Geometry is hardwired into our brains

The Mundurucu tribe are an isolated group living deep within the Amazon rainforest. Their language doesn't have exact terms for numbers or words for most geometric shapes...and yet they outperformed French and American schoolchildren on a geometry test.

Leaving aside the knee-jerk reaction that this simply means American and French students are that horrendous at math, this new research seems to suggest that the human understanding of geometry is somehow innate, meaning people can pick it up even when they live in a culture that completely lacks the basic vocabulary and concepts required to even discuss these ideas.

Lead researcher Pierre Pica of France's National Center of Scientific Research explains why he decided to focus on the Mundurucu:

"Mundurucu is a language with only approximative numbers. 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."

Of course, Dr. Pica didn't just hand out a standardized test to the Mundurucu test subjects. He asked the 22 adult and 8 child participants to engage with geometry through more practical applications, such as working with a map of two nearby villages. And yet as they got to the geometry questions, the Mundurucu didn't miss a beat, revealing a good working intuition for lines and shapes without any formal education...or, indeed, without even the basic words in their language to express these ideas.

In general, the Mundurucu performed at a comparable level as French and American schoolchildren do on geometry tests, but in one particular area they actually outperformed their counterparts. When Dr. Pica moved away from more traditional Euclidean geometry and introduced a sphere, the Mundurucu were far better at recognizing that parallel lines on a sphere can actually cross - a notion that eluded most schoolchildren.

That concept might seem counterintuitive, but then, intuition is pretty much the only thing the Mundurucu were working with. Dr. Pica suggests that the heavy emphasis on Euclidean geometry in school might actually detract from our natural geometric intuition, and that's something that doesn't even need language to express itself:

"The question is to what extent knowledge - in this case, of geometry - is dependent on language. 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. 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."

PNAS via BBC News. Image via.