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Chapter Eight— Descartes in Relational Garb
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Mallarmé and the Light of Reciprocal Reflections

In the first part of this book I suggested that Mallarmé was satirizing the Cartesian method in his introduction to English Words . If that is true, then it is no surprise to see the young Mallarmé in 1869 dreaming up a project for a book in which all the factors I've been talking about come together. It seems that in the late 1860s Mallarmé was considering taking a degree in linguistics, and in a fragmentary note somehow related to this plan he writes:

A strange little book, very mysterious, a bit in the manner of the Fathers, very distilled and concise—this in places that could give rise to enthusiasm (study Montesquieu).

In others, the great and long period of Descartes.

Then, in general, some La Bruyère and some Fénelon with a hint of Baudelaire.

Finally, some me [du moi ]—and some mathematical language.
(OC, , p. 851)

A paragraph or two farther on, he mentions the Discourse (misquoting the title) and then says, "We have not understood Descartes, foreigners have taken possession of him: but he did arouse French mathematicians" (OC, p. 851). Mallarmé never explains the intriguing little phrase about mathematical language. If by chance he meant something like the rigorous, methodical mode of exposition that Descartes's principles suggested, then we know that the closest he ever came to adopting the Cartesian method in his own writing was to parody it. And perhaps the


effort to parody that method was made only as the result of Mallarmé's having first internalized it.

The mathematical imagination had clearly seized hold of Mallarmé. But it is the "modern" kind of mathematics, the relational kind, that shows up time and again in his writings. Earlier I said that the theory Mallarmé appears to be proposing in "Crisis in Verse" led to a relational notion of language. In fact, if we look at that essay again, we can see that Mallarmé, without knowing it, is essentially giving us an illustration of Serres's argument about linear and tabular meanings. The "uniquestamp" view of meaning, where words turn out to be "materially truth itself," is really the linear view, or the symbolist view (in Serres's sense of symbolism). In this view one can draw a straight line from the signifying object to the thing it signifies. But in Mallarmé's enlightened view of language, meaning comes from the "reciprocal reflections" of words, and this sounds like Serres's notion of tabular meaning.

The idea of a group of relations appears several times in Mallarmé in one form or another. Later in "Crisis in Verse" he refers to music as "the set [ensemble ] of relations existing in everything" (OC, p. 368). Virtually the same phrase occurs in "The Book, Spiritual Instrument." Just after Mallarmé says, "Everything, in the world, exists to end up in a book," he lists the qualities that will be required in his book: "hymn, harmony and joy, like the pure set, grouped in some fulgurating circumstance, of relations between everything" (OC, p. 378). These phrases were composed later in Mallarmé's life. But even as early as 1866 he had adopted a relational view of poetic language. In a letter to François Coppée he says, "What we need to aim for above all in the poem is for words . . . to reflect on one another to the point where they appear no longer to have their own color but to be only the modulations of a scale ."[7] In a curious passage in a letter to another friend that same year, Mallarmé uses an image that suggests the same model. The young poet writes that he has just cast the plan for his entire oeuvre, after having discovered his own "center," "the center of myself, where I sit like a sacred spider, on the principal threads that have already come out of my mind and with whose help I will weave at the points of contact marvelous lacework."[8]

The place where we see Mallarmé's mathematical imagination at its best is his writings about the Book. In chapter 4 I described the manuscript notes that have been published under the title Le "Livre" de Mallarmé . It is full of numbers, calculations, and geometric designs. Some of the calculations appear to have to do with the number of spectators


at a performance of this mysterious work. Others have to do with the arrangement of pages in the work. Still others are about as apparently mundane a question as the amount of money the author will be able to collect from ticket sales at the performance. Sometimes all three appear together (see illustration).[9]

But even though it's hard to say what these manuscript notes are, we can see that the numbers are an essential part of the work that Mallarmé was contemplating. This is not just scratch paper on which the author figured his monthly budget. The recurrence of certain significant numbers, usually multiples of four, shows that all these details were integral to the work. Whatever this "work" was supposed to be, we can say with some confidence that its numerical properties were not going to be left to chance. In fact, one has the impression that the "content" could never be more precisely spelled out than it was because the essential nature of the work was not the content but exactly these numerical properties. Consider again the drawing on page 95. What is it? Not just doodling, because there are other designs in the manuscript that look similar and are accompanied by various terms that have occurred in lots of other places in the manuscript notes. It appears thus to have something important to do with what the work is. It's as if Mallarmé had set out to determine a set of geometric coordinates for his work and once that was done had decided nothing more was necessary.

How can a work have geometric coordinates? For one thing, it can be a performance in which the disposition of seats, spectators, and performers (the "operator") is an integral part of the work. In that case the work has coordinates in the literal sense, coordinates that belong to actual points in the space in which the performance takes place. Or it can be the sort of thing where there are mystical numerical correspondences between numbers of spectators and the amount of cash they pay for admission. Then the coordinates cannot be assigned to actual physical locations but exist instead as abstractions, and these abstractions are diagrammed in the manuscript notes. Or it can be a book whose pages may be shuffled and reshuffled in any number of combinations to generate as many different "works." In this "mobile-pages" conception the pages of the book are distributed in various determined locations of the space where the book is performed. In any of these cases the essential point about the work is that it is a relational structure.

One of the strangest things Mallarmé wrote is the text called Un coup de dés (A throw of the dice), published in 1897. There's no exact word for what this work is. In fact it's not even clear that Un coup de dés is


From Jacques Scherer,  Le "Livre" de Matllarmé: Premières recherches sur des documents inédits
(Paris: Gallimard, 1957), pp. 37(A)–38(A).


the title. The text, twenty-one pages long, contains the sentence "Un coup de dés jamais n'abolira le hasard" ("A throw of the dice will never abolish chance") spread out in four pieces over seventeen pages ("Un coup de dés / jamais / n'abolira / le hasard"). This central sentence is printed in oversize type. In between its fragments are numerous phrases and sentences written in a variety of smaller types. The "poem," if that's what it is, is of course tricky to read. The main sentence gives it a kind of syntactic completeness and serves as a unifying device. The problem is what to do with all the other words. It is tempting to read them as a highly complex network of parenthetical and dependent clauses, where the clauses printed in smaller type depend on the ones printed in larger type. But even if you try to read it in this way, you get hopelessly bogged down in twenty-one pages of interlocking grammatical dependence and soon give up. Paul Valéry, who claims to be the first human being (other than the author) ever to see this work, says that Mallarmé first read it to him "in a low, even voice, without the slightest 'effect,' almost to himself."[10] The text actually may be read in many different ways: you may read one type size at a time, you may read through the text in the order in which the words are printed, or you may simply read in any order you choose. Once again we have a shuffling game, a relational scheme whose most prominent feature is precisely its refusal of linearity. This refusal is both syntactic and semantic—syntactic because a linear reading of the text is almost impossible, and semantic because this is one place where even the most old-fashioned thinker will see that meaning does not arise word by word in a linear fashion.

There is also no linear connection between the text and the person who wrote it. How do you establish an authorial voice for a thing that can't really be read in any of the traditional senses? no, there can be no sign of the author's presence, and strikingly enough, the disappearance of the author (a much-touted idea in Mallarmé's age) seems to be explained by the relational quality of the text. Think back to the passage in "Crisis in Verse" in which the notion of reciprocal reflections is introduced: "The pure work implies the elocutionary disappearance of the poet, who instead yields the initiative to words, mobilized by the clash of their inequality; they light up from their reciprocal reflections, like a trail of fire on gems, taking the place of that palpable breath in the lyric inspiration of yore or the enthusiastic personal direction of speech" (OC, 366). Once words start reflecting off each other, they can no longer reflect back to the author, or so the author appears to be suggesting. Right before the passage where Mallarmé talks about the "pure set . . .


of relations between everything" he says that the volume should "require no signatory" (OC, p. 378). In his autobiographical letter he speaks of a "text speaking of itself and without an author's voice" (OC, p. 663). And in Scherer's manuscript notes we read on the next-to-last page about a volume "for whose sense I am not responsible—not signed as such," this in the midst of a flurry of calculations determining the order and placement of pages (201 [A]).

"Things exist, we don't have to create them; all we have to do is grasp the relations between them; it is the threads of these relations that form verses and orchestras" (OC, p. 871). A sentence like this looks very structuralist avant la lettre . In fact, this and other passages convinced James Boon to write From Symbolism to Structuralism, in which he points out the affinities between the thought and poetics of French symbolist poets (Baudelaire, Mallarmé, Rimbaud, Verlaine, and, oddly, Rousseau and Proust) and the ethnology of structural anthropologist Claude Lévi-Strauss. For Boon, the passage I just quoted is emblematic of the whole worldview he sees in Mallarmé. Everything in Mallarmé's universe is relation, analogy, connection, and structure, just as it is in Levi-Strauss. The emphasis in both writers is always decisively shifted away from content. The one thing Boon doesn't discuss is the mathematical foundations of this type of thinking, but we know it's there for Mallarmé as it is for the entire structuralist movement.[11]

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