Handedness in coordinate systems

When I learned about handedness in coordinate systems, it was algebraically (AxB=C, BxA=-C), which is interesting but doesn't build much intuition. I enjoy analytic arguments, but ultimately it's the intuitive reasoning that tends to stick with me and inform new insights.

I often had trouble remembering which meant which, staring at my hands trying to remember how "that stuff" went, looking rather silly the while. I recently wanted to recall what OpenGL and D3D respectively do, and came across this discussion on real-time rendering, pointing out that even the pros get mixed up sometimes.

His example gave me, finally, a good piece of intuition about handedness: label your thumb X, index Y, and middle Z.

A right-handed coordinate system is what you have when you imagine your world relative to your desk: X goes east, Y goes north, and Z goes into the sky.

A left-handed coordinate system is what you get when you imagine your world relative to your monitor: X goes right, Y goes up, and Z goes into the monitor.

A perfectly good reason why modellers would prefer their object coordinates to be in a RHS, and programmers might convert it to LHS.