Final answer:
The particular event prompting the narrator to write to his imprisoned brother cannot be determined from the given excerpts, as they focus on broader themes like confinement and freedom without specifying the context of the letter.
Step-by-step explanation:
The event that makes the narrator write to his imprisoned brother is not explicitly mentioned in the provided excerpts. To adequately address this question, one would need further context from the work being referenced. However, using the information provided, it seems that the narratives focus on themes like confinement, freedom, the struggle for autonomy, and the impact of significant life changes such as death, birth, release from imprisonment, or the end of enslavement. The nature of confinement and struggle for freedom is a recurring theme, as seen with the unreliable narrator's misinterpretation of her confinement, the significance of the Emancipation Proclamation for slaves, and Socrates's allegory of the cave.