to the same total, or that two parallel lines never cross.
The ideas are profoundly ingrained in formal education, but what remains a matter of debate is whether the capacity, or intuition, for geometry is present in all peoples regardless of their language or level of education.
To that end, Pierre Pica of the National Centre for Scientific Research in France and his colleagues studied an Amazon tribe known as the Mundurucu to investigate their intuitions about geometry.
"Mundurucu is a language with only approximative numbers," Dr Pica told BBC News.
"You don't have a lot of geometrical terms like square or triangle or anything like that, and no way of saying two lines are parallel... it looks like the language does not have this concept."
Dr Pica and his colleagues engaged 22 adults and eight children among the Mundurucu in a series of dialogues, presenting situations that built up to questions on geometry. Rather than abstract points on a plane, the team suggested two villages on a notional map, for instance.
'Playing tricks' Similar questions were posed to 30 adults and children in France and the US, some as young as five years old.
The Mundurucu people's responses to the questions were roughly as accurate as those of the French and US respondents; they seemed to have an intuition about lines and geometric shapes without formal education or even the relevant words.
"The question is to what extent knowledge - in this case, of geometry - is dependent on language," Dr Pica explained.
"There doesn't seem to be a causal relation: you have a knowledge of geometry and it's not because it's expressed in the language."
Most surprisingly, the Mundurucu actually outperformed their western counterparts when the tests were moved from a flat surface to that of a sphere (the Mundurucu were presented with a calabash to demonstrate).
For example, on a sphere, seemingly parallel lines can in fact cross - a proposition which the Mundurucu guessed far more reliably than the French or US respondents.
This "non-Euclidean" example, where the formal rules of geometry as most people learn them do not hold true, seems to suggest that our geometry education may actually mislead us, Dr Pica said.
"The education of Euclidean geometry is so strong that we take for granted it's going to apply everywhere, including spherical surfaces. Our education plays a trick with us, leading us to believe things which are not correct." |