Fracturing and Distorting . . . continued
Section Four.  Author: Elizabeth Brunner
       Marilynne Robinson and Topology
While Morrison probes the inner voices of characters haunted by a tragedy of national and historical scope, Marilynne Robinson stretches her characters' perceptions outward to transcend domestic tragedy. Contemporary mathematicians also work in both directions; fractal geometry explores increasingly smaller dimensions, and the speciality of topology investigates the stretching of limits. This math of distortion illuminates Ruthie's choice of transience over stability in the novel Housekeeping. 
The current mathematical fascination with topology examines geometric figures which remain fundamentally unchanged when distorted until reaching a particular rupture point. Carl Boyer offers a technical definition of topology: "the study of intrinsic qualitative aspects of spatial configurations that remain invariant under continuous one-to-one transformations" (603). At the simplest level, topology studies mathematical proportions in the blowing up a balloon, stretching of latex, or contorting of a circle into an ellipse -- earning the nickname rubber-sheet geometry. Topology also measures more complex distortions, such as the stretching of a doughnut shape into a coffee cup with the hole preserved in the handle. But ultimately as Stephen Barr explains, no matter what the geographic shape, topologists focus on "the most permanent" properties of an object, "the ones that will survive distortion and stretching" (3). 
The dysfunctional history of the Foster family demonstrates opposing perspectives on spatial distortion. The saga begins with the grandfather Edmund Foster who paints expansive mountains and boards a train to new territory to escape Midwest landscapes of "perfect horizontality" that "foreshortened the view so severely" (3). He arrives in Fingerbone, a realm of "puzzling margins" between "modified" dimensions (4). A legendary derailment ends the grandfather's life, and while the widowed grandmother hopes that death will change his essence, she "distrusted the idea of transfiguration" (10). Her clinging to the safe restrictions of proper widowhood inverts Edmund's need for expansion. These spatial dichotomies continue into the next generation: daughter Molly expands boundaries as a missionary in China, daughter Helen leaves the home in an "out-of-state marriage" (10), and daughter Sylvie adopts a life of transiency. Helen returns home first, but only long enough to leave her own daughters on the porch before committing suicide by "swerving and sailing off the edge of the cliff" over Fingerbone Lake (23). Those odd margins noted by the grandfather allow this swift distortion from live to dead. For five years, the grandmother cares for the orphaned girls, but remains off-balanced because "this disaster had taken shape" from among the "familiar" comforts. The grandmother's death brings great-aunts Lily and Nona as caretakers who continue striving for "habit and familiarity" (32). But Ruth and Lucille exhibit tendencies to align with the dangerous, expansive side of the family by skating to the "farthest edge" of the "swept ice" and examining the "comfortable yellow lights" of Fingerbone from a distance (34, 35). A legacy of family death and alternating guardians leaves the girls distorted, awkward, and insular, yet still courageous. 
The arrival of flamboyant Aunt Sylvie as the latest caretaker forces the sisters along divergent paths, distorting the cocoon which envelopes them as a pair until they stretch and break in opposing directions. Sylvie's housekeeping consists of wildness and randomness, symbolized by the flood which dissolves boundaries between lake and home, nature and civilization. Sylvie welcomes this rupture of spatial distinctions; she sweeps leaves into corner piles rich in "cold brown liquors of decay and regeneration" and opens windows to welcome "wasps and bats and barn swallows" flying in with the cleansing air (85). Critic Sonia Gernes describes how Lucille "rejects the instability of Sylvie's household, longing for order, solidity, well-planned menus and sturdy shoes" while Ruth becomes "enticed by Sylvie's world of transience, ephemeral beauty, and a quasi-mystical quality that defies the body's demands and limits . . ." (155). 
Exhausted by the changing shape of their family, by the leaving and the dying, Lucille seeks to recover solidity; topologists might say her tolerance for distortion has reached the breaking point. Paulos illuminates two crucial topological properties: "the number of holes" a figure contains and "the maximum number of cuts passing all the way through" before an object breaks "into two pieces" (247). More sensitive to small humiliations and more concerned with public approval, Lucille begins to resent sequined slippers and dime-store treasures. Ruthie realizes that "Lucille's loyalties were with the other world" and notices her sister's "tense and passionate campaign to naturalize herself" to a stable state of being (95). Lucille suffers more from the holes in her psyche, the cuts left by abandonment -- and these vulnerabilities lead her to turn on lights, seek outside friends, and finally escapes to a home economics teacher as the paragon of convention. 
Ruth proves to be the more adaptable sister, able to thrive under distortion and expand possibilities. When night encroaches after a fishing excursion, Ruth "simply let the darkness in the sky become coextensive with the darkness in my skull and bowels and bones" (116). By allowing the spiritual and natural domains to fill the holes within, Ruth's topological capacity inflates until the liberation of darkness seems "perfect and permanent" (116). In language resembling the transcendentalists admired by Robinson, topologist Barr mediates on his chosen field: "One might almost say it is a state of mind . . . . beginning with the continuity of space, or shapes . . . leads into other kinds of continuity -- and space as we usually understand it is left far behind" (2). Ruth discovers the correlation between hole and whole: "For need can blossom into all the compensation it requires" (152). The ache of abandonment verifies the capacity for love, so that the powers of nature, spirit, and self can enlarge to fill up this capacity. And, in the process of recognizing desires and welcoming fulfillment, the dimensions of inner capacity expand further. Ruth's expansion becomes so "gigantic and multiple" that she may either "fill the whole house" or completely dissolve through "the membranes that separate dream from dream"  (195). 
Freed from spatial restrictions, Ruth no longer needs the sanctity of home and can follow Sylvie across the railroad bridge into the freedom of transiency. Ruth uses an analogy to describe the expansiveness felt as she ventured across that bridge: "if you dive under water and stay down till your breath gives out, when you come up into the air again, you hear space and distance" (211). Spatial dimensions merge (Inward = Upward = Outward) as sensory perceptions merge (Sound = Sight = Knowing). Abandoning, even destroying, a four-walled house allows Ruth to carry the essence of home within herself. As literary critic Marcia Aldrich assesses, "In setting fire to what has served as a female house of mourning, they set free what has been suppressed and regulated . . ." (138). And this liberation of the spirit allows transcendence of absence. 
From Ruth's expansive quest to fill empty space and Sethe's longing to merge with dismembered rememories to Oedipa's search for patterns beyond symmetry, each heroine of these three postmodern novels must seek new definitions of reality before finding resolution. Overcoming constraints of conventional reality in order to find deeper truths also characterizes the postmodern challenge. N. Katherine Hayles, a pioneer in the application of science to literature, explains that pre-WWII "many disciplines were preoccupied by attempts to develop totalizing theories that could establish unambiguous connections between theory and observation, articulation and reality," but by the "mid-century, virtually all of these attempts had been defeated or had undergone substantial modification" (xii). While scholars of literature recognize the emergence of new narrative strategies for capturing the fragmentation of contemporary life, mathematicians pursue increasingly complex models for representing a fluid, baffling universe. And these theoretical challenges become complicated by threats of technology. Novelists must overcome the exhaustion of literary topics and maintain the vitality of language despite mass media numbing. Mathematicians must find new territory for analysis despite predictions that all major equations have already been solved while also protecting their "calculations" from mis-use by the Defense Department. But as these forces guide academics into the further unknowns of the twenty-first century, the desire for meaning preserves a link with antiquity.