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Mathematics and numbers permeate every aspect of life in the One State. Characters are referred to not by conventional names, but by a letter-number sequence, such as O-90 or R-13. Romantic evenings are spent with “arithmetical problems” (14), and even the very means characters use for expressing themselves are couched in mathematical or geometric terms. For example, D-503 talks about how I-330 “had a disagreeable effect on me, like an irrational component of an equation, which you cannot eliminate” (3). The predominance of numbers and math symbolizes how, in the One State, impersonal logic and reason have replaced personality and feeling. Numbers also come to symbolize how individuals are interchangeable, replaceable parts of a greater numerical whole. Indeed, D-503 at one point talks approvingly about how the Integral’s production process moves on seamlessly after the death of a “Number.”
However, math and mathematical metaphors are also used to describe the disorientation of the neat mathematical world created by the One State. D-503 talks about how the square root of negative one disturbed him as a child. I-330 represents this irrational number, which “could not be thought out” (15) or reduced to any rational schema. She symbolizes a world beyond control and reasoning that metamorphizes and grows within D-503 as the novel progresses. D-503 sees this after he has sex with I-330 and discovers the underground tunnels of the Mephi when he says that he “saw the square root of minus one” (38). It reaches its apotheosis when D-503 starts to feel that his self-identity is breaking down and becomes “infinitesimal, a geometric point” (57) with limitless possibilities. Significantly, the last conversation D-503 notes in his journal is with a man who claims he discovered the impossibility of infinity. It is also significant that the spaceship is named Integral, which in mathematics refers to the continuous analog of a sum and is one of the two fundamental operations in calculus; the other is differentiation. In this way, We explores the irrational and subversive potential at the heart of reason itself, and the impossibility of a pure mathematical order.
When D-503 first walks around the Ancient House he observes how “our contemporary beautiful, transparent, eternal glass was represented here only by pitiful, delicate, tiny squares of windows” (11). This comment captures the centrality of glass in the One State. While some pre-One State cultures used glass in architecture, it is only with the One State that glass replaces all other building materials and becomes a focal point of culture itself. This is depicted in the dwellings of One State citizens. As D-503 says, “We live surrounded by transparent walls… we have nothing to conceal from one another” (7). Glass serves to ensure that everyone can observe everyone else, eliminating the possibility of transgression, and re-enforcing a sense of communal existence.
Glass also assumes a symbolic significance in the One State. D-503 talks about “our glass paradise” (50), and both the vast cube used for public events and the Integral, the pinnacle of One State technology, are constructed from glass. Glass not only represents technological accomplishment but the elimination of anything unknown or unseen. Within the One State’s glass utopia, there is no room for the shadow of ignorance or unhappiness. For this reason, when D-503 starts to question the One State, his relationship with glass shifts. After he has sex with I-330, he describes the glass city as a “desert made of glass” (32). He begins to see in glass not absolute clarity or communal connection, but the absence of the depth and privacy which give life meaning. He starts to see that it is the ambiguity that glass suppresses, which allows for a deeper connection to others and the world.
D-503 and the poet R-13 discuss the difference between math and poetry and R-13 tells D-503 that “you want to encircle the infinite with a wall and you fear to cast a glance behind the wall” (15). In this instance, the wall symbolizes how D-503, and the One State generally, despite claiming to be fearless pursuers of truth, want to set a limit on understanding. They want to circumscribe knowledge according to a narrow rationalistic and mathematical schema and are afraid to look beyond this. At the same time, walls symbolize disconnect or dishonesty between characters. When I-330 conceals from D-503 the meaning of the tunnels under the Ancient House and her plans, he says, “You are here, near me, yet you seem to be behind an opaque ancient wall” (52).
Near the novel’s end, this sense of walls as wholly negative is problematized. In a speech to the Mephi, I-330 declares that “the day has come for us to destroy that Wall and all other walls, so that the green wind may blow all over the earth” (61). And, with this, I-330 suggests that they must destroy all barriers between people and between humans and nature. The practical consequences of this act are in many ways problematic. When a hole is blown in the Green Wall, and nature literally and metaphorically floods into the One State, there is violence, disorder, and corpses in the streets. Further, it is this chaos which pushes the One State into the extreme policy of removing citizen’s imaginations. We suggests that sometimes walls may be necessary, or that their destruction has dire effects. D-503 also finds this true on a personal level. His quest to destroy the walls that defined his life threatens his sense of self and causes him to accept the One State’s operation.
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