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In a story called "The Birthmark," Nathaniel Hawthorne tells about an extraordinarily lovely woman whose beauty was perfect except for a small birthmark on her cheek. This flaw would not have mattered if found on the face of an ordinary woman, but because of this woman's near perfection, the birthmark could never be ignored. Her husband, a brilliant natural scientist, grieved over the one imperfection and took up research to discover a cure. He finally developed a potion and the birthmark began to disappear. At the moment when the birthmark completely vanished from her skin and she was perfect, she died.
Kotler et al. (Fri,) studied this question.