Geometry/Labor = Volume/Mass?*

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 con- struction 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). OCTOBER 106, Fall 2003, pp. 3–34. © 2003 October Magazine, Ltd. and Massachusetts Institute of Technology. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/016228703322791007 by guest on 28 September 2021 4 OCTOBER 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. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/016228703322791007 by guest on 28 September 2021 Geometry/Labor = Volume/Mass? 5 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. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/016228703322791007 by guest on 28 September 2021 6 OCTOBER * 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.

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