Measuring The World Part 4

They'd done enough, said Humboldt.

Bonpland offered up that there must surely be more unknown plants deeper inside the mountain.

Better to turn back, said Humboldt. Enough was enough.

They followed a stream in the direction of the sunlight. Gradually the number of birds diminished, their screaming quieted, and soon they could extinguish the torches.

In front of the cave mouth the Indian guide was turning their two birds over a fire to render the fat. The feathers, beaks, and necks were already scorched, blood was dripping into the flames, the fatty tissue was hissing, and a bigger smoke hung over the clearing. The best fat, he explained. Odorless, and it would stay fresh for more than a year.

Now they would need two more, said Bonpland, furious.

Humboldt asked Bonpland for his brandy flask, took a big swallow, and set off on the path back to the mission with one of the monks, while Bonpland returned the other way to shoot two more birds. After several hundred yards, Humboldt stopped still, tilted his head back, and looked up into the tree-tops which were holding up the sky high above his head.

Reverberation!

Reverberation, repeated the monk.

If it wasn't a sense of smell, said Humboldt, it must be the resonance. That clicking, echoing back off the walls. That must be how the creatures worked out their direction.

As he went on, he made notes. A system that people could utilize on moonless nights or underwater. And the fat: its odor-lessness would make it ideal for manufacturing candles. He threw open the door to his monastery cell, and a naked woman was there waiting for him. At first he thought either she was there because of the lice, or she'd brought a message. Then he understood that this time it wasn't the case, and she wanted exactly what he thought she wanted, and that there was no way out.

Obviously the governor had sent her, it fit with his idea of a rough joke between men. She had been waiting alone in the room for a night and a day, out of sheer boredom she'd taken the s.e.xtant to pieces and muddled up all the collected plants, drunk the spirits intended for the preparation of specimens, and then slept off her drunkenness. After waking up she'd found a funny portrait of a dwarf with pursed lips, which she naturally failed to recognize as Frederick the Great, and colored it in quite well. Now that Humboldt was finally here, she wanted to get it over with.

While he was still asking where she'd come from, what she wanted, and if there was anything he could do for her, she was already undoing his trousers with a practiced hand. She was small and plump and couldn't be much older than fifteen. He moved backwards, she followed him, he b.u.mped against the wall and as he tried sharply to set her straight, he found he'd forgotten his Spanish.

Her name was Ines, she said, and he could trust her.

As she pulled up his s.h.i.+rt, a b.u.t.ton tore off and rolled across the floor. Humboldt followed it with his eyes until it hit the wall and fell over. She put her arms round his neck and pulled him, while he murmured that she was to let go, he was an official of the Prussian Crown, into the middle of the room.

Oh G.o.d, she said, listen to your heart pound.

She dragged him down with her onto the carpet, and for some reason he allowed her to roll him onto his back while her hands wandered down over him until she stopped, laughed, and said there wasn't much going on. He looked at her bent back, the ceiling, and the palm leaves s.h.i.+vering in the wind outside the window.

Now, she said. He was to trust her!

The leaves were short and pointed, it was a tree he had never inspected until now. He wanted to sit up, but she laid her hand on his face and pushed him down, and he asked himself how she could fail to understand that he was in h.e.l.l. Later on he couldn't have said how long it lasted before she gave up, pushed back her hair, and looked at him sadly. He closed his eyes. She stood up.

It didn't matter, she said quietly, it was her fault.

His head hurt, and he had a raging thirst. Only when he heard the door shut behind her did he open his eyes.

Bonpland found him at his desk, surrounded by the chronometers, the hygrometer, the thermometer, and the rea.s.sembled s.e.xtant. Magnifying gla.s.s clenched in his eye, he was looking at palm leaves. Interesting structure, remarkable! It was getting to be time they moved on.

So suddenly?

According to old reports, there was a natural channel between the great rivers of the Orinoco and the Amazon. European geographers took that to be mere legend. The dominant school of theory held that only mountain ranges could act as watersheds, and there was no possible linkage between inland river systems.

Oddly enough, he had never thought about it, said Bonpland.

The theory was wrong, said Humboldt. He was going to find the channel and solve the riddle.

Aha, said Bonpland. A channel.

He didn't like his att.i.tude, said Humboldt. Always complaining, always objecting. Would it be too much to ask for a little enthusiasm?

Bonpland asked if something had happened.

There was about to be an eclipse of the sun! This would enable him to establish the exact coordinates of their coastal town. Then it would be possible to construct a net of measuring points all the way to the end of the channel.

But that would be way deep in primeval forest!

Primeval was a big word, said Humboldt. It shouldn't be allowed to frighten him. Primeval forest was still just forest. Nature spoke the same language everywhere.

He wrote to his brother. The journey was magnificent, with a plethora of discoveries. New plants cropped up every day, more than one could count, and his observations of tremors were suggesting a new theory of the earth's crust. His knowledge of the nature of head lice was also becoming unusually advanced. Yours as always, please put this in the newspaper!

He checked to see if his hand was still trembling. Then he wrote to Immanuel Kant. A new concept of the science of physical geography was forcing its way into his mind. At different alt.i.tudes, although at similar temperatures, similar plants grew all over the planet, so climate zones stretched not just laterally but also vertically: at some given spot the earth's surface could thus run the gamut from tropical to arctic. If one connected these zones into lines, one would get a map of the major climate currents. Thanking him for any comments, and in warmest hopes that the professor was in good health, he remained his humble ... He closed his eyes, inhaled deeply, and signed with the boldest signature he could muster.

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 s.h.i.+p 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 pus.h.i.+ng 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 s.e.xtant 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 s.e.xtant and also track the exact time. There had been no time to look up.

There wouldn't be a second chance, said Bonpland hoa.r.s.ely. 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?

NUMBERS.

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 compa.s.ses. 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 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 ap.r.o.n, who was saying it hadn't been so bad, had it? 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 ap.r.o.n, 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 n.o.body would lose their hair. He was amazed that n.o.body 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 Kastner 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. n.o.body could take that long to think!

This is a great moment, said Zimmerman finally.

Gauss asked for a gla.s.s 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 publis.h.i.+ng on their own.

Gauss tried to reply, but when Zimmerman brought him the gla.s.s 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 Gottingen. 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 n.o.body 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 Inst.i.tute 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 Universal Advertiser and and Literary Supplement 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 embarra.s.sing. 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 cla.s.sical philology, and he still liked the idea of writing a commentary on Virgil, in particular Aeneas' descent to the underworld. He felt that n.o.body 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 n.o.body 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 b.u.mping 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 wh.o.r.es. There weren't that many in Gottingen, 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 doc.u.ment itself, he had to wait in the corridor. He ate a piece of dry cake and read the Gottingen Scholars' Bulletin Gottingen 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 G.o.d 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 doc.u.ment: pa.s.sed, summa summa c.u.m laude. c.u.m 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. 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 relations.h.i.+ps 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 G.o.d had permitted Himself to be negligent and hoped n.o.body 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 Gottingen, 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 G.o.d'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 s...o...b..a.l.l.s 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 d.a.m.nation 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 sn.i.g.g.e.ring 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 n.o.bility 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 embarra.s.sment. Letters from Lichtenberg, b.u.t.tner, 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, G.o.d 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 pa.s.sed, like everything else.

And then one rainy day, he was finished. He laid down his pen, blew his nose with extreme precision, and ma.s.saged 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 ma.n.u.script 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 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. 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.