Book Review: The Measure of All Things

The Measure of All Things
The Seven-Year Odyssey and Hidden Error that Transformed the World
by Ken Alder
New York: The Free Press, 2002. ISBN 0-7432-1675-X
Paperback: New York: The Free Press, 2003. ISBN 0-7432-1676-8

This book would’ve made for quite the shocker in the 1970s, when the United States attempted and failed to convert to the metric system. Highway crews added kilometers to road signs, grocery stores handed out brochures on cooking with metric units, and metric advocates championed the natural basis of the new measurements. One kilogram of mass for each liter of water, 100 Celsius degrees between freezing and boiling, and 10 million meters from the pole to the equator. Imagine what the opponents of metric units could've done with a book like The Measure of All Things, which exposes the basis of the entire metric system as a fraud!

Specifically, Ken Alder follows the expedition dispatched by the French Republic to survey the length of the meridian from Dunkirk to Barcelona. During that seven-year journey, Pierre-François-André Méchain and Jean-Baptiste-Joseph Delambre would be attacked by peasants, trapped behind enemy lines in a war, and beset by malaria. While revolutions and counterrevolutions roiled Paris, they would continue working on the task that they set out to accomplish.

That the undertaking was completed under such circumstances is remarkable, but the results are less so. After digging through the original correspondence and Delambre's published account of the expedition, the author discovers that Méchain had made errors in his measurements, then altered data to cover them up. Ever mindful of his partner's seniority, Delambre papered over the errors and preserved Méchain's reputation. Yet Delambre, having been so meticulous with his own data, nevertheless recorded the discrepancies for posterity.

Shocking? Hardly. The earth's circumference is not 40 million meters exactly. The strength of the metric system lies in its universality and decimal nature, not in its basis in the natural world. The meter itself has changed in definition, first etched on a bar of platinum, later defined in terms of krypton state transitions and the speed of light. None of the latter two definitions are particularly round numbers, but they are repeatable, each more precise than the last.

And so, when Alder writes in the prologue that “a secret error lies at the heart of the metric system” (p.5), a theme repeated sporadically and played up by the jacket copy, it seems to be much ado about very little. Considering the errors that Méchain and Delambre did not discover, the errors that they did make seem rather inconsequential today. He eventually alludes to the arbitrary nature of measurements when he covers later metric conferences, where the delegates decided to enshrine the then-current values for all time.

Ultimately, Alder develops his theme into an exposition on the nature of error and the progress of science. Where once savants regarded measurements as their prerogative to perfect, the later scientifiques (scientists) understood Gaussian distributions and least-squares error. But unfortunately, this theme is developed in fits and starts, a couple of pages at a time amidst the more interesting narrative of the two men's journeys. It feels like one of those television shows where every 12-minute segment is followed by a teaser for the big finale, which comes at last after two hours and falls far short of expectations.

Technical shallowness

As a professor of history who focuses on science and technology, Alder is surprisingly light on the technical details. Often he launches into several awkwardly-phrased paragraphs of prose to explain a concept that would be much better presented with a few equations or a nice diagram. The one time that he uses a diagram to explain the use of the repeating circle to eliminate angular error, the figure used is a period illustration and much more confusing than a modern illustration would be.

In fact, Alder states several times that the instrument can “double” measurements to reduce error, when the instrument shown actually adds measurements to yield multiples. An error in wording or a conceptual error on the part of the author? Alder gives the first three terms of such a doubling of successive measurements: 1, 2, 4. It sure seems like he believes what he said. Common sense would tell you that continued doubling would eventually lead you to measure an angle greater than 360 degrees on the repeating circle. This is actually an important point, since an instrument that progressively doubles would require fewer measurements for a given error tolerance, and minimizes the scope of the task faced by the two surveyors for each and every angle measurement they made.

This technical shallowness also carries across to more incidental anecdotes. Alder admiringly describes Eratosthenes' estimation of the earth's circumference, without mentioning that this accomplishment is disputed due to uncertainties about the actual length of a stade. He also gives the simplistic “evening news” explanation for the loss of the Mars Climate Orbiter, when it was the more serious process issues that allowed the discrepancy in units to build up. It's a bit like picking up a business book and reading about the failure of the Ford Nova in the Latin American market — a “fact” that everyone knows to be true, but is actually false.

Interesting anecdotes

To a reader with a scientific or engineering background, the book is thus quite infuriating at times. Yet it also makes some excellent points about the meaning of metric reform, and deftly ties in the personalities and attitudes of the period. Alder is a historian, after all, and he has a solid understanding of the context in which the expedition took place. He describes the Republican calendar, the decimalization of currency, the proposed base-12 counting system, and alternative proposals to define the meter using a pendulum rather than a survey. He also explains the difference between the ancien régime concept of measurement, based on just price, and the modern understanding, based on accuracy. A similar clash of value and precision would take place in modern standardization movements, from post-metric British merchants continuing to sell cloth in square yards to fool shoppers, to the post-euro Italian lament that they earn money in lira and spend it in euros.

Such anecdotes are Alder's strength, and they carry over to his account of the voyage itself. We read about freezing nights on mountain slopes, pervasive fog blocking sight lines, primitive accommodations far from major cities, and an overall determination to get the job done. There are more pages on Méchain than on Delambre, but it was Méchain, after all, who covered the southern leg of the journey, found himself behind enemy lines in Spain, made the much-ballyhooed mistakes, and had the nervous breakdown. Méchain ultimately dies of malaria, and in the fine spirit of technological history, Alder points out that the cinchona extract used to treat him does indeed contain quinine.

There are similarly interesting anecdotes throughout the book. Just as we are beginning to get bored with a lengthy description of the surveyors' mentor Joseph-Jérôme Lalande, Alder tells us that he ate caterpillars. Those aristocrats of the ancien régime certainly cultivated some interesting quirks! Colorful details are mixed with vivid descriptions of Revolutionary tumult to set the scene. There is a mixture of dread and wonder when the Bourbons are removed from their resting places in the Basilica of Saint-Denis and the popular king Henry IV is found “perfectly preserved, his face black as pitch” (p.36) after over a century.

We get a good sense of how the Revolution affected people's lives by learning the social particularities of the scientific establishment. We follow the personal story by tracking Madame Méchain as she moves from dwelling to dwelling while her husband's fortunes rise and fall with each change of government. The French Revolution was just as bloody and vicious a revolution as more modern ones, a fact that is often obscured by lists of the guillotined. Alder's chronicle of quotidian happenings disabuses us of any revolutionary romanticism.


It's easy to see why the jacket copywriter chose to focus on the “secret error,” though. Such anecdotes are difficult to summarize into book-selling copy, even though they form the backbone of the book. This is unfortunate, for the book is very readable and brings many specifics to the cut-and-dry history that one learns in European History classes. Alder, a devout Francophile (in the acknowledgments: “I thank my parents for first introducing me to matters scientific and French”), has biked across the surveyors' entire route, and his geographical descriptions possess the verisimilitude of personal presence.

Alder’s immersion in the French culture also enables him to make unanticipated links, for example, between the villagers who pulled down Méchain's geodetic signals and the activist José Bové, who arrived at the 1999 Seattle WTO protests bearing a package of the banned Roquefort cheese and bulldozed a local McDonald's for its standardized food (p.228: “since rebuilt, [it] is the world's most famous, and certainly the most charming ... with ... a soothing view over a bucolic valley”).

Although Alder's own book is, as Gauss said of Delambre's textbooks, “mathematically simplistic” (p.314), he manages to escape the other half of Gauss' assessment: “dull and craftsman-like.” The book is indeed devoid of any mathematics, but it is also quite engaging, chock-full of the facts that bring life to a little-remembered expedition. Those with a technical background will on occasion gulp at the errors in the book, but they will find continued reading rewarding. The Measure of All Things is also handsomely-designed by Dana Sloan, with well-chosen illustrations and an elegantly readable typeface that fits well into the era.

Read the book not to learn about the “secret error,” for it has long since been forgotten, and the unsealed correspondence lay largely unread for most of the twentieth century before Ken Alder picked it up. Rather, read it to get a glimpse of how science was conducted in the era of savants rather than scientifiques, to marvel at the fortuitous political maneuverings that somehow managed to leave the mission alive, and to appreciate the determination that ultimately completed the mission.