The dungeon that the protagonist of Poe's story is trapped within enters the narrative as an unsolved question. It is tabula rasa; it is pure unknown possibility. It is only through making use of what little he has with him that the protagonist is able to learn anything about its environs:
My outstretched hands at length encountered some solid obstruction. It was a wall, seemingly of stone masonry -- very smooth, slimy, and cold. I followed it up; stepping with all the careful distrust with which certain antique narratives had inspired me. This process, however, afforded me no means of ascertaining the dimensions of my dungeon; as I might make its circuit, and return to the point whence I set out, without being aware of the fact; so perfectly uniform seemed the wall. I therefore sought the knife which had been in my pocket, when led into the inquisitorial chamber; but it was gone; my clothes had been exchanged for a wrapper of coarse serge. I had thought of forcing the blade in some minute crevice of the masonry, so as to identify my point of departure. The difficulty, nevertheless, was but trivial; although, in the disorder of my fancy, it seemed at first insuperable. I tore a part of the hem from the 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. So, at least I thought: but I had not counted upon the extent of the dungeon, or upon my own weakness.
Note, though, that exploration and making use of unconventional tactics is itself an incomplete strategy. It's missing an essential underworld logic. It surveys the field, and the narrator learns that the space is "fifty yards in circuit," but it does not in itself provide an answer that solves the dungeon. Ultimately, the dungeon is only subverted by meeting it on its own illogical, madness-inducing, mythological terms.
In fact, the protagonist's initial measurements may have been incorrect; the logic of the mundane world holds no sovereignty in the mythic underworld. There is no Enlightenment where there is only flickering torches.
As the pendulum begins to swing down, it is only through indulging in dungeon logic that the protagonist figures out how to use the rats to escape bondage and certain death:
Observing that I remained without motion, one or two of the boldest leaped upon the frame-work, and smelt at the surcingle. This seemed the signal for a general rush. Forth from the well they hurried in fresh troops. They clung to the wood -- they overran it, and leaped in hundreds upon my person. The measured movement of the pendulum disturbed them not at all. Avoiding its strokes they busied themselves with the anointed bandage. They pressed -- they swarmed upon me in ever accumulating heaps. They writhed upon my throat; their cold lips sought my own; I was half stifled by their thronging pressure; disgust, for which the world has no name, swelled my bosom, and chilled, with a heavy clamminess, my heart. Yet one minute, and I felt that the struggle would be over. Plainly I perceived the loosening of the bandage. I knew that in more than one place it must be already severed. With a more than human resolution I lay still.
Nor had I erred in my calculations -- nor had I endured in vain. I at length felt that I was free.
I struggled no more, but the agony of my soul found vent in one loud, long, and final scream of despair. I felt that I tottered upon the brink -- I averted my eyes --
And then catharsis. Not the pit and certainly not the pendulum. Instead, the French army enters Toledo. "It's okay," they say, "Gary sent us."