The Archimedean Point: From Fixed Positions to the Limits of Theory

Abstract

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 applicabil