In Clifford’s words, “Immensity and Eternity [are] replaced by knowledge of Here and Now.”

In christening his doctor “Sloper,” James puts the physician’s cherished Euclidean certainties in doubt. The trigonometric concept of a slope—“the rate at which a curve rises or falls per horizontal unit”—connects Sloper to the new, curved notions of space that, by the 1870s, were rendering the doctor’s axiomatic metaphors out of date (Kline, “Geometry”). Inasmuch as the new, non-Euclidean universe was governed by dynamic, empirical forces like gravity, so notions of space and time changed accordingly. When Einstein later observed that space-time assumed the form of a “curvature” when confronted with a massive body, he was working from a set of assumptions in which “the propositions of Euclidean geometry cannot hold exactly,” and the very “idea of a straight line also loses its meaning” (Einstein, quoted in Dimock, “Rethinking Space, Rethinking Rights,” p. 256). In Washington Square, such curvature necessarily undermines not only Dr. Sloper’s sanguine view of surface geometry, but also the “moral satisfaction” that such mathematical assumptions produce (p. 133).

Indeed, the rejection of Euclidean absolutism had a seismic impact on Western political philosophy. To challenge Euclid was to challenge the presumption of pure reason that his axioms had inspired. Within the Kantian world of categorical imperatives, moreover, democracy existed as a vaunted if speculative set of civic promises. In the hyperbolic world of empirical events and sensate bodies, however, democracy became a matter of concrete, practical choices (see Dimock, p. 249). In such a new, relativistic space, as Wai Chee Dimock observes, “compromises and concessions, rather than absolute victories, mark the endpoint ... of democracy” (p. 263).

James’s vision of non-Euclidean democracy is evident in his representation of Catherine Sloper, the character he modestly regarded as “the only good thing in the story” (Henry James: Letters, p. 316). Catherine’s robustly corporeal embodiment—her “clear, fresh complexion,” her physical resilience, and her status as someone “strong and solid and dense,” indeed someone who “would live to a great age—longer than might be generally convenient”—all highlight her physical immediacy. Hers is a somatic sturdiness that belies the abstract postulates deployed by those around her. Unlike her fellow characters, for example, Catherine can distinguish form from content. She can appreciate the aesthetics of a given representational strategy, that is, without losing track of the underlying import. Thus, despite the fact that her father speaks ill of Morris, she nonetheless admires the “neatness and nobleness” of the Doctor’s expression—“even while she felt that what he said went so terribly against her” (p. 117). Later, after reading Townsend’s devastating farewell letter and letting “her sense of the bitterness of its meaning and the hollowness of its tone ... [grow] less acute,” Catherine “admire [s] its grace of expression” (p. 217). This skill arms her with the ability to distinguish radical democracy from its more conventional counterpart, true democracy, and real participation from mere political show. Although she fails to recognize Townsend’s duplicity, Catherine’s myopia is less a testament to her foolhardiness than it is a mark of her fundamental trustfulness. Whereas her father dis misses Townsend as a generic rogue, Catherine appreciates the embodied presence of the “beautiful young man.” Indeed, we are mistaken if we see the rightness of Sloper’s verdict as vindication of his jaded approach. While Catherine’s naive devotion to Morris is misguided, it is also genuine. By refusing to marry anyone else (even, as it turns out, an older but none the wiser Townsend), Catherine demonstrates the authenticity of her trust.