Fracturing and Distorting . . . continued
Section Two.  Author: Elizabeth Brunner
       Thomas Pynchon and the Disruption of Symmetry
Postmodern author Thomas Pynchon explored advanced mathematics while studying Engineering Physics at Cornell. His encyclopedic references to thermodynamics, entropy, magnetic fields, and Maxwell's demon in The Crying of Lot 49 have provided ample starting points for critics. But by beginning my analysis with mathematics rather than physics, I focus instead on Pynchon's overturning of the classical aesthetic of symmetry through postmodern exploration of asymmetry and complexity. 
Before Mrs. Oedipa Maas leaves the rigid predictability of Tupperware parties, Muzak, and gourmet dining to begin her interpretive quest, she exists in symmetrical harmony with the dictates of corporate culture: she shops and she consumes. In keeping with the mathematical definition of symmetry, the housewife Oedipa maintains a similarity of form with all other brand-name-loyal consumers and appears identical to neighbors on a parallel plane in groupings of "census tracts, special purpose bond-issue districts, shopping nuclei, all overlaid with access roads to its own freeway" (24). Such stable conformity has precedence; mathematician John Allen Paulos explains that symmetry, coupled with invariance, provides the historical foundation for "mathematical aesthetics," dating from the ancient Greeks' focus on balance through "Einstein's insistence that the laws of physics should remain invariant for all observers" (234). 
But contemporary mathematical theory questions whether the changeable or the unchangeable governs the universe, just as Pynchon questions the potential of free will in a mass-produced age. Chapter One begins with Oedipa's transformation from middle-income obscurity to "executrix" of "real estate mogul" Pierce Inverarity's estate (9). Pynchon's wordplay in naming the deceased appears to combine Invariant, an entity that remains unchanged during a transformation process, with Invert, the process of reversing position. This semantical paradox proves appropriate. At one level, Inverarity's estate reverses Oedipa's perception of the underbelly of America, while at another level, she remains unchanged, still waiting for answers during the final auction. 
To investigate Inverarity's assets and investments, Oedipa drives to San Narciso, past factories and commercial buildings with street addresses in the 80,000's. Oedipa reflects on these high numbers: "It seemed unnatural" (25). Given Pynchon's familiarity with math terms, this three-word comment provides a multidimensional warning. Natural numbers are whole, representing a fusion between cardinal numbers for counting (one, two, three) and ordinal numbers for ordering (first, second, third). To be unnatural, these two functions must be splintered. With natural numbers, we would expect street addresses to grow as urban blight extends far beyond the city core (an increasing number of miles) while the relevancy of these outlying commercial lots diminishes (the 68th textile factory in the metropolitan area). And yet, Oedipa next approaches a fortressed division of the aerospace corporation Yoyodyne, surrounded by "miles of fence topped with barbed wire," "guard towers," and a symmetrical pair of "sixty-foot missiles" (25). Ordinal importance inverts: Yoyodyne represents the enormity of the military-industrial complex: stealing patent rights from inventors, replacing employees with automation, causing an unloved former-executive to found Inamorati Anonymous, and stockpiling weapons of mass destruction. 
Unnatural also refers to the sinister, conspiratorial power of the military over both the domestic economy and the global future. As Oedipa later extrapolates from the "metaphor" of "delirium tremens" when she meets a tattooed sailor, DT's = dt = "time differential, a vanishingly small instance in which change had to be confronted . . . where velocity dwelled in the projectile though the projectile be frozen in midflight . . . " (128, 129). Pynchon offers hope for activism against the encroaching system, against the militarization and industrialization of society -- but the potential for change disappears quickly in the onslaught of mass culture. A differential is the infinitesimal difference between two consecutive values of a variable quantity; in Lot 49, the differential marks the thin gap between reality and paranoia, between meaning and the void, with an ever-growing database of coded information blurring the distinctions. Calculus can only imagine the final time differential at a theoretical level, not as a quantifiable number -- just as Oedipa's hope may rest only in comprehending the general socio-political factors which overwhelm our efforts at self-determination, rather than in explicating the particulars of the Trystero. But Theodore Kharpertian points out that contemporary calculus also indicates the reverse, with the "concept of limits" serving as "a metaphor for the ultimate inaccessibility of the revelation or apocalypse" (106). Once again, Pynchon leaves his heroine in an ambiguous zone, grasping too small and too large -- ignoring the realities of the excluded middle. 
The author at least offers Oedipa a concrete clue: the tattooed sailor provides directions to the "secret mailbox . . . . a can with a swinging trapezoidal top" (129). And the geometric shape of the W.A.S.T.E. lid reveals a further clue to an eager mathematician. A trapezoid defies symmetry: only two of the four sides are parallel. Drawing from postmodern developments in chaos theory, Scientific America columnist Ian Stewart explains that "tiny asymmetric disturbances" can potentially "trigger an instability of the fully symmetric state" (86). By analogy, small disruptions in the political system can lead to revolutionary changes system-wide. But Stewart's analysis can move us even deeper: ". . . the same basic method of pattern formation, the same mechanism of symmetry breaking in a mass-produced universe, governs the cosmos, the atom, and us" (91). Whether the disguised trash can disrupts the government postal service or a confused housewife breaks through class barriers or a questioning agnostic challenges divine prescriptions, issues of symmetry and asymmetry force contemplation of our fate. 
While readers perform the literary task of closely analyzing coded words in Pynchon's text, Oedipa learns to decipher patterns in the plot, almost in a parody of academic labors. Similar detective work fulfills the parameters of mathematics, defined by Stewart as "a formal system of thought for recognizing, classifying, and exploiting patterns" (1). However, Stewart warns that "numerical pattern-seeking . . . generates millions of accidentals for each universal" (6). And, as Pynchon-scholar Tony Tanner notes, "the need to see patterns . . . may easily turn into the tendency to suspect plots." (17). 
The equivalent symmetry which balances Image = Pattern = Meaning easily disintegrates into Coincidence = Conspiracy = Paranoia. The novel closes with Oedipa still waiting, either "for another set of possibilities to replace those" of San Narciso or "for a symmetry of choices to break down, to go skew" (181). Oedipa fears that if Trystero proves false, her only option for surviving in the disappointment of "just America" will be "as an alien, unfurrowed, assumed full circle into some paranoia" (182). Pynchon's choice of a circular image refers to the ultimate in symmetry; a circle maintains the same balanced shape through infinite rotations. Thus, the continuous questions and suspicions feed upon themselves to preserve a ambiguous balance. In a 1976 article in The New Review, F.S. Schwarzbach argues that by "re-interpret[ing] empty data into complete, coherent systems," paranoids prove both creative and heroic: "We abdicate in the face of overwhelming odds -- they fight back" (59). 
For mathematicians, Oedipa's passive wait for the truth as the "auctioneer clear[s] his throat" could also lead to breakthroughs (183). As Morris Kline explains: ". . . mathematical truth is discovered and not invented. What evolves is not mathematics but man's knowledge of mathematics" (Qtd. in Gregory 171-2). Likewise, in the unwritten next page, Oedipa may realize new truths, not by creatively deciphering the conflicting symbols of man-made culture but by the very act of seeking grander, broader revelations available only when we wait patiently.