[twangist]

Fine point: in the case of "negative" (clockwise) rotations, the negative sign applies only to a scalar (an angle), not a vector. Surely even negative money is a real thing too: debt, or anyway debit. (Granted, debt can be less real than a pile of cash: if you're owed you might never be repaid, if you owe you might default. But that's a case of reality not matching theory well :)

In physical applications, relative to a coordinate system negative numbers have perfectly intuitive meanings. A negative spatial coordinate simply indicates a point in one of the quadrants or octants other than the all-positive-coords one. A negative acceleration means something is slowing down.

I see no good purpose served by special-casing "negative" integers, and many needless ensuing headaches.