The narrator is very curious and logical, and his ability to distract himself from his terror by considering his space and how best to understand his situation likely saves him from losing his mind in the dungeon. He's very observant in terms of using his senses to gain information about his surroundings, and he is a good problem-solver, too. The narrator determines a way to map the layout of his cell:
I tore a part of the hem from [my] robe and placed the fragment at full length, and at right angles to the wall. In groping my way around the prison, I could not fail to encounter this rag upon completing the circuit.
Although he falls and then begins to move in the opposite direction from which he started, throwing off his calculations about the size of his dungeon, this activity serves as a constructive one rather than allowing himself to descend into the depths of despair and horror which the idle mind might be more inclined to do.
"The Pit and the Pendulum" by Poe is a story about a victim of the Spanish Inquisition who finds himself at the bottom of a pit. The last thing he remembers is having fainted at hearing he would be sentenced to death. The story follows as the narrator offers his perceptions of the black pit and as he experiences new tortures until he is finally rescued.
While very little explicit information is given about the narrator, indirect characterization allows us to analyze his words and actions in order to get to know him. The two characteristics that best support the narrator's survival are his practicality and resolution.
For evidence of his practicality, we must analyze how the narrator studies his prison and how he outsmarts the officials of the Inquisition. He uses a knife and piece of his clothing as a marker in order to study the size of the pit as he paces around its edges in search of the marker. He drops a fragment of stone down the pit and waits to hear it drop in order to guess at its depth. To break free of rope restraints, he lies still enough for rats to ignore him and crawl onto him long enough to chew through his bindings. This resourceful nature keeps him from carelessly falling into the pit in the dark and allows him to escape the various near-death instances he faces while imprisoned.
The second useful character trait the narrator exhibits is his resolution, his sheer determination to survive. We know that he must be a man of principle, since the Spanish Inquisition only punished those with the courage to oppose the Catholic Church. In the pit, the narrator faces every temptation to give in and let himself die rather than to fight back. He is abandoned in a black hole full of rats and he's given food he supposes to be drugged. He is left strapped on a board while a razor slowly descends toward him at a maddening pace, and after he escapes that, he is surprised by heat emanating from the walls that are inching in closer to him, forcing him toward the pit. The fact that the narrator doesn't give up, doesn't stop trying to survive, is ultimately what keeps him alive long enough to be rescued.
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