Who is a static character in Raymond Carver's Cathedral?

When we're talking about characters in literature, "static" means "staying the same," and "dynamic" means "experiencing an important change." They are opposites, and it's helpful to look at which characters are static and which are dynamic so we can understand what's going on in the characters' development.

In "Cathedral" by Raymond Carver, the static characters are the blind man, named Robert, and the narrator's wife, whose name we don't know.

These static characters are, by definition, the ones who basically stay the same, who don't experience any major changes in how they see the world or how they think.

It would be important to note who they are in comparison to the more important "dynamic" character: the narrator himself, whose name we also don't know, and who does undergo a serious change in his personality. Let's take a closer look.

As the story begins, we know that Robert and the narrator's wife are very close friends. Ever since she met him when she responded to an ad in the paper that called for someone to read to a blind man, they have been close, and they confide in each other. Their friendship is evident throughout the story as they have a good time together at dinner, despite the husband's grouchiness. Both of them are sensitive and open, both in the narrator's recollections of their early friendship and in his description of their behavior at dinner. So, those aspects of their personalities don't change, and we don't see either the wife or Robert talking about changing their minds about something, or seeing something important in a different way.

But we do see the narrator change his mind about something important. That means he's the dynamic one, not the static one, and it's why the story is really about him. 

At the beginning, he's bothered by the fact that his wife's friend is blind and has a very unwelcoming attitude toward Robert:

"My idea of blindness came from the movies. In the movies, the blind moved slowly and never laughed. Sometimes they were led by seeing-eye dogs. A blind man in my house was not something I looked forward to."

But then the three of them share the meal together, and they smoke together and watch television. The narrator starts to realize that the blindness isn't that important, that Robert is just a person he can connect with, like any other human. And when Robert and the narrator draw a cathedral together, that experience cements the narrator's change of heart:

"So we kept on with it. His fingers rode my fingers as my hand went over the paper. It was like nothing else in my life up to now. ... I was in my house. I knew that. But I didn’t feel like I was inside anything."

Although the narrator doesn't come right out and say "I am more accepting and understanding toward blind people now, not like I was before," we can still tell that his transformation is complete because he's hanging out with Robert, doing something meaningful and enjoyable with him, and making physical contact with him as well.

In contrast, the static characters (the wife and Robert) don't experience that kind of spiritual growth. They are just the people who happened to be involved in the narrator's experience.