\In*quis"i*tive*ness\, n.
The quality or state of being inquisitive; the disposition to
seek explanation and information; curiosity to learn what is
unknown; esp., uncontrolled and impertinent curiosity.

      Mr. Boswell, whose inquisitiveness is seconded by great
      activity, scrambled in at a high window. --Johnson.

      Curiosity in children nature has provided, to remove
      that ignorance they were born with; which, without this
      busy inquisitiveness, will make them dull. --Locke.