the circumference of earth -- 11/29/23

Today's selection -- from The Measure of All Things by Ken Alder. In the 1790s, a geodetic survey was carried out by France’s Jean-Baptiste Delambre and Pierre Méchain to measure an arc between Barcelona and Dunkirk, thus calculating the circumference of Earth:

“For those who wish to know the origins of the metric system, there is one place to turn: the official account composed by one of the leaders of the meridian expedition, the north-going astronomer, Jean-Baptiste-Joseph Delambre, Delambre wrote the Base du systeme metrique decimal--which we might translate as The Foundation of the Metric System--in order to present all the expedition's findings ‘without omission or reticence.’ At over two thousand pages, this magisterial work certainly appears thorough enough. But bulky and authoritative as it is, the Base is a strange book, with puzzling contradictions. Reading it, I began to get the sense that this was not the complete history of the meter, and that Delambre had himself scattered clues to this effect throughout the text. For instance, in Volume 3 he explained that he had deposited all the records of the metric calculations in the archives of the Observatory of Paris lest future generations doubt the soundness of their procedures. 

“The records are still there. The Observatory of Paris is an imposing stone structure just south of the Luxembourg Gardens in the heart of modern Paris. In the 1660s, when Louis XIV founded the Royal Observatory and Royal Academy of Sciences, his goal was to couple the glory of his rule with the new heavenly science, and also to supply his savants with the tools they would need to assemble an accurate map of his kingdom here on earth. The building is perfectly aligned along the nation's north-south meridian. Like France, it presents two faces. From the north, it might almost be mistaken for a royal fortress, with austere stone walls guarding a gray plain of mist and gravel that stretches toward the North Sea. From the south, it resembles an elegant residential palace, with octagonal pavilions looking out over a terraced park that seems to step, via an alley of plane trees, down to a remote Mediterranean. During the Ancien Regime, most of France's finest astronomers lodged within its green precincts. Today, the site remains the privileged workplace of its leading astrophysicists. 

“The Observatory archives are located in the southeastern octagon, where the papers of the meridian expedition fill twenty cartons. They include thousands of pages of computation in logbooks and on scraps of paper, along with maps, protocols, diagrams, and formulas that comprise the seven years of calculation which went into the making of a single number: the length of the meter. Leafing through one of Mechain's logbooks, I found an extended commentary written and signed by Delambre. 

The meter was originally defined to be one ten millionth of the distance between the North Pole and the Equator through Paris.

“I deposit these notes here to justify my choice of which version of Michain's data to publish. Because I have not told the public what it does not need to know, I have suppressed all those details which might diminish its confidence in such an important mission, one which we will not have a chance to verify. I have carefully silenced anything which might alter in the least the good reputation which Monsieur Michain rightly enjoyed for the care he put into all his observations and calculations. 

“I can still remember the shock I felt upon reading those words. Why was there more than one version of Mechain's data? What exactly had been hidden from the public? Part of the answer lay in the one carton that had not been deposited with the rest, but stored separately by Delambre and placed by him under seal as a special precaution. Inside, there are no logbooks or calculations. Instead there are letters, dozens of letters between Delambre and Mechain, as well as letters between Delambre and Madame Mechain. Had I stumbled, amid all these dusty calculations, on a scandal of intrigue and deception? Reading through these letters, I began to realize that I had discovered something much more interesting: a tale of scientific error and the agonizing choices it forced upon men and women of integrity. In the margin of Mechain's last letter to Delambre, mailed from the abandoned monastery of Saint-Pons in the remote Montagnes Noires (the Black Mountains) of southern France, Delambre had scribbled a final explanatory note. 

“Though Michain more than once begged me to burn his letters, his mental state, and my fear that he would one day turn against me, led me to keep them in case I ever needed to use them to defend myself. ... [B]ut I thought it prudent to place them under seal so that they could not be opened unless someone needed to verify the extracts I published in the Base du systeme metrique. 

“The remaining clues to the mystery lay elsewhere, scattered not only across France and the sources Delambre preserved, but also in the records of the savants' many correspondents in Spain, Holland, Italy, Germany, Denmark, England, and the United States, including a cache of Delambre's papers which had mysteriously vanished from a French archive--along with the garbage, said the archivists--to find its way, via a London auction house, to the library of Brigham Young University in Provo, Utah. And finally, I tracked down something long presumed lost: Delambre's own copy of his magisterial work, the Base du systeme metrique decimal.

“Those volumes are located today in the private home of David Karpeles, a collector of rare books and manuscripts in Santa Barbara, California. There, on the title page, in his angular hand, Delambre had inscribed Napoleon's grand prophesy: ‘Conquests will come and go, but this work will endure,” words of Nap. Bonaparte to the author of the Base.’ Yet the title page was not the only page on which he had recorded his marginal comments. 

“Together, these documents reveal a remarkable story. They reveal that Mechain--despite his extreme caution and exactitude--committed an error in the early years of the expedition, and worse, upon discovering his mistake, covered it up. Mechain was so tormented by the secret knowledge of his error that he was driven to the brink of madness. In the end, he died in an attempt to correct himself. The meter, it turns out, is in error, an error which has been perpetuated in every subsequent redefinition of its length, including our current definition of the meter in terms of the distance traveled by light in a fraction of a second. 

“According to today's satellite surveys, the length of the meridian from the pole to the equator equals 10,002,290 meters. In other words, the meter calculated by Delambre and Mechain falls roughly 0.2 millimeters short, or about the thickness of two pages of this book. It may not seem like much, but it is enough to feel with your fingers, enough to matter in high-precision science, and in that slender difference lies a tale of two men sent out in opposite directions on a Herculean task--a mission to measure the world-who discovered that integrity could carry them in directions as contrary as their carriages. Both were men in their mid-forties, men of humble origins from the French provinces who had risen to prominence on the basis of talent and a mind-numbing capacity for work. Both had been trained by the same astronomer, Jerome Lalande, and elected to the Academy of Sciences in time for the Revolution to hand them the career opportunity of a lifetime: the chance to sign their names to the world's measure. But during their seven years of travels, the two men came to have a different understanding of their metric mission and the allegiance it commanded. That difference would decide their fates.

“This then is a tale of error and its meaning: how people strive for utopian perfection--in their works and in their lives--and how they come to terms with the inevitable shortcomings. What does it feel like to make a mistake, and in a matter of such supreme importance? Yet even in failure, Delambre and Mechain succeeded, for by their labor they rewrote not only our knowledge of the shape of the earth, but our knowledge of error as well. In the process, scientific error was transformed from a moral failing into a social problem, forever altering what it meant to be a practicing scientist. Indeed, this expedition--an odyssey of self discovery--is the story of how the Ancien Regime savants became modern scientist. And the consequences of their labor resonated far outside the realm of science. We can trace the impact of their work in the globalization of economic exchange, and in the way ordinary people have come to understand their own best interest. In the end, even the French countryside they traversed has been transformed."



Ken Alder


The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World


Free Press


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