More than once, I’ve voiced the view that we tend to put the cart before the horse when it comes to learning, understanding, and knowing. Over the last few years, I’ve become relatively convinced that we only truly understand and learn what we already know intuitively. My suspicions began during our home schooling days as I began seeing subtle indications of this.
When I first brought this up with my family, they all rolled their eyes, “Yeh, right” they said. However, constant brainwashing finally brought them to see my point. Brainwashing? Well, not exactly. I offered concrete examples that gradually helped sell them on my case — or are they just humoring me?
I understand, but do I know? (p.70) is a recent post that attempts to deal with this off-the-wall point of view. Yes, all this may seem bizarre, but then knowing and understanding are mysterious, bottomless issues.
Low and behold, research reported in Science News, Geometric minds skip school (1), comes to the rescue. (Google: Flexible intuitions of Euclidean geometry in an Amazonian indigene group.) It seems Amazonian villagers grasp abstract spatial concepts despite lacking formal math education. They know geometric principles intuitively. Granted, my views on knowing and understanding are more radical, but then I don’t have skeptical peer-reviewing scientists insisting on proof. 😉
I regard the advanced knowledge civilization prides itself on as actually being based in innate knowing, as this research implies. The emergent property principle (see Tao as Emergent Property, p.121) helps support and give deeper context to my view that we only truly understand what we already innately know. Additionally, what often passes for understanding is merely mimicry as noted in Learning What You Know, p.112. That said, mimicry is certainly a key step on the path to tapping intuitive knowing and understanding.
(1) Here are a few excerpts from this article.
In a South American jungle, far from traffic circles, city squares and the Pentagon, beats the heart of geometry.
Villagers belonging to an Amazonian group called the Mundurucú intuitively grasp abstract geometric principles despite having no formal math education, say psychologist Véronique Izard of Université Paris Descartes and her colleagues.
Mundurucú adults and 7- to 13-year-olds demonstrate as firm an understanding of the properties of points, lines and surfaces as adults and school-age children in the United States and France, Izard’s team reports online May 23 in Proceedings of the National Academy of Sciences.
U.S. children between ages 5 and 7 partially understand geometric space, but not to the same extent as older children and adults, the researchers find.
These results suggest two possible routes to geometric knowledge. “Either geometry is innate but doesn’t emerge until around age 7 or geometry is learned but must be acquired on the basis of general experiences with space, such as the ways our bodies move,” Izard says.
Both possibilities present puzzles, she adds. 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.
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