Some time has passed. From Ophelia’s remarks in III.ii. (which happens the day after II.i), we learn that Old Hamlet has now been dead for four months. Shakespeare telescopes time. We learn (in this scene) that Ophelia has (on Polonius’s orders) refused to accept love letters from Hamlet and told him not to come near her. We learn in the next scene (which follows soon after) that the king and queen have sent to Wittenberg for Hamlet’s long-time friends, Rosencrantz and Guildenstern (two common Danish surnames), and that they are now here. Hamlet has been walking around aimlessly in the palace for up to four hours at a time.
Polonius, in private, sends his servant Reynaldo to spy on Laertes. Polonius reminds him of how an effective spy asks open-ended questions and tells little suggestive lies. Polonius likes to spy.
Ophelia comes in, obviously upset. She describes Hamlet’s barging into her bedroom, with “his doublet all unbraced” (we’d say, his shirt open in front), his dirty socks crunched down, and pale and knock-kneed, “as if he had been loosd out of hell / to speak of horrors.” Or, as might say, “as if he’d seen a ghost.” Hamlet grabbed her wrist, stared at her face, sighed, let her go, and walked out the door backwards.
What’s happened? Hamlet, who has set about to feign mental illness, is actually just acting on his own very genuine feelings. Hamlet cares very much about Ophelia. He must have hoped for a happy life with her. Now it is painfully obvious that they are both prisoners of a system that will never allow them to have the happiness that they should.
When Hamlet act like a flesh-and-blood human being showing authentic emotions, people like Polonius will say he is insane. And Polonius suggests Hamlet is lovesick. Maybe Polonius really believes this. Maybe he just realized that perhaps his daughter might be the next Queen of Denmark.
The king and queen welcome Rosencrantz and Guildenstern. Claudius says that except for the death of Hamlet’s father, he’s clueless as to why Hamlet is upset. (Uh huh.) He asks them very nicely to try to figure out what’s wrong so Claudius can help. (Now Claudius might well be sincere.) Gertrude says she wants them to make Hamlet happy, and that the good and generous king will reward them well. Both say how much they appreciate the opportunity, and Claudius thanks them. Often a director will have Claudius call each by the other’s name, and Gertrude point out which is which (lines 33-34). They go off to find Hamlet.
Polonius comes in and announces that the ambassadors from Norway have returned, and that after their report he will tell them why Hamlet is acting strange. Gertrude thinks that Hamlet is simply distressed over his father’s death (which Claudius thought of) and her remarriage (which Claudius pretended he couldn’t think of.)
The ambassadors are back from Norway. Fortinbras was indeed mounting an army to attack Claudius’s Denmark. The King of Norway was sick and supposedly thought Fortinbras was going to invade Poland instead. (Uh huh.) When he “learned the truth”, the King of Norway arrested Fortinbras, made him promise not to invade Denmark, and paid him to invade Poland instead. The King of Norway now requests that Claudius let Fortinbras pass through Denmark for the invasion. (Denmark is on the invasion route from Norway to Poland if the Norwegian army is to cross the sea to Denmark. And we know a sea-invasion was expected from the amount of shipbuilding mentioned in I.i.) This all seems fake and for show, and probably Claudius (who doesn’t seem at all surprised) and the King of Norway had an understanding beforehand.
As before, Polonius can be a foolish busybody or a sinister old man. (Foolish busybodies do not usually become chief advisors to warrior-kings.) Polonius launches into a verbose speech about finding the cause of madness, prompting the queen to tell him to get to the point (“More matter with less art”; the queen actually cares about Hamlet.) He reads a love letter from Hamlet. It’s about the genuineness of his love. Polonius asks the king, “What do you think of me?” The king replies, “You are a man faithful and honorable.” Now Polonius tells a lie. He emphasizes that he had no knowledge of Hamlet’s love for Ophelia until she told him and gave him the love letter. Polonius tells how he forbade Ophelia to see or accept messages from Hamlet. Polonius does not mention the wrist-grabbing episode. He then reminds the king of how reliable an advisor he has always been, and says “Take this from this” (my head off my shoulders, or my insignia of office from me; the actor will show which is meant) “if this be otherwise.” He finishes, “If circumstances lead me i.e., allow, I will find / Where truth is hid, though it were hid indeed / Within the center of the earth.” He suggests he and the king hide and watch Ophelia and Hamlet. Polonius likes to spy.
At this time, Hamlet (who may have been eavesdropping), walks in reading a book. Polonius questions him, and Hamlet pretends to be very crazy by giving silly answers. They are pointed, referring to the dishonesty of Polonius (“To be honest, as this world goes, is to be one man picked out of ten thousand.”) Hamlet is well-aware that Polonius has forbidden Ophelia to see him, and he refers obliquely to this. Polonius notes in an aside (a movie director would use a voice-over), “Though this be madness, yet there is method in it” — another famous line often misquoted. The speech of the insane, as Polonius notes, often makes the best sense.
Polonius leaves, and Rosencrantz and Guildenstern (who have been watching) enter. Hamlet realizes right away that they have been sent for. They share a dirty joke about “Lady Luck’s private parts” which would have been very funny to Shakespeare’s contemporaries, and Hamlet calls Denmark a prison. When they disagree (“Humor a madman”), Hamlet says “There is nothing either good or bad but thinking makes it so. To me it is a prison.” (Note that Hamlet is obviously not referring to the idea that there are no moral absolutes — as do certain contemporary “multiculturalists”.) The idea that attitude is everything was already familiar from Montaigne, and from common sense.