;)
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-Fran�ois-Andr� M�chain 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.
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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 R�gime 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 M�chain 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
R�gime. 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 M�chain 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 syst�me m�trique d�cimal -
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 R�gime, 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
M�chain'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 M�chain'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 M�chain
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 M�chain'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 M�chain, as well as letters
between Delambre and Madame M�chain. 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 M�chain'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 M�chain 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 syst�me m�trique
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 syst�me m�trique
d�cimal.
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 M�chain - 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. M�chain 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
M�chain 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, J�r�me 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 M�chain 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
M�chain. 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 M�chain 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.
Excerpted from The Measure Of All Things
by Ken Alder Copyright � 2002 by Ken Alder
Excerpted by permission. All rights reserved. No part of
this excerpt may be reproduced or reprinted without
permission in writing from the publisher.
