It was both odd and unjust, said Gauss, a real example of the pitiful arbitrariness of existence, that you were born into a particular time and held prisoner there whether you wanted it or not. Each gave you an indecent advantage over the past and made you a clown vis-à-vis the future.
Eugene nodded sleepily.
Even a mind like his own, said Gauss, would have been incapable of achieving anything in early human history or on the banks of the Orinoco, whereas in another two hundred years each and every idiot would be able to make fun of him and invent the most complete nonsense about his character.
Aha! Enter Daniel Kehlmann with his fictionalized biography – a dual biography, in fact, of both Gauss and Alexander Humboldt – ready to supplement history with a little fun, slipping in “complete nonsense” as well as sly meta-comments along the way. It’s great fun to read.
Alexander Humboldt and Carl Gauss: The two men were contemporaries, were both famous in Europe, and published vast works that established new fields of science and mathematics. Yet they were quite different. One was from a wealthy Prussian family, the godson of a Duke, and was made a Baron; the other was the son of a German gardener. One wanted nothing more than to explore and document the world; the other preferred to stay home and work in a room, reasoning out abstractions. One never married; the other took a second wife to make up for the loss he felt when his first wife died. And yet, by the end of the book, they have more in common than we might suppose.
I spent a lot of time initially trying to determine what was documented fact and what was fancy, but eventually gave that up. I found an article by an eminent Dutch mathematician (all links provided below) castigating Kehlmann for taking such liberties (I hope he never reads Irving Stone or watches Amadeus). Then I found a Harvard mathematician who was a lot more enthusiastic, particularly about the film made from the book.
One of the scenes that so irritated the Dutch professor concerned a balloon ride that almost certainly never happened, as it appears to have taken place after the balloonist died (in a balloon accident, tragically). It’s one of my favorite passages:
And seizing him partly by his collar, partly by his hair, he hauled Gauss up.
The curve of the earth in the distance….
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 thatheld them all, even him, even Pilâtre and this basket, in its embrace. Space, that …
They crashed into the wooden frame of a haystack….
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.
I’ve found several sources that credit Gauss with coining the term “non-Euclidean geometry” and conducting an exploration of the Fifth Postulate as a way into the curvature of space; he never published anything on these topics, apparently feeling it would seem too fanciful, but the ideas were passed down to others, culminating in Riemann and Einstein. So while this particular incident may never have happened, its point – that inspiration and insight, comes from many other sources other than the hard work credited with 99% of genius – is well-taken.
Kehlmann relates the more familiar story of the discovery of Gauss’ mathematical talent by a schoolteacher who, as punishment or pedagogy, who knows, has the young children add the numbers from 1 to 100. Gauss completes the task in moments, using the method that is now codified for summing consecutive integers, and is thus vaulted into serious mathematical study. Whether or not this tale, which exists in several versions, is true is debated; maybe it’s more like George Washington telling the truth about cutting down the cherry tree, a legend that has become so ingrained it’s inseparable from fact. In any case, it’s told charmingly. Humboldt’s childhood inspiration was a bit different:
Once they stumbled on a story about Aguirre the Mad, who had renounced his king and declared himself emperor. He and his men traveled the length of the Orinoco in a journey that was the stuff of nightmares… Hardly any scholars had ever penetrated this region, and there was no reliable map.
But he would, said the younger brother. He would make the journey.
Naturally, the elder brother replied.
He really meant it!
Yes he understood that, said the elder brother and summoned a servant to note down the day and the exact time. The day would come when they would be glad they had fixed this moment.
The chapters alternate between Gauss and Humboldt, proceeding chronologically after a brief opening section preparing us for their eventual meeting later in life. Possibly because Humboldt’s life reads like an adventure novel while his personal life was rather limited, we see a great deal of him travelling, particularly of his trip to Latin America, collecting samples, and, indeed, measuring the world. Gauss’ studies, once his Disquisitiones Arithmeticae was published in his early 20s, are more summarized than dramatized, at least until his work with Wilhelm Weber on magnetism later in his life.
Yet Kehlmann gives us a picture of him through various short scenes, such as the (presumably fictional) moment he met his first wife, Johanna, while working as a surveyor shortly after qualifying for his doctorate:
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.
The Prussian scientist mentioned is, of course, Humboldt, off looking for the mysterious channel between the Orinoco and the Amazon. This was a culmination of sorts for him; we watched him attend the completion of the triangulation of longitude that defined the meter: “People wanted to name it ‘the meter.’ It always filled Humboldt with exultation when something was measured; this time he was drunk with enthusiasm.”
Both men had to search for funding for their projects, as much a major, if unpleasant, effort then as it is today. Kehlmann’s fiction has a lot of fun with some of this: as Humbolt is trying to charm sponsorship out Mariano de Irquijo, the minister of Madrid (who did initially sponsor him), he is mistaken for a physician there to provide the regent with an aphrodesiac (“His power over the land rested on his power over the queen. She was no longer a young woman, nor was he a young man now.”) Quick-thinking Humboldt starts listing ingredients from all over the world, and offers to collect them to make a superb remedy. “Never before had foreigners received such documents.”
This use of humor is, for Kehlmann, the point:
Some readers, he concedes, may have bought it because they were flattered to be reminded of Germany’s role in the Enlightenment’s avant garde.
In fact, he says, it was intended as the antithesis of that – “a comedy about German high culture, about the German cult of genius”. “I have met people who didn’t want to read Measuring the World because they thought it was a serious, educated, self-important book about intellectual history. It has gained an aura that is the very opposite of what it really is, and I do regret that a bit. I also think it’s problematic that it is now on the school syllabus, because, in reality, it’s a parody about how we deal with educational values.”
Interview in The Guardian with Philip Oltermann
One of the clearest examples of this poke at German genius comes from Humboldt’s measuring of a solar eclipse while in South America. His assistant/collaborator, Aimé Bonpland, was astounded by the fading light, the momentousness of it all. Humboldt was too busy taking measurements to pay attention. “Did one always have to be so German?” sighs Bonpland.
Some of that humor has an ironic bite. While discussing the miracle of a parrot who is the last surviving speaker of a tribal language, Bonpland asks the head of the mission where the scientists are staying what happened to the tribe, why it disappeared.
It happened, said Pater Zea.
Why?
Pater Zea stared at him with narrowed eyes. It was easy to be like that. A person came here and pitied anyone who looked sad, and back home there would be bad stories to tell, but if that person suddenly found himself with fifty men ruling ten thousand savages, wondering every night what the voices in the forest meant, and being amazed each morning to find himself alive, perhaps he would judge things differently.
A misunderstanding, said Humboldt. Nobody had intended to criticize.
On a later stop in Mexico (New Spain at the time), Humboldt recommends to the Spanish overseer that the mine passages be repaired, to reduce accidents. “They had enough people, said Don Fernando. Anyone who died could be replaced. Humboldt asked if he’d read Kant.” This sly way of bringing up the categorical imperative to treat people as ends, not as means, doesn’t land for the overseer, but it does for the reader.
And also in Mexico:
Shortly afterward, as Humboldt packed up his instruments, he knew that on the day of the solstice, the sun when seen from the highway rose exactly over the top of the largest pyramid and went down over the top of the second-largest. The whole city was a calendar. Who had thought it up? How well had these people known the stars, and what had they wanted to convey? He was the first person in more than a thousand years who could read their message.
Why was he so depressed, asked Bonpland, awakened by the sound of the instruments being closed.
So much civilization and so much horror, said Humboldt. What a combination! The exact opposite of everything that Germany stood for.
That Spain inflicted horror on the New World is without doubt, but those of us who are familiar with the 20th century, yet future to Humboldt, might find somber irony in his exclamation.
I’m impressed with Kehlmann’s ability to compress these ideas into short statements, but the best is yet to come. Towards the end of his life, Humboldt and his brother, always close, speak of destiny:
Nobody, said Humboldt, had a destiny. One simply decided to feign one until one came to believe in it oneself. But so many things didn’t fit in with it, one had to really force oneself.
The elder brother leaned back and gave him a long look.
Still boys?
You knew?
Always.
That exchange of five words carries great impact. Yes, biographers and scholars of Humboldt’s travels have assumed, with varying degrees of certainty, that he was gay. I keep thinking of a trope that runs through the Gauss chapters, how he recognizes, as in the first quote above, that the state of knowledge, and society,, is always in flux, and what we accept today will most likely be different in fifty or a hundred or two hundred years. Humboldt didn’t have the luxury of waiting around for acceptance; I think that underlines some of his obsessive work.
Last year I read Kehlmann’s more recent book, Tyll, and enjoyed it so much I decided to read this earlier book. I’m glad I did. While the august personages, mathematics and science might intimidate some readers, it’s not a problem. Of course, the more one knows, the more one gets out of it (I love recognizing things I’ve heard of), but Kehlmann makes a point of not worrying about explaining background, be it of the Thirty Years’ War in Tyll, or the discoveries of Gauss – or, for that matter, the Napoleonic Wars which play in the background as Gauss moves from one university town to the next in search of a position.
I feel like you can never leave out enough explanation. We humans are actually used to working with incomplete information, for all our lives, all the time.
Measuring the World was a novel about two German scientists. It did very well in Germany, but then foreign publishers said, “We need footnotes because in our country nobody knows Carl Friedrich Gauss.“ I said, “Very few people in Germany knew Carl Friedrich Gauss either!“ When I read Dostoevsky, there’s so much about the politics of nineteenth-century Russia that I don’t understand, but it doesn’t matter at all. I feel like we should always trust the reader to deal with incomplete information—because that’s what all of us do all day long anyway!
Interview in Bomb Magazine with Álvaro Enrigue
The book ends not with the deaths of the scientists, but with Gauss’ son, Eugen. Throughout the book, Gauss has dumped on the poor boy, disappointed that he had little facility for mathematics. In more historically accurate materials, he urged the boy to go into law rather than science, fearing he would not be able to uphold Gauss’ name. Eugen leaves Germany, travelling somewhat the same route as Humboldt many years ago, but missing the excitement the journey brought the naturalist; he clearly doesn’t measure up to either man. He ended up in America, and, in historical accounts, became quite a successful businessman. The last word of the book, in fact, is America. If one wishes to deduce a shift in polarity from this, from Gauss the father, German genius, to the son, American entrepreneur, one is free to do so.
But I found the emotional end of the book to be earlier: as they exchange letters towards the ends of their lives, they end up feeling sorry for each other. Gauss pities Humboldt because he can’t explore Russia with the degree of freedom he needs, and Humboldt feels bad that Gauss has seen so little of the world. Humboldt, who yearned for travel and direct experience to measure everything in existence; Gauss, who valued thinking through principles to find truth. Yet, like those parallel lines that intrigued Gauss from an early age: seemingly different, yet they meet.
Kehlmann’s book made me want to read more factual biographies of both men, and I can think of no greater compliment for fiction.
* * *
Philip Oltermann,The Guardian, 11/15/2014: Interview, “Daniel Kehlmann: ‘German writers have been taught to hide their humour'”
Álvaro Enrigue, Bomb Magazine, 2/26/2020 : Interview, “Daniel Kehlmann”
St. Andrews Math Histories: Carl Friedrich Gauss
Eleanor Jones Harvey, Smithsonian Institution: “Who Was Alexander Von Humboldt?”
Frans Oort: Book Review
Michael Harris, Mathematics Without Apologies: “Three mathematicians, three novels, only one movie, part 3”
Oliver Knill, 9/27/2020: “Measuring the World [Film]“
A Just Recompense 