What is the significance of Louisa's obsessive neatness in "A New England Nun"?
Under a modern perspective one could certainly argue that Louisa's compulsive and obsessive neatness is a consequence of the repressed emotions that she has pushed down within regarding the wait for her fiance. She had been waiting already fourteen years, but that is not all that she is holding upon her shoulders: She is slowly realizing that she really does not want to marry him, and that she would prefer to do the unthinkable for her day and time: To live independently without a husband.
Given the societal expectations of the time, Louise is really having dangerous thoughts that may have put her at a level of anxiety that she can only channel through consistently operating in the same way over and over. In fact, doing this is the only thing that puts her in control of a life she is trying so desperately to control in terms of its fate. In her time and place, women had control of nothing. She wants control of everything. Hence, it may very well have been that she developed an obsession with doing things she could do and undo, clean and soil, fix and break as a way to show herself (in a modern OCD way) that she can hold control at least of some of her choices.