We watch Louisa, Gradgrind's daughter and human guinea pig, grow from about twelve to about twenty-two years old. Her dad raises her to disregard emotions and see everything in terms of facts or statistics. This is a disaster. She becomes trapped in a loveless marriage, almost has an affair, and spends the rest of her life trying to learn to be a normal human being with feelings.
Actually, for Dickens, not just girls but all people should be allowed to have fun. But Louisa has been brought up to only consider life in Utilitarian terms (check out Shmoop's "In a Nutshell" section for some background info on Utilitarianism). She tries to see everything numerically, either through the hard sciences or through statistical evaluation of human behavior. This is as unnatural as it sounds. She is so completely detached that most human emotions and experiences are beyond her grasp. In a novel full of some of the most tragic characters Dickens ever wrote, she is probably the saddest.
Louisa's life is so wasted on a loveless (read: really, really repulsive) marriage and a would-be affair with a cynical opportunist (read: soulless jerk) that she is not even allowed to have a second chance at a more fulfilling existence. Think about it – Dickens could have made her story end any way he wanted to. She's only 22 years old at the end of the novel, after all! But no, she dies a lonely and childless spinster. Louisa is denied the kind of domestic and maternal life that was for Dickens the height of what women should aspire to. There is a pretty direct and awful connection between her childhood and adulthood here. She is damaged by her father's desire to remove her from the world of emotions, morality, and anything else that can't be put into numbers. By the time she's an adult, she's lost a large part of her humanity, the part that makes her a woman (or was considered to, back in the day).
Why finish her plot line this way? Why give Louisa such a sad ending? We'll suggest a couple of possibilities, and you see what you think. Perhaps the idea is that she is such a one-note embodiment of the Gradgrind philosophy that she really can't be allowed to reproduce. To save the rest of the world, this philosophy and its products must die out with her (and with her brother Tom, who also dies childless). Or maybe the key is the way the novel's last paragraph name-checks the reader directly – maybe the best way to motivate some kind of action is this kind of no-holds-barred heartstring tugging. Are there other possible explanations?
OK, that's probably enough about Louisa as a person. Let's take a step back and check out the way she fits into the novel's structure. We're going to get all metaphorical here and say that Louisa is the Kevin Bacon of this novel – pretty much every other character is one degree of separation away from her. There is almost no one that she is not a foil for or a comparison to. She is the female version of Tom (though unlike him, who is universally shown to be a selfish jerk, she seems to have been able to go either way). Louisa is the opposite of the emotionally competent Sissy (for whom she is a dire warning to never let the head totally rule the heart). To Mrs. Sparsit, Louisa becomes the wife to Bounderby that Mrs. Sparsit doesn't get to be (but would probably have been better as). We also see that Louisa is ruined by the same system that destroys Stephen Blackpool (who has an even worse fate, to be sure, but they are both living wasted lives). Can you pair her like this with any other characters – Rachael? Harthouse? Bounderby? Her father?