When Hamlet and Polonius meet in II,ii Hamlet calls Polonius a fishmonger and makes strange conversation with him.
In IV,iii Hamlet refuses to tell Claudius were he has hidden the body of Polonius and goes on about how Polonius is at supper.
When Hamlet encounters Gertrude in her closet, an unusual place, in III,iv.
Madness is defined as the state of being mentally ill or having extremely foolish behavior.
Only a sane and rational person could devise such a plan as to act insane to convince others that he is insane when he actually has complete control over his mind.
Hamlet only acts mad when he is in the presence of certain characters.
An example of this is when he asks, “You could, for a need, study a speech of some dozen or sixteen lines, which I would set down and insert in ‘t, could you not? Gertrude, not being able to see the ghost, says to Hamlet, “No, nothing but ourselves… This bodiless creation ecstasy is very cunning in” (3. Gertrude is bound to think Hamlet is mad since she sees him talking to nobody. Hamlet cleverly insults Polonius here and his wit shows how he is not mad.
The audience knows that Hamlet is not in fact mad and is actually talking to the ghost of his father. By feigning his madness, it allows him to speak whatever is on his mind without anyone being suspicious. Expressing his feelings induces reactions from others just as he wants.
From the very start, the ghost of Hamlet’s father tells him that Claudius is the one who murdered him. An antic disposition means to act in a grotesque manner.
As soon as he is aware of the news, Hamlet begins to plan his next steps, saying, “How strange or odd soe’er I bear myself, as I perchance hereafter shall think meet to put an antic disposition on” (1. This simply means that Hamlet is going to play a role of a mad person throughout the play.