Simplicity is a deceptively simple thing. Recently, a scientist who was trying to explain something in general relativity to me did so in the following way:

One simple way to understand … is as follows. Imagine that one sets up spherical polar coordinates, so that space is described by r, \theta, \phi and time is described by t. Then in this frame what one would normally call a non-rotating observer is one who has no angular velocity in \theta and \phi i.e. if the proper time of the observer is \tau, then {d \theta \over d \tau} = {d \phi \over d \tau} = 0.