Inferno Canto XXVI (the Eighth Circle, Eighth Pouch: the Fraudulent Counselors)
Dante’s takes this opportunity to diss Florence. He does it ironically, saying how "great" the city is because of those thieves that Dante recognized, five were Florentines.
He prophecies that rival cities, like Prato, will one day battle Florence. Dante only wants that day to come faster. No love for his hometown.
Our dynamic duo makes its way into the next pouch. And it only gets harder. This time they have to crawl on their hands and knees up and down jagged rocks that serve as a makeshift staircase into the next valley.
Because crawling on gravel makes people (even epic poets) grumpy, Dante begins griping about the sinners. He says that they should use their talents (because obviously thieves and counselors have some talent) for good, not evil.
At first sight of the next pouch, Dante describes it with a metaphor, comparing it to the swarms of fireflies a resting farmer can see hanging over his crops in the evening. Because in this pouch, there are a lot of flames.
Ready for another metaphor? The movement of the flames is like that of Elijah’s chariot, which rose to Heaven as a star.
So why are there rising tongues of flame? Because each individual flame contains a sinner that moves when he moves. Cool, right? Also: really painful.
Dante is so interested that he leans dangerously over the bridge to see the sinners.
Virgil senses his eagerness and decides to show off his knowledge. He tells Dante that each flame contains a sinner.
Dante already knows this and politely tells Virgil so, but it’s obvious he’s proud that he outguessed Virgil.
Instead of dwelling on it, he assumes the position of ignorant student again and asks who that double flame is that is approaching.
Virgil, the all-knowing, answers him: Ulysses and Diomedes. He explains with authority that these two were almost single-handedly responsible for the Trojan horse and the sacking of the Palladium (Athena’s temple) and that’s why they’re punished together in a single flame. This was something Virgil happened to recount in his Aeneid.
Dante begs Virgil to let him talk to the two sinners. He’s pretty desperate.
Virgil indulges him. But on one condition, that Dante doesn’t speak. Virgil wants to talk to them and his excuse is that because they’re Greek, they might look down on Dante’s Italian.
Virgil approaches them, obsequiously and politely asking one of them to describe his death.
So the bigger of the twinned flames (because Ulysses was a greater hero than Diomedes) begins to wag back and forth like a tongue trying to speak. Well, in fact, that’s exactly what it is.
Eventually the flame-tip/tongue finds its voice and tells its story. Here's his tale:
Ulysses’ return journey from the Trojan War (recounted in the Odyssey) isn't as straightforward as he might have hoped. Instead, because of a few mishaps, he ends up doing a lot more exploring.
He sails past Spain and Morocco and even passed the pillars of Hercules, which at the time are the boundaries of the known world.
Then, to encourage his tired crew, he gives a grand speech. "Brothers, we’ve explored further than any man ever has before. And we should continue exploring. Because we’re men, not animals! And we crave knowledge."
So with the men rearing to go, they sail out with the wind and with joy in their hearts until they reach (gasp)… the Southern hemisphere. (We know this because suddenly the stars turn upside down.)
They sail for five days until they see a really high mountain rising in the distance. This is the Mount of Purgatory. Apparently, God decides "this is far enough" because then a whirlwind springs up, heads straight for the boat, and everyone dies.