Interpreting is making meaning out of signs. A text can be spoken to mean different things and the same happens with music or choreography. Every artistic director can understand slightly different things from a set piece and, if they restage it, this understanding is what will make their production different from the others. That is part of the game, because art, as opposed to science, is concerned with subjectivity. It’s great that art validates human nature in this way, because humans are not gauges; our take on things is always an interpretation. Being aware of this (and of when our interpretation is becoming a distortion) can make communicating and relating to others and the world a lot simpler.
