Pink Noise -- Andrew Joron

To paraphrase Gödel: No system of rules can produce a poem unless that system also allows words to relate in ways that exceed guidance by the system.

Mary Margaret Sloan's "On Method" is a poem conditioned, but not controlled, by the application of rules. Indeed, tension between the method and its poetic dépassement is one of this work's most compelling features. In poiesis (as opposed to verbal game-playing), words are arranged more or less methodically, but only in order to go beyond words, to say the unsayable.

At the same time, there can be no poetry without constraints. Language is the most complex medium available to any artist; it is never given in a "pure" state, but arrives (always, already) layered and overdetermined by conventions and formalizations of every kind. A poem inevitably must be played upon the interwoven strings of these language-constraining systems.

In the case of "On Method," an explicitly artificial system of rules overrides and filters "natural" language protocols, creating a clearing, an elsewhere. As the poem slowly builds and recycles in accordance with Sloan's formalism, the experience of reading acquires a trance-like quality similar to the experience of viewing Alain Resnais's film Last Year at Marienbad (a work whose mystery likewise depends on the unfolding of a formal pattern). In Sloan's poem, we "pass the threshold into the palace of our instructors"--that is, into an architext replete with formal devices--just as in Resnais's film, the protagonists become caught in a complex temporal loop and wander through the endless corridors of a castle. Both works play out as inexorable rituals set among relics of classical reason.

The formalism of "On Method," as Sloan indicates in her preface, is designed to "wreck itself from within." Her work thereby alludes to and allegorizes those developments in logic and mathematics that, since the end of the nineteenth century, have shaken the foundations of classical reason (viz. Riemann's discovery of non-Euclidean geometries, Cantor's discovery of irresolvable paradoxes in number theory, and Gödel's discovery of axiomatic incompleteness).

However, the specific formalism that Sloan has chosen--a rondel whose repeating lines increase in length (i.e., number of words) according to an algebraic function--never abandons the classical confines of the Cartesian coordinate system. While the arrangement of words within the poem is made to undergo a "mathematically determined deterioration," the mathematical model itself maintains its stability in relation to "a central Cartesian axis."

Moreover, the uncanny lyricism of this work cannot be attributed entirely to its mathematical method, since the method does not pertain to word choice. Yet the semantic surface of the text shares the paradoxical, counter-intuitive, and non-formalizable qualities of post-Cartesian mathematics, even as the poem's deep structure conserves the "clear and distinct" ideals of Cartesian method. Here, formal constraint serves as a propaedeutic for the poetic imagination, which in the end is driven by inspiration rather than rules.

Indeed, Sloan's language may be most "mathematical" when it is most inspired: for we are living in an era--though few seem to realize it--of the convergence of science, mathematics, and poetry. Christopher Langton, a leading researcher in the science of complex systems, has said that the understanding of nonlinear interactions can be enhanced by poetic thought: "Poetry is a very nonlinear use of language, where the meaning is more than just the sum of the parts. I have the feeling that culturally there's going to be something like poetry in the future of science" (Scientific American, June 1995).

Even in the mid nineteenth century, as cracks were beginning to appear in the foundations of reason, the German mathematician Karl Weierstrass observed that "A mathematician who is not also something of a poet will never be a perfect mathematician."

Weierstrass is credited with the discovery of the first fractal object--a curve consisting completely of corners (that is, every corner is made up of further corners ad infinitum). Such a curve occupies more space than a one-dimensional line, but occupies less space than a two-dimensional circle or square. Its dimensionality is fractional, thus prompting the descriptive term fractal. Subsequently, many more patterns exhibiting fractal self-similarity have been discovered both in mathematics and in nature.

By the mid twentieth century, the Polish mathematican Benoit Mandelbrot had discovered an extraordinarily intricate class of fractals based on complex numbers (i.e., numbers generated by the square roots of negative numbers). Patterns produced by the Mandelbrot set are highly nonlinear, bifurcating chaotically while remaining self-similar at all scales.

Poets who seek to infuse language with the counter-intuitive and vertiginous properties of post-Cartesian mathematics might be tempted to adopt a fractal-based method of writing. The Mandelbrot set, however, is spectacularly unsuited to such procedures, mainly because the square roots of negative numbers have no counterparts in the world of physical objects (including linguistic objects such as letters, words, lines of verse, or stanzas). It is true that complex numbers can be represented geometrically as points, but the points cannot be located on a standard coordinate grid of whole numbers. Instead, they must be displayed on a modified grid called the Argand plane, where imaginary and real numbers intersect. However, no part of language can be made to correspond--without violence--to this dizzingly abstract intersection. (Leibniz referred to complex numbers as a "sublime outlet of the divine spirit, an amphibian between being and not-being"; Euler deemed them to be not only imaginary, but "impossible" numbers.)

Still, not all fractals derive from complex numbers or exhibit chaotic patterns. Such "linear" fractals may prove more amenable to linkage with systems of language. An example is provided by the "Sierpinski gasket," constructed by inscribing an inverted equiltateral triangle inside another equilateral triangle (so that the apex of the inner triangle touches the base of the outer one). This means that the enclosed area on each side of the inverted triangle also becomes a triangle. The procedure is repeated for each successively appearing triangle ad infinitum. The resulting pattern, despite its simplicity, possesses the primary feature of fractal entities: self-similarity at all scales (i.e., each part is identical to the whole).

Thanks to L.S.D. (Littérature Semi-Définitionnelle), a project undertaken by French writers Marcel Bénabou and Georges Perec, we can cite a writing procedure analogous to the Sierpinski gasket. Take a sheet of lined paper; write one word on the first line; on the next line, write the definition of that word; on the next, the definitions of each word of the preceding definition; and so on. The result is an expansion of the meaning of one word, comparable to the numeric expansion of Pascal's Triangle (a stack of numbers in which any number is the sum of the two numbers situated immediately above it). Furthermore, it can be demonstrated that Pascal's Triangle is an arithmetic version of the Sierpinski gasket.

Bénabou and Perec later became founding members of Oulipo (Ouvroir de Littérature Potentielle), a French movement devoted to the use of formal procedures in literary writing. Formulated in opposition to surrealist methods of automatic writing, the Oulipians' "bon usage de la contrainte"nonetheless similarly strives to free literature from the domination of conscious intentionality and to allow literary language somehow to construct itself.

Mary Margaret Sloan, as the author of "On Method," now must be considered the foremost oulipienne américaine. Perhaps we have not yet arrived at the point, to paraphrase Weierstrass, where "a poet who is not also something of a mathematician will never be a perfect poet," but at least an idea may be dawning on poets that language is capable of levels of organization far beyond personal, or even social, experience. Mathematics offers a significant means of accessing these levels.

As Sloan implies in her preface, post-personal poetic language must "develop as a complex adaptive system," poised on the cusp between order and chaos, between the "white noise" of utter randomness and the "brown noise" of repetitive-signal transmission. The zone in which surprising information can be transmitted is termed "pink noise," and it is precisely toward this interzone that Sloan has adjusted the modulation of her marvellous device.