I doubt that babies are capable of abstract thinking. (BTW, the games on this video are really interesting.)
I remember that at a young age, maybe 9 or 10, I was fascinated with any kind of grid, like a tiled surface. I would imagine a ball traveling along a diagonal and bouncing off an edge at a right angle and continuing on bouncing off other edges. This was long before ball and paddle video games were invented that did essentially the same thing.
My point is that humans have a natural fascination with geometric patterns and chess is a geometric game.
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