Crazy

Ok so here I am reading Hamlet and watching David Tennant's Hamlet on YouTube and once again I'm faced with the same question that has been bothering me from the beginning of the whole play.

Is Hamlet going crazy?

I have absolutely no idea whether I should trust in Hamlet as a reader or whether I should pity his condition. In all of ACT III we can see a Hamlet that shows illogical and nonsensical traits although there is a certain "method to his madness." An example is when he is with Rosencrantz and Guildenstern and begins to randomly talk about the recorders. At first I thought, "Oh lord, here we go again with his foolish behavior" but then out of no where, Hamlet actually turns the whole recorder business into a way of insulting Rosencrantz and Guildenstern.

Also, the whole play that Hamlet decides to put on is very curious with all the absurd players with absurd dialogs. To most of the people in the court, Hamlet has gone crazy. They think that his actions are completely irrational when the truth is that Hamlet is actually thinking quite clearly through it all. His lucidity contrasts greatly to his odd behavior.

I am interested in hearing all of my classmates' opinions on this subject and I hope that in the play we may pick up more clues that might help me answer this question of Hamlet's sanity.