Review of The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World by Ken Alder: Free Press, New York, 2002, ISBN: 0-7432-1676-8, Price: $15.00, 436 pp.

After reading a book on the origin of the meter, I had to go back to my old college textbooks just to see what we were told as engineering students. In my surveying textbook, I found this explanation:

The meter is a unit of French origin and its application in the United States in the past has been almost entirely limited to geodetic surveys. In 1866 the U.S. Congress legalized the use of the metric system by which the meter was defined as being equal to $3.280833\mathrm{ft}$ (or $39.37\mathrm{in.}$ ) and $1\text{inch}$ was equal to $2.540005\text{centimeters}$ . These values are based on the length at $0°\mathrm{C}$ of an International Prototype Meter bar consisting of 90% platinum and 10% iridium which is kept in Sevres, France, near Paris. (McCormac, 1983 p. 33)

It was good that the author was kind enough to relate the meter to the units I had grown up with, because to be quite honest, the meter still gives me headaches as a sort of second language. And, like some of the textbooks that I consulted, it promised the “inevitable” adoption of the metric system. Other textbooks were a little more circumspect and said that the adoption was just “likely” to happen. Of course, I’m sure some people of a certain generation had hoped to see flying cars in the year 2000.

You would expect something perhaps a little more high-tech from a physics textbook, and I was not to be disappointed:

Before 1960, the standard for length, the meter, was defined as the distance between two lines on a specific platinum-iridium bar stored under controlled conditions. This standard was abandoned for several reasons, a principal one being that the limited accuracy with which the separation between the lines on the bar can be determined does not meet the present requirements of science and technology. Until recently, the meter was defined as 1 650 763.73 wavelengths of orange-red light emitted from a krypton-86 lamp. However, in October 1983, the meter was redefined as follows:

One meter—the distance traveled by light in a vacuum during a time of $1∕299792458\text{second}$ . (Serway 1986, p. 5)

In civil engineering the precision seems a little extravagant, but, as a freshman in college, it may have been comforting to know that something was knowable to that degree. Surely, I thought then, scientific progress holds the promise of knowing “the truth.”

It was not until I dusted off my chemistry textbook that I found this description. I doubt that I appreciated the full import of this statement the first time I read it some $18\text{years}$ ago (about the time that the freshmen that I will teach in the fall of 2004 were born!) but nonetheless, here is proof that I should already have known some of the story:

Prior to the French Revolution the system of measurement in France varied from province to province, making commercial transactions difficult to conduct. The need for a uniform system was clear, and in 1790 a commission of scientists was established to propose one. The commission chose as the unit of length, called a meter (m), 1/10,000,000 of the distance at sea level from the North Pole to the equator along a meridian passing through Paris. The fact that the original measurement was in error is interesting but not significant. (Petrucci 1985, p. 5)

“Interesting but not significant.” Of course, Petrucci did not have the benefit of reading The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World, by Ken Alder, first published by Free Press in 2002 and reissued in paperback in 2003. Alder, writing for a general audience with a novelist’s eye for plot, character, and setting, provides a fascinating read that proves that the history of the error is both interesting and significant.

When I first saw the paperback on a bookstore shelf, I thought it would be a promising night-time read. Having taught surveying to archaeology students at the University of Evansville for several semesters, I appreciated the value of being able to tell a few historical stories to pique the interest of students who sometimes did not know what to think of being in a classroom with an engineering professor. But, as so often happens during the school year, a nighttime read gets put off for summer-time reading. Perhaps I was a little reluctant to really invest the time because I had bought too many books in search of good histories about science and engineering that remained untouched after the first, sometimes dull, chapter. Then again, the title did promise an epic adventure and also a bit of mystery, perhaps a conspiracy, and maybe a scandal. Not always what you expect from a history of science but great ingredients for a summer-time read.

When first published, the book received generally excellent reviews in the popular press but also good reviews and recommendations in publications for physicists (the two main protagonists are astronomers and geodesists), historians, and, specifically, historians of science. It must help that the author is in fact a novelist, having published The White Bus in 1987. However, the author, as a history professor from Northwestern University specializing in the history of science, had access to primary sources and could piece them together to form a coherent picture of that time.

And what a time it was. Dry textbook definitions, constrained by space, leave a freshman engineering student to connect France in 1790 to the beginning of its Revolution. And, therein, lies the much larger drama that is the background (that sometimes jumps to the foreground) of the quest to define the meter. The commission of 1790 sent two of France’s leading astronomers, Jean-Baptiste-Joseph Delambre (1749–1822) and Pierre-Francois-Andre Méchain (1744–1804), both members of the Academy of Sciences, to measure the distance of the meridian that passes through Paris from Dunkerque to Barcelona, a distance of some $800\text{kilometers}$ or, if you prefer, some $500\text{miles}$ . Delambre traveled the country north of Paris while Méchain traveled in the south, both intending to meet halfway along the meridian to close the series of triangles that they surveyed with the most precise instrument designed to that day for measuring angles, the Borda repeating circle, named for its inventor Jean-Charles de Borda, then France’s leading experimental physicist. To complete the calculation, Delambre and Méchain would need to measure baseline distances as well as calculate as precisely as possible the latitude of the terminal points of the French meridian. From there, and given what was then known about the shape of the earth (an ellipsoid, not a spheroid), the commission could extrapolate the distance of the meridian from the North Pole to the equator and thus establish the meter.

The quest is simple to explain on face value, and optimistic estimates predicted completion in a matter of months. But, as Alder’s subtitle suggests, this was not to be. Alder gives us insight into the social and philosophical climate that gave birth to this odyssey, much more nuanced than a simple replacement of a “Babel of measurements” (Alder 2002, p. 2) in the provinces of France. Just as the French Revolution transformed society with the promise of government freed from arbitrary rule by a monarch, so it promised an opportunity to transform a measurement so vital to economy and science (and therefore progress) by basing it on a rational foundation and to give this new measurement to all the French people (and indeed all people) by using the earth itself as this basis. No more confusion based on arbitrary provincial and even national measures.

Alder paints a vivid portrait of this social, philosophical, and economic setting with all the turbulence of the political factions in Paris at the time as well as the reach of the Revolution in the provinces through which Delambre and Méchain traveled and worked. While this setting helps explain to some degree how this expedition turned into a $7\text{-}\text{year}$ odyssey, Alder does an admirable job describing the natural setting so important to the success of a survey party. It helps that Alder bicycled the length of the meridian in 2000, retracing the path of Méchain and Delambre. As Alder writes of one leg of Delambre’s journey: “Money was not the only obstacle. Geography also presented a challenge. The mournful region between Orleans and Bourges—triste (dreary) Sologne—was one of France’s most level. Where the expedition had once battled suspicious peasants and northern fogs, they now confronted a marshy terrain almost impossible to survey. The green ponds, tall grasses, and patchy forests offered few views into the distance.” (Alder 2002, p. 156)

Perhaps the biggest obstacle for the completion of the expedition lay not in the external but in the internal, in particular the internal demons of Méchain. Alder, perhaps as novelist, does an admirable job “developing” the characters in his story, and this has been a source of some of the criticism of “pop-psychology” in his book. To be fair, Alder had access to a chest of correspondences among the major players that were archived by Delambre, who eventually became the leader of the expedition.

The example that resonated most with me and highlighted the contrast between the characters of Delambre and Méchain are the following passages about how these two savants kept their notes. When Méchain, in a letter written $3\text{years}$ after the start of the expidition, asked his compatriot about the methods he used for keeping his records, Alder describes the response:

[Delambre] gladly detailed his methods for his colleague [Méchain]. He always recorded all his observations in the exact order he took them, in a logbook kept in ink with each page numbered. Only then did his assistant copy the data into another notebook in a sequence more convenient for calculation. He always noted who performed the observation, the instrument used, as well as the time, the weather, and any other relevant circumstances, including a hand-drawn sketch of the site with all its features labeled. He did so with the conviction that as an emissary of the state he was leading a mission of national importance. “The Commission will ultimately decide what to publish; in the meantime, I suppress nothing.” (Alder 2002, p. 183)

Except for writing in ink, these are essentially the same instructions I give to surveying students. But, it is the attitude of openness and order that is perhaps the more important lesson. Later in the book Alder describes the state of Méchain’s notes, notes that he had taken great pains to hide from his colleague. But upon Méchain’s death, Delambre (who was writing the definitive history of the $7\text{-}\text{year}$ expedition) became Méchain’s scientific executor and finally had full access to Méchain’s data. Alder writes:

[Méchain] had recorded all of his observations on loose sheets of paper rather than in a bound notebook with numbered pages. He had also recorded them all in pencil. As Delambre wryly remarked, “Loose pieces of paper can be lost; pencil marks fade.” More to the point, loose pieces of paper can be torn up; pencil marks can be erased. In some cases Méchain had recopied observations onto pages dressed up to look like originals, whereas the true originals had vanished. In other instances he had erased values, or rewritten his pencil marks to alter the numbers beneath. (Alder 2002, p. 292)

This is not to say that Méchain was a man unworthy to take on the task of such critical measurements. Alder points out that it was Méchain’s insistence on eliminating scientific error that obsessed him and, as we come to learn, paralyzed his progress through self-doubt, perhaps compounded by competitiveness and mistrust of the younger Delambre. And, herein lies the error of the title, at least the error as perceived by Méchain. After many observations of several stars to determine the latitude of the southern terminus of the meridian at Barcelona, Mechain discovers a discrepancy of about $3\text{degrees}$ of arc. For Méchain, this was a devastating discovery that he confessed directly to only one other scientist (safely isolated in Genoa), although he hinted his fault to Delambre in a series of letters. Alder uses correspondences between Delambre and the wife of Méchain (herself accomplished in astronomy) to “triangulate” the inner state of the troubled Méchain. Madame Méchain traveled to Rodez to meet with her husband whom she had not seen for $6\text{years}$ . She did not know of the error; she only knew of his despair and its effects on the accomplishment of the mission: “I am hopeful that the esteem and absolute trust he places in me will allow me to dissipate the unwholesome thoughts which devour his spirit, and which, against his will, distract him from his purpose” (Alder 2000, p. 220).

The sharp contrast with which Alder draws the portraits of Delambre and Méchain helps to give us insight into the character necessary for the success (or failure) of a momentous scientific undertaking. Of Delambre as leader, a contemporary noted: “To complete such a task in the face of so many physical, moral, and political obstacles, it is essential that the expedition leader have this calm temperament, this tranquil joy, this perseverance” (Alder 2002, p. 219). Given the recent effort to define the body of knowledge and attitudes necessary for civil engineering practice (ASCE 2004), The Measure of All Things proves to be a timely lesson.

Alder holds off discussing the exact nature of the error until the end, and, while sometimes frustrating, added to the suspense that drove me to finish the book. How Alder treats this error is admirable in that it provides insight into the nature of science, indeed the transformation from savant to scientifique or scientist. As the reader later learns, the data meticulously and obsessively gathered by Méchain helps give birth to the method of least squares by the scientist Legendre (although independently arrived at in Germany by Gauss) and used by statisticians, scientists, and engineers to this day. As Alder writes:

Yet none of these great minds had ever treated their own data as rigorously as they treated the movements of the heavens or the shape of the earth. They averaged results, they looked for discrepancies, and they tossed out the data they considered unworthy of nature’s perfection. The question they asked one another was not which data to trust but whose. An honorable savant made himself personally responsible for the consistency of nature’s data, without defining what that consistency consisted of. What counts as an error? Who is to say when you have made a mistake? How close is close enough? Neither Méchain nor his colleagues could have answered these questions with any degree of confidence. They were completely innocent of statistical methods. (Alder 2002, p. 214)

Alder proves that he has a good grasp of the mathematics involved, providing a clear explanation written for the layperson. Our students will certainly understand and appreciate Alder’s explanation, for example, of the difference between precision and accuracy set in this context.

I leave it to the readers to enjoy for themselves the resolution of this error and the denouement of this well-told tale. It is a wonderful and much needed addition to works on the history of science and technology. Indeed, The Measure of All Things won the Watson Davis Prize from the History of Science Society. Much has been made about the necessity of providing a broad perspective for engineering students through a liberal education (see for example, Grose 2004). Engineering educators, practitioners, and students have at their disposal many chroniclers and commentators of the engineering enterprise, some from within the engineering community itself. Henry Petroski is a wonderful example of an engineer who closely chronicles and ponders the triumphs (and also the errors) of the engineering profession. David Billington and Samuel Florman provide the broad perspectives of aesthetics (and play), philosophy, and public policy that place the engineering endeavor squarely in the midst of the human experience. Alder provides yet another perspective from which we might “triangulate” the place of engineers in this world through the telling of a rich and engaging story that shows in part how the government and economy impact our work as engineers and scientists, how local communities hurt or hinder our progress, how technological change is accepted or rejected by communities and nations, and how, on a smaller scale, individual attitudes and character affect the success or failure of a scientific or engineering mission. As the engineering and engineering education communities continue to discuss the liberal education of engineering students, these types of works are necessary not only for our students but also for professors to remind them that sometimes (maybe oftentimes) that what we take for granted in our profession is interesting and significant enough to revisit.