The coolest example of this imo would be a purely mechanical sphere -- lets say opaque -- that displayed spinorial behavior because of some clever arrangement of its insides. A start might be a sphere with several smaller spheres inside it. Its state, as measured by the motion of the spheres inside, depends not only on the rotational position of the outer sphere, but on its path of rotations. Dan -------------- Bill T. wrote: << Obviously it *could* be done. I imagine that it wouldn't be hard for an iphone developer to write an iphone app that would do this . . .

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On May 22, 2011, at 9:57 AM, James Propp wrote:

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Has anyone built a macroscopic object that has spinorial behavior[?]

[as has been noted: I.e., its state (like color and/or sound) -- after it goes through a continuous path P of rotations, starting from the identity -- is not determined by rotational position alone. Instead it's determined by the lift of P from SO(3) to its Lie-group double cover: Spin(3) ~~ SU(2) == S^3 --d.a.] I envision an egg that emits a hum when it's resting on its base and is in the correct spinorientation. Rotate it 360 degree about any axis: no hum. Rotate it again about any axis: it hums.

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Sometimes the brain has a mind of its own.