Symbolism and Motifs
Math Problems
Math problems are frequently invoked throughout the story as metaphors for different elements of the story, including the plot as well as the characters and their relationships with each other. Below are some examples of how this occurs in the novel:Four-Color Problem:A geometry problem in which one must prove that it is possible to draw contiguous shapes of different colors such that no two contiguous shapes share the same color. This geometry problem is quite apropos from the standpoint of the story’s plot, since Ishigami must construct a plausible cover-up scenario in which neither he nor Yusako (including her daughter Misato) will appear to have any kind of overlapping involvement in the murder of Togashi. Each must play a role that is distinct and separate from that of the hypothetical murderer and from that of each other (See more about this in the analysis of Chapter 6).Additionally, the four-color problem comes to symbolize the many varieties of interplay among the characters: can the involvement of Kusanagi be kept separate and distinct from that of Yukawa's? Can the involvement of Ishigami be kept separate and distinct from that of Yusako's? Kusanagi, while not wanting to betray his friendship with Yukawa nor violate Yukawa's sense of privacy with regard to his feelings towards Ishigami, attempts to follow Yukawa's tracks in order to gain insight into the case. He also must struggle to honor his promise to keep Yukawa's secret, a promise he swore to keep in his capacity as a friend, in spite of his duties as an investigator. Yukawa, for his part, despite not wanting to incriminate Ishigami or interfere with Kusanagi's work, can't help intervening in the case out of intellectual curiosity about Ishigami's methods, not to mention his compassion for Ishigami as an old friend with whom he shares a common bond of being a misunderstood genius. While Ishigami attempts to keep Yasuko at a distance, he can't help avoiding the lunch box shop (where she works) against his better judgment, nor can he help expressing jealousy over Kudo's appearance later on (which culminates in him following Kudo, taking pictures in secret of both Kudo and Yasuko, and finally writing a threatening note to Yasuko in which he warns her not to continue her relationship with Kudo). Yusako, for her part, while wishing to respect Ishigami's sacrifice and not wanting to appear ungrateful, can't help but get involved with Kudo, which prompts feelings of jealousy on the part of Ishigami and also upsets her daughter Misato. The ways in which these character arcs mesh and interweave with each other will seem to confound the simple assumptions made by the four-color problem, suggesting that human beings are not like contiguous shapes that can be drawn on simple planes and spheres such that they can be colored separately. The lives of people are often interconnected in all kinds of subtle and intricate ways, making it hard to discern the boundaries delineating people’s distinct spheres of activity.N = NP Problem: This problem basically poses the question as to whether it is easier to solve a problem for oneself or to disprove a solution that someone else has offered for the same problem. In terms of the story's plot, it serves a metaphorical function by which it becomes the task of the investigator either to solve the murder case on its own merits or to focus on proving Yusako's culpability in the matter by demonstrating the inadequacy of her alibi. After Yukawa figures out the nature of Ishigami's cover-up, he claims that it is easier to solve a problem for yourself so long as you understand the person who has devised the problem. Because Yukawa respects Ishigami's genius and understands his motives, he is able to see through the ruse that is created by Ishigami in making March 10 the time of the murder with Yusako as the prime suspect.Science Experiments
Science experiments occur frequently throughout the novel. They occur as symbols for the empirical approach that Yukawa relies upon to solve murder mysteries and for a general worldview based on empirical observation. For example, when Kusanagi visits Yukawa's lab with Ishigami, he touches a levitating ring, believing that Yukawa would never leave dangerous equipment out in the open, only to get burned. This is symbolic in demonstrating how faulty assumptions about people and events can lead to setbacks and "getting burned" in a figurative sense. When Kusanagi visits Yukawa later on to ask about Ishigami's role in the murder, Yukawa is seen using an oil drum, which he explains is more effective than a shredder, to burn various papers that he wants to dispose of. Kusanagi takes this at face value, underscoring how false assumptions about people lead to a failure to appreciate their ulterior motives. It is false assumptions like these that make the police vulnerable to such deceits as the trick alibi that Ishigami devised to help Yasuko and fool the police.Experiments are for Yukawa what math problems are for Ishigami. Just as Ishigami's apartment is littered with math books and his desk drawers filled with notes on various math problems, Yukawa's lab is strewn with lab equipment used for different kinds of tests and experiments. Just as Ishigami has students whom he guides, instructs, and assesses with math exams, so Yukawa has graduate students whom he also guides and asssesses.Time, Clocks, and Numbers
Chapter 15 opens with the statement: "The clock showed the time as 7:30 a.m." Clocks and time figure as prominent motifs in Chapter 15 (and the novel as a whole). Ishigami, reflecting upon the amount of time it would take to complete the math problem related to his senior thesis, "calculates that it would take him roughly another twenty years to complete his work on this particular theory. Possibly even longer." Yukawa laments the fact that both he and Ishigami lead lives forever governed by the necessity of their synchronization with the clockwork of society: "too bad it's impossible for you and me to ever be off the clock. Like it or not, we are stuck in the cogs of society. Take them away, and are clocks spin out of control." Hearing this, Ishigami admonishes him for wasting time: "Keep chatting like this and you'll use up your two or three minutes in no time." The final words of the first section (i.e. "It's over") have a finality suggestive of one's time having run out. The presence of time as a constraining influence upon human freedom thus constitutes a central motif that organizes the first half of the chapter.Ishigami's life is limited by time. He laments the fact that he can't dedicate himself fully to solving the math problem related to his senior's thesis. He views his own life quantitatively in terms of the amount of time required to perform various tasks. Hence, he notes the time when the chapter starts. He calculates the time needed to complete his senior thesis math problem. He chides Yukawa for wasting the time allocated for their conversation. Ishigami's entire life can be reduced to a temporal quantity that can be subdivided, allocated, wasted, or made use of. When Yukawa states, "You've got a precious brain and I don't want it being wasted like this," Ishigami responds, "I don't need you tell me that. I already abhor wasted time." It's no coincidence that Ishigami extends his sense of self as a time-dependent being to the homeless people whose routines he likens to "clockwork."Since Ishigami is obsessed with numbers, mathematics, and time almost to the total exclusion of human feeling and compassion, Yukawa must use Ishigami's own metaphor of clockwork to convey the inherent value of human life. Hence, Yukawa goes out of his way to emphasize that "even a cog may say how it gets used." By speaking to Ishigami in a language that is comprehenible to him, Yukawa attempts to reprimand Ishigami for having taken his clockwork metaphor to such an extreme as to commit a horrible atrocity. It's noteworthy that Ishigami's morning commute follows the same pattern as in Chapter 1, echoing the prose and language of that chapter, except for the notable absence of the "Engineer," who is no longer to be found sitting on his usual bench. This absence, as we will find out, is the doing of Ishigami himself and the result of his mathematical and quantitative worldview taken to an extreme. It's for this reason that Yukawa attempts to remedy Ishigami's lack of remorse by couching his language in terms that Ishigami can understand.
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