Original, I know, but I think we all have to examine exactly what constitutes craziness for ourselves, and Firefly* is a logical starting point for me (total nerdery: check).
River seems to cross between craziness and normality without much warning or incentive. She often doesn't appear to recognize 'normal' objects (like guns in "Objects in Space") or differentiate between a 'normal' form of objection (sticking her tongue out) and 'crazy' forms of objection (slashing Jayne's chest, although some would argue that this is in fact a very normal thing to do). Her condition is probably best and most succinctly put by Wash and Zoe: "What's she going to do next?" "Either blow us all up or rub soup in our hair, it's a toss-up**."
We've established, then, that River is... not normal. Is she therefore crazy? insane? What's the difference? Leave that question for a moment while we discuss something entirely different.
Social responsibility is another one of those things that everyone eventually has to examine for himself or herself. What many of us don't realize is that we start thinking about this from a preformed set of assumptions. These assumptions are things like, "We don't kill people without good reason" but can be as simple as "We don't cut in line." We start from these conclusions when we ask "Under what circumstances would it be acceptable to kill someone?" We're assuming, with this question, that there are circumstances in which it would be acceptable (at least to ourselves) to kill someone. To return to Firefly, even Jayne, who would (and did) sell out the crew for the right amount, has his own set of morals: "Hell, I'll kill a man in a fair fight. Or if I think he's gonna start a fair fight, or if he bothers me, or if there's a woman, or if I'm gettin' paid - mostly only when I'm gettin' paid. But [...] eatin' people alive? Where does that get fun?" Even Jayne has his limits.
To put it another way, let's butcher classical French philosophy: Rousseau's Social Contract***. Essentially, we're all in this together. None of us had a choice about being here, but since we are here, let's play nice. It's expected that we won't kill each other, rob each other, scribble in each other's books, or cut in line, and it's expected that our parents and other adults teach us these things as children. How many of us, as three-year-olds, hit the neighbor kid in the head so we could play with his truck, only to be grabbed by our mothers and told, "No, no. We don't hit. That's not nice."
We're expected to be nice. Those of us who aren't - those who run through the store, knocking things off of shelves or those who kick pigeons when we walk through the park (I confess I am guilty of this) - are looked at as if we have done some horrible, rude, offensive thing. Technically, nobody has said, "Don't knock everything off the shelves." It's vandalism, sure, and there are laws against that, but if one managed to do it without damaging anything? No laws have been broken. It's legally okay, and it's legally okay because no one thought that we needed to have laws against it: we're expected to play nice.
There are always those who don't play nice, those who look at the rules and think, "These don't apply to me if I don't want them to." Take Carcer Dun, of the Discworld^ series. Sam Vimes is trying to arrest Carcer, who looks at him and asks, quite innocently, "But what did I do?^^" After he escapes, Captain Carrot asks Vimes exactly what Carcer is guilty of. "He's just guilty^^," Vimes answers, not because he, Vimes, is a bully who likes to arrest people who irritate him, but because, as he explains later, some people are just naturally guilty. He calls it having a criminal soul - people who would steal the humanity from others.
These are the people we call 'insane.' They know "the rules," they simply choose not to abide by them. Very frequently, they break laws and can therefore be incarcerated, but it is certainly possible to be a Carcer Dun without doing anything technically illegal. Sometimes they go over a certain edge and this, I would argue, is when we see serial killers and the like. Certainly there are exceptions to this, but in most cases, when we see these people after their capture, are we not chilled? Who could do this, we ask ourselves; have they no remorse? They haven't. They have chosen to break the social contract, and it is for this we condemn them as guilty. It may require prosecuting them for murder through the court system, but every person who sees this behavior knows that the perpetrator is really guilty of stealing the humanity from others.
Here is where I propose the difference between 'insane' and 'crazy.' This behavior is not the behavior of River Tam. There may be malice in her actions, but it is directed at those who made her the way she is; it is no more than revenge. Those who are 'insane' have seen the social contract and broken it; River, I think, has trouble understanding what language the social contract is in, so to speak. She has lost her bearings.
It is appropriate that we meet River as she emerges from a sealed cryogenic chamber, and that we continue to see her aboard a spaceship; these are metaphors for her mental state. She is isolated from 'the real world,' from any concept of normality, and she only touches sanity briefly, the way Serenity lands on a world only to take off quickly. We begin to see her find her bearing in Serenity the movie, and although she will always be separate from and different than the rest of the world, she may yet learn to relate to it on its terms - on the terms we all accept as so basic we often have no conscious realization of them. This is River's 'craziness,' that she cannot understand the social contract. She is not insane in the way that I define insanity; she has not deliberately broken the social contract. She is simply - hopefully temporarily - incapable of understanding the social contract. But it wasn't a choice on her part, and it is possible that there is at least a partial cure; she is merely 'crazy,' and she may one day be termed 'normal.'
And there you have it: insanity and craziness defined in terms of social responsibility. I wonder how much I've inadvertently stolen from Rousseau and his colleagues?
*Firefly was a television show that aired on FOX for eleven episodes in 2002. It was unrated. Fans rioted after the series was cancelled mid-season, eventually leading to production of a full-length movie and release of the TV series on DVD. Copyright Joss Whedon and Mutant Enemy.
**Quoted from Firefly, the episode titled "Objects in Space."
***Social Contract was written in French by Jean-Jacques Rousseau some time in the 1700s, probably the 1780s. No, I don't know exactly when, nor have I read it in its entirety, nor do I know who publishes it or what copyright it is. (The text is public domain, but each translation is individually copyrighted.) My apologies to Rousseau's ghost for probably misinterpreting everything he said.
^(I was losing track of the numbers of asterisks.) The Discworld series is an ongoing series by British author Terry Pratchett, published in paperback form by Harper Torch. All characters and titles are copyright Terry Pratchett.
^^These quotes are inexact, but the general idea is taken from Night Watch, a Discworld book.
^^^Yes, I know the credits and references probably constitute a full third of the article by now. I also know it is disjointed and may not make very much sense to you. To this I reply, Nuts to you.