There are many discussions about the use of the number "three" and its various symbolic uses. But seldom is there any discussion of the number "two." However, looking at the beginning of Hell Proper and the ending of Hell Proper would demonstrate two contrasting pairs forever bound together.
Canto V, therefore, enters Hell Proper, which may be said to begin with the second circle, because here Minos is seated as the judge to determine where the sinners before him are sent for punishment. Thus, Hell Proper begins with Canto V and the punishment of Francesca and Paolo.
In contrast, Hell Proper closes with another pair — Count Ugolino and Ruggieri — locked in an embrace, with Ugolino gnawing on the brainpan of Ruggieri. Even though the final canto presents the horrors of being exposed to Satan itself, it is in the ending of Canto XXXII, where Dante first sees this gruesome pair, and in Canto XXXIII, where their story is told with such power and perfection, that Dante provides the thematic ending of Hell Proper.
Thus, Hell Proper begins with love joining two delicate souls together throughout eternity. In contrast, Hell Proper may be said to end with hate joining two violent, vicious men together throughout eternity.
Paolo and Francesca are bound together in a type of embrace and in a love that knows no bounds — a never-ending love that will continue throughout all eternity.
The other pair, Ugolino and Ruggieri, are at the bottom of Hell and are also bound together through a hate that can never be satiated — if anything, Ugolino's hatred will increase throughout all eternity.
It is also significant that their partners are not named and do not speak, but their presence is strongly felt during the narration. The partners do not speak because Paolo is enchanted with the manner in which Francesca defends their beautiful love. Ruggieri does not speak because the horror of his betrayal might cause even more torment. Furthermore, throughout this canto, it always seems that, at any moment, Ugolino will suddenly stop his narration and go back to his gnawing more fiercely than before.
Compare the introduction of both speakers: When Dante asks Francesca what brought her to this dreadful situation, she answers: "Thou shall see me speak and weep together" (V, line 26). And Ugolino says: "I will answer like one who weeps and tells" (XXXIII, line 26).
Francesca's answer includes her lover and the fact that as she speaks, they will both "weep together." Francesca and Paolo will weep together because of the difficulty it is, in such present misery, to recount such ultimate joy, as was their love for each other. Ugolino will weep, holding in his embrace the man whose evil caused him such ultimate pain and suffering.
Francesca is a fragile lady, guilty only of letting her overpowering love for Paolo become her sole desire. Love, love, love — so begins the three tercets describing her love for Paolo. Her speech has enormous, moving sincerity and beauty to it. "He loved me and I loved him!" And that is all. Never does she stoop to something so vulgar as to defend her love by saying something so mundane as: "Yes, but they tricked me, they betrayed me, I thought I was marrying the handsome Paolo with his beautiful body; instead, it was his ugly hunch-back vicious brother." This would not be her nature. She does not dwell on her betrayal because her essence is defined by her love and her essence is that of pure womanhood ("l'essere gentile e puro") — soft, pure, modest and tender — and in Hell, she retains those qualities that inspired Paolo's love.
The mark of Hell is that the sinners retain those earthly qualities that condemned them. Francesca loved Paolo at first sight, loves him now, and will never cease to love him. Likewise, Ugolino hated Ruggieri in life, viciously hates him now, and no amount of hate and suffering will ever satisfy his desire for more and more hate.
Dante's genius is further seen in the fact that while Ugolino is in Hell for being a traitor, he is, instead, presented not as a traitor but as one who has been betrayed. The horror of his action is mitigated by the sufferings of a father. This is the law of retaliation: Ruggieri becomes the savage feast for the man who died of starvation along with his four sons. The horrifying image of Ugolino's savage repast is always before us — from the moment that Ugolino lifts his head from the "skull and other parts of the brain" and cleans his mouth by wiping off the "brain" matter, using his neighbor's hair as a napkin.
He, then, recites his tender narration of the horror of watching his four sons die one by one of starvation. Thus Ugolino hates violently because he loved his sons so intensely. His hatred is so great because his love was infinite, and his grief is so desperate because nothing can assuage him. As he finishes his story, he returns immediately to the gnawing of the brains and the crackling of the bones beneath him.
Both Francesca and Ugolino recollect the past with the same words, they both express their grief, and they both answer Dante's inquiries about their fate, but one emphasizes the controlling beauty of love, while the other dwells on the savage emotions of rage and hatred.