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At a rest stop in Kentucky, Hassan alters some carved graffiti to read, “GOD HATES BAGUETTES.” When Colin returns from the bathroom, the updated inscription reminds him of France. The thought of France, in turn, reminds him of his most recent Katherine, Katherine XIX, because she and Colin used to talk of visiting Paris. Later, back on the road, Colin rejects Hassan’s suggestion that they stop to see the World’s Largest Wooden Crucifix. Crucifixes also remind Colin of Katherine. When Hassan objects that she was an atheist, Colin replies that she wasn’t always one. She used to wear a silver crucifix.
Hassan started attending Kalman in tenth grade, after being homeschooled. In calculus class, he watched Colin, a freshman, ask to be excused so he could deal with an eyelash in his pupillary sphincter. Hassan later explained to Colin that a joke about an eyelash in one’s sphincter (any sphincter) does not make a favorable impression on high schoolers. That was when Colin and Hassan became friends. In contrast to Colin, Hassan is lazy, but he is quick-witted enough to keep up with Colin in conversation, and he is much better at reading social situations.
Colin and Hassan see a sign inviting motorists to visit the grave of Archduke Franz Ferdinand. It is unlikely that Franz Ferdinand would really be buried in rural Tennessee. However, Colin was thinking about him just hours before, and the coincidence is too bizarre to ignore. In a town called Gutshot, a dozen or so miles off the highway, the boys stop at a general store painted bright pink. Lindsey Lee Wells sits behind the counter. She is the guide for tours of the archduke’s gravesite. Lindsey is short, skinny, and more interesting-looking than pretty, but she has a smile “that could end wars and cure cancer.” As the boys follow Lindsey to the gravesite, Colin stumbles. He loses his glasses and hits his head on a rock, cutting his forehead. When Hassan refuses to donate his shirt as a bandage because he is self-conscious about his body, Lindsey stops the bleeding with her shirt instead. She tells Hassan to continue applying pressure while she fetches a first-aid kit. As Colin puts his glasses back on, he mumbles “Eureka.”
Lindsey’s bra is bright purple, the same color as Katherine’s on the evening she and Colin broke up. On the night of their graduation, they had gone out to celebrate. Back in his bedroom, however, they argued about Colin’s fear that others were catching up to him intellectually, and about his constantly asking if Katherine still loved him. When she ended their relationship that night, Colin felt as though a piece of his gut had been torn out.
Colin’s “Eureka” after hitting his head is due to a sudden idea. Pulling out a notebook, he sketches x- and y-axes and a curve that rises and then falls. The graph, Colin explains to Lindsey and Hassan, relates to a mathematical formula he has developed for predicting the course of any relationship based on the personality traits of the people involved. Colin classifies people as dumpers, who tend to initiate breakups, and the rest as dumpees. When Lindsey learns that Colin has dated nineteen Katherines, she laughs. She has dated just one boy, another Colin.
Colin’s first Katherine was the pretty girl in third grade. Because he was socially so unskilled, he did much of his schooling away from Kalman under the tutorship of Keith Carter, a friend of his father’s. The tutor had a daughter who was impressed that Colin already knew Latin. She started playing the “why game,” asking him questions and following up every answer of his with “Why?” Eventually, Colin admitted that he did not know why the poet Ovid was born in ancient Rome instead of elsewhere. Then the girl, Katherine I, asked Colin if he wanted to be her boyfriend. When he said yes, she kissed him on the cheek.
The flashback to the beginning of Hassan and Colin’s relationship in Chapter 4 gives more insight into both characters and provides a greater understanding of the way their friendship functions. The “pupillary sphincter” incident that sparked their friendship illustrates that while Hassan may not have been a child prodigy, he had better social skills than Colin as well as a better understanding of how to interact with other people. From their first interaction, Hassan coaches Colin to understand his audience and to carefully consider when he should share his prodigious bank of knowledge with others and when he should keep it to himself. Hassan still helps Colin by telling him when the facts he reflexively shares become uninteresting.
In Chapters 4 through 6, romantic love remains a focus as Colin continues to connect almost everything he sees to Katherine XIX. In his mind, he connects the World’s Largest Wooden Crucifix to the silver crucifix that Katherine used to wear, and Lindsey’s purple bra reminds him of the bra Katherine wore on the night they broke up. Colin’s mourning and his constant memories feel like love to him, but to the reader, they serve as a reminder that Colin’s understanding of love might be incomplete—in this case, he equates love with an unhealthy fixation. Indeed, when Colin finally experiences his Eureka moment, his idea is to create a mathematic formula that can predict the outcome of any romantic relationship, an idea that is completely antithetical to the emotional unpredictability of romantic love.
The missing piece motif reappears in Chapter 5 as Colin and Hassan arrive in Gutshot, Tennessee, after seeing a sign advertising the burial place of Archduke Ferdinand, who, incidentally, died from a shot in the gut. Although Colin and Hassan don’t know it yet, this is where their literal journey ends, while their metaphorical coming-of-age journey and Colin’s search for his missing piece are just getting started. The town of Gutshot becomes the setting for the rest of the novel, and it is important to the story because it represents a completely different world than the one Colin and Hassan come from, giving them the opportunity to experience and think about themselves and others in new and unexpected ways.