inquisitiveness
In*quis"i*tive*ness, n. Defn: 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.