  A grid poset -- or grid for short -- is a product of chains. We ask, what
does a random linear extension of a grid look like? In particular, we show that
the average "jump number," i.e., the number of times that two consecutive
elements in a linear extension are incomparable in the poset, is close to its
maximum possible value. The techniques employed rely on entropy arguments. We
finish with several interesting questions about this wide-open area.
