Measuring the World (7 page)

The day before the eclipse something unpleasant occurred. As they were taking air pressure measurements down on the beach, a Zambo, part black, part Indian, leapt out of the bushes clutching a wooden club. He growled, hunched his body, stared, and then attacked. An unhappy accident, Humboldt called it, as he wrote his account by flickering candlelight at around 3 a.m. some days later on board ship to Caracas in a wild sea. He had ducked left away from the blow, but Bon-pland on his right had not been so lucky. But as Bonpland remained lying motionless on the ground, the Zambo missed his opportunity; instead of going for Bonpland again, he had chased after Bonpland's hat as it flew off, and strode away while putting it on his head.

At least no damage to the instruments was incurred and even Bonpland came to after twenty hours: face swollen, one lost tooth, the shape of his nose somewhat altered, and dried blood around mouth and chin. Humboldt, who had been sitting by his bed through the evening, night, and long hours of the morning, handed him some water. Bonpland washed himself, spat, and looked mistrustfully into the mirror.

The eclipse of the sun, said Humboldt. Would he manage?

Bonpland nodded.

Was he sure?

Bonpland spat and said thickly that he was sure.

Great days were coming, said Humboldt. From the Orinoco to the Amazon. Into the heart of the interior. Bonpland must give him his hand!

With great effort, as if pushing against some force of resistance, Bonpland raised his arm.

At the predicted time in the afternoon, the sun was extinguished. The light faded, a swarm of birds flew up into the air, screeching, and swooped away, objects seemed to absorb the brightness, a shadow fell across them, and the ball of the sun became a dark curve. Bonpland, head bandaged, held the screen of the artificial horizon. Humboldt set up the sextant on it, and used the other eye to squint at the chronometer. Time stood still.

And started to move again. The light returned. The ball of the sun emitted rays again, the shadow detached itself from the hills, the earth, then the horizon. Birds called, someone somewhere fired a shot. Bonpland let down the screen.

Humboldt asked what it had been like.

Bonpland stared at him in disbelief.

He hadn't seen any of it, said Humboldt. Only the projection. He had had to fix the constellations in the sextant and also track the exact time. There had been no time to look up.

There wouldn't be a second chance, said Bonpland hoarsely. Had he really not looked up?

This place was now fixed forever in the maps of the world. There were only ever a few moments in which one could use the sky to correct clock time. Some people took their work more seriously than others!

That could well be, but … Bonpland sighed.

Yes? Humboldt leafed in the astronomical almanac, took up his pencil, and began to calculate. So what was it now?

Did one always have to be so German?

N
UMBERS

On the day everything changed, one of his molars was hurting so much he thought he'd go insane. In the night he had lain on his back, listening to the landlady snoring next door. At about six thirty in the morning, as he blinked wearily into the dawn light, he discovered the solution to one of the oldest problems in the world.

He went staggering through the room like a drunk. He must write it down immediately, he must not forget it. The drawer didn't want to open, suddenly the paper had hidden itself from him, his quill broke off and made blotches, and then the next thing to trip him up was the chamber pot. But after half an hour of scribbling there it all was on some crumpled piece of paper, the margins of a Greek textbook, and the tabletop. He laid his pen aside. He was breathing heavily. He realized that he was naked, and registered the dirt on the floor and the stink with surprise. He was freezing. His toothache was almost unbearable.

He read. Worked his way through it, followed the proof line by line, looked for errors, and didn't find any. He roamed over the last page and looked at his distorted, smeared, seventeen-sided figure. For more than two thousand years, people had been constructing regular triangles and pentangles with ruler and compasses. To construct a square or to double the angles of a polygon was child's play. And if one combined a triangle and a pentangle, what one got was a fifteen-sided figure. More was impossible.

And now: seventeen. And he had a hunch there was a method that would allow him to go further. But he would have to find it.

He went to the barber, who tied his hands tight, promised it really wouldn't be bad, and with one quick movement pushed his pincers into his mouth. The very touch of them, a blinding flash of pain, almost made him faint. He tried to gather his thoughts, but then the pincers took hold, something went
click
in his head, and it was the taste of blood and the pounding in his ears that brought him back to the room and the man with the apron, who was saying it hadn't been so bad, had it?

On his way home he had to lean against walls, his knees were weak, his feet weren't under control, and he felt dizzy. In another few years there would be doctors for teeth, then it would be possible to cure this kind of pain and you wouldn't have to have every inflamed tooth pulled. Soon the world would no longer be full of the toothless. And everybody wouldn't have pockmarks, and nobody would lose their hair. He was amazed that nobody else ever thought about these things. People thought everything was naturally the way it was. Eyes glazed, he made his way to Zimmerman's rooms.

Entering without knocking, he laid the pieces of paper out in front of him on the dining table.

Oh, said the professor sympathetically, teeth, bad? He himself had been lucky, he'd only lost five, Professor Lichtenberg was left with a mere two, and Kästner had been toothless for years. With the tips of his fingers, because of a bloodstain, he picked up the first sheet. His brow furrowed. His lips moved.It went on so long that Gauss could hardly believe it any more. Nobody could take that long to think!

This is a great moment, said Zimmerman finally.

Gauss asked for a glass of water.

He felt like praying. This must be printed, and it would be best if it appeared under the name of a professor. It wasn't the done thing for students to be publishing on their own.

Gauss tried to reply, but when Zimmerman brought him the glass of water, he could neither speak nor drink. He made a gesture of apology, wobbled home, lay down in bed, and thought about his mother up there in Brunswick. It had been a mistake to come to Göttingen. The university here was better, but he missed his mother, and even more so when he was ill. At about midnight, when his cheek had swollen still further and every movement in every part of his body hurt, he realized the barber had pulled the wrong tooth.

Luckily the streets were still empty in the early morning so nobody saw him stopping continually to lean his head against the house walls and sob. He would have given his soul to live a hundred years later when there would be medications for pain and doctors who deserved the name. Nor was it that hard. All that was necessary was to numb the nerves in the right spot, the best thing would be little doses of poison. Curare needed to be researched better! There was a flask of it in the Institute of Chemistry, he would go and have a look. But his thoughts slid away from him and he was only more aware of his own groaning.

It happens, said the barber cheerfully. Pain spread itself wide, but Nature was intelligent and man came with plenty of teeth. At the moment when he pulled the tooth, everything around Gauss went black.

As if the pain had wiped the event from his memory or from time itself, he found himself hours or days later—how could he tell—back in the chaos of his bed, with a half-empty bottle of schnapps on the night table and at his feet the
Universal Advertiser
and
Literary Supplement
, in which Privy Councilor Zimmerman laid out the latest method for constructing a regular seventeen-sided figure. And sitting beside the bed was Bartels, who had come to congratulate him.

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.