  Knotted and tangled structures frequently appear in physical fields, but so
do mechanisms for untying them. To understand how this untying works, we
simulate the behavior of 1,458 superfluid vortex knots of varying complexity
and scale in the Gross-Pitaevskii equation. Without exception, we find that the
knots untie efficiently and completely, and do so within a predictable time
range. We also observe that the centerline helicity -- a measure of knotting
and writhing -- is partially preserved even as the knots untie. Moreover, we
find that the topological pathways of untying knots have simple descriptions in
terms of minimal 2D knot diagrams, and tend to concentrate in states along
specific maximally chiral pathways.
