>Ok, I'm still convinced we can do better than either, will try to figure
it out.


Can't blame a man for trying :)
Food for thought though:

http://en.wikipedia.org/wiki/Hairy_ball_theorem

The hairy ball theorem! It basically says that a tangent field on the
surface of a sphere in an odd dimensional vector space
must partition somewhere. Couldn't help bring it up since it's a classic :)
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