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The Trend: The comic is told by caption boxes containing the protagonist's thoughts. These are not inherently better or worse than most storytelling tools, but the trend refers to when the captions have the character going into long internal monologues about their personal problems, talking about their tragic past/present relationship problems/fears about the future/whathaveyou in very elaborate prose. It's bad when it sounds so melodramatic and over-the-top it could have come from a high school English class, it's worse when these caption boxes are used so often that they crowd out the art in the panels, and it's worst when the information in the captions is something we could have easily figured out on our own ( like a character being punched in the face, grimacing, then having the narrative caption, " This punch to the face hurts worse than when my uncle used to beat me! " ).
The Culprits: Pretty much any solo superhero comic will do this to some extent, so I'll list the most egregious examples from the past ten years;
-- Geoff Johns' Green Lantern ( see above cartoon )
-- J. Michael Stracynski's Spider-Man ( especially the purple prose in the 9/11 tribute issue )
--Jeph Loeb's Superman/Batman ( for a particularly homo-erotic example, Clark and Bruce talking about how awesome the other is )
--Brad Meltzer's Justice League of America ( similar to Superman/Batman, except pulled across the entire ensemble cast, with each character getting their own narrative caption color )
--Chuck Austen's Uncanny X-Men ( Particularly the issues with Nightcrawler's thoughts on religion; " More people die of religion than cancer. And we try to cure cancer. " )
The Problem: In previous years, comics used thought balloons in the same excess, having the characters go on endless internal soliloquies. With thought balloons, anyone could go off on a long whine to themselves ( and to a lesser and more unfortunate extent, the audience ), even characters less important to the main plot. The gradual shift over to narrative captions over thought balloons seems to have been motivated by a need to focus the narration more by only giving us one character's thoughts. However, this didn't do anything to help or hurt the contents of the character's thoughts. A good writer would still give characters good internal dialogue, and a less-good writer would give them the same whiny, drawn-out nonsense. The fact that the thoughts were restricted to one or even a few characters only served to exacerbate the feeling that the heroes are gazing longingly into their own navels, making whatever problems they face irritating and contrived instead of dramatic and sympathetic. Horse carcass, meet spiked club, repeat.
( And for the sake of fairness, I should note that I've been guilty of this too.Since then, I've tried to ease up on internal narrations. )
The Solution: Don't make the contents narrative boxes so literal. The problem that thought balloons were accused of was that they didn't sound like something a person would actually think during a tense moment-- writers like Chris Claremont had a tendency to use them for obvious plot purposes, like telling us about a bit of character backstory informing the current scene, or giving us characterization in a very artificial context that treated it like an essay requirement ( " You have to tell us how Nightcrawler feels about this! " ). The latter can be communicated much more eloquently by the way the artist draws the character's facial expressions, and the former is rendered moot by recap pages. Instead, we should see things in the character's head that give us information we don't know. Just read any Ed Brubaker comic with a first person narrator*-- his characters only sound completely articulate and intentionally poignant when they're actually in a scene where they're alone with their thoughts. In the midst of an action scene, their thoughts will sound choppy and incoherent as befitting of someone busy, y'know, trying not to die.
Alternately, a simple framing device can do wonders to make melodramatic writing work. As obnoxious as Hal Jordan's green-boxed whining can get, his narrative in Secret Origin was much easier to tolerate, because he was recounting events from the past and talking about how he felt THEN. Grant Morrison gave us Xorn's narrative in an issue of X-Men as a letter to Professor X, which was pretty good then, but was later elevated to brilliant when we learned that Xorn was Magneto in disguise all along**. And one of Neil Gaiman's Death stories ( " The High Cost of Living " ) used internal narration to express what good writers tend to avoid-- that the character was LITERALLY a whiny, navel-gazing teenager with no serious problems.
And then there's Alan Moore, who does write caption boxes full of purple prose, but gets away with it because he's Alan Moore and he's that damned good. But unless you are Alan Moore, it's best to err on the side of caution.
* I'd recommend his and artist Sean Phillips' Sleeper for a particularly good example of this.
** I'm not going any further than that. You can't make me.