Any division or deliberate dissection into two parts or more suggests a movement away from unity, from a state of perfection.
Psychological / emotional perspective: To divide into parts signifies creating manageable portions, perhaps breaking down a series of actions to understand them better. Crossing a divide is similar to crossing a chasm: we must face our own fears.
Material aspects: When we are dissecting a body or animal we are trying to learn how something works or what relationships the various parts might have with one another. This might apply to a task or project in waking life.