I agree that programming is much more related to logic and analytical thinking than to math.

"Math" of the kind that's taught in school/college is really a specialized kind of logical/analytical thinking. You wouldn't expect to use, say, calculus or linear algebra in a Rails database application, but math-heavy computer science (databases, parsing and whatnot) comes up all the time.

fiction -- especially fiction that the liberal-arts people revere -- nope.

Even literary fiction uses common narrative tropes all the time. And one ingredient that makes it popular in liberal-arts academia (and that's sorely lacking in the likes of Tolkien, and most sci-fi/fantasy) is basically characterization of an introspective kind. But HP:MoR is heavily based on that kind of introspection. Also, even James Joyce only used "non-logical" language as a hack to immerse the reader in the characters' thought process. A lot of poetry does the same thing: it's highly evocative and not at all "logical', but that doesn't mean it can't be understood on its own terms. There's no real divergence, only a contingent cultural divide.