Michel Chaouli

“Theory of the Combinatorial Method” of Poetry

[Excerpt]

It may have become clear how Schlegel’s efforts distinguish themselves from the long tradition of combinatorial efforts—some systematic, some playful—preceding him: while the traditional combinatorics relies on a mathematical model, which goes back at least to the ars combinatoria of the thirteenth-century Franciscan friar Ramón Llull, Schlegel, as we have seen, prefers chemistry. Llull’s is a strange and complicated system in which the nine essential qualities of God (goodness, truth, glory, etc.) are assigned to the letters B through K (skipping J) and then combined and recombined to produce all propositions that are true of God. In his 1666 dissertation De arte combinatoria, Leibniz develops the Llullian scheme into a project that would occupy him throughout his career, namely the invention of a “calculus of concepts” based on an “alphabet of thought.” [62] In essence, this is an attempt to render language in mathematical terms: if thoughts could be reduced to their simplest elements, if those elements could be assigned to signs (letters or numbers), and if, moreover, the combinatorial rules governing these signs could be laid out completely, then a calculation would reveal the truth or falsehood of a proposition. What is more, an infinity of completely new propositions could be derived by nothing more complicated than applying the combinatorial operations to the elements of the system.

I would like to set aside the many fascinating features of Leibniz’s stupendously ambitious, and utterly mad, project to focus attention on two aspects that it shares with all mathematically based combinatorial systems: first, such a combinatorial system is universally applicable in its domain, that is, it produces all combinations and permutations of a set of elements with complete regularity. Thus a system with three elements A, B, and C yields (assuming that repetitions are not allowed and the order is insignificant) three, and only three, two-letter combinations: AB, AC, BC. To Leibniz and its other practitioners, the chief attraction of this combination-generating system lies precisely in its reliability, for it allows, they believe, the creation of a language that is universally comprehensible. (Llull invents his to convert the many infidels in his Judeo-Muslim-Christian Majorca; Leibniz is interested in establishing peace between nations.) But for this feature of the ars combinatoria to function properly, a second must obtain: the system must be entirely formalistic. It must yield its results in a predictable, algorithmically unimpeachable—which is to say: mechanical—fashion regardless of its content. No matter what may be understood by A, B, and C, the fact that, given the formal constraints I mentioned earlier, there are exactly three ways of pairing them up remains true. It is because of the radical formalism of the system that, lest his system refer to nothing but itself, Leibniz is required to assume a preexisting harmony of the order of signs and the order of things: “There exists,” he writes, “between signs . . . a relationship or an order that corresponds to the order of things.” [63]

John Neubauer, to whose informative book Symbolismus und symbolische Logik (Symbolism and Symbolic Logic) I owe this last passage from Leibniz, uses the idea of combinatorial art to establish a continuity of practice from the hermetic work of Ramón Llull via the playful combinatorics of Baroque poetry to the writings of Schlegel and Novalis and, finally, the “poésie pure” of the French symbolist poets, notably Stéphane Mallarmé and Paul Valéry. It is his contention that the ars combinatoria is an attempt “to help poetry out of its crisis by means of a mathematical form,” a crisis provoked by the “jolting consequences of scientific discoveries.” [64] What on his account makes combinatorics useful for romantic and post-romantic poetic practice is the willingness of poets not to make the Leibnizian assumption about a preestablished harmony of signs and things, to sever instead the presumed link between signifiers and signifieds; thus Valéry’s pronouncement: “It is the faculty of speech that speaks.” [65] Once released from the necessity of reference, poetry can devote itself entirely to pure language, to exploring its breadth and depth by means of mathematical techniques.

This reading, while suggestive and original, strikes me as problematic, certainly with regard to Schlegel. The problem lies not merely in the paucity of evidence provided by Schlegel’s writings for such a reading, especially in comparison with those of Novalis and Valéry (Mallarmé’s case is again more ambiguous, I think). A far greater difficulty lies in the inadequacy of the mathematical model of combinatorics in describing the innovative features of Schlegel’s—and not only Schlegel’s—poetic practice and poetological conception. It stands in violation of the two crucial features of Leibnizian mathematical combinatorics that I mentioned a moment ago: the universality in the application of operational rules and the strict formalism separating the rules from the material upon which they act. His combinatorial conception does not function homogeneously, but is rather, as we have seen, contaminated by strange and unaccountable forces of attraction and repulsion. Its material—words, syllables, and letters—can never be fully abstracted, but always infects the formal rules—its syntax—with semantic remainders. And it is precisely the strength of this method that combinations cannot always be controlled and, hence, predicted. In short: the system behaves far too bizarrely and chaotically to comply with the mandates of variation, permutation, and combination inherent in a mathematically combinatorial system. [66]

Instead, Schlegel’s combinatorics inhabits the dubious region of eighteenth-century chemistry, with its mysterious forces of affinity and repulsion that attempt to regularize the otherwise unaccountable behavior of the elements. It is this unaccountability, rather than the clockwork mechanism of mathematics, that appeals to Schlegel. “The most important scientific discoveries are bons mots of the [Leibnizian and Baconian] kind,” he writes in an Athenäum fragment. “They achieve that through the surprising contingency of their formation, through the combinatorial quality of thinking.” [67] Far from approaching the Truth with the help of a machine that generates well-ordered combinations, his science—Wissenschaft—moves by leaps and bounds, by small and large eruptions of combinatorial contingency, by the explosions of wit. Thus “the encyclopedia can simply and absolutely only be presented in fragments,” which Schlegel glosses as “combinatorial ideas.” [68] The mathematically inspired model of combinatorics has no room for such contingency; it is methodical and dull (which is precisely why Leibniz favored it) and hence ill-suited as a model for both the excess of sense produced by a genius-poet and the excess of “error and of madness, or of obtuseness and of stupidity” that can shine through poetic language. I suspect that this inadequacy also applies to the other modern writers discussed by Neubauer. Does the line from Valéry, quoted with a bit more context, not point to this excess from the strictly mechanical in mathematics? “It is the faculty of speech that speaks; and speaking gets drunk, and drunk dances.”

This hybrid logic powerfully describes the ambiguous relationship of part and whole that we observed in the fragments, a relationship that is crucial as an allegory for aesthetic theory. The chemical model of constant combination and separation allows for a notion of fragments whose sheer numerical plenitude plunges them into a force field of reciprocal attractions and repulsions that, as such and without dialectical sublation, constitutes a whole. Schlegel himself offers a conception to distinguish this form of totality from the organicist totality prevalent in the writings of his contemporaries: “Where one attempts to form elements not merely homogeneously but also heterogeneously, there one strives for totality not merely for unity.” [69] Totality—Ganzheit—achieves its infinite reach precisely by abandoning unity in favor of the nonidentical, combinatorial, differential system that requires heterogeneity. The insertion of merely (bloß) before homogeneously and unity makes amply clear which term Schlegel, at this point, prefers. How clear his preference is becomes even more evident when we consider the way he maps the distinction between heterogeneous totality and homogeneous unity onto the historical axis of Ancients and Moderns that we encountered earlier: “The Classical poetic genres have only unity; the progressive genres alone have totality.” [70] While Athenäum fragment 24 (“Many works of the Ancients have become fragments. Many works of the Moderns are fragments the moment they are made”) registers the discontinuity between Ancients and Moderns with an equanimity that at least permits us to imagine hearing a faint longing for a lost wholeness, the fragment just quoted—probably written in 1797 or 1798, almost coincident with the Athenäum fragment—polemically favors the romantic Moderns. And it does so because of the lack of homogeneous unity exhibited by their works. The logic that governs much of the essay “On the Study of Greek Poetry,” published in 1797 but largely completed in the autumn of 1795, is turned on its head: if there the advantage that Classical works enjoy lies in their organic articulation, here, merely two or at the most three years later, it is precisely chemical fragmentation that has been turned into the distinguishing feature of Modern works. Fragmentation is the mark that lifts Modern texts above the “mere” unity of the Classical, because fragmentation—and only fragmentation—offers the possibility of totality. As Schlegel sharply recognizes in lines I quoted earlier, universality is a function of fragments imbued with “combinatorial quality . . . for only where a plenitude of heterogeneous substances are united can new chemical combinations and their permeations occur.”

62. I am indebted to Eco, The Search for the Perfect Language, 53-72, for information about Llull, and 269-92 about Leibniz.

63. Leibniz, Die philosophischen Schriften, 7:192.

64. Neubauer, Symbolismus und symbolische Logik, 11.

65. Valéry, Oeuvres, 1:635.

66. It is true that twentieth-century mathematics has had to confront the specter of regions of undecidability and incoherence within its borders, but this has not changed the validity of the two features I mentioned earlier: algorithms continue to work mechanically (if not always universally), and the formalistic distinction between rule and input continues to obtain. I am grateful to Barry Mazur for clarifying this issue for me.

67. “Die wichtigsten wissenschaftlichen Entdeckungen sind bonmots der Gattung. Das sind sie durch die überraschende Zufalligkeit ihrer Entstehung, durch das Kombinatorische des Gedankens,” KA 2:200, No. 220/PF 47.

68. “Die Encycl[opädie] läßt sich schlechterdings und durchaus nur in Fragmenten darstellen—Diese combinat[orischen] Ideen... ,” KA 18:485, No. 141.

69. “Wo man die Bestandtheile nicht bloß gleichartig sondern auch verschiedenartig zu bilden strebt, da strebt man nach Ganzheit nicht bloß nach Einheit,” KA 16:89, No. 46.

70. “Die class.[ischen] Gedichtarten haben nur Einheit; die progressiven allein Ganzheit,” KA 16:122, No. 446.

SOURCE: Chaouli, Michel. The Laboratory of Poetry: Chemistry and Poetics in the Work of Friedrich Schlegel (Baltimore: Johns Hopkins University Press, 2002), Chapter 4: “Theory of the Combinatorial Method” of Poetry, excerpt, pp. 124-128, 246-247.

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