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The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the Worldby Ken Alder
In June 1792 — in the dying days of the French monarchy, as the world began to revolve around a new promise of Revolutionary equality — two astronomers set out in opposite directions on an extraordinary quest. The erudite and cosmopolitan Jean-Baptiste-Joseph Delambre made his way north from Paris, while the cautious and scrupulous Pierre-François-André Méchain made his way south. Each man left the capital in a customized carriage stocked with the most advanced scientific instruments of the day and accompanied by a skilled assistant. Their mission was to measure the world, or at least that piece of the meridian arc which ran from Dunkerque through Paris to Barcelona. Their hope was that all the world's peoples would henceforth use the globe as their common standard of measure. Their task was to establish this new measure — "the meter" — as one ten-millionth of the distance from the North Pole to the equator.
The meter would be eternal because it had been taken from the earth, which was itself eternal. And the meter would belong equally to all the people of the world, just as the earth belonged equally to them all. In the words of their Revolutionary colleague Condorcet — the founder of mathematical social science and history's great optimist — the metric system was to be "for all people, for all time."
We often hear that science is a revolutionary force that imposes radical new ideas on human history. But science also emerges from within human history, reshaping ordinary actions, some so habitual we hardly notice them. Measurement is one of our most ordinary actions. We speak its language whenever we exchange precise information or trade objects with exactitude. This very ubiquity, however, makes measurement invisible. To do their job, standards must operate as a set of shared assumptions, the unexamined background against which we strike agreements and make distinctions. So it is not surprising that we take measurement for granted and consider it banal. Yet the use a society makes of its measures expresses its sense of fair dealing. That is why the balance scale is a widespread symbol of justice. The admonition is found in the Old Testament: "Ye shall do no unrighteousness in judgment, in meteyard, in weight, or in measure. Just balances, just weights, a just ephah, and a just hin, shall ye have." Our methods of measurement define who we are and what we value.
The men who created the metric system understood this. They were the preeminent scientific thinkers of the Enlightenment, an age which had elevated reason to the rank of "sole despot of the universe." These savants — as the investigators who studied nature were known in those days — had a modern face looking toward our own times, and an older face glancing back toward the past. In their own minds, of course, they were not two-faced; it was their world which was two-faced, with its burdensome past obstructing progress and a utopian future waiting to be born.
The savants were appalled by the diversity of weights and measures they saw all around them. Measures in the eighteenth century not only differed from nation to nation, but within nations as well. This diversity obstructed communication and commerce, and hindered the rational administration of the state. It also made it difficult for the savants to compare their results with those of their colleagues. One Englishman, traveling through France on the eve of the Revolution, found the diversity there a torment. "[I]n France," he complained, "the infinite perplexity of the measures exceeds all comprehension. They differ not only in every province, but in every district and almost every town...." Contemporaries estimated that under the cover of some eight hundred names, the Ancien Régime of France employed a staggering 250,000 different units of weights and measures.
In place of this Babel of measurement, the savants imagined a universal language of measures that would bring order and reason to the exchange of both goods and information. It would be a rational and coherent system that would induce its users to think about the world in a rational and coherent way. But all the savants' grand plans would have remained fantasy had not the French Revolution — history's great utopian rupture — provided them with an unexpected chance to throw off the shackles of custom and build a new world upon principled foundations. Just as the French Revolution had proclaimed universal rights for all people, the savants argued, so too should it proclaim universal measures. And to ensure that their creation would not be seen as the handiwork of any single group or nation, they decided to derive its fundamental unit from the measure of the world itself.
For seven years Delambre and Méchain traveled the meridian to extract this single number from the curved surface of our planet. They began their journey in opposite directions, and then, when they had reached the extremities of their arc, measured their way back toward one another through a country quickened with revolution. Their mission took them to the tops of filigree cathedral spires, to the summits of domed volcanoes, and very nearly to the guillotine. It was an operation of exquisite precision for such violent times. At every turn they encountered suspicion and obstruction. How do you measure the earth while the world is turning beneath your feet? How do you establish a new order when the countryside is in chaos? How do you set standards at a time when everything is up for grabs? Or is there, in fact, no better time to do so?
At last, their seven years of travel done, the two astronomers converged on the southern fortress town of Carcassonne, and from there returned to Paris to present their data to an International Commission, the world's first international scientific conference. The results of their labors were then enshrined in a meter bar of pure platinum. It was a moment of triumph: proof that in the midst of social and political upheaval, science could produce something of permanence. Accepting the fruit of their labor, France's new supreme ruler made a prophesy. "Conquests will come and go," Napoleon Bonaparte declared, "but this work will endure."
In the last two hundred years, conquests have indeed come and gone, but the meter has become the measure of all things. The metric system serves today as the common language of high-tech communications, cutting-edge science, machine production, and international commerce. Older forms of measurement have receded as the metric system has made possible trade and economic coordination on a fully global scale. Paradoxically, the leading nation in the global economy remains the sole exception to this rule. Thomas Jefferson failed to convince Congress to make the United States the second nation to adopt the metric system, and every reformer since has met the same fate. John Quincy Adams, asked to consider whether the United States should adhere to the metric system, called it the greatest invention since the printing press and predicted it would save more human labor than the steam engine. Yet he recommended against its adoption. Only in recent years have American manufacturers begun retooling for metric units. Few Americans realize that a silent revolution is finally underway in their nation, transforming their measures under the pressures of the new global economy.
As things stand, of course, this conversion is embarrassingly incomplete. Americans became painfully aware of this fact in 1999 with the loss of the Mars Climate Orbiter. A NASA investigation into the satellite's failure revealed that one team of engineers had used traditional American units, while another had used metric units. The result was a trajectory error of sixty miles, and a $125-million disappearing act.
The Revolutionary scientists created the metric system two hundred years ago to avoid just this sort of fiasco. One of their aims was to facilitate communication among scientists, engineers, and administrators. Their grander ambition was to transform France — and ultimately, the whole world — into a free market for the open exchange of goods and information. Today, their goal seems within reach. Over 95 percent of the world's population now officially uses the metric system, and its success is touted as one of the benign triumphs of globalization.
But behind the public triumph of the metric system lies a long and bitter history. The fundamental fallacy of utopianism is to assume that everyone wants to live in the same utopia. France, it turns out, was not only the first nation to invent the metric system; she was also the first to reject it. For decades after its introduction ordinary people spurned the new system, and clung to their local measures and the local economies they sustained. In the face of this revolt from below, Napoleon, on the eve of his disastrous invasion of Russia, returned France to the Paris measures of the Ancien Régime. Now he mocked the global aspirations of the men he had once admired. "It was not enough for them to make forty million people happy," he sneered, "they wanted to sign up the whole universe." Not until the middle of the nineteenth century did France revert to the metric system, and even then use of the old measures persisted into the twentieth. It would take enormous scientific effort and years of bitter conflict to make metric measurement banal, just as it had taken a Revolution to bring the metric system into being. Things might easily have turned out differently.
What neither advocates nor opponents of the metric system could have known is that a secret error lies at the heart of the metric system — an error perpetuated in every subsequent definition of the meter. Indeed, as I discovered in the course of my research, the only people who could have known the full extent of this error were Delambre and Méchain themselves.
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 système métrique décimal — 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 Régime, 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 Méchain's logbooks, I found an extended commentary written and signed by Delambre.
I deposit these notes here to justify my choice of which version of Méchain'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 Méchain 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 Méchain'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 Méchain, as well as letters between Delambre and Madame Méchain. 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 Méchain'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 Méchain 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 système métrique.
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 système métrique décimal.
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 Méchain — 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. Méchain 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 Méchain 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, Jérôme 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 Méchain 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. 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.
To come to terms with this history, I set out to retrace their journey. In the year 2000, at a time when France was celebrating the millennium along the Meridienne Verte — a six-hundred-mile row of evergreen trees which was meant to mark out the national meridian, but which was somehow never planted — I set out on the zigzag trail of Delambre and Méchain. I climbed the cathedral towers and mountain peaks from which they conducted their survey, and combed the provincial archives for traces of their passage. It was my own Tour de France. Delambre and Méchain had demonstrated that the judicious application of scientific knowledge might, as Archimedes once boasted, move the world. Where they traveled by carriage and on foot, I substituted a bicycle. After all, what is a bicycle but a lever on wheels? — a lever which allows the cyclist to move along the surface of the world, or, which is much the same thing, move the world.
Copyright © 2002 by Ken Alder
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