When We Cease to Understand the World

“An ingredient in Dippel’s elixir would eventually produce the blue that shines not only in Van Gogh’s Starry Night and in the waters of Hokusai’s Great Wave, but also on the uniforms of the infantrymen of the Prussian army, as though something in the colour’s chemical structure invoked violence: a fault, a shadow, an existential stain passed down from those experiments in which the alchemist dismembered living animals to create it, assembling their broken bodies in dreadful chimeras he tried to reanimate with electrical charges, the very same monsters that inspired Mary Shelley to write her masterpiece, Frankenstein; or, The Modern Prometheus, in whose pages she warned of the risk of the blind advancement of science, to her the most dangerous of all human arts.”

This quote highlights how the beneficial fruits of the technological advances of civilization can be intrinsically tied to “violence.” The paintings Starry Night and Great Wave are two of the most recognizable and celebrated works of art in the modern era, but the scientific innovations used to make them also contributed to military technology prefigured by “the uniforms of the infantrymen of the Prussian army.”

“Among the few possessions Fritz Haber had with him when he died was a letter written to his wife. In it, he confessed that he felt an unbearable guilt; not for the part he had played, directly or indirectly, in the death of untold human beings, but because his method of extracting nitrogen from the air had so altered the natural equilibrium of the planet that he feared the world’s future belonged not to mankind but to plants, as all that was needed was a drop in population to pre-modern levels for just a few decades to allow them to grow without limit, taking advantage of the excess nutrients humanity had bestowed upon them to spread out across the earth and cover it completely, suffocating all forms of life beneath a terrible verdure.”

The motif of verdure or greenness is introduced in this quote. Fritz Haber is unconcerned about the deaths he causes in wartime, but he is afraid of the excess of plant life that his work on isolating nitrogen could lead to in the future. The idea of a suffocating excess of plant life as a result of human technologies is revisited in Chapter 5.

“And yet, he could not get it out of his head. Even immersed in the chaos of war, the singularity spread across his mind like a stain, superimposed over the hellscape of the trenches; he saw it in the eyes of the dead horses buried in the muck, in the bullet wounds of his fellow soldiers, in the shadowy lenses of their hideous gas masks. His imagination had fallen prey to the pull of his discovery: with alarm, he realized that if his singularity were ever to exist, it would endure until the end of the universe.”

This quote describes Schwarzschild’s state of mind after discovering the singularity while fighting in WWI. It layers the horrors of war with the devastating implications of Schwarzschild’s research, thematically drawing together destruction and scientific progress.

“He was convinced that mathematics, physics and astronomy constituted a single body of knowledge and believed that Germany was capable of exercising a civilizing force comparable to that of ancient Greece. To do so, however, its science must be raised to the heights already achieved by its philosophy and art, for ‘only a vision of the whole, like that of a saint, a madman or a mystic, will permit us to decipher the true organizing principles of the universe.’”

Many of the scientists in the text experience something akin to a religious ecstasy when achieving scientific breakthroughs, as described here by Schwarzschild. However, in his vision, the purpose of this scientific progress is a nationalistic one: to promote German civilization. This is an eerie premonition of the rhetoric that the Nazis would later use during WWII to justify their Aryan supremacist goals of European domination.

“Alarmed by the manic fervour of his academic output, his colleagues advised him to slow down, fearing that his inner fire would consume him. Schwarzschild paid them no attention. Physics was not enough for him. He aspired to the type of knowledge the alchemists had pursued, and laboured beneath the sway of a strange urgency that not even he could fully explain: ‘Often I have been unfaithful to the heavens. My interest has never been limited to things situated in space, beyond the moon, but has rather followed those threads woven between them and the darkest zones of the human soul, as it is there that the new light of science must be shone.’”

The protagonists, including Schwarzschild, are extremely ambitious and pursue their work to the detriment of their own well-being. Schwarzschild expresses his ambition as a desire to understand the foundational structure of all things in the universe and the way that heavenly bodies and human experience are connected. This is similar to “the type of knowledge the alchemists had pursued” because medieval and early modern alchemists like Swedenborg likewise believed that the microcosm was analogous and connected to the macrocosm through a series of correspondences.

“Like many sensitive people, Schwarzschild felt overcome by a sense of imminent disaster as the First World War approached. In him, this took the peculiar form of a fear that physics would be incapable of explaining the movement of the stars, or of finding an order in the universe.”

One of the motifs of When We Cease to Understand the World is the structure of the universe. This quote highlights one example of a protagonist who is afraid that his work will indicate that humanity lives in a disordered, chaotic universe rather than in a cosmos that adheres to fundamental universal laws. This fear is echoed by Albert Einstein.

“If matter were prone to birthing monsters of this kind, Schwarzschild asked with a trembling voice, were there correlations with the human psyche? 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.”

Before WWI and in the initial months of his military service, Schwarzschild believes that scientific progress will advance German civilization. However, in this quote toward the end of his life, he has come to fear the destructive potential of scientific discovery and the potential repercussions of nationalism. This can be read as a premonition of the way that the Western powers would harness scientific innovation during WWII to devastating effect.

“The a + b = c conjecture reaches down to the roots of mathematics. It proposes a deep and unexpected relationship between the additive and multiplicative properties of numbers. If it is proven, it will become a formidable tool capable of dispelling, as if by magic, a vast quantity of long-standing enigmas. But Mochizuki’s ambition was even greater than that; he did not stop at verifying the conjecture, but even invented a novel type of geometry, one that required mathematicians to conceive of numbers in a radically different way.”

This quote is another example of the motif of the structure of the universe. In this case, Mochizuki’s ambition is to understand the foundations of the universe through mathematics.

“His was the power of unbridled abstraction. He championed an approach that was based on wild generalizations, zooming further and further out and then focusing sharply, as any dilemma became clear when one viewed it from a sufficient distance. Numbers, angles, curves and equations did not interest him, nor did any other mathematical object in particular: all that he cared for was the relationship between them. ‘He had an extraordinary sensitivity to the harmony of things,’ one of his disciples, Luc Illusie, recalled. ‘Not only did he introduce new techniques and prove major theorems: he changed the way we think about mathematics.’”

The mathematician Grothendieck’s work illustrates the narrow boundary between genius and “madness.” While he has incredible insights that “chang[e] the way we think about mathematics” (67), they are based on “wild generalizations” that are the result of his “extraordinary sensitivity” and unbalanced mind.

“The pinnacle of his investigations was the concept of motive: a ray of light capable of illuminating every conceivable incarnation of a mathematical object. ‘The heart of the heart’ he called this strange entity located at the crux of the mathematical universe, of which we know nothing save its faintest glimmers.

Even his closest and most loyal collaborators believed he had gone too far. Grothendieck wanted to hold the sun in the palm of his hand, uncover the secret root that could bind together countless theories that bore no apparent relation to one another.”

Like the other protagonists of the novel, Grothendieck seeks to understand the fundamental structure of the universe, one of the recurring motifs. The text here makes an illusion to the ancient Greek myth of Icarus, who flew too close to the sun which melted his wings, causing him to fall to earth and die. Like Icarus, Grothendieck wants to “hold the sun in the palm of his hand,” but he ultimately will crash and burn as a result of his hubris.

“His neighbours in Lasserre—who knew he did not tolerate visitors—were surprised to hear beautiful polyphonies coming from his home, as though in his seclusion he had learned Mongolian chant and could intone multiple notes simultaneously. Grothendieck explains the matter in his diaries: at nightfall, he is visited by a woman with two faces. He calls her gentle side Flora and her demonic side Lucifera. They sing together to oblige God to make himself manifest, but ‘he is silent, and when he speaks, he does so in a voice so soft that no one can understand it.’”

Grothendieck is the only protagonist who exchanges the ecstasy of scientific discovery for an explicitly religious one. The two-faced woman that he has visions represents how seeking the numinous has both a positive element (“Flora”) and negative one (“Lucifera,” meaning light but also associated with the devil).

“Towards the end of his life, his point of view was so remote that he was only capable of perceiving totality. Of his personality, nothing but tatters remained, tenuous threads pulled apart by years of constant meditation. ‘I have an irrefutable and perhaps blasphemous sense that I know God more intimately than I do any other being in this world, even though He is an impenetrable mystery, infinitely vaster than any physical entity.’”

Grothendieck is completely consumed by his religious experiences and entirely loses his individual humanity. This is one example of The Price of the Quest for Knowledge. His ego-less nature prefigures the dream Schrödinger has of the goddess Kali with her necklace of skulls of people “freed from the principal object of their identification” (137).

“Using formulae similar to those employed to predict the movement of waves in air and water, Schrödinger had achieved something apparently impossible: he had reined in the chaos of the quantum world, illuminating the orbits of electrons around the nucleus with an equation so elegant, exquisite and bizarre that some did not hesitate to call it ‘transcendent.’

Yet its greatest charm was neither its beauty nor the myriad natural phenomena it was capable of describing; what seduced the entire physics community was how it enabled them to visualize things taking place at the smallest levels of reality. For those whose ambition was to scrutinize matter down to its most basic constituents, Schrödinger’s equation was a Promethean fire capable of dissipating the darkness of the subatomic realm, revealing a world that until then had been veiled with mystery.”

This quote describes Schrödinger’s realization of the structure of the universe. It contains the second reference to the myth of Prometheus; the first reference is found in the title of Mary Shelley’s Frankenstein; or, The Modern Prometheus. In ancient Greek myth, Prometheus steals fire from the gods on Mount Olympus and gives it to humanity. Fire is symbolic of the knowledge and civilization-advancing technologies of humankind. Even though fire leads to the rise of human civilization, it is also a destructive force like the scientific discoveries described in the novel.

“Heisenberg insisted on working on his matrices even when ill: while Frau Rosenthal covered him in cool compresses, hoping to lower his temperature, and tried to convince him to call a doctor, he would rant about oscillators, spectral lines and harmonically bound electrons, convinced he need only hold out a few more days for his body to overcome the illness and his mind to find the way out from the labyrinth in which he had imprisoned it.”

This quote gives one example of the Price of the Quest for Knowledge. Even though Heisenberg is extremely ill, he refuses to abandon his quest to solve the problem posed by his matrices.

“The father of relativity was a great master of visualization: all of his ideas about space and time had been born of his capacity to imagine himself in the most extreme physical circumstances. For this reason, he was unwilling to accept the restrictions demanded by Heisenberg, who seemed to have gouged out both his eyes in order to see further. Einstein sensed that if one followed that line of thinking to its ultimate consequences, darkness would infect the soul of physics: if Heisenberg triumphed, a fundamental aspect of the laws that governed the physical world would remain forever obscure, as if chance had somehow nested in the heart of matter and become inextricably bound to its most fundamental constituents.”

Like Schwarzschild, Einstein is convinced that the structure of the universe must follow clear laws and is afraid of the implications if it does not. The description of Heisenberg “goug[ing] out both his eyes in order to see further” is a reference to the ancient Greek prophet Tiresias. Tiresias is blinded by the gods but is also given the gift of prophesy, or the ability to see into the future.

“‘And yet today I say to you with absolute certainty that all things can exist in two ways, and that nothing is as solid as it appears; the stone in the child’s hand, which he aims at the idle sparrow on its branch, could run like water between his fingers.’ De Broglie had lost his mind.”

This quote relates to the theme of The Intersection of “Madness” and Genius. De Broglie is able to understand the foundational structure of the universe—that all matter exists both as particle and wave—but it costs him his sanity.

“In his nightmare, the goddess Kali would sit on his chest like an enormous beetle, crushing him so that he could not move. With her necklace of human heads, and brandishing swords, axes and knives in her many arms, she would bathe him in drops of blood that fell from the tip of her tongue and jets of milk from her swollen breasts, rubbing his groin until he was no longer capable of bearing the arousal, at which point she would decapitate him and swallow his genitals. Miss Herwig listened to him impassively and told him his dream was not a nightmare, but a blessing: of all the forms taken on by the female aspect of the divine, Kali was the most compassionate, because she granted moksha—liberation—to her children, and her love for them extended beyond all human comprehension. Her black skin, she said, was the symbol of the void that transcends all form, the cosmic uterus in which all phenomena gestated, while her necklace of skulls comprised the egos she had freed from the principal object of their identification, which was nothing less than the body itself. The castration Schrödinger suffered at the Dark Mother’s hands was the greatest gift he could receive, a mutilation necessary so that his new consciousness could be born.”

This quote uses the symbol of the dream to give insight into Schrödinger’s character. Miss Herwig’s interpretation suggests that Schrödinger needs to forgo his erotic desires in order to access “new consciousness” or new scientific breakthroughs. This specific dream is a variant on the folkloric German “night-mare,” a mare being a female being that sits on the chest of the sleeper and often has an erotic, seductive element.

“Rather than working to resolve the contradictions between the two approaches, Bohr embraced them. In his view, the attributes of elementary particles were only valid in a given context and arose from a relationship. No single frame of reference could encompass them. Measured in experiments of one type, they would exhibit the properties of a wave; in another, they would appear to be particles. These perspectives were mutually exclusive, antagonistic, and at the same time complementary: neither was a perfect reflection, and both were models of the world. Combined, they gave a more perfect notion of nature.”

In this quote, the theoretical physicist Niels Bohr synthesizes the findings of Schrödinger and Heisenberg to create an understanding of the structure of the universe, “a more perfect notion of nature.” That these two insights are complementary suggests that both had real insight into how particles work at a subatomic level despite pursuing different methods of understanding.

“Impotent, I suffered as I saw how my consciousness of time was destroyed, my resolve, my sense of duty and proportion! And to whom do we owe this magnificent inferno if not to you, to people like you? Tell me, Professor, when did all this madness begin? When did we cease to understand the world?”

This quote comes from an unnamed demon-like figure that Heisenberg meets at a bar in Copenhagen. It is unclear from the passage whether he is real or a product of Heisenberg’s vision. He accuses scientists like Heisenberg of creating new technologies, specifically the telephone, that fundamentally complicate and obscure people’s understanding of the world.

“There simply existed no ‘real world’ outside that science was capable of studying. ‘When we speak of the science of our era,’ Heisenberg explained, ‘we are talking about our relationship with nature, not as objective, detached observers, but as actors in a game between man and the world. Science can no longer confront reality in the same way.’”

In this quote, Heisenberg explains how the findings of the Copenhagen Interpretation have fundamentally changed understandings of the structure of the universe and how humans can instrumentalize nature. Throughout the novel, scientists reach their conclusions at least in part through the illogical tools of dreams, visions, and hallucinations. This quote emphasizes how the new understanding of the world this way of knowing has generated is itself subjective.

“Let it burn and watch the flames reach up to the sky, for left alone it will consume the world, feeding on the death of others, nurtured by all the green grass turned grey.”

This quote is a poetic expression of the dangers of The Impact of Scientific Discovery. If left unstopped, scientific innovations will lead to out-of-control consequences that will cause destruction.

“According to the night gardener, the Mapuche Indians would crush the skeletons of their vanquished enemies and spread that dust on their farms as fertilizer, always working in the dead of night, when the trees are fast asleep, for they believed that some of them—the canelo and the araucaria, the monkey puzzle—could see into a warrior’s soul, steal his deepest secrets and spread them through the shared roots of the forest, where plush tendrils whispered to pale mushroom mycelium, ruining his standing before the community. His secret life lost, exposed and bared to the world, the man would slowly begin to shrivel, drying up from the inside out, without ever knowing why.”

Mapuche Indians are people indigenous to modern-day Chile and Argentina. This story relates to the notion of tree roots spreading “a vegetable plague” mentioned in Part 1 of Chapter 5 that threatens to destroy the world. It also illustrates the recurring idea that the natural world has enormous powers that humans have only begun to grasp.

“The night gardener’s decision to drop out of life was not merely because of his admiration for Grothendieck, of course. He had also gone through a bad divorce, become estranged from his only daughter and been diagnosed with skin cancer, but he insisted that all of that, however painful, was secondary to the sudden realization that it was mathematics—not nuclear weapons, computers, biological warfare or our climate Armageddon—which was changing our world to the point where, in a couple of decades at most, we would simply not be able to grasp what being human really meant.”

This quote highlights the impact of scientific discovery on the world. To the night gardener, while many of the technologies developed by science are terrible, its worst effect has been the way that the pursuit of knowledge has degraded and obscured people’s humanity.