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The main theme of "The Cold Equations" is also the aspect of the story that makes it striking and important. It is the inexorable nature of the physical universe.
The cold equations that give the story its title are the math governing the pilot's decisions. Barton (the pilot) is not free to act on his own, and can't allow Marilyn to stay on board, because there is not enough fuel. As his commander says over the communicator, " You know you have a limited supply of fuel; you also know the law as well as I do."
It is these equations, and the strict laws of the physical universe that they express, that force Barton to jettison Marilyn. Because he knows the rules of the universe and she does not, he cannot try to take her to see her brother, or compromise in any way, because if he does, all the sick people on the planet Woden will die.
The main theme of "The Cold Equations" is about sacrifice. One person, although a young, pretty teen who has seen very little of life yet, has to be sacrificed for the good of others. Along with the pilot of the EDS, seven other people would die if she remained. Her life was just one life. If the pilot would not have followed the law, eight more lives would be lost. There had to be a sacrifice, and hers was the smaller of the two choices.
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