In “Geometric Principles Appear Universal in Our Minds” (*Wired Science*, May 24, 2011) , Bruce Bower reflects on the fact that research among peoples who do not even count suggests that abstract geometric principles are probably innate in humans:

If geometry relies on an innate brain mechanism, it’s unclear how such a neural system generates abstract notions about phenomena such as infinite surfaces and why this system doesn’t fully kick in until age 7. If geometry depends on years of spatial learning, it’s not known how people transform real-world experience into abstract geometric concepts — such as lines that extend forever or perfect right angles — that a forest dweller never encounters in the natural world.

As always, we needn’t wait long for a Darwin answer:

Whatever the case, the Mundurucú’s keen grip on abstract geometry contrasts with past evidence from Izard’s group that these Amazonian villagers cannot add or otherwise manipulate numbers larger than five. Geometry may have a firmer evolutionary basis in the brain than arithmetic, comments cognitive neuropsychologist Brian Butterworth of University College London.“If so, this would support recent findings that people who fail to learn arithmetic, or ‘dyscalculics,’ can still be good at geometry,” Butterworth says.

Some find the leap here puzzling: That “dyscalculics” can learn geometry better than arithmetic sheds no light in particular on evolution: Both are branches of mathematics are abstract arts.

It’s one thing to say that evolution explains why wolves are better at sniffing than at the times tables; another to simply plunk an assertion about “evolution” in the midst of discussion of variable human groups’ performance with abstractions, providing no evidence apart from the humble assent of millions that “evolution is true.” But Butterworth is on safe ground. Hard to imagine Bower asking him to explain.

These data are interesting in the light of the fact that the historical development of mathematics puts geometry about a millennium and a half before the development of algebra, implying that the latter follows the former in a hierarchy of concepts. Thoughts?

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