From "The Tell-Tale Heart," what is some evidence that the narrator is insane?
One of our first clues that the narrator is not in his right mind is that he has become obsessed with the old man's "vulture eye," as he calls it. He says that once he conceived of the idea to kill the old man, he becomes obsessed with it. However, he says, "Object there was none. Passion there was none. I loved the old man. He had never wronged me. He had never given me insult. For his gold I had no desire." First, he wants to murder the old man, a big clue to his insanity on its own. In addition, the only reason he has to kill him is to get rid of the man's eye; it freaks the narrator out. If there is such a thing as a good reason to kill someone, this is not it. We might be able to comprehend greed or passion or something like this, but murdering someone because their eye is offensive to you is not sane.
Another clue is the narrator's obsessive, seemingly compulsive repetition, night after night, of approaching the old man's door "just at midnight" and the slow process of inserting his head and lantern into the old man's room. A totally sane person would simply not feel such satisfaction in this repetition, or the need to continually repeat the same process again and again. Further, he cannot kill the old man when he is sleeping, with his eye closed. It is the rage produced by the sight of the eye that finally enables the narrator to complete the deed.
Further, the narrator believes that he is hearing the old man's heartbeat, first across the room when the old man lies awake and listening, next after the narrator has actually killed and dismembered the man and buried him beneath the floorboards. A sane person would realize that someone's heart cannot continue to beat after they have died.