My first dog, Mercy, was a border collie mix whose body could convey an epic narrative—especially when she was in the dog park communicating at once with dozens of her kind. I soon began to wonder just what they were all saying. Their gestures were obviously dense with meaning. At times, a nearly invisible movement by another dog would change Mercy’s course dramatically: She would bend into a play bow, or stiffen in alarm, or look away as if hoping that the dog enthusiastically eyeing her would suddenly forget she existed. Often he would.

Watching...