  We argue that the mean crossing number of a random polymer configuration is
simply a measure of opacity, without being closely related to entanglement as
claimed by several authors. We present an easy way of estimating its asymptotic
behaviour numerically. These estimates agree for random walks (theta polymers),
self-avoiding walks, and for compact globules with analytic estimates giving
$\log N, a-b/N^{2\nu-1},$ and $N^{1/3}$, respectively, for the average number
of crossings per monomer in the limit $N\to \infty$. While the result for
compact globules agrees with a rigorous previous estimate, the result for SAWs
disagrees with previous numerical estimates.
