Source : Webster's Revised Unabridged Dictionary (1913)

Barrenness \Bar"ren*ness\, n.
   The condition of being barren; sterility; unproductiveness.

         A total barrenness of invention.         --Dryden.

Source : WordNet®

barrenness
     n 1: the state (usually of a woman) of having no children or
          being unable to have children
     2: a condition yielding nothing of value [syn: {fruitlessness},
         {aridity}] [ant: {fruitfulness}]