Murders in the Rue Morgue

I believe the center of this story can be found in rationale or rational thought.  As the reader follows Dupin through the narrative we observe his use of his rationale to make conclusions, even if they do not seem likely they are rational.   In the beginning of the story Poe talks of a chess game in which the "Our player confines himself not at all; nor, because the game is the object, does he reject deductions from things external to the game."   Poe is asserting right away that a rational mind must take into account all things, not just make assumptions from the way one thinks things should be - just like the missing money was a wild goose chase that didn't amount to anything in the story in the end.  

If we take the opposite of rational thought, we are left with irrational thoughts.   In this story the orangoutang actually somewhat represents the irrational.  If irrationality were to take the center of this tale, than the murders, though gruesome, would not be perplexing, they would actually be the norm, and the man or woman who would attempt to put the pieces together to find out what happened would be the outcast.