71 pages • 2 hours read
Ted ChiangA modern alternative to SparkNotes and CliffsNotes, SuperSummary offers high-quality Study Guides with detailed chapter summaries and analysis of major themes, characters, and more. For select classroom titles, we also provide Teaching Guides with discussion and quiz questions to prompt student engagement.
The story is formally divided into 9 segments, each of which begins with theoretical mathematic inference, followed by two subheadings, a and b, which tell the story from the third person omniscient narrative viewpoint. Mathematical segments deal with historical attempts to prove the inconsistency of mathematics, especially with respect to division by zero, which “allows one to prove not only that one and two are equal, but that any two numbers at all—real or imaginary, rational or irrational—are equal” (71).
Renee is a mathematics professor who tried to commit suicide and spent a brief time in a psychiatric ward. Her biologist husband, Carl, feels numb and tired due to her previous erratic behavior: “[H]e felt no more than a sense of duty towards her” (72).
As a child, Renee became infatuated with the precision of mathematics. She was a prodigy, receiving her doctorate at 23, but for her it was all about the sense of rightness that mathematics gave her.
A few weeks before her suicide attempt, Renee asks her colleague, Fabrisi, to look at her newest calculations—the first time she has ever asked anyone for help. The new formalism she developed contradicts itself. Although she knows Fabrisi will be unable to grasp the full meaning of her work, he will be useful in checking its mechanical aspects. Fabrisi soon confirms Renee’s fears about the correctness of her calculations and the essential contradiction in her work. She contacts another mathematician, Callahan, who confirms her findings are “fundamental and disturbing” (81).
At home, Carl witnesses Renee’s frustration with her current work and tries to cheer her up, to no avail. He is unable to understand the source of her frustrations. When he confronts her, she tells him she discovered “a formalism that lets you equate any number with any other number. That page there proves that one and two are equal” (79). The proof employs only allowed axioms and operations. Her conclusion is that “‘arithmetic as a formal system is inconsistent’” (79). Renee’s profound sense of disturbance lies in the fact that she has disproved most mathematical rules, which are rendered meaningless because “now mathematics has absolutely nothing to do with reality” (80).
As Renee feels as if she is losing her mind, she dreams of a formalism equating life with death. Her work, though catastrophic in consequence, feels right and precise. Carl tries to comfort her by mentioning how quantum physics and irrational numbers first made no sense, but she informs him indignantly that her work proves things a priori—meaning, through theoretical deduction. Renee adds, “I can’t maintain the concept of distinct quantities in my mind anymore; they all feel the same to me” (83). A few days later, she attempts suicide, which reminds Carl of his youth, when he tried to kill himself. During his healing, he learned about empathy from his girlfriend Laura who helped him. He realizes there is nothing he can do for Renee because he cannot grasp what led her to such an action.
After her release from a psychiatric ward, Renee wonders if she will ever be able to function normally again. For her, mathematics no longer gives meaning to the universe. It is inconsistent—merely empirical—and therefore of no interest to her. Carl, meanwhile, falls out of love with Renee, whom he can no longer reach. He plans to leave her after she gets better, but Renee causes him to feel like a hypocrite by thanking him for being there for her as support. He understands that they share the same feeling: as Renee feels alienated from mathematics, having proven it unstable, Carl feels alienated from her, having witnessed her instability. However, “this was an empathy that separated rather than united them, and he couldn’t tell her that” (87-88).
Ted Chiang uses a mathematical expression which has no meaning—division by zero is undefined in mathematics, as such arithmetic operation does not assign meaning—as a scientific framework for a personal story of a couple who cannot comprehend each other anymore. Renee is a gifted mathematician who defines her life through her belief in the inherent mathematical order and the ability of mathematics to describe the world. Her husband, Carl, is a man who finds that Renee’s preoccupation with symbolic order leaves him without a course of action that would help him understand and empathize with her.
The author states in his Story Notes that “a proof that mathematics is inconsistent, and that all its wondrous beauty was just an illusion, would, it seemed to me, be one of the worst things you could ever learn” (267). This is what happens to Renee in the story. Her genius leads her to discover a mathematical formalism that proves essential inconsistency in mathematics, which shatters her reason to exist in a world that is not circumscribed by mathematical rules. Her attempt at suicide is not a call for help; it is Renee’s only way out from a hellish existence without belief in mathematical logic. Chiang depicts her depression and apathy as akin to any person who loses what they deeply believe in: the fundamental core of their personality. As such, Renee sees no point in living.
Carl, on the other hand, experiences a similar despair as a young adult. From his experience, however, he learns there are things he cherishes in life because he never bound his existence to a single—or single-minded—notion that defines his whole being. He believes in his marriage and in his love for Renee, but he comes to understand that her loss of faith is ultimately unknowable to him. Carl cannot empathize because he does not understand that Renee values her belief in mathematics more than her life or her husband. In consequence, he loses his faith in Renee, just as she lost her faith in science. And just as Renee finds herself unable to move on, so does Carl understand that he cannot continue his life with Renee.
Through the introductory parts of each numbered section, the author charts the progress of mathematical thought, especially where it concerns establishing axioms and foundational ideas that support mathematics as a consistent core science. These sections serve as counterpoints to Renee’s unraveling and acquire an ironic edge, by distancing the reader from Renee’s suffering and emphasizing the immensity of her despair.
Asian American & Pacific Islander...
View Collection
Books Made into Movies
View Collection
Chinese Studies
View Collection
Fantasy
View Collection
Magical Realism
View Collection
Philosophy, Logic, & Ethics
View Collection
Religion & Spirituality
View Collection
Science Fiction & Dystopian Fiction
View Collection
Science & Nature
View Collection
Short Story Collections
View Collection