Deep in the Amazon jungle lives a group of indigenous people called the Munduruku. In their language, there are no words for squares, triangles, or parallel lines. In fact, the only geometric shape for which they have a specific word is the circle. Although they are expert at navigating up and down the rivers where they live, their directional vocabulary consists of sunrise, sunset, upstream, and downstream. They don't have many words for numbers higher than five except for the vague "few" and "many." Yet, when pitted against upper-crust,
educated Boston schoolchildren in a battle of geometric wit, they perform just as well as the Americans. Even up against highly educated adult Bostonians, the Munduruku put in a respectable performance on a geometry exam, although scoring slightly lower than their competition.
The Munduruku groups, living in isolated villages through several Brazilian states and making up a total of a little over 8,000 people, also never use maps. A warrior-based nation with a previous reputation for prizing enemy heads as trophies, they first encountered nonindigenous people in the latter 18th century. Despite the intervening 200-plus years, they have not incorporated Western ways or vocabulary. This isolation and their lack of map use and geometric and directional vocabulary made the Munduruku subjects of great interest to scientists curious about the core of human instinctive knowledge. As far back as Socrates, this core has been thought to include an instinctive understanding of geometry and of the layout of the three-dimensional world. According to Plato, Socrates tested an uneducated slave on his grasp of geometry. Finding that the slave exhibited an impressive native ability with the subject, Socrates concluded that knowing geometry must be part of the soul. What he and the scientists who followed him have explored since is how humans have this native understanding of geometry and math. The Munduruku's idiosyncrasies of language and culture provide a "blank slate" of sorts that researchers used to test the human tendency to instinctively comprehend geometry. A group of researchers that included linguists and psychologists traveled to the Amazon to give the Munduruku a test. They presented 44 members of the group, as young as age 5 or 6, with a series of 45 slides. Each slide had six images on it, and one of those images didn't belong with the other five, geometrically speaking. For example, five of the images might be of parallel lines while the sixth contained two lines that were not parallel, or the there might be five right triangles and one isosceles. The Munduruku participants had to choose which image was "the ugly one," in their linguistic parlance. The Bostonian schoolkids and adults also took the test. Interestingly, the Munduruku scored about the same as the schoolchildren, even though the Munduruku had no formal training in geometry and the schoolchildren had been learning it for years. In addition, the Munduruku adults scored pretty well, but not as well as the highly educated adult Bostonians who took the test. If the Munduruku were simply choosing shapes randomly, their expected success rate would have been about 16.6%; instead, they scored an average of 66.8% correct as a group. The researchers also conducted a "map test" with the Munduruku participants to examine how instinctive it is for people to orient themselves in space using two-dimensional representations. There were three boxes represented on the map, laid out in various geometric configurations, and in one box there was a "treasure" to be found. The map used a star to indicate the location of the treasure, and the layouts varied. Even when the Munduruku participants received the map in the wrong orientation, they oriented it properly and correctly identified the location of the box with the treasure 71% of the time. These findings indicate that geometric understanding is a native human talent, although whether or not humans acquire the talent by interacting with the world around them or are born with it remains in doubt. Researchers plan to extend their investigations by using brain imaging techniques to identify the parts of the brain that are active when people engage in geometrical cogitations.