Alberto said:

> It looked like nonsense because you are too Cartesian. 
> Maybe you should think in some Riemmanian space, where 
> the theorem of Pythagoras is no longer valid. 

Nevertheless, a Riemannian space has a metric (by definition), and so we
can still generate scalars from the inner products of vectors (as long
as the vectors are elements of the same tangent space).

Rich
GSV Differential Geometry Is Fun

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