by Ken Alder
As Legendre presented it, the great advantage of his least-squares rule was that it could be easily and systematically applied. It gave savants a workable method for weighting data. And in a few years, it became something more. It became a method with meaning.
Four years after Legendre’s paper, the mathematical genius Karl Friedrich Gauss claimed that he had been using the least-squares rule—which he called “my method”—for nearly a decade. As often happens, this simultaneous discovery was no coincidence. Both men were working on the same geodetic problem. Indeed, Gauss was working on the same data set, the meridian data gathered by Delambre and Méchain, which had been published in Germany in 1799. They were also reading the same mathematicians, especially Laplace. And, as often happens, this simultaneous discovery prompted a bitter dispute over priority: first, because both parties wanted credit for the discovery and finishing in the rear meant running the risk of being accused of plagiarism; and second, because the two parties differed on the meaning of the discovery. In this instance, there seems little doubt that the two men arrived at the method independently, although it was Legendre who published first. Nor is there any doubt that it was Gauss who suggested the method’s deeper meaning.
Legendre presented his method of least squares as workable and plausible. Gauss justified it by showing that it gave the most probable value in those situations where the errors were distributed along a “bell curve” (known today as a Gaussian curve). This probability-based approach prompted Laplace to show in 1810–11 that the least-squares method had the following advantages: it best reduced the error as the number of observations went up; it indicated how to distinguish between random errors (precision) and constant errors (accuracy); and it suggested how likely it was that the chosen curve was best. This was new. In their search for an illusory perfection, the savants had learned not only how to distinguish between different kinds of error, but also that error could be approached with quantitative confidence. The years between 1805 and 1811 saw the rise of a new scientific theory—not a theory of nature, but a theory of error. It was this theory that would allow Nicollet to redeem Méchain’s honor by distinguishing between those errors that were random and those that were systematic.
Some experiments were inherently erratic; others could be refined. Some investigators took pains with their observations; others were sloppy. The appeal of the new approach was that colleagues could now begin to distinguish between these two forms of uncertainty, and judge one another with the same impersonal techniques by which they judged nature. It was at this time that Delambre, Laplace, and the rest of the French savants started to come to terms with something their British colleagues had just discovered: that even the most fastidious astronomers were subject to idiosyncrasies in their observations (depending on their reaction time and the like), and that these idiosyncrasies introduced a constant bias into their observations, a “personal equation” as it came to be called. This recognition that they themselves were fallible instruments was followed by a program to tame error. Astronomers began to calibrate themselves against one another and to divide their labor to average out personal influences. Over the course of the next few decades astronomy became something of a bureaucratic science, in which a staff of junior observers (career-minded young men) and an office full of calculators (underpaid young women) toiled for a senior astronomer who directed their efforts, analyzed their data, and then published the results under his name.
Approach the world instead through the veil of uncertainty and science would never be the same. And nor would savants. During the course of the next century science learned to manage uncertainty. The field of statistics that would one day emerge from the insights of Legendre, Laplace, and Gauss would transform the physical sciences, inspire the biological sciences, and give birth to the social sciences. In the process, “savants” became “scientists.”
Méchain lived and died a savant. Measurement mattered to him as much as it did to the Ancien Régime peasants, bakers, and families who grew wheat, baked bread, and bought loaves in the marketplace. Whether it was the height of a star or the weight of a loaf, measurement expressed value. It was a moral act, an exercise in justice. For the savant, the pattern of the heavens revealed a comprehensive plan. To measure the shape of the earth or the height of a star was to glimpse its place in that pattern, just as the weight of a loaf sustained the just price for bread.
Men like Delambre, Laplace, Legendre, and their generation had a foot in each world. I have called them savants, but the term no longer fits. They were henceforth engaged in a struggle to quantify their uncertainty. They would ask: how confident are we that we know what we think we know? They sought to rid themselves of value judgments about nature and to cordon off meaning from their measurement of the world. They had launched themselves on a very different kind of career. In 1792 Jean-Paul Marat had been the first person to tag savants with the name of scientifiques (scientists), when he referred sneeringly to the academicians’ self-serving project to measure the earth in order to create uniform weights and measures. For better or worse, the savants were now on their way toward becoming scientists.
As for Lalande, he chafed under the new régime even more than he had under the old. He was the last of the philosophes, now in his seventies: a freethinker who preferred monarchy, an atheist who admired the Jesuits, a feminist who propositioned young women, ugly as ever and still just as vain. The new régime had little patience for these old-time contradictions. Lalande had initially welcomed Napoleon’s rise to power, proud that the general called him “Grandpapa.” Napoleon had studied astronomy under one of Lalande’s students, and had written to Lalande in a manner calculated to flatter the old man. “To divide one’s night between a beautiful woman and a clear sky, and then spend the day matching theory and observation, that is my idea of heaven on earth.”
Lalande’s ego was pure as platinum. When his star chart hit fifty thousand—thanks to the labors of his daughter and his nephew—he published a massive compendium under his own name. Surveying the fifty-four auditors who attended his lectures at the Collège de France, he admitted in his journal that “Lalande is still the one who interests me most.” In the summer of 1798, he handed the lovely Citoyenne Henry, the world’s first woman aeronaut, into a balloon for her maiden voyage, in spite of a ban on female ascension. The next spring, he tried to visit Germany by balloon while observing the stars above the atmosphere’s veil. A wit composed the following verse to accompany him.
Observe the dwarf of academicians
Whose pride could fill a room.
He wanted to hear it straight from the winds
If they talked of him
On the moon, the moon, the moon.
The balloon never made it past the Bois de Boulogne, and he canceled the trip. He was always good copy. When a traveler brought back news of an African people who, like him, ate spiders, the newspapers advised Lalande that he would now have to switch to “insects of distinction.” Yet he was living proof that vanity could serve noble causes. Lalande did not care what people thought. As the editor of the Dictionary of Atheists, he maintained its honor roll of eight hundred adherents: from Socrates to Lalande. In 1799 he signed up several of his colleagues, including “Buonaparte of the Academy of Sciences.”
This was risky. After the vandalism of the Revolution, piety was making a comeback. Wags claimed that Lalande had turned to atheism out of revenge, because God had made him so ugly. “Look at his knock knees and rickety legs, his hunched back and little monkey’s head, his pale wizened features and narrow creased forehead, and under those red eyebrows, his empty glassy eyes.” Lalande answered insults with epigrams:
That men are witless, wicked fools
Proves there’s evil in this house of rot.
A scoundrel’s word can make heads roll;
If God existed, Man would not.
Not all his colleagues appreciated this frankness on their behalf. Lalande’s antics put Delambre in an awkwa
rd spot. At first the dilemma was amusing. Delambre had agreed to serve as godfather to Lalande’s granddaughter, Uranie, but her baptism had been postponed until Delambre returned from his mission. By then the child was seven, and able to respond on her own behalf. Asked by the priest if she renounced Satan and all his works, she said “I do renounce.” Asked if she renounced all worldly vanities, she said “I do renounce.” Asked if she swore to live and die in the Catholic Church, she said, in a loud clear voice, “I do renounce.” Everyone in the church laughed, including the priest.
Then Napoleon decided to buy peace among the French by reconciling with the Catholic Church. These delicate negotiations resulted in the Concordat of 1802, and were to culminate in the Pope’s arrival in Paris for the coronation of Napoleon as Emperor. In the midst of these delicate accommodations, Lalande had the temerity to reissue his Dictionary. The Emperor was furious. But was it atheism that enraged him, or something worse? The Dictionary dared to preach peace: “It is up to the philosophes to spread the light of science, so that one day perhaps they may curb those monstrous rulers who bloody the earth; that is to say, the warmongers. As religion has produced so many of them, we may hope to see an end to that as well.”
From the battlefield of Austerlitz—after the finest victory in his career—the Emperor wrote a searing rebuke: Lalande had fallen into dotage, atheism destroyed the moral order, and Delambre, as Permanent Secretary, must convoke the Academy to silence their senior colleague. Delambre tried to make Lalande’s compliance appear voluntary, preserving a semblance of intellectual freedom while bowing to authority, but Lalande refused to be silenced. In 1806, he published another edition of the Dictionary, albeit without Napoleon’s name.
That year Lalande fell ill with a chest ailment. Right to the end, he was insufferable and self-mocking in alternate breaths. In his final moral testament he wrote: “I have sometimes amused myself by saying that I thought I possessed all the human virtues. This phrase of mine has been bitterly cast up against me as if I had claimed ‘to have all the human virtues.’ In fact, what I said was that ‘I thought I had them,’ which is quite a different matter. Nevertheless, I was perhaps wrong to have said as much; but my conscience required it of me.”
In the evening of April 3, 1807, after his daughter had read him the evening papers, he sent her to bed, saying “I don’t need anything else.” At two in the morning he died. Even beyond the grave, he shocked the public. Two days after his death, his family had to deny rumors that Lalande had asked for his dissected body to be put on display in the Museum of Natural History. The eighteenth century was finally over.
This earthly transience—of knowledge, of men, of régimes—was not necessarily a cause for melancholy. On the contrary, in a world of confounding factors, in an age of Revolutionary terror, Delambre felt joy, only joy. Joy had accompanied him through all his travels, through all his labors, through all his life. Not the ecstatic joy of transcendence, but the modest joy of immersion. He had long ago passed the age of illusion. Delambre could accept that we live on a fallen irregular planet, in a world of imperfection and error, because by the collective labor of honest scientists this imperfection could be contained, and error tamed. In 1806 he wrote to a friend who had suffered much during the Revolution:
I have all my life experienced a happiness so gentle, so peaceful, and so untroubled, that if I were truly persuaded that it is man’s lot to discharge a debt of suffering and pain, I would fear for the future. But I like to think that there are exceptions, and I dare to hope that I will be one of them. My good fortune, I think, is due to my character and my temperament. The only passion I have ever known is the one which has never yet caused misfortune; and that is work. My passion for work is not diminished. I continue to give myself to my labors with all my strength.
Delambre’s face had thickened, but his eyes had strengthened with the years. His legs were chancy, but his hand was firm. The traveler who had once traversed much of France could no longer cross a Paris street; in 1803 he had been hobbled by a rheumatic fever. He had seen much in the way of suffering, but his optimism was unabated.
In 1804, after a liaison of several years, he married Elisabeth de Pommard, the mother of his young assistant. He was fifty-five; she was in her forties, a spirited widow with some well situated property to the west of Paris. They made a good match. She read Virgil’s epics in Latin, Addison’s essays in English, and Metastasio’s librettos in Italian. For several years before they exchanged vows, she and Delambre had traded low-interest loans. While the d’Assy family remained in the country, Delambre and his wife could live on the sumptuous rue de Paradis. There they read the classics, followed the Amazon voyages of their young friend Humboldt, and planned a brilliant career for her son, whom Delambre loved as his own.
Young Pommard, who had once planned to be an astronomer like his stepfather, enrolled instead in the Ecole Polytechnique to study the earth: mining and mineralogy. Two years later, he left to join Napoleon’s finance bureaucracy. Pommard was serving in Naples when he died in 1807, at the age of twenty-six, an inconsolable loss to his mother and her new husband. Delambre transcribed this English translation of an Athenian poem for his wife:
Ah! Love how soft and tender
Begins thy happy reign,
But when our heart surrenders
Thou’rt bitterness and pain.
If from the Daylight flying
The shaded woods we rove
Or thro’ the slow night sighing
Of breath but for my love.
Tempt not the soft illusion
DELAMBRE AS PERMANENT SECRETARY OF THE ACADEMY OF SCIENCES
Delambre in his fifties, at the height of his academic influence. (From the Archives de l’Académie des Sciences, Dossier Delambre; photograph by Charmet)
Ye wand’rers free of air
’Tis nothing but delusion
The voice that calls you there
Or tells the heart to languish
The youthful bloom to glow
Then damps that heart with anguish
And fills that heart with woe.
Yet sorrow too is transient. And Delambre would find renewed satisfaction here on earth. He spent the final decades of his life as a power broker of imperial science: dispensing favors, deciding careers, disciplining colleagues. He was simultaneously Permanent Secretary of the Academy, Lalande’s successor at the Collège de France, a member of the Bureau of Longitudes, and Treasurer of the University of Paris. He also became the nation’s premier historian of science. On the title pages of his books his honorary titles took up half the page. He became a star of the cumul system, the deplorable French practice of gathering multiple offices into one thick fist. Although the salaries came to a hefty sum, Delambre denied any worldly ambition. “Official positions have come to me unbidden, and I received what I did not covet.”
Generosity during war, honesty under empire, science in an age of puffery: these are the trials of integrity. He conducted fewer astronomical sightings now, and concentrated instead on the inner science of synthesis. For one thing, he had lost easy access to his private observatory. In 1808, he and his wife moved out of the rue de Paradis and into the official residence of the Treasurer of the University. After her son’s death, wife and husband relied on one another more than ever. She learned enough mathematics to help him with calculations. Delambre had an endless appetite for work. In 1806 he published a revised set of solar tables, the most exact to date. In 1813 he published an Abridged Astronomy, and a year later a three-volume Treatise on Astronomy. According to Gauss, these latter works were dull and craftsman-like, mathematically simplistic and lacking conceptual elegance. In other words, they were textbooks.
Delambre made himself useful to the Napoleonic régime, even as he kept his distance from palace intrigue. In 1803, as the Treaty of Amiens faltered, Napoleon ordered detailed maps of landing sites along the south coast of Britain. He also asked which French tower was best situated for his s
upervision of the planned invasion. No one knew more about the geodesy of the north coast of France than Jean-Baptiste-Joseph Delambre. Within a week, he had supplied a set of tables of optimal viewing sites, based on his own research and that of the 1788 Greenwich–Paris survey. As a servant of the state, he was duty-bound to put peaceful science to bellicose ends. But then, throughout the war, he worked with his opposite number in Britain, Sir Joseph Banks, President of the Royal Society, to save their respective colleagues caught up in the conflict. Banks helped the French geodesers sail home from Egypt; Delambre helped release those trapped on the Continent. Their nations might be at war, but scientists could maintain civility. Delambre shipped multiple copies of the Base du système métrique to Britain—accompanied by hopes for more peaceful times to come.
In 1809 Napoleon directed the Academy to conduct a prize competition for the best scientific publications of the decade. In the category of applied science, the Academy unanimously nominated “the work of Delambre on the meridian.” The work of Delambre? Méchain’s sons wrote to defend their father’s honor and to petition to have his name included. A committee of the Academy, asked to adjudicate, noted that while Delambre and Méchain had split the latitude measurements equally, Delambre had measured 89 out of 115 triangles and both baselines. More to the point, Delambre had refined all the geodesic methods, recalculated all Méchain’s latitudes, and written virtually the entire text of the Base du système métrique. Despite the fact that Méchain’s name came first on the title page, Delambre alone deserved the prize. Deserved perhaps, but would not accept. Delambre withdrew the Base from consideration on the grounds of conflict of interest.