"The Other" is a theme, motif or figure which seems to appear over and over in the movie. It could be nature, women, other races, other cultures, homosexuals, criminals, rulers, Gods, monsters, etc. In the film, the protagonist becomes just like "The Other" in order to resolve the problem. Usually, "The Other" is killed by the protagonist at the end of the movie. "The Other" is always the victim in the movie, it is a scapegoat: it is the focus of the resolution of the problems. In "Taxi Driver", "The Other", according to me, is two elements: women an criminals (gangsters). In the beginning of the film, the protagonist, Travis Bickle falls in love with a woman who works for Palantine as a volunteer. After going out with each other for a couple of times, the woman decides not to see Travis again. Travis says that she's just like the others, meaning just like all the other women. In order to take revenge, he tries to assassinate Palantine in front of her. "The other" also appears as gangsters in the movie. Travis, in order to eliminate them, becomes a criminal just like them. Therefor in "Taxi Driver",we see two good examples of "The Other".
In "Taxi Driver" we see that Travis Bickle still has an identity forming problem, or I might say that he has unconsciously formed an identity during his childhood, but he's trying to find it. It was his curiosity about his identity that was giving him problems to sleep. Basically, his identity should be formed based on his father's identity, but nothing is obvious. Whoever his (Travis) model was, planted the confidence in Travis to form his identity. For example, if our parents don't tell us in early our childhood about a certain quality that we have, we might have an identity crisis in our adult lives. In this film, we have a good example of "identity and rivalry". After Travis based his identity upon his model, he started a competition with his model, he tried to do something that his model wouldn't have done: he went out there and killed the gang members.
In "Taxi Driver", we get introduced to two types of women: "the good girl" and "the bad girls". Both of them are introduced in the beginning of the movie, but the first one, "the bad girl", appears more frequently in the first part of the movie. She is the one that Travis desires, the one that he would like to go to bed with. He even takes her out to an X-rated movie. this, of course, is way of saying let's get laid. He might have done it unconsciously, but it is obvious that he desired her. Although we are introduced to "the good girl" in the beginning of the film, She appears towards the end of it.
She is introduced to us as a hooker, getting into Travis' cab by saying: "get me out of here". Now, we all know that hookers make part of "the bad girls", but according to Travis, she's not. She's the girl that he wants to help, he would do anything to get her out of her miseries, so he does: he goes and eliminates the gang members that have control over her.
Therefor, here we have a perfect example of "Madonna/Whore Complex".
"Taxi Driver" is a film that doesn't have only one end. Certain events bring an end to story, where everything goes back to normality. The first event is when Travis tries to assassinate Palantine. The second one is when he takes out all the gang members in the building to save "the good girl", and the third is when "the bad girl" gets into his cab, and he completely ignores her because he has gotten over it.
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