by Lewis Cobbs

Mathematical and scientific concepts and terminology offer dynamic and practical resources for teaching literary analysis. Tapped as supplements to more traditional approaches, mathematical and scientific analogies can help reveal a “calculus,” in the fundamental sense of the word, to literary language: an inner logic and set of processes by which literal and figurative meanings cohere.  Metaphors function as “equations”; ideas, characters, and plot elements connect through “transitive” relations; like “multivalent” atoms, images bond with other images in complex arrangements that can suggest multiple levels of significance in a given text. Beyond firing interest in classrooms that are too often discipline-constricted, such applications can add elegance and clarity to interpretation, help create a rational and systematic grounding for a field of study that students may perceive as merely intuitive and, inviting breadth of intellectual perspective, help reveal the beauty and power of both artistic and scientific ways of knowing.

A straightforward starting point for mathematical conceptualization is the teaching of metaphor and simile as simple equation, a formulation of identity. This perspective delivers (as do, broadly speaking, all of the math/science analogies) a kind of meta-metaphor—a metaphor that elucidates the nature of metaphors. A literal term equals a figurative term; the comparison can be expressed as A=B. Assuming the identity as a starting point and using context clues to define the anchor terms, students can sort and map the language of a given figure or text, with literal words and images on one side and figurative on the other; they are then positioned to discover implied meaning. Potential examples and applications are innumerable. Keats’s “On First Looking Into Chapman’s Homer” equates reading with traveling. With the first quatrain of the sonnet, students might ultimately create a chart as follows:

This multi-termed equation grounds and focuses further analysis. As Keats’s poem unfolds, “travel” becomes exploration and discovery; the “states” and “kingdoms” become planets and seas. And the equation can, of course, generate relations far beyond the initial A=B. The metaphor may be extended, for instance; it may be modified or transformed (or both, as in Keat’s sonnet), and it may dissociate as well as (or rather than) affirm identity of literal and figurative terms.

The transitive property in mathematics describes a more complex kind of identity: If A=B and B=C, then A=C. Again, the literary applications, extending beyond words to characters and plot configurations, are potentially powerful. In act 3, scene 1, of A Midsummer Night’s Dream, reference to the transitive property can illuminate the wit and genius of Shakespeare’s conceptual design. As the mechanicals rehearse Pyramus and Thisby, the figurative identity Shakespeare has already established for Nick Bottom is now comically literalized: Puck gives him an ass’s head because he is an ass. In fact, however, Shakespeare conjures here a double identity transformation: Before he is metamorphosed into an ass, Bottom has assumed his stage role as “Pyramus.” Puck charms Bottom when he is playing the part of young lover.  But Pyramus, in turn, images all of the larger play’s lovers, and the play within the play as a whole mirrors MND’s plot. The transitive property permits us to map the action as follows:

            Bottom             =            Pyramus            [= lovers]            =            ass
                                               
The play thus reveals—and the transitive property helps readers and viewers grasp—that any young lover by definition is an ass. Indeed, Shakespeare’s plotting further reinforces this set of parallels. When his friends desert him in the wood, Bottom concludes that he is the victim of a conspiracy (“This is a knavery of them to make me afeard”)—just as Helena will do one scene later (“Now I perceive they have conjoined all three / To fashion this false sport . . .”). Bottom next finds himself the object of a most unexpected infatuation, again as Helena will in act 3, scene 2.

Another example further underscores the suggestiveness of the transitive concept as a vehicle for interpretation. Edgar Allan Poe constructs “The Fall of the House of Usher” almost entirely around reflecting images: the house = image of the house mirrored in the tarn = Roderick = Madeline= Roderick’s painting = “The Haunted Palace” = “Mad Trist” = narrator. Use of the transitive property helps not only to establish these links but also to formulate essential questions provoked by the reciprocal relations: Who is Roderick? What happens to Madeline? To what degree, if at all, can we trust the narrator?

Through the concept of multivalency, borrowed from chemistry, students can with fresh insight observe the power of words or images, patterned with repetition and variation, to elicit both stable, core concepts and a range of associated meanings or connotations. The term valence in chemistry means the combining capacity of an atom; multivalency describes the high capacity of a particular atom for combining with others. (Polyvalency, a synonymous term in chemistry, is at times used in literary theory to denote not a pragmatic strategy for critical reading but rather the open-ended assignment of meaning to texts.)This analogy can elucidate at least some of the ways in which writers build complex frameworks of idea and perspective—ways in which whatever it is that we choose to call “meaning” in literature emerges as a function of language design. In complex works such as Inferno, The Great Gatsby, The Road, and Heart of Darkness, we can think of any given thematic issue or question as a “molecular” construct developed through the “bonding” of a constant image-“atom” with a series of contextual details. Such an approach does not exclude or limit but complements a more traditional metaphor—say, a tapestry woven of multiple strands—for suggesting the vitality of literary language. Consider, for example, instances of “whiteness” in Heart of Darkness: European outposts, viewed from afar, in the African jungle; the thread around a dying native’s neck; the clothing of the accountant; ivory; the boilermaker’s serviette; the fog that besets Marlow’s steamer. A class exercise would start with isolation of the pattern (I ask students to recall and locate examples of notable terms or images repeated in the text); then students would attempt to define a constant or stable value for “whiteness” that links all of the instances (“imperialism,” they might say, or “European values”). Next, readers would aim to refine specific significance according to context—i.e., the nature of the particular bond the “whiteness” atom has formed in the context of other details and ideas. In the case of the dying native, then, students might conclude that “whiteness” symbolizes the tendency of imperialism to oppress, enslave, or destroy that which it also fascinates (the African has himself tied the string around his own neck). In the case of the accountant, described only a few paragraphs later in the text, however, “whiteness” bespeaks seemingly positive attributes of “civilization”: a capacity for work—or, in Marlow’s words, “devotion to efficiency.” Proceeding thus with this pattern and numerous others in Conrad’s novel (e.g., darkness, light, blackness, religion, fascination, hell), students are poised to begin articulating central issues and adumbrating the associated shades of meaning, subtleties, and paradoxes.

The patterning of language in literature—its logos rhythm, we might say—allows us thus to devise a set of algorithms, computational procedures, as a strategy for approaching significance. Judiciously employed, math and science analogies can bring clarity and rigor to students’ understanding of a field that, many may come to feel, rewards imprecision. (When students encounter a classroom culture that rewards them for expressing almost any kind of response to a story or poem, they can learn to think of interpretation as a simply intuitive, even mushy endeavor, whether or not the teacher has explicitly presented it in such a way. The “no-wrong-answers-in-English” outlook is the wrong answer for teaching literary interpretation: While a given poem, novel, or play may of course elicit a range of sound readings, groundless, speculative responses are “wrong.”) The incorporation of mathematic and scientific terminology can also help counter the tendency of young people to classify themselves as “math/science” or “language/arts” in their intellectual orientation. It attracts students who think of themselves as mathematical or scientific in their intellectual orientation, and it can balance an overreliance on feeling in those who might see themselves as primarily intuitive. All gain a useful tool for critical reading. All come to see that “scientific” as well as artistic thinking is commensurate with the gauging of self-knowledge and human experience, whether rational or emotional, and with the expressive capacity of language in conveying that experience.

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