In her role as the narrator, Gordimer is afraid because of the fear she possesses towards the world around her. The exploration of her fear is the root of her similarity to and difference from the world around her.
Gordimer's initial fear in the middle of the night is reflective of the panic that others in the community possess. She is aware of the crime around her, and this represents the root of her fear:
I have the same fears as people who do take these precautions, and my windowpanes are thin as rime, could shatter like a wineglass. A woman was murdered (how do they put it) in broad daylight in a house two blocks away, last year, and the fierce dogs who guarded an old widower and his collection of antique clocks were strangled before he was knifed by a casual laborer he had dismissed without pay.
When Gordimer says that she holds "the same fears as people who do take these precautions," it shows how the alarm of crime has impacted her. She believes every sound is a confirmation of her worst fears. Like the world around her, Gordimer feels "threatened."
Gordimer's difference is that she does not allow these fears to define her identity. She envisions something more than simply the paranoia within her. While she initially classified "every faintest sound" as a "possible threat," Gordimer sees a rational explanation beyond the irrationality of her fear. She understands that what she thought was reflective of crime was actually the natural condition of the house in which she lived. In being able to explore the actual causes as opposed to seizing on her fearful element, Gordimer shows herself as different than the people in her community.
Gordimer is different than those around her because she does not let fear control her. She demonstrates this in her embrace of a creative outlet for her fright. She asserts that she "couldn't find a position in which my mind would let go of my body." Her thoughtfulness from this position results in a "bedtime story" that depicts the terror in letting fear control one's life. This insight further differentiates her from the other people in her community.