  The convex hull of a set K in space consists of points which are, in a
certain sense, "surrounded" by K. When K is a closed curve, we define its
higher hulls, consisting of points which are "multiply surrounded" by the
curve. Our main theorem shows that if a curve is knotted then it has a nonempty
second hull. This provides a new proof of the Fary/Milnor theorem that every
knotted curve has total curvature at least 4pi.
