Tom Godwin's famous story "The Cold Equations" is available for .51 from Fictionwise, if you don't want to read about it without reading it. This 1955 story concerns a spaceship pilot who is on a single-person ship carrying vaccine to a plague-ridden planet when he discovers that an attractive young woman has stowed away on the ship. The "plot," such as it is, consists of the pilot trying to figure out some way that he can keep her on board without using up the ship's resources before making landfall anywhere, thus resulting in not only the deaths of the pilot and the young woman, but also of all the plague victims whom the vaccine will not reach. This is the original cold equation: the girl's life occupies one side of the scales and the pilot, along with the planet full of sick people, tips the other side.

The story is an exercise in dry logic, which simultaneously functions as a tearjerker. Needless to say, Godwin stacked the deck with his auctorial control of resources the pilot has on hand—if he hadn't done so, there would be no story. The situation is poignant enough to have kept the story alive for fifty years, to have generated reams of discussion of what options the pilot might have missed and how else he might have looked at the stacked-deck problem. The story was alive enough to be reprinted in a book of the same title, along with a much less famous novel of Godwin's, in 2003.

Alice Sheldon, writing as James Tiptree Jr., wrote a clear lineal descendant of "The Cold Equations," called "The Only Neat Thing to Do", (not available online) in 1985. The 1950s had made way for the 1980s and in this story the young female protagonist makes the decision for herself. The situation is somewhat different; she is alone in a spaceship with a parasitical alien that could be a danger to her world if she returns, so she does the "only neat thing" by heading outward forever, in effect committing suicide by eventual diminution of resources. As Godwin did, Tiptree stacked the deck to make only one neat thing available to her protagonist.

While these are two of the most raw examples, stories like this abound through the history of science fiction: scarce resources and/or dangers beyond imagination call for the ultimate sacrifice. (For a twist on this story, read Joanna Russ's We Who Are About To . . . [1977], in which the lone spacewoman refuses to do her reproductive duty for the marooned crew, who then all die without a new generation.)

Even in its more twisted versions, the cold equation always results in the death of one person or group to save the lives or honor of another person or group. The story tension is driven by the "fact" that both groups cannot survive under the given circumstances. The cold equation is simple: some limited resource must be preserved for a specific purpose and thus use of that resource for other purposes equals misuse. The stories work as fiction by using "cold" logic to result in consequences (generally deaths) that have an emotional effect on the reader.

Another common science fiction trope could reasonably be called "the hot equations," although as far as I know the term is original to this article. In this trope, the attacking aliens cannot be communicated with. Usually, they are insectoid, hive-minded, ruthless, and relentless. The author stacks the deck so that any kind of diplomacy, negotiation, or live-and-let-live strategy is impossible, and thus presents an ironclad justification for all-out bloodthirsty (ichor-thirsty?) war. The best-known example of this trope is probably Robert A. Heinlein's Starship Troopers (1959). Other examples include Joe Haldeman's award-winning The Forever War (1976) and David Gerrold's series The War Against the Chtorr (begun in 1984; currently five volumes and as yet unfinished).

Again, the decks are stacked, in this case, against compromise or resolution. All the aliens must die or all humans will die. The authors stress again and again just how impossible it is to understand the aliens' motivations: they have to be treated as evil incarnate. Showing them any sort of mercy is tantamount to self-destruction; showing them compassion is more literally impossible as we by definition cannot understand what drives them.

Perhaps the most interesting twist on the "hot equation" stories is Orson Scott Card's Ender series, which begins with Ender's Game (1985), a very standard retelling of the kill-the-bug-aliens story, followed by a second volume, Speaker for the Dead (also 1985), in which the aliens are portrayed as having a complex and layered culture, and in which the consequences of the simplistic attacks on their culture in the first volume are examined in detail. (The series goes on for several more volumes after those two.)

The "hot equation" is also simple: making any concession to the enemy equals self-destruction. The "cold equation" stories use an underpinning of logic to create a deeply emotional effect: readers experience the loss of characters we have come to care for. The stories I'm dubbing "hot equations" also employ an underpinning of terrifying threat to create a deeply emotional effect: readers experience the fear of blindly malevolent attack and the comfort of bonding with others to fight the inhuman intruder.

Now don't get me wrong; I've enjoyed both kinds of stories many times. They make for ripping good yarns. They engage the heart. The first group in particular is designed to engage the mind as well, and the second group certainly can. The "history and moral philosophy" classes in Starship Troopers have made a lot of people think over the last 45 years.

And it's certainly not the case that the authors of these stories are somehow cheating by stacking the deck. All authors are always stacking the deck—it's marginally more obvious in science fiction and fantasy stories than in mainstream stories, but it's always true. The author has a story to tell, and the world has to be molded to tell that story.

And yet equations are an interesting metaphor: one side of an equation must, by definition, equal the other side. Everything has to balance, or we no longer have an equation; we have, in mathematical terms, an inequality. Choice is erased; only one option, one "neat thing to do" remains.

Science fiction abounds with great works that are written in terms of inequalities rather than equations: The Left Hand of Darkness by Ursula K. LeGuin (1969) comes to mind, as does Childhood's End by Arthur C. Clarke (1953), and one of particular immediacy right now, Kim Stanley Robinson's Forty Signs of Rain (2004), which ends with a hurricane storm flooding Washington, D.C. In these stories, the protagonists are faced with a variety, sometimes a dazzling variety, of choices. Their next move is not dictated by the circumstances, or the enemy: instead, the circumstances (or the enemy) conspire to create confusions out of which the characters are forced to make their own choices: physical, emotional, and/or moral.

Now this is the point at which the columnist is supposed to pull all the thoughts above into a neat little package and tie it with a ribbon. If I were going to do that, the ribbon would be striped red and blue.

It would be very easy to say that in the current polarization of the United States the red contingent is drawn to equations and the blue contingent is drawn to inequalities. (And the pun is almost irresistible—because Democrats and progressives tend to want a governmental focus on social inequalities, while Republicans and conservatives tend to believe that forces such as the cold hand of the market function appropriately to ensure that equations are balanced.)

There is some truth to this oversimplification: the U.S. government's response to 9/11 has had a significant flavor of the hot equations: if members of a group do something as egregious and unforgivable as the attack on the Twin Towers, that equals proof of enmity. This belief is the underpinning for, among other things, the denial of virtually all rights to the prisoners in Guantánamo. And the early days of Katrina response had a significant flavor of the cold equations: remaining in New Orleans as the storm hit, regardless of one's reasons or circumstances, equals a lesser status and a lower priority for aid and attention.

However, it's never that simple. As I pointed out above, the cold equations are heart-wrenching and the hot equations create bonds of community and connection. And the people who see the world in terms of inequalities also stack the deck, and often draw very simplistic conclusions even from the most complex of premises. Just because characters are left to make choices doesn't mean that the author has thought out the implications of those choices, or that the reader can learn anything from them or find anything to care about.

And yet, this contrast of equations and inequalities feels important to me, and useful. It may be yet another way that the extrapolations of science fiction can serve as a reflecting pool for the world that we live in, another tool we can use to comprehend how people look at the world. For me, the really good inequality stories offer more, in the long run, than even the best of the equation stories: they tell more truth and tell it with more texture. I'm less interested in the circumstances that force the pilot to throw the girl off the spaceship than I am in the circumstances that affect her choice to stow away in the first place. I'm less interested in how to defeat the aliens that can't be communicated with than I am in the consequences of that defeat for the losers—and for the victors.

We live in a world where the need for serious, thoughtful attention to consequences is becoming more paramount almost by the moment—and where the pressures against responding to that need sometimes seem to overwhelm us. Science fiction is, in one significant aspect, a laboratory for looking at consequences: it's just possible that paying some attention to how our stories are structured and the rules by which authors stack their various decks can still give us a little insight into the attention that needs to be paid in the greater scheme of things.