  We show that the number of stabilizations needed to interchange the
handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is
bounded below by the smaller of twice its genus or half its Hempel distance.
This is a combinatorial version of a proof by Hass, Thompson and Thurston of a
similar theorem, but with an explicit bound in terms of distance. We also show
that in a 3-manifold with boundary, the stable genus of a Heegaard splitting
and a boundary stabilization of itself is bounded below by the same value.
