I really don't like the coordinate-free explanations; which should be reserved for when you are comfortable with how two multivectors are multiplied. But Geometric Algebra is the most profound idea in geometry and mathematics. Forget about imaginary numbers for a while; and realize that they can be factored into a pair of orthogonal directions in space.
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@robfielding this is great stuff and so are Clifford algebras in general. Also very relevant to tuning theory
