Gueorgi writes,

I read in your blog a few days ago about “square” and “diamond” treated as different “shapes” in Curious George’s Big Book of Curiosities.

You may find it interesting that children of an indigenous Amazonian tribe are able to spontaneously (“in the absence of schooling”) make use of rotation invariance and other geometric principles, according to this paper just published in Science:

Core Knowledge of Geometry in an Amazonian Indigene Group
Stanislas Dehaene, Veronique Izard, Pierre Pica, and Elizabeth Spelke

Abstract: Does geometry constitute a core set of intuitions present in all humans, regardless of their language or schooling? We used two nonverbal tests to probe the conceptual primitives of geometry in the Munduruk, an isolated Amazonian indigene group. Munduruk children and adults spontaneously made use of basic geometric concepts such as points, lines, parallelism, or right angles to detect intruders in simple pictures, and they used distance, angle, and sense relationships in geometrical maps to locate hidden objects. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

My reply: This doesn’t surprise me one bit. After all, I don’t recall them teaching us about rotation invariance at school. Although I’ve noticed that it’s a difficult concept for a two-year-old. Reflection invariance too.