the cold equations
I had previously been under the impression that one of the pivotal characters was a child (of perhaps nine or ten), not an eighteen-year-old. I found that this affected my enjoyment of the story; the character makes a mistake with consequences (not following directions, in a really big way), and when I thought those mistakes were being made by a child I had more sympathy. As it is, it's hard for me to really appreciate this character's angst. The story is also somewhat a product of its time (the 50s); the other main character makes a point of saying he would have handled things differently if it had been a "man". (Aside: she's a "girl".) It's still a good story, but I liked it better with my mistaken impressions. :-)
There was a Twilight Zone episode based on the story (the series from about a decade ago, which I mostly missed due to not having the right cable channels available). I'd kind of like to see that.

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It's actually one of the things that I appreciate about the story -- that that character isn't wholly sympathetic, based on her personality. I think that gives the story more bite, because we wind up being sympathetic to her not because of who she is and what she's like, but because of her basic humanity. We look at the consequences of her act, and are appalled at the price she has to pay. We want to be able to blame her for her predicament, but it's hard to blame her that much.
Had the character been wholly sympathetic, the audience would be, essentially, reacting to the suffering of that particular character -- "Oh, what a terrible thing to happen to such a nice girl". Because she's not wholly sympathetic, we are forced to confront her as everyman, and react to the essential humanity of her -- "Oh, what a terrible thin to happen to anyone"
I just realized all this just now; your saying that sparked the spark-plug of my mind, and I suddenly saw the parallel between this story and Vis' recent interpretation of King Lear. As I wrote elsewhere, he had Lear start out as an unsympathetic character, in precisely the same way: he does stupid things out of self-centeredness. But by the end of the play, you're going "Yeah, he was a total bastard and an utter fool, but he doesn't deserve this. This is too much. No one deserves this."
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I agree (and had not previously noticed either). At several times I wanted to whap the character with a clue-by-four and shout "stop sniveling as if he can wave a wand and make it better!", but in the end I was still sad for her.
"Yeah, he was a total bastard and an utter fool, but he doesn't deserve this. This is too much. No one deserves this."
I've had similar thoughts during recent B5 viewings. :-) (Londo, of course.) I agree; this kind of storytelling has the potential to work really, really well. (It's also easy to screw up, of course.)
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If you found the story on the web, it probably is a copyright violation, and you might want to track it down in a library to make sure that the version you read was accurate. It's been anthologized a lot, so it's not hard to find.
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Now that I'm thinking about it, Knight's list reminds me of the scene in Apollo 13 where the astronauts and engineers are trying to jury-rig an air filter(?) out of whatever equipment they have left in their craft. They didn't just say, "well, the cold equations of the universe have decreed that we're all going to die".
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Sure, but the question of what to do when you've already done all that makes a more interesting story, so I'm willing to grant that the pad of paper, case containing the medicine vials, chair, tools, and clothing don't add up to enough. I think the conceit of this story is that the only way to solve the problem is going to be unpleasant for someone.
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I loved Godwin's story, and here's why I don't think the age of the girl is quite that significant. I hope this isn't too spoilerish, but the impression I had was that the girl who stowed away did so innocently. She wasn't explicitly trying to avoid paying a fare. She just wanted to see her brother stationed far away. When confronted with the fact that she was on an emergency transport and that this wasn't simply a minor infraction any longer, her reaction was the heartrending (for the reader and the other principal protagonist) "I didn't do anything to die for."
I don't think the story would have had less of an impact for me had she been 10, 18 or an innocent twentysomething. I'm thinking in particular of the radio (or whatever the medium was) conversation she had with her brother, which hit me like a hammer when I read it decades ago. An adaptation of that story, true to the original, would be something I'd consider a must see.
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Ok, stories about jetisoning all possible equipment (down to the clothing) and succeeding aren't very interesting, so I guess you have to end up with either the original answer or the pilot sacrifice you describe. (Or a crash, but let's assume that's not acceptable.) But that does not make for a story that satisfies me, perhaps because the passenger is insufficiently sympathetic for me. Maybe I'm too cold-hearted or something, but I would have more sympathy for a toddler or dog that wandered on by accident than I would for someone who walked past the "no trespassing" signs and stowed away. I mean yeah, it's sad -- that's the point -- but it was avoidable.