Poe-tic Mathematics: Detecting Topology in “The Purloined Letter”

PaulA. Harris Poe-tic Mathematics: Detecting Topology in “ThePurloined Letter” “As poet and mathematician, he would reason well; as meremathematician, he could not havereasoned at all.” -Dupin, in “ThePurloined Letter” In his tales of ratiocination, Edgar Allan Poe sought nothing less than to invent a model of sheer genius. At play in Poe’s stories is the image of a raw power of mind able to exert control over language, other people, and enigmatic situations. The epigraphic remark, made by C. Auguste Dupin, Poe’sdetectivehero,would no doubt seem unreasonable to those who champion mathematics as the highest or purest form of thought, from Plato to Stephen Hawking. Conversely,though, if the creativeimagination of poets has been undervalued by mathematiciansand scientists,the mathematical dimension of Poe’s epistemological model has gone largelyunrecognized by his readers . In the debates touched off byJacques Lacan’s andJacques Derrida’sreadings of “ThePurloined Letter,” the story became a blueprint for several forms of “analysis”-including psychoanalysis, deconstruction, and several other types of litera r yinterpretation. Butapproachesto the talefrom within the human sciences-with the notable exception ofJohn T. Irwin’s-have passed overPoe’s specific stipulation that the reasoning displayed in the detective stones incorporates poetic and mathematical principles.’ Reinscribing the disciplinary divide between the “soft”and ”hard”sciences , such readings miss much of what makes Poe’s integrated model of thought so radically different. For Poe did more than simply incorporate mathematics in his story in an odd, allusive, or metaphorical fashion. Embedded in “ThePurloined Letter” is a complex intervention in the mathematical debates of his day. In retrospect, Poe’sresolution to certain problems may even be seen as anticipating in nascent, intuitive form the invention of topology-a branch of mathematics formulated forty years after the publication of “ThePurloined Letter.” Poe critics have presumed that his detective is modeled after AndrC-Marie-Jean-JacquesDupin (1783-1865), a prominent French political figure of the time. In the April 1841 issueof Graham’s Magazine, in which Poe published the first of the Dupin stories, he also reviewed a book titled Sketches o f Conspicuous Living Characters o f France that features a chapter describing the Frenchman ’scareer. As Irwin notes, the historical Dupin certainly resembled Poe’s detective in important ways: he was an encyclopedic thinker who possessed many antithetical traits,just as the fictional Dupin is a polymath who, as “poetand mathematician ,” embraces several opposing qualities and kinds of knowledge. Irwin then speculates that Poe based the figure of the Minister D - on Charles Dupin, the historical Dupin’s brother, who was a minister under Louis XVII and a renowned mathematician.2 This supposition is based on the fact that Poe informs us that the Minister D - “haswritten learnedly on the Differential Calculus” (Works, 3:986). But Poe’s Dupin in fact resembles Charles Dupin in certain crucialways, especiallyasregards the specifickind of mathematical research he pursued. Charles Dupin made his intellectual reputation doing work opposed to those who employed the calculus , and therefore differs importantly from the mathematical interest attributed to Poe’s Minister D - . As we shallsee,Poe’s detectiveespouses the very mathematical approach to which Charles Dupin made significant contributions. It is quite T o p o l o g yin “ThePurloined Letter” 19 plausible,then, that Poe’s Dupin, the figure who embodies the powers of the mind, is based on a mathematician. It is understandable that Poe’smathematical interesthasgone almostundetected. Literarycritics are, asDupin saysof the Parisian police, “‘persevering , ingenious, cunning, and thoroughly versed in the knowledgewhich their duties seem chiefly to demand” (Wonks, 3983).Given that a critic’sprimary duty is to read, it seemsonly logical that “ThePurloined Letter” has been read as a paradigm of reading. Irwin has differentiated Poe’s mystery tales from other writings in the genre on the grounds that they are “analyticdetectivestories ,“in that the solutionto the mystery isonlythe firststagein the interpretivegame they initiate. Poe, Irwin writes, is able to “presentthe analyticsolutionof a mystery andat the sametime conserve the sense of the mysterious on which analysis thrives.”sThe singular twist in “ThePurloined Letter” is that it dramatizes quite explicitly and precisely the reading process necessary to detect the lettered treasures it has hidden in plain...