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Character Role Analysis
Batman and Joker
It takes crazy to fight crazy, and both Batman and Joker are crazy in their own ways. Batman is a crazy loner who was all but created by Joker when, as Jack Napier, he killed young Bruce's parents in front of him. Ever since, Bruce has isolated himself and devoting his life to fighting crime.
After accidentally dumping Napier in acid, Napier becomes Joker. It's not quite up there with seeing your parents get murdered, but it's still a traumatic event that would make a man go a little crazy. Joker devotes himself to anarchy and what he calls "art."
Batman himself is an anarchist of sorts, taking the job of the police into his own hands. And both he and Joker appreciate different forms of art. It's the methods to their madness (or should it be "method to their madnesseseses"?) that sets these two apart.