He came to believe dreams were not proper to human beings, but missives from an external entity he called Le Rêveur, who sent them to allow us to recognize our true identities. For more than two decades, he kept a log of his evenings—The Key to Dreams—which allowed him to understand the Dreamer’s nature: Le rêveur n’est autre que Dieu.
In June 1991, he attempted to cut all ties to the world. He incinerated twenty-five thousand pages of personal writings, burned his portrait of his father and gave away his mother’s death mask. He handed over his final investigations—the notes from his failed attempt to illuminate the motive, that dark heart beating in the furthest depths of mathematics—to his friend Jean Malgoire to donate to his alma mater, the University of Montpellier. This marked the beginning of a period of flight that would last for the rest of his life, as he moved from village to village, shunning the journalists and students who sought him out, and returned letters sent to him by his family and friends without even bothering to open them.
For more than a decade, no one knew where he was. It was said he had died, that he had lost his mind, that he had gone off into the depths of the forest so no one would find his remains.
After rambling through the south of France with no fixed address, he took refuge in the hamlet of Lasserre, in Ariège, in the shadow of the Pyrenees, less than an hour from the concentration camp where his father had spent his final months before being sent to die in the Nazi gas chambers. As a child, Grothendieck had escaped barefoot in the middle of the night from Rieucros, the camp where he and his mother were interned, with the firm intention of walking to Berlin to assassinate Hitler with his own hands. The guards found him five days later, unconscious and a step away from death, shivering inside a hollowed-out tree trunk.
He played the piano at night. 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.”
In 2001, these same neighbours saw smoke and fire rising up from his home. According to Alain Bari, the mayor of Lasserre, Grothendieck did everything possible to prevent the firemen from intervening, and begged them to let it burn.
In 2010, his friend Luc Illusie received a letter from Grothendieck containing his “Declaration of Non-Publication”. In it, Grothendieck prohibits all future sales of his work and demands the withdrawal of all his writings from libraries and universities. He threatens any and all who try to sell, print or disseminate his texts, published or unpublished. He wishes to unmake his influence, to dissolve into silence, to erase the last trace of his existence. “Make it all disappear, at once!”
The American mathematician Leila Schneps was one of the few people Grothendieck had contact with in his final years. She spent months looking for him, travelling through all the villages where she suspected he had lived, an old photograph of him in hand, asking people if they had seen him, unaware of the extent to which his physical appearance had changed. Tired of walking, she spent several days sitting on a bench in front of the only organic market in the region, hoping to see Grothendieck appear, and finally she saw an old man buying green beans, in a monk’s habit, leaning on a cane. His face was obscured inside his hood and his features hidden behind an unkempt beard, long as a wizard’s, but she recognized his eyes.
She approached him cautiously, imagining the recluse would run as soon as he saw her, and was surprised by the kindness with which Grothendieck greeted her, although he explained at once that he did not wish anyone else to find him. Barely capable of containing her emotion, she told him that one of the conjectures he had devised in his youth had finally been solved. Grothendieck smiled faintly. He said he had lost all interest in mathematics.
They spent the afternoon together. Schneps asked him why he had isolated himself. Grothendieck told her he did not hate human beings, nor had he turned his back on the world. His isolation was neither an escape nor a rejection; he had done it for the protection of mankind. Grothendieck said that no one should suffer from his discovery, but he refused to explain what he meant when he spoke of “the shadow of a new horror”.
For a few months, they exchanged letters. Schneps was interested in learning about the ideas he had developed in physics—rumoured to be the last thing he was working on before his retirement. Grothendieck said that he would tell her everything if she could answer one single question: what is a metre?
Schneps did not respond until some weeks later, and her reply was more than fifty pages long, but Grothendieck returned her envelope without opening it, just as he would all those that followed it.
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.”
*
He died at Saint-Girons hospital on Thursday, November 13, 2014. The cause of death is still unknown; he asked that it never be divulged.
The lone testimony of his final days comes from a nurse who cared for him at the hospital. According to her, Grothendieck refused to see his family and received only a single visitor, a tall, timid Japanese man too shy to enter the room until she invited him in.
The man, whom the nurse remembered as handsome but slightly hunchbacked, spent five days sitting on the edge of the bed during visiting hours, bent over in a very uncomfortable posture to bring his ear as close as possible to the patient’s mouth, all the while scribbling in a notebook. He stayed with Grothendieck until he took his final breath, never speaking, and remained beside his body until they came to take it to the morgue.
The same man, or someone very similar, was stopped two days later by the guards at the University of Montpellier. He had been found kneeling in front of the door to the room that contained the four boxes of papers Grothendieck had left to the university—wrinkled scraps and equations written on napkins, which Grothendieck had dismissed as “little more than scribbles”—on condition that they never be opened.
The guards discovered a book of matches in the man’s hand and a small jar of lighter fluid in his pocket, but they did not call the police. They expelled him from the campus, imagining he was insane or suffered from a mental handicap of some kind, because he would not look up from the floor and insisted repeatedly—yet always in the softest of voices—that they must let him go, as he had a very important seminar to present in the Department of Mathematics.
WHEN WE CEASE TO UNDERSTAND THE WORLD
“The more I reflect on the physical part of Schrödinger’s equation, the more disgusting I find it … What Schrödinger writes makes scarcely any sense. In other words, I think it’s bullshit.”
Letter from Werner Heisenberg to Wolfgang Pauli
PREFACE
In July 1926, the Austrian physicist Erwin Schrödinger travelled to Munich to present one of the strangest and most powerful equations that the human mind has ever created.
He had become an international superstar overnight for his discovery of a simple way to describe the interior workings of atoms. 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 ne
ither 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.
Schrödinger’s theory seemed to confirm that elementary particles behaved in a manner similar to waves. If indeed this was their nature, they would obey well-known laws, ones that all the physicists on the planet could accept.
All except one.
Werner Karl Heisenberg had been forced to beg for loans to attend Schrödinger’s seminar in Munich, and after buying his train tickets he barely had money left to cover his room and board in a shabby student pension. But Heisenberg was not just anyone. He was only twenty-three, but his colleagues already considered him a genius, as he had been the first to formulate a series of rules explaining the same matters as Schrödinger, but six months before him.
Their two theories could not have been more opposed; while Schrödinger had needed only a single equation to describe virtually the whole of modern chemistry and physics, Heisenberg’s ideas and formulae were exceptionally abstract, philosophically revolutionary, and so dreadfully complex that only a handful of physicists understood how to use them, and even they suffered headaches trying to solve the simplest problems.
At the conference in Munich there was not a single empty seat. Heisenberg had to listen to Schrödinger’s presentation sitting on the stairs of the auditorium, biting his nails. He could not contain himself until the end. When Schrödinger had reached the midpoint of his talk, Heisenberg leapt up, walked to the chalkboard before the astonished eyes of all present, and shouted that electrons were not waves and that the subatomic world could never be visualized. “It is far stranger than you can imagine!” A hundred people hissed at him and jeered, so vehemently that Schrödinger himself had to intervene and plead that they let Heisenberg speak. But no one cared to listen to the young man who demanded they give up any mental image they had of the atom. No one was willing to look at things as he did. When Heisenberg began to fill the chalkboard with his objections to Schrödinger’s theory, he was pushed up the stairs and thrown out of the room. He was asking for too much. Why should scientists have to abandon common sense to peer at the smallest scale of matter? Surely Heisenberg was driven by envy. After all, Schrödinger’s ideas had completely eclipsed his own discovery, denying him his place in history.
But Heisenberg knew they were all wrong. Electrons were neither waves nor particles. The subatomic world was unlike anything they had ever known. Of this he was utterly certain, his conviction running so deep that he was incapable of putting it into words. Because something had been revealed to him. Something that defied all explanation. Heisenberg had glimpsed a dark nucleus at the heart of things. And if that vision was not true, had all his suffering been in vain?
I
NIGHT IN HELIGOLAND
A year before the Munich conference, Heisenberg had become a monster.
In June 1925, while he was working at the University of Göttingen, an allergic reaction to pollen had deformed his face so that he was no longer recognizable. His lips looked like a rotten peach with the skin ready to come off, his eyelids puffed up until he could barely see. Unable to tolerate even one more day of spring, he boarded a ship to travel as far as possible from the microscopic particles that were torturing him.
His destiny was Heligoland—the name translates as “holy land”—Germany’s only outlying island, so dry and inclement that trees barely rise from the ground and not a single flower blossoms amid its stones. He spent the boat journey locked up in his cabin, nauseated and vomiting, and when he set foot on the red dust of the island, Heisenberg felt so miserable that it took great effort for him not to look at the sheer cliffs—which rose more than seventy metres over his head—as the most expeditious solution to the multiple physical and psychological afflictions that had beset him since he had resolved to decipher the mysteries of the quantum realm.
Unlike his colleagues, who were enjoying the new golden age of physics by exploring novel ideas and undertaking ever more complex and precise calculations, Heisenberg was tormented by what he considered a fundamental flaw in the groundwork of the discipline: the laws that had served so well for the macroscopic world since the time of Isaac Newton fell apart when applied to the interior of the atom. Heisenberg wished to understand what elementary particles were and to unearth the common root of all natural phenomena. But that singular obsession—which he pursued unbeknownst to his supervisor—was consuming him completely.
The woman who received him in the small hotel where he had reserved a room could hardly conceal her shock when she saw him. She insisted on calling the police, certain the young man had suffered a beating at the hands of some drunken sailor during his crossing. When Heisenberg managed to convince her that it was only his allergies, Frau Rosenthal swore she would care for him until he had recovered completely, and devoted herself to this task as though the physicist were her only son, bursting into his room at all hours and forcing on him a fetid, supposedly miraculous elixir which Heisenberg pretended to drink, suppressing his retches until he could spit it out the window when the woman had finally left him in peace.
During his first days in Heligoland, Heisenberg followed a strict regimen of physical activity: at dawn he would leap into the sea and swim until he had rounded the huge outcrop where, according to the owner of the hotel, Germany’s greatest pirate treasure was hidden. Heisenberg only returned to the shore when he was completely exhausted, almost on the point of drowning. He had acquired this strange habit as a child, when he competed against his brothers to see who could swim more laps around the pond on his parents’ property. Heisenberg confronted his research with that same dogged attitude, working for days in a trance, forgetting to eat or even sleep. If he did not achieve a satisfactory result, he would find himself on the brink of a nervous breakdown; if he did, he would fall into an exalted, almost religious ecstasy—a fleeting state to which his friends believed he was slowly growing addicted.
From the window of his hotel, he enjoyed an unobstructed view of the sea. Looking at the waves scudding outwards and getting lost on the horizon, he could not help but recall the words of his mentor, the Danish physicist Niels Bohr, who had once told him that a part of eternity lies in reach of those capable of staring, unblinking, at the sea’s deranging expanses. The summer before, they had explored the hills surrounding Göttingen, and Heisenberg felt that it was only after those long walks that his scientific career had truly begun.
Bohr was a colossus in the world of physics. The only scientist to achieve a similar degree of influence during the first half of the twentieth century was Albert Einstein, who was as much his rival as his friend. In 1922, Bohr had already received the Nobel Prize, and he had a gift for discovering young talents and bringing them under his wing. Such was the case with Heisenberg: during their strolls in the mountains, he convinced the young physicist that, when discussing atoms, language could serve as nothing more than a kind of poetry. Walking with Bohr, Heisenberg had his first intuition of the radical otherness of the subatomic world. “If a mere particle of dust contains billions of atoms,” Bohr said to him as they were scaling the massifs of the Harz range, “what possible way is there to talk meaningfully of something so small?” The physicist—like the poet—should not describe the facts of the world, but rather generate metaphors and mental connections. From that summer onwards, Heisenberg understood that to apply concepts of classical physics such as position, velocity and momentum to a subatomic particle was sheer madness. That aspect of nature required a completely new language.
During his Heligoland retreat, Heisenberg decided to pursue an exercise of radical restriction. What could really be known of all that occurred i
nside an atom? Each time an electron changes its energy level while circling the nucleus, it emits a photon, a particle of light. That particle can be registered on a photographic plate. And that is the only information that can be directly measured, the only light that emerges from the obscurity of the quantum realm. Heisenberg decided to turn away from everything else. He would derive the rules governing existence at that scale armed only with that meagre handful of data. He would rely on no concepts, no images, no models. Reality itself would dictate what could (and what could not) be said about it.
When his allergies abated, allowing him to return to work full time, he arranged these data in an endless series of tables and columns, forming a complex set of matrices. Like a child attempting to put together a puzzle after losing the box top, enjoying the pleasure of assembling the pieces but ignorant of its true design, he spent days ordering and reordering them; little by little, he began to make out subtle relations, ways of adding and multiplying these matrices that revealed a new, increasingly abstract form of algebra. He would play with these matrices while he walked the footpaths that snaked across the island with his eyes pinned to the ground and no idea of where he was going. Each step forward in his calculations drew him further from reality. As the operations he managed to carry out grew more complex, the more obscure his underlying reasoning became. What possible relation existed between those lists of abstract numbers and the concrete molecules forming the stones scattered at his feet? How could he arrive at something that resembled, if only a little, the contemporary idea of the atom, starting from his rows and tables more befitting a lowly accountant than a proper physicist? The nucleus as a little sun, with electrons orbiting around it like planets; Heisenberg loathed that infantile, simplistic image. In his vision of the atom, those mental representations vanished: the little sun was snuffed out, and the electron stopped spinning like a top and dissolved into a formless mist. All that remained were numbers. A landscape as sterile as that which separated the two ends of the island.
When We Cease to Understand the World Page 7
