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Lumifer comments on Succeess depends on finding a balance between "geek" and "jock" - Less Wrong
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I agree that programming is much more related to logic and analytical thinking than to math. I, too, think that math and programming are not as close as they are usually made out to be.
I disagree that literature (fiction) and writing are close to programming. Academic or technical writing, maybe, but fiction -- especially fiction that the liberal-arts people revere -- nope.
Yes, there is Tolkien with his world-building, but notice how he is beloved by (techie) geeks and looked down at by (poet) high-culture literary types. Those literary types much prefer writers like James Joyce, or Nabokov, or maybe Marquez, writers who are not analytic and are not much concerned with logic, consistency, etc. And, of course, there is poetry.
Yeah. Reminds me of an old joke about a programmer who each evening would put two glasses on his nightstand: one full of water if he gets thirsty during the night; and one empty one if he doesn't :-)
"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.
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.
Technically speaking, yes, practically speaking, no. In particular, people good at logical/analytical thinking are not necessarily good at math and vice versa.