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In Shakespeare's Hamlet, the characteristics of Hamlet in Act IV, scenes ii and iii, are that of feigned madness.
In Act III, scene iv, Hamlet had mistakenly killed Polonius, who was hiding behind a curtain in Gertrude's room in order to spy on Hamlet. At the end of the scene, Hamlet takes Polonius' body with him to dispose of it.
As scene ii begins, Hamlet has hidden Polonius' body, and Rosencrantz and Guildenstern arrive, at the King's request, to find out where the corpse is. Hamlet refuses to tell them, and plays word games with them. I believe, based upon what Hamlet said to his mother when they last spoke, that this is still part of his "antic disposition."
Hamlet becomes insulting, covering it with the show of madness. He has little regard for the pair before him, as he knows they are in the King's employ, and he knows they have no concern for him.
Hamlet refers to Rosencrantz as a sponge (one that simply soaks up that which is around him, not truly having a brain or will of his own):
sponge . . . that soaks up the King’s countenance, his rewards, his authorities....
But such officers do the King best
service in the end. He keeps them, like an ape, in the corner
of his jaw; first mouth'd, to be last swallowed. When he
needs what you have glean'd, it is but squeezing you and,
sponge, you shall be dry again.
Hamlet agrees to go with the two men to the King, but then darts, off (still acting the fool), with both men pursuing him, keeping up his sham of madness.
In scene iii, Claudius tries to get the location of Polonius' body from Hamlet, who resists. As with Rosencrantz and Guildenstern, he plays more word games, this time with the King. He tells Claudius that Polonius is at supper, but that he is not eating, but is, in fact, dinner: food for the worms. Hamlet continues his "nonsense," giving all the sense that he is, indeed, insane.
king and your lean beggar is but variable service, two
dishes, but to one table...
A man may fish with the worm that hath eat of a
king, and eat of the fish that hath fed of that worm.....to show you how a king may go a
progress through the guts of a beggar.
Then Hamlet says that Polonius is in heaven...or in hell. Finally he admits:
nose him as you go up the stair, into the lobby...He will stay till you come.
Claudius tells Hamlet he must go to England. (The King plans to have him killed there.) Hamlet is fine with this, but continues his word-play, this time, thinly veiling his insults toward the King, accusing him of an incestuous relationship with Gertrude.
Throughout both scene ii and scene iii, Hamlet continues to present the facade of insanity with his words and actions. In doing so, he can say what he wants, and others will chalk it up to an unhinged mind.
It is somewhat childish, in that it does not bring him any closer to avenging his father's murder, but at least it gives the King no clear evidence that Hamlet is aware of Claudius' murder of Old Hamlet. (Still, Hamlet's words hit home closely enough that Claudius fears he will inadvertently expose the King's crime, and Hamlet is antagonistic enough, that Claudius decides to send him to his death in England. Remember, the story takes place in Denmark.)