  Stirring a two-dimensional viscous fluid with rods is often an effective way
to mix. The topological features of periodic rod motions give a lower bound on
the topological entropy of the induced flow map, since material lines must
`catch' on the rods. But how good is this lower bound? We present examples from
numerical simulations and speculate on what affects the 'gap' between the lower
bound and the measured topological entropy. The key is the sign of the rod
motion's action on first homology of the orientation double cover of the
punctured disk.
