I need to come up with one big idea present in Hamlet , or something the reader can learn from examing one of the characters. But I can't think of any think good, I really need help please.
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I believe the perfect theme for your project would be that of the "appearance of madness." Feining madness when backed into a corner or in defending oneself from criminal prosecution is a centuries old practice. The following is Gradesaver's take on the theme of the appearance of madness.
By the time Hamlet was written, madness was already a well-established element in many revenge tragedies. The most popular revenge tragedy of the Elizabethan period, The Spanish Tragedy, also features a main character, Hieronymo, who goes mad in the build-up to his revenge, as does the title character in Shakespeare's first revenge tragedy, Titus Andronicus. But Hamlet is unique among revenge tragedies in its treatment of madness because Hamlet's madness is deeply ambiguous. Whereas previous revenge tragedy protagonists are unambiguously insane, Hamlet plays with the idea of insanity, putting on "an antic disposition," as he says, for some not-perfectly-clear reason.
Of course, there is a practical advantage to appearing mad. In Shakespeare's source for the plot of Hamlet, "Amneth" (as the legendary hero is known) feigns madness in order to avoid the suspicion of the fratricidal king as he plots his revenge. But Hamlet's feigned madness is not so simple as this. His performance of madness, rather than aiding his revenge, almost distracts him from it, as he spends the great majority of the play exhibiting very little interest in pursuing the ghost's mission even after he has proven, via "The Mouse Trap," that Claudius is indeed guilty as sin.
No wonder, then, that Hamlet's madness has been a resilient point of critical controversy since the seventeenth century. The traditional question is perhaps the least interesting one to ask of his madness -- is he really insane or is he faking it? It seems clear from the text that he is, indeed, playing the role of the madman (he says he will do just that) and using his veneer of lunacy to have a great deal of fun with the many fools who populate Elsinore, especially Polonius, Rosencrantz and Guildenstern. Perhaps this feigned madness does at times edge into actual madness, in the same way that all acted emotions come very close to their genuine models, but, as he says, he is but mad north-nothwest, and knows a hawk from a handsaw. When he is alone, or with Horatio, and free from the need to act the lunatic, Hamlet is incredibly lucid and self-aware, perhaps a bit manic but hardly insane.
So what should we make of his feigned insanity? Hamlet, in keeping with the play in general, seems almost to act the madman because he knows in some bizarre way that he is playing a role in a revenge tragedy. He knows that he is expected to act mad, because he thinks that that is what one does when seeking revenge -- perhaps because he has seen The Spanish Tragedy. I'm joking, of course, on one level, but he does exhibit self-aware theatricality throughout the play, and if he hasn't seen The Spanish Tragedy, he has certainly seen The Death of Gonzago, and many more plays besides. He knows his role, or what his role should be, even as he is unable to play it satisfactorily. Hamlet is beautifully miscast as the revenger -- he is constitutionally unfitted for so vulgar and unintelligent a fate -- and likewise his attempt to play the madman, while a valiant effort, is forced, insincere, anxious, ambiguous, and full of doubts. Perhaps Hamlet himself, if we could ask him, would not know why he chooses to feign madness any more than we do.
Needless to say, Hamlet is not the only person who goes insane in the play. Ophelia's madness serves as a clear foil to his own strange antics. She is truly, unambiguously, innocently, simply mad. Whereas Hamlet's madness seems to increase his self-awareness, Ophelia loses every vestige of composure and self-knowledge, just as the truly insane tend to do.