Measuring the World

  Gauss fingered his cheek. Oh, Bartels. He knew all about it. He himself came out of poverty, had been considered a wunderkind, and believed himself chosen for great things. Then he had met him, Gauss. And he knew, meanwhile, that for the next two nights after they met, Bartels had lain awake and thought about whether he should go back to the village, milk cows, and muck out stalls. Sometime during the third night, he had realized that there was only one way to save himself: he would have to like Gauss. He would have to help him, no matter where it led. From that moment on, he had thrown all his strength into working with Gauss, he had talked to Zimmerman, written letters to the duke, and one difficult evening, by means of threats none of them wanted to remember, he had got Gauss's father to agree to let his son go to high school. And the next summer he had gone with Gauss to visit his parents in Brunswick. Suddenly the mother had taken him aside, her face small with worry and shyness, to ask if there was any future for her son at the university with all the educated people. Bartels hadn't understood. What she meant was, did Carl have any future researching things? She was asking in confidence, and promised not to repeat anything. As a mother, one always had worries. Bartels had remained silent for a while, before asking with a contempt which shamed him later if she didn't know that her son was the greatest scientist in the world. She had wept and wept, and it had been extremely embarrassing. Gauss had never succeeded in forgiving Bartels.

  He had come to a decision, said Gauss.

  For what? Bartels looked up distractedly.

  Gauss gave an impatient sigh. For mathematics. Until now he had wanted to concentrate on classical philology, and he still liked the idea of writing a commentary on Virgil, in particular Aeneas’ descent to the underworld. He felt that nobody yet had correctly understood this chapter. But there would still be time for that, after all he had only just turned nineteen. But above all he had realized that he could achieve more in mathematics. If one had to be born, even if nobody had bothered to ask, then one could at least try to accomplish something. For example, solving the question of what a number is. The foundation of arithmetic.

  A life's work, said Bartels.

  Gauss nodded. With a little luck he'd be finished in five years.

  But soon he realized it would go faster than that. Once he had begun, ideas came crowding in with a force he hadn't experienced before. He barely slept, he stopped going to the university, ate the bare minimum, and rarely went to visit his mother. When he wandered through the streets murmuring to himself, he felt he had never been so awake. Without looking where he was going, he avoided bumping into people, he never stumbled, once he leapt to one side for no reason at all and wasn't even surprised when a roof tile landed in the same second at his feet and shattered. Numbers didn't seduce one away from reality, they brought reality closer, made it clearer and more meaningful in a way it had never been before.

  Numbers were his constant companions now. He thought of them even when he was visiting whores. There weren't that many in Göttingen, they all knew him, greeted him by name, and sometimes gave him a discount because he was young, good-looking, and well-mannered. The one he liked best was called Nina and came from a distant town in Siberia. She lived in the old lying-in house, was dark-haired, with big dimples in her cheeks and broad shoulders that smelled of the earth; when he was holding her tight, looking up at the ceiling as he felt her rocking on him, he promised he would marry her and learn her language. She laughed at him, and when he swore that he meant it, she answered that he was still very young.

  The examination for his doctorate was supervised by Professor Pfaff In response to his scribbled request, he was exempted from the oral exam, as it would have been quite risible. When he went to collect the document itself, he had to wait in the corridor. He ate a piece of dry cake and read the Göttingen Scholars’ Bulletin, which contained a report by a German diplomat about his brother's visit to New Andalusia. A white house on the edge of town, evenings cooling off in the river, women who came frequently to visit to have their lice counted. He turned the pages with a vague excitement. Naked Indians in the Chaymas mission, birds that lived in caves and used their voices to see, the way other creatures use eyesight. The great eclipse of the sun, then the departure for the Orinoco. The man's letter had taken eighteen months to arrive, and only God knows whether he was still alive. Gauss lowered the newspaper, Zimmerman and Pfaff were standing in front of him. They hadn't dared to disturb him.

  That man, he said, impressive! But crazy too, as if truth was something you found out there and not here. Or as if you could run away from yourself.

  Pfaff hesitantly handed him the document: passed, summa cum laude. Of course. People were saying, said Zimmerman, that some great work was in progress. He was delighted that Gauss had found something that could occupy his interest and dispel his melancholy.

  Yes, he was working on something of the kind, said Gauss, and when it was done, he would be going.

  The two professors exchanged glances. Leaving the Electorate of Hannover? They did hope not.

  No, said Gauss, please not to worry. He would be going far, but not out of the Electorate of Hannover.

  The work advanced quickly. The law of quadratic reciprocity was worked out, and the riddle of the frequency of prime numbers came closer to a solution. He had completed the first three sections and was already into the main part. But again and again he laid his quill aside, propped his head in his hands, and wondered whether there was a proscription against what he was doing. Was he digging too deep? At the base of physics were rules, at the base of rules there were laws, at the base of laws there were numbers; if one looked at them intently, one could recognize relationships between them, repulsions or attractions. Some aspects of their construction seemed incomplete, occasionally hastily thought out, and more than once he thought he recognized roughly concealed mistakes—as if God had permitted Himself to be negligent and hoped nobody would notice.

  Then the day came when he had no more money. As he was no longer a student, his stipendium had run out. The duke had never been pleased that he had gone to Göttingen, so there was no question of an extension.

  He could get relief, said Zimmerman. By chance there was a job, a temporary one; they needed an industrious young man to help with land surveying.

  Gauss shook his head.

  It wouldn't last long, said Zimmerman. And fresh air never hurt anybody.

  Which was how he found himself unexpectedly stumbling through the countryside in the rain. The sky was low and dark, the earth was muddy. He climbed over a hedge and landed panting, sweating, and strewn with pine needles in front of two girls. Asked what he was doing here, he nervously expounded the technique of triangulation: if you knew one side and two angles of a triangle, you could work out the other sides and the unknown angle. So you picked a triangle somewhere out here on God's good earth, measured the side that was most easily accessible, and then used this gadget to establish the angle of the third corner. He lifted the theodolite and turned it this way, and then this way, and do you see, like this, with awkward fingers, as if doing it for the first time. Then you fit together a whole series of these triangles. A Prussian scientist was in the process of doing exactly this among all the fabulous creatures in the New World.

  But a landscape isn't a flat surface, retorted the bigger of the two.

  He stared at her. There had been no pause. As if she had needed no time to think it over. Certainly not, he said, smiling.

  A triangle, she said, had one hundred and eighty degrees as the sum of its angles on a flat surface; but it was on a sphere, so this was no longer true. Everything would stand or fall based on that.

  He looked her up and down as if seeing her for the first time. She returned his look with raised eyebrows. Yes, he said. So. In order to even things out, you had to scrunch the triangles, so to speak, after measuring them until they were infinitely small. In and of itself, a simple exercise in differentials. Although in this form … He sat down on the ground
and took out his pad. In this form, he murmured, as he began making notes, it's never been worked out in this form yet. When he looked up, he was alone.

  For several weeks he went on crisscrossing the region with the geodetic implements, ramming stakes into the ground and measuring their relative distances. Once he rolled down a slope and dislocated his shoulder, more than once he fell into stinging nettles, and one afternoon when winter had almost arrived, a horde of children hurled dirty snowballs at him. When a sheepdog bounded out of a wood, bit into his calf almost gently, and vanished again like a ghost, he decided this must stop. He was ill-suited to such dangers.

  But he saw Johanna quite often now. It seemed as if she had always been somewhere nearby, only hidden from him by camouflage or lapses in his attention span. She walked ahead of him in the street, and it was as if his wish that she stop was enough to make her slow her step. Or she sat in church three rows behind him looking tired but concentrated as the pastor laid out their future damnation if they failed to make Christ's suffering their own, his cares their cares, his blood their blood; Gauss had long since given up wondering what this was supposed to mean, and was quite aware of how sarcastically she would look at him if he turned around now.

  Once they went for a walk outside the town with her silly, perpetually sniggering friend Minna. They talked about new books he didn't know, how often it rained, the future of the Directory in Paris. Johanna often answered him before he'd finished speaking. He thought about seizing her and pulling her down onto the ground, and knew for sure that she could read his thoughts. Did they have to go through all this hypocrisy? Of course it was necessary, and when he accidentally touched her hand, he made a deep bow, as the nobility did, and she made a curtsey. On the way home he wondered if the day would ever come when people could deal with one another without lying. But before he could pursue that thought, he realized that every number could be expressed as the sum of three triangular numbers. Hands shaking, he groped for his pad, but he had left it at home by accident, and had to keep murmuring the formula softly to himself until they reached the next inn, where he tore a slate pencil out of the waiter's hand and scrawled it down on the tablecloth.

  After that he never left his rooms. The days turned to evenings, the evenings to nights, which soaked up watery light in the early hours until day began again, all of it apparently as a matter of course. But it wasn't, death could arrive in a flash, he had to hurry. Sometimes Bartels came, bringing food. Sometimes his mother came. She stroked his head, looked at him with eyes swimming with love, and flushed with joy if he kissed her on the cheek. Then Zimmerman appeared, asked if he needed help with his work, saw his look, and went his way, mumbling in embarrassment. Letters from Lichtenberg, Büttner, and the secretary of the duke arrived; he didn't read any of them. Twice he had diarrhea, toothache three times, and one night such violent colic that he thought here it was, God wouldn't permit him to do this, the end was near. Another night, science, his work, his whole life all suddenly seemed strange and superfluous to him because he had no friend and no one apart from his mother to whom he meant anything. But that too passed, like everything else.

  And then one rainy day, he was finished. He laid down his pen, blew his nose with extreme precision, and massaged his forehead. Already the memories of the last months, all the struggles, the decisions, the intellectual effort, were a thing of the past. They were the experiences of someone he suddenly no longer was. In front of him was the manuscript that this previous self had left behind, hundreds of tightly written pages. He leafed through it and asked himself how he could have pulled it off. He recalled no inspiration, no flashes of illumination. Just work.

  The costs of having it printed meant he had to borrow from Bartels, who was almost penniless himself. Then there were problems when he insisted on reproofing the typeset pages personally; the idiot of a bookseller simply didn't understand that no one else was capable. Zimmerman wrote to the duke, who disgorged a little more money, and the Disquisitiones Arithmeticae could appear. He had just turned twenty and his life's work was done. He knew: however long he remained on earth, he would never be able to achieve something comparable again.

  He wrote a letter requesting Johanna's hand in marriage, and was refused. It was nothing to do with him personally, she wrote, it was just that she doubted anyone could exist side by side with him. She suspected he absorbed life and strength from the people around him the way the earth absorbed the sun or the sea absorbed the rivers, and that his company would condemn her to the pallid semi-unreality of a ghostly existence.

  He nodded. He had expected this answer, if not its excellent underpinnings. Now only one thing remained.

  The journey was a nightmare. His mother wept so copiously when they said goodbye that he might have been leaving for China, and then, although he had sworn he wouldn't, he wept too. The coach set off, and to begin with it was crammed with evil-smelling people; a woman ate raw eggs, shell and all, and a man kept up an uninterrupted stream of jokes that were blasphemous without being funny Gauss tried to ignore it all by reading the latest issue of the Monthly Correspondence Concerning the Advancement of Global and Celestial Knowledge. The astronomer Piazzi's telescope had captured a ghost planet for several nights in a row, but before anyone could plot its course, it had vanished again. Perhaps an error, but then again perhaps a planetoid wandering between the inner and outer planets. But soon Gauss had to fold the newspaper away, as the sun was going down, the coach was jolting too much, and the egg-eating woman kept peeping over his shoulder. He closed his eyes. For a time he saw marching soldiers, then a firmament crisscrossed with magnetic lines, then Johanna, then he woke up. Rain was falling from a dull morning sky, but night was not over yet. The thought of more days and more nights, eleven and twenty-two respectively, beggared the imagination. Traveling was a horror!

  When he reached Königsberg he was almost out of his mind with exhaustion, back pain, and boredom. He had no money for an inn, so he went straight to the university and got directions from a stupid-looking porter. Like everyone here, the man spoke a peculiar dialect, the streets looked foreign, the shops had signs that were incomprehensible, and the food in the taverns didn't smell like food. He had never been so far from home.

  At last he found the address. He knocked; after a long wait a dust-enshrouded old man opened the door and, before Gauss could introduce himself, said the most gracious gentleman was not receiving visitors.

  Gauss tried to explain who he was and where he'd come from.

  The most gracious gentleman, the servant repeated, was not receiving. He himself had been working here longer than anyone would believe possible and he had never disobeyed an order.

  Gauss pulled out letters of recommendation from Zimmerman, Kästner, Lichtenberg, and Pfaff He insisted, said Gauss again. He could well imagine that there were a lot of visitors and that self-protection was necessary. But, and he must say this unequivocally, he was not just some nobody.

  The servant had a think. His lips moved silently, and he didn't seem to know what to do next. Well, he murmured eventually, went inside, and left the door open.

  Gauss followed him hesitantly down a short, dark hallway into a little room. It took a moment for his eyes to adjust to the half-light before he saw an ill-fitting window, a table, an armchair, and in it a motionless little dwarf wrapped in blankets: puffy lips, protruding forehead, thin, sharp nose. The eyes were half-open but didn't look at him. The air was so thick that it was almost impossible to breathe. Hoarsely he enquired if this might be the professor.

  Who else, said the servant.

  He moved over to the armchair and with trembling hands took out a copy of the Disquisitiones, on the flyleaf of which he had inscribed some words of veneration and thanks. He held out the book to the little man, but no hand lifted to take it. The servant instructed him in a whisper to put the book on the table.

  In a hushed voice, he made his request: he had ideas he had never been able to share with anyone. Fo
r example, it seemed to him that Euclidean space did not, as per the Critique of Pure Reason, dictate the form of our perceptions and thus of all possible varieties of experience, but was, rather, a fiction, a beautiful dream. The truth was extremely strange: the proposition that two given parallel lines never touched each other had never been provable, not by Euclid, not by anyone else. But it wasn't at all obvious, as everyone had always assumed. He, Gauss, was thinking that the proposition was false. Perhaps there were no such things as parallels. Perhaps space also made it possible, provided one had a line and a point next to it, to draw infinite numbers of different parallels through this one point. Only one thing was certain: space was folded, bent, and extremely strange.

  It felt good to utter all this out loud for the first time. The words were already coming faster, and his sentences were forming themselves of their own accord. This wasn't just some intellectual game! He maintained that … He was moving toward the window but a horrified squeak from the little man brought him to a halt. He maintained that a triangle of sufficient size, stretched between three stars out there, if measured exactly would have a different sum of its angles from the hundred-and-eighty-degree assumed total, and thus would prove itself to be a spherical body When he looked up, gesticulating, he saw the cobwebs on the ceiling, in layers, all woven together into a kind of mat. One day it would be possible to achieve measurements like that! But that was a long way off, and meanwhile he needed the opinion of the only man who wouldn't think he was mad, and would definitely understand him. The man who had taught the world more about space and time than any other human being. He crouched down, so that his face was level with the little man's. He waited. The little eyes looked at him.

  Sausage, said Kant.

  Pardon?

  Buy sausage, said Kant to the servant. And stars. Buy stars too.

  Gauss stood up.

  I have not lost all my manners, said Kant. Gentlemen! A drop of spittle ran down his cheek.