Parabola Nation; or, the Power of Disparate Things, by Patrick Chura

The Gateway Arch is a 630-foot-high (192 m) monument in St. Louis

 In “Walking,” Thoreau not only defines sauntering as one of his cherished pursuits; he also self-consciously chooses a “perfectly symbolical” shape or contour for his sauntering journeys: "The outline which would bound my walks would be, not a circle, but a parabola . . .like one of those cometary orbits, which have been thought to be non-returning curves, in this case opening westward, in which my house occupies the place of the sun."

The importance of the curvilinear, open-ended route is heightened when we consider Thoreau’s work as a land surveyor.  My recent book on this topic looked at the frequent surveying references in “Walking” and suggested that the parabola constituted a compromise with the straight lines and closed figures Thoreau had often inscribed upon the landscape in his paid boundary work for clients.   The book also looked at how the directional matrix Thoreau created by marking out True North in the front yard of his home on Main Street backed up this essay’s claims of “good authority” for his life’s course and lent meaning to the statement, “Eastward I go only by force; but westward I go free.”  


While Thoreau’s westward-opening parabola obviously has both national and personal significance, the synergy between these meanings is far from simple. Instead the essay offers an unusually complex interpretation of Manifest Destiny, one that does not in every way emulate or endorse the imperialistic tendencies of continental conquest.  Merely by walking West, Thoreau conforms to prevailing ideology, but he does so at some variance with his countrymen’s desire to settle, civilize and tame. By rejecting straight lines and closed figures, Thoreau limns out an arc that is expressive but anti-utilitarian. The contour of his walk is less economically purposeful, for example, than the monotonous grid-like squares and rectangles that were being created by the Survey of Public Lands then going on in the West.  

Moreover, the parabola is a U-shaped curve with interesting specific properties. By definition, all points on a parabola are equidistant from a fixed line (the directrix), and a fixed point not on the line (the focus). A parabola is created by stringing together a set of points such that the distance to the focus always equals the distance to the directrix.  [figure 1] Philosophically and mathematically, the shape is explicable as a visible act of mediation. Its graceful arc is created by perfectly bisecting a gap between opposed shaping forces or bodies as that gap moves through time and space, through history and geography. In other words, the figure epitomizes both mathematical law and a form of transcendent reconciliation, putting on display the single middle path between seemingly unrelated disparities and showing that they are actually co-responsive. 

Gateway Arch and Old Courthouse

If this is what Thoreau’s sauntering parabola implies, it is also what the modernist Finnish-American architect and designer Eero Saarinen expressed in his masterwork, the Gateway Arch and Jefferson National Expansion Memorial in St. Louis. [figure 2] Saarinen said that his “major concern” in designing the memorial over the period from 1947 to his death in 1961 was “to create a monument which would have lasting significance and would be a landmark of our time.” He wanted a shape and structure "transcending in spiritual and aesthetic value” but also of supreme national significance: “something that would symbolize American culture and civilization.”   

Saarinen’s solution to the problem of spatially representing the national narrative was identical to Thoreau’s in “Walking”: a parabola, opening to the West.  Just as significant are the geometric forms that Saarinen rejected as unsuitable to his purpose: “Neither an obelisk nor a rectangular box nor a dome seemed right on this site or for this purpose. But here, at the edge of the Mississippi River, a great arch did seem right.”   Like Thoreau, whose parabola shunned the linearity of surveyed lines in favor of a redemptive alternative, Saarinen chose what he called “a completely natural figure”  and refused to adopt standard imperial forms—the phallic obelisk, the closed rectangle, the classical dome.  Essentially, Saarinen re-imagined Thoreau’s horizontal figure, unleashing the spectacular power it achieved when verticalized to a height of 630 feet and encased in stainless steel.

The genius of Saarinen’s design stems not only from its visual appeal but from its preservation of a crucial historical vocabulary to which Thoreau’s parabola also responded. Both parabolas, for example, symbolize the historical process of westward expansion and therefore implicitly locate the parabolic directrix to the East, and its focus to the West. Thoreau states plainly that his shape opens to the West, “the prevailing tendency of [his] countrymen”; Saarinen’s shape is a metaphoric portal or threshold for civilizational migration in the same direction. This is appropriate because in American cosmology, the East is the source and locus of law-bound society, a place where Thoreau goes “only by force.” 

But law-bound, economically determined society, which Thoreau aided as a land surveyor but opposed as an abolitionist, is only one of two influences guiding the arc of the figure.  Thoreau’s focus, the countervailing power that cooperates equally in determining the path of a parabola, is his “house,” which “occupies the place of the sun” in a figurative perihelion orbit. Exerting gravitational influence against the infinite points on the line of the directrix—and exactly matching the influence of the directrix—is a single separate point: the dwelling of a writer and surveyor who was also a nonconformist and determined abolitionist. The parabola is Thoreau’s method of representing not only the type of beauty he would wish his walks to have, but the shaping and altering effects he would wish his life to have—the visible, measurable results of civil disobedience.

The Last Sale of Slaves, 1861, St. Louis Courthouse

Saarinen’s parabola has a focus as well. Prominent on the centerline or “axis of symmetry” of the arch is the Old Courthouse of St. Louis, a structure of historical fame as the place “where the Dred Scott Case was tried”  or, more accurately, where Dred Scott sued for his freedom in 1846.  Eleven years later, Scott lost his case before a Supreme Court which declared that African Americans possessed “no rights which the white man was bound to respect.”  The Old Courthouse, a principal ideological battleground over slavery (and the site of St. Louis's slave auctions until 1861), exerts a general influence on perceptions the Jefferson National Expansion Memorial, just as the focus of a parabola interacts with its directrix to negotiate the shape’s final meaning.  Its specific effect is to trouble notions of the monument as simply a triumphal arch. 

St. Louis CourthouseIn making his final designs for the memorial, Saarinen devised clear connections between the great steel parabola and the courthouse centered in its background.  Photos of the project in its developing stages show that the environment Saarinen envisioned steered the pedestrian directly through the arch to the steps of the courthouse—as if the architect sought to temper the patriotic elation the arch elicited with a reminder of its human costs.  His revised design for the project—presented to the public in October 1957 in the Old Courthouse’s west chamber (where the Dred Scott case was heard)—sought to strengthen, in Saarinen’s words, “The axial relationship” between the Arch and the courthouse it frames.  As Saarinen explained, the elements of his landscape, including especially the courthouse, “all belong to the same ‘parabolic’ family as does the Arch itself.”   

Fully half of the mathematical “story” of the parabola is created by its focus, as fully half of the national narrative Saarinen conceptualized is less than celebratory.   The Old Courthouse, a prominent location in mid-nineteenth century history, is also a vestige of Thoreau’s world and an object contemporary with Thoreau’s parabola.  The two locations invite us to consider how the home of a prominent abolitionist during a period when slavery was the law of the land, and the site of an unsuccessful suit for freedom, are comparable elements, in physics and in ethics, because both counteract American triumphalism. 

catenaryThe idea that the St. Louis Arch has something to do with slavery is reinforced by the special variant of the parabola Saarinen used—a weighted and inverted catenary.  A catenary, derived from the Latin word catena or “chain,” is the curve a chain assumes when hanging from two level points. Though this curve is imperfectly parabolic, what Saarinen’s formal adaptation of the shape sacrificed in mathematical purity, it gained in cultural relevance.  Essentially, the catenary shape assured that the nation’s most colossal tribute to human aspiration retained associations with its most colossal injustice—human bondage. 

Louis & Clark Quarter

Interestingly, Missouri’s recent state-commemorative quarter asserts that this figure was, in some anachronistic but allegorical way, the shape through which Lewis and Clark passed at the the outset of their exploration of the Louisiana Purchase territory.  [figure 3] St. Louis, Saarinen’s parabola declares, is a place where the journeys of explorers and settlers began, where the promises of boundlessness and freedom central to our national mythology were realized. 

But the city was also a way station for the slave trade.  And, as the great wave of nineteenth century settlers that followed Lewis and Clark crossed the river from Illinois on the east to Missouri on the west, they passed from a free state to a slave state. It seems that Saarinen’s parabola asserts stark contradictions predicated on the recognition that any “gateway” located in St. Louis could also be a gateway to captivity, depending on the color of one’s skin. Encoded within Saarinen’s vocabulary is an equivocation of the symbol of Jeffersonian Democracy with a symbol of bondage—a chain that liberated whites but enslaved blacks.

4th of July Fireworks, St. Louis

A typical postcard photo of the St. Louis Arch offers further opportunity for exegesis. [Figure 4] The primary elements in the composition are freedom and egalitarianism (July 4 fireworks), American imperialism and manifest destiny (the parabola’s yonic invitation to free settlement), and slavery (the courthouse where the nation’s greatest contradiction to egalitarianism was unsuccessfully contested).  The fourth element in the narrative—the shape of the inverted chain—certifies that in this montage the two icons proclaiming freedom are offset by two that insinuate the opposite of freedom.  

How did Saarinen arrive at such a rich conceptualization of American history, one obviously of a piece with Thoreau’s?  Saarinen may have imbibed Thoreau at Yale, where he spent three years as an undergraduate in the early 1930s. But it seems unlikely that he consciously based his Gateway Arch on a few sentences from “Walking.” Saarinen was, however, both a modernist and a transcendentalist, a visionary idealist who evinced a life-long interest in organic harmonies and believed, like Kant, in a priori wisdom. Asked to name the source of his inspiration, Saarinen declared his belief that emotion and perception superseded reason or custom as guides to truth: “The spirit of the time speaks to us: what it is we do not know.  Its influence comes through intuition and it has to be felt with intuition.”  

Though re-imagined for modernity, Saarinen’s parabola is informed by the same cultural tensions Thoreau struggled with a century earlier. Looking at the two figures side-by-side as culturally complex responses to Manifest Destiny reveals thought-provoking similarities grounded in the ability of both to embody inquiry, ambiguity, and dissent.



  1.  See Patrick Chura, Thoreau the Land Surveyor (Gainesville, UP of Florida, 2010, 2011): 166-171.   

  2.   Harold Cobb, The History of Stainless Steel (Materials Park, OH: ASM International, 2010), 172. 

  3.   National Park Service, Cultural Landscape Report for Jefferson National Expansion Memorial, St. Louis, Missouri, (May 2012), 31.

  4.   National Park Service, Cultural Landscape Report for Jefferson National Expansion Memorial, St. Louis, Missouri, (May 2012),  39-40.

  5.   Jayne Merkel, Eero Saarinen (London: Phaidon Press, 2005), 195. 

  6.   National Park Service, Cultural Landscape Report for Jefferson National Expansion Memorial, St. Louis, Missouri, May 2012),  47. 

  7.   Pierluigi Serraino, Eero Saarinen: A Structural Expressionist (Koln, Germany: Taschen, 2005), 11. 

Patrick Chura teaches courses in nineteenth and twentieth century American literature and culture studies. He is the author of two books and has published articles on a variety of literary-historical topics. His second book, Thoreau the Land Surveyor, won the 2012 Dasher Award for outstanding literary criticism. His new edition of Ernest Poole’s The Harbor was recently published in the Penguin Classics series. He has been a Peace Corps Volunteer in the Republic of Lithuania and is a two-time Fulbright lecturer, teaching in Lithuania in 2009 and in the UK in 2012.