When We Cease to Understand the World

Karl Schwarzschild is a Jewish-German astronomer who is the protagonist of Chapter 2. As a child, he is a prodigy, particularly in math and science. As an adult, he is a genius who works obsessively, compulsively, and even recklessly. When he is given a prestigious position at the University of Göttingen observatory, he fails to take good care of the equipment and leaves the place in chaos. Schwarzschild is a patriot and volunteers to fight in World War I for Germany, even though he could have avoided military service altogether as a professor. He enjoys the close friendships he makes in the military, although eventually the horrors of combat wear on his psyche. While serving, he continues to work on his astronomical research and applies some of his expertise to his military service, such as working at a weather station.

He is haunted by his discovery of the nature of collapsing stars, which suck everything into their orbit and seal themselves off space and time, known as the “singularity.” Schwarzschild is highly imaginative, and his discovery begins to haunt his waking hours. He writes to his wife that “[something strange] has an irrepressible force and darkens all my thoughts” (41). Later, this imaginative sense of dread expands to his feeling about the German nation in general. In talking to the mathematician Courant, he wonders:

Could a sufficient concentration of human will—millions of people exploited for a single end with their minds compressed into the same psychic space—unleash something comparable to the singularity? Schwarzschild was convinced that such a thing was not only possible, but was actually taking place in the Fatherland [Germany] (56).

Shinichi Mochizuki is an eccentric, brilliant Japanese mathematician born in Tokyo who is a secondary protagonist in Chapter 3. He is a former child prodigy in mathematics and attends Princeton at the age of 16. He is extremely shy and awkward. He is good-looking, with a passing resemblance to Clark Kent, Superman’s alter ego, but he walks a slouch. He is incredibly soft-spoken. As a young university student, he became obsessed with the work of French mathematician Alexander Grothendieck and works feverishly on proving his conjectures. As an adult, he becomes increasingly agoraphobic. He eventually only leaves his house to go to his office in Kyoto and back again.

As a researcher he publishes a proof of a + b = c on his blog. However, perhaps due to his extreme shyness, he refuses to give any interviews or talks defending his work. He visits Grothendieck shortly before the latter’s death and is later caught attempting to burn Grothendieck’s archives in Montpellier. After this event, he takes down his proof and threatens to sue anyone who publishes it, echoing Grothendieck’s own exhortations that he never wanted his findings disseminated or published.

Alexander Grothendieck is an eccentric, genius French mathematician who is the protagonist of Chapter 3. He has a tumultuous upbringing due to his parents’ involvement in leftist activism at the turn of the 20th century and spends most of his childhood in a French internment camp, where his mother is sent after fighting against Franco in the Spanish Civil War. It is possibly this heritage that leads Grothendieck to engage in militant leftist movements in France as an adult. In 1970, he resigns from his post at a research institute when it accepts a contract from the French Defense Ministry. He starts a commune devoted to ecology and pacifism.

Grothendieck works obsessively: “He could begin working out an idea in the morning and not move from his desk until dawn the next day” (72). His work is also characterized by extreme abstraction and a desire to find the ultimate foundation of mathematics, which he calls the scheme. However, he becomes increasingly concerned about “the destructive power of science” and “the possible effects that his own ideas could have on the world” (75). This obsession about the negative potential of his ideas leads him to become increasingly reclusive and secretive about his work. Ultimately he follows the model of the French Catholic mystic Marthe Robin and lives like an ascetic so as to not cause harm. Grothendieck’s religious views are somewhat obscure, and he develops his own idiosyncratic theology, which includes a belief in a Rêveur, or a Dreamer, who sends sleeping people their dreams. He also believes he is visited nightly by a two-faced woman whose good side is called Flora and whose evil side is called Lucifera. Their song encourages God to appear, but “he is silent, and when he speaks, he does so in a voice so soft that no one can understand it” (83).

Erwin Schrödinger is an Austrian physicist and one of the protagonists of Chapter 4. He has unusually good hearing. As a student, he is considered a prodigy and a genius. Throughout his life he suffers badly from tuberculosis, which requires him to periodically take leave from his lecturing and recover in a sanatorium in the Swiss Alps.

Schrödinger is a misogynist and a womanizer. He forces his wife to leave her relatively well-paid job to follow him around to various low-paid university posts. He pursues many affairs but grows increasingly resentful of his wife’s own affair with his colleague, the Dutch physicist Peter Debye. He is also attracted to and molests the 16-year-old daughter of the director of the sanatorium, Miss Herwig, to whom he gives private lessons.

Like many Germans of his day, Schrödinger is fascinated by Hindu philosophies such as those described in the Bhagavad Gita. He is particularly captured by the imagery of the Hindu goddess Kali, who is associated with time and death.

Karl Heisenberg is a German theoretical physicist who is one of the protagonists of Chapter 4. He is a Nazi who holds a senior position in the German nuclear weapons program. He is best known for his Heisenberg uncertainty principle, which holds that a subatomic particle can never be entirely measured. He is isolated, strange, and obsessive. He tends to work for days until he either fails and has a nervous breakdown or succeeds and “fall[s] into an exalted, almost religious extasy” (96).

He suffers from extreme allergies that require him to travel to the dry climate of Heligoland to recover. There, he experiences fever and migraines and barely leaves his room. While in a feverish state, he obsessively reads Goethe’s Hafez-inspired poetry and eventually hallucinates Goethe “straddling the corpse of [Sufi mystic] Hafez, now drained of all its blood, and yet still capable of maintaining a glorious erection, which the German poet attempted to invigorate with his lips” (105). This is not the only ominous premonition that Heisenberg has. Although he is a man of science, he is open to these visions. However, because of his ambition, he uses them to further his scientific discoveries rather than accept their warnings about the destruction those discoveries will cause.

De Broglie is an eccentric French theoretical physicist who is one of the protagonists of Chapter 4. He comes from a royal family and has a sheltered childhood. His parents are neglectful, but he is doted upon by his sister Pauline. He is a child genius and reads extensively, but he is fearful of “the most innocuous circumstances” (110). Despite being a pacifist, he is obliged to enlist in the French military and serves as a telegraph operator during WWI, an experience that haunts him for the rest of his life.

De Broglie falls in love with his friend, the painter and collector Jean-Baptiste Vasek, founder of the art brut movement. When Vasek dies by suicide, de Broglie abandons his scientific work to hold an exhibition of Vasek’s work. When the exhibition gets mixed reviews, de Broglie locks himself into his house for three months, working obsessively. His key insight is that not only light but all matter exists simultaneously as a particle and a wave.

Albert Einstein, “the pope of physics” (118), is a minor character in When We Cease to Understand the World. Einstein is a Jewish-German theoretical physicist best known for his theory of relativity. He supports de Broglie’s dualism principle and comes into conflict with Heisenberg and Bohr over their uncertainty principle. He is also supportive of Schwarzschild’s work, although he contests the notion of the singularity. Einstein stubbornly seeks to find a unifying principle of quantum mechanics, despite being unable to disprove the theories of Schwarzschild, de Broglie, or Bohr. He refuses to believe that the world is chaotic and is passionate in his defense of an order underlying the structure of all matter in the universe.

Miss Herwig is the young daughter of Dr. Herwig, who runs the sanatorium in the Swiss Alps where Schrödinger goes to recover. She is ethereally beautiful, kind, and seems wiser than her years. She has spent much of her life convalescing from her periodic bouts of tuberculosis. She has quasi-mystical abilities. For instance, when she is in good health, the other residents at the sanatorium seem to improve, and when she is in poor health, they decline.

Miss Herwig is a minor character who functions primarily as the object of Schrödinger’s desire. Schrödinger lusts after her, masturbates to thoughts of her, and ultimately molests her while she sleeps. She is symbolic of eroticism and how temptation can lead to “madness.” This is most clearly symbolized when she manifests as Kali, the Hindu goddess of death.

Niels Bohr is a Danish theoretical physicist. He is a minor character in When We Cease to Understand the World. He is primarily portrayed as Karl Heisenberg’s mentor and collaborator. He comes into conflict with Heisenberg when he embraces both Heisenberg’s uncertainty principle and Schrödinger’s wave theory. Ultimately, he supports Heisenberg at the Fifth Solvay Conference, even after Heisenberg confesses to him that his findings were partly inspired by hallucinations.