  It has long been known to mathematicians and physicists that while a full
rotation in three-dimensional Euclidean space causes tangling, two rotations
can be untangled. Formally, an untangling is a based nullhomotopy of the
double-twist loop in the special orthogonal group of rotations. We study a
particularly simple, geometrically defined untangling procedure, leading to new
conclusions regarding the minimum possible complexity of untanglings. We
animate and analyze how our untangling operates on frames in 3-space, and teach
readers in a video how to wave the nullhomotopy with their hands.
