How we cite our quotes:
How is it with you, lady?
Alas, how is't with you,
That you do bend your eye on vacancy
And with the incorporal air do hold discourse?
Forth at your eyes your spirits wildly peep;
And, as the sleeping soldiers in the alarm,
Your bedded hair, like life in excrements,
Starts up, and stands on end. O gentle son,
Upon the heat and flame of thy distemper
Sprinkle cool patience. Whereon do you look?
What's striking about this passage is the fact that Hamlet is the only one who can see and hear the Ghost when it appears in Gertrude's bedroom. (Earlier in the play, the castle guards and Horatio could see the spirit but Hamlet is the only one who has ever spoken with it.) So, what's going on here? What's changed? One possible explanation is that the Ghost chooses to appear only to Hamlet. (This kind of thing is common in the literature of the period.) Another possibility is that Hamlet's the only one who can see the Ghost here because it's a figment of his imagination, which would mean that Hamlet has broken down and has lost his mind.
What, Gertrude? How does Hamlet?
Mad as the sea and wind, when both contend
Which is the mightier: in his lawless fit,
Behind the arras hearing something stir,
Whips out his rapier, cries, 'A rat, a rat!'
And, in this brainish apprehension, kills
The unseen good old man.
This is an incredibly interesting passage. In the previous passage, Hamlet tells Gertrude that he isn't crazy but he asks her to lie and tell Claudius that he is in fact mad. As we can see here, Gertrude tells the king that Hamlet's as "mad as the sea and wind." Why does she do this? Is she trying to protect her son by lying to Claudius? Or, does she really think Hamlet's gone off the deep end? Where do Gertrude's loyalties lie at this point in the play?
[…] poor Ophelia
Divided from herself and her fair judgment,
Without the which we are pictures, or mere beasts:
Here, Claudius describes Ophelia as being "divided from herself." In other words, she's lost her mind. But what causes Ophelia to go mad? Duh: her ex-boyfriend has murdered her father. Right? Well, maybe it's more complex than that. Maybe she's actually just cracked under the patriarchal pressures of the court. Throughout the play, Ophelia is ordered around by her brother and her father and has no control over her social or love life. Madness might just be the only way she has of fighting back.