The Perfect Woman in M. Butterfly and Cloud 9

When I was reading M. Butterfly I was struck by the term "the Perfect Woman". It reminded me of Cloud 9, specifically the character of Betty. In M. Butterfly the perfect woman of Song is literally a man. He is pretending to be a woman in order to gain information on American activities in Vietnam. This "perfect woman" is literally a man creating a female alter ego which is tailored to the wants of Gallimard. Even when Gallimard is reflecting on his relationship with Song after he knows that she is actually a man he still insists he was loved by the perfect woman. This can be compared to Betty from Cloud 9 who, in Act 1, is a man playing a woman. This similarity is interesting because they are both supposedly the ideal or perfect woman. This begs the question of what makes the perfect woman. According to these two plays it is not the physiology of the person, it is the gender identity they choose to perform. This challenges the generally accepted idea of gender being determined by a person's physical body and is very intriguing to think about in my opinion.