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I had a quick look at John's paper G2 and the rolling ball. I only have a vagure idea about what G2 is or what a spinor is. I was just thinking in pictures and wondered... If you have a hollow sphere of radius 3, and two balls of radius 1, one on the inside and one on the outside, constrained to touch the sphere at the same point, would the orientations of the two balls taken together make a spinor by any chance? The idea is that the inner one rotates at half the speed of the outer.