Is Macbeth Mad?

Macbeth, the protagonist of Shakespeare's "Macbeth", begins to go mad at the beginning of act two. Now, at this point in the narrative Macbeth is an interesting position, He has been given  the title,"Thane of Cowador",  by Duncan, who just happens to be the king. Duncan is at this point being a complete idiot and staying at the new thane's castle. Yes, because it's not like the last on tried to kill him or anything. On top of that Macbeth is in a very clear position to become king so long as he kills Duncan. So then , the moment he's alone he begins talking aloud to a floating dagger. Of course no one hears him because throughout the entire play no one really listens to Macbeth any ways. But hey, he's only the protagonist. Anyways at this point Macbeth starts losing it, "Thee handle toward my hand?/ come, let me clutch thee."(33-34). See, Macbeth is talking to an imaginary dagger. An imaginary dagger that convinces Macbeth to dutifully kill Duncan. So either Macbeth is on some kind of crazy medieval hallucinogenic  club drug, or he has gone mad.