American Scientist

Measuring the World. Daniel Kehlmann. Translated from the German by Carol Brown Janeway. iv + 259 pp. Pantheon Books, 2006. $23.

Daniel Kehlmann's novel Measuring the World features two heroes: one who restlessly travels the world in an effort to subsume nature's diversity to his vision of a unified cosmos, and another who rarely strays from home yet manages to explore nature's deepest patterns. The globe-wanderer is Alexander von Humboldt (1769-1859), a naturalist, intrepid explorer and scientific statesman who compiles a comprehensive catalogue of the American continents, an achievement that makes him one of Europe's most illustrious personages in the age of Napoleon. The homebody is Carl Friedrich Gauss (1777-1855), the preeminent mathematician of the modern era, whose innovations in number theory and geometry are followed by discoveries in astronomy and geodesy (the discipline that deals with determining the size and shape of the Earth and the position of points on its surface, and with the measurement of its gravitational and magnetic fields). Around this odd couple Kehlmann has constructed a marvelous novel, a wry meditation on the idea that because there is more than one way to measure the world, there is more than one way to create it anew.

Both Humboldt and Gauss shaped the assumptions of the next generation of scientists, among them Lord Kelvin (William Thomson), who once said that if you cannot measure a thing, your knowledge of it is "unsatisfactory"—with unsatisfactory to be understood as British understatement for nil. Yet this remark presumes that the world will sit still for our measurements and that investigators can agree on the axes along which they should lay their gauges. Indeed, it is agreement about what the telling properties of nature are that makes any measurement of difference meaningful. For the generation of Humboldt and Gauss, the time was not long past when, as one character tells Humboldt,

Things weren't yet used to being measured. Three stones and three leaves were not yet the same number, fifteen grams of peas and fifteen grams of earth were not yet the same weight.

This novel recounts the labors of Gauss and Humboldt to make the world measurable.

The book opens in 1828; the two men, middle-aged and world-renowned, are about to meet for the first time in Berlin. Humboldt has invited Gauss to his first scientific conference; to get there, Gauss has had to make a traumatic trip from his home in Göttingen. From there the novel flashes back to tell the life stories of Humboldt and Gauss in alternating chapters, revealing how their two lives become increasingly entangled and then, after 1828, drift apart. All along, the two men share one consuming ambition: a passion for precision. Indeed, it is this telling similarity that makes their differences worth assessing.

Humboldt traces new lines of commonality throughout nature: isotherms (lines connecting points of equal temperature) that link habitats across altitudes and latitudes; currents of water and air that encircle the planet; continents now remote that had perhaps long ago been in contact; even the relics of human civilizations against which one might assess human progress. Humboldt wrests knowledge from the Earth through self-discipline, self-experimentation and even self-immolation. To prove that muscle fibers convey electrical current, he opens wounds in his back in which he places electrodes; to access remote biomes, he penetrates the Amazon and climbs Mount Chimborazo, reaching an altitude higher than that attained by any previous traveler.

For Humboldt, measurement is a "responsibility" and "high art," but his instruments cannot gauge the human heart. Like Candide (that other long-suffering voyager), Kehlmann's Humboldt remains naive about human cupidity, cruelty and concupiscence. When an official asks for a bribe, he doesn't notice. Confronted with evidence that tens of thousands of Aztecs were once sacrificed in a single day, he refuses to believe it (asserting that such a thing is at least unthinkable in Germany). And he has no clue as to why his French colleague Aimé Bonpland slinks off at night to visit local women.

As portrayed by Kehlmann, the South America that Humboldt visits is akin to the continent of such magical realists as Jorge Luis Borges and Gabriel García Márquez. It is subject to its own dreamlike coherence and reluctant to yield to theodolites (surveying instruments), barometers and thermometers. Although Humboldt's frenzied exertions provide the novel with its narrative excitement, it is refreshing to return intermittently to the cool, gray North, where Gauss is pursuing his inner voyage.

In Göttingen, Gauss builds a world from numbers, even while doubting their capacity to express fully that world's plenitude. He suspects there will never be a formula to calculate the prime numbers. He wonders whether the laws of nature might be merely probabilistic. He speculates about the curvature of space. Perhaps it is Gauss's appreciation of the mutability and accidental nature of the physical world that makes him a sensualist. He takes delight in the embrace of his favorite prostitute and that of his first wife too. He's not so enamored of his second wife, despite having had three children with her. He likes the fact that there are things he doesn't understand. He is also irascible and moody, an apolitical person who is oblivious to social scheming and is infuriated by the dunderheads around him, including his own son.

One of the book's charms is its ironic touch. We see these great men through the eyes of their sidekicks: the sardonic Bonpland, who accompanied Humboldt throughout his American adventures but whose contributions have since been systematically erased from the official history of the expedition, and Gauss's ill-fated son Eugen, who must bear up under his father's contempt. The novel also follows the two men well past their heroic discoveries into the long twilight of their fame. One of the novel's themes is the allure of scientific reputation: Humboldt assiduously cultivates his public fame, whereas renown comes to Gauss unbidden.

As a card-carrying historian of science, I am duty-bound to note that the book includes numerous minor deviations from the historical record. However, I am delighted to report that Kehlmann maintains a scrupulous imaginative fidelity to his characters and their era. As a result, his novel is a meditation on creativity, not just in science but in any human endeavor. The reader sides with Kehlmann rather than his protagonists when the two men denounce those novelists who dare to append their own speculations to the lives of famous people. Yet Kehlmann's self-deprecation and his deliberate anachronisms only deepen our appreciation for his treatment of characters who are hopeful about the future despite the realization that the scientific progress they ardently seek will only overturn their discoveries and their fame. As Kehlmann has Gauss observe,

It was both odd and unjust, . . . 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. It gave you an indecent advantage over the past and made you a clown vis-à-vis the future.

Kehlmann never uses his hindsight against his characters. As a result, the story he tells will speak to anyone who has tried to make sense of the world. Gauss served for a time as a local surveyor and geodesist, and in later years he speculates that the region he surveyed had only "achieved its reality" through his exertions. "Nothing someone had ever measured was now or ever could be the same as before," Kehlmann has Gauss observe before wondering "if Humboldt would understand that." Most readers will understand, I think, by the time they finish this delightful book.