The Archimedean Point

The Archimedean Point:From Fixed Positions to the Limits of Theory Jocelyn Holland (bio) and Edgar Landgraf (bio) There is no authoritative biography of Archimedes, but there are moments from his life which, apocryphal or not, have become the stuff of legend. These include accounts of Archimedes running naked through the streets after realizing that his body displaces water in the bath (“Eureka!”), how he sat musing over diagrams in the sand as sword-bearing Romans descended upon him during a siege of Syracuse, and of course, his mechanically-informed claim that a firm resting place is all he would need to dislodge the world from its axis. This is the birth of the Archimedean point, which latter-day interpretations craft into a figure of thought that works according to the mechanical principle it describes: effortlessly, it turns a simple law of physics into an image of unlimited strength, absolute stability, and world mastery.1 Both literally and figuratively, it aligns minimal with infinite force, immobility with movement, eccentricity—the point’s location outside the world it purports to dislodge—with centrality, the idea of a single location central to the actions of the world. But it is not merely the promise of sheer omnipotence that explains the extensive reception of Archimedes’ point in the history of Western thought. Equally important is the complexity and ambivalence of its pragmatic structure. Applied to the world as a whole, a straightforward mechanical device turns into a figure that is both easy to visualize and abstract enough to make it transferable to almost any context. The ambiguous, if not paradoxical structure of the Archimedean point also extends to its foundational gesture: even as it avows its point of absolute stability rhetorically—that is, even as it asserts firm ground—it simultaneously questions the possibility of its very existence. Despite the many prominent appearances of the Archimedean point throughout the history of Western thought, the figure itself has rarely been the object of concrete analysis and historical contextualization. Its explanatory force seems to have prevented the closer examination of it as a conceptual device. This oversight is indicative of the broad applicability [End Page 3] of the figure, its malleability, as well as the impossibility to confine it to one particular knowledge system. It also reveals the longstanding preference of the conceptual over the figural and literary in the history of science and philosophy. The Archimedean point is neither a proper concept nor a simple metaphor; rather, it is an assemblage with various components and moving parts (literally and figuratively) that, because of its narrative form, can be adapted to different conceptual and historical contexts. In other words, the anecdotal form of the Archimedean point is not accidental, but a central aspect of its particular mode of knowledge production, one that allowed for the figure to be handed down and embellished over generations and ages. Furthermore, the effectiveness of this literary device lies in its ability to elucidate what are literally fundamental questions of philosophy and science. As the contributions of this volume demonstrate, in the rational universe we call modernity, the anecdote has functioned as a myth of sorts: it is used to illuminate what are perceived as foundations and last ends of the world without itself inviting further (critical) reflection. What, then, does the closer examination of the anecdote of the Archimedean point have to offer? Within the varied reception history of the Archimedean point, we can identify a trajectory that moves from the search for a point of strength, stability, and mastery toward an increased awareness of the ambiguity and aporia surrounding it. This history is perhaps nowhere more apparent than in its adaptation in modern philosophy. The canonical example is Descartes’ invocation of the point as the basis of his philosophical system in the second of his Meditations, where it appears in tandem with his discovery of a firm standpoint in the self-assertion of the thinking subject. By equating the cogito with the Archimedean point, Descartes appropriates it as a metaphor for a subject of seemingly limitless capacity. Well into the eighteenth century, attempts were made to extend and protect this hard-won ground, recasting it in new philosophical

Fixed point · Mathematical analysis · Mathematical economics · Mathematics · Quantum Mechanics and Applications

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