Geometry/Labor = Volume/Mass?*

DARCY GRIMALDO GRIGSBY

This is a story about geometry and engineering and also modern hubris. If someone, besides myself, is to be blamed for my title, it is Charles de Freycinet, although to be fair, he is merely an especially useful representative of late-nineteenth- century France.1 An engineer and graduate of the École Polytechnique, he like so many other engineers of this period was a successful politician during the Third Republic. Freycinet was Prime Minister four times between 1879 and 1892, senator for more than forty-three years, and coauthor of a key project for the national construction of some eighteen thousand kilometers of railway crisscrossing France. He also wrote a book on modern Egypt and a small lovely treatise called De l’Expérience en Géométrie (Of Experience in Geometry).2 I begin by quoting the latter at length: The bodies of Nature, particularly solid bodies, are the origin of the fundamental concepts of Geometry.

First we distinguish volume, that is to say the portion of space or the extension occupied by the body. To give it a concrete representation, one can imagine that the body is replaced by a very thin envelope which exactly reproduces the exterior form. . . . The ﬁrst abstraction made by Geometry consists therefore of retiring from the body its own

* This essay represents aspects of my new book, Colossal Engineering, and was funded by an Andrew W. Mellon New Directions Fellowship and a U.C. Berkeley Townsend Center Initiative Grant for Associate Professors. I would like to thank Professor Kathleen James-Chakraborty, architectural historian, for her suggestions as well as the engineers at U.C. Berkeley who have generously attempted to teach me the basics of structural engineering: Professor Gregory Fenves, Sebastien Payen, and especially Charles Chadwell, whose tutoring was essential. I am also indebted to my graduate research assistant Amy Freund and undergraduate research apprentices Adam Cramer and Elizabeth Benjamin. Adam Cramer also elucidated principles of mathematics and was wonderfully imaginative about the implications of my work. Audiences at the University of Southern California assisted me with their stimulating queries, especially Todd Olson, Vanessa Schwartz, Debora Silverman, and Nancy Troy. All translations are mine unless otherwise indicated. 1. On Freycinet, see Theodore Zeldin, France 1848–1945 (Oxford: Clarendon Press, 1973–77), vol. 1, pp. 589–90, 595, 627, 631–38, 646; see also Bruno Marnot, Les Ingénieurs au Parlement sous la IIIe République (Paris: CNRS, 2000). 2. Charles de Freycinet, La Question d’Egypte (Paris: Calmann-Lévy, 1905).

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material and leaving only the place it occupies in space. Contrary to Mechanics which . . . neglects the form of the body and retains only the mass, Geometry ignores the mass and only retains the form, which it supposes to be invariable after the disappearance of the matter. This abstraction seems to us very simple because we have been habituated to it. . . . But it is one of the boldest [abstractions] one can make, and it requires a very great effort of imagination. We need to withdraw from a body that which constitutes it, that by which it exists, and speculate on a sort of phantom. . . .

The body being thus led to a state of simple volume or geometric form, we envision its exterior contour, the ideal envelope which contains the volume, and we give the name of surface to this inﬁnitely thin skin, or better, to this appearance of skin under which it seems to us that the body still subsists. The surface is not at all material, it is . . . a “being of reason.” It is the separation between the body and the space which everywhere surrounds it. It is like the imprint that the body leaves in space after it has been removed from it. . . .

The suture of two [surfaces] to one another has received the name line. It is by an even larger effort . . . that one comes to conceive the existence of line, to isolate it from the surfaces which give it birth. It is the abstraction in the abstraction. . . . This ideal object . . . is figured to our eyes as an extremely thin thread whose thickness tends to disappear. But however far we go down this path of attenuation, our mind goes further still and perceives a line whose fineness defies all realization.

One degree further in abstraction and we create the point, the place of the encounter of two lines, as the line is the place of the encounter of two surfaces. We accomplish this wonder of seeing a being there where all elements of being have disappeared. . . . To make a concept rest on nothing, on the successive suppression of all conditions of reality, and at the same time to have such a need for this concept that it imposes itself on us at the most decisive occasions! We would not know how, without it, to mark the place, the position; it responds to our desire for precision and unity; it summarizes the object whose placement alone interests us. . . .

Consequently, the idea of matter must henceforth be excluded from these different concepts. They are beings of reason, but invincibly linked to the body itself.3

3. Charles de Freycinet, De l’Expérience en Géométrie (Paris: Gauthier-Villars, 1903), pp. 13–17. Italics in original.

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Freycinet begins with the body and subtracts its matter to achieve the abstract, emptied space with which most geometers begin. When he does so, he inverts Euclid’s procedure which still determines the teaching of elementary geometry today. Euclid began with the point as a self-evident entity and built progres- sively to line and plane and surface and body, even space, as various relations among points. By contrast, Freycinet sustains the materialist conception of geometry offered by Aristotle and repeated by France’s positivist philosopher Auguste Comte.4 Freycinet begins with our world of bodies and describes the excavation of an ideal space as an act requiring great effort: we might say labor. He underscores the fact that mechanics and transport are preoccupied with mass, with matter’s weight and substance, while geometers focus only on abstract volumes, surfaces, lines, and points—the spaces designated by paper-thin, vanishing skins, threads, and grains, which our imagination alone is capable of conjuring and ever further attenuating. Freycinet wrote about geometry as an engineer and was therefore fully cognizant of its “bold,” “wondrous,” “surprising” elimination of matter. Such an effort of imagination, he argues, becomes habitual, but geometry’s nonmateri- ality requires effort nonetheless. Geometry, Freycinet tells us, entails work: the eradication of mass in order to produce an ideal space outside time. But it also effaces labor altogether. Once you have slipped into the massless, timeless space of geometry, mass and time are no longer at issue.5 Nineteenth-century Frenchmen were enamored of geometry; they associated modernity with geometry’s bold, beautiful, pristine clarity. What varied was the extent to which they appreciated the difference between volume and mass. All four of the French monuments that concern me, the Suez Canal, Statue of Liberty, Eiffel Tower, and Panama Canal, required the elimination of mass; their modernity was tied by contemporaries to their emptied spaces. The relative success of the realization of these projects can be correlated to the alertness of their makers to the difference between geometry’s abstraction and the world’s matter. In this regard, engineers had certain advantages over those who mistook imagination, one could say geometry, for the world itself. But engineers also understood what Freycinet does not admit here: that geometry and abstractions like line could contain mass within their immaterial selves, at least for those who had been trained to see it. Geometry did not always leave physicality as far behind as Freycinet implies, but it certainly translated it. Many remained blind to the ways in which geometry’s lines could sequester material constraints.

4. On Aristotle’s Metaphysics, see B. A. Rosenfeld, A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, trans. Abe Shenitzer (New York: Springer-Verlag, 1988), p. 111; on Auguste Comte, Cours de philosophie positive (Paris, 1830–1842), see ibid., pp. 199–200; see also the discussion of the Austrian physicist Ernst Mach’s work of 1905 in ibid., pp. 201–02. 5. Freycinet discusses the absence of time and, thus, of transport in geometry; see De l’Expérience en Géométrie, p. 7.

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The French sculptor Frédéric-Auguste Bartholdi made his ﬁrst journey to Egypt in 1855 in the company of the Orientalist painters Léon Belly, Narcisse Berchère, and Jean-Léon Gérome.6 He produced extensive photographs while he was there; for instance, of the Colossi of Memnos and himself in Oriental drag, standing self-consciously beside Gérome. Bartholdi was repeating what by 1855 was a cliché—artistic rejuvenation in the Orient, but the Orient to which he traveled was a land already imaginatively subjected to French engineering. Masterminded by the diplomat Ferdinand de Lesseps, the Suez Canal set the stage for Bartholdi’s career in its scale and global ambition.7 Begun in 1854, the sea-level Suez Canal required nothing less than the excavation of seventy- four million cubic meters of earth, initially carried out by forty thousand workers using only pickets and baskets.8 Contemporaries were quick to compare its labor and cost to the building of the pyramids. For example, as Lesseps recounts in his Souvenirs, MacClean made another calculation; he says that to elevate in Europe a monument resembling the greatest pyramid of Giza would require 6. Pierre Provoyeur, “Artistic Problems,” Liberty: The French-American Statue in Art and History, exh. cat., New York Public Library (New York: Harper and Row, 1986), pp. 78–99; D’un Album de voyage: Auguste Bartholdi en Egypte (1855–1856), exh. cat. (Colmar: Association “Culture et Loisirs,” Musée Bartholdi, 1990). 7. On the Suez Canal, see Tom F. Peters, Building the Nineteenth Century (Cambridge, Mass.: MIT Press, 1996), pp. 178–202; Ferdinand de Lesseps, Lettres, journal et documents pour servir à l’histoire du canal de Suez, 5 vols. (Paris: Didier, 1875–1881). On Lesseps, see Ghislain de Diesbach, Ferdinand de Lesseps (Paris: Perrin, 1998). 8. Peters, Building the Nineteenth Century, p. 185.

Frédéric-Auguste Bartholdi. The Colossi of Memnos. 1855. Musée Bartholdi, Colmar. Photo: Christian Kempf.

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twenty-ﬁve million francs, and that the Suez Canal will represent a work (in displacement of earth and movement of materials) thirty times superior to that of the pyramid and it will cost only eight times what it would cost to build [the pyramid] today, that is, two hundred million.9 Thirty times the work, thirty times the matter that needed to be moved, but only eight times the cost of erecting the Giza pyramid in Europe today! The resemblance between two colossal projects of mass-moving in Egypt—pyramids and canal—under- scored the grand scale of Lesseps’s ambition, but it also heightened sensitivity to their similar conditions of labor. Lesseps was relying, after all, on Egyptian serfs. In 1863 with more than half of the remaining kilometers left to dig, the British, who had hoped to thwart the French canal from its inception, suddenly persuaded the Egyptian government to withdraw what it called its “slave laborers” from the project.10 The French company’s manpower abruptly dropped from forty thousand to less than six thousand men. Incredibly, the Egyptian government was forced to pay the Suez Canal Company eighty-four million francs in compensation.11 Enter modernization. The Suez Canal might have been aborted had not Lesseps and his engineers had recourse to machines that extracted earth and sand, bucket by bucket. Lesseps had, in a sense, sold “slaves” back to their original owner and bought machines with the income. Only the abolition of what the British called “slavery” led to modern mechanization, but mechanization of a remarkably simple sort.12 As an 9. Ferdinand de Lesseps, Souvenirs de quarante ans dédiés à mes enfants, 2 vols. (Paris: Nouvelle Revue, 1887), vol. I, p. 336, p. 225. 10. Peters, Building the Nineteenth Century, pp. 185–86. 11. S. C. Burchell, Building the Suez Canal (New York: Harper and Row, 1966), p. 121. 12. Peters, Building the Nineteenth Century, pp. 185–88.

“Dry Excavator” at the Suez Canal. Illustration in Louis Figuier, Les Nouvelles Conquêtes de la Science (Paris, 1883–85).

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engineer in charge indicated, “One of the advantages of the type of work we do lies in its utter sameness. Cubic meters follow one another, always the same.”13 This is not to imply that the dredging of the canal proceeded effortlessly. In fact, cubic meters are not always the same. Cubic meters, it is worth underscoring, are volumes, not measures of mass: they indicate the size of containers, not what they contain. Cubic meters can be airy or dense, wet or dry, slippery or sticky. At Suez, some silty kinds of sand adhered to the buckets and were extracted with difficulty. Everywhere, determining the ratio of water to sand was challenging and slowed the progress of the excavation. Nevertheless, machines manned by fewer men ultimately did the job and these machines did so in ways that minimized the difference between geometry and matter. The completed Canal replaces sand’s mass with an emptied volume, a great straight channel, which could thereafter be refilled. Bartholdi hoped to author a colossal sculptural punctuation to Lesseps’s out- sized engineering feat. The sculptor’s plan for an immense statue of an Egyptian peasant woman to serve as a lighthouse at the entrance of the Suez Canal stems from his first visit in 1856, although he did not officially propose the sculpture, grandiosely titled “Egypt Bringing Light to Asia,” until his return to Egypt in 1869 just prior to the celebratory opening of Lesseps’s canal. The Egyptian leader Ismaïl Pasha rejected Bartholdi’s plan.14 Disappointed but typically undaunted, Bartholdi recycled the colossal female sculpture six years later when he planned a 151-foot-high Statue of Liberty to overlook New York City’s harbor. Egyptian peasant and Republican

13. Ibid., p. 201. 14. Provoyeur, “Artistic Problems”; see also my “Out of the Earth, Egypt’s Statue of Liberty?” in Edges of Empire: Orientalism and Visual Culture, ed. Mary Roberts and Jocelyn Hackforth-Jones (forthcoming).

Left: Bartholdi. Egypt Bringing Light to Asia. 1869. Right: Bartholdi. Statue of Liberty as Lighthouse. Undated. Musée Bartholdi, Colmar. Photos: Christian Kempf.

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Liberty shared the same form and purpose, but Bartholdi consistently attempted to repress his later statue’s origins. Not only did he eliminate the pyramidal base of the New York statue, but he also deeply resented and lashed out at those who drew attention to Liberty’s Egyptian predecessor. He defended Liberty by dis- tinguishing between what he claimed were the self-interested motives of the Egyptian statue and the selfless motives of the New York City statue: “My Statue of Liberty was a pure work of love. . . . The Egyptian affair would have been purely a business transaction.”15 But of course the Statue of Liberty was nothing if not an ambitious, fund-raising, entrepreneurial venture that required great revenues and organized manufacture by an extensive labor force. Lesseps eventually served as one of Bartholdi’s key promoters. Egypt’s monuments had played a determinant role in Bartholdi’s conceptu- alization of the role that sculpture could play in the vast engineered spaces of modernity. Egypt had prescribed monu- Statue of Liberty up to the waist. mental gigantism, but Bartholdi ultimately 1881–84. Musée Bartholdi, Colmar. Photo: Christian Kempf. turned to modern construction in order to trump Oriental monumentality. The sculptor had originally entrusted the architect Eugène Viollet-le-Duc to make his colossus stand; the architect had planned to fill the statue with sand-filled metal coffers, thereby updating the stone core of early colossal sculptures.16 Viollet-le-Duc’s death led Bartholdi to seek out the young, accomplished engineer Gustave Eiffel, who replaced the solid sand-filled interior with a relatively inexpensive, simple iron armature on which thin sheets of copper would hang.17 In contrast to antiquity’s reliance on stone mass, the Statue of Liberty, with the help of Eiffel, became a hollow giant that could be built in Paris, dismantled, shipped in labeled cartons across the world, and reassembled.

15. Provoyeur, “Artistic Problems,” p. 92. Bartholdi was replying in the press to charges in the New York Times. See also Frédéric-Auguste Bartholdi, The Statue of Liberty Enlightening the World (1885) (New York: New York Bound, 1984), p. 37. 16. Such as the seventeenth-century, sixty-foot-high statue of Saint Charles Borromeo in Arona. 17. Pierre Provoyeur, “Technological and Industrial Challenges,” in Liberty: The French-American Statue in Art and History, pp. 106–19.

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After all, weren’t the Egyptian colossi and pyramids strikingly old-fashioned in their reliance on stone and mass as the means to achieve immense scale? Was not the modernity of the Suez Canal, by contrast, defined by its colossal excision of mass? The pyramid betrayed in a photograph of the canal represents the achievement of engineered emptiness, an emptiness that permitted transport and commerce as well as empire. Lesseps’s feat in Egypt was to have removed earth, not to have amassed it. Engineering’s redefinition of Bartholdi’s sculpture made it more like a canal, more like a passageway. The visitor to the Statue of Liberty was invited to ascend her colossal height by entering the sole of her foot or to wander inside her head. Emptied volumes permit traversal. What is striking about Bartholdi’s bold and modern project, however, was the extent to which he did not author its radical elimination of mass. Equally astonish- ing was Bartholdi’s blithe confidence that his one-meter, promotional model blown up some fifty times would be structurally feasible. Bartholdi simply did not think in terms of structure. He did not worry about how the hell the thing would stand. He thought in terms of form, surface, and aesthetic impact; he spoke of the need to simplify drapery and to keep planar surfaces broad.18 The sculptor thought as a sculptor, and for this reason he also adhered to traditional methods of making and enlarging sculpture. He turned, for surface, to a foundry, Gaget and Gauthier; and for structure, to an architect and, later, to an engineer.19 His presumption was that artisan-experts with the assistance of designers could make his aesthetic object beautiful, erect, permanent, transportable, and also colossal. How was the sculpture made?20 A series of magnifications were executed from a model designed by Bartholdi: the first a little taller than a meter, the 18. Bartholdi, The Statue of Liberty, p. 42. 19. Provoyeur, “Technological and Industrial Challenges,” pp. 97–98. 20. Bartholdi, The Statue of Liberty, pp. 43–52. See also J. B. Gauthier, “La Statue Colossale: La Liberté éclairant le monde,” in La Plomberie au XIX siècle (Paris: Imprimerie Chaix, 1885), pp. 18–21.

Anonymous photograph of the Suez Canal. Reproduced in The Suez Canal: Notes and Statistics (London, 1952).

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second almost three meters, the last about eleven meters high. Each magnifica- tion entailed the traditional, laborious gridding of measurements, or points, which mapped the complex, swelling, irregular shape. It was a system that relied on geometry, but which remained three-dimensional, tactile, and physical. Objects became bigger objects: no calculation other than multiplication was needed. Carpenters built the boxlike frame and men proceeded to measure. If the distance from tip of head to elbow was a given measure, this needed to be multi- plied so many times. The biggest eleven-meter model was then divided into fragments that were enlarged about five times to create the 151-foot-high final work. The foundry’s report emphasized the workers’ physical enactment of geometry: One makes thereby the definitive form by the principles of geometry in space, by locating a considerable number of points determining the lines and surfaces. On the contours thus established, marked by the heads of nails more or less driven into the plaster, the artist finished the work . . . by bringing into line and making flush all the marks, as is done with the mise au point of sculpture.21 After carpenters made broadly accurate, hollow wood enlargements of each section, plasterers covered and refined them by matching precisely some nine thousand measured points. Point after point, swelling planes were thereby defined. Once the immense plastered section was completed, carpenters returned to execute a grid-like wooden mold that corresponded at every point to the plaster: thus an inverse of the entire statue, a mold, was made out of wood. Gaget and Gauthier rightly attempted to convey how laborious and impressive was this process: Layer by layer, one has, one could say, sculpted in wood the statue itself in all its parts and, if, by some means, one could have reunited these pieces by placing them in their respective positions, one would have in the interior the spectacle of a statue sculpted negatively like a mold, a gigantic mold representing thousands of pieces of wood sawed, cut, tried, sized and hammered . . . adjusted, nailed without an appreciable mistake, without an error.22 In his geometry treatise, Freycinet emphasizes that surface, the ideal envelope that contains the volume, can be imagined as an “infinitely thin skin,” an “imprint that the body leaves in the space after it has been removed from it.” The photographs of the Gaget and Gauthier workshop dramatize how laborious it was to manufacture such a skin. They also demonstrate that one can imagine the surfaces of volumes from inside and out. The cumbersome wooden molds were an imprint, but they offered a view of the sculpture’s surface only as seen from its interior. By contrast, the copper sheets, which were subsequently hammered

21. Gauthier, “La Statue Colossale,” p. 20. 22. Ibid.

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/016228703322791007 by guest on 28 September 2021 Top: The wooden hand of the Statue of Liberty in the Gaget and Gauthier workshop, Paris. 1878–1884. Right: The plaster arm and hand of the Statue of Liberty in the Gaget and Gauthier workshop, Paris. 1878–1884. Musée Bartholdi, Colmar. Photos: Christian Kempf.

onto them, at last attained the thinness required for substance to serve as a skin both without and within. The copper sheets cladding the Statue of Liberty are only two and a half millimeters thick. Relative to the statue’s size, they are a very thin surface. The wonderful, crowded, and disorienting photographs of the sculpture’s construction indicate, however, that the hollowing out of Bartholdi’s solid plaster models necessitated the appearance and disappearance of vast amounts of different kinds of material: wood, nails, cords, rulers, wires, weights, plaster, trowels, wood and

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nails again, copper, hammers, and chisels. The process of hollowing also required the impressive expertise of numerous artisans who specialized, not in excavation, but in specific kinds of construction. And yet none of this accomplishment addressed or answered the problem of the statue’s erection. In the real world of things, unlike the abstract, typically drawn, space of geometry, the skins of hollowed solids will not necessarily stand. Surfaces, in and of themselves, are not self-supporting. (Thus the humor of Claes Oldenburg’s soft sculptures.) Enter Eiffel, the engineer. And enter geometry and calculation not in the workshop, not in space, but on paper. This is the paradox that most interests me. Geometry is an analysis of abstract entities best conceived in ideal space and best explored on paper. Geometry, as Freycinet points out, typically excludes the notion of matter, despite the fundamental relation it bears to bodies in space. When the artisans making the Statue of Liberty restricted their uses of geometry to our three-dimensional space and moved and managed actual matter in that space, even to constitute surfaces through points, they would seem to have materialized the dangerously immaterial methods of geometry. Here was geometry returned to mechanics, to problems of mass and gravity. Yes, to some extent, but the Gaget and Gauthier workshop was littered with immense sheets that were only fragments of the body designed by Bartholdi. The question was how to reassemble the whole. The workers’ physical manipulation of parts may eventually have led to a structural solution, but not necessarily and certainly not quickly. (Appreciate Gaget and Gauthier’s conditional phrase “If, by some means, one could have reunited the pieces.”) Eiffel was remarkably efficient and successful, and he was both because of the key role of drawing as a site of experimentation and calculation for engineers. As we have seen, Bartholdi had made several sketches when he initially conceived his sculpture, but once execution began, all drawings stopped because Gaget and Gauthier were able—indeed inclined—to work from three- dimensional, not two-dimensional, models. The problem with three-dimensional models, however, is that they do not anticipate, predict, or control the effects of dimension.23 A two-inch-tall Statue of Liberty is subject to different forces, stresses, and strains than a two-mile-high Statue of Liberty. To blow up the skin of Bartholdi’s eleven-meter model was not to know whether it would stand or how to make it do so. Physical translation from one size to another seems, to the untrained like myself, such an anchored means to insure the realism of the product—it seems to guarantee a material solution. And yet even the ancients were confounded to find that the behavior of catapults could not be predicted from small-scale models: matter’s behavior changes according to its size.24

23. Edwin T. Layton, Jr., “Escape from the Jail of Shape: Dimensionality and Engineering Science,” in P. Kroes and M. Bakker, eds., Technological Development and Science in the Industrial Age (Netherlands: Kluwer Academic Publishers, 1992), pp. 35–68. See also Barbara Rose, “Blow Up---The Problem of Scale in Sculpture,” Art in America 56 (1968), pp. 80–91. 24. Layton, “Escape from the Jail of Shape.”

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As one engineer explains it to the layman: The difﬁculty is that models are all very well if one just wants to see what the thing will look like, but they can be dangerously misleading if they are used to predict strength. This is because as we scale up, the weight of the structure will increase as the cube of the dimensions; that is, if we double the size, the weight will increase eightfold. The cross-sectional areas of the various parts which have to carry this load will, however, increase only as the square of the dimensions, so that, in a structure of twice the size, such parts will have only four times the area. Thus the stress will go up linearly with the dimensions, and, if we double the size, we double the stress and we shall soon be in serious trouble.25 “If one just wants to see what the thing will look like” summarizes Bartholdi’s strangely exteriorized and visual perspective on the immense sculpture he hoped to build. What engineers knew, and sculptors like Bartholdi did not, was how to predict the variable effects of dimension (the above “square-cube law,” for example) and they did so in drawings, which analyzed not only weight and gravity, but also force, loads, stress, shear, fatigue, air resistance, and temperature changes. Their job was to combine geometry with physical conditions, to take into account not just shape or volume, but also mass and the physical force of immaterialities like wind, heat, or cold. The only drawings that I have found pertaining to the execution phase of the Statue of Liberty are Eiffel’s drawings, and they show a structure radiated by lines of force. Eiffel knew that the colossal statue would be plummeted by wind and that its metal skin would expand and contract with changes of temperature. Unlike Bartholdi, Eiffel knew that he needed to allow the statue to breathe in order to make it stable. (Material surfaces, even those of the sculpted body, cannot always be ﬁxed, given that they must exist in the world’s variable conditions.) The engineer knew what he knew because he was a scientist and an experienced maker of bridges and viaducts—one of which collapsed in 1884, a failure from which he, like all engineers, learned.26 Eiffel straddled concept and materials, theory and practice, volume and mass. An 1889 poster pretended that he was a manual laborer who also drew.27 This was not the case: he was an engineer who drew and who told other engineers, including draftsmen, and manual laborers

25. J. E. Gordon, Structures or Why Things Don’t Fall Down (New York: Da Capo, 1978), p. 192. Gordon adds that “we can neglect the square-cube law with most masonry buildings because . . . the stresses in masonry are so low that we can afford to go on scaling them up almost indeﬁnitely.” Thus the Colossi of Memnos and the Egyptian pyramids ill-prepared Bartholdi to take seriously this structural problem of dimension. 26. Bernard Marrey, La Vie et l’oeuvre extraordinaires de Monsieur Gustave Eiffel ingénieur . . . (Paris: Graphite, 1984), p. 61. 27. Reproduced in Musée d’Orsay: Catalogue sommaire illustré du fonds Eiffel (Paris: Réunion des Musées Nationaux, 1989), p. 19.

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what to do. From what these workers made, he learned whether his drawings had successfully predicted how matter of a speciﬁc sort and shape behaves at a certain scale under certain conditions. Eiffel’s preparatory drawing for the armature’s design is entirely unlike the process by which Bartholdi imagined the sculpture’s construction. Here, instead of a three-dimensional model, a solid mass laboriously translated into material surfaces, we confront an emptied two-dimensional contour drawing of the sculpture’s shape. That shape is divided evenly into cross sections that provide the basis for calculations of the impact of wind on the structure and the means to design the armature needed to make it stand. The statue’s contour, its swelling variable shape, matters here only to the extent that it determines the amount of surface area exposed to the wind (these variable surface areas are indicated by the numbers straddling the armature’s crossbeams; for example, section twenty-one, at the bottom, is labeled “s=21m80”). The emphatic, thick, black line tracing the contour of Bartholdi’s statue thus counts not as image, nor as body, but as a

Gustave Eiffel. Drawing of the armature for the Statue of Liberty. Published as plate 1 in Le Génie Civil (August 1, 1883). Courtesy Science, Industry & Business Library, The New York Public Library, Astor, Lenox, and Tilden Foundations.

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sequence of two-dimensional areas (square meters) subjected to the impact of force (wind stopped and turned into pressure). The beautiful, most continuous, arcing curve plotted closest to the statue and titled “Courbe des moments ﬂéchissants dus au vent” (curve of the bending moments due to wind) shows us the increasing burden borne at the statue’s base. Although wind exerts progres- sively more force on the structure as it rises, its pressure is carried by the structure’s base, which must prevent it from turning over. In engineering terms, “the bending moment” is necessarily largest at the statue’s base because only there does the structure bear the entire cumulative force of the wind. Eiffel’s drawing does not show how he will solve the problem, but it indicates the extent to which his calculations for the armature take into account the statue’s envelope as exposed surface area but fully disregard the surface’s physical object- hood: there is no notation of the weight of all of those hammered copper sheets. Rather, the armature must answer a structural problem in which surface as a thing matters not at all. In this drawing, surface is only an exposed square area subjected to force. Eiffel’s computation relies here on static graphical analysis. In the drawing’s right half, the three sloping lines graph different kinds of force that are determined geometrically. The ghost of that process is recorded in the many dashed lines subdividing the drawing. Static graphic analysis refutes the elementary model of geometry proposed by Freycinet. As Freycinet well knew, engineers and geometers from mid-century had come to appreciate that calculations of force could be determined geometrically, not simply arithmetically.28 Moreover, geometry was often far more efﬁcient than numerical calculation.29 Geometry was also consummately visual. At a glance, an engineer could appreciate the forces with which he needed to contend. In static analysis, a line represents not the edge of a thing that had been evacuated—a line here is not the intersection of surfaces, as Freycinet would have it—but forces: pressures like wind or gravity or someone pushing. Draw several vectors pointing in different directions. Then, if you want equilibrium to be achieved, let us say, in a structure so that it remains standing, connect the vectors to one another (so that each vector’s point meets the next vector’s end) and supply the missing line that connects one side of the polygon to another. Point this arrow in the opposite direction of the other vectors.30 You have determined the size and direction of the countervailing force required to balance

28. In his 1881 Graphical Determination of Forces in Engineering Structures, for instance, “Chalmers emphasized the underlying geometric concept of engineering designs, remarking that structures are geometric forms whose forces, governed by the law of statics, act along geometric lines. Of the engineer he said, accordingly, ‘It is natural that he strove to follow a train of geometric thought’” (T. M. Charlton, A History of Theory of Structures in the Nineteenth Century [Cambridge: Cambridge University Press, 1982], p. 58). 29. Ibid. 30. The sides of a polygon of forces “represent in magnitude and direction a system of concurrent forces in equilibrium”; “it was not long after the adoption of the metal framework (including trusses) for structures that powerful graphical methods of analysis were developed on the basis of the triangle and polygon of forces” (ibid., pp. 59–60).

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Polygon of force. Published as plate 1 in Maurice Lévy, La statique graphique et ses applications aux constructions (Paris, 1874). Vectors 1 and 2 are assembled point to tail as OC and CA. The closing vector is OA with A as the point; that is, OA opposes the direction of vectors OC and CA and thus represents the countervailing force that establishes equilibrium.

the vectors of force with which you began. Overall shape in polygons of force is entirely arbitrary (you can arrange the given vectors, point to end, in whatever order you choose and the answering vector will be the same). In polygons of force, shape encloses nothing, no core whether full or empty. Rather, the game is one of offsetting angled lines understood as force (or action) by closing them into a shape. The last line that turns a series of vectors into a closed shape is the answer. It tells you how to make a structure conform to Newton’s law: stasis means that for every force there is a counterforce. Stasis is what we want in all buildings and most sculptures, especially colossal ones, and stasis in the engineer’s model of proliferat- ing forces must be carefully achieved. It is not the place from which we start as in Freycinet’s body, but the place at which we end after the hard work of determining a counterforce to every force, or more likely, to a series of forces. For engineers, we discover, stasis—the body at rest, the standing structure—is a profound accomplishment. The chair is being pushed up by the ﬂoor. Does Eiffel, in this drawing, disregard mass as thoroughly as did Bartholdi? No, not precisely. Instead mass is translated into force, which is the measure of mass accelerated. Force in this diagram is the means by which mass is reintroduced to an evacuated Statue of Liberty, but the force in this particular drawing is the force of the wind. Thus mass is hidden in that which we most associate with immateriality, not only the abstraction “force,” but wind’s elusive surge (rather than gravity’s ponderous weight, for example). In other drawings, the weight of those copper sheets and the iron crossbars were surely taken into account. This design only assesses the demand that the wind places on the structure, not the required answering forces, which would include the force of gravity, the weight of mass.

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What astonishes me thus far is the extent to which I cannot make Bartholdi’s Statue of Liberty and Eiffel’s Statue of Liberty meet. Bartholdi began with mass, the solid sculpted model, and then excised its core, leaving an atelier crowded with fragments of surface, those thin but nonetheless cumbersome and substantial copper sheets (weighing more than 160,000 pounds).31 Eiffel began with surface as a series of computed areas, so many square meters—21m80, 21m00, 18m10, 18m20, 18m40, 18m60, 18m40, and so on. Maximally attenuated in Freycinet’s terms, surface area does not participate in the materiality of the outer limit of a thing; it is a size not a substance. Moreover, the continuous transition between the discrete sections of surface area (between 21m00 and 18m10, for example) is only perfunctorily signaled in Eiffel’s drawing by the black outline of the statue. The continuity of the sculpture’s surface is of no signiﬁcance to his computation. The structural engineers with whom I have consulted all concur that they would not have expected Eiffel to make much of the statue’s shape; a column would offer an adequate approximation for these calculations. This disregard for the colossal sculpture’s shape, and in this drawing even for its mass, is stunning to me, especially given its dramatic contrast to Bartholdi’s process, which privileged shape— the surface—above all else and also the onerous procedure by which surface must be constructed. Eiffel assumed an emptiness, which he would ﬁll with structure. The container of that emptiness was only of slight importance to him. What mattered most in this context was the container’s size, height, and surface area. The forces on that size and area would be received and answered by the armature’s crossbeams, by Eiffel’s structure, which concentrated and answered their force. The outer envelope in such a model almost seems transparent; it is certainly useless. And as the envelope approaches transparency, the accomplishment and labor of all those artisans in the Gaget and Gauthier atelier also strangely disappear.

The Eiffel Tower was quite consciously intended to dwarf Bartholdi’s creation, as can be seen in a drawing by one of Eiffel’s employees. Not surprisingly, the engineer sought to free engineering from its role as hidden helpmate to other artistic and architectural forms and to trump the most recent and spectacular colossus to have loomed over Paris. If Bartholdi repeated ancient Egyptian ﬁgural gigantism, Eiffel would make what he repeatedly called a modern “pyramid” of such enormous proportions that Bartholdi’s colossal woman would come to appear human-scale, sadly perched on top of the cathedral of Notre Dame. Eiffel’s 300-meter-high modern pyramid was almost ten times the size of Bartholdi’s giant, and twice as high as any extant structure. Neither his inspiration nor his ambition were lost on his contemporaries. Numerous laudatory poems and a number of 1889 prints pair Tower and the

31. Bartholdi, The Statue of Liberty, p. 52.

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32. The hundreds of celebratory letters and poems sent to Eiffel in 1889 include dozens of references to Egypt’s pyramids; see Fonds Eiffel, Musée d’Orsay. 33. Reproduced in Henri Loyrette, Gustave Eiffel (Paris: Payot, 1986), p. 11. 34. Fonds Eiffel, Musée d’Orsay, ARO 1981–1286; cited in Daniel Bermond, Gustave Eiffel (Paris: Perrin, 2002), p. 277. 35. Michel Serres, Statues (Paris: Édition Bourin, 1987), pp. 128–29; Roland Barthes, The Eiffel Tower and Other Mythologies, trans. Richard Howard (New York: Hill and Wang, 1979).

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engineering needed to erect a structure more colossal than the monuments of Egyptian antiquity. Its job was also to make that engineering, no longer sequestered within a beaux-arts female shell, a monument to be climbed in ways that recreated its making, its vertical surge, its achievement. While Michael Baxandall has distinguished painting from the engineering of bridges by pointing to the ways pictures direct attention to the process of their making, Eiffel devised an engineered monument that forced awareness, a girder at a time, of its construction, a construction determinant and constitutive of its ﬁnal form.36 There is a discrepancy, however, between the visitor’s awareness of the fabri- cated, constructed nature of this engineered product and his or her awareness, then and now, of the kinds of labor it required. Look at the startling difference between the photographs of the cluttered, inhabited Gaget and Gauthier workshop and the most famous photographs of the construction of the Eiffel Tower. Between January 1887 and May 1889, Eiffel’s modern pyramid was erected so efﬁciently it seemed to rise miraculously, even inevitably, without the hand of

36. Michael Baxandall, “The Historical Object: Benjamin Baker’s Forth Bridge,” in his Patterns of Intention: On the Historical Explanation of Pictures (New Haven: Yale University Press, 1985), pp. 12–40.

Anonymous. Construction of the Eiffel Tower as seen from one of the towers of Trocadero Palace (two of twenty photographs). 1888–1889. Musée d’Orsay, Paris, Fonds Eiffel. Réunion des Musées Nationaux/Art Resource, New York.

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man. The medium of photography perfectly matched this technological feat. Machine seems to capture self-generating machine. Look at these photographs and listen to the astute diplomat and critic Eugène-Melchior de Vogüé37 writing in 1889: From the second platform . . . the work of the construction escaped our view. . . . We [only] saw the sky redden from the fire of a forge, we barely heard the hammers which riveted the iron fittings. . . . We almost never saw the workers on the Tower; [it] rose alone, by the incantation of genii. We associate the great works of other ages, like those of the pyramids for example, with the idea of human multitudes, pressing hard on levers and groaning under cables; [this] modern pyramid was raised by a spiritual command, by the power of calculation requiring a very small number of hands; all the force needed for its elevation seemed to have been drawn in a mind which operated directly on the material. It required few people and there was hardly any action at the worksite because there never was a stroke of a file or a strike of a chisel; every one of these ribs of iron—numbering 12,000—arrived perfect from the factory and came to be added to the prescribed place in the skeleton without any welding. Over many years, the Tower had been assembled in the head of the geometer and realized on paper; all that was needed was to prepare the infallible drawing in cast iron. Here, at least, was what mathematicians call an “elegant demonstration.” . . . One admires above all the visible logic of this construction, the accordance of the parts with the result to be attained. In every logic that has been translated to the eyes, there is an abstract, algebraic beauty. . . . 38 In 1889, the French engineer Emile Cheysson had also marveled at the accomplishment of the Eiffel Tower, but he rushed immediately to anxieties concerning the workers who had made it: When [the visitor] admires this audacious tower, the highest pedestal that man up to this point has known how to erect by his hands . . . a thought arises, which . . . can no longer be ignored: [the visitor thinks] of the men to whom is owed all this magnificence, [he thinks] of their material condition, of their state of morale. Here is a new world which comes into view, that of iron and of grand industry. What does it do to these actors? The peasants once sacrificed by the pharaohs have spoiled the pyramids for us.39

37. On Vogüé, see Jennifer Shaw, Dream State: Puvis de Chavannes, Modernism, and the Fantasy of France (New Haven: Yale University Press, 2002), pp. 119–21, 165–75. 38. Vicomte de Vogüé, Revue des Deux Mondes ( July 1, 1889), pp. 194–95. 39. Emile Cheysson, L’Economie sociale: L’Exposition universelle de 1889. Communication faite au Congrès d’économie sociale, le 13 juin 1889 (Paris: Librairie Guillaumin, 1889), p. 5.

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Cheysson, the Frenchman famous for the invention of social engineering, the expansion, that is, of engineering to include conditions of labor, asked his readers whether the Eiffel Tower would be ruined for us as well.40 Scale, according to Cheysson, did not divide West from East, nor present from past. Immensity was not new, but what may have been were the means of manufacture, the working conditions that either spoil a monument or make it worthy of celebration. Was the price of erecting the Eiffel Tower too high in terms of human suffering? Vogüé offered one answer to Cheysson’s queries: if the Egyptian pyramids had been ruined for us by the peasants who groaned under its cables, the modern pyramid did not require the oppression of multitudes (note how persistently Egyptian pyramids come to mind as the means to discuss labor). According to Vogüé, the Tower was a demonstration of the mathematician’s calculations on paper and required little physical exertion at all. Vogüé knew of what he spoke: all the measurements enacted in the actual space of the Gaget and Gauthier foundry were here enacted on paper away from the site and also prior to the site. Solutions were not improvised by experienced artisans; instead, decisions were made by men with pencils in hand. Among the effects of engineering’s “separation of thinking from making” is the splitting up of the process of production, the increase in scale made possible by directing workers from above, and the speed of production. According to a twentieth-century engineer, “The effect of concentrating the geometric aspects of manufacture in a drawing is to give the designer a much greater ‘perceptual span’ than the craftsman had. The designer can [thereby] see and manipulate the design as a whole. . . . Using his ruler and compasses he can rapidly . . . predict the repercus- sions that changing the shape of one part will have upon the design as a whole.”41 Vogüé underestimated the Eiffel Tower’s number of “iron ribs”—there were eighteen thousand, not twelve thousand, and each one had been drawn over a period of two years by forty of Eiffel’s calculators and draftsmen. Those 5,300 drawings indicated the dimension and shape of each piece as well as the position of every one of the tower’s 2.5 million rivet holes to one tenth of a millimeter.42 Here are the kinds of drawings typically discussed when considering the role of drawing in engineering: those “views from nowhere,” perspectiveless, orthographic rendi- tions that best serve as templates for making things since they do not distort form according to a particular point of view.43 Shapes par excellence. At an off-site

40. See Bernard Kalaora and Antoine Savoye, Les Inventeurs oubliés: Le Play et ses continuateurs aux origines des sciences sociales (Paris: Champ Vallon, 1989), p. 175; Paul Rabinow, French Modern: Norms and Forms of the Social Environment (Cambridge, Mass.: MIT Press, 1989), pp. 170–78. 41. J. Christopher Jones, Design Methods: Seeds of Human Futures (London: Wiley-Interscience, 1970); cited in Ken Baynes and Francis Pugh, The Art of the Engineer (Woodstock, N.Y.: Overlook Press, 1981), p. 11. 42. François Poncetton, Eiffel: Le magicien du fer (Paris: Éditions de la Tournelle, 1939), p. 186; also see Bernard Lemoine, La Tour de Monsieur Eiffel (Paris: Découvertes Gallimard, 1989), p. 38. 43. Thomas Nagel, The View from Nowhere (Oxford: Oxford University Press, 1986); cited in Lorraine Daston, “Objectivity and the Escape from Perspective,” Social Studies of Science 22 (1992), p. 599. See also Ken Alder, Engineering the Revolution: Arms and Enlightenment in France, 1763–1815 (Princeton: Princeton University Press, 1997), especially pp. 127–62, 292–318. As Molly Nesbit has argued, education

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factory, 150 workers prefabricated each piece according to these drawings’ specifi- cations; the pieces were then inspected and, if necessary, remade at the factory. While concurrent nineteenth-century engineering projects like the Forth Bridge discussed by Baxandall entailed continual improvisations, design alterations, welding and manufacture on site, Eiffel seized full control of his tower’s construction through the medium of drawing.44 The Eiffel Tower is a monument to modern manufacture, to prefabricated assembly. The job of Eiffel’s employees on the Champ de Mars was, above all, the placement of iron pieces and the insertion of rivets into predetermined holes. I exaggerate, of course. Stone foundations for the tower’s four piers needed to be excavated and built. Wooden scaffolding needed to be constructed until the tower became self-supporting after the first platform. Vogüé correctly emphasizes that the higher the tower rose the less it seemed a matter of men’s labor; workers were progres- sively reduced in number and also in visibility to those on the ground. We are therefore right to look at the Eiffel Tower and to see, like Vogüé, a drawing remade in iron. The Tower is a structure whose height is made possible by its radical reduction of mass, the maximal attenuation of matter, iron, into line. Moreover, Vogüé was exactly right to describe the tower as an elegant mathematical demonstration. Eiffel was designing a structure in which the bending moment (or risk of overturn) produced by the force of the wind was exactly offset by the opposing bending moment produced by the force of gravity (that is, the structure’s weight).45 This balance can be expressed as a calculus equation wherein one bending moment must equal the other: ∫ h 2 ∫ h 0 4Df (x)f0 (x) = 0 2Pf (x) xdx But such an equation in all its opacity (it cannot signify, for example, unless I define its terms) was not how Eiffel and most French engineers conceived of engineering problems and their mathematical expression. In 1889 Eiffel and his employees would have relied on the graphical analysis we have already seen in Eiffel’s drawing for the armature for the Statue of Liberty. That is, they relied on the efficient visualization offered by geometry.46 Look back at the arc indicating the demand of “the bending movements due to the wind.” That curve is the shape of the Eiffel Tower itself. The Tower is a materialized graphing of the

reforms during the Third Republic included mandatory drawing education for all children, which included both perspective drawing (what we see) and orthographic drawing (what we know). Nesbit has importantly elucidated the gender implications of this program in “Ready-Made Originals: The Duchamp Model,” October 37 (Summer 1986), pp. 53–64, and in “The Language of Industry,” in The Definitively Unfinished Marcel Duchamp, ed. Thierry de Duve (Cambridge, Mass.: MIT Press, 1991), pp. 351–84. 44. David P. Billington, The Tower and the Bridge: The New Art of Structural Engineering (Princeton: Princeton University Press, 1983), p. 65. 45. Joseph Gallant, “The Shape of the Eiffel Tower,” http://faculty.trumbull.kent.edu/gallant/eiffel_tower.html. 46. Specifically that of Carl Culmann, disseminated in France by Maurice Lévy in his La statique graphique et ses applications aux constructions (Paris: Gauthier-Villars, 1874), as well as by Eiffel’s employee, the engineer Maurice Koechlin, who was trained by Culmann. See Charlton, A History of Theory of Structures, pp. 170–71; Maurice Koechlin, Les applications de la statique graphique (Paris: Librarie Polytechnique Baudry, 1889).

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statue’s bending moment; it demonstrates how structural form follows the equilibrium of forces.47 Thus the Tower’s very form efficiently answers the force of the wind. Eiffel needed to maximize the weight at its base where exposure of surface area to wind is negligible, but where the risk of rotation due to the cumulative impact of the wind across the structure’s entire height is most acute. He also needed to minimize the surface area at the tower’s top where the force of the wind is greatest. Thus the Tower’s tapering shape, which at every point establishes the optimal equilibrium between the bending moment due to wind and the bending moment due to weight (like a suspension bridge in which the curve of the flexible cables responds at every point to the required load, no more, no less). The Eiffel Tower is what engineers call a funicular structure: every one of its sections bears and answers precisely the same load. Funicular structures are therefore optimally lean and strong. No part of the structure is stronger or weaker than it need be. In the Eiffel Tower, therefore, lines of iron are not just the means by which the structure is built; they are fully determinant of its very form. Eiffel himself described the tower’s structural answer to prevailing forces in a language that seems to move between drawn and material lines: All the cutting force of the wind passes into the interior of the leading edge of the uprights. Lines drawn tangential to each upright with the point of each tangent at the same height, will always intersect at a second point, which is exactly the point through which passes the flow resultant from the action of the wind on that part of the tower situated above the two points in question.48 A “mathematical demonstration” indeed, but an engineering one as well. And significantly, this mathematical demonstration was conceived geometrically, not algebraically (as lines, not equations). Engineers were trained to see forces and a structure’s answer to those forces in geometric terms, and it was consummately easy, perhaps inevitable, that this visualization would come to be seen as a template, a model for physical structure itself. Stare at those graphed curves long enough and they might transmute into form. Lightness is the achievement of funicular structures. Eiffel continually boasted that the Tower put little pressure on its foundation, no more, in fact, than a person sitting on a chair, about three or four kilograms per square centimeter. One writer has pointed out that the air inside a cylinder of the same breadth and height would weigh almost as much as the iron structure.49 Nonsense to me, but

47. Conversation with Professor Gregory Fenves, March 3, 2003. Not many structures do this; exceptional are suspension bridges, the Eiffel Tower, and Chicago’s John Hancock Tower. 48. Gustave Eiffel, La Tour de Trois Cent Mètres (Paris, 1900); cited in Gallant, “The Shape of the Eiffel Tower,” p. 2. 49. “Eiffel’s use of wrought iron in an open-lattice design produced such an extremely light structure that the Tower has approximately the same weight as the air that surrounds it. The mass of the air in a box

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correct, and also evocative of how much contemporaries admired the emptiness of Eiffel’s structure; his radical transformation of iron mass into empty volume. Yet it is wrong to describe the Eiffel Tower as an empty volume; this implies, à la Freycinet, that the mass was extracted to leave a volume defined by surfaces. Instead, the Tower’s form is rendered maximally light, efficient, and visible because it is not clad by surfacing: no copper sheets, no beaux-arts woman, not even a circum- scribing container like a cylinder or box. Remove the container and the spread of the Tower’s base can be determined by the desired height rather than by the stride of a sculpted woman. Eiffel was able to elevate his structure ten times the height of the Statue of Liberty because he could greatly widen the distance between its surging piers and, equally importantly, he could deprive the wind of surface area. The Tower radically minimizes surface area because it is conceived as vectors of force rather than as an emptied mass. Freycinet’s empty volumes will not stand at a colossal scale. They are not adequate structures. Solid masses of masonry can attain remarkable size, as the Egyptian pyramids make clear, but hollowed shapes cannot. They require structure, and structure is not surface. Eiffel recognized that it was precisely the sacrifice of surface, not mass, that enabled his tower’s achievement of unprecedented heights. Indeed, the Tower undoes Freycinet’s notion of mass and volume and surface altogether; there is no outside versus inside. Exterior and interior are collapsed and yet mass, even if minimized, remains. Remember that the Eiffel Tower, despite its lightness, depends on the exact offsetting of wind and gravity, lateral and vertical forces, the pressure of air and the pressure of weight. Mass was attenuated, indeed excised from the pyramid’s core, but it was also exactly calibrated because mass alone provided the countervailing force to that of the wind. Surface, not mass, was most radically redefined by Eiffel’s Tower, becoming line not plane, networks of iron bars punctured by emptiness at every point where no carrying of force was required. Vogüé had referred both to the geometer’s “infallible drawing” and to “abstract, algebraic beauty.” The Tower’s beauty could have been expressed algebraically, but in nineteenth-century French engineering practice, it was more often expressed geometrically, as shapes on paper. That propensity to visualize forces and a structure’s capacity to bear them would have made the Eiffel Tower seem to many a physical realization of drawing and also a proof of drawing’s irrefutable logic, its capacity to speak force through line. Vogüé gave voice to a characteristically nineteenth-century fascination: a three-hundred-meter tower born and assembled in the geometer’s head; such a pragmatic, intellectual, and empirical transcendence of material limits! Accompanying the disappearance of labor no less! No Egyptian slaves! I broadly conjure the seduction here, not the reality. Two work strikes stopped the building of the Eiffel Tower. This was a decade of agitation by laborers, union organizers, socialists, and anarchists, to

just large enough to enclose the tower (1,252 meters2 x 312 meters) is 6.28 million kilograms, which is 86.0% of the tower’s 7.30 million kilograms” (Gallant, “The Shape of the Eiffel Tower,” p. 7).

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name a few. Construction and metalworkers were some of the most active protest- ers.50 But Eiffel had engineered his colossal monument with great skill. He had diverted labor to drafting tables and to off-site factories. He had made the spectacle of erection seem inevitable, unstoppable, the geometer’s mind realized when in fact it was the engineer’s. Vogüé had said that the Eiffel Tower was an incantation of “génie.” Is it any surprise that civil engineers were called Génie civil ? Magic workers. And yet Eiffel reminds us not to substitute drawing for the Tower itself. When he was attacked by upholders of high culture—artists, poets, architects, writers—he turned, as I have said, to the counterexample of the Egyptian pyramids. That turn entailed directing attention to the colossal thing in and of itself. With palpable frustration, Eiffel also cautioned that drawing and monument were fundamentally unlike: I would like to know on what [the protesting artists] have based their judgment. Because, note this, sir, no one has seen this tower and no one, before it is built, can say what it will become. Until now it has been known only by a simple geometric drawing, and although it has been reproduced in hundreds of examples, can one appreciate with competence the general artistic effect of a monument from a simple drawing when this monument truly exceeds [all] dimensions previously constructed and [all] forms previously known?51 Drawing, Eiffel well knew, had made possible the calculation of a funicular structure and thus the realization of heretofore unknown colossal scale. But drawing, Eiffel reminds us, could not convey the impact of that size. Since no such height had yet been attained, its effect could not be anticipated—even, Eiffel suggests, by its makers.

But he does steer: he makes the balloon turn in every direction and then go like an arrow to the point he has fixed upon. For the first time the line of a human will has been marked in space, the plan of a human thought developed. Until now balloons could only be steered in a vertical direction, and that very clumsily. . . . Man, suddenly helpless and paralyzed, was swallowed up by space. . . . So until now it was only a sort of effigy of man and not man himself who braved the heights. Now at last man with his imperious will and his definite and vigorous thought is asserting himself in the upper spaces. . . . Here was no longer the light caprice of natural forces, no longer the terrifying lawlessness

50. See, for instance, Zeldin, France 1848–1945, vol. I, pp. 198–284, 640–788; Michelle Perrot, Workers on Strike: France 1871–1890, trans. Chris Turner (Leamington Spa, U.K.: Berg, 1987). 51. Incompletely cited in Lemoine, La Tour de Monsieur Eiffel, p. 100; Frédéric Seitz, La Tour Eiffel: Cent ans de sollicitude (Paris: Éditions Belin, 2001) p. 21.

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of the currents and winds. In their place had been substituted the rectitude of human thought, the systematic inﬂexibility of the human will, master at last of what had been for us hitherto the region of the formless, the unregulated, and the chaotic. It was a splendid sight. . . .

In that frail balloon moving deliberately toward its goal I see a part of the immense human problem. I might express it in this way: to make life, social life as well as natural life, a thing that can be steered. . . . Thus the thoughts familiar to Socialists took on fresh shape and meaning to me. . . . While I was rejoicing in a free and impersonal pride, the pride of the human race and of Socialism, and was looking with emotion on the spectacle presented by victorious man, master of nature and of himself, a knot of curious observers had been formed . . . nearly all enthusiastic and sympathetic. But I recognized one of my friends whose conclusions often distress me, on the outskirts of the group. . . . “How strange!” he murmured; “here is a justiﬁcation of all our suspicions. He could turn from right to left and he turns from left to right, the direction of every treachery. . . . Don’t you see that this man has agreed to go around the Eiffel Tower that was built with the stolen Panama money? Don’t you see that in bringing the Eiffel Tower into an experiment that is, anyway, of very doubtful value but that has excited all the faddists of progress and science, they wished to rehabilitate the Panama Company and Eiffel. . .? I say to you, I who have not been bought by either cheats or fools, what you see up there is a trick of the Ministry and the Panama Company. That man has stolen right and left: he has stolen from public secret funds and I, I alone will denounce him.”

And as the balloon disappeared behind the glowing tops of the autumn trees, he cried in a voice that was rather sharp and shrill: “Panamiste! Panamiste!” —Jean Juarès, Petite République, October 21, 190152 In 1879, while Bartholdi was constructing the Statue of Liberty at the Gaget and Gauthier workshop and attracting crowds of visitors at the outskirts of Paris, Lesseps orchestrated an international meeting to sanction his second sea-level canal across an isthmus. No engineer, Lesseps nonetheless insisted that the Panama Canal was “an operation the exact mathematics of which is perfectly well known.” Only “two things need to be done: to remove a mass of earth and stones, and to control the river Chagres . . . ”53 Lesseps’s faith led him, criminally,

52. “Truth or Fiction?,” reprinted and translated in Studies in Socialism, trans. Mildred Minturn (New York: G. P. Putnam’s Sons, 1906; reprinted New York: Kraus Reprint Company, 1970). 53. Logan Marshall, The Story of the Panama Canal (L. T. Myers, 1913), p. 101.

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to mistake paper and matter, geometry and mass. In 1886 he told a journalist, “We have changed the whole course of the river and made it run on the other side of the mountains altogether.”54 He meant on paper, and for Lesseps paper was a place subject to few limitations. His sin was that of the geometer and also the imperialist. He believed not only that everywhere was subject to his control, his abstraction, but also that everywhere was the same: what worked at Suez would work in Panama. Digging of the Panama Canal began in 1882. As workers labored to raise high a hollow sculpture in Paris, tens of thousands of other laborers, including fifty thousand men from the West Indies, removed the earth of Panama, even attempting to level a 330-foot mountain at the Culebra Pass.55 If the making of the Suez Canal had required the replacement of “slaves” by machines, the Panama Canal witnessed the return of the dirt-cheap laborer. The Panama Canal was in every way a visible excision—a cut—of the continent’s dense, impacted, and substantive interiority. It was an endless disembow- eling of earth by way of men and also by cranes, dredges, and railways, that is, by machines. But unlike the relatively flat sandy desert of Egypt, the mountainous, geologically unusual, wet terrain of Panama—its mass—would not be emptied.56 Panama’s mudslides continually refilled the space so arduously opened by men and by machines. A historian has stressed that the engineer’s imagination had difficulty keeping up with the endlessness of Panama’s mass, a mass that literally twisted and overturned pristine lines like those of railway tracks in photographs.

54. David McCullough, The Path Between the Seas: The Creation of the Panama Canal, 1870–1914 (New York: Simon and Schuster, 1977), p. 188. This is the best general history of the making of the Panama Canal. 55. Michael L. Conniff, Black Labor on a White Canal (Pittsburgh: University of Pittsburgh Press, 1985). 56. On Panama’s geological speciﬁcity, see McCullough, The Path Between the Seas, pp. 167–68.

“Ofﬁcial Photographer of the Isthmian Canal Commission” (Ernest Hallend or unknown predecessor). Mudslide engulﬁng U.S. steam shovel 201, February 7, 1913. National Archives, Washington, D.C.

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The amount of digging involved was always greater than one might imagine, for the reason that the canal was being dug through a saddle between steep hills. So as the Culebra Cut was made steadily broader at the top, its sides, against the bordering hills, rose steadily higher. . . . This meant that the volume of excavation, the total cube, was being compounded steadily and enormously. The deeper the Cut was dug, the worse the slides were, and so the more the slopes had to be carved back. The more digging done, the more digging there was to do. It was a work of Sisyphus on a scale such as engineers had never before faced.57 Although some sixty-five million cubic meters of dirt had been removed by 1887, Lesseps had finally come to recognize that his vision of clean unhindered lines— the channel cut sea level across an isthmus—had been defeated by engulfing wet earth. What Barbara Johnson has called the “revenge of the referent” forced a man prone to symbolist simplifications to concede that he needed the help of more pragmatically minded engineers.58 In 1887, a year after the inauguration ceremony of the Statue of Liberty in New York at which Lesseps had proclaimed, “Soon, gentlemen, we shall meet again to celebrate a peaceful conquest. Good-bye until we meet at Panama,” Lesseps finally and reluctantly approached Eiffel to design locks for the canal and to supervise their building, including the removal of earth required to install them.59 Like Bartholdi, Lesseps needed Eiffel’s colossal engineering to realize his colossal ambition. Even at the 1879 international meeting at which Lesseps had overwhelmed considerable dissenting opinion by the sheer force of his personality, Eiffel had argued that the Panama Canal required locks that could move ships up and across the mountains of the isthmus. His was one of the few opposing votes to Lesseps’s plan. Eiffel’s contract with Lesseps is dated December 10, 1887. Lesseps paid dearly for the engineer’s expertise and prestige, raising the cost of digging, as one lawyer later put it, from seven francs per cubic meter to thirty-three francs per cubic meter.60 Eiffel undoubtedly enjoyed the opportunity of proving Lesseps wrong and succeeding where he had failed. He also appreciated the advance of eighteen million francs that would offset the costs of building the Eiffel Tower, which he had only just begun and to which he had committed his fortune. In January 1888 Eiffel ordered the making of enormous locks for the Panama Canal, some seventy-nine feet high, sixty-nine feet wide, and thirteen feet deep, to be made at Nantes. In 1888 he began to supervise two sets of labor crews, one removing matter in Panama and one erecting it in Paris. I would like to emphasize the simultaneity of the events, to evoke the trains and cranes that brought iron to the Tower to be raised on high and the hundred-train carloads daily removing earth at the Panama Canal.

57. Ibid. 58. Barbara Johnson, “Erasing Panama: Mallarmé and the Text of History,” A World of Difference (Baltimore: Johns Hopkins University Press, 1987), pp. 57–67. 59. Diesbach, Ferdinand de Lesseps, p. 367. 60. Bermond, Gustave Eiffel, p. 350.

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Gatun Upper Locks, Panama Canal. Reproduced in Logan Marshall, The Story of the Panama Canal (1913). Relative to Lesseps, Eiffel was responsive to the specificity of Panama’s geography. The lock system devises a vertical as well as a horizontal set of solutions to the job of transport, the job of moving goods and persons across. It raises ships up and over the mountains. One can appreciate why Lesseps could not accept the proposal of a lock-based rather than sea-level canal. Locks impede the view. They chop up space into small units, and they enclose the ships, sometimes hiding them completely. They do not produce the endless views to the horizon so dear to Lesseps. Locks serve short-term mechanical purposes rather than ﬁguring sublimely abstract truths: geometry’s promise. Juarès’s tale of ballooning helps us to understand Lesseps (in more ways than one). In that parable, geometry is what demonstrates and makes visible man’s will and his power. Only the pilot’s capacity to steer the tossing balloon to an intended point, to trace a line, indicates his control over chaos, and the straighter the path, the greater the achievement. Mastery’s sign is geometry, even drawing, in the midst of a turbulent and beautiful nature, but not engineering, not mechanics, not prosthetics, not locks. Lines in space, I understand the seduction. Eiffel’s locks could have successfully completed the Panama Canal, but Lesseps had turned to the engineer too late. The Panama Canal Company declared bankruptcy December 14, 1888. Eiffel believed it would still be saved and continued the project until the spring of 1889. This is why Lesseps chose to erase the Panama Canal from the Universal Exhibition, which opened in May 1889, and Eiffel did not. After the bankruptcy of the Panama Canal, the Suez Canal Company hastily removed the Mesoamerican half of the pavilion

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intended to celebrate the two canals as rhyming achievements. Eiffel by contrast devoted half the length of his pavilion at the foot of the Eiffel Tower to the Panama Canal and its lock system. At the 1889 Exhibition, Eiffel’s pavilion was the only space in which the debacle of Lesseps’ sea-level sequel to the Suez Canal was referenced and also corrected.61 Nevertheless Eiffel would be injured by his belated attempt to move the mud of Panama. His soaring reputation was smeared in Paris by the Panama scandal of 1892, that sensationalist indictment of the colossal financing necessitated by colossal engineering, the behind-the-scenes traffic in money and profit, in millions of francs bribing and buying off government officials.62 The funicular structure maximally optimizes materials: what this means, of course, is that it maximally cuts cost and increases profit. Camille Pissarro and other critics, many of them anarchists, were right to make the Eiffel Tower the sign of Capitalism.63 Profits had been immense. Workers had been sacrificed to profit but not just in Paris; 22,000 West Indians and Frenchmen had died digging the Panama Canal during the French phase. The suspicious onlooker mocked in Juarès’s story recounts a truth. It was the failure of Panama’s canal that paid in part for the Eiffel Tower. Panama’s mud, its sacrificed workers, its duped subscribers, Lesseps’s desperation: Eiffel had profited from them all. He had been paid no less than sixty-three million francs, ten times the price of the Tower, to save the Panama Canal and this at a time when thousands of subscribers faced bankruptcy. (Headlines screamed “THIRTY-THREE MILLION NET?” One paper caustically referred to the “pyramidal farce.”64) 61. 1889: La Tour Eiffel et l’Exposition universelle, exh. cat., Musée d’Orsay (Paris: Éditions de la Réunion des Musées Nationaux, 1889), pp. 119–21. 62. On the Panama scandal, see Jean-Yves Mollier, Le Scandale de Panama (Paris: Fayard, 1991); Bermond, Gustave Eiffel, pp. 345–70. 63. See Richard Thomson, “Camille Pissarro, ‘Turpitudes Sociales,’ and the Universal Exhibition of 1889,” Arts Magazine 56, no. 8 (April 1982), pp. 82–88. 64. Cited in Bermond, Gustave Eiffel, pp. 351, 356.

Scientiﬁc American illustration. Reproduced in Willis J. Abbot, Panama and the Canal in Pictures and Prose (London: Syndicate, 1913).

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Leading, I might add, to the downfall of Freycinet who was then Prime Minister, the Panama scandal would permanently stain Eiffel. In newspaper after newspaper, illustrations indicted him. He might have been only one among many guilty men, but he could not hide in the crowd. Always the Eiffel Tower gave him away. The scandal had, however, diminished his giant tower to the human scale of a commodity. The structure that had once loomed over ancient Egyptian pyramids shrank pitilessly into an object, or perhaps worse, into a model. In the press images in the early 1890s, the Tower was borne on Eiffel’s back, pushed in a cart, or perched on a mantel. Eiffel was convicted to two years in prison. Although ultimately he was not jailed, he never built another monument. Instead he conducted scientiﬁc experiments at the top of the Tower that had promised that engineering could move you high above the corruption and the earth that had engulfed French machinery and French fortunes in Panama. Eiffel’s late experiments in telegraphy, meteorology, and aerodynamics were persistently airborne, avoiding the problems posed by earthbound structures. At the end of his life, Eiffel’s concern was to give mass flight, to steer the balloon, and for reasons Juarès’s paranoid observer got right.

The extraction of mass to make simple volumes is, as Freycinet argued, one of our most hardy, one could say reckless, habits. And colossal mass proves

Scientiﬁc American illustration. Reproduced in Panama and the Canal in Pictures and Prose (1913).

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“Ofﬁcial Photographer of the Isthmian Canal Commission” (Ernest Hallen or unknown predecessor). Laborers dig a ditch at the Cucaracha Slide, October 11, 1913. National Archives, Washington, D.C.

remarkably difficult to visualize, to keep in mind. Millions of cubic meters of earth are hard to fathom. And while mathematics homogenizes its quantities—we do not subtract three apples from five oranges—a cubic meter of matter is an exceed- ingly diverse thing. Egypt’s sand and Panama’s mud are not the same; flesh and rock are not either. Nor in the manufacture of modern colossi are human lives. They cost more, for instance, in Paris than in Panama. Volumes do not indicate mass: cubic meters can be light as a feather or weigh five tons. Nevertheless, when Americans wanted to boast their achievement of a colossal removal of earth where the French had failed, they overlaid sixty-three volumes, outlined Pyramids of Cheops, over a cityscape of Manhattan. The caption of a 1913 illustration, the year of the Panama Canal’s opening, reads: “A graphic comparison. The ‘spoil’ taken from the canal would build 63 pyramids the size of Cheops in Broadway from the Battery to Harlem.” Another illustration places a transparent pyramid over a skyscraper and some seventeen city blocks to indicate the amount of earth removed from the Culebra Cut alone. Modern channels, even Panama’s, could not be conceived separately from

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ancient Egypt, nor from the simple geometric shapes Egypt’s solid stone monuments had left to haunt us. From these emptied volumes and the scale New York City affords, we are asked to imagine the mass such pyramids represent. Our job, the prints tell us, is to put mass back after geometers and so many valiant, sometimes desperate, workers had taken it away.

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