Let me muse that it seems to me that this decision ( to distinguish right
vs left handed systems, the RHR, etc) must have arisen from our desire to
model rotational velocity with a vector - we found that the best we could
do was to invent the pseudo-vector with the above mentioned baggage.
Instead Clifford Algebra invents the "bivector", a circulation in the
plane, with no necessary reference to a new dimension out of the plane.