When We Cease to Understand the World

“According to Schwarzschild, the most frightful thing about mass at its most extreme degree of concentration was not the way it altered the form of space, or the strange effects it exerted on time: the true horror, he said, was that the singularity was a blind spot, fundamentally unknowable. Light could never escape from it, so our eyes were incapable of seeing it. Nor could our minds grasp it, because at the singularity the laws of general relativity simply broke down. Physics no longer had any meaning.”

“We can pull atoms apart, peer back at the first light and predict the end of the universe with just a handful of equations, squiggly lines and arcane symbols that normal people cannot fathom, even though they hold sway over their lives. But it's not just regular folks; even scientists no longer comprehend the world. Take quantum mechanics, the crown jewel of our species, the most accurate, far-ranging and beautiful of all our physical theories. It lies behind the supremacy of our smartphones, behind the Internet, behind the coming promise of godlike computing power. It has completely reshaped our world. We know how to use it, it works as if by some strange miracle, and yet there is not a human soul, alive or dead, who actually gets it. The mind cannot come to grips with its paradoxes and contradictions. It's as if the theory had fallen to earth from another planet, and we simply scamper around it like apes, toying and playing with it, but with no true understanding.”

“The case of Shinichi Mochizuki, one of the protagonists of “The Heart of the Heart,” is a peculiar one: I did take inspiration from certain aspects of his work to enter into the mind of Alexander Grothendieck, but most of what is said here about him, his biography, and his research is fiction.”

This book is about what happens when we reach the edges of science; when we come face to face with what we cannot understand. It is about what occurs to the human mind when it pushes past the outer limits of thought, and what lies beyond those limits.

but for a strange reason he could explain neither to himself nor to Bohr, for it was one he would not understand until decades later, he was incapable of confessing his vision of the dead baby at his feet, or the thousands of figures who had surrounded him in the forest, as if wishing to warn him of something, before they were carbonized in an instant by that flash of blind light.

Sweating from head to toe, he spent the day memorizing the West Eastern Divan, a book of poems by Goethe that a previous guest had left behind in his room. He read the poems aloud, over and over, and certain verses echoed from his room and through the empty hallways of the hotel, to the bafflement of the other guests, who heard them as if they were the whispers of a ghost. Goethe had written them in 1819, inspired by the Sufi mystic Khwāja Shams-ud-Dīn Muḥammad Ḥāfeẓ-e Shīrāzī, known simply as Hafez. The German genius encountered the great Persian poet of the fourteenth century in a bad translation published in his home country and came to believe he had received the book at the behest of the divinity. He identified with him so closely that his voice changed completely, melding with that of the man who had sung the glories of God and wine four hundred years before. Hafez had been a drunken saint, a mystic and a hedonist. He devoted himself to prayer, poetry and alcohol. When he turned sixty years old, he traced a circle in the desert sand, sat down in its centre, and swore not to rise until he had touched the mind of Allah, the one and only God, mighty and sublime. He spent forty days in silence, tormented by the sun and wind, and when he broke his fast with a cup of wine given to him by a man who had found him on the verge of death, he felt a second consciousness awaken within him, superimposing itself over his own. That other voice dictated more than five hundred poems to him, helping Hafez to become the pinnacle of Persian literature. Goethe also had help writing his Divan, but his inspiration was not divine, rather the wife of one of his friends, Marianne von Willemer. She was as fanatical an admirer of Hafez as Goethe himself, and they wrote the book together, revising the drafts in letters rife with eroticism, in which the German poet imagines biting her nipples and ejaculating in her mouth, while she dreams of sodomizing him, in spite of the fact that they met only once, and there is no evidence they were able to fulfil any of their fantasies. Marianne composed the songs to the East Wind in the voice of Suleika, lover of Hatem, but she kept her co-authorship a secret until the night before she died, reciting those same verses Heisenberg read aloud, quaking with fever: Where is the colour that might tame the sky? / The grey mist leaves me blind / the more I look, the less I see.

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. Although he could hardly turn the pages, he continued reading those verses of Goethe, and each of them seemed an arrow aimed directly at his breast: I only treasure those who long for death / in flames love has embraced me / in ashes every image of my mind. When he managed to fall asleep, Heisenberg would dream of dervishes spinning in the centre of his room. Hafez pursued them on all fours, drunk and naked, barking at them like a dog. He threw his turban at them, his glass of wine, then the empty jug, trying to dislodge them from their orbits. When he could not wake them from their trance, he pissed on them one by one, leaving a trace of yellow spots on the pale fabric of their tunics, a pattern in which Heisenberg thought he could glimpse the secret of his matrices. Heisenberg stretched out his hands to grab them, but the spots became a long chain of numbers that danced all around him, girdling his neck in a tightening circle until he was scarcely able to breathe. Those nightmares were a welcome respite from his erotic dreams, which grew more intense as his strength failed him, and made him stain his sheets like an adolescent. Though he tried to prevent Frau Rosenthal from changing them, she would not let a day pass without cleaning his room from top to bottom. The shame he felt was nearly unbearable, but Heisenberg refused to masturbate: he was convinced that all his body’s energies must remain bottled up so that he might devote them to his work.

Most nights he fell prey to insomnia. In his delirium, his mind would establish strange connections that allowed him to achieve direct results, forgoing any intermediate steps. He felt his brain split in two: each hemisphere worked on its own, without needing to communicate with the other, and as a result his matrices violated all the rules of ordinary algebra and obeyed the logic of dreams, where one thing can be many: he was capable of multiplying two quantities together and obtaining different answers depending on the order in which he proceeded. Three times two was six, but two times three might be eight. Too weary to question himself, he continued working until he had reached the final matrix. When he solved it, he left his bed and ran around his room shouting, “Unobservable! Unimaginable! Unthinkable!” until the entire hotel was awakened. Frau Rosenthal entered in time to see him collapse on the floor and recoiled at the stench of his soiled pyjama bottoms. When she managed to calm him, she put him back to bed and ran off to fetch a doctor, paying no attention to his complaints, as he was passing in and out of his hallucinations.

Sitting at the foot of his bed, Hafez offered him a glass of wine. Heisenberg took it and drank it in long gulps, letting it run over his beard and chest, before realizing it contained the blood of the poet, who was now masturbating furiously while bleeding from his wrists. All this food and drink have made you fat and ignorant! Hafez hissed. But if you give up sleep and nourishment, you will have one more chance. Don’t just sit there thinking. Go out and submerge yourself in God’s sea! Wetting a single hair won’t bring you wisdom. He who sees God doesn’t doubt. His mind and his vision are pure. Woozy and confused, Heisenberg tried to follow the ghost’s instructions, but his fever had flared up again, and his teeth would not stop chattering. He recovered his lucidity only to feel the prick of a needle and to hear Frau Rosenthal crying on the doctor’s shoulder while he assured her that everything would be all right, that it was nothing more than a badly neglected cold, yet neither of them could see Goethe there, straddling the corpse of 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, like a man blowing on the embers of a dying fire.

Heisenberg woke in the middle of the night. His fever had broken and his mind was exceptionally clear. He stood up from the bed and dressed mechanically, feeling himself totally alienated from his body. He approached his desk, opened his notebook and saw that he had finished every one of his matrices, though he did not know how he had constructed half of them. He took his coat and walked out into the cold.

"Lo que me estimula no es la ambición ni el afán de poder. Es la percepción aguda de algo grande, muy real y muy delicado a la vez." Grothendieck