This doesn't answer Cuculiere's question, but HM'ers may find the following excerpt of interest. It comes from a long piece by Dale Keiger in the Johns Hopkins Magazine titled "A Sleuth in the Garden of Forking Paths," which can be read in its entirety at http://www.jhu.edu/~jhumag/495web/sleuth.html .
Barry Cipra email@example.com
.... John T. Irwin is Decker Professor of the Humanities, professor of English, and chair of the Hopkins Writing Seminars. In 1981, four years after returning to Hopkins from a stint as editor of the Georgia Review, he put aside projects on Hart Crane and F. Scott Fitzgerald to explore his fascination with a set of six detective stories. Three were by Edgar Allan Poe, three by Jorge Luis Borges, the late Argentine writer of short stories and essays. Irwin began puzzling out the myriad arcane references and sly allusions contained in these texts, and the more he found, the more curious he became. He expected to divert himself from his other projects for perhaps two years.
Thirteen years later, he finally delivered a manuscript that he says, with a typically boisterous laugh, "consumed my middle years." The Mystery to a Solution: Poe, Borges, and the Analytic Detective Story (Johns Hopkins University Press, 1994) is an intellectually muscular 452-page analysis of what Poe said was "little susceptible of analysis"--the nature of analysis. If that sentence gives you vertigo, you've had but a taste of what the book will do to you.
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Irwin did get stuck now and then, he admits. One major block occurred over a section of "The Purloined Letter." Poe, a concise writer, had included a strikingly long passage on mathematics, in which Dupin alludes to a debate over whether algebra constitutes the highest form of analysis. Irwin didn't understand the reference.
He spent three years trying to understand what Poe was getting at. He tracked down the titles of the math books Poe had possessed, and the math curriculum he had studied at the U.S. Military Academy at West Point. The trail led Irwin to the French Ecole Polytechnique, England's Cambridge University, early 19th- century French politics, and the real Dupin brothers, who lived in Paris in the early 1800s and were models for various aspects of Poe's characters of the detective and the evil minister.
What Irwin finally deduced was that at the time Poe studied mathematics, there was an intellectual debate underway as to the merits of algebraic versus geometrical analysis. In Paris, because Ecole Polytechnique had been established to train engineers for the new French republic, says Irwin, "The math taught there was in the popular mind the math of Revolutionary France." Thus the debate had political implications, and Irwin reminds that "Purloined Letter" is a story of political intrigue. Poe had tied his story to actual events and the intellectual milieu of his day.
Beyond that, Irwin believes that many of Poe's readers in the 1840s would have been conversant with the math debate, much as modern readers would be aware of debates about deconstruction or political correctness, and thus might have equated analysis with algebra. Poe disagreed with that equation. He notes, through his character Dupin, that analysis comes from a root meaning "to take apart," and algebra from a root meaning "to put together." Anyone who equates the two, Dupin says, is not to be trusted. Poe makes Minister D-- (Dupin's nemesis) a "poet and mathematician"; by having Dupin solve the mystery by thinking like the poet/mathematician minister, Poe argued that mathematical analysis alone was insufficient to solve a deep mystery. What one needed, Poe believed, was to marry the resolvent logic of higher mathematics with a higher, poetic creative power. A "true" mathematician was also a poet.
In the same passage from "The Purloined Letter," Dupin discusses a formula: x2 + px = q. The literature professor was stumped by this, too. "I'd only had first-year calculus in college," Irwin says. "I had to go back and learn more math." It occurred to him that the formula might not mean anything, might just be an invention of Poe's. But, he says, "Once you've lived with a writer's work for so long, you get a sense of what they invent and what they don't invent. In Poe, when information has a certain level of specificity, that's generally a clue that it's not made up--that it has a reference and you will learn something if you find that reference. I knew that formula was not the sort of thing Poe would invent. I was going to look for the answer until I dropped."
Knowing that Poe had owned a translation of S. F. Lacroix's Elements of Algebra, Irwin went to the Hopkins Eisenhower Library Rare Book Room, looked up the book, and found the equation, which turned out to be a well-established formula for solving quadratic equations with one unknown. Irwin links quadratic and square, then offers an interpretation of Poe's use of the equation that creates a striking image of thought and the self-conscious mind.
A square, Irwin says, seems to be a straightforward construct. After all, it's precisely quantifiable, describable, measurable, and therefore rational. The square is a classical figure of perfection, an image of rectitude and stability that persists in sayings like "a square deal."
Yet, as Irwin points out, a square contains an implicit diagonal, and that diagonal is the hypotenuse of each of the two resulting triangles (that three/four business again). If we assign a value of one to each side of the square, the length of the hypotenuse is the square root of two--an irrational number of infinite decimal places. In other words, Irwin says, at the heart of the square, this image of all that is rational, measurable, and stable, lies irrationality and infinite possibility. Says Irwin, "In something that seems so finite, the abyss of the infinite yawns."