meanerelk comments on Why Quantum? - Less Wrong
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I think is is a common problem for many mathematical conventions in physics.
The same thing happened be me in high school physics. I was confused by the torque vector, and I spent an entire year thinking that somehow rotation causes a force perpendicular to the plane of motion. I just could not visualize what the heck was going on.
Finally I realized the direction of the torque vector is an arbitrary convenience. My teacher and textbook both neglected to explain why it works like that.
The "why's" are important!