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, since I'm pretty sure there's enough access to sensors in the iPhone to keep track of a path in SO(3) from which it is trivial to lift it to Spin(3). Probably for lots of android phones, as well. I'd like to mention that when we (in particular, my son Nathaniel) were making the "Outside In" video at the geometry center, we found it extremely convenient to specify camera orientation in Spin(3) i.e. unit quaternions, rather than SO(3). This makes interpolation between camera positions much easier, since any two points in $S^3$ except an antipodal pair is connected by a unique shortest geodesic. In SO(3) = RP(3), there is a large cut locus (for each point, the cut locus is an RP(2)), and it's much harder to program interpolation to avoid unwanted jumps in camera position when you, unless you pin down by hand a sequence of camera positions that is fairly close together, to be interpolated. Bill On May 22, 2011, at 9:57 AM, James Propp wrote:
Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".)
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.
It's okay with me if the egg's mechanism "tethers" it via electromagnetic waves to an external device that tracks it in 3D and tells it when to hum.
It's also okay with me if the egg isn't an egg but a sphere or cube (or a doll resembling P. A. M. Dirac).
Jim Propp
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