To make vain efforts against insurmountable difficulties. This expression, with its vivid image of futility, dates from the sixteenth century, when John Lyly (or some other author) wrote, “Thou shalt . . . have thy head runne against a stone wall” (1589). Other equally hard objects, like doors, were cited in similar fashion. By 1887, however, it was “If we run our heads against walls we’re safe to hurt ourselves” (M. Sergeant, Jacobi’s Wife, 1.1).