I don't mean to diss basic research, which is incredibly valuable and important as a whole, but the mechanisms for awarding grants, tenure, and professional prestige in academia can get almost totally decoupled from the realistic value of the research. When I was finishing my thesis and deciding not to apply to academic jobs, a fairly prominent mathematician told me that he thought the average readership of a published mathematical paper was slightly less than one, even if you included the referees.
Much depends on what you mean by "productive", of course. Whatever one does that draws a paycheck, it's "productive" in the sense that someone thinks it was worth paying for, right? And it puts food on your family, finances your camera addiction, and keeps a person from becoming an idle, destructive vacuum with nothing to do with their lives.