It might be a good idea to familiarize yourself with the plot of the adaptation here:
The Coen brothers’ film, O Brother, Where art Thou?, loosely adapts the plot elements of Homer’s Odyssey, but, given that the Coen brothers admitted not having read the canonical text before making their movie, we find that thematic and structural divergences are quite frequent between the two. The film opens with an invocation of the Muses—as the text does—both by displaying a still shot of Homer’s initial lines paired with a chain gang rhythmically singing to inspire their Sisyphean task, which sets the tone for the cyclical nature of the narrative that will ensue.
The initial meanderings of Telemachus within Ithaca for the opening four books of the Odyssey are left untouched and we find ourselves immediately immersed the narrative of Ulysses (the latinized name for Odysseus) and his two companions, Pete and Delmar. We follow these men nearly without digression for the majority of the film, and the arch follows a progressive, chronological course, as opposed to Homer’s intricate weave of storytelling and parallel narratives. While we cannot entirely attribute this to intent (if we accept that the Coen brothers never read Homer’s text), it still retools the themes. Homer’s prominent use of storytelling is at some level a self-referential element, one that served to immortalize the bard by appealing to the continuity of myth as a medium. What the Coen brothers submit instead is a present, clear account of Ulysses’ wanderings, which fixes our perception of events: they can be in no way mutated by a storyteller, but are experienced visually, as they occur, and the focus hones in on the relationship between the three main characters.
In terms of plot, within the Odyssey, we first find Odysseus wallowing in self-pity on Calypso’s island, but the characters in our film have already executed their escape from their island (jail). What characters stand to lose or gain on Calypso’s island is markedly different in jail: Odysseus fears being forgotten whilst enjoying the god-like existence afforded him on Calypso’s island. Obviously, the opportunities afforded in jail are considerably less, but the risk of an escape mission is the possibility of seeing even more time in jail. The images granted us by the Coen brothers depict imprisonment as a laborious, ceaseless, anonymous life, and thus the fear of falling out of remembrance is not entirely lost. What drives Odysseus, contrastedly, is a desire to see his family as well as, at some level, immortality through memory, losing the chance of a literal immortality on Calypso’s island. Ulysses, under the pretense of buried treasure, wishes to stop his wife from getting remarried, and risks much less, and thus the goals are to some end similar, but Ulysses’ choice is much more heavily weighed towards escape.
Ulysses’ group attempts to board a moving train soon after their escape, still chained together (foreshadowing the necessity of their friendship). Ulysses lifts himself into an open car and starts to inquire whether the vagabonds aboard it have any experience in the “metal-urgic arts.” Ulysses fails to help Pete and Delmar onto the car in ignorance of their struggle to board, and here we have a parallel between the characters of Ulysses and Odysseus: a sort of selfish hubris, which manifests itself within the Odyssey in the Cyclops scene (wherein Odysseus shouts his name out of pride) and in book ten, immediately after Odysseus receives the bag of winds and insists on commandeering the ship for ten successive days and nights to see the men to Ithaca. Not only does Ulysses declare himself the leader of the group, but he convinces the two men to escape with him under the false assurance of a $1.2 million fortune. Both Odysseus and Ulysses operate selfishly, but, whereas Odysseus largely overcomes obstacles by his own agency (and is the only one to survive from his crew), we understand in O Brother that Ulysses must compromise his hubris at some level to make his way back home, collaborating with Pete and Delmar on a song recording that—unbeknownst to them—acquires them fame that ultimately inspires the pardoning of their crimes and completes their homecoming.
Both stories also present a prophecy, given by Teiresias in the Odyssey and an old man on the railroad in O Brother. What plays out differently between the two is the faith placed in that prophecy: both seers set out a long and arduous course for our heroes, but Odysseus undertakes to perform the tasks ordained to him, whereas Ulysses—often outright critical of superstition and religion—believes to an even greater degree in his own agency. Ulysses attempts to qualify anything that could be chalked-up to superstition or divine intervention as a scientifically plausible reality, until he is faced with imminent death that is, a scene which recalls a prominent narrative device the Coen brothers employ: deus ex machina, or “god from the machine.” Perforated within the film are brief moments of inexplicable luck: when Pete throws a torch that—by extremely fortunate circumstances—leads to one instance of escape from the police, and the flood scene when the boys stand in front of the noose set out for them by the “devil,” saved only by Ulysses’ sincere appeal to God. This last event is a quintessential example of deus ex machina, where the characters are only saved by a Divine flood; but Ulysses, ever the pragmatist, attempts to attribute the flood to a government hydroelectric power initiative. In favor of Odysseus’ greater level of faith, the gods are present at many stages of Odysseus’ tale, from giving instructions to preventing the prospect of bloodshed in the last scene of the text (the confrontation between Odysseus and the people of Ithaca). While not as prevalent in O Brother as the Odyssey, Divine intervention serves to monitor the narrative and compensate for the failed tactics of Ulysses, despite his hesitation in accepting that help. These respective final scenes also expose the lack of development in our main characters: Odysseus attempts to enforce the rage-begets-rage system until Athena intervenes, and Ulysses still applies a scientific lens to that which is ostensibly Heaven-sent.
Generally, though the two stories differ on specifics, the overarching narrative follows a similar structure as it pertains to achieving the desired homecomings. We see within the Odyssey that Odysseus and his crew often come close to reaching their destination, or at least find themselves in a good spot, only to have that progress thwarted by a crew member’s ignorance (the bag of winds and Hyperion’s livestock). In O Brother, the boys experience car problems, get rich through the machinations of a bank-robber, have run-ins with the law, and, particular to Ulysses, find that the homecoming itself is wrought with difficulties: Ulysses must contend with a suitor and distinguish himself to both his children and his wife (which he achieves with the performance of the Soggy Bottom Boys’ famous song). The ups and downs of the main characters parallel those of Odysseus, often bringing the characters a small victory followed by some hiccup that reverses their progress at every turn. The Coen brothers expose this narrative device with the George Nelson character, who feels the thrill of quick cash and the lows experienced by the emptiness of his profession. His depiction also calls to mind the Cyclops scene in which Odysseus insists that the Cyclops know his name: George Nelson declares his name ad nauseam, but we see the price of his pride in his capture near the end.
Joel and Ethan Coen, O Brother, Where art Thou?, 2000