  Given a knot K in the 3-sphere, consider a singular disk bounded by K and the
intersections of K with the interior of the disk. The absolute number of
intersections, minimised over all choices of singular disk with a given
algebraic number of intersections, defines the framing function of the knot. We
show that the framing function is symmetric except at a finite number of
points. The symmetry axis is a new knot invariant, called the natural framing
of the knot. We calculate the natural framing of torus knots and some other
knots, and discuss some of its properties and its relations to the signature
and other well-known knot invariants.
