Quote 4
HAMLET
I am but mad north-north-west: when the wind is
southerly, I know a hawk from a handsaw.
(2.2.402-403)
First, this seems to be Hamlet telling Rosencrantz and Guildenstern that he knows exactly what they're up to: spying on him. But we also included this as a little lesson in how things get lost in translation. "Handsaw" is almost certainly a corruption of "heronshaw," i.e. a heron—which sounds a lot less crazy than comparing a bird to a carpentry tool.
HAMLET
How is it with you, lady?
QUEEN GERTRUDE
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?
(3.4.132-141)
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.
Quote 6
HAMLET
O, what a rogue and peasant slave am I!
Is it not monstrous that this player here,
But in a fiction, in a dream of passion,
Could force his soul so to his own conceit
That from her working all his visage wanned,
Tears in his eyes, distraction in his aspect,
A broken voice, and his whole function suiting
With forms to his conceit—and all for nothing!
(2.2.577-584)
After watching one of the traveling players (actors) deliver a moving speech, Hamlet berates himself for his inability to avenge his father's murder. If an actor can weep for a fictional character, why can't Hamlet get himself moving for his actual dad? (If you've ever cried over a movie romance while remaining stony-hearted during an actual fight, you know this feeling.)