For someone who thinks so much, Julian's inaction says volumes about his character. During a good chunk of the story he thinks, broods, contemplates, imagines, and fantasizes: "He began to imagine various unlikely ways by which he could teach [his mother] a lesson" (72). But that's all he does. (Well, presumably he sells typewriters. But we best he isn't very good at it.) And from this inaction, we get a pretty negative view of the guy.
Julian's mom, on the other hand, is a woman of action. She goes to her weekly Y class, she shops for food and clothes, and pays the bills. Even on the the bus she's active, "[removing] from her purse a folding fan, black with a Japanese scene on it, which she began to flutter before her" (48) and later playing peek-a-boo with Carver. Julian may think he's the progressive one, but, from where we're sitting, Julian's mom looks like the only one who actually does anything.
And of course we can't forget the story's major action: Carver's mom taking a pretty effective swing at Julian's mom. What do we know from that? Well, she's had it. She's (presumably) been trampled on for decades, and she's not going to take it anymore. Oppression has turned her into more of a force of nature than an actual person—and that's not good for anyone.
Julian thinks culture and class isn't in what you wear, but what you think, yet he wears a tie when he goes with his mother to her Y class. For Julian's mother, dress and presentation is a source of pride and distinction. We know that "She was one of the few members of the Y reducing class who arrived in hat and gloves […]" (9).
She believes clothes do make the man, and that presenting yourself in a certain way can elevate your status. Ironically enough, the black passengers on the bus seem to share this view. More attention is given to the minor characters who are black than white, and all of them are dressed rather spiffily: "The Negro was well-dressed and carried a briefcase" (63); Carver wears a "short plaid suit and a Tyrolean hat with a blue feather in it" (76); and Carver's mother wears a dress, hat, and has a huge red pocketbook. By focusing on appearance, O'Connor shows us the changing landscape of the South when it comes to economic and social status.
With just a few words, O'Connor nails down a character's persona. Julian's mother, for example, believes "if you know who you are you can go anywhere" (16) and her catchphrase is "Rome wasn't built in a day" (8).
So, we know that Julian's mother is a glass-is-half-full type. Even though she's old-fashioned, we think that maybe she could come to terms with integration. And we also know that she's got a kind of folksy wisdom that Julian, for all his edumacation, lacks. She may speak in clichés, but those clichés may be more useful than Julian's fancy philosophies and theories.
And then there's Carver's mother. She doesn't say much, but her words pack a punch: "Come heah!" (84), "quit yo' foolishness […] before I knock the living Jesus out of you!" (94), and "[…] [Carver] don't take nobody's pennies!" (102). Not only does she speak with stereotypically African-American dialect, but everything she says is either a warning or an order. This is one woman we'd want to be careful around.
If we had a penny for all of Julian's thoughts, we'd be rich. (Maybe we'd even give him a handout.) For most of the bus ride, Julian is silent, yet his thoughts reveal much about his character. Take, for example, this little gem: "When he got on a bus by himself, he made it a point to sit down beside a Negro in reparation as it were for his mother's sins" (33). Or, "The further irony of all this was that in spite of her, he had turned out so well" (62).
We think somebody's been drinking a little too much delusional juice.