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Really he does;t have a direct purpose in the play. He serves to contrast Torvald's relationship with Nora. Dr. Rank would have treated Nora more like a person than property or a child. He listens to Nora and does care about her. Unfortunately Nora just doesn't seem attracted to him or perhaps cannot handle being treated as an individual person. Dr. Rank's spinal sickness is often seen as symbolic of the disintegration of the backbone of society.