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Mike Sigman wrote:
.... the key to understanding and to set up a basis for definitions is to find a common parlance. I think western physics is better suited than the ki paradigm, overall.
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Amen and Hallelujah. FWIW, vectors, historically, are degenerated forms of Hamilton's quaternions. Assymmetries matter because the order of action changes the result (non-commutative):
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A simple exercise of applying two rotations to an asymmetrical object (e.g., a book) can explain it. First, rotate a book 90 degrees clockwise around the z axis. Next flip it 180 degrees around the x axis and memorize the result. Then restore the original orientation, so that the book title is again readable, and apply those rotations in opposite order. Compare the outcome to the earlier result. This shows that, in general, the composition of two different rotations around two distinct spatial axes will not commute.
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Mostly, vectors work the same in the case of gross rotations -- but not in dealing with assymmetries, (like, say, gravity) -- or at cusps or reversal points. Like navigating close to a pole -- the grid references change scale (or sign in the case of assymetry) too fast to disregard and small changes in inputs have increasingly disproportionate outputs. Since that area of critical change is what we are interested in -- it makes sense that vectors, as such, become less and less useful at those critical points -- even though they are related.