Measuring the World

  The same afternoon a young man knocked at the door of Gauss's parents’ home. He was seventeen, his name was Martin Bartels, he was studying mathematics, and he was working as Büttner's assistant. Might he have a few words with the son of the house?

  He only had one son, said Gauss's father, and he was eight years old.

  That was the one, said Bartels. Might he have permission to do mathematics with the young gentleman three times a week? He didn't wish to speak of lessons, because the very concept was inappropriate, and here he smiled nervously, when this was an activity from which he might learn more than his pupil.

  The father told him to stand up straight. The whole thing was absolute nonsense! He thought for a time. On the other hand, there was really nothing to say against it.

  They worked together for a year. At the beginning Gauss enjoyed the afternoons, which broke up the monotony of the weeks, although he didn't have much time for mathematics; what he really would have wanted were Latin lessons. Then things got boring. Granted, Bartels didn't think as laboriously as the others, but he still made Gauss impatient.

  Bartels announced that he'd talk to the rector at the high school. If his father would permit, Gauss would be given a free place.

  Gauss sighed.

  It wasn't right, said Bartels reproachfully, that a child should always be sad!

  He thought about this, it was an interesting idea. Why was he sad? Maybe because he could see his mother was dying. Because the world seemed so disappointing as soon as you realized how thinly it was woven, how crudely the illusion was knitted together, how amateurish the stitches were when you turned it over to the back. Because only secrets and forgetfulness could make it bearable. Because without sleep, which snatched you out of reality, it was intolerable. Not being able to look away was sadness. Being awake was sadness. To know, poor Bartels, was to despair. Why, Bartels? Because time was always passing.

  Together, Bartels and Büttner persuaded his father that he shouldn't be going to work in the spinning mill, he should be going to high school. The father gave his unwilling consent, along with the advice that he should always stand up straight, no matter what happened. Gauss had already been watching gardeners at work for years, and understood that it wasn't lack of human moral fiber that upset his father, it was the chronic back pain that attended his profession. He got two new shirts and free room and board with the pastor.

  High school was a disappointment. There really wasn't much to learn: some Latin, rhetoric, Greek, laughably primitive mathematics, and a little theology. His new classmates were not much smarter than the old ones; the teachers resorted to the stick just as often, but at least they didn't hit as hard. At their first midday meal, the pastor asked him how things were going at school.

  Passable, he replied.

  The pastor asked him if he found learning hard.

  He sniffed and shook his head.

  Take care, said the pastor.

  Gauss looked up, startled.

  The pastor looked at him severely. Pride was a deadly sin!

  Gauss nodded.

  He should never forget it, said the pastor. Never in his whole life. No matter how clever one was, one must always remain humble.

  Why?

  The pastor apologized. He must have misunderstood.

  Nothing, said Gauss, really—nothing.

  On the contrary, said the pastor, he wanted to hear it.

  He meant it strictly theologically, said Gauss. God created you the way you were, but then you were supposed to spend your life perpetually apologizing to Him. It wasn't logical.

  The pastor theorized that he must be having trouble hearing properly.

  Gauss pulled out a very dirty handkerchief and blew his nose. He was sure he must be misunderstanding something, but to him it seemed like a deliberate reversal of cause and effect.

  Bartels found a new place for him to board free, with Privy Councilor Zimmerman, a professor at Göttingen University. Zimmerman was a lean, affable man, always looked at him with polite awe, and took him along to an audience with the Duke of Brunswick.

  The duke, a friendly gentleman with a twitch in his eyelids, was awaiting them in a room all decorated in gold, with so many candles burning that there were no shadows, only reflections in the mirrored ceiling which created a second room that swayed above their heads, except inside out. Ah, so this was the little genius?

  Gauss made a bow, as he had been taught. He knew that there would soon be no more dukes. Then absolute rulers would only exist in books, and the idea that one would stand before such a person, bow, and await his all-powerful word would seem so strange as to be a fairy tale.

  Count up something, said the duke.

  Gauss coughed, and felt hot and faint. The candles were using up almost all the oxygen. He looked into the flames and suddenly understood that Professor Lichtenberg was wrong, and his phlogiston hypothesis was superfluous. It wasn't some light-producing matter that was burning, it was air itself.

  If he might be permitted, said Zimmerman, there was a misapprehension here. The young man was no arithmetical artist. On the contrary, he wasn't even that good at reckoning. But mathematics, as His Highness naturally knew, had nothing to do with the gift of doing addition. Two weeks ago the boy had deduced Bode's law of planetary distances all on his own, followed by the rediscovery of two of Euler's theorems he hadn't met before. He had contributed astonishing things to the setting of the calendar: his formula for working out the correct date for Easter had meantime become standard for the whole of Germany His achievements in geometry were exceptional. Some of them had already been made public, although naturally under the name of this or that teacher because no one wanted to expose the boy to the corrosive effects of early fame.

  He was more interested in things to do with Latin, said Gauss huskily with a frog in his throat. And he knew dozens of ballads by heart.

  The duke asked, Did someone just say something?

  Zimmerman poked Gauss in the ribs. He begged pardon, the young man's origins were uncouth, his manners left something to be desired. But he would vouch for the fact that a stipendium from the Court was the only thing standing between him and the achievements that would redound to the glory of his country.

  So was he saying nobody was going to do any counting right now, asked the duke.

  Alas, no, said Zimmerman.

  Ah well, said the duke, disappointed. But he should have his stipendium all the same. And come back when he had something to show. He was all for science. His favorite godson, little Alexander, had just left to look for flowers in South America. Maybe what they would be doing here was breeding another fellow just like him! He made a gesture of dismissal, and Gauss and Zimmerman bowed just the way they had practiced as they retreated backwards through the door.

  Soon after that, Pilâtre de Rozier came to town. He and the Marquis d’Arlandes had gone up in a basket which the Mont-golfiers had attached to a hot-air balloon, and flown five and a half miles over Paris. After they landed, it was said, two men had had to help the marquis walk away, as he was babbling nonsense, insisting that luminous creatures with bosoms and bird's beaks had flown around them. It had taken hours for him to calm down and blame it all on an attack of nerves.

  Pilâtre had his own flying machine and two assistants, and was on his way to Stockholm. He had spent the night in one of the cheaper hostelries and was about to set off again when the duke sent word that he would like him to do a demonstration.

  Pilâtre said it was a waste of time and inconvenient to boot.

  The messenger indicated that the duke was unaccustomed to having his hospitality rejected so vulgarly.

  What hospitality, said Pilâtre. He had paid for lodging and just preparing the balloon would cost him two days of travel time.

  Perhaps it was possible to talk that way to one's superiors in France, said the messenger, in France anything was possible. But in Brunswick he would do well to reflect before sending him back with any such messa
ge.

  Pilâtre gave in. He should have known, he said wearily, in Hannover it had been the same and in Bavaria too, for that matter. So in the name of Christ he would go up in his balloon tomorrow afternoon in front of the gates of this filthy town.

  Next morning there was a knock at his door. A boy was standing outside, looking up at him intently, and asked if he could fly with him.

  Travel with him, said Pilâtre. In a balloon, it's travel. You don't say fly you say travel. That was what balloonists said.

  What balloonists?

  He was the first, said Pilâtre, so it was his to decree. But no, of course nobody could travel with him. He tickled the boy's cheeks and tried to close the door.

  This wasn't the way he usually behaved, said the boy wiping his nose on the back of his hand. But his name was Gauss, he wasn't some nobody, and before long he would be making discoveries that would equal Isaac Newton's. He wasn't saying this out of vanity, but because time was getting short and he had to be part of the flight. You could see the stars much better up there, couldn't you? Clearer, and not obscured by the haze?

  He could bet on it, said Pilâtre.

  That's why he had to go too. He knew a lot about stars. You could test him on it as much as you wanted.

  Pilâtre laughed and asked who had taught this little man to talk so well. He thought for a while. All right, he said finally, since it was about the stars … !

  That afternoon, before a throng of people, the duke, and a saluting battalion of guests, a fire gradually filled the parchment sac with heat through two tubes. No one had expected it to take so long. Half the spectators had already left when the balloon filled out, and barely a quarter were still there when it started to move upright and jerkily began to lift off the ground. The ropes went taut, Pilâtre's assistants loosened the knots, the little basket moved, and Gauss, huddling on the woven bottom of the basket and whispering to himself, would have leapt to his feet if Pilâtre hadn't pushed him down again.

  Not yet, he panted. Are you praying?

  No, Gauss whispered, he was counting prime numbers. That's what he always did when he was nervous.

  Pilâtre stuck up a thumb to check the direction of the wind. The balloon would rise, then head wherever the wind took it, before sinking again when the air inside it cooled. A seagull shrieked somewhere close to the basket. Not yet, yelled Pilâtre, not yet. Not yet. Now! And seizing him partly by his collar, partly by his hair, he hauled Gauss up.

  The curve of the earth in the distance. The deep horizon, the hilltops half-hidden in mist. The people staring upward, tiny faces in a ring around the still-burning fire, and next to them the roofs of the town. Little clouds of smoke, tethered to chimneys. A path snaked through the green, and on it a donkey the size of an insect. Gauss clung on to the rim of the basket and it was when he closed his mouth that he realized he had been screaming.

  This is how God sees the world, said Pilâtre.

  He wanted to say something back, but he'd lost his voice. How fiercely the air was shaking them! And the sun—why was it so much brighter up here? His eyes hurt, but he couldn't close them. And space itself: a straight line from every point to every other point, from this roof to this cloud, to the sun, and back to the roof. Points making lines, lines making planes, planes making bodies, and that wasn't all. The fine curve of space was almost visible from here. He felt Pilâtre's hand on his shoulder. Never go down again. Up and then up further, until there would be no earth beneath them any more. One day this is what people would experience. Everyone would fly then, as if it were quite normal, but by then he would be dead. He peered excitedly into the sun, the light was changing. Dusk seemed to be rising in the still-bright sky like fog. A last flame or two, red on the horizon, then no more sun, then stars. Things never happened this fast down there.

  We've started to drop, said Pilâtre.

  No, he begged, not yet! There were so many of them, more every moment. Each one a dying sun. Every one of them was decaying, and they were all following their own trajectories, and just as there were formulae for every planet that circled its own sun and every moon that circled its own planet, there was a formula, certainly infinitely complicated, but then again maybe not, perhaps hiding behind its own simplicity, that described all these movements, every revolution of every individual body around every other; maybe all you had to do was keep looking. His eyes smarted. It felt as if he hadn't blinked for a long time.

  We're about to land, said Pilâtre.

  No, not yet! He rose on tiptoes, as if that could help, stared upward, and understood for the first time what movement was, what a body was; most of all, what space was, the space that they stretched between them, and that held them all, even him, even Pilâtre and this basket, in its embrace. Space, that …

  They crashed into the wooden frame of a haystack, a rope tore, the basket tipped over. Gauss rolled into a mud puddle, Pilâtre fell so awkwardly that he sprained his arm, and when he saw the tear in the parchment skin, he began to curse so dreadfully that the farmer who had come running out of his house stopped dead and raised his spade threateningly. The assistants arrived breathless to fold the crumpled balloon together. Pilâtre nursed his arm and gave Gauss a slap that was hard enough to hurt.

  Now he knew, said Gauss.

  What?

  That all parallel lines meet.

  Fine, said Pilâtre.

  His heart was racing. He wondered if he should explain to the man that all he would need was to add a hanging rudder to the basket, and he could turn the air current to make the balloon move in any specific direction. But he kept quiet. Nobody had asked him, and it wouldn't be polite to force his ideas on these people. It took no stretch of the imagination, and one of them would think of it soon.

  But now what this man wanted to see was a grateful child. With an effort, Gauss put a smile on his face, stretched his arms wide, and bowed like a marionette. Pilâtre was happy, laughed, and stroked his head.

  THE CAVERN

  After six months in New Amsterdam, Trinidad, Humboldt had examined everything that lacked the feet and the fear to run away from him. He had measured the color of the sky, the temperature of lightning flashes, and the weight of the hoarfrost at night, he had tasted bird droppings, investigated earth tremors, and had climbed down into the Cavern of the Dead.

  He lived with Bonpland in a white wooden house on the edge of the town, which had recently suffered earthquake damage. Aftershocks still jolted people awake at night, and when they went to bed and held their breath, they could still hear movement deep down beneath them. Humboldt dug holes, dropped thermometers on long threads down wells, and put peas on drumheads. The quake would certainly begin again, he said cheerfully. Soon the whole town would be in ruins.

  In the evenings they ate at the governor's mansion and afterwards there was bathing. Chairs were set down in the river, they put on light clothes and sat in the current. Now and then small crocodiles swam by. Once a fish bit off three toes of the viceroy's nephew. The man, his name was Don Oriendo Casaules and he had a huge mustache, twitched and stared blankly in front of him for a few moments before pulling his now-less-than-whole foot disbelievingly out of the red water. He glanced around as if searching for something, then fell sideways and was caught by Humboldt. The next ship took him back to Spain.

  Women were frequent visitors: Humboldt counted the lice in their plaited hair. They came in groups, whispered to one another, and giggled at the little man in his uniform with the magnifying glass firmly clamped in his left eye. Bonpland was made miserable by their beauty. He wanted to know what statistics about lice were good for.

  One wanted to know, said Humboldt, because one wanted to know. Nobody had yet investigated the presence of these remarkably resistant creatures on the heads of inhabitants of equatorial regions.

  Not far from their house, people were auctioned off. Muscular men and women with chained ankles stared empty-eyed at local landowners as they probed inside their mouths, peered into
their ears, and went down on their knees to touch their anuses. They felt the soles of their feet, pulled their noses, checked their hair, and fingered their genitalia. Most of them left afterwards, without buying; it was a shrinking branch of the economy. Humboldt bought three men and had their chains removed. They didn't understand. They were now free, Humboldt said through an interpreter, they could go. They stared at him. Free? One of them asked where they were supposed to go. Wherever you wish, said Humboldt. He gave them money. Cautiously they tested the coins with their teeth. One of them sat down on the ground, closed his eyes, and didn't stir, as if there were absolutely nothing in the world to interest him. Humboldt and Bonpland moved away under the mocking eyes of the bystanders. A couple of times they turned around, but none of the freed men was looking after them. In the evening it began to rain, and that night the town was shaken by a fresh earthquake. Next morning the three men had disappeared. No one knew where, and they never turned up again. When the next auction took place, Humboldt and Bonpland stayed at home, working behind closed shutters, and only went outside after it was over.

  The journey to the Chaymas mission led through thick forests. At every stop they saw plants they'd never seen before. The ground seemed not to have enough room for so much growth: tree trunks squeezed against one another, plants clambered over other plants, lianas swept over their heads and shoulders. The monks of the mission greeted them warmly, although they didn't understand what the two men wanted of them. The abbot shook his head. There must be something else behind it! Nobody traveled halfway round the world to measure land that didn't even belong to him.

  The mission was home to baptized Indians, who lived under their own self-government. There was an Indian commandant, a chief of police, and even a militia, and provided they obeyed all the rules, they were allowed to live as if they were free. They were naked, wearing only individual items of clothing they had picked up here or there: a hat, a stocking, a belt, an epaulette tied securely to a shoulder. It took Humboldt some while to behave as if he were accustomed to this. It offended him to see that women had hair in so many places; it struck him as incompatible with natural dignity. But when he said as much to Bonpland, the latter looked at him with such amusement that he turned red and began to stutter.