Interesting, Important, and Authentic (1)

Nothing is absolutely interesting. A lot of what I care about, for example, is of little or no interest to most people, and a lot of what many people in the world care about (at least insofar as the media pays attention to it) is of little or no interest to me - like who wins a golf or tennis tournament, or whether a certain movie star is having an affair with another movie star.
Since I am a translator and editor, I am very interested in correct and effective word choice, issues of fidelity to the author's intention, sentence structure, and a great many other technical matters that I wouldn't necessarily care very much about if it weren't my job to care about them. I certainly don't expect anyone in a casual conversation to respond to these topics without a yawn.
Similarly, as an amateur musician interested in improving my improvisational skills, I am concerned with harmony, rhythm, phrasing, originality, coherence, and so on, with specific application to playing a melody over a series of chords. There is no reason why anyone who isn't trying to improvise in music to have the slightest interest in these things. You can enjoy listening to jazz without knowing how Sonny Rollins handled a half-diminished chord.
Yet good writers and movie-makers do manage to make technical details interesting even to people who ordinarily don't care about them. How?

**

Long ago, when I was a student of literature, I never considered the issue of why some writing is boring and other writing is fascinating. All the works we were reading in the courses that I took were more or less universally acknowledged to be important, hence interesting. And the better teachers managed to bring us into the works and make them interesting for most of us, because they themselves were interested in them. That, perhaps, is they key to arousing interest in an audience of readers, listeners, or viewers. One manages to make oneself interesting, and, consequently, what interests one will also interest others. Though, obviously, some of the students in general literature courses in college were only taking them because they were required to, and the only interest they developed in the books they read was related to passing the course. The charisma of the professors, if there was such, was lost on them.
I majored in French literature because I thought it was important, not just because I was good in French and enjoyed reading. I was interested in literature because I was convinced that it was important.
But what did I mean by important? In what way is literature important? How could I convince an economics or engineering major, for example, that he or she ought to care about Shakespeare? For that matter, how could they convince me that it was more important to master economics or electrical engineering than to understand King Lear?
Is "importance" just as relative as "interest"?