Measure of All Things: The Seven-Year Odyssey and Hidden Error That
Transformed the World
Free Press, The
Date: October 2002
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.
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
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.
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.
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
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.
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?
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."
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.
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
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.
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.
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.
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.
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.
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.
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."
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.
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.
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.
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.
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.
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
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.
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.
© 2002 by Ken Alder