OuLiPo and the Mathematics of Literature 1789977800, 9781789977806

Table of contents :
Cover
Contents
List of Illustrations
Acknowledgments
Introduction
Chapter 1 Set Theory
Chapter 2 Algebra
Chapter 3 Combinatorics
Chapter 4 Algorithms
Chapter 5 Geometry
Conclusion
Annex: Ouvroir de Peinture Potentielle (OuPeinPo)
Bibliography
Index
Series Index

Citation preview

OuLiPo and the Mathematics of Literature

Modern French Identities Edited by Jean Khalfa Volume 141

PETER LANG Oxford • Bern • Berlin • Bruxelles • New York • Wien

Natalie Berkman

OuLiPo and the Mathematics of Literature

PETER LANG Oxford • Bern • Berlin • Bruxelles • New York • Wien

Bibliographic information published by Die Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available on the Internet at http://dnb.d-nb.de. A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Names: Berkman, Natalie, 1989- author. Title: OuLiPo and the mathematics of literature / Natalie Berkman. Description: Oxford ; New York : Peter Lang, [2022] | Series: Modern French identities, 1422-9005 ; 141 | Includes bibliographical references and index. Identifiers: LCCN 2020034970 (print) | LCCN 2020034971 (ebook) | ISBN 9781789977806 (paperback) | ISBN 9781789977813 (ebook) | ISBN 9781789977820 (epub) Subjects: LCSH: Oulipo (Association)—History. | Mathematics and literature. | Literature, Experimental—France—History and criticism. | French literature—20th century—History and criticism. Classification: LCC PQ22.O8 B47 2022 (print) | LCC PQ22.O8 (ebook) | DDC 841/.9140936—dc23 LC record available at https://lccn.loc.gov/2020034970 LC ebook record available at https://lccn.loc.gov/2020034971 Cover image: Projection of the Galaxy of Oulipo Members on a Logarithmic Spiral according to the subgroup considered by NB. Cover design by Peter Lang Ltd. ISSN 1422-9005 ISBN 978-1-78997-780-6 (print) ISBN 978-1-78997-781-3 (ePDF) ISBN 978-1-78997-782-0 (ePub) © Peter Lang Group AG 2022 Published by Peter Lang Ltd, International Academic Publishers, Oxford, United Kingdom [email protected], www.peterlang.com Natalie Berkman has asserted her right under the Copyright, Designs and Patents Act, 1988, to be identified as Author of this Work. All rights reserved. All parts of this publication are protected by copyright. Any utilisation outside the strict limits of the copyright law, without the permission of the publisher, is forbidden and liable to prosecution. This applies in particular to reproductions, translations, microfilming, and storage and processing in electronic retrieval systems. This publication has been peer reviewed.

This book is dedicated to my family, near or far. During the course of my research, writing, and revisions for this book, the fabric of my family changed beyond measure. In my second year of graduate school, I lost my biggest supporter, my father Brian Berkman, to malignant melanoma; in my fourth year, we lost the patriarch of the Philips family, my grandfather, Constantine Philips. Just a few months after defending my dissertation, we lost my strong-​willed Italian grandmother, Concetta Potenza. However, it is in times of great trouble that you realize the strength of your family. I am especially grateful to my Aunt Mary and Uncle Steve, and my earliest childhood friends –​my cousins –​for all they have done when we needed them most. In the time since these tragedies, our family has been blessed with a new generation –​Sarah, Poppy, Sammie, Parker, Sophia, and Trey –​who have brought new joy to our lives. Most importantly, my mother and brother have been my two anchors no matter where on earth I have been. I will never cease to be amazed by their strength, resilience, and love. I consider myself especially lucky that I met my husband, Eric Alterio, exactly when I needed him most. During a year abroad that was primarily for research, he made me feel as though I had a permanent home in Paris and has been there for me through the good times and the bad. Thank you, Eric, for the emotional support, the beautiful home, and for offering me a much-​needed escape from the life of the mind.

Contents

List of Illustrations

ix

Acknowledgments

xiii

Introduction

1

Chapter 1 Set Theory

23

Chapter 2 Algebra

71

Chapter 3 Combinatorics

117

Chapter 4 Algorithms

173

Chapter 5 Geometry

223

Conclusion

263

Annex: Ouvroir de Peinture Potentielle (OuPeinPo)

277

Bibliography

291

Index

305

Illustrations

Figure 0.1. Vocalocolorist transposition of the rhyming words of the sestina by OuPeinPo member George Orrimbe. Reproduced with the artist’s permission. Figure 0.2. Artistic representation of the sestina’s spiral form by OuPeinPo member Eric Rutten. Reproduced with the artist’s permission. Chapter 1 Cover Image: Illustration of the mathematical formula, borrowed from set theory, A ∩ (B ∩ C) =​ (A ∩ B) ∪ (A ∪ C), designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission. Figure 1.1. A visual illustration of the squares of all sides of a right triangle, designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission. Figure 1.2. A visual proof of the Pythagorean theorem, designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission. Figure 1.3. A Boolean comic strip, Contes et décomptes (p. 16). Reproduced with the artist’s permission. © Etienne Lécroart & L’Association, 2012. 

3 4

22 25 26 65

Chapter 2 Cover Image: 8+​1=​9, Nature morte arithmétique (Arithmetic Still Life), designed by OuPeinPo member Philippe Mouchès. Reproduced with the artist’s permission.70 Figure 2.1. Infinite comic strip from Contes et décomptes (p. 24). Reproduced with the artist’s permission. © Etienne Lécroart & L’Association, 2012. 80 Figure 2.2. Excerpt from “Compter sur toi” in Contes et décomptes (p. 5). Reproduced with the artist’s permission. © Etienne Lécroart & L’Association, 2012. 83

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Illustrations

Figure 2.3. Excerpt from Mes Hypertropes (p. 167). Reproduced with Oulipo's permission. Chapter 3 Cover Image: Puzzle Theorem of the Four Colors, designed by OuPeinPo member Eric Rutten. Reproduced with the artist’s permission. Figure 3.1. An example of a surrealist cadavre exquis. Reproduced with permission from the Association Atelier André Breton and the photographer. See Bibliography for full citation. Figure 3.2. An example of the children’s book Têtes folles. Reproduced with permission from Pascal Kummer. See Bibliography for full citation. Figure 3.3. A photograph of Robert Massin’s design for the Cent mille milliards de poèmes, beautifully executed by Maxime Fournier of SAE Institute Paris and reproduced with his permission. Figure 3.4. The game of Go represented in Jacques Roubaud’s poetry collection, ∈ (p. 151). Reproduced with the permission of the publisher. © Éditions Gallimard. Figure 3.5. The completed tarot card design of the first half of Italo Calvino’s Il castello dei destini incrociati (p. 538). Figure 3.6. The completed tarot card design of the second half of Italo Calvino’s Il castello dei destini incrociati (p. 590). Figure 3.7. The knight’s tour problem solved by Perec for determining the chapter order of La Vie mode d’emploi, as reimagined by OuPeinPo member Philippe Mouchès. Reproduced with the artist’s permission.

105

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123 124

127 136 153 156

164

Chapter 4 Cover Image: Self portrait as Les Demoiselles d’Avignon, designed by OuPeinPo member Helen Frank. Reproduced with the artist’s permission. 172 Figure 4.1. A visual illustration of the Bridges of Königsberg problem in graph theory, beautifully reimagined as

Illustrations

xi

Immanuel Kant’s face by OuPeinPo member Helen Frank. Reproduced with the artist’s permission. 192 Figure 4.2. The graphical representation of Raymond Queneau’s Un conte à votre façon, taken from La Littérature Potentielle (p. 51). Reproduced with the permission of the publisher. © Éditions Gallimard. 197 Figure 4.3. The graphical representation of who met whom upon visits to the Duke’s island, taken from Claude Berge’s “Qui a tué le duc de Densmore?” (p. 145). Reproduced with Oulipo’s permission. 219 Chapter 5 Cover Image: Vocalocolorist portraits of Michèle Audin and Italo Calvino by OuPeinPo member George Orrimbe. Reproduced with the artist’s permission.222 Figure 5.1. The parallelogram created using the numbers in the Indice of Italo Calvino’s Le città invisibili, artistically imagined by OuPeinPo member Philippe Mouchès. Reproduced with the artist’s permission. 229 Figure 5.2. An illustration of the notion of the cross-​ratio superimposed over Michel Chasles’s portrait, designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission. 235 Figure 5.3. The table of contents of Michèle Audin’s Mai quai Conti Reproduced with the author’s permission. See Bibliography for full citation. 236 Figure 5.4. The first mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. 250 Figure 5.5. The second mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. 251

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Illustrations

Figure 5.6. A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. Figure 5.7. A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. Figure 5.8. A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. Figure 5.9. A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. Figure 5.10. A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation. Figure 5.11. A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

252 254 256 257 258 259

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Acknowledgments

I would like to thank David Bellos, whose attention to detail, critical feedback, and enthusiasm for my work allowed for my doctoral dissertation to be the best that it could be. I am eternally grateful for his guidance and attribute this current publication in large part to him. Additionally, Christy Wampole and Arielle Saiber provided me with intellectual, emotional, and professional support throughout the critical stages of this project. I would also like to thank Cliff Wulfman for his technical insights; Michael Barany for his history of mathematics expertise; and Hélène Campaignolle-​Catel and Camille Bloomfield for welcoming me into the Oulipo Archival Project. It is equally important to mention the support of the late Stéfan Sinclair, who truly believed in this project. I will always regret never having met him in person. Additionally, a certain number of Oulipians helped me immensely with my research, affording me access to their archives, and having wonderful mathematical discussions with me over coffee: Paul Fournel, Michèle Audin, Olivier Salon, Étienne Lécroart, and the late Paul Braffort. Certain members of the OuPeinPo (Ouvroir de Peinture Potentielle) also deserve a great deal of admiration and thanks for their hard work on this project, illustrating this book so beautifully with constrained artwork. Their generous contribution has allowed this book to reflect the nature of mathematical literature through their imaginative visualizations. Therefore, special thanks are in order to George Orrimbe, Eric Rutten, Philippe Mouchès, ACHYAP, and Helen Frank. Beyond the academic professionals who helped make this project possible, I must also thank the friends and colleagues who have made up a supportive community in which I carried out this work. Thank you to Alix Punelli, Mélanie Monjean, Tuo Liu, Nicolas Verastegui, Colin Azariah-​ Kribbs, Liliane Ehrhart, Andréa Toucinho, Eileen Williams, Rosalind Resnick, Fu-​Fu Lin, Melissa Verhey, and Charlotte Werbe for being there for me no matter where you were.

Introduction

I. The Spiral of Literature and Mathematics In twelfth-​century Provence, a medieval troubadour named Arnaut Daniel invented a new kind of fixed form poem which is now known as the sestina. This 39-​line poem, divided into six sestets and one three-​ line envoi, may not have the same legacy as its more famous relative, the sonnet, but its poet was lauded by Dante (who included Daniel in Purgatorio) and Petrarch (who called him the first great master of love in Trionfi d’amore). Daniel’s original sestina, Lo ferm voler qu’el cor m’intra, tells the story of a lovesick poet who desperately wants one forbidden thing: to enter into his lady’s room. Given that the thematic material is about rules and restrictions, the form itself demonstrates a number of rules: each verse of every sestet ends with one of six rhyming words, which repeat throughout the first six stanzas in a specific order, as well as in a distinct configuration of pairs in the three-​line envoi, which serves as an autograph. Observe the rhyming words as they appear in the first stanza of the poem, which I have bolded for convenience (Daniel, n.d.): Lo ferm voler qu’el cor m’intra no’m pot ges becs escoissendre ni ongla de lauzengier qui pert per mal dir s’arma; e pus no l’aus batr’ab ram ni verja, sivals a frau, lai on non aurai oncle, jauzirai joi, en vergier o dins cambra.

The firm will that my heart enters can’t be scraped by beak nor by nail of slanderer who damns with ill speaking his soul since I don’t dare beat them with bough or rod, at least, secretly, where I won’t have any uncle, I’ll enjoy pleasure, in the garden or in the room.

2

introduction

Of the rhyming words, five are nouns and one (intra) is a verb. Given the subject matter of courtly love, it is easy to see why this verb would be privileged –​it has a certain proclivity for double-​entendre, signifying at once the poet’s desire to enter his lover’s room and to make love to her. However, given that each of these rhymes is repeated seven times within the fixed form, all of Daniel’s rhymes demonstrate a similar fluidity of meaning. As a result, the erotic nature of the poem is not particularly subtle, and is often evidenced by the interplay between the two rhymes intra and cambra: initially, the two are separated by the entire stanza; in the second stanza, while they are the first and second rhymes, the verb is negated (“Quan mi sove de la cambra/​on a mon dan sai que nulhs om non intra”1 (v. 7–​8)); as the poem progresses, the poet likens the woman to this room that he is not permitted to enter (“qu’ilh m’es de joi tors e palais e cambra”2 (v. 33)). It is only in the envoi that the words are finally joined in one line, but even then, the meaning is not physical: “son cledisat qu’apres dins cambra intra”3 (v. 39). Arnaut sends his song to his desired, this song that can penetrate into the chamber while he cannot. Since Troubadour poetry was an oral genre, the poem itself must train the reader to listen for what is important, namely the repetition of the rhymes. The rhymes at the end of each verse all end in A or E (both pronounced as E muets in Provençal). Furthermore, the versification teaches the reader to hear the change in stanzas: the first line of each stanza has only seven syllables whereas the others each have ten, indicating where a new stanza begins. With the repeated rhyming words featured prominently at the end of each line and the number of syllables demarcating the stanzas, the evolving order of these words becomes a central focus, although the pattern may not be immediately discernible. The repetition of each rhyme becomes more obvious as the poem continues, since the first line of each new stanza repeats the rhyme that ended the previous one. At the close of the poem, five of the rhymes have repeated in this fashion, while the first rhyme occupies an even more important position at the beginning and end of the poem. The envoi as well puts these rhymes in the spotlight, with each of the three lines ending with a particular pairing. 1 2 3

“When I remember the room/​where, to my scorn, I know no man enters.” “she is to me tower, palace and room.” “a framework-​song which, learned, the room enters.”

Introduction

3

While Daniel was no mathematician, it turns out that his peculiar repetition of these rhymes appealed to the mathematical sensibilities of the Collège de ‘Pataphysique, a group founded in the winter of 1948 which included “… some of the most ruggedly individualistic names in the arts, cinema, and literature …”, drawing on the philosophy of Alfred Jarry to study the “science of imaginary solutions” (Hugill, 2012, p. 115).4 Given this eclectic group straddled both the literary and mathematical, they realized that it was possible to abstract the sestina and understand how the rhyme order really functions. The first step is numbering the six rhyming words and looking at how the order of these rhymes changes, as artistically visualized by OuPeinPo member George Orrimbe in Figure 0.1:

Figure 0.1.  Vocalocolorist transposition of the rhyming words of the sestina by OuPeinPo member George Orrimbe. Reproduced with the artist’s permission.

4

It is worth mentioning that the members of the Collège de ‘Pataphysique (whose name really does include that apostrophe, mandated by founder Alfred Jarry in order to avoid “un facile calembour”) who wrote about the sestina were not the first to recognize its mathematical nature ( Jarry, p. 21). Indeed, Michèle Audin has detailed in her short text, “Histoire du pli cacheté,” how both Fermat and Euler recognized the mathematical structure of this poetic form and how Pierre Agnès Inès Prompt, member of the Académie des Sciences, had discovered a generalization of this pattern long before either the Collège de ‘Pataphysique or its subgroup, Oulipo.

4

introduction

Written out in this chart, the pattern might not be immediately discernible. However, this reordering of words is what is known as a transformation in mathematics: for every stanza, the sixth rhyming word will become the first in the following stanza; the first will become the second; the fifth will become the third; the second will become the fourth; the fourth will become the fifth; and the third will become the last. Performing this transformation on the rhyme order of any stanza will produce the subsequent one and applying it to the final sestet will reproduce the order of the initial stanza. With the words and superfluous explanations removed, Antoine Tavera, “Régent d’Hypothétique Pratique” of the Collège de ‘Pataphysique published an article in the ‘Pataphysics journal, Subsidia Pataphysica, entitled “Arnaut Daniel et la spirale.” To the best of my knowledge, this article represents the first instance of a literary interest in the mathematical nature of the sestina, in which Tavera explains that the particular permutation of the rhyming words in a sestina follows a spiral pattern (Figure 0.2).

Figure 0.2.  Artistic representation of the sestina’s spiral form by OuPeinPo member Eric Rutten. Reproduced with the artist’s permission.

Introduction

5

As illustrated in Figure 0.2, drawing a spiral starting from the last rhyme of any stanza generates the order of the subsequent stanza, in this case (615234). Given that the spiral (specifically this type of spiral, the Gidouille) was an important symbol for the Collège de ‘Pataphysique (it appears on Ubu Roi’s stomach, for instance), it is unsurprising that Tavera found this aspect to be particularly appealing. At the end of his article, Tavera (1963, p. 78) poses an interesting question: Neuf eût tenté Dante, à coup sûr ; mais je croirais bien qu’Arnaut l’a rejeté parce que neuf strophes de neuf vers –​81 vers –​c’est déjà bien long. En tout cas entre cinq et six, rien, pour un troubadour ne préjugeait du choix : point d’interdit sur l’impair. Cependant, qu’a choisi Arnaut ? La forme la plus mystérieuse, la plus insolite, puisque six est le seul nombre non premier (au moins avant quatorze, mais je pense qu’il n’est pas allé jusque là) qui se prête à la permutation en spirale. Et cela, le mystère dans le pair, on peut dire que c’est le fin du fin.

This question of why Arnaut Daniel chose the number six when this spiral permutation works with other integers is as much poetic as it is mathematical. In the subsequent article from that issue of Subsidia Pataphysica entitled “Note complémentaire sur la sextine,” fellow pataphysician Raymond Queneau remarks that sestina-​like permutations are possible with some numbers but not with others, giving a list of 31 positive integers less than 100 that conform, defining a generalized sestina which he called an n-​ine (where n represents the chosen integer). Queneau’s (1965, p. 79) article distinguishes itself from Tavera’s given its recourse to formal, mathematical language rather than poetic, producing a generalized formula for making sestina-​like permutations. Despite the jocular nature of ‘Pataphysics, Queneau’s “Note complémentaire sur la sextine” is indeed a serious mathematical study that has since sparked others, most notably by his friend, poet and mathematician Jacques Roubaud, and mathematicians Monique Bringer and Jean-​Guillaume Dumas.5 5

For a complete history of the subsequent mathematical developments, see Michael P. Saclolo’s (2011) article in the Notices of the AMS, “How a Medieval Troubadour Became a Mathematical Figure.” See Bibliography for the full citations of this as well as all mathematical studies on the sestina mentioned above.

6

introduction

For the purposes of this study, it is important to note two extremely original aspects of this intertwining tale of mathematics and literature. First, in a very unlikely scenario, poetry actually created new mathematics. Indeed, while mathematics can be found just about anywhere and has in the past been influenced by developments in non-​mathematical activities, to the best of my knowledge, this is the only case of mathematics being inspired by literature (whereas the opposite is quite common). Furthermore, the mathematical studies were returned to the field of literature, as this discovery led Queneau to create “quenines,” or variants on the original form with a different number of stanzas and verses.

II. Oulipo This story of the discovery of mathematics in a medieval poetic form seems to contradict the premise of British scientist and novelist C. P. Snow’s (1959 [1993], p. 4) Rede Lecture on what he termed the “Two Cultures,” which posited that the great failure of intellectual life in western society can be attributed to the fact that humanists and scientists had between them “… a gulf of mutual incomprehension –​sometimes (particularly among the young) hostility and dislike, but most of all lack of understanding.” Snow’s speech was provocative, giving a vocabulary to an ongoing disciplinary debate that was not unique to England. Indeed, since the end of World War II, French authors, poets, and playwrights had been engaged in a variety of experimental artistic movements such as the “théâtre de l’absurde,” the “nouveau roman,” and the parallel cinematic movement of the “nouvelle vague.” In literary criticism too, changing times produced new methods. A delayed French discovery of the influential school of literary criticism from the early 1900s known as Russian formalism prompted the translation of a great number of Russian and Soviet scholars, generating a renewed interest in the functional role of literary devices and creating a “scientific” method for studying language. This coincided with a particular moment in the legacy of Ferdinand de Saussure’s structural linguistics, as various scholars in the humanities began

Introduction

7

to borrow Saussure’s analysis of the systems that underlie language to use in their own fields of study. With the publication of Claude Lévi-​Strauss’s Les structures élémentaires de la parenté in 1948, “structuralism” became a widespread methodology, which, like Russian formalism before it, proposed to study cultural artifacts scientifically. In the midst of these literary movements and theories, a small group of French intellectuals quietly assembled, proposing their own solution to the two-​culture debate. Oulipo (Ouvroir de Littérature Potentielle) was founded in Paris by Raymond Queneau and François Le Lionnais in 1960. The name is an acronym, loosely translated into English as “Workshop of Potential Literature.” It was born at a conference at Cerisy-​la-​Salle entitled Une nouvelle défense et illustration de la langue française, dedicated to the work of Raymond Queneau (CERISY, Les Colloques (1952–​2016)). The conference title referenced Joachim Du Bellay’s sixteenth-​century call for action, the Défense et illustration de la langue française (1549), a canonical essay written at a time when great changes were occurring both politically and linguistically, resulting in the standardization of the French language. Du Bellay’s text can be understood as a manifesto of sorts, promoting the literary project of the author’s poetic circle, known as the Pléiade: to elevate the status of French, the vulgar language, to that of a scholarly one such as Latin or Greek by enriching it with a body of literature that imitates (but does not aim simply to reproduce) ancient classics. In the postwar period in twentieth-​century France, Queneau’s peculiar manner of writing the French language as it is pronounced, as opposed to using the standard orthography that was first solidified in the time of Du Bellay, served as a point of departure for the development of a new literary collective with its own explicit goal that responded to one of the great debates of its time. The resulting Oulipo sought to differentiate itself from surrealism and “Sartrian trends,” (Bénabou, “Quarante siècles d’Oulipo”) proposing mathematics as a solution. At the outset, the group was somewhat clandestine, publishing very few texts in its early years. However, on September 28, 1967, an article by co-​founder Raymond Queneau appeared in the Times Literary Supplement alongside similar disciplinary reflections from other prominent intellectuals of the time –​Italo Calvino, Umberto Eco, and Roland Barthes. Queneau’s piece, “Science and Literature,” can be taken as

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a response to Snow’s Two Cultures, but within the more restricted context of this issue, it seems to be at odds with Barthes’s contribution, “Science versus Literature.” Queneau’s article (1967, p. 865) highlights a persistent threat in the humanities, that of a general attitude of fear, ignorance, and disdain toward science from those who produce literature, criticizing a superficial understanding and use of scientific terminology and developments by literary writers and regretting the lack of scientific poetry, “… that is, in which not only is the subject scientific but in which the language of science is also transmuted into poetry.” On the other hand, Barthes attempts to bridge science and literature, arguing that the two differ only in society’s perception of them. While Queneau’s (1967, p. 866) article promotes Oulipo, which “… has been working towards the discovery of new or revived literary forms, this research being inspired by an interest in mathematics,” Barthes (1967, p. 897) praises the science of structuralism, which he claims “… gives special attention to classification, hierarchies and arrangements; its essential object is the taxonomy or distributive model which every human creation, be it institution or book, inevitably establishes, since there can be no culture without classification.” According to Dennis Duncan (2017), these complementary yet conflicting points of view demonstrate a more pervasive incompatibility between the two groups: “Structuralism, it seems, occupies a fraught spot in Queneau’s imagination: as the Oulipo’s academic Other, lurking a few streets away at the Collège de France, or a few pages away in the TLS.” To understand Oulipo’s apparent reticence to align itself with the cultural and intellectual mainstream, it is useful to look at the steps the founding members took to define the group. At first, they called themselves Séminaire de Littérature Expérimentale (Sélitex) but abandoned this name at the second official meeting on December 22, 1960 in favor of “Oulipo” to distance themselves from the type of academic work evoked by the word “seminar”6 and unintentional associations with “experimental

6

The word “seminar” also has a particular tradition in the history of mathematics. See: Kathy Olesko, Physics as Calling [1991]; Michèle Audin, Le Séminaire de mathématiques 1933–​ 1939 [2014]; Anne-​ Sandrine Paumier, Le séminaire de mathématiques : un lieu d’échanges défini par ses acteurs. Incursion dans la vie

Introduction

9

literature” such as Émile Zola’s Le roman expérimental (1881) and more recent literary trends such as the Nouveau roman of the 1950s (Bens, Genèse, p. 28). Instead, Albert-​Marie Schmidt, Renaissance expert and one of the founding members, proposed the archaic word, ouvroir. Etymologically related to œuvrer (“to work”) and œuvre (“a work”), the term designates a sewing circle, where religious women share patterns. In addition to the Pléiade movement, which can be seen as a literary precursor to Oulipo, Schmidt was also a specialist of the Grands Rhétoriqueurs, an early collection of Renaissance poets that could be considered an ouvroir, passing patterns from one generation of court poets to the next. In fact, Queneau’s Cent mille milliards de poèmes (1961), considered the first Oulipian text, has much in common with rhétoriqueur Jean Molinet’s fifteenth-​century experimental poem, Sept rondeaux sur un rondeau, applying a similar principle to create seven potential poems from one. If Oulipo is an ouvroir, then its purpose is the creation of Littérature Potentielle. As defined by Oulipo on its website (“Qu’est-​ce que l’Oulipo ?”), literature is “ce qu’on lit et ce qu’on rature,” a play on the final two stanzas from the 1895 poem by Stéphane Mallarmé (1951, p. 73), “Toute l’âme résumée”: “Le sens trop précis rature/​Ta vague literature.” James Housefield (2016, p. 209) notes that this Mallarmé poem anticipates “… the ways [Marcel] Duchamp and his friends among the Parisian Surrealists transformed the journal named Littérature into Lits et Ratures,” to link literary creation with sleep and dreams (lits) while emphasizing the importance of making errors and erasing them (ratures7). Rather than deal with literature or its surrealist definitions, Oulipo adds an adjectival modifier, defining Potential Literature as: “De la littérature en quantité illimitée, potentiellement productible jusqu’à la fin des temps, en quantités énormes, infinies pour toutes fins pratiques” (Qu’est-​ce que la littérature?). In French, potentiel has an additional meaning as it is the adjectival form of puissance or an exponential power. Potential Literature is thus both “potential” as in

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collective des mathématiques autour de Laurent Schwartz (1915–​2002) [2015]. (See Bibliography for full citations.) The use of the term “ratures” here could also be a reference to Jacques Derrida and deconstruction, in which this is a key term. See: Jacques Derrida, De la grammatologie [1967]. (See Bibliography for all full citations.)

10

introduction

“not yet existing” as well as in an exponential sense, literature that can be produced in exponential quantities. This definition, as Le Lionnais points (1973a, p. 15) out in the first Oulipian manifesto, however, is nowhere to be found in any dictionary: “Ouvrons un dictionnaire8 aux mots: ‘Littérature Potentielle.’ Nous n’y trouvons rien. Fâcheuse lacune.” The eclectic nature of the group’s founders explains this recourse to a mathematical vocabulary. Raymond Queneau (1903–​1976) was a French novelist, poet, philosopher, and amateur mathematician. Known for his sense of humor, phonetic transcription of the French language as it was pronounced at the time, and rhetorical acrobatics, Queneau participated in several literary and intellectual circles during his lifetime, including Surrealism, ‘Pataphysics, and Oulipo. He was also the secretary of the reader’s panel and director of the Encyclopédie de la Pléiade at the Gallimard publishing house, an extremely powerful position that granted Queneau considerable control over French literary culture. His cofounder, François Le Lionnais (1901–​1984), was a chemical engineer and mathematician by trade, but also a general erudite. After being interned in the Dora concentration camp (a subsidiary of Buchenwald) during World War II as a POW, Le Lionnais served as the general editor of the mathematical treatise, Les Grands Courants de la pensée mathématique (1948). Contained within this collected volume was the first popular article by Nicolas Bourbaki, an imaginary French mathematician born of a collaboration of mathematicians trained at the École Normale Supérieure in the 1930s that influenced Oulipo’s mathematical theorizations and group culture. Many of the founding members of Oulipo belonged to the pseudo-​ scientific Collège de ‘Pataphysique, including Queneau, Le Lionnais, Noël Arnaud, Latis, and Jacques Bens. Indeed, Oulipo was first conceived as a subsection of the Collège, inheriting terms such as clinamen and potential, eventually becoming autonomous and breaking ties. Beyond those affiliated with ‘Pataphysics, other founding members, such as Claude Berge, were mathematicians themselves. Berge was well known in the mathematical world for his contributions to the field of graph theory, which in turn influenced Oulipo and certain texts. Paul Braffort, a computer scientist, 8

N’importe lequel. (This footnote is in the text.)

Introduction

11

introduced theoretical aspects into his writing as well as practical programming into the activities of the group. Similarly, poet and mathematician, Jacques Roubaud, created a literary corpus that seamlessly combines mathematics and poetry across a variety of genres. Other members of Oulipo entered the group with no formal mathematical background, such as Georges Perec, whose participation in the group helped him to develop as an author and gain renown for his aptitude for constrained writing. Even a foreign, established literary author such as Italo Calvino published some of his most popular novels under the influence of Oulipo. While mathematics does not seem to play as central a role in the literary activity of the current members, two members in particular stand out for their continuation of this tradition: first, Étienne Lécroart has reinvented certain mathematical constraints for a new genre, the bande dessinée; and most importantly, mathematician Michèle Audin has developed her own mathematical project that blends history, mathematics, and politics. While each Oulipian author approaches the task of producing potential literature differently, the common element is the principle of constraint. A constraint is a rigorously defined rule for composition: sometimes a generative device that produces a text through an easily applied procedure; sometimes, it is rather a challenge that incites textual production on the part of an author. Early Oulipian constraints often created new texts from preexisting ones, such as Jean Lescure’s (1973) S+​7 method, which replaces every noun or substantif in a text with the one seven entries later in a dictionary of the author’s choosing. These early procedures were not necessarily all categorized as constraints, and the term evolved as the group began to co-​opt new members. Several authors in the second generation of members, including Jacques Roubaud, Georges Perec, and Italo Calvino, developed and popularized constraints that did not necessarily depend on a preexisting text, such as the lipogram, which can be defined etymologically as the removal (lipo) of a letter (gram). While Georges Perec did not invent the lipogram, he famously employed it in La disparition (1969), an entire novel without the use of the letter “e.”9 9

Much of La disparition is the result of a related constraint, the lipogrammatic translation, which required Perec to rewrite preexisting texts without the letter “e.”

12

introduction

II. State of the Field It is important to reiterate that this type of constrained literature is not unique to Oulipo. There is a long history of mathematical literature that extends back to the Middle Ages and earlier. The lipogram, for instance, which can be viewed as a set-theoretical constraint (see Chapter 1), can be traced back at least to the sixth century bce in Greece. More explicitly mathematical literature can be found across centuries: for instance, in the work of the Grands Rhétoriqueurs during the Renaissance; the mathematical methods of seventeenth-​ century French philosophers René Descartes and Blaise Pascal; in popular texts of the nineteenth century, such as Alice’s Adventures in Wonderland by English mathematician Charles Lutwidge Dodgson (more commonly known by his pseudonym, Lewis Carroll) and Flatland: A Romance of Many Dimensions, a satirical novel by English schoolmaster Edwin Abbott. One often finds mathematical elements in poetry, as both share a proclivity for patterns and repetitions, with the aforementioned sestina being a particularly important example. Given the prominence and history of mathematical literature, Oulipo can be considered just one iteration; however, it is a particularly important one. This is due to the fact that Oulipo, unlike the preceding, isolated examples, tasks itself with an overarching, systematic approach to the topic, dealing with the categorization and invention of constraints. The goal is twofold: an analytic orientation (anoulipisme) aims to explore constrained writing from the past, seeking out and evaluating authors who predate Oulipo and its use of constraint-​based writing (otherwise known as plagiarists by anticipation); the second goal is synthetic (synthoulipisme), which seeks to propose new constraints (Le Lionnais, 1973c, p. 18). This distinction, which has fallen out of use since it was introduced in the group’s first manifesto, has nevertheless remained a common topic of discussion by literary scholars on Oulipo. Furthermore, it is evidence of the early Oulipo’s recourse to a mathematical vocabulary, as the terms “analysis” and “synthesis” have been cornerstones of the discipline since Ancient Greek mathematics. In mathematics, analysis is the procedure by which

Introduction

13

mathematicians break down a problem into its component parts and synthesis is the opposite, by which one combines separate elements to form a coherent whole. Just as in mathematical work, the two types of Oulipian work go hand in hand: Le Lionnais (1973a, p. 18) notes in the first Oulipian manifesto that “De l’un à l’autre existent maints subtils passages.” It should be noted that Oulipo does not deal with the texts these constraints can, in theory, produce. Instead, it is the work of individual Oulipian authors to produce constrained literature. Furthermore, the use of constraints is not limited to Oulipian authors. In this light, it is useful to consider the mathematically constrained texts produced by individual members of Oulipo as contributions to a longer history of mathematical literature. But more importantly, it is necessary to analyze the effects of this collaborative, group effort on literary –​as well as cultural and scientific –​history. Perhaps due to its unconventional goals and group culture, Oulipo, still present today over 60 years after its founding, has outlived every other literary movement of the twentieth century. In dialogue with such diverse collectives as surrealism, Bourbaki, and the Collège de ‘Pataphysique, Oulipo occupies an interstitial position, straddling the avant-​garde and the formal; the literary and the scientific. Therefore, a close examination of what Oulipo borrows from mathematics, why it chooses to model itself after this specific discipline in this particular time, and what effect these strict mathematical rules have on the texts contributes to a greater understanding of both literature and mathematics. In fact, in the age of Digital Humanities, Oulipo and the questions it continues to pose are more relevant than ever. Given the importance accorded to mathematics in the definition of Oulipo’s objectives, the selection of its members, and the composition of some of its most well-​known works as well as the popularity of interdisciplinary scholarship in the humanities today, it is surprising that few scholars have broached this topic. As a whole, scholarship on Oulipo is extensive and varied, as evidenced by the Bibliographie des études oulipiennes, which was undertaken by Virginie Tahar (2013) on the occasion of the fiftieth-​ anniversary colloquium held at the University at Buffalo in 2011. In this monumental work (which is currently being updated and expanded by the DifdePo research group as part of their Édition électronique Archives de l’Oulipo project), Tahar divides the written scholarship on Oulipo into

14

introduction

three primary categories: first, “Textes théoriques écrits par les oulipiens”; second, “Textes théoriques sur l’Oulipo en général”; and finally, “Textes théoriques sur les oulipiens en particulier.” For the first category, while many Oulipians do write critical articles on their own methods or the group’s use of mathematics ( Jacques Roubaud and Michèle Audin being two prime examples),10 it is a serious matter whether to take them at face value. Within Oulipo, there is an ongoing debate between members about whether or not to reveal the true nature of their constraints. In some cases, this uncertainty has resulted in partial revelations, red herrings, delayed published manuscripts, or even all of the above. For instance, Italo Calvino classified Se una notte d’inverno un viaggiatore (1979) as partially Oulipian in Atlas de littérature potentielle and even published an article about its Oulipian constraints twice (once in the Bibliothèque Oulipienne and again in A. J. Greimas’s Actes sémiotiques), but when his drafts for the novel were published posthumously, it became apparent that his own revelation of his compositional methods should not necessarily be trusted.11 Given the problematic nature of Oulipian theoretical writings, I consider such documents part of the larger work of the group and as such, subject to the same rigorous analysis as their literary writings. Of the longer scholarly texts produced by Oulipians, two in particular stand out: Hervé Le Tellier’s L’Esthétique de l’Oulipo (2006) and Daniel Levin Becker’s Many Subtle Channels (2012). Furthermore, The Oulipo Compendium (1998), edited by Oulipian Harry Mathews as well as Alastair Brotchie, can be viewed as an expository, English-​language volume on the group and its work, but with some useful insights as well. Tahar’s second category of critical works on Oulipo as a whole rather than on individual authors is the most important for the purposes of the current study. Of these, the primary critical volumes on Oulipo (in English and French) are the following: Warren Motte’s Playtexts: Ludics 10 See: Michèle Audin, L’Oulipo et les mathématiques : une description [2010], L’Oulipo a cinquante ans [2010], Mathématiques et littérature: un article avec des mathématiques et de la littérature [2007]; Jacques Roubaud, La mathématique dans la méthode de Raymond Queneau [1981], L’auteur oulipien [1991]. 11 For more information about this, see my article in Genesis 45, “Comment j’ai écrit un de mes livres: La double genèse de Si par une nuit d’hiver un voyageur.”

Introduction

15

in Contemporary Literature (1995); Peter Consenstein’s Literary Memory, Consciousness, and the Group Oulipo (2002); Marc Lapprand’s Poétique de l’Oulipo (1998); Christelle Reggiani’s Rhétoriques de la contrainte, Georges Perec et l’Oulipo (1999); and Alison James’s Constraining Chance: Georges Perec and the Oulipo (2009). These five volumes stand out from others in the way they analyze Oulipo as a whole through different theoretical lenses: ludics, literary memory, poetics, rhetoric, and chance. Of these, the final two come the closest to studying Oulipo’s mathematical dimensions (as classical rhetoric draws from logic, and chance is a key notion in mathematics); however, both studies deal primarily with Georges Perec. Reggiani, it should be noted, has recently published a collection of essays, Poétiques oulipiennes: La contrainte, le style, l’histoire (2014), in which she does address the question of Oulipo’s use of mathematics directly, writing it off as a fiction mathématique, a largely symbolic gesture that never resulted in any serious mathematical endeavor. More recently, Brazilian author, literary scholar, and mathematician Jacques Fux’s Literatura e Matemática: Jorge Luis Borges, Georges Perec e o Oulipo (2016) offers the first discussion of the mathematical methods of the group in the introduction, with the body of the work devoted to a comprehensive study of Perec and Borges. The most recent addition to this list comes from Camille Bloomfield in Raconter l’Oulipo (1960–​2000): Histoire et sociologie d’un groupe (2017), who through a historical, sociological, and archival analysis, situates Oulipo within a larger cultural and intellectual history. This comprehensive volume deals with the group’s mathematical influences (notably Bourbaki), its relationships with other groups and movements of the time that were engaging in similar practices, but does not delve into the group’s actual rhetorical use of mathematics.

III. Methodology and Contribution With this in mind, this book is the first study of the mathematical methods of Oulipo as a group and aims to provide the foundation for future studies on Oulipo, experimental literature, and history of science

16

introduction

and mathematics by retracing the historical origins of this interdisciplinary endeavor and analyzing the effect of the group’s methods on the reading experience. In order to understand exactly why Oulipo is using mathematics, how the group proposes to use mathematics, and what the effect of the mathematics is on the reading experience, the following general questions underlie this study:





1. Given the ludic nature of Oulipo and its tendency toward humor, is it wise to take the members at face value when they declare an explicit mathematical project? In other words, is Oulipo’s use of mathematics a serious scientific exploration of language and literature or rather a symbolic, metaphorical reference to another discipline? 2. If Oulipo’s use of mathematics is indeed to be taken seriously, is it feasible? Mathematical language is a formal, non-​natural language and seems incompatible with literary language. How then does Oulipo propose to write literature with mathematics? 3. If Oulipo is using mathematics to write, the resulting texts are meant to be read by a reader who may have little to no formal mathematical training. What can literature teach such a reader about mathematics or rather, about mathematical thought?

Using these general questions as a guide, the work of this book makes use of three primary methodologies: literary, historical, and digital humanities. First, given the intentional nature of Oulipian work, the heart of my analysis draws on close readings of passages that reference the author’s compositional means. Complementing this traditional method, I also employ genetic criticism techniques to analyze the paratextual and manuscript clues used by Oulipian authors to produce constrained literature and indicate the text’s constraint to the reader. Second, by tracing the history and legacy of the twentieth-​century crisis of mathematics that resulted in the creation of a formalized language known as set theory, it is possible to identify the mathematical influences of Oulipo. Through an examination of archival sources (at the Bibliothèque de l’Arsenal in Paris) and the sociology of the

Introduction

17

group in its early years, it is then possible to understand Oulipo as a product of its time and see how it was shaped by contemporary mathematical, scientific, and literary debates. Furthermore, a more thorough understanding of the group’s interdisciplinary collaborations with mathematicians and computer scientists12 solidifies the group’s role as a major historical actor in the history of science, producing some of the earliest examples of digital humanities research and electronic literature. Finally, by relying on digital methods such as exploratory programming of Oulipian texts, my research exposes the difficulties Oulipo encountered in its collaborations with computer scientists in the 1960s and 1970s, which compelled the group to distance itself from purely mechanical procedures and focus instead on the role of the reader. Furthermore, as a major contributor to the Oulipo Archival Project, the transcription and encoding of the first 30 years of Oulipo’s meeting minutes has allowed for data analysis on the evolution of the group’s vocabulary and practices. This study focuses primarily on the early production of Oulipo from its founding in 1960 to the publication of its second anthology, Atlas de littérature potentielle in 1981, with three main exceptions: first, when certain authors of the first two generations of Oulipo continued to produce mathematically interesting constrained literature in the 1980s and later (as is the case with Jacques Roubaud, Paul Braffort, Paul Fournel, and Claude Berge); second in the case of Michèle Audin, symplectic geometer who was co-​opted in 2009 and who represents the last true vestige of original mathematical work being done in the group; finally, in the case of Étienne Lécroart, member of both Oulipo and the OuBaPo (Ouvroir de Bande Dessinée Potentielle) who has returned to the mathematical roots of Oulipo in his volume Contes et décomptes (2012). The texts in this corpus were produced through constraints that can be interpreted as drawing from abstract mathematical principles, and therefore this book does not treat the entire repertoire of Oulipian constraints. Given the highly intentional nature of Oulipian texts and taking 12 As computer science was a fledgling discipline at the time when Oulipo was engaging in its experimental electronic literature, the distinction between mathematicians and computer scientists was not firm. Indeed, many mathematicians of the 1960s and 1970s were dabbling in computers.

18

introduction

the aforementioned paratextual elements into consideration, the close readings carried out in this study tend to focus on specific passages within Oulipian texts that reference the texts’ compositional means. A text that speaks about itself and its composition in such a way can be said to complicate the reading experience, training the reader in a new kind of reading. In the case of Oulipian texts that speak about explicitly mathematical constraints, this means that the reader is being trained in a specific form of mathematical thought, which I define as recognizing abstract patterns and making generalizations. The texts and procedures discussed in this work are divided into chapters based on the mathematical discipline13 by which they are inspired, facilitating a practical introduction to mathematics and its various objects of study for non-​mathematicians. Within each chapter, specific Oulipian developments are addressed chronologically and progress from the simplest examples to more complex ones, reflecting the group’s own mathematical trajectory of increasing complexity. Oulipo’s various uses of mathematics drawn from different disciplines resulted in the creation of a specific vocabulary, which I discuss thematically by chapter (italicized below). Chapter 1 deals with Set Theory, an early twentieth-​century development in the history of mathematics which resulted in the creation of a new formal language based on the notion of “sets” (collections of mathematical objects). Leading this development, a relatively limited group of mathematicians, philosophers, and logicians believed that by manipulating a formal language within a rigorous axiomatic framework, mathematicians could discover eternal truths. Popularized in postwar France by Bourbaki, set theory and a structural understanding of mathematics (as a discipline) was influential not only to Oulipo but also within the larger context of the prevalent literary theories of the era, such as structuralism. Through this influence, mathematics and humanistic work have a conjoined history and share similar formalisms. This chapter begins with an introduction to abstract mathematical thought and the historical development of set theory, then traces the influence of these developments on Oulipo, 13

While mathematics as a whole makes use of certain basic tenets of abstract thought, individual disciplines can be defined based on the specific object of study.

Introduction

19

addressing Oulipian formalism, defining and analyzing terms such as constraint and structure. Chapter 2 groups Oulipian texts and procedures that are inspired by the study of algebra taken broadly to mean the study of mathematical symbols and the rules for manipulating them. Letters and numbers have a long and intertwining history. Oulipo expands upon this already important relationship, drawing from a variety of techniques such as basic counting (of letters, numbers, words, etc.), simple arithmetical procedures (such as addition and subtraction), and algebraic language (using variables to generalize objects with certain commonalities). Studying the properties of numbers is the object of the mathematical discipline known as number theory, a result of which provides the compositional principle for Paul Braffort’s Mes Hypertropes (1979). Abstracting operations and their properties leads to the study of abstract algebra, which was employed by Jacques Roubaud in La Princesse Hoppy (1990), an Arthurian-​style fairytale with a mathematical pedagogical intent. In short, Oulipian authors take as a starting point that literature is composed of a finite number of basic elements and aim to demonstrate that the act of reading is a reaction to new manipulations of familiar structures. By looking specifically at these procedural and semantic constraints and their development within the group, this chapter reveals new insights into the analytic and synthetic goals of the group. Combinatorics is the study of combinations of finite sets of elements, a field that forces one to consider questions of probability and chance, to which Oulipo claims to be opposed. Chapter 3 investigates the Oulipian conception of chance in literature and the strategy the second-​generation members devised to oppose it, the clinamen or the purposeful deviation from constraint on aesthetic grounds. This chapter begins with a reading of Queneau’s Cent mille milliards de poèmes (1961), the first and quintessential Oulipian text that relies on combinatorics, producing 1014 “potential” sonnets from an initial 10. This text provides the foundations for Oulipian notions of constraint and potential. Then, the chapter turns to game-​based constraints of three second-​generation Oulipians: Jacques Roubaud’s first volume of poetry, ∈ (1967); Italo Calvino’s Il castello dei destini incrociati (1973); finally, Georges Perec’s 1978 novel, La vie mode d’emploi. These texts build on the pedagogical intent, combinatorial play, and treatment of

20

introduction

chance established in Cent mille milliards de poèmes, with the latter two in particular crucial in the definition of the Oulipian principle of clinamen. Chapter 4 deviates from pure mathematics in its focus of algorithms, or step-​by-​step procedures that form the basis of computer science. Algorithmic thought proved to be richly productive for certain authors such as Le Lionnais, Perec, Calvino, Berge, and Queneau who used algorithms, programming languages, and flowcharts as compositional principles. Parallel to these individual texts, Oulipo engaged in a series of computer experiments in the 1960s and 1970s, constituting some of the earliest examples of electronic literature and digital humanities work. Through an analysis of the group’s archives, I argue that Oulipo abandoned these efforts due to a disappointment in the reduced role of the reader, a decision that has important implications for the study of digital humanities. Finally, Chapter 5 focuses on geometry or the study of mathematical space. While the etymological roots of the word “geometry” imply the practical task of measuring the earth, the mathematical discipline is concerned with abstracted, ideal figures and their properties. This chapter deals with questions of form and content, investigating the pedagogical nature of Oulipian constraints through two specific texts. Calvino’s Le città invisibili (1972) hinges on a geometrical form that can be derived from the table of contents, a paratextual indication of its own organizational principle. The novel continually references its structure within the text. Geometer Michèle Audin’s historical novel in blog form Mai quai Conti (2014) recounts the proceedings of the Académie des Sciences during the Paris Commune in parallel with a table of contents that is also a theorem, which directs the content of the novel it organizes. As with geometry, these works struggle to reconcile the abstracted, ideal form the authors create for their works with the messiness of the intellectual topics they address. I conclude that Oulipo makes intentional use of mathematics, capitalizing on an image of mathematics that was popular in the postwar era and contributing to mathematics and computer science in the process. Furthermore, the use of mathematics as a compositional method invites the reader to participate in abstract, mathematical thought, taking an important role in literary creation. This work has three main contributions to literary scholarship more largely. First, understanding Oulipo’s mathematical

Introduction

21

methods and group culture can explain the group’s singularity among other twentieth-​century artistic movements, why it is so long-​lasting and how it has evolved over time. Second, Oulipo’s computer experiments are critical to understanding the history and practice of digital humanities. Furthermore, understanding why Oulipo abandoned such efforts is essential for a more nuanced understanding of the potential and limitations of the field. Finally, understanding Oulipo sheds new light on disciplinary questions. Oulipo proposes its own response to the divide between the humanities and STEM fields and can help bridge that gap today in the university.

Illustration of the mathematical formula, borrowed from set theory, A ∩ (B ∩ C) =​(A ∩ B) ∪ (A ∪ C), designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission.

Chapter 1

Set Theory

The study of mathematics is far more rich, beautiful, and human than many would believe. Keith Devlin (2012, p. 3) defines mathematics as the study of different types of abstract patterns: … arithmetic and number theory study patterns of numbers and counting; geometry studies patterns of shape; calculus allows us to handle patterns of motion; logic studies patterns of reasoning; probability theory deals with patterns of chance; topology studies patterns of closeness and position; fractal geometry studies the self-​similarity found in the natural world.

While mathematicians study abstract mathematical objects (such as numbers or shapes), any sort of abstraction can be viewed as mathematical thought. For instance, to recognize that the sun, full moon, and center of a flower share a circular shape is to engage in mathematical thought. However, mathematical work is concerned with finding patterns and generalizing them, for example, by studying an abstract circle and determining which properties hold for every example. In light of this definition, any human being is capable of exploring relationships and patterns and is therefore equipped to engage in abstract, mathematical thought. For the purpose of this study, it is important to acquaint the reader with the basic tenets of mathematical thought: formalism, abstraction, logic, axioms, and proofs. While many would consider these elements to be pillars upon which mathematical work relies, they actually have a fraught history of disagreement, culminating in an attempt by a few key figures to rebuild the discipline on new foundations in the late nineteenth and early twentieth centuries. This attempted revolution in the practice of mathematics had a wide-​reaching impact on other disciplines, influencing the development of various formalisms that also sought to understand cultural objects scientifically, including Ferdinand de Saussure’s structural

24

chapter 1

linguistics, Russian formalism and structuralism. In a similar vein, Oulipo has drawn from mathematics, but blatantly distinguishes itself from these other philosophical movements. This chapter introduces mathematical thought as well as this fascinating history of cultural influence, which is key to understanding Oulipo’s inheritance of these disciplinary and historical aspects of mathematics.

I. From Euclid to Bourbaki: A Brief History of Mathematical Formalism The Elements, dating back to the third century bce and attributed to Euclid, is often lauded for introducing the idea of mathematical rigor by use of the axiomatic method. In essence, the axiomatic method is a procedure by which one begins with a few basic propositions (called axioms or postulates) and builds upon them logically. Through the proper definition of these axioms, followed by logical deductions and proofs, the axiomatic method generates a system that is in accordance with specified rules. The Elements creates such a system for the study of geometry. While the etymological origins of the term literally mean measuring (metron) the earth (geo), the Elements were more concerned with abstracting this system of measurement to its most basic elements, points and lines. Using very basic tools, Euclid constructs shapes of increasing complexity through a series of 465 theorems, demonstrating properties that might not be immediately understandable through this logical reasoning. Like later mathematical writing, the Elements is literally meant to be read with a pencil. In other words, unlike a novel which can involve a certain amount of passivity on the part of the reader, a reader of the Elements is expected to reproduce the geometric constructions. This is perhaps the most identifying feature of reading mathematics –​it requires the reader to follow the logic step by step. In this way, at the end of every mathematical proof, the reader understands how precisely the solution holds for every possible case. In the Elements, the theorems build upon one another, allowing the reader to understand an impressive system of geometric results,

25

Set Theory

with one of the culminations being the famous Proposition 47, a proof of what is now known as the Pythagorean theorem. Given that Euclid’s proof which depends upon geometric constructions is oddly foreign to those of us whose mathematical educations involved algebraic language, I will demonstrate this theorem using our modern notation, which represents another important cornerstone of mathematical work, formalized language. The Pythagorean theorem deals with the specific shape of the right triangle, proving that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Figure 1.1 illustrates this mathematical truth, which certainly is not obvious at first glance.

Figure 1.1.  A visual illustration of the squares of all sides of a right triangle, designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission.

Based on Figure 1.1, the sum of the areas of squares a and b (or the two legs of the right triangle) should be the equivalent of the area of square c (or that of the hypotenuse). In our modern-​day algebraic language, this can be expressed with the following equation: c2 =​a2 +​b2

26

chapter 1

Such formalized language must be learned and manipulated according to strict rules. However, thanks to its formal nature, such algebraic language can be used to understand properties that might not be immediately discernible, such as this theorem. Indeed, one proof of the Pythagorean theorem can be represented as a combination of visual and algebraic language.

Figure 1.2.  A visual proof of the Pythagorean theorem, designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission.

In Figure 1.2, we see that four right triangles have been combined to create c2, with an additional square completing the shape. Based on how it was constructed, the length of each side of that central square can be represented algebraically as (b − a), given that it represents the difference between the two legs of the right triangle. Therefore, we can represent this

27

Set Theory

image algebraically as the sum of the areas of these four triangles1 as well as this square: c2 =​4(½ab) +​(b − a)2 This equation can be simplified by manipulating its parts in accordance with mathematical rules as follows: c2 =​2ab +​b2 +​a2 − 2ab By cancelling the positive and negative 2ab terms, we arrive at the famous formula: c2 =​a2 +​b2. Typically, at the end of a proof, a mathematician writes QED (Quod erat demonstrandum, Latin for “that which was to be demonstrated”) or CQFD in French (ce qu’il fallait démontrer). As Alex Bellos notes in his book Here’s Looking at Euclid, the feeling at the end of a proof is a unique pleasure: “The thrill of math is the moment of instant revelation, from proofs such as this, when suddenly everything makes sense” (p. 53). The important thing to note about such formalized mathematical language is that it simply has no use out of this context. Just as musical notes would be incomprehensible outside of a musical score, mathematical language is appropriate only within its proper context. However, Raymond Queneau has attempted a translation of sorts, attempting to rewrite a story mathematically in a short book that predates the founding of Oulipo, Exercices de style (1947). In this fascinating text, the author turns an everyday occurrence –​a spat in a city bus –​into a proliferation of styles. The first “style” in the text, Notations, recounts this relatively insignificant event in an ostensibly objective tone, with short, declarative sentences: Notations Dans l’S, à une heure d’affluence. Un type dans les vingt-​six ans, chapeau mou avec cordon remplaçant le ruban, cou trop long comme si on lui avait tiré dessus. Les gens descendent. Le type en question s’irrite contre un voisin. Il lui reproche de le

1

The generalized equation for the area of a triangle is: A =​½ × base × height.

28

chapter 1 bousculer chaque fois qu’il passe quelqu’un. Ton pleurnichard qui se veut méchant. Comme il voit une place libre, se précipite dessus. Deux heures plus tard, je le rencontre Cour de Rome, devant la gare Saint-​Lazare. Il est avec un camarade qui lui dit : « Tu devrais faire mettre un bouton supplémentaire à ton pardessus. » Il lui montre où (à l’échancrure) et pourquoi. (Queneau, 1947, p. 7)

While the basic story remains the same, each iteration brings a different aspect of the original to light, revealing how much of any story is communicated with the style, rather than the content. Queneau (1947, p. 146) even translates this original into mathematical language, focusing on geometrical properties: Géométrique Dans un parallélépipède rectangle se déplaçant le long d’une ligne droite d’équation 84x +​S =​y, un homoïde A présentant une calotte sphérique entourée de deux sinusoïdes, au-​dessus d’une partie cylindrique de longueur l < n, présente un point de contact avec un homoïde trivial B. Démontrer que ce point de contact est un point de rebroussement. Si l’homoïde A rencontre un homoïde homologue C, alors le point de contact est un disque de rayon r < l. Déterminer la hauteur h de ce point de contact par rapport à l’axe vertical de l’homoïde.

Queneau’s playful gesture is revealing, giving a new meaning to the word exercice. In this case, the exercise is literal, demanding that the reader demonstrate that the “point de contact” is in fact a “point de rebroussement” and to calculate the height of the aforementioned “point de contact.” The real exercise here is not to calculate these values (indeed, from the information given, that is impossible), but rather to find the original story in the mathematical notation. For these two “homoïdes” or man-​shaped bodies, a “point de rencontre” results in a mere “brush.” This “point de contact” with a “trivial” second party occurs at a “disque,” otherwise a lost button. Mathematical notation is arguably the perfect medium to transmit mathematical information. However, while Queneau’s use of mathematical notation appears to be an eccentric joke, the application of mathematical language to storytelling does communicate a story, although in the

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form of a homework problem. This problem is for the reader to resolve, thinking back to his high school mathematics and using the preliminary information from the original story to understand the solution. In this case, Queneau’s “Géométrique” functions like a math problem for literature, forcing the reader to intuit meaning using pre-​disclosed information and mathematical notation. While the axiomatic method has existed since Greek mathematics, in the late nineteenth and early twentieth centuries, a number of mathematicians attempted to refound the discipline on the basis of extreme rigor, driven in part by German mathematician, David Hilbert. During the winter semester of 1898–​1899, Hilbert gave a series of lectures, which were published in 1899 under the title Grundlagen der Geometrie (The Foundations of Geometry), on how we conceive space, beginning with three basic systems –​points, straight lines, and planes. He establishes relations between them, creating a system of axioms. Hilbert’s (1903, p. 1) goal was simple, yet paramount: Die vorliegende Untersuchung ist ein neuer Versuch, für die Geometrie ein vollständiges und möglichst einfaches System von Axiomen aufzustellen und aus denselben die wichtigsten geometrischen Sätze in der Weise abzuleiten, daß dabei die Bedeutung der verschiedenen Axiom-​gruppen und die Tragweite der aus den einzelnen Axiomen zu ziehenden Folgerungen möglichst klar zu Tage tritt.2

Hilbert’s work was a success for modern logicians, who held that various branches of mathematics (or maybe even all of mathematics) could be derived from a consistent collection of basic axioms. While Hilbert glorified axiomatic mathematics, the recourse to this method was not a new development and draws from Euclid’s Elements. Indeed, right from the start, Hilbert begins by lauding the axiomatic method and defining the elements (a clear reference to the work of his

2

“The following investigation is a new attempt to choose for geometry a simple and complete set of independent axioms and to deduce from these the most important geometrical theorems in such a manner as to bring out as clearly as possible the significance of the different groups of axioms and the scope of the conclusions to be derived from the individual axioms” (Hilbert, 1950, p. 1).

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esteemed Greek predecessor) of geometry: points, straight lines, and planes. It is important to note that Hilbert never defines his elements of geometry, but rather uses the axioms to describe their properties. For instance, Hilbert’s (1903, p. 3) first “Axiom of Connection” claims that a line is completely determined by only two points: “I 1. Zwei von einander verschiedene Punkte A, B bestimmen stets eine Gerade a … I 2. Irgend zwei voneinander verschiedene Punkte einer Geraden bestimmen diese Gerade.”3 Likewise, the “Axioms of Order” culminate in a theorem that expands on this property: “Satz 3. Zwischen irgend zwei Punkten einer Geraden gibt es stets unbegrenzt viele Punkte”4 (Hilbert, 1903, p. 5). In dispensing with Euclid’s initial definitions, Hilbert purges geometry of all extraneous elements and views axioms not as universal truths, but rather as a way to enable a clearer understanding of our provisional conceptions, according to Leo Corry (1997, p. 20). François Le Lionnais (1981b, pp. 35–​36) has written that Raymond Queneau was not only a reader of mathematics, but a serious mathematician. Jacques Roubaud (1981b, pp. 42–​43) notes that : “Etre mathématicien, ce sera d’abord être lecteur de mathématiques –​ses jeux … –​son histoire … –​ ses anecdotes … –​ses fous; entre autres.” This conflation of mathematical work and reading mathematics is a quintessential element of Queneau’s Oulipian work. His enthusiasm for mathematical substitutions and love of mathematical anecdotes find the perfect marriage in the third fascicule of the Bibliothèque Oulipienne,5 Les Fondements de la littérature d’après David Hilbert (1976), which begins with this anecdote:

3 4 5

“Two distinct points A and B always completely determine a straight line a … Any two distinct points of a straight line completely determine that line …” (Hilbert, 1950, p. 2). “Theorem 3. Between any two points of a straight line, there always exists an unlimited number of points” (Hilbert, 1950, p. 5). Also in the collected volume, La Bibliothèque oulipienne vol. I, published by Seghers. As the original published fascicule was only printed 150 times, all citations in this book refer to the collected volume. See Bibliography.

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Après avoir assisté à Halle à une conférence de Wiener (pas Norbert6 bien sûr) … David Hilbert, attendant le train pour Koenigsberg en gare de Berlin, murmura pensivement : « Au lieu de points, de droites et de plans, on pourrait tout aussi bien employer les mots tables, chaises et vidrecomes » … M’inspirant de cet illustre exemple, je présente ici une axiomatique de la littérature en remplaçant dans les propositions d’Hilbert les mots « points », « droites », « plans », respectivement par : « mots », « phrases », « paragraphes ». (Queneau, 1987, pp. 37–​38)

The anecdote is characteristic of Hilbert’s conception of his axioms as strictly independent. While he chose to manipulate the same terms as Euclid, he might have attributed different names to these elements. However, the statement cannot be taken literally regarding Hilbert’s axioms. For instance, there are times when tables do not contain beer mugs. While Queneau understood this, he takes the anecdote at face value and follows it to its logical conclusions regarding literature, substituting these words in a selection of Hilbert’s axioms and encouraging the reader to try the same method with the others. Through this simple transposition of words, Queneau facetiously claims to create the mathematical foundations of literature. Queneau plays with both mathematics and literature, using the one to critique the other. For instance, his transposition of the first axiom takes an example that would be mathematically incorrect and uses it to produce a grammatically correct sentence: I, 1 –​Il existe une phrase comprenant deux mots donnés. COMMENTAIRE : Evident. Exemple : soit les deux mots « la » et « la », il existe une phrase comprenant ces deux mots : « le violoniste donne le la à la cantatrice. » (Queneau, 1987, p. 39)

Queneau’s choice of words, which should be distinct as in the mathematical example, are homonyms. This sleight of hand indicates that, despite his formal, mathematical game, Queneau is aware that the word “point” is not replaceable with “word.” To create a line from two given points, the

6

Hermann Wiener. Norbert Wiener was an American mathematician, best known for his work on cybernetics (which he is considered to have invented).

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points must be distinct; however, in literature, a sentence can contain two homonyms, words that are identical in spelling and pronunciation but not in meaning. This example is a critique of the mathematical principle that allows Hilbert not to define “point” and to leave it an empty signifier, and a statement about language itself. Following this first axiom is a second, related one: I, 2 –​Il n’existe pas plus d’une phrase comprenant deux mots donnés. COMMENTAIRE : Voilà, par contre, qui peut surprendre. Cependant si l’on pense à des mots comme « longtemps » et « couché », il est évident qu’une fois écrite cette phrase les comprenant, à savoir : « longtemps je me suis couché de bonne heure », toute autre expression telle que : « longtemps je me suis couché tôt » ou « longtemps je ne me suis pas couché tard » n’est qu’une pseudo-​phrase que l’on doit rejeter en vertu du présent axiome. SCHOLIE : Naturellement si l’on écrit « longtemps je me suis couché tôt », c’est « longtemps je me suis couché de bonne heure » que l’on doit refuser en vertu de l’axiome I, 2. C’est-​à-​dire qu’on n’écrit pas deux fois A la recherche du temps perdu. (Queneau, 1987, p. 39)

Choosing a famous sentence brings to light another difference between mathematics and literature. Just as words were not perfectly analogous to points, sentences and lines are not interchangeable. The opening sentence from A la recherche du temps perdu is not abstract, but a specific, recognizable sentence. Queneau’s axiom can be understood as a literary insight: Proust has occupied this sentence in literary space, and similar sentences such as “longtemps je me suis couché tôt” will therefore always be seen as reminiscent of the original. Given that Queneau’s text uses words, sentences, and paragraphs to describe properties of words, sentences, and paragraphs, each axiom can be used to analyze itself. For instance, each axiom is a sentence that contains the words “two” and “words.” Therefore, their recurrence in the text violates the second axiom. Paradoxically, the second axiom forbids its own enunciation, a fact of which Queneau is aware: “On peut donc formuler cet axiome de métalittérature: Les axiomes n’obéissent pas aux axiomes” (Queneau, 1987, p. 40). Mathematician Robert Tubbs (2014, p. 27) understands Queneau’s use of this paradox as a key element in the text:

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Even though Queneau’s axioms for literature fall short of actually providing a philosophical basis for all of literature, there are two important points to take away from this brief discussion of them. The first is that two axioms can contradict one another, or that a single axiom can even contradict itself … The second point … is that a literary work can be viewed as a collection of words subject to certain constraints.

While Tubbs is correct that, mathematically, axioms can contradict each other given the proper circumstances, Queneau’s claim to provide an axiomatic foundation for literature is facetious. With his mathematical background, Queneau was perfectly aware that his substitution of words would not produce analogous axioms for literature. Rather, his substitutions force one to consider literature differently. Queneau’s meta-​commentary on his own axioms results from his original transposition: by replacing the word “points” with “words” and then using words to describe them, he encounters a paradox. By using mathematics and its tools to analyze the discipline itself (metamathematics), the shape of the field was changed. Queneau’s text represents a parallel endeavor –​by creating an axiomatic approach to literature, he uses literature to explore literature, tearing away the façade and showing the reader the foundations on which literature is built. Two of Queneau’s faux-​mathematical principles are analogous to Oulipian aesthetics. In a first example, Queneau (1987, pp. 44–​45) encourages the reader to carry out literary constructions of axiom II: II, 4 –​Soit trois mots d’un paragraphe n’appartenant pas tous à la même phrase et soit une phrase ne comprenant pas ces trois mots mais appartenant au même paragraphe, si cette phrase comprend un mot de la phrase déterminée par deux de ces mots, elle comprendra toujours un mot commun avec la phrase déterminée par l’un de ces mots et le troisième. COMMENTAIRE : Pour éclaircir cet axiome, revenons à Hilbert qui le formule ainsi « d’une façon plus intuitive : si une droite entre dans un triangle, elle en sort » (p. 15 de la traduction française). Nous laissons au lecteur le soin de chercher ou de construire des paragraphes conformes à cet axiome.

In order to be comprehensible, the reader must transpose Queneau’s axiom back into the mathematical realm and Queneau even refers the reader to the French translation of Hilbert and suggests simplifying the

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problem with a diagram. The reader is then invited to “construct” or find an example of a paragraph that conforms to the axiom. This invitation to consider literary creation mathematically is an essential element of Oulipian aesthetics. On the one hand, a mathematical substitution in a source text serves an analytic purpose, as Queneau’s jocular translations pave the way for greater reflection; on the other hand, the mathematical nature of the text is synthetic, encouraging further production, constrained by specific mathematical results. While the analytic and synthetic goals are representative of the work of Oulipo, the following example illustrates a central motive in Oulipo’s aesthetics –​the role of the reader. Queneau (1987, p. 45) describes what Hilbert calls the “consequences” of these axioms, two theorems about the properties of lines, one of which is philosophically rich: “Théorème 7: Entre deux mots d’une phrase, il en existe une infinité d’autres.” Taken metaphorically, with the presence of a reader, every sentence is potentially greater than the sum of its parts and can lead to greater reflection. This theorem is not unlike Queneau’s thoughts about novels: “… Queneau déclarait déjà que le roman doit ressembler à un bulbe ‘dont les uns se contentent d’enlever la pelure superficielle, tandis que d’autres, moins nombreux, l’épluchent pellicule par pellicule’ ” (Bens, 1981, p. 3). Oulipian work calls upon the reader to do mathematical work on literature, a fundamentally different type of reading, more active and more rewarding. The philosophical issues raised by Hilbert’s work regarding the definition of mathematical objects and the formal nature of mathematical language are fundamental in understanding the mathematical revolution that took place in the nineteenth and early twentieth centuries, leading to the development of set theory. Formalization and axiomatization are pillars upon which mathematical work is carried out, however the language of mathematics has varied throughout history. In this sense, Hilbert’s work can be understood as one example in a trend, where mathematicians and logicians began to work on the foundations of the discipline, developing set theory as an alternative foundation for mathematical work. While most have an intuitive understanding of numbers, the mathematical object remains unclear. Numbers do not necessarily conjure a specific image, just as a word represents a more generalized object in the real world.

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Mathematical objects are even more complicated, because “numbers” are not restricted to the set of positive, natural integers, but include negative, rational, irrational, and even imaginary ones. Set theory defines a new unit, a set, as a collection of objects, or elements, all of which share a common property, and develops a formalized language to deal with such elements. Set theorists concern themselves only with the number of distinct elements belonging to a set, as well as the set’s cardinality, or the number of elements the set contains. The fascinating part of set theory is that, while the cardinality of a set is represented as a number, it is not equivalent to the number that represents it, but rather a particular instance of it. The number 3 is equivalent to the (much larger) set of all sets of cardinality three. As Bertrand Russell explained, a “… particular number is not identical with any collection of terms having that number: the number 3 is not identical with the trio consisting of Brown, Jones, and Robinson. The number 3 is something which all trios have in common, and which distinguishes them from all other collections” (Quoted in Hodges, 2012, p. 31). As with mathematical formalism and axiomatization, Raymond Queneau was aware of set theory and its implications for literature. Exercices de style implements the language of sets (ensembles in French) as well, introducing the terms elements (éléments) and subsets (sous-​ensembles) into the tale of the argument on the bus: Dans l’autobus S considérons l’ensemble A des voyageurs assis et l’ensemble D des voyageurs debout. À un certain arrêt, se trouve l’ensemble P des personnes qui attendent. Soit C l’ensemble des voyageurs qui montent; c’est un sous-​ensemble de P et il est lui-​même l’union de C’ l’ensemble des voyageurs qui restent sur la plate-​forme et de C’’ l’ensemble de ceux qui vont s’asseoir. Démontrer que l’ensemble C’’ est vide. Z étant l’ensemble des zazous et {z} l’intersection de Z et de C’, réduite à un seul élément. À la suite de la surjection des pieds de z sur ceux de y (élément quelconque de C’ différent de z), il se produit un ensemble M de mots prononcés par l’élément z. L’ensemble C’’ étant devenu non vide, démontrer qu’il se compose de l’unique élément z. Soit maintenant P l’ensemble des piétons se trouvant devant la gare Saint-​Lazare, {z, z’} l’intersection de Z et de P, B l’ensemble des boutons du pardessus de z, B’ l’ensemble des emplacements possibles des dits boutons selon z’, démontrer que l’injection de B dans B’ n’est pas une bijection. (Queneau, 1947, pp. 103–​104)

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According to the definition, all the travelers in the bus constitutes a proper set, but mathematically speaking, such a set does not tell us much about the world. While at first glance, one might consider this a superficial use of the mathematical language, it is in fact representative of what is called naïve set theory. Naïve set theory, unlike axiomatic set theories, is defined informally rather than through formal logic. While not formalized, naïve set theory is an important bridge, allowing one to apply mathematical settheoretical ideas to non-​mathematical objects, using natural language to describe sets and their operations. Queneau creates a mathematical problem from his initial situation. At a stop, a set of people wait (P), a subset of which (C) gets on the bus. The subset C is composed of two further subsets, C’ and C”, or the set of passengers who will remain standing or find a seat respectively. Queneau then asks the reader to “Démontrer que l’ensemble C’’ est vide.” To translate this into plain language, Queneau expects the reader to prove that the bus is full. By definition, mathematical language is not funny. However, there is something clearly sarcastic in Queneau’s literary formalism. Irony and sarcasm cannot be represented in a formalized way. They depend on context, which does not align with the purpose of mathematics, which is to recognize abstract patterns. Set theory as a mathematical tool and historical development is far from humorous. Given its goal to reduce all of mathematics to this formal language governed by the rules of logic, it is rather dry. Bertrand Russell’s landmark Principia Mathematica (1910–​ 1913), for instance, is a long and tedious book, laying out in the most elementary terms the logical basis of what everyone already knew intuitively. Queneau’s added context renders the mathematical language humorous. For the reader to solve Queneau’s problem, it suffices to understand that the subset C’’ is empty, which means there are no free seats. The most remarkable part of this text is that the point where the reader understands the joke is equivalent to the moment in which he or she understands the mathematics. That “eureka!” moment, so fundamental to mathematical thought, finds its literary equivalent in humor. Queneau plays upon this relationship by literally combining the two. The rest of the text plays on the operations of formal logic, intersections, unions, surjections and bijections. The set Z represents the passengers

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on the bus who are dressed eccentrically, whereas its intersection with the newly arrived passengers is reduced to a single element, z. This is, of course, the man in the funny hat who has a spat with his neighbor. The terms surjections and bijections were introduced by Bourbaki in Éléments de mathématique (1931). A surjective function is a way to map every element from one set onto another, such that every element in the latter set has a corresponding element in the former; injective functions, on the other hand, never map distinct elements from one set to the same element in the latter set; finally, a bijective function (also known as one-​to-​one) pairs each element of one set with exactly one element of the corresponding set and vice versa. A “surjection des pieds de z sur ceux de y” treats z’s feet as an element of his body, being forced upon one of the standing passengers. The “ensemble M de mots” pronounced by z, his excuse for moving to a seated position, is another example of Queneau’s appropriation of set theory to suit his story. However, it is also representative of how one can view applications of set theory to literature. Oulipo went on to view texts as sets of words, words as sets of letters, etc. Queneau’s exercise is a precursor to the Oulipian understanding of the fabric of language whose properties lead to consequences (intended or unintended), and which can be manipulated by an author. Given that set theory was founded in an 1874 mathematical paper by German mathematician Georg Cantor and generated quite a bit of excitement in early twentieth-​century England with the work of logician, Bertrand Russell, it seems historically removed from a group of French authors in the 1960s. However, the key link between the two developments is the French mathematician collective who wrote under the pseudonym, Nicolas Bourbaki. Beginning in the 1930s, this group published a series of textbooks known as Eléments de mathématique that attributes a great importance to set theory, claiming in the first volume that it can be used as the foundation for all of mathematics. While the mathematician “himself ”7 is not particularly well known, it is undeniable that his work changed the face of mathematics, especially in the years 1950–​1970 (Mashaal, 2002, p. 4). This revolution was not accomplished through specific mathematical 7

For convenience, I will refer to Bourbaki as if he were an actual individual, simplifying how I would otherwise have to address him grammatically.

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advancements, but rather through the grandiose vision of mathematics Bourbaki proposed, which is now considered by most mathematicians to be outdated. However, according to historian of science David Aubin, Bourbaki served an important role as a “cultural connector,” influencing a variety of non-​mathematical fields, inspiring proponents of structuralism, and even reaching Oulipo. Nicolas Bourbaki was not an individual, but the pseudonym8 of a group of (mostly) French mathematicians at the Ecole Normale Supérieure (Paris) in the 1930s, including some of the greatest mathematicians of the century: André Weil, Henri Cartan, Claude Chevalley, Laurent Schwartz, Alexandre Grothendieck, Jean-​Pierre Serre, Szolem Mandelbrojt, and others. While the last name Bourbaki seems to refer to Charles Bourbaki (1816–​1897), the failed general of the Franco-​Prussian War, there is no clear rationale behind the choice of the first name, Nicolas, which does not appear on the covers of the original Eléments de mathématique volumes, but does on the group’s historical text, Éléments d’histoire des mathématiques (1960). The name also seems to have been a collective joke at the ENS around the same time (Mashaal, 2002, pp. 25–​26). The collaborators of Bourbaki went far beyond this amusing pseudonym, inventing a detailed biography for this fake mathematician in the “Notice sur la vie et l’œuvre de Nicolas Bourbaki.”9 Bourbaki was from the imaginary country of Poldavia (Poldévie),10 a professor in a Poldavian university, a member of the major Poldavian Academy of Science, and even had an invented CV and several signatures in different handwriting. Not only does this document cite Henri Poincaré and David Hilbert as Bourbaki’s mathematical influences, but it even claims that Bourbaki attended their lectures. Additionally, 8

9 10

Outside of France, this singularity of an individual composed of a collective was often treated as problematic –​Bourbaki was refused entrance into the American Mathematical Society, for instance, due to the fact that he applied as an individual rather than as a group (Mashaal, 2002, p. 35). Reproduced in full in Mashaal, Bourbaki, pp. 32–​34; probably written in 1960 and first brought to light in Judith Friedman’s doctoral work on Bourbaki in 1977. For the “truth” about Poldavia, see Michèle Audin’s extremely well-​researched article, “La vérité sur la Poldévie” (2010), in which Audin provides a timeline and bibliography of mentions of this imaginary country.

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the biography of Bourbaki is plagued with political setbacks: his brilliant mathematical work is interrupted by World War I; he becomes implicated in the Poldavian nation’s future, but is then displaced due to a civil war and is forced to become a refugee in Iran (p. 32). The notice details Bourbaki’s arrival in France and influence on his collaborators, leading to their decision to publish “… sous le seul nom de leur Maître, et de renoncer délibérément à revendiquer leur part personnelle dans le travail commun” (Mashaal, 2002, p. 33). This humorous backstory created a folklore surrounding the work of the group, which influenced its reception and subsequent appropriation: first, the humor surrounding the name and pseudo-​scientific and historical work that went into defending this fictitious biography makes an otherwise dry treatise more digestible; second, the collaborative efforts were not only productive, but enabled the group to persist until this very day; finally, the aims of the group were explicitly pedagogical, which might have helped in promoting Bourbaki’s texts in the French university setting. This folklore has not been beneficial to historians, with Leo Corry (1992, p. 319) noting: “The legend of Bourbaki has, more often than not, impaired the objectivity of appraisals of Bourbaki’s scientific output.” For the purposes of this study, the fabricated history and unique sociology of Bourbaki and his collaborators offers a model through which we can understand Oulipo’s group culture. Furthermore, Bourbaki’s emphasis on mathematical rigor expressed through formal, set-theoretical language and an axiomatic system also appears to be a prototype for Oulipian potential literature in the early stages of the group. Bourbaki published a series of textbooks called Eléments de mathématique (the first volume was first published in 1939, and the last dates to 1998), of which the goal was to reformulate mathematics based on set theory. The peculiar style of the textbook contributed to its popularity and effects: while there were exercises, they were not meant as part of a “learning experience” but rather as useful diversions; many of Bourbaki’s invented notations (such as the symbol for the empty set, ø) became standard; and while Bourbaki’s practice of set theory was impractical, the claims made about the nature of mathematical work created a lasting image of the discipline itself. While it never became a canonical textbook as intended, it

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did help one non-​professional mathematician engage with the topic, and that was Raymond Queneau. The title, Eléments de mathématique references Euclid’s Elements and Hilbert’s basic elements of geometry. The singularity of the noun mathématique is indicative of Bourbaki’s perception of the discipline: rather than a disparate collection of branches, Bourbaki understands mathematics as singular, unified by the formal language of set theory and a rigorous axiomatic system. Reinforcing this interpretation, Bourbaki only refers to mathematics in the plural form at two separate instances: in the title of the group’s Éléments d’histoire des mathématiques (1960), which is not a chronological history, but rather divided by mathematical subfields; and more relevantly in the group’s first published non-​technical essay, “L’Architecture des mathématiques,” which first appeared in 1948. This essay, discussed below, is subtitled La Mathématique, ou les Mathématiques?, reinforcing the question of plurality (Bourbaki, 1962, p. 35). The first volume of Eléments de mathématique, Théorie des ensembles, begins with a Mode d’emploi de ce traité, in which the first claim is that: Le traité prend les mathématiques à leur début, et donne des démonstrations complètes. Sa lecture ne suppose donc, en principe, aucune connaissance mathématique particulière, mais seulement une certaine habitude du raisonnement mathématique et un certain pouvoir d’abstraction. (Bourbaki, 1939, p. I.3)

This ambitious introduction begins with the plural, mathématiques, which the authors intend to unify by means of the common language of set theory presented in the first volume. The rest of the mode d’emploi touts an axiomatic method that “… procède le plus souvent du général au particulier …” (Bourbaki, 1939, p. I.3) and highlights the centrality of “… les définitions, les axiomes et les théorèmes,” (Bourbaki, 1939, p. I.4) which are followed by their logical consequences. The main focus is on the language itself: “La terminologie suivie dans ce traité a fait l’objet d’une attention particulière. On s’est efforcé de ne jamais s’écarter de la terminologie reçue sans de très sérieuses raisons” (Bourbaki, 1939, p. I.3). Additionally, Bourbaki notes that the use of this precise terminology is rigorous: “Autant qu’il a été possible, les abus de langage ou de notation, sans lesquels tout texte mathématique risque de devenir pédantesque et

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même illisible, ont été signalés au passage” (Bourbaki, 1939, pp. I.3–​I.4). While in the Eléments de mathématique, the authors do indeed aim for a strict use of notation and formal language, this is not always true in the group’s popular writing, which will become apparent below. Following the mode d’emploi, Bourbaki’s introduction to the first volume of Eléments de mathématique begins by praising the rigor of ancient Greek mathematics: “Depuis les Grecs, qui dit mathématique dit démonstration; certains doutent même qu’il se trouve, en dehors des mathématiques, des démonstrations au sens précis et rigoureux que ce mot a reçu des Grecs et qu’on entend lui donner ici” (Bourbaki, 1939, p. I.7). Bourbaki considers that a return to these Greek origins is necessary whenever the notion of mathematical truth is challenged, turning to a discussion of mathematical language. Bourbaki claims that mathematical work depends upon the double foundations of formal language and axioms, which he compares to vocabulary and syntax: … un texte mathématique suffisamment explicite pourrait être exprimé dans une langue conventionnelle ne comportant qu’un petit nombre de ‘mots’ invariables assemblés suivant une syntaxe qui consisterait en un petit nombre de règles inviolables : un tel texte est dit formalisé … La méthode axiomatique n’est à proprement parler pas autre chose que cet art de rédiger des textes dont la formalisation est facile à concevoir. Ce n’est pas là une invention nouvelle ; mais son emploi systématique comme instrument de découverte est l’un des traits originaux de la mathématique contemporaine. (Bourbaki, 1939, pp. I.7–​I.8)

This formal language serves to connect all mathematics, unifying the field through the study of common structures: De plus, et c’est ce qui nous importe particulièrement en ce Traité, la méthode axiomatique permet … d’en dissocier les propriétés et de les regrouper autour d’un petit nombre de notions, c’est-​à-​dire, pour employer un mot qui sera défini plus loin avec précision (chap. IV), de les classer suivant les structures auxquelles elles appartiennent …. (Bourbaki, 1939, p. I.9)

The notion of structures is fundamental for Bourbaki’s conception of mathematics, though it is never properly defined in this introduction. Rather, the term is used in a metaphorical sense that is meant to reinforce the notion that rigorous formal language and the axiomatic method can

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correct the aforementioned gaps in the study of mathematics. The end of Bourbaki’s introduction explains how this mathematical language of structures finds an analog in natural language, referring to the fact that speech pre-​exists the construction of a formal grammar (Bourbaki, 1939, p. I.9).11 The innovation Bourbaki proposes in this book is first to describe a generalized language (set theory), and then to use that language to derive the rest of mathematics: En effet, alors qu’autrefois on a pu croire que chaque branche des mathématiques dépendait d’intuitions particulières qui lui fournissaient notions et vérités premières, ce qui eût entraîné pour chacune la nécessité d’un langage formalisé qui lui appartînt en propre, on sait aujourd’hui qu’il est possible, logiquement parlant, de faire dériver toute la mathématique actuelle d’une source unique, la Théorie des Ensembles. (Bourbaki, 1939, p. I.9)

Because of the complicated nature of set theory, the task of formalizing it entirely in one volume is impossible, so the mode d’emploi merely introduces this ideal goal and hopes to return to it later. Since pure formalism is unattainable, the author must rely on ordinary language, formulae, clarifications, and other tools: “… l’emploi des ressources de la rhétorique devient dès lors légitime, pourvu que demeure inchangée la possibilité de formaliser le texte” (Bourbaki, 1939, p. I.11). The strict use of the axiomatic method and the ideal of a total formalization still allow the mode d’emploi to stake a claim to “une rigueur parfaite; prétention que ne démentent point les considérations qui précèdent, ni les feuillets d’errata au moyen desquels nous corrigeons les erreurs qui se glissent de temps à autre dans le texte” (Bourbaki, 1939, p. I.12). This explanation is unsatisfying precisely because of the lofty formalist goals that were presented at the outset, unifying mathematics through a formal language. Now, Bourbaki reneges, admitting that the description of set theory will be carried out in ordinary language, however insufficient. Corry (1992, p. 321) acknowledges the slippery nature of Bourbaki’s use of formal language: “In the end, we obtain 11

Bourbaki’s comments that the faculty of speech pre-​exists grammar must be taken in a pre-​Chomskyan sense.

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a book which, like any other mathematical book, is partially written in natural language and partially in formulae but which, like any partial formalization, is supposed to be in principle completely formalizable.” In Chapter I, Bourbaki introduces the rigorous mathematical language of set theory, and with it a myriad of original symbols accompanied with extraneous explanations in natural language. Chapter II introduces basic concepts in set theory, often preferring natural language to the formalist one established in the previous chapter. Chapter III deals with ordered sets, cardinals, and integers while the concept of structure is formally developed in Chapter IV. In a circuitous manner, this chapter defines a structure by way of an axiom about an analogous term, “species of structures.” The fascicule following the final chapter continues to problematize the notion of formal definition, oscillating between the necessity of formalized mathematical language and what the authors term a “naïve” point of view in a footnote to the introduction: Le lecteur ne manquera pas d’observer que le point de vue ‘naïf ’, qui est adopté dans ce fascicule pour exposer les principes de la théorie des ensembles, est en opposition directe avec le point de vue ‘formaliste’ adopté dans le livre de la Théorie des ensembles dont ce fascicule est le résumé ; bien entendu, cette opposition est voulue, et correspond aux buts différents en vue desquels sont écrites ces deux parties de notre ouvrage. (Bourbaki, 1939, p. E.R.1)

Corry (1992, p. 327) has a detailed analysis of the publication history of this textbook, claiming that the fascicule (1939) predates the first edition of the preceding four chapters (between 1954 and 1957) and arguing that the emergence of category theory in this time would have forced the collaborators to rethink various aspects of the main chapters. While Bourbaki’s constant oscillation between strict formalism and naïve explanations in this textbook are not unique within the genre of mathematical textbooks, the metadiscourse of the mode d’emploi renders it not only more obvious to the reader, but also an inherent contradiction in the project. This oscillation, it should be noted, can also be found in Oulipo’s theoretical and collective writings.

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II. Literary Formalisms: Structuralism and Oulipo What is truly at stake in the work, culture, and legacy of Bourbaki is the image of mathematics that his work perpetuated. David Aubin (1997, p. 299) tracks that influence, noting that by the 1970s, mathematicians had declared the age of structures over. That said, it is undeniable that Bourbaki irrevocably changed the terrain of French mathematics, and mathematics in general (Mashaal, 2002, p. 154). This effect is described by Corry as the “image” of mathematics, which he distinguishes from the “body.” Bourbaki, according to Corry’s (1997) analysis, produced a “body” of mathematical work that is both related to but distinct from the “image” that work went on to create. As Bourbaki’s work was concerned with laying out literal foundations for mathematics and also justifying this decision within a larger conception of mathematics as architecture, the “image” and not the “body” of his work can be considered the immortal result. Bourbaki’s primary topic of research was the essence of what he termed mathematical structures. As explained in the first volume of Eléments de mathématique, all of mathematics was just a hierarchy of structures of increasing complexity. In addition to the inconsistencies he found in the definition of structures, Corry (1997, p. 270) notes a disparity between Bourbaki’s formal, mathematical use of the word and its metaphorical meaning in his popular writing: On the one hand, there is the above mentioned, formal concept of structure. On the other hand, there is a more general, undefined and non-​formal idea of what a ‘mathematical structure’ is. Bourbaki’s theory of structures is hardly used in developing the theories that Bourbaki included in the treatise, and where it does appear, it can absolutely be dispensed with … On the contrary, the structural conception of mathematics, understood as a non-​formally conceived image of mathematical knowledge, proved extremely fruitful for Bourbaki’s own work, and at the same time erected a profound influence on generations of mathematicians all around the world.

Bourbaki endeavored to define structure in a strict mathematical sense in the Eléments de mathématique and did so in a way that these structures could be akin to the notion of “patterns” in Keith Devlin’s definition of

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mathematics (the study of abstract patterns). However, the nontechnical use of the word describes an image of mathematics as an architecture or structure. Corry’s analysis of the confluence of these two meanings of structure explains how Bourbaki used these intertwining notions to extend the idea that mathematics produces eternal truth. Bourbaki defined his image of mathematics in the popular article, “L’Architecture des mathématiques,” published under the direction of François Le Lionnais in the collected volume Les Grands Courants de la pensée mathématique (1948). Jean Dieudonné, the author of the article, calls mathematics a “tour de Babel,” complaining about the disconnect between mathematical disciplines. The article proposes a different solution: “… c’est à l’intérieur de la mathématique que nous entendons rester, et chercher, en analysant ses démarches propres, une réponse à la question que nous nous sommes posée [whether mathematics is singular or plural]” (Bourbaki, 1962, p. 36). While this essay touches upon many of the same themes as the introduction to the textbook, including the singularity or plurality of mathematics and the notion of mathematical rigor through formal language and axiomatic set theory, the lack of a formal definition of the term structure complicates the use of the term. Corry (1997, p. 280) notes: The notion of mother structures and the picture of mathematics as a hierarchy of structures are not results obtained within a mathematical theory of any kind. Rather, they belong strictly to Bourbaki’s non-​formal images of mathematics: they appear in non-​technical, popular, articles, such as in the above quoted passage, or in the myth that arose around Bourbaki. And yet, because of the blurred mixing of the two terms, structures and “structures” in Bourbaki’s work, they have been accorded a status of truth similar to the one accorded to other mathematical results appearing in Bourbaki’s treatise, namely, that of eternal truths.

Today, this vision of mathematics is considered obsolete and unsustainable by most mathematicians. For Corry (1992, p. 320), Bourbaki’s insistence on unifying mathematics through the common language of set theory was doomed to failure precisely because it was overly ambitious: Bourbaki’s work was originally motivated by the idea that the whole of mathematics may be presented in a comprehensive treatise from a unified, single best point of view, and the concept of structure was to play a pivotal role within it. This initial

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Regardless of its lack of success within mathematics itself, however, this non-​formal image of mathematics is important to consider when one turns to the influence Bourbaki had on non-​mathematical disciplines. While a trained mathematician might have read “L’Architecture des mathématiques” with a more complete understanding of the term “structure” as it was defined in the Eléments de mathématique, Le Lionnais’s volume was primarily intended for non-​specialists, resulting in a largely incomplete understanding of Bourbaki’s overall project. The popularity of Bourbaki, perpetuated by the myth and popular publications such as “L’Architecture des mathématiques” reached a much larger audience than just mathematicians. In “The Withering Immortality of Nicolas Bourbaki,” David Aubin (1997, pp. 312–​313) speaks of Bourbaki’s legacy: “… Bourbaki was more than just another successful author. His vision permeated all of mathematics … Moreover, Bourbaki’s logical rigor, his conspicuous modernity, the proclaimed exhaustiveness of his enterprise, and the absolute certainty of the results he exposed in his treatise, all exerted a powerful appeal for the younger generation of the cold war.” Aubin (1997, p. 299) proposes that Bourbaki’s sphere of influence was not restricted to mathematics, but reached a variety of fields specifically in the 1950s and 1960s, but began to fade by the 1970s: “Paralleling the trajectory of structuralism, Bourbaki’s rise and decline in postwar France provides, I believe, a perfect case by which to exhibit the possibilities and limits of the cultural history of science.” He proposes the idea of a “cultural connector”: “… more or less explicit references allowing actors to connect different spheres of culture in order to strengthen the meaning of their own work” (Aubin, 1997, p. 299). Aubin’s article finds a number of convincing links between structuralism and Bourbaki’s notion of structure, devoting much less time to Oulipo, which is out of the scope of his project. That said, his article can be considered an important contribution to the intellectual history of structuralism, and for the purposes of this study can help frame a discussion of Bourbaki’s influence on Oulipo.

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If structuralism today can be a useful tool for both the humanities and the social sciences, it is perhaps due to its double origins in the structural linguistics of Ferdinand de Saussure and Russian formalism. Both of these movements are notable for the formal approaches they use to examine subjects that “… were traditionally considered to lie outside the scope of science” (Onega, 2006, p. 259). Saussure was a Swiss linguist/​semiotician whose 1916 Cours de linguistique générale (published posthumously by former students) purported that language is a formal system and, much like in mathematics,12 developed a vocabulary and rules in order to understand the system better. While this impulse to approach linguistics formally may seem reminiscent of Bourbaki’s project, the irreconcilable difference between the two is that Saussure rejects written language as the object of his study, focusing instead on spoken language and phonemes while Bourbaki prioritized the written language of mathematics. An important feature of Saussure’s linguistics, however, is an emphasis on combinatorics: in Saussure’s language system, different combinations of basic elements generate meaning (Onega, 2006, p. 261). The second main influence in the development of structuralism was Russian formalism, a literary school that was mainly popular around 1915 and then censured by Stalin in 1929–​1930. This school was largely a reaction against the romantic principle of “artistic genius,” focusing instead on the text itself and how it is indebted to forms and other works that preceded it. The group was comprised of two primary circles: the first, the Moscow Linguist Circle, founded in 1915 by Roman Jakobson, considered poetics as a part of linguistics and proposed to treat it scientifically; the second, the Petrograd OPOJAZ (acronym for the Formalists’ Society for the Study of Poetic Language), founded in 1916 by Viktor Shklovky and others, considered literature separately from linguistics (Onega, 2006, p. 263). As with Saussure’s linguistics, Russian formalism considers language to be more 12

I am not the first to note the mathematical nature of Saussure’s work. Vladimir Tasić, in his Mathematics and the Roots of Postmodern Thought remarked that: “… Hilbert’s ‘ideal mathematics’ is a system that in a sense parallels Saussure’s langue” (p. 109). While Tasić introduces this parallel purely to explain what Lévi-​Strauss went on to do with Saussure’s linguistics, there is more research that should be done on the influence of formalist mathematical thought on Saussure.

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than a medium, but rather an object worthy of scientific study. The Swiss and Russian origins of structuralism not only parallel various mathematical endeavors of the time, but can represent for this study the literary origins of formalist and axiomatic thought. In 1942, these influences combined when a French anthropologist/​ ethnologist, Claude Lévi-​Strauss, attended a course at the New School in New York that was taught by Jakobson, introducing Lévi-​Strauss to Saussure’s structural linguistics and Jakobson’s own modifications of this theory within the Russian formalist context (Onega, 2006, p. 264). Applying this method to his anthropological work on kinship, Lévi-​Strauss published his seminal text on structural anthropology, Les Structures élémentaires de la parenté, in 1949. His theory was that elements of human culture must be understood in terms of their relationship to a larger, overarching system or structure. This work, largely influenced by the Russian and Swiss linguistic and literary theories that preceded it, was also influenced (albeit to a much lesser extent) by Bourbaki through a chance encounter between André Weil (one of Bourbaki’s collaborateurs who was affiliated with the Institute of Advanced Study at Princeton at the time) and Lévi-​Strauss in 1943 in New York, which resulted in a small collaboration and an appendix written by Weil (Mashaal, 2002, p. 75). Aubin (1997, p. 311) notes that this “… intersection of Lévi-​Strauss, Jakobson, and Weil, in New York in 1943, by cross-​breeding anthropology, linguistics, and mathematics, helped make structuralism possible. And although the dialogue between mathematics and structuralism failed to be sustained, this fortuitous encounter was the seed of a lasting cultural connection.” While Aubin (1997, p. 333) admits that this interaction was: “… on the whole, […] forced on them, unsustained, and ultimately rather superficial …”, this peculiar tale of influence is indicative of the power of mathematical thought. Even though some mathematicians (including Bourbaki) believed that mathematics was self-​contained and removed from other fields of study,13 mathematical thought –​and especially formal language 13

Aubin notes, however, that Bourbaki’s use of the word “structure” was most likely influenced by both prior mathematical uses of the term as well as Saussure’s linguistic use (p. 309).

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and axiomatic structures –​are often facets of various schools outside of the pure mathematical realm. While Bourbaki’s role in the development of structuralism may indeed have been superficial, it is nevertheless true that this mathematical spirit pervaded the work of an entire generation of thinkers, resulting in a proliferation of the use of the term “structure,” of which the meaning is at least in part influenced by Bourbaki’s formal and metaphorical use of the word. Unlike the structuralist use of the term, however, Oulipo is acutely aware of the mathematical and metaphorical meanings and its use of the term “structure” is therefore distinct. While structuralist thinkers absorbed the term “second-​hand” from linguistics and Russian formalism, Oulipo read and interacted with both mathematics and literature. While Bourbaki’s influence on Oulipo is clear, literary criticism on the subject tends to be superficial or incomplete. Texts on Bourbaki tend to attribute the legacy of the movement to Oulipo, as in Mashaal’s (2002, p. 75) book, in which he claims: [La vision bourbachique des mathématiques] s’est manifestée en particulier en littérature avec le groupe Oulipo … proche du surréalisme … Oulipo s’est donné pour objectif d’explorer les formes de littérature obtenues en s’imposant des contraintes (des ‘structures’) nouvelles d’ordre mathématique …. L’Oulipo, qui compte parmi ses rangs quelques mathématiciens ( Jacques Roubaud, Claude Berge notamment), eut des contacts directs avec le groupe Bourbaki (Queneau a ainsi, en 1962, assisté à un congrès de Bourbaki). L’humour et le goût du secret, en plus des questions de structures, faisaient partie des affinités …

This simplistic point of view is also factually incorrect as Oulipo defines its goals in strict opposition to surrealism. Michèle Audin cites this and other texts in her sharp criticism of scholars who have mentioned a commonality between Bourbaki and Oulipo without properly developing the idea. She also cites Aubin’s article, which she claims: “… bien que peu argumenté, repose peut-​être sur des bases un peu plus sérieuses” (Audin, 2010, p. 2). While she is right to criticize Aubin’s treatment of Oulipo, Aubin’s article is still a pioneering piece of scholarship on the influence of Bourbaki outside of the realm of mathematics. Although his treatment of Oulipo is superficial, it seems to have been intended as a footnote on a larger

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discussion of cross-​disciplinary influence. The heading he chooses for his treatment of Oulipo is representative of his hesitance: “Oulipo: Bourbakist Literature?” (Aubin, 1997, p. 320) Yet even with Aubin’s (1997, p. 323) brief analysis, he rightfully concludes that Oulipo’s appropriation of Bourbaki is more serious than the structuralist one. The remainder of this chapter aims to answer Aubin’s question through a comparative study of both groups and close readings of Oulipo’s evolving textual production, including its double mathematical theorizations by François Le Lionnais and Jacques Roubaud, as well as certain set-theoretical constraints. Aubin attributes Bourbaki’s influence on structuralism and literature to two main publications: Lévi-​Strauss’s seminal Les Structures élémentaires de la parenté and Le Lionnais‘s Les Grands Courants de la pensée mathématique. Le Lionnais, a supporter and popularizer of Bourbaki, shared the work on this volume with Raymond Queneau, who contributed an article. While this publication is just a single project in the diverse careers of the founding members, there are several direct points of contact between Bourbaki and Oulipians, many of whom (including Le Lionnais, Roubaud, and Berge) were French mathematicians who were well aware of Bourbaki’s activities and publications. It is clear from the early meeting minutes that the founding members borrowed some of Bourbaki’s terminology, often using the term structure before ultimately defining constraint. Le Lionnais in particular insisted most strongly on the use of the term structure within Oulipo, emphasizing his commitment to fashion Oulipo in the image of Bourbaki.14 Roubaud is a particularly interesting point of contact, as he was taught directly by both proponents (such as Gustave Choquet) and collaborators (such as Laurent Schwartz and Claude Chevalley) of Bourbaki, much of which he discusses in Le Grand incendie de Londres. Roubaud cites Bourbaki in his autobiographical texts as an inspiration that helped him conceptualize what mathematics truly is. His literary project, he claims on many occasions, is almost the equivalent of Bourbaki’s mathematical work. For his autobiographical series, Le Grand incendie de Londres, Roubaud adapted the peculiar way in which Bourbaki’s (1939, p. I.4) textbooks reference and 14

See Jacques Bens, La Genèse de l’Oulipo [2005].

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annex results in fascicules, described in the mode d’emploi: “A certains Livres (soit publiés, soit en préparation) sont annexés des fascicules de résultats. Ces fascicules contiennent l’essentiel des définitions et des résultats du Livre, mais aucune demonstration.” In addition to such direct links between members of Oulipo and Bourbaki, there are a number of key parallels between both groups. Aubin’s article provides an initial list of similarities: “Beyond humor, Oulipo was much like Bourbaki. Both were semi-​secret societies founded on myths; both looked at the formal bases of their respective disciplines and wished to rewrite their histories from the current structural perspective; and both left to their members the task of producing original work based on structural approaches (new texts, new theorems)” (Aubin, 1997, p. 323). Camille Bloomfield’s (2017, p. 57) recent work seems to confirm Aubin’s suspicions, declaring Bourbaki the only true viable model for Oulipo’s group culture: Le seul modèle collectif vraiment revendiqué par l’Oulipo est d’ailleurs un autre groupe, se présentant comme une personne unique, les mathématiciens de Bourbaki. Avec ce dernier, les oulipiens partagent plus que les trois traits relevés par Marcel Bénabou : caractère collectif du travail ; volonté d’embrasser dans sa totalité un champ donné, utilisation d’un outil stratégique privilégié (méthode axiomatique pour l’un, contrainte pour l’autre).

To expand on these observations, it makes sense to begin with the names of both groups, both of which are now used as eponymous adjectives in French,15 solidifying their cultural importance. Oulipo and Bourbaki both have humorous backstories behind their respective names: Bourbaki, as mentioned earlier, was a group of mathematicians that chose to write under the pseudonym of an imaginary mathematician from an invented country, whose name was also reminiscent of a failed French war general; Oulipo, while not claiming to be an individual, selected a name that is reminiscent of one of the greatest poets of China’s Tang dynasty, Li Po. Both of these names and their backstories are indicative of the parallel myths surrounding both groups, each of which began clandestinely (though both later became 15

Though, it should be noted that Oulipo chose its own eponym in an early meeting on April 17, 1961 (Bens, Genèse, 2005, p. 48).

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more open to the public). While Bourbaki is now synonymous with mathematical formalism and axiomatic thought, Oulipo is known as an experimental writing group that has produced such texts as La disparition. Aubin’s article indicates that another commonality between Oulipo and Bourbaki can be found in the way members are co-​opted and participate. Both groups have a core of founding members and continue to co-​opt new members, thereby prolonging their activities indefinitely. The humor with which Oulipo characterizes its members’ involvement (for instance, when one dies, he/​she is only excused from attending monthly meetings) is also characteristic of the nature of Bourbaki’s internal correspondence while also a criticism of André Breton’s practice of expelling certain surrealists from the group for personal reasons (as he did with Queneau) (Becker, 2012, p. 21). With Bourbaki, members contribute anonymously to the overall pedagogical goals of the group, but have their own personal mathematical careers in their own name and right. Similarly, Oulipo concerns itself primarily with the theorization and categorization of constraints, whereas the individual members are free to write constrained or unconstrained texts as they wish. This freedom is reflected in both groups’ collective and individual publications. Just as Bourbaki published the Eléments de mathématique series collectively, Oulipo publishes collected volumes such as La Littérature Potentielle (1973) and Atlas de littérature potentielle (1981) and smaller, individual texts in the Bibliothèque Oulipienne. Each group also has its own internal publication, La Tribu for Bourbaki and Oulipo has its own system of invitations for the monthly meetings and circulated minutes following each monthly meeting. Both of these internal publications exhibit similar eccentricities in their orthography, including replacing the letter F with Ph in the style of Alfred Jarry and the Collège de ‘Pataphysique. I would argue that Oulipo’s group culture, which borrows heavily from Bourbaki’s, is one of the main reasons for its continued relevance today. Unlike other twentieth-​century collectives, the continued renewal of members, the tradition of collective writing, and the overall sense of humor that Oulipo absorbed from Bourbaki has allowed the group to continue to evolve. While Oulipo’s project, as with Bourbaki’s, has changed with each

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new generation of members, this has afforded the group a certain flexibility with its literary equivalent of Bourbaki’s ambitious project, allowing Oulipo to maintain its cultural relevance in changing times. In addition to the sociological commonalities between Oulipo and Bourbaki, the members of the first two generations of Oulipo explicitly referenced Bourbaki and his notion of structures in the foundational documents of Oulipo. Le Lionnais in particular imbued the language of the Oulipian manifestos with formal, mathematical language. The first manifesto was published in the Dossiers Acénonètes du Collège de ‘Pataphysique on December 22, 1961 and the second in La Littérature Potentielle, the first Oulipian book-​length publication in 1973. Both were later published in the Bibliothèque Oulipienne (often abbreviated as BO).16 The third Oulipian manifesto was never published, but has a space reserved for it under BO30, Jacques Roubaud has commented on it in BO85, “Un certain disparate,” and an unedited version recently appeared in another collected volume, Anthologie de l’Oulipo (2009). While this seems a mocking reference to André Breton’s two surrealist manifestos and draft of a third, the content of Le Lionnais’s manifestos is much more influenced by Bourbaki and his project than by automatic writing. Camille Bloomfield (2017, p. 366) suggests the unfinished nature of this third manifesto contributes to a greater Oulipian myth, important for both academics and members of the group: Peut-​être les pistes ouvertes par ces deux documents permettront-​elles un jour d’écrire réellement, collectivement, ce Troisième Manifeste, mais il est plus probable que sous sa forme actuelle, mystérieuse, excitante, presque, ce spectre de texte n’en soit que plus stimulant pour hanter les oulipiens, condamnés (ou encouragés) à poursuivre des recherches théoriques restées à l’état d’ébauche.

While it does have a certain aura, I contend rather that the third manifesto represents Le Lionnais’s attempt at a mathematical project for the group, which was never finished and ultimately not continued by any other member. The first manifesto has a lacuna in the title: La Lipo (Le Premier Manifeste). The Ou seems to be missing, until the first word: “Ouvrons un dictionnaire aux mots: ‘ Littérature Potentielle. ’ Nous n’y trouvons 16

In the BO, texts are printed a total of 150 times at Oulipo’s expense.

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rien. Fâcheuse lacune” (Le Lionnais, 1973c, p. 19). Immediately, this lacuna is resolved by the etymologically similar ouvrons and replaced with yet another absence: that of the LiPo from the dictionary, a reference to the first surrealist manifesto in which André Breton writes his own dictionary definition of the movement. It is also representative of Bourbaki’s aim to rewrite mathematics. Bourbaki’s textbooks sought to redefine mathematics based on set theory; Oulipo, on the other hand, determines a series of structures composing “Potential Literature,” which can be taken as the entirety of literature –​what has been and has yet to be written. Le Lionnais (1973b, p. 19) continues the first manifesto with a discussion of capitalized words –​Etat, Nature, Anciens, Modernes, Zinjanthrope, Mutants –​in which he situates this problematic of the missing LiPo within the history of the “invention du langage.” The debate between the Ancients and the Moderns he describes situates Oulipo and its efforts, which “ne représente qu’une nouvelle poussée de sève dans ce débat” (Le Lionnais, 1973c, p. 20). All the mathematical developments I have mentioned thus far aimed at creating a language in an ongoing debate about origins. Teetering on the bridge between the discipline’s ancient origins and modernity, Bourbaki discussed the invention of a language and the subsequent application of grammar. Oulipo does not cut itself off from the past as the avant-​ garde of the prior generation attempted. As with mathematics, Oulipo believes in invigorating its work through a re-​examination of the foundations. Le Lionnais then arrives at the heart of Oulipian production: constraint. “Toute œuvre littéraire se construit à partir d’une inspiration (c’est du moins ce que son auteur laisse entendre) qui est tenue à s’accommoder tant bien que mal d’une série de contraintes et de procédures qui rentrent les unes dans les autres comme des poupées russes” (Le Lionnais, 1973c, p. 20). Oulipo proposes to attack this issue “… systématiquement et scientifiquement, en recourant aux bons offices des machines à traiter l’information” (Le Lionnais, 1973c, p. 21). Le Lionnais explains the division of tasks into anoulipisme and synthoulipisme, particularly emphasizing the role of mathematics. Just as Bourbaki and his predecessors looked to the past for models of mathematical rigor, they also forged their own paths creating a new language of logic that was unknown to those who came before them. As with these two branches of mathematical work, Le Lionnais

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explains that these two research approaches are not totally separate: “De l’un à l’autre existent maints subtils passages” (Le Lionnais, 1973c, p. 22). The analogy with mathematics does not stop there: Le Lionnais (1973c, p. 21) proposes quite literally to use mathematics as a tool for production: Les mathématiques –​ plus particulièrement les structures17 abstraites des mathématiques contemporaines –​nous proposent mille directions d’explorations, tant à partir de l’Algèbre (recours à de nouvelles lois de composition) que de la Topologie (considérations de voisinage, d’ouverture ou de fermeture de textes).

The language of structures is a clear reference to Bourbaki, but which type of structure does Le Lionnais intend? While the use of mathématiques in the plural seems to indicate Bourbaki’s metaphorical use of the term in “L’Architecture des mathématiques,” the list of mathematical disciplines that follows seems to ground this occurrence in the context of the Eléments, thereby solidifying Le Lionnais’s conception of structures littéraires as analogous to mathematical objects, or patterns. The end of the first manifesto is a quasi-​mathematical proof that jokes can be serious. Le Lionnais defends the manifesto against all those who “… condamnent sans examen et sans appel toute œuvre où se manifeste quelque propension à la plaisanterie,” arguing that even a joke falls into the realm of poetry when it is the work of poets: “C.Q.F.D” (Le Lionnais, 1973b, p. 22). This “eureka” moment when one finally understands a difficult concept at the end of a mathematical proof could be seen as analogous to the punchline of a joke. Given Le Lionnais‘s proof is not rigorous in a mathematical sense, the mathematical language itself is funny precisely due to its inappropriate context. While the two manifestos were written with a considerable amount of time between them, Le Lionnais begins the second where the first left off: “Je travaille pour des gens qui sont intelligents avant d’être sérieux. –​P. Féval” (Le Lionnais, 1973c, p. 23). This focus on humor is one reason that some consider Oulipo and its production to be frivolous. However, I would argue that Oulipo’s use of humor is not only justified within the mathematical project Le Lionnais is laying out in the manifestos, but also a rhetorical tool to make the group’s constrained literature more 17

Emphasis not mine.

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engaging. This “aha” moment, which Le Lionnais indicates is analogous to the conclusion of a mathematical proof, is also the wittiest part of French culture and thereby the easiest to absorb, even for foreigners. This is perhaps a reason behind the international popularity and success of Oulipo. The second manifesto is titled as such, and immediately defines its goals: “De ce point de vue ce Second Manifeste n’entend pas modifier les principes qui ont présidé à la création de notre Association (on en trouvera une esquisse dans le Premier Manifeste) mais seulement les épanouir et les revigorer” (Le Lionnais, 1973c, p. 23). Le Lionnais explains the types of Oulipian work that have been accomplished since his last manifesto: “La très grande majorité des œuvres OuLiPiennes qui ont vu le jour jusqu’ici se place dans une perspective SYNTAXIQUE structurEliste (je prie le lecteur de ne pas confondre ce dernier vocable –​imaginé à l’intention de ce Manifeste –​avec structurAliste, terme que plusieurs d’entre nous considèrent avec circonspection)” (Le Lionnais, 1973c, p. 23). By spelling the word in this way, Le Lionnais insists that Oulipian structures have nothing to do with structuralism as it was practiced by the literati of the 1960s and confirms that Oulipo has a more developed notion of what a structure is, informed by Bourbaki and his mathematical work and image of the discipline. Whether this mathematical structure is the formal term proposed by Bourbaki in the Eléments de mathématique or the popularized term dealing with the image of mathematics is open to question. The Oulipian notion of constraint as defined in the manifestos and as practiced by its members owes much to the axiomatic method described by Bourbaki in Eléments de mathématique. In the second manifesto, Le Lionnais includes a list of formal research Oulipo has carried out: Dans ces œuvres, en effet, l’effort de création porte principalement sur tous les aspects formels de la littérature : contraintes, programmes ou structures alphabétiques, consonnantiques, vocaliques, syllabiques, phonétiques, graphiques, prosodiques, rimiques, rythmiques et numériques. Par contre les aspects SÉMANTIQUES n’étaient pas abordés, la signification étant abandonnée au bon plaisir de chaque auteur et restant extérieure à toute préoccupation de structure. (Le Lionnais, 1973c, pp. 23–​24)

As with mathematics, Oulipo deals with formal aspects of literature that exist to be manipulated by an author according to formal rules. The

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objects of study for Oulipo are not mathematical objects that one might use in traditional set theory work, but rather formal aspects of language and literature. These elements of writing, language, and literature –​analogous to mathematical objects –​are then manipulated according to constraints, the Oulipian equivalent of axioms. Oulipo’s mission is to examine what these artificial structures can bring to literature: L’activité de l’OuLiPo et la mission dont il se considère investi pose le(s) problème(s) de l’efficacité et de la viabilité des structures littéraires (et, plus généralement, artistiques) artificielles. L’efficacité d’une structure –​c’est-​à-​dire l’aide plus ou moins grande qu’elle peut apporter à un écrivain –​dépend d’abord de la plus ou moins grande difficulté d’écrire des textes en respectant des règles plus ou moins contraignantes. (Le Lionnais, 1973c, p. 24)

Le Lionnais understood this –​and not textual production –​as the primary focus of Oulipo, adapted from the Bourbakian notion that the fascicules need not provide definitions or explanations. This is why he did not insist on the creation of texts, but focused on the proper definition of the constraints themselves, an opinion which he voiced in an early meeting in August 1961 and which echoes Bourbaki’s reticence to include examples: “… la méthode se suffit à elle-​même. Il y a des méthodes sans exemple. L’exemple est un plaisir que l’on se donne en plus –​et que l’on donne au lecteur” (Bens, 2005, p. 88). Le Lionnais is far more concerned about the potential rewards of a formal system for literature, and not the practical results that could be gained from writing under constraint. Through this analysis, we can see that according to the manifestos he produced, Le Lionnais intends to adapt Bourbaki’s mathematical methods for constrained literature. To achieve this, he borrows Bourbaki’s vocabulary of structures. With regard to which type of structure Le Lionnais makes use of, the answer is double just as it was with Bourbaki. When he speaks about specific mathematical methods that can be applied to Oulipian work, Le Lionnais seems to prefer the purely mathematical notion of structure proposed in the Eléments de mathématique. The resulting literary structures can be considered objects of study and not necessarily demonstrations or examples for the pleasure of the reader.

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That said, classifying all possible structures of Potential Literature requires an overarching metaphorical structure such as was proposed by Bourbaki in “L’Architecture des mathématiques.” In the pursuit of this goal, Le Lionnais wrote “Prolégomènes à toute littérature future,” otherwise known as the third manifesto. Here, he exposes “la vocation majeure de l’Oulipo … un programme de construction de toutes les structures littéraires possibles …” that would be accomplished in three phases: “ la première … pose un problème théorique, aussi simple que la découverte de tous les théorèmes de mathématiques possibles … La seconde phase, également théorique, vise à extraire de cet amoncellement des structures d’une efficacité reconnue. Essentiellement pratique, la troisième phase se donne pour ambition de conduire au Seuil de l’Œuvre” (Le Lionnais, 2009, p. 798). This division reflects the theoretical nature that Le Lionnais draws from Bourbaki: he first hopes to define and organize these literary structures in a theoretical manner; and then, to a lesser extent, does he intend to produce texts. The rest of the third manifesto defines the “GRAND TABLEAU,” a “… quadrillage à double entrée, chaque colonne correspondant à une structure mathématique, chaque rangée à un objet littéraire. Chaque case sera donc définie par l’action d’une structure mathématique sur un objet littéraire” (Le Lionnais, 2009, p. 799). Filling these boxes constitutes the first phase of Oulipian work according to the manifesto, and the second phase therefore consists of grouping several boxes together and studying their juxtapositions, or what Le Lionnais terms ARMATURES, a word he proposes to avoid the confusion produced by words such as “structure” and “fixed form.” In a series of interviews conducted in 1976 with Jean-​ Marc Lévy-​Leblond and Jean-​Baptiste Grasset, Le Lionnais admits that he intended this third manifesto as a solution to what he considered a failure of Oulipo: “A cause de cela, nous n’avons pas abouti à des structures importantes et le but de mon troisième manifeste est de remettre l’OULIPO vigoureusement en selle. Dans ce troisième manifeste je ne m’adresse plus aux membres de l’OULIPO mais à des gens qui viendront dans vingt ou quarante ans et qui pourront réaliser quelque chose dans ce domaine” (Un certain disparate, Le Lionnais, 2009, n.p.). If Le Lionnais considered Oulipo’s work up until 1976 as a failure he intended to rectify through the third manifesto, the question arises of who took up his gauntlet?

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Le Lionnais passed away in 1984, but before that, the group had co-​ opted several new members including Jacques Roubaud. What Roubaud published in the group’s subsequent anthology, Atlas de littérature potentielle (1981), has become a second mathematical theorization of the group’s work. Of Jacques Roubaud’s critical writings, two stand out due to their quasi-​ mathematical language and insistence on the formal, axiomatic nature of Oulipian work: an essay on “La mathématique dans la méthode de Raymond Queneau”; and the second, his famous “Deux principes parfois respectés par les travaux oulipiens.” “La mathématique dans la méthode de Raymond Queneau” takes the form of a numbered list of mathematical aspects of Queneau’s work, gradually building up to Roubaud’s mathematical theorization of Oulipo. While the singularity of mathematics in the title alerts the reader to the importance of Bourbaki in Queneau’s methods, the article begins with Queneau’s love of reading mathematics and continues to detail Queneau’s “amateur”18 mathematical work, specifically in the field of combinatorics (Roubaud, 1981b, pp. 42–​45). Through three propositions that apply equally to Oulipian work and are reminiscent of Le Lionnais’s comments in the second manifesto, Roubaud (Roubaud, 1981b, p. 47) makes claims about language itself: Proposition 5 : La nature des phrases est lacunaire et la combinatoire de leur construction est plutôt de l’ordre de l’intrication que de la concaténation, la substitution et la permutation d’éléments insécables. On retrouve, derrière, une préoccupation plus générale de Queneau qu’exprime la Proposition 6 : Se comporter, vis-​à-​vis du langage, comme s’il était mathématisable ; et le langage est, de plus, mathématisable dans une direction bien spécifiée. Proposition 7 : Le langage, s’il est manipulable par le mathématicien, l’est parce qu’arithmétisable. Il est donc discret (fragmentaire), non aléatoire (continu déguisé) sans taches topologiques, maîtrisable par morceaux.

These remarks are indicative of a more basic Oulipian point of view: since language and literature are nothing more than combinations of basic 18

In French, Roubaud’s use of this term does not imply that Queneau did not excel in mathematics as it would in English, but is rather used exclusively to indicate that Queneau was not a mathematician by profession.

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elements, these varied combinations are regulated by mathematical rules. By returning to mathematics as a means to understand this arithmetical and combinatorial nature of language, rather than pseudo-​scientific theories that borrow the underlying mathematics indirectly, Oulipo proposes a far more interesting solution. By the time Roubaud arrives at Oulipo in his essay, the importance of Bourbaki has already been made clear. Proposition 8 reinforces the settheoretical basis of Queneau’s Oulipian conception: “Le travail oulipien est naïf. Le commentaire de Queneau à cette proposition dit: ‘Je prends le mot naïf dans son sens périmathématique, comme on dit la théorie naïve des ensembles’” (Roubaud, 1981b, p. 51). Roubaud (1981b, p. 52) argues that this explicit reference to Bourbaki indicates the “pre-​formalized” nature of Oulipian practice, “mais qu’en même temps est prévue la possibilité d’une syntaxe formelle, d’une ‘fondation à partir de laquelle la démarche pratique, ‘naïve’, donc, serait déplacée vers une activité de ‘modèles.’ ” Roubaud (1981b, p. 54) continues to discuss the artisanal nature of Oulipian work, and begins with his explanation of constraint through a discussion of the lipogram, claiming that “Proposition 12: Une bonne contrainte oulipienne est une contrainte simple.” Then, for the first time within the article, he arrives at an axiom: “La contrainte est un principe non un moyen” (p. 55). This axiom is modified by the following corollary: “Proposition 16: La contrainte idéale ne suscite qu’un texte … Proposition 16a: Une contrainte doit ‘prouver’ au moins un texte” (p. 63). The first proposition about an ideal constraint declares mathematically that such a constraint will produce one and only one text, while 16a admits that a viable constraint must “prove” at least one text. This philosophy contradicts Le Lionnais’s own opinion on the validity of constraints. While it is only later that Roubaud speaks specifically about the axiomatic method, this axiom is extremely important. The constraint itself is a principle, not meant to produce a specific text, but rather a fundamental truth in the fabric of language that has the potential to produce one or more texts. Roubaud (1981b, p. 59) claims later in his discussion of the axiomatic method, citing Bourbaki on the subject, that “… la méthode oulipienne mime la méthode axiomatique, qu’elle en est une transposition, un transport dans le champ de la littérature. Proposition 14: Une contrainte est un

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axiome d’un texte. Proposition 15: L’écriture sous contrainte oulipienne est l’équivalent littéraire de l’écriture d’un texte mathématique formalisable selon la méthode axiomatique.” While Roubaud (1981b, p. 60) admits that his analysis is ideal and cites the great difficulty that arises when categorizing constraints, he raises an interesting question: “Qu’est-​ce qu’une démonstration oulipienne?” He states that the composition of a text according to a constraint would be a proof of that constraint, but recognizes the limits of this theory. Indeed, a specific text demonstrates the validity of a constraint, however given the nature of these specific mathematical notions, Roubaud’s remarks contradict each other. If a constraint is an axiom of the text, it does not require a proof, as axioms are accepted as true without proof; furthermore, if we understand the constraint as a statement (that which is to be demonstrated by the proof ) in a textual theorem, how does one consider constrained writing where the constraint is not made explicit? To conclude his already ambitious article, Roubaud (1981b, p. 66) claims that “L’épuisement de la tradition, représentée par les règles, est le point de départ de la recherche d’une seconde fondation; celle des mathématiques.” Roubaud’s article on Queneau is only superficially mathematical. The points he raises are pertinent to Oulipo studies, but must be taken with a grain of salt. For instance, Roubaud’s mathematical definition of constraint as an axiom invalidates his later statement that texts are the proofs of constraints. The final claim that Oulipo aims to create a second foundation of literature based on mathematics has a historical basis in the foundational crisis of mathematics, but given the more recent work of Oulipo, seems to have been forgotten. At the time Roubaud wrote this article, the group was hard at work at developing a strict classification of its constraints, but has since abandoned such taxonomic efforts. After the lofty mathematical goals Roubaud outlined in the Queneau article, his principles have become the literary equivalent of Bourbaki’s image of mathematics. Cited in almost every critical text on Oulipo or its individual authors, these two principles have become the most lasting legacy of the group, even though the title indicates they are only “sometimes” respected: “Deux principes parfois respectés par les travaux oulipiens: Premier principe: Un texte écrit suivant une contrainte parle de cette contrainte …

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Deuxième principe: Un texte écrit suivant une contrainte mathématisable contient les conséquences de la théorie mathématique qu’elle illustre …” (Roubaud, 1981a, p. 90). The first principle necessitates a metamathematical approach to literature. The author who writes according to a certain rule implicitly or explicitly speaks of the rule within the text, whether or not adhering to the rule would complicate speaking of its application. For instance, while Perec cannot use the letter E, the thematic substance of La disparition is about loss and the language alludes to the missing letter throughout the novel. While not all Oulipian authors are as explicit as Perec, Roubaud’s first principle indicates that at some level, the constrained text points toward its own constrainedness. Such a principle inherently complicates issues of form and content. In the case of Oulipian texts that adhere to this rule, form is content, as the writer speaks of his own means of production within the work. Addressing the second principle, Roubaud is not clear about the meaning of a mathematizable constraint. In practice, it has meant texts based on a specific mathematical principle, such as Paul Braffort’s Mes Hypertropes or Roubaud’s La Princesse Hoppy (see Chapter 2), both of which contain mathematical consequences of the principles they use as constraints. While this study focuses primarily on Oulipian production of the 1960s and 1970s, it is important to remember that this quasi-​mathematical literary work has an important precursor: Bourbaki, who had also proposed a similar theory of structures. Roubaud’s article gives the impression that Oulipo as well uses the mathematics of set theory to create a lasting image of possibilities in literature, rather than proposing a fully rigorous system. In this sense, Roubaud’s principles are the perfect example: they need not hold, have no mathematical argument behind them, and only give the impression of mathematical formalism. However, perhaps this perceived formalism is important for the reader, who is encouraged to use these two criteria to evaluate the nature of Oulipian texts. The ubiquitous nature of these principles in contemporary criticism is indicative of how Oulipian readers have accepted them as valid mathematical arguments, allowing Oulipo to guide the reception of their work by arming potential readers with their own rules for reading. With this background on how Oulipo has borrowed elements of Bourbaki’s group culture and theoretical project, let us turn to Oulipian

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constraints that are set-theoretical in nature, understanding texts as sets of words and considering subsets. The first Oulipian publication, Dossier 17 in the Cahiers du Collège de ‘Pataphysique entitled Exercices de Littérature Potentielle, is an excellent example of the mindset of the founding members of Oulipo, how they understood the constrained literature that they created, and how they wanted to present this work to the Collège de ‘Pataphysique (of which they were a sous-​commission at the time). Published in 1961, the same year as Queneau’s Cent mille milliards de poèmes, the exercises contained within this volume demonstrate a wide range of constraints, all of which depend upon a set-theoretical understanding of language and literature in order to be applied. For instance, Lescure’s S+​7 method debuted in this volume, and while the procedure could be categorized as algebraic (as I have done by devoting a longer discussion to it in Chapter 2) or algorithmic (as it can and has been implemented on machines, leading to its brief inclusion in Chapter 4 as well), every step of this procedure demands a set-theoretical mathematical abstraction of language. For instance, to group words according to their respective parts of speech is analogous to defining sets in mathematics. Lescure’s procedure requires him to consider the subset of any given text that consists of nouns (substantifs or the S in S+​7), as well as the set of nouns in a given dictionary that he uses to replace those in the text. In this sense, Lescure not only employs formalized mathematical language in order to describe his procedure, but the method itself depends upon a mathematical sensibility to language. Many of the other Oulipian exercises published in this early collection depend upon these same basic principles of mathematical abstraction and formalization, but like Lescure’s S+​7, draw on another field of mathematics for their generative principles. For instance, Permutations draws from combinatorics and Chez Victor Hugo relies on counting in order to detect accidental alexandrines in Victor Hugo’s prose works (this is also discussed in Chapter 2). As Oulipo draws from Bourbaki’s structural understanding of mathematics as a field of disciplines that can be connected by the language of set theory, it is therefore logical that a set-theoretical understanding of language can be found at the core of many Oulipian constraints. Furthermore, many of the constraints that were debuted in the Dossier 17 have been reprised in the group’s later collected volumes in an expanded

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form. Two of these in particular, Queneau’s La Redondance chez Phane Armé and Le Lionnais’s Poèmes Booléens, are more directly inspired by set theory. In La Redondance chez Phane Armé, Queneau considers Mallarmé’s poetry as redundant sets. By reducing them to their most important words, the rhymes, Queneau produces “des poèmes haï-​kaïsants” that can elucidate the originals (Oulipo, 1961, p. 181). Queneau’s insistence on using this method to illuminate the original, thereby rendering the complete poem redundant, is mathematically interesting. Just as a university professor of nineteenth-​century poetry would place a special emphasis on Mallarmé’s choice of rhymes, Queneau restricts his attention to precisely those words with matching phonemes. Set-theoretically, this subset of the poem groups certain words according to their common elements, inferring by this classification that together, the rhyming words of a poem constitute an essential element. By reducing the poem entirely to these words, Queneau keeps the repetitions that allow for poetry to act mathematically upon a reader (as we saw with the case of the sestina), but in removing what he deems the extraneous words, he loses Mallarmé’s original meaning and meter. While the new poems may be informative in that they allow a reader to focus more closely on the rhymes, they also depend upon the reader’s familiarity with the rest of the poem. This analytic intent is reprised in many of the group’s algebraic constraints discussed in Chapter 2. In Poèmes Booléens, Le Lionnais (1973e, pp. 258–​262) considers poems as sets of elements, determining specific sets, subsets, and operations to create new poetry using prewritten verses by Corneille and Brébeuf. This method was reprised in Duchateau’s Projet de Roman intersectif in the same volume. Le Lionnais has also proposed a “Théâtre booléen” that would consist of either “intersection” theatre (two plays performed simultaneously, with their point of intersection on the stage forming a distinct third play in the center) or “union” theater (two totally different plays performed simultaneously on one stage). Applying this mentality to detective fiction, Le Lionnais’s (1973d, pp. 62–​65) early research on the possible structures of detective novels applies this type of classification work to a genre to which future members would also be attracted. More recently, Étienne Lécroart has followed Le Lionnais’s theater model, producing Boolean comics in Contes et décomptes (2012), of which the first page is pictured in Figure 1.3.

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Figure 1.3.  A Boolean comic strip, Contes et décomptes (p. 16). Reproduced with the artist’s permission. © Etienne Lécroart & L’Association, 2012.

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This text is composed of two separate comics: the first is of mathematician George Boole, whose wife would prefer he pay more attention to her; the second, deals with Buffalo Bill. In the center, the intersection of these two stories creates “L’histoire de Boole et Bill,” a reference to the famous comic “Boule et Bill.” The implication that the characters Boule and Bill can exist at the intersection of two unrelated stories contributes to our settheoretical understanding of Oulipian potential literature. Even the most mismatched tales have something in common, and any piece of literature could potentially be understood as existing at the borders between other unwritten works. To conclude this section, let us look more closely at the most famous and obvious of Oulipo’s set-theoretical constraints, Georges Perec’s La disparition (1969), a text which forces one to consider the question of how to read constrained literature. The lipogram can be considered a settheoretical constraint, requiring the author to write a text without the use of one letter. Perec chose to deprive himself of the most frequently occurring letter in French, the E. This constraint is easily defined, formal, rigorous, and demonstrable in the sense that Perec did succeed in writing this novel of 300-​or-​so pages entirely without the letter E. That said, La disparition is neither the first lipogram nor the first novel written without any E’s, as Ernest Vincent Wright’s 1939 novel of over 50,000 words, Gadsby, predates it. Wright (1939, Introduction) wrote of his difficulties in his preface to Gadsby: “The entire manuscript of this story was written with the E type-​bar of the typewriter tied down; thus making it impossible for that letter to be printed. This was done so that none of that vowel might slip in, accidentally; and many did try to do so!” Perec’s approach was much different. While Wright literally deprived himself of the letter by sabotaging his typewriter, Perec kept journals of E-​less words, preferring to understand his constraint in terms of the freedom he still had (Bellos, 1993, p. 399). His work created a subset of the French language, an E-​less French that, while impoverished by a great loss of words, could perhaps say something different than the complete language. Whereas Wright considered himself deprived of the past tense, Perec rather considered the resulting changes in diction, grammar, and subject matter as the law of his novel. Beyond the obvious effect on the language, the thematic matter of

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the story is also affected by the constraint. In accordance with Roubaud’s first principle, La disparition is a text that constantly speaks of its compositional means, both structurally (there are 26 chapters, of which the fifth is missing) and thematically (the story’s protagonist, Anton Voyl –​whose name is just the French word for vowel, voyelle, without E’s –​is missing). Reading the book is reconciling the way it was written, the logical consequences of the constraint, and the text itself, creating multiple levels. One could read the novel as a plain story, albeit poorly written, without noticing the constraint, as René-​Marie Albarès famously did in his 1969 review, “Drôles de drames,” published in Les Nouvelles Littéraires. In the section of this article devoted to Perec’s text, it is clear that Albérès (1969, no page) was not impressed with the work, claiming: Je crains, hélas ! que depuis 1965 Georges Pérec [sic], justement encouragé, mais trop vite félicité et adulé, n’ait un peu forcé son inspiration, son talent et surtout sa spontanéité et sa sincérité, pour retrouver son premier succès … La Disparition est un roman violent, cru et facile.

He continues to criticize the writing style, which he deems “… heurtée et subtile de reportage psychologique mêlé à des notations psychologiques hachées,” noting: “… c’est, comme chez Robbe-​Grillet, mais dans un autre style, la forme actuelle du roman policier “littéraire”. Parfaitement réussi, captivant, bien mis en scène, mais sentant l’artifice” (Albérès, 1969, no page). In hindsight, this review is amusing to read today, as it is clear that Albérès failed to notice what has now become the most well-​known aspect of the novel, the lipogrammatic constraint. While many today know the story of the literary critic who failed to notice the most obvious aspect of this text without necessarily knowing Albérès by name, it is too easy to write him off as a “bad reader” of this constrained text. Indeed, his focus on the novel’s sociological aspects is informative about the expectations of readers after 1968, and Albérès’s possibly flawed method can therefore be considered a viable way to approach a text written according to a constraint. Additionally, one could view it as a linguistic exploit of unprecedented difficulty. In this reading, the constraint is impossible to ignore and takes on the thrill that comes with watching an acrobat. Finally, one can read

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La disparition (as many already have) as an autobiographical allegory, in which the self-​deprivation of the most common letter in the French language is symbolic of the loss of Perec’s parents during the Holocaust (indeed, without the letter E, Perec cannot use such words as père, mère, or even his own name). One could additionally understand La disparition as composed partly of lipogrammatic translations, or rewritings of pre-​existing literature, or even as a collective work with passages contributed by at least 15 other people, many of whom were members of Oulipo. With Le Lionnais and Roubaud, Oulipo created its own mathematical foundations, defining a mathematical project that aims to understand literature structurally, drawing on both of Bourbaki’s structures. Following this theoretical groundwork, these examples have demonstrated how various members of Oulipo have made use of set-theoretical thought in the creation of certain constraints and texts. In this sense, while Bourbaki’s reputation and mathematical vision have lost power over the years, Oulipo can be seen as a true intellectual inheritor of this project. This multiplicity of possible readings, however, is a central feature not only of La disparition, but of all constrained literature. In one sense, it is not drastically different from any other narrative, whose interpretation changes from reader to reader. In another, it is infinitely more complicated. Perec’s novel, and indeed much of constrained literature, merges content and form (as the constrained text speaks of its constraint). But perhaps it is precisely here that the Oulipian text is different from others. By providing these various layers of possible readings directly in the text and the paratextual discourse that surrounds it, the Oulipian author shows all these possibilities at once. Such mathematizable structures create a new kind of reader who enters into an unfamiliar game and must detect (possibly hidden) rules and deduce their logical consequences. This chapter has outlined the logical foundations upon which mathematical work is carried out, demonstrating the discipline’s emphasis on formalized language and axiomatic rules. Drawing on these cornerstones of mathematical thought, Nicolas Bourbaki developed an image of the discipline as an architecture, attributing a special importance to the field of set theory, a language that could connect all of mathematics. While Bourbaki’s vision is now obsolete, by applying a mathematical approach

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to language and literature –​treating both as formal objects to study and manipulate according to pre-​established rules –​Oulipo’s project results in a literary equivalent of Bourbaki’s project, using linguistic and literary tools as a means to experiment on themselves. The vital difference, however, between the mathematical development of set theory and the Oulipian project is that Oulipian readers are not trained as mathematicians are to recognize and decipher formal language. Oulipian authors must therefore choose either to educate their readers by using paratextual clues (often consisting of non-​formalized, unconstrained writing) or by trusting that the formally constrained writing of the text will speak for itself, destabilizing the reader and forcing him or her to develop new strategies for reading.

8+​1=​9, Nature morte arithmétique (Arithmetic Still Life), designed by OuPeinPo member Philippe Mouchès. Reproduced with the artist’s permission.

Chapter 2

Algebra

Prior to the development of set theory, numbers constituted the foundation of mathematical study. Numbers are the result of counting (for example, days between harvests, objects to trade, and relative wealth) and were therefore an important tool in even the earliest civilizations. The original Sumerian system of writing, for instance, developed as a system of tokens used to represent amounts, which were sealed into clay envelopes to prevent tampering. To avoid having to crack open the clay to verify the balance, the Sumerians developed a system of writing to detail the contents of each envelope, eventually realizing that the tokens were redundant and that the abstracted writing alone was sufficient. The understanding that one need not count things but could deal with numbers directly is one of the most important developments in early mathematics. After the establishment of formal systems of notation, people realized that numbers had specific properties, could be manipulated according to certain rules, and could even be abstracted further. Algebra is a broad mathematical discipline that deals with the study of mathematical symbols and the rules for manipulating them, covering basic counting numbers, operations that can be performed on them, elementary equation solving, and the study of various properties of numbers, groups of numbers, and operations. This simplified history is just one instance of the long and intertwining history of mathematics and written language. Language as well can be represented in terms of its components and manipulated within a formal system. Spoken language, for example, is composed of phonemes, of which the French language has 37. Writing can be broken into constituent parts such as words, sentences, and paragraphs as Queneau noted in Les Fondements de la littérature d’après David Hilbert. In theory, these analytic units can be combined in infinitely many ways, but in practice only certain combinations create meaning. Literature depends upon the manipulation of basic

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units of meaning, and that often involves counting. For instance, poetry depends upon counting, capitalizing on the repetition of rhymes and the rhythmic qualities of language that create the meter. This chapter traces Oulipo’s development and categorization of such constraints. The early Oulipo was conscious of the connection between literature and mathematics and at the outset created a range of procedural constraints that treat language mathematically by manipulating its constituent elements. Some of the earliest and most famous Oulipian constraints operate based on the counting of characters, syllables, words, and more. To engage in a more abstract mathematical exploration of language, Oulipo progressively developed substitutional constraints which allowed the group to abstract basic units into general categories (often grammatical) and replace them with others, as in the case of the S+​7 (1961). Replacing an object with a variable allowed Oulipo to perform more complex operations, manipulating language mathematically as in the case of Raymond Queneau’s x takes y for z (1966) and Harry Mathews’s algorithm (1982). These basic constraints of counting, substitutions, and operations tend to be of an analytic nature, investigating the structure of language through playful experimentation. However, certain Oulipians have used more abstract aspects of algebraic study to create longer works such as Paul Braffort’s Mes Hypertropes (1979) and Jacques Roubaud’s La Princesse Hoppy (1990). These works, which find a literary language to describe abstract mathematical theorems are indicative of a rhetorical shift from procedural to abstract mathematics, demonstrating the more complex pedagogical goals of Oulipian production.

I. Counting While language is not a mathematical object, certain aspects of it can be counted, which led the early Oulipo to do just that, enumerating everything from characters and letters to syllables and words and investigating the relationship between length and meaning and how this could be used to a writer’s advantage. Oulipo has used basic counting for both analytic

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and synthetic goals, and early Oulipian counting constraints tend toward both: anoulipisme, in the sense that they often chose a prewritten text as a starting point to manipulate algebraically; synthoulipisme, in the sense that these early constraints prompted the creation of new texts based on a prescribed numerical rule. In general, the way various Oulipians have employed basic counting in their writing represents one of the most diverse branches of their mathematical work, which at first glance seems surprising as basic counting seems to be the polar opposite of what are generally considered to be fundamental aspects of great literature: creativity, inspiration, style. This survey of Oulipian counting procedures and texts is by no means exhaustive, but nevertheless demonstrates the creativity that can be born from even the most rudimentary constraints. Counting forces an author to consider the purely mechanical aspects of his or her craft and how they contribute to its reception by the reader, fostering new reflections on the relationship between visual aspects of language and meaning. One of the most obvious examples of Oulipian counting is the boule de neige: “Une boule de neige de longueur n est un poème dont le premier vers est fait d’un mot d’une lettre, le second d’un mot de deux lettres, etc…. Le nième vers a n lettres” (Oulipo, “Boule de Neige”). While a boule de neige, or snowball, does not necessarily have to be arranged in an elegant way on the page, the act of counting individual characters in this way and producing a poem in which the length of each verse is predetermined often results in a visually appealing shape, which gets wider as the reader proceeds. This type of visual layout belongs to the more general category of pattern poetry. Pattern poetry has a long history, originating in ancient Greece where the genre was known as “Technopaegnia.” This was reprised during the Renaissance, and subsequently adapted throughout the centuries. Snowballs and pattern poetry more generally were not invented by Oulipo. A particularly famous example of a snowball poem was written by Victor Hugo in the nineteenth century, however Hugo does not count characters, but rather counts syllables. The resulting poem, “Les Djinns,” is what one could call a syllabic snowball with 15 stanzas of eight verses each. In the first stanza, every verse has exactly two syllables. Each subsequent stanza adds one syllable to the pattern, until the central eighth

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stanza, in which every verse contains ten syllables. The remaining stanzas shrink progressively, losing one syllable at a time to return to two-​syllable verses in the final stanza. While Hugo’s constraint is not determined by the number of characters and the verses therefore do not look perfectly uniform, the poem’s shape is still apparent on the page and when recited. Oulipo would define what Hugo has done to be a syllabic snowball combined with a “melting” syllabic snowball1 of the same length. Oulipo has created variants on this form as well, each of which counts a different aspect of written or spoken language. In Oulipo’s first collected volume, La Littérature Potentielle (1973), the members included an entire section on snowballs, which begins with five short examples that are not written out line by line, but rather as short sentences or paragraphs. For instance, Jacques Bens published the following snowball in that volume: “A la mer nous avons trempé crûment quelques gentilles allemandes stupidement bouleversées” (Oulipo, 1973a, p. 103). The reader of these exercises must notice the increasing length of each word in order to recognize the compositional principle at play. These initial examples are followed by two more interesting typographical snowball poems that are not only compound (both traditional and melting), but which are also printed line by line, one of which was penned by Georges Perec (Oulipo, 1973a, p. 106). Perec’s snowball is a particularly poetic example of this genre, speaking of the charms of the bloody tale of Lombard queen Rosamund. Much like Mallarmé’s Un coup de dés jamais n’abolira le hasard (1897) or Apollinaire’s Calligrammes (1918), the typography of the poem contributes to the way it is read. While snowballs that count characters are naturally more visually appealing than others, these types of poems are challenging exercises for both the author and the reader. To produce a snowball, the poet must overcome the practical constraints of the genre in order to communicate a theme. To read a snowball is therefore to reconcile the artificiality of the language composing the poem with its meaning. While formal analysis of metered poetry already requires a reader to evaluate poetic themes that conform to rules of versification, the snowball is even more challenging as 1

A melting snowball “… commence par un vers de n lettres, après quoi le nombre des lettres diminue d’une unité à chaque vers” (Oulipo, “Boule de Neige”).

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it owes its existence to the arbitrary nature of orthography itself, creating an artificial and jarring juxtaposition of spelling and meaning. J

AI CRU VOIR PARMI TOUTES BEAUTÉS INSIGNES ROSEMONDE RESPLENDIR FLAMBOYANTE ÉCARTELÉE ÉVOQUANT QUELQUE CHARME TORDU SCIÉ SUR UN X

In Atlas de littérature potentielle Oulipo defines a more general type of counting-​based constraint known as “Mesures”: “Produire un texte qui satisfasse à certaines contraintes sur la longueur des éléments qui le composent” (Oulipo, 1981c, p. 227). This constraint could be considered a more general literary structure, based on Le Lionnais’s foundational goals in the manifestos. “Mesures” in this sense is an umbrella category, comprising a myriad of particular constraints such as the traditional poetic task of counting verses (as in the case of alexandrines or iambic pentameter) or the more typographical one of counting characters (as in the case of the snowball). The article is mostly theoretical and does not provide examples for every proposed sub-​constraint, which count similar units as snowballs, but the short texts provided by specific Oulipians are ambitious and challenging. Roubaud, for instance, produced a sonnet of which the syllables are as short as possible while still respecting the meter (Oulipo, 1981c, pp. 227–​228). Perec’s contribution demonstrates an extreme symmetry as

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all the relevant poetic aspects have the same numeric count: 4 stanzas, 4 verses, 4 words, 4 letters. Rail Tout sera pâle, gris Tout sera trop long Aube, soir, jour, mois Faim, soif, rêve noir. Vers quel état muet Tend leur fils aimé, Noué dans tels sacs Dont sort même gêne ? Midi doré, élan haut, Ciel bleu, eaux dont Eole ride vent doux Pour dire code bête Cela veut dire quoi ? Plus rien : lieu sans Joie, rues sans fête, Dure nuit sans lune. (Oulipo, 1981c, p. 229)

This type of poetic composition is visually stimulating, but lacks two critical elements of traditional poetry: rhyming and meter. Indeed, while Perec’s poem looks extremely symmetrical, it does not sound as elegant as it looks. Perec’s poem therefore draws the reader’s attention to the strange relationship between French spelling and pronunciation. A counting example that predates “Mesures” can be found in Jacques Bens’s sonnet irrationnel (1963), a 14-​line sonnet whose five stanzas are composed of 3, 1, 4, 1, and 5 verses respectively, to represent the values of the digits in pi (Bens, 1973, p. 254). While the digits of pi produce an oddly shaped poem, Bens (1973, p. 255) use the unexpected repetition of the one-​verse stanzas as a sort of refrain, giving the sonnet irrationnel a musicality, inscribing his newly invented fixed form within a much longer tradition of musical French poetry such as “le rondeau, le rondel, le triolet, la villanelle.” By inscribing his new form within a larger tradition of French poetry, Bens’s sonnet irrationnel resembles other Oulipian

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work on fixed-​form poetry, a topic that is very present in Queneau’s work. For instance, Cent mille milliards de poèmes can be considered an explanation of the sonnet form. In this sense, the sonnet irrationnel is a first, powerful example of the Oulipian development of new forms, based on mathematical ideas, that do not attempt to break with a larger poetic tradition. The classical alexandrin in French poetry depends upon an ability to count to 12, placing a caesura after the sixth syllable. Oulipo has used this propensity for counting to find accidental alexandrines in prose, composing poetry with Victor Hugo’s “alexandrins blancs”: C’est un sonnet inédit de Victor Hugo Tout le monde dormait toujours dans le palais Il cria d’une voix terrible : –​Colonel Je voudrais le mal que je ne le pourrais pas Vous violez la loi vous êtes criminel Les soldats firent les faisceaux dans l’avenue L’ex-​colonel Espinasse baissa la tête L’état de siège est décrété dans l’étendue Étant servi je mangeai une côtelette Portant une lanterne sourde et un merlin On entrait sans obstacle chez Monsieur Dupin Et lui remettait à bout portant une lettre On se serra la main Michel me dit : “Hugo Que voulez-​vous faire ?” Je lui répondis : “Tout” Je posai sur le lit de ma femme une boîte. (Queval, 1973, pp. 207–​208)

This exercise is an example of the interrelated nature of anoulipisme and synthoulipisme. Locating accidental alexandrines within Hugo’s prose writing and turning it into a sonnet (with a few approximate rhymes) calls attention to a natural byproduct of being a writer, habit formation. In other words, prolonged constrained writing impacts an author’s so-​called “free” writing. In a facetious manner, the author claims: “Outre une mise en valeur éventuelle des obsessions de l’auteur (et la fréquence de ces alexandrins en prose), on peut retenir le mouvement retourné: c’est le poète, croirait-​on, qui enlèvera la forteresse” (Queval, 1973, pp. 207). Through his poetic writing, Hugo internalized the rhythm

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of the alexandrine and became “fluent” in verse. Prior to the twentieth century, all educated French men were similarly trained to write proper verse, implying that one could find accidental alexandrines in the prose writing of any educated French historical figure. This method can be understood as capitalizing on an inherent aspect of the French language, where six-​syllable groups are almost unavoidable. Ordinary French speakers likely speak from time to time in involuntary alexandrines, and such slips are often taken as style faults in prose. The real question is whether the reconstituted Hugo poem is to be taken as an attack on Hugo for lack of control, or for a certain surrealist-​like automatism that created unintentional poetry within his prose. Alternatively, one might consider this example as an Oulipian “discovery” of a Victor Hugo poem that the poet simply did not write. As with La disparition, this plurality of possible interpretations is at the core of Oulipian aesthetics. What seems to be a frivolous exercise is in fact fruitful for both analytic explorations of Hugo’s language and the French language as a whole while also synthetic, producing a new poem. This explicitly mathematical constraint incites a reader to engage in his or her own abstract exploration of the nature of language on multiple levels. There are two notable philosophical conundrums associated with counting: zero and infinity. François Le Lionnais (1981a, p. 19) was curious about working at these limits and formulated the problem of the: “… plus petit nombre de mots capable de former un poème valable” in Atlas de littérature potentielle. Tending toward formalization of the problem, he defines: “D’une manière plus générale, l’étude de la validité des poèmes dont le nombre est compris entre 0 et +​∞ mériterait d’être entreprise et poursuivie scientifiquement” (Le Lionnais, 1981a, p. 20). Asking such a question forces Le Lionnais to ponder the richness of individual words, beginning with poems consisting of a few words and progressively making his way to a poem of zero words. In this way, he ascribes poetic properties to numbers, attempting to make generalizations about the relationship between the number of words in a poem and its meaning. One-​or two-​word poems, he explains, necessarily describe something so specific to the life of the poet and render interpretation impossible. However, he finds a potential solution by considering culturally rich words,

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which evoke specific emotions among those who share that particular reference. In this case, fewer than five words could accomplish a great deal. While Le Lionnais’s “scientific” approach to considering poetry could be interpreted as a joke, the reasoning he uses to address the question is reminiscent of literary scholarship. For instance, it is often prudent to consider an author’s life and culture when analyzing a poem. Furthermore, the cultural and historical position of the reader of a poem with respect to the author does indeed influence a poem’s reception. Le Lionnais (1981a, p. 20) then asks what a poem with 0 words might be: C’est une émotion ressentie comme douée d’une qualité poétique potentielle et qui a été exprimée avec moins d’un mot. Il est vraisemblable que tous les poèmes connus (à quelques exceptions près) ont commencé par être des poèmes de zéro mot. Selon cette définition, il existe un bien plus grand nombre de poèmes. On remarquera cependant que, malgré toute cette richesse, l’anthologie des poèmes en zéro mot tiendrait aisément sur un timbre-​poste. Le problème de zéro mot =​PzM (resp. : Poèmes de un mot =​P1M ; poèmes de n mots =​PnM) gagne à être traité par l’approche ensembliste. Un PzM ou un P1M est constitué par le (resp. : Un PnM peut être extrait du) vocabulaire de l’intersection des vocabulaires (ordonnés ou non) de x poèmes de y mots. Lorsque cette intersection est un ensemble vide (resp. : Un singleton), on obtient un PzM (resp. : P1M).

These musings are described using the language of set theory: if a poem is a set of words with a certain cardinality (the number of words in the poem), then a PnM is a poem composed of n words. Then, one could imagine a set of all poems of cardinality n –​for instance, the totality of poetry composed of exactly 20 words. Le Lionnais’s use of set-theoretical vocabulary here treats poetry as an abstract, mathematical object. By his definitions, poetry is a set of lexical units meant to evoke a certain affect. The strength of poetry lies in its efficiency –​a limited number of words can generate a wealth of reflection when shared with a reader. By applying Le Lionnais’s brand of mathematical thinking, one can gain analytic insights into the nature of poetry itself. Opposite zero in a mathematical sense is infinity, which Étienne Lécroart applies to literature through the creation of an infinite bande dessinée in his collection Contes et décomptes (2012) (Figure 2.1).

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Figure 2.1.  Infinite comic strip from Contes et décomptes (p. 24). Reproduced with the artist’s permission. © Etienne Lécroart & L’Association, 2012.

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Lécroart’s comic makes use of counting as a productive constraint, generating an infinite amount of text and images with very little effort. To create an infinite comic from the first three panels, Lécroart simply needs to produce one panel per line, each of which precedes the repeated first three panels. This is made possible by his ingenious incipit of “Je vous en prie, laissez-​moi tout recommencer” (Lécroart, 2012, p. 24). Since the beginning of the comic shows a man being threatened, begging to start his explanation over again from scratch, Lécroart can progressively multiply this man’s protests line by line, always ending with the refrain of beginning again. In this way, Lécroart’s comic generates the impression of infinity as he runs out of room on the page. While it is impossible to read the further one progresses in the comic, the final panels are always repetitions and every line therefore ends with “Ça suffit! Ton histoire s’arrête là! Il est temps de tourner la page!” (Lécroart, 2012, p. 24) This visual embedding creates a potentially never-​ending sequence, and the only way to break free is simply to turn the page. This is an excellent example of synthoulipisme, in that a simple, mathematical constraint is a powerful generative force, requiring little effort on the part of the author to produce what is in this case an infinitely large text. Lécroart’s comic is a demonstration and visual illustration of the mathematical discovery of countably infinite sets. While anyone who can count intuitively realizes that there is no upper limit to how high numbers go, it is a less intuitive mathematical property that there are different degrees of infinity. While the set of counting numbers is indeed infinite as Lécroart demonstrates in this text, it is small compared to the set of all real numbers (which includes rational and irrational numbers). Between Le Lionnais’s tentatives à la limite and Lécroart’s infinite comic strip lies a countably infinite set of whole numbers, any one of which can be used as a generative constraint according to “Mesures.” Additionally, the space between these two texts represents an important shift in Oulipian aesthetics. While Le Lionnais considers numbers as an abstract way to understand the potential of poetry, a primarily analytic method, Lécroart uses a mathematical discovery as a tool for creation, a synthetic endeavor. This shift is fundamental to understanding Oulipo in its current state. Le Lionnais and the rest of the founding members had an ideal project that

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was analytic in nature, proposing to use mathematical tools to understand language. While these mathematical tools could indeed create texts, they were often applied to pre-​existing ones in order to discover greater insights. This type of work stems from a fundamental understanding of mathematics on the part of an author, but does not necessarily produce texts that are mathematically instructive to a reader. Indeed, the goal was not to create texts at all. Lécroart, on the other hand, is not a mathematician but uses mathematics to produce a text, which is then pedagogical for the reader, illustrating difficult mathematics. Lécroart’s infinite comic is a simple example of how Oulipian authors have recently employed counting-​based constraints rhetorically, but the narrative produced by this method is rather thin. Another longer comic in his Contes et décomptes counts visual elements as well as words, telling a heart-​breaking story of family and loss. As the title of Lécroart’s collection implies, it contains both contes (tales) and décomptes (calculations). The title is not only audibly clever as both contes and comptes are pronounced the same, but these two words share an etymological origin. Drawing once again from the intertwined history of letters and numbers, to count is related to recounting a story (not only in English and French, but in other languages as well). In “Compter sur toi” (Figure 2.2), Lécroart describes his sister’s premature death at 50 years old through 50 panels, each of which represents one year of her life. The first panel contains 50 visual elements and a caption of 50 words, with each subsequent panel losing one word and one visual element. As the story progresses from her childhood to adulthood, from the onset of the disease to her death, the comic becomes emptier both visually and rhetorically, ending with the void left by his sister’s passing. In this sense, the counting constraint not only produces the text, but is completely integrated into the story being told. Lécroart’s attempt to capture his sister’s short life in a narrative literally measures her life in memories, years, words, and elements. Counting backward from 50 produces a narrative that, once over, disappears in the same way as the life it recounts.

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Figure 2.2.  Excerpt from “Compter sur toi” in Contes et décomptes (p. 5). Reproduced with the artist’s permission. © Etienne Lécroart & L’Association, 2012.

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Paul Fournel has also made use of counting in La liseuse (2012), in which an old-​school publisher’s life is turned upside-​down when an intern offers him an e-​reader to facilitate his work. At first, he believes he has seen the whole of the publishing world and is no longer capable of being surprised, but the introduction of this digital method of reading forces him to question the true nature of his profession –​namely, what are books and what is reading? The first description of the liseuse, or e-​reader, is that of an unwanted intruder: “Elle est noire, elle est froide, elle est hostile, elle ne m’aime pas. Aucun bouton ne protrude au-​dehors, aucune poignée pour la mieux tenir, pour la balancer à bout de bras comme un cartable mince, que du high-​ tech luxe, chic comme un Suédois brun. Du noir mat, du noir glauque (au choix), du lisse, du doux, du vitré, du pas lourd. Je soupèse” (Fournel, 2012, p. 15). Without physically carrying the weight of his work, he does not know how to process his assignments; without the smell of the paper, he is no longer sure he is reading well; the light now comes from the e-​reader itself, for otherwise the reflection is bothersome; pages disappear with the flick of the screen. In short, his typical methods for measuring are disrupted:





1. Weight: “Dans les gros doigts rouges de René, c’est donc le poids définitif de toute la littérature mondiale. 730 grammes. Hugo +​ Voltaire +​Proust +​Céline +​Roubaud, 730 grammes. Je vous rajoute Rabelais? 730 grammes. Louise Labé? 730 grammes” (Fournel, 2012, p. 22). 2. Page numbers: “D’un doigt je fais tourner les pages qui se déposent nulle part. Elles disparaissent corps et biens dans un endroit imaginaire que j’ai du mal à imaginer. Ma poitrine est inquiète et aucun indice ne filtre sur l’avancement de ma lecture” (Fournel, 2012, p. 18). 3. Number of books: “J’ai soudain une vision de ce que sera mon bureau un jour prochain: rien. Un petit écran noir posé à plat sur une belle planche en loupe de noyer. Des étagères vides point encore démontées. Pas d’autre odeur que la mienne” (Fournel, 2012, p. 43).

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More than just a plot device, the e-​reader is the pretext for a change in writing, as Fournel uses two compositional constraints, which he enumerates in an explanatory note following the novel: counting and the sestina. As we saw in the introduction, a sestina is a six-​stanza poem (that sometimes includes a three-​line envoi) of which the same six words (that do not necessarily rhyme) permute from stanza to stanza according to a simple spiral pattern. Fournel’s repeated words are: “lue, crème, éditeur, faute, moi et soir” (Fournel, 2012, p. 191). Given their placement at the end of long chapters rather than short stanzas, the alternation of these rhymes is less visible than in a traditional sestina, as readers rarely pay attention to the last words of chapters. While narrative beginnings are often the result of a great deal of reflection and more often analyzed in literary criticism, Fournel draws the reader’s attention to the end of each chapter, using repetition to give certain words the weight of rhymes in poetry. Fournel’s second constraint must have made the editorial process exceptionally frustrating: Les vers sont mesurés. Comme ils servent à conter le destin d’un homme mortel, cette mesure subit une attrition (boule de neige fondante) : la première strophe est composée de vers de 7 500 signes et blancs, la deuxième de 6 500 signes et blancs, et ainsi de suite jusqu’à la sixième qui comporte des vers de 2 500 signes et blancs. L’ensemble constituant un poème de 180 000 signes et blancs. (Fournel, 2012, p. 191)

To satisfy his constraint, therefore, upon completing a chapter and arriving at the proper “rhyme,” Fournel must then have had to reread everything and add or delete characters as needed. While writing on a computer facilitates counting the characters, editorial cuts, adjustments, and corrections are bound to disrupt it again. Indeed, character counts are a standard measurement tool in French publishing houses, making Fournel’s constraint more appropriate for both his subject matter as well as a nightmare in terms of publishing. By turning the character count into a fundamental aspect of the book’s structure, publishing becomes both the content and style of the book in a hyperbolic, almost ironic way. These texts demonstrate that when a counting constraint is properly integrated into the narrative being told, the result is a multifaceted work

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in which the content and form are working together to communicate a theme. While this revelation is hardly new to literary studies and authors often seek to tell a story within an appropriate structure, these texts which depend upon counting return to the etymological origins of storytelling, an endeavor that bridges the modern-​day gap between literature and mathematics.

II. Substitutions While early formal systems of notation allowed one to count and record large amounts, later systems arose that facilitated calculations and commerce. With the four basic operations of arithmetic (addition, subtraction, multiplication, and division), one could represent different combinations of physical objects through a symbolic language. For instance, two apples plus three apples equals five apples; in formal mathematical notation, 2 +​3 =​5. Such a systematic generalization allows one to apply operations like addition to any objects, and not just to apples. These algebraic procedures depended on two mathematical advancements: first, operations had to be formally defined and uniformly applied, creating a stable structure for mathematical work; second, with a fixed structure, numbers could be abstracted to variables, allowing for more generalizable results that could then be solved for particular cases using substitutions. Some of the earliest Oulipian constraints depended on substitutions. The fact that members could count semantic elements and their constituent parts meant that they were also able to substitute these basic units of meaning. Jean Lescure’s S+​7 method, proposed at one of the first Oulipo meetings on February 13, 1961, is not only one of the group’s first official creations, but also a prototype for future Oulipian semantic substitutional procedures (Beaudouin, “S+​7”). S+​7 begins with a pre-​existing text, locates all the nouns (S stands for substantif, or noun) and replaces them with the noun that comes seven entries later in a dictionary of the author’s choosing. This operation depends upon the generalizable nature of language and what is called parsing. Given the way words are used in

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context, they can be classified into grammatical subclasses or parts of speech (such as nouns, verbs, or adverbs). This procedure applies the mathematical impulse to generalize to literature by recognizing every token of a noun and then replacing each token with another from the same part of speech, thereby preserving the grammatical structure of the sentence. The S+​7 is similar to Mad Libs, the famous American phrasal template word game (invented in 1953) that produces comical or nonsensical stories by prompting a reader to contribute words given a specific lexical category, which are then substituted into a pre-​written text. While more limited in scope, the S+​7 also takes a pre-​existing text and replaces key words with new ones. What distinguishes the S+​7 from Mad Libs is primarily the choice to substitute only the nouns of a text, as nouns are particularly important for communicating specificity in a text by identifying categories of people, places, or things. Furthermore, the algorithmic procedure of replacing each noun with another that is not too distant alphabetically contributes to the hilarity of some of the results, as the substituted nouns are often similar enough to remind the reader of the original, but not necessarily semantically related. Lescure never explained why he chose the number 7 for the method as opposed to another single-​digit number that would have produced similar results. A potential reason is that the number 7 has significant numerological and symbolic meanings in the Bible.2 However, for a number with such inherent Biblical baggage, the S+​7 method hardly seems divine –​it has the power to take a perfectly good text and butcher it. Lescure (1973, p. 143) details the method in the collected volume, La Littérature Potentielle, in which he explains the requirements of the S+​7 operator in terms of raw material: “Cette méthode exige donc, en dehors de l’opérateur réduit à une fonction purement mécanique, un texte quelconque, choisi ou non parmi ceux réputés littéraires, et un dictionnaire, vocabulaire, glossaire ou lexique également quelconque.” The original text provides the 2

A few examples: seven is God’s preferred number in the Bible, tied directly to the creation of all things (in seven days); the creation of Adam falls on the first day of Tishri, the seventh month in the Hebrew calendar; the Sabbath or day of rest also falls on the seventh day; there are seven major divisions in the Bible (the Law, the Prophets, Psalms, the Gospels, the General Epistles, the Epistles of Paul, and the Book of Revelation); and Jesus performs seven miracles on the Sabbath.

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basic syntactic structure, while the specificity of the dictionary impacts the choice of the replaced words. Lescure (1973, p. 145) applies the method to several examples from literature, including famous maxims from Aristotle and La Rochefoucauld, noting that “Appliquée à des textes présentant dans l’ordre de la littérature traditionnelle la plus grande rigueur, cette méthode donne des résultats généralement aberrants mais plaisants …” Lescure (1973, p. 145) seems particularly intrigued by the results produced using La Rochefoucauld’s maxims, claiming that: “Cependant il arrive que, des maximes, se dégage une potentialité tout à fait distincte des pouvoirs de conviction que la sentence originale avouait … Si distinctes que soient ces propositions de celles publiées par La Rochefoucauld, elles demeurent cependant cohérentes à l’humanisme moralisant de leur auteur.” Lescure’s comments on La Rouchefoucauld are indicative of an important principle of the S+​7, that the S+​7 owes its effect to the structure of the original text. It is precisely for this reason that some of Lescure’s chosen source texts produce more interesting results. Applying the S+​7 to one of La Rochefoucauld’s maxims is a syntactically recognizable but semantically incongruous result, whereas a newspaper article does not necessarily have such a familiar structure. For instance, Lescure (1973, p. 145) produces “Nous n’avons pas assez de forêts pour suivre tout notre ralentissement” from the original, “Nous n’avons pas assez de force pour suivre toute notre raison.” While Lescure does not experiment much with the choice of dictionary, Queneau adds his own contribution to the S+​7 technique in another article in La Littérature Potentielle. For his source text, Queneau chooses Notations from Exercices de style (1947), one of his most popular texts and particularly recognizable due to the nature of the book as a whole, which reproduces this base story in 99 different ways. As for Queneau’s selection of a dictionary, he applies the method twice using two different dictionaries: first, the Nouveau Petit Larousse Illustré (1952 edition); second, using a list of 1,300 elementary French words (published in 1954). In both S+​7 transformations, Queneau (1973a, p. 149) cleverly replaces the S bus line (the setting for the first half of the story) with S+​7, thereby inscribing the name of the constraint into the text produced by it. The other modifications depend on which dictionary was used. The Nouveau Petit Larousse results in a text filled with bizarre and antiquated words, replacing the title

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Notations with Notonectes (a family of aquatic insects commonly known as “backswimmers”). The smaller dictionary turns Notations into Oeufs, and transforms many of the nouns in the text into food or cuisine-​related terms. A particularly striking implication of Queneau’s method is that, given the nature of Exercices de style, his two S+​7 variants could be considered new styles to be added to the collection. In essence, this insertion a posteriori forces one to reconsider the question of style in the original text within the context of Oulipo and constraints. As Lescure notes in the title to his presentation of the S+​7 in La Littérature Potentielle, the method is a “cas particulier de la méthode M±n” in which M represents any taggable part of speech and n represents any integer value (Lescure, p. 139). Queneau (1973f, p. 152) employs this generalization of the form to produce his “La cimaise et la fraction,” a modification of the La Fontaine fable, “La cigale et la fourmi,” in which all adjectives, nouns, and verbs are substituted accordingly: La cimaise ayant chaponné Tout l’éternueur Se tuba fort dépurative Quand la bixacée fut verdie : Pas un sexué pétrographique morio De moufette ou de verrat …

As with the S+​7 examples, this extremely recognizable fable retains its syntactic structure even with numerous substitutions, allowing any French reader to hear the source text and identify that it has been changed. However, the substitutions disrupt the original meter and rhymes, as the process of changing words based on their parts of speech does not necessarily consider other aspects of the pronunciation of these words, including syllables and rhymes. It is strange, in this sense, that the original La Fontaine remains so audible, even while the poetry is disrupted by the procedure. Queneau must have been selective in the composition of this text, picking replacements that were close enough to seven while sharing other attributes with the original content. If this is the case, deviating from the strictly formal nature of the S+​7 procedure both confirms and

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rejects the power of the S+​7, indicating the need for flexibility depending on the source text and intended result. The S+​7 and its variations are examples of lexical substitutions, but Oulipo has invented a more general substitutional method known as homomorphisms3 that modify an original text while preserving a specific aspect of its structure. In La Littérature Potentielle, Oulipo debuted a specific type of homomorphism that is closely related to the S+​7, the homosyntaxism: “Il s’agissait d’écrire un texte en prose en respectant la structure suivante (V =​Verbe, S =​substantif, A =​adjectif ): VVSSSSAS SVVSSSVSVASASVSASSSSVVSSASSV” (Oulipo, 1973b, p. 176). The article exhibits 11 homosyntaxisms written that follow this specific structure (taken from an excerpt from Queneau’s Les Enfants du Limon, once again inscribing a pre-​Oulipian Queneau novel within the work of Oulipo), which are all noticeably different despite the common syntactic structure, with each Oulipian resorting to specific strategies to produce a satisfactory example. For instance, Lescure reproduces the given structure three times to continue his thought, Noël Arnaud avoids all parts of speech except for those proposed and a few inevitable articles and prepositions, and François Le Lionnais uses the constraint as an excuse to write about the form itself and more generally about Oulipo: “J’aimerais lire des homosyntaxismes, des exercices de style et autres structures oulipiennes, mais surtout pas de plagiats par anticipation” (Oulipo, 1973b, p. 177). The wide range of texts produced by this relatively simple constraint is indicative of a certain freedom that individual Oulipians have to interpret what is not made explicit by the rule. The article notes that “Ce genre d’exercice ne représente certes pas de grandes difficultés mais il peut servir de gamme à des débutants et, qui sait, moyennant quelques contraintes supplémentaires ouvrir la porte à des œuvres de haute qualité” (Oulipo, 1973b, p. 176), implying that the difficulty of the constraint is associated with the result and that the purpose of constrained writing is pedagogical, potentially helping an author produce high-​quality work.

3

Morphism is a term common to mathematics, mapping elements from one structure onto another while preserving the overall structure.

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Atlas de littérature potentielle contains examples of homomorphisms that preserve structures other than syntax: “Les divers types d’homomorphismes dépendent du choix de la structure …” (Oulipo, 1981b, p. 159). Homovocalismes reproduce the same vowels, but change all the consonants; similarly, homoconsonantismes freeze the consonants while changing the vowels (Oulipo, 1981b, pp. 160–​161). A particularly difficult variation is the homophonie, which aims to produce a text with the same phonemes in the same order, but with a different meaning, illustrated in the following example: “Queneau (Raymond), très haut pape, l’a répété.” and “Que nos raies, montrées aux papelards, aient pété” (Oulipo, 1981b, p. 162).4 In addition to the pieces that compose them and categories into which they fall, words have a semantic meaning, which Oulipo realized could also be substituted. Queneau proposes La littérature définitionnelle in La Littérature Potentielle, a constraint which treats every word as equivalent to its definition, allowing an author to replace every “significant word” (verbs, nouns, adjectives, and adverbs in -​ment) by its definition. This method is recursive, meaning it can be applied to the same text multiple times, with an interesting result: “Une phrase de six mots ainsi traitée donne un texte de près de 180 mots au troisième traitement” (Queneau, 1973b, p. 115). For instance, starting with the simple sentence, “Le chat A BU le lait,” the method first produces : “Le mammifère carnivore digitigrade domestique A AVALÉ un liquide blanc, d’une saveur douce fournie par les femelles des mammifères” (Queneau, 1973b, p. 119). The subsequent iteration results in: Celui qui a des mamelles, mange de la viande, marche sur l’extrémité de ses doigts et concerne la maison A FAIT DESCENDRE PAR LE GOSIER DANS L’ESTOMAC un état de la matière sans forme propre, de la couleur du lait, d’une impression agréable sur l’organe du goût et procuré par les animaux du sexe féminin qui ont des mamelles. (Queneau, 1973b, p. 120)

The third stage of substitutions creates a text that is so long that typographical distinctions are necessary to keep track of the original meaning. 4

This is far easier in French than in English, for French has a relatively small number of phonemes. It is for this reason that these results are often very humorous, since almost any expression in French can be written in more than one way.

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Interestingly, by replacing certain words with their semantic equivalents, the result is much less clear. For instance, the first section of this third iteration (in italics) is incomprehensible without the context. This compound definition of the definition of a cat is more easily interpreted as a sexist portrayal of a housewife (who has breasts, eats meat, wears high heels, and stays at home). Likewise, the last part of the sentence (in lowercase letters), given the phrase “de la couleur du lait” does not seem to describe milk, but rather another liquid of the same color, potentially making this an oddly phrased dirty joke. Proposed at the same time by Marcel Bénabou and Georges Perec, La Littérature Sémo-​Définitionnelle (or LSD for short) functions as follows: “On choisit deux énoncés aussi différents que possible. Dans chacun de ces énoncés, on remplace les mots signifiants par leur définition pour obtenir une citation ‘à la manière de …’. Au terme d’une série de transformations, les deux énoncés de départ aboutissent à un texte unique” (Bénabou and Perec, 1973, p. 123). By applying this procedure to two quotations –​“Le presbytère n’a rien perdu de son charme ni le jardin de son éclat” (Bénabou and Perec, 1973, p. 123), the famous line from Gaston Leroux’s novel, Le Mystère de la chambre jaune and the famous communist rallying cry, “Prolétaires de tous les pays, unissez-​vous!” (Bénabou and Perec, 1973, p. 129) –​Perec and Bénabou hoped to show that the two sentences were semantically equivalent. Since dictionary definitions are necessarily longer than the word they define, and since there are often several definitions for the same word, there are a number of possibilities at every juncture. With enough repetitions of this same procedure, the definitions would get so inflated with “meaningful” words that Perec and Bénabou could in theory prove what they hoped. In his biography of Perec, David Bellos (1993, p. 342) notes that a refutation of this hypothesis might indeed be even scarier than the semantic equivalency of an enigmatic phrase and a communist cry: “… if no intersection were possible, then the two lines would belong to two different languages, perhaps even to two different worlds.” Definitional rewriting makes a text less clear, even though readers often have recourse to dictionaries to learn the definitions of words with which they are not familiar. Mathematically, replacing a unit with something equivalent should not change the overall expression, but this incompatibility with semantic meaning is disconcerting.

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In light of this result, Marcel Bénabou (1973, p. 200) proposed the opposite constraint in La Littérature Potentielle, poésie antonymique: “… une technique de création poétique qui consiste à remplacer chacun des mots d’un poème donné par son antonyme.” While such a technique might be interpreted as satiric commentary, Bénabou (1973, p. 204) disagrees: On ne cherche pas, ici, à dévoiler l’absurdité d’une pensée, d’une maxime, en énonçant la maxime contradictoire : il s’agit d’autre chose que d’une inversion de signe. C’est chaque mot pris en lui-​même qui est ici ‘traité.’ Ainsi est sauvegardé le caractère potentiel du procédé : il préserve la possibilité d’obtenir des séquences parfaitement inattendues.

Bénabou (1973, p. 205) notes that this constraint can be considered a variation on certain others: a specific case of S +​n, or rather S × n where n =​−1; or rather an instance of LSD, where the dictionary used is one of antonyms. In this sense, Bénabou’s method is just another instance of Oulipo’s prolonged work on substitutional constraints, which often produce humorous results through purely mechanical procedures. Oulipo seems to have noticed that simple substitutions have the potential to generate new insights from old texts, as evidenced by the group’s categorization of all these procedures under anoulipisme in both La Littérature Potentielle and Atlas de littérature potentielle.

III. Operations Substitutions are only one half of algebraic work. To accomplish anything significant with variables, one must determine the relationships between them and define their interactions using operations. However, operations are not necessarily restricted to mathematical objects, as Oulipo found in the case of substitutions. At an Oulipo meeting in 1966, Paul Braffort proposed to represent relationships between characters mathematically by multiplication: “… on peut représenter la relation ternaire ‘X prend Y pour Z’ par une multiplication: XY =​Z” (Queneau, “La relation X prend Y pour Z,” p. 62). Elementary algebra defines relationships between

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mathematical elements with operations. Braffort’s insight is that one can apply the same logic to regulate characters and their actions in literature. In response to Braffort, Queneau (1973d, p. 62) uses multiplication tables to illustrate how characters recognize one another with two examples. The first is a “normal situation”: a b c

a a a a

b b b b

c c c c

In this situation, one must understand that the character (denoted by either a, b, or c) in the left column is the first actor in this relation, the one who is identifying (well or badly) another character. In this normal situation, character a takes character “a” (himself ) to be “a.” In other words, he recognizes that he is himself. He also properly identifies the other characters, as do the others. The following example is the vaudeville example, where characters fail to recognize others (Queneau, 1973d, p. 62): a b c

a a c b

b c b a

c b a c

In this new scenario, a, b, and c recognize themselves (obviously), but mistake the remaining two characters for each other. The graph is humorous precisely because this mathematical representation is not an appropriate or efficient way to represent something that is intuitively obvious. As in the mathematical variations in Queneau’s Exercices de style, the mathematical language simultaneously obscures what would be obvious to someone reading the accompanying text and also reveals something about the genre. In short, it allows for a generalization, which in this case, shows the commonalities between plays in a specific genre. Queneau (1973d, p. 63) uses his general knowledge of mathematics and literature to propose a theorem about these multiplication tables:

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La table de multiplication d’un groupe (abélien5 ou non) correspond à la situation suivante : personne ne se prend pour ce qu’il est, ni ne prend les autres pour ce qu’ils sont, à l’exception de l’élément unité qui se prend pour ce qu’il est et prend les autres pour ce qu’ils sont.

The “identity” element in typical multiplication is an element that, when introduced into the operation (in any order), does not change the value of the object on which it operates. For instance, in standard multiplication, one can multiply by 1, but that does not change the value; in addition, one can add 0 infinitely many times. In the dramatic situation Queneau (1973d, p. 63) describes, the identity element is an “observateur lucide,” who always recognizes each character for who he or she is and also how he or she is misidentified by the others. The author satisfies the identity operator in most cases, and the reader as well could be represented on the table. As he did in Exercices de style and Les Fondements de la littérature d’après David Hilbert, Queneau assigns the reader exercises. The first: “Trouver des exemples concrets de cette situation [commutativity] dans la littérature théâtrale ou romanesque, française ou étrangère” (Queneau, 1973d, p. 64). This example requires the reader to imagine literary situations in which two characters mistake each other for the same person (ab =​ba =​c). Another exercise has the reader invent concrete situations corresponding to half-​ groups developed by mathematician R. Croisot. In this way, the mathematics becomes fuel for inspiration, leading the author to imagine complex scenarios. Finally, Queneau (1973d, p. 65) proposes a multiplication table describing the relationships between characters in Oedipus:

Fils de Jocaste Œdipe Père nourricier Jocaste

5

= = = =

a b c d

a

b

c

d

b 0 b 0

b b a b

c c c c

d d d d

“Abelian” in this sense means commutative. In mathematics, an operation is commutative if one can reverse the order without changing the result. The vaudeville example is abelian, for instance.

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The exercise demands that the reader reformulate this table to avoid the 0’s. The complication is that Oedipus is listed twice in this scenario, given he is also the son of Jocaste. Therefore, Oedipus believes that Jocaste has no sons (as he is ignorant that he is her son), resulting in a 0. Likewise, Jocaste believes her son to be dead, resulting in a second 0. This could be resolved by eliminating the element a (fils de Jocaste), however then the table would not accurately depict the central plot complication, in other words, that Jocaste believes her son to be dead and that Oedipus believes she has no sons. Atlas de littérature potentielle proposes a more formal definition of such multiplication tables and their application to literature, generalizing the procedure even further: Considérons un énoncé qui lie trois actants (par exemple trois personnages). Chaque instance valide de cet énoncé définit un triplet : l’ensemble des trois actants qui le satisfont. L’ensemble des triplets forme ce que les mathématiciens appellent une loi de composition interne (comme l’addition, le ‘ou’ logique, etc.). Comme, dans les exemples qui nous occupent, l’univers des actants possibles est fini, on peut exhiber la loi de composition par sa table de Pythagore. (Oulipo, 1981d, p. 174)

The procedure no longer needs to be “x prend y pour z,” but could be “A s’adressant à B l’appelle C” (Oulipo, 1981d, p. 174). Abstracting Queneau’s original statement produces tables with more mathematically interesting results: “Il est difficile, avec un tel énoncé, de construire des univers plausibles où la table de Pythagore de la loi de composition associée à l’énoncé ait des propriétés algébriques intéressantes (groupe abélien, par exemple). Aussi est-​il conseillé de construire d’autres énoncés générateurs de telles lois” (Oulipo, 1981d, p. 175). Perec proposes: “x estime que y est z” and “x croit que y aime z” (Oulipo, 1981d, p. 175). One can note from the evolution of this constraint between La Littérature Potentielle and Atlas de littérature potentielle that Oulipo’s objectives shift from analytic to synthetic. While Queneau had initially proposed his operation as a commentary on literature, Perec and Mathews propose to use these tables as a generative device. By first coming up with a new generalizable situation that can be represented in Queneau’s terms, the two then use the generated table to write a short explanatory text.

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Another Oulipian use of operations comes from American member Harry Mathews, who created his own algorithm which he published in French in Atlas de littérature potentielle and in English in Warren Motte’s Oulipo: A Primer of Potential Literature (1986). In the French version of the article, Mathews (1981, p. 91) introduces his algorithm by addressing Oulipian reading, and not writing: “La lecture potentielle a le charme de faire ressortir la duplicité des textes, qu’ils soient oulipiens ou non.” The preceding substitutional constraints were considered by Oulipo to be examples of anoulipisme rather than synthoulipisme, procedures that serve as a commentary on a source text rather than producing a stand-​alone work. Mathews (1981, p. 91) acknowledges the analytic nature of Oulipian reading: … n’importe quelle prose, si robuste soit-​elle dans son apparente unicité, fera preuve de la même fragilité dès qu’on pense à ce que lui apporterait le L.S.D. ou le S+​7. Au-​ delà des mots qu’on lit, d’autres attendent, qui vont ébranler les premiers et peut-​ être les éclipser. On ne peut plus compter sur rien. Chaque mot devient une peau de banane. La belle surface unie du texte est démentie et démantelée : derrière elle, dans la potentialité, une dialectique s’érige.

The fact that Mathews chooses to comment on the reading of the text, and not on the writing, is significant. His analysis of these analytic procedures indicates that they force the Oulipian writer and his or her readers to approach source texts –​either constrained or unconstrained –​in a different way, as constrained writing allows one to remove outer layers and understand what is truly at the heart of writing. An Oulipian reader, according to Mathews’s analysis, must never consider a text as finished, for it always hides an additional potentiality. In other words, constrained writing becomes a mode of reading. This way of thinking is inherently mathematical, as per the axiomatic nature of the discipline, previous mathematical work is used to deduce new results. Mathews (1981, p. 91) claims that language, like mathematics, hides more truths than those of which readers are initially aware: “L’algorithme en question s’ajoute aux moyens qui servent à débusquer cette altérité qui se cache dans le langage et peut-​être dans ce dont parle le langage: c’est encore une façon de dire deux choses à la fois.” His algorithm, which aims to treat language mathematically through a simple system, was created to

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manipulate these two intertwining elements: the language itself and the meaning behind it. However, Mathews (1981, p. 91) describes the functioning of the algorithm as arbitrary: “Si ces matières exigent des soins de rédaction pour constituer un tableau algorithmique, leur duplicité potentielle se réalise d’une façon quasiment automatique.” The use of the word automatic is dangerous and provocative. Unlike surrealist automatic writing, which was meant to be driven by the unconscious and not by a procedural method, Mathews builds upon previous Oulipian methods to discover patterns and relationships that already exist in language, and then processes those using an arbitrary operational method. This method explicitly plays with the potentiality created by the mechanical aspects of language and has less to do with the whims of the author. While the author in Mathews’s algorithm has a certain amount of freedom in selecting the elements to be manipulated, the automatic nature of the procedure speaks nothing of the subconscious desires of that author, but rather operates as a tool forcing the author to be even more conscious about his/​her intended results. The algorithm is simple to explain, but much harder to detect within a text:

1. Data: The author chooses “data”: several (at least two) sets of heterogeneous elements (Mathews, 1981, p. 92). The selection of these sets depends upon a set-theoretical notion of language, much like the mechanism that allows Oulipian authors to perform substitutions. Choosing words that share the same part of speech, for instance, would be an appropriate way to categorize these elements. However, Mathews (1981, p. 92) remarks that: “Cette hétérogénéité peut être minime –​parfois elle sera purement nominale –​mais elle n’en est pas moins essentielle au bon fonctionnement de l’algorithme: moins elle est respectée, plus les chances augmentent de voir la machine tourner en rond, en produisant de simples répliques des ensembles de départ”. For the strict algorithmic procedure to function properly, the distinct nature of the elements does need to be respected, but Mathews

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recommends that in a table of n elements, n2 − (n − 2) of them should be different. 2. Arrangement: From the data sets the author has chosen, each set must contain the same number of elements. Each element must be equivalent to the corresponding elements in the other sets according to its function (syntactic is proposed as an example). The sets are then superimposed to form tables consisting of rows (the sets) and columns (the corresponding elements) (Mathews, 1981, p. 93). For his examples, Mathews relies exclusively on square tables where the number of elements in every set is equivalent to the number of sets. However, he claims this is not necessary. 3. The Operation: The author shifts each set n − 1 spaces to the left (an operation that results in diagonals of common elements, in which each column now contains four unique elements from the four original sets). Then he or she reads the columns from the top to bottom beginning with the first element a of the sets. One can then repeat this procedure by shifting the elements to the right instead of to the left, in this case reading from bottom to top, still beginning with the a-​th element of each new set. In this way, one turns n sets into 2n new sets (p. 94). To illustrate, this is the table created by step 2: Arrangement: 1. 2. 3. 4.

a1 a2 a3 a4

b1 b2 b3 b4

c1 c2 c3 c4

d1 d2 d3 d4

This is the table created by the leftward shift in step 3: 1. 2. 3. 4.

a1 b2 c3 d4

b1 c2 d3 a4

c1 d2 a3 b4

d1 a2 b3 c4

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Note the mathematical arrangement of the elements, which cycle accordingly. The diagonals represent all occurrences of one particular letter; every column contains all four numbers in ascending order and all four letters in the same order, displaced vertically; every row, on the other hand, represents a unique permutation of the letters, the totality of which is exhaustive. This table represents the new sets of four, ordered elements: 1. 2. 3. 4.

a1 a4 a3 a2

b2 b1 b4 b3

c3 c2 c1 c4

d4 d3 d2 d1

Shifting the elements to the right produces a similar table, but the procedure remains the same. The nature of the elements determines the type of solution. For instance, creating sets of letters (individual words composed of the same number of letters to respect the square tables) at the outset will generate new words (Mathews, 1981, p. 96). Syllables are a possibility as well, which Mathews (1981, p. 96) does not include in his demonstrations because of the difficulty. The procedure can also be applied to words arranged according to their syntactic order. The words can be new material produced by the author or come from prior material. Mathews (1981, p. 97) demonstrates using the first verses of Mallarmé sonnets, which he reduces to their four main words, creating the following table: adj Fatal Haut Tel que Courroucé

subst ombre ongles Lui-​même roc

subst loi onyx éternité bise

v menaça dédiant change roule

(auxiliares) (quand, de) (très, ses purs, leur) (en, enfin, le) (noir, que, le)

Mathews’s selection of words is similar to the S+​7 procedure or Queneau’s poèmes haï-​kaïsants, in that he chooses to set aside what he considers to be

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the “empty words” consisting of prepositions, adverbs, articles, etc.6 This procedure produces new incipits of these famous poems, reintroducing the auxiliaries to produce the new verses:

1. De ses ongles fatals L’éternité le roule … 2. Quand l’onyx courroucé que leur ombre le change … 3. Tel ce roc fatal dédiant la noire loi … 4. Quand la bise Lui-​même très haut menaça …

Mathews (1981, p. 101) does not only apply the procedure to letters, words, or even groups of words, but also to “… des épisodes de fictions résumés en une ou deux phrases.” These episodes bear a great resemblance to Vladimir Propp’s functions from Morphology of the Folktale, a well-​known Russian formalist text. In Chapter 1, I briefly mentioned Russian formalism due to its influence on structuralism, however it is necessary to consider its direct relationship to Oulipian aesthetics for several reasons. Russian formalism reached French intellectuals in translation long after the publication of Lévi-​Strauss’s Structures élémentaires de la parenté in 1948. In the 1960s and 1970s, the young Bulgarian student, Tzvetan Todorov, informed Parisian intellectual circles of Russian formalism. With the publication in 1965 of Théorie de la littérature, a French translation of key Russian formalist texts, Todorov made the school accessible to the French literary milieu. Propp’s Morphology of the Folktale also appeared in French translation that same year. Propp’s theory was that his corpus of Russian folktales, a genre known as the skazka, was produced through the combination of a limited number of prefabricated elements subject to fixed rules. He analyzed basic plot components of this primarily oral genre and identified their simplest, irreducible narrative elements, of which he claimed there were 31 following an initial situation. Propp’s study then went on to analyze the patterns these functions could exhibit within his corpus, essentially carrying out mathematically inspired work on a non-​mathematical object, a body of text. No folktale contained all 31 functions, but the functions that appeared always 6

The choice of discarding adjectives as “empty words” is debatable. Mathews only does it once (noir), and is required to make the choice given the rules he established.

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did so in the same order and contributed in similar ways. Theorists in the 1960s and 1970s built on such structural analysis of language and meaning, dubbing their work semiotic or structural in nature. Although each of Mathews’s original summaries forms a coherent sketch of a story, permuting them in such a seemingly arbitrary (yet mathematically controlled) way both acknowledges Propp and criticizes him. By viewing these episodes as analogous and replaceable, Mathews uses Propp’s morphological analysis in his own set-theoretical understanding of literature. However, by recombining these functions according to a mechanical algorithm rather than according to the pure logic of the tale lightly mocks the overtly mathematical nature of Propp’s study. The procedure does produce some amusing new stories, such as: “1 a A et B sont mari et femme. b A tombe amoureux d’une connaissance de B. c B apprend que sa mère est gravement malade. d Touchée par ces nouvelles circonstances, B demande à A d’oublier ses anciennes obligations. e A et B ne se reverront jamais” (Mathews, 1981, p. 102). The Oulipian experimentation with semantic substitutions and operations demonstrates a surprising commonality with Russian formalism while remaining distinct. Propp’s morphology, by its very nature, is a mathematically inspired search for patterns in his corpus of Russian folktales. To accomplish this, he defines his functions, irreducible narrative elements that can be understood as a generalized category or variable. Propp’s study then defines a formal system in which these functions interact. The work of Oulipo in its early years is similar in that the members also break literature into its composite parts for the purpose of analyzing the way it functions. However, Propp’s exhibits a purely analytical goal, explaining through the establishment of a formal language and axiomatic framework the means through which folktales operate on a reader. Conversely, Oulipo creates new axiomatic frameworks within which to manipulate its constituent parts, thereby defamiliarizing a reader with texts he or she already knows. The similarities between these two movements are striking, but the differences radically transform the way we understand Oulipo and its mathematical project. Unlike Russian formalism and other literary movements that propose to analyze cultural objects mathematically, Oulipo’s method is far more active. It not only accomplishes an analytic process through its

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algebraic procedures, but produces something new and unexpected. In the hands of a willing reader, this textual production –​both familiar and strange –​teaches the reader about the artificiality of literature and how it is produced. Moving beyond purely algebraic operations, number theory deals with the study of integers in an abstract sense, concerning itself with properties of these numbers rather than with specific applications. Given the foundational role of numbers in the history and practice of mathematics, many know the field of number theory by a more colloquial name: The Queen of Mathematics. In this field, a certain importance is given to prime numbers, which –​due to their indivisibility –​are considered the elements of arithmetic. Prime numbers are no less important for Oulipo. While the distribution of prime numbers appears random to the non-​mathematician, most mathematicians are convinced that there are certain laws governing the way they behave. This is analogous to the idea of constraint, which silently directs a text whether or not the reader is aware of its existence. The Fibonacci sequence is common in number theory, as it demonstrates interesting properties. The sequence derives from an arithmetic exercise proposed in the volume Liber Abaci by Leonardo Pisano (commonly referred to today as Fibonacci) about how quickly rabbits reproduce. Should one man have one pair of rabbits that reproduces once per month, how many rabbits would that man have at the end of a year? Fibonacci’s solution is that after 1 month, there will be 2 pairs; after 2, there will be 3; after 3, there will be 5; after 4, 8; and so forth. The sequence itself (1, 1, 2, 3, 5, 8, 13, …) is simple to generalize: every term is the sum of the two that come before. In number theory, these numbers are an important object of study because of the properties they share; in nature, these numbers can be found in many patterns, contributing to their allure. The 20 poems of Paul Braffort’s Mes Hypertropes: Vingt-​et-​un moins un poèmes à programme (1979) depend upon Fibonacci numbers. The volume is regulated by a number of algebraic constraints, of which the main organizational principle borrows from Braffort’s (1987, p. 169) understanding of Roubaud’s second principle, which he rephrases as follows: “–​on n’utilisera une structure mathématique comme contrainte maîtresse d’une œuvre littéraire que si l’on y exploite aussi un ou plusieurs théorèmes attachés à

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cette structure.” Braffort makes use of Zeckendorf ’s 1972 theorem, which proves that one can represent any natural number as a unique sum of non-​ consecutive Fibonacci numbers. While there are many ways to represent natural numbers as the sum of Fibonacci numbers, Zeckendorf proves that there is only one way to represent natural numbers using non-​consecutive Fibonacci numbers. To use Zeckendorf ’s theorem to structure his poems, Braffort recognizes that each poem in his list can be assigned a numeric index that is either a Fibonacci number or that can be represented as the unique sum of non-​consecutive Fibonacci numbers. For example, the Zeckendorf representation of poem 4 would be 4 =​1 +​3. Poem 4 is therefore connected with poems 1 and 3, sharing certain characters or images. This structural repetition acts as a generative device, which forces Braffort to construct thematic parallels between poems that are related by the theorem, of which the overall structure can be best visualized through the graph in Figure 2.3.

Algebra

Figure 2.3.  Excerpt from Mes Hypertropes (p. 167). Reproduced with Oulipo's permission.

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In the graph, the Fibonacci sequence (1, 2, 3, 5, 8, 13) occupies a central path, the vertical line that cuts through the center. These poems are connected to each other as each Fibonacci number can be represented as the sum of the two that came before it. The other numbered poems are placed in a constellation around these main ones, connected to their non-​ consecutive Fibonacci representations in a network graph. The first poem, “L’explication préalable ou La raison des rimes” is in theory not influenced by any of the others, but rather provides the thematic material that will find its way into many of the other poems. The number 1 is very common in the Zeckendorf representations, meaning that the thematic material from poem 1 influences not only poems 2 and 3 (its successors in the Fibonacci sequence) but also poems 4 (1+​3), 6 (1+​5), 9 (1+​8), 12 (1+​3+​8), 14 (1+​13), 17 (1+​3+​13), and 19 (1+​5+​13). As this first poem is so important in the collection, I will reproduce it: C’est mon devoir, c’est mon défi, tel Jarry, Cyrano, bouffi, de chercher des poux à Rimbaud, et sur les zizis des bobos. Qu’il neigeât ou bien qu’il fit beau à Lhassa Emma Sophie Bo-​ vary veuve d’un lent cornac se donnait au dieu de l’arnaque. Leibniz, disant : “Vers …” Quel bon ac-​ teur pour ce “Vers …” superbe. Oh “nach” ! Il vise, Emma, l’apoplexie des grands buveurs de galaxie. Au club des rois du “spinach” (si Bach n’y vint jamais, Banach si !) Leibniz –​son graphe ico n’a qu’six mus, trois nus, un phi bon à xi -​ hante sans profit Bonn : “Ach ! Si j’étais le grand Fibonacci !!! …” (Braffort, 1987, p. 170)

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What looks like a simple group of nine couplets borrows from the structure of the Fibonacci sequence, first and foremost in the rhymes. The first couplet’s rhyme is fi-​whereas the second is -​bo; the third (the sum of the first two according to the sequence) is therefore Fibo-​. Next comes -​nac, followed by its composite -​bonac; -​xie (pronounced -​si) followed by -​nachsi; finally, the last couplet makes this progression explicit, with “(pro)fit Bonn: “Ach! Si” and finally, “Fibonacci.” This explains the Fibonacci structure, but the Zeckendorf structure further problematizes a linear reading with the use of networks. To the right of various lines in each poem are arrows indicating which poem will then borrow the thematic material from a certain line. For instance, it is Cyrano who finds his way into poem 2, whereas Emma Bovary can be found again in poem 4. The reader can read each poem linearly, relying on memory to recall which poem an individual reference was from; alternatively, one can follow the graph, which has its own implicit hierarchy, reading each series of two poems and their arithmetic consequence; or one can follow the arrows within the text, breaking the individual readings of poems in favor of thematic readings. In short, due to the structure of this text, the opportunities for different modes of reading are varied. Tubbs (2014, p. 98) claims that: “The structure does not entirely determine these poems, but it does provide connections between the poems that might not be there otherwise.” I would argue that Braffort goes even further. While the structure does not entirely determine the poems, a great portion of them is determined in advance based on Braffort’s structure. Upon completion of his first poem (which was further constrained by the Fibonacci rhymes), a large part of the thematic material for the rest was already predetermined, which is constraining, but also facilitates the writing of the rest in a way. Furthermore, the structure provides connections precisely because they are explicit. The connections between the numbered poems and the thematic links are Braffort’s literary equivalent of the Fibonacci sequence, which is a ubiquitous aspect of both mathematics and life. Indeed, reading these poems in various ways to find new links and constraints between them (for instance, the system that determines the number of stanzas, verses, syllables, etc.), is akin to mathematical work. The reader must look for patterns and, through the

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process of reading, abstract Braffort’s rules. This is precisely what a number theorist does with numbers.

IV.  Abstract Algebra While the algebra discussed above was mostly restricted to operations and variables, abstract algebra deals with algebraic structures, a more abstracted type of mathematical structure that consists of a set of objects and an operation. This is similar to the principle at play in Queneau’s “x prend y pour z,” in which one can take two elements of a set and produce a third. The operation can be represented as a multiplication table, which represents the entire structure. While the elements x, y, and z can be replaced by real numbers or characters, they are empty signifiers in this particular branch of mathematics. As with set theory or Hilbert’s points, lines, and planes, it does not matter what they stand for. The importance lies in the relations between them. In fact, Queneau’s example is not only an algebraic structure, but it is what is known as a semigroup, or a set combined with an associative binary operation, most often denoted multiplicatively. In Queneau’s first example, a mathematically inclined reader can verify that the operation is indeed associative, or that (x * y) * z =​x * (y * z). A semigroup is defined exclusively based on an operation and associativity, but to define an algebraic group, four axioms must be satisfied: closure (the performance of the operation on members of the set will only produce a member of the set); associativity (the grouping of numbers undergoing the operation does not change the result); identity (that there exists one element which leaves the others unchanged when combined); and invertibility (that each element in the set has another which, when combined, produce the identity element). Queneau’s case does not include an identity element, however he does acknowledge that the author would be an appropriate example. Tubbs (2014, p. 42) lauds Queneau’s choice of the semigroup, but explains its shortcomings: “Because each element in a group has an inverse element, if a, b, and c are different elements of a

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group, say with an operation *, it is not possible to have all of the possible combinations of misunderstandings Queneau proposed.” At the end of variations on Queneau’s method in Atlas de littérature potentielle, Oulipo explained that: La forme la plus raffinée d’une telle contrainte se trouve développée dans l’ouvrage de Jacques Roubaud La Princesse Hoppy ou Le conte du Labrador … il exploite les deux relations : x complote avec y contre z x fait de la compote avec y pour z qui obéissent à une loi de composition particulièrement simple (il s’agit d’un groupe de quatre éléments). (Oulipo, 1981d, p. 179)

Jacques Roubaud was well versed in algebraic language and its implications, since at the time he published this novel, he was a university mathematics professor who specialized in abstract algebra. La Princesse Hoppy is Roubaud’s most mathematical literary work, in which mathematics is not only a generative force, but the subject and purpose. On the surface, La Princesse Hoppy tells the tale of a princess and her faithful dog who is also a mathematician. It reads almost like a cross between a medieval romance and Alice in Wonderland, given it is filled with improbable situations, fantastical languages, poems, games, and even math problems. Beneath this Arthurian adventure, Roubaud’s text can be read as an allegory to the author’s own personal quest to be a mathematician or even as abstract algebra. Perhaps due to the daunting mathematical nature of this text, there is very little criticism written on it. Elvira Monika Laskowski-​Caujolle7 is the only scholar to date who has conducted a thorough analysis (mathematical or otherwise) on this text. In an English-​language article published on part of her extensive study on this topic, “Jacques 7

See her English-​language article, “Jacques Roubaud: Literature, Mathematics, and the Quest for Truth,” in SubStance, Vol. 30, No. 3, Issue 96; her French-​language article, “L’Épluchure du conte-​oignon” at the end of the illustrated edition of La Princesse Hoppy, Collection “La Reverdie” Éditions Absalon; or her longer volume in German, Die Macht der Vier –​Von der pythagoreischen Zahl zum modernen mathematischen Strukturbegriff in Jacques Roubauds oulipotischer Erzählung “La princesse Hoppy ou le conte du Labrador”. Frankfurt am Main: Peter Lang, 1999.

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Roubaud: Literature, Mathematics, and the Quest for Truth,” she insists on the importance of biographical elements: The author compares his search for mathematical truth [a]‌with the quest for the grail [b], and applies the adventures of Chrétien de Troyes’s hero Perceval to the dog’s situation [c] in his novel. Since mathematics are omnipresent in Roubaud’s oeuvre, we can conclude (if a =​b and b =​c then a =​c) that the princess’s dog –​the main character, in quest of the solution to the novel’s enigma –​symbolizes Roubaud and his quest for truth. (Laskowski-​Caujolle, 2001, pp. 74–​75)

Laskowski-​Caujolle (2001, p. 75) demonstrates how Labrador is an old French anagram of Roubaud (Perceval =​Labrador =​Rrobaald =​Roubaud), a word game that demonstrates Roubaud’s tendency to play with the basic units of literary creation, also demonstrates the specific confluence of Roubaud’s literary and mathematical influences. Long interested in medieval literature, the word game using old French spellings combined with the mathematical combinatorial shuffling of letters is just one example of Roubaud’s playful Oulipian techniques. What is arguably the most important wordplay found in the conte is that on the word conte itself. First, in Chapitre 0: Indications sur ce que dit le conte, Roubaud toys with the homonyms conte and comte: “1. Celui qui raconte, c’est le Conte et celui qui raconte le conte c’est le comte, le Comte du Labrador. Aussi le conte est-​il dit le Conte du Labrador … 4. Peut-​être avez-​vous du mal à croire que le co(n,m)te est l’auteur de l’histoire; et si vous le croyez, peut-​être avez-​vous tort de le croire” (Roubaud, 2008, p. 7). This wordplay is the first step in a mathematical game that further plays with the aural ambiguity of the word conte, as it can also be confused with compte or count. Roubaud’s next step is to introduce the notion of truth and falsehood: “Le conte dit le vrai. Cela ne veut pas dire que le Comte du Labrador dit le vrai. Le vrai du conte n’est pas toujours le vrai du comte. Le conte n’en reste pas moins vrai” (Roubaud, 2008, p. 8). The various points in this category of “Que le Conte dit vrai” play on the notion of truth and falsehood. Given the prior wordplay on the two co(n,m)tes, this further complicates Roubaud’s truth statements, which must be logically deconstructed in order to make any sense at all: “Le conte dit toujours vrai. Ce que dit le conte est vrai parce que le conte le dit. Certains disent que le

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conte dit vrai parce que ce que dit le conte est vrai. D’autres que le conte ne dit pas le vrai parce que le vrai n’est pas un conte. Mais en réalité ce que dit le conte est vrai de ce que le conte dit que ce que dit le conte est vrai. Voilà pourquoi le conte dit vrai” (Roubaud, 2008, p. 7). While the first sentence would have sufficed, the logical propositions that follow speak more about grammatical aspects of truth than the truth of the conte. The final sentence, for instance, is such a verbal jumble that it can be reduced to a tautology. In the following section, Roubaud then problematizes the language further, by claiming that the conte is told in both French and in dog (Roubaud, 2008, p. 9). This Chapter 0, while reminiscent of Roubaud’s mode d’emploi for his first poetry collection, ∈ (see Chapter 3), is incomplete. Roubaud supplements it with a c­ hapter 00 (inserted between the fourth and fifth chapters), which is a “literal” translation of Bourbaki’s mode d’emploi in the style of Queneau’s Les Fondements de la littérature. Roubaud has replaced the word “mathématiques” by the word “conte,” leading to the identity Laskowski-​ Caujolle (2001, p. 75) proposes: “mathématiques =​conte.” However, Laskowski-​Caujolle’s analysis does not touch upon the singularity or plurality of the word mathématiques, a central aspect of Bourbaki’s corpus. Roubaud replaces “ce traité” in the original Bourbaki with “Le Conte” (capitalized), for instance, reiterating the differences between “un conte,” “le Conte,” and “le Comte” who tells it all. Compounded with the question of truth, this new mode d’emploi throws even more of the Conte into question. Roubaud then replaces “une certaine habitude du raisonnement mathématique et un certain pouvoir d’abstraction” (Bourbaki, 1939, p. I.3) with “une certaine habitude des histoires et un certain pouvoir d’audition” (Roubaud, 2008, p. 45). While Laskowski-​Caujolle’s identity still holds, I believe it could be nuanced. If “Le Conte” is the equivalent of Bourbaki’s treatise, then the reader needs to be familiar not only with reading stories such as Chrétien de Troyes’s Conte du Graal, but also with mathematical thought. The most telling aspect of these relations is found in Roubaud’s “4. Le mode d’exposition suivi dans la première partie est oral et concret …” (oral and concret replacing axiomatique and abstrait in the original Bourbaki), “… il procède le plus souvent du particulier au particulier par le général (ou

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l’inverse)” (Roubaud, 2008, p. 45) (replacing “du général au particulier” in the original Bourbaki). While the axiomatic method and abstract thought are characteristic of Bourbaki, giving mathematics its air of eternal truth, Roubaud praises instead the oral and concrete aspects of stories, as well as their episodic nature that capitalizes on the generalized nature of each of the parts. Roubaud’s discussion shares much with Propp’s Morphology of the Folktale. His “translations” à la Queneau speak to the nature of the genre: “Le choix de cette méthode était virtuellement imposé par l’objet principal de cette partie qui est de donner des fondations solides à l’ensemble du conte moderne” (Roubaud, 2008, pp. 45–​46). Roubaud follows this user’s manual with a series of questions to ensure that the reader has grasped the point, rather than passively absorbing the words. Laskowski-​Caujolle (2001, p. 77) speaks about what it means to read Roubaud: … not only to interpret and to analyse, but to translate (literary language into mathematical language, “ordinary Dog” language into French), to explain (the History of Mathematics), and especially to decipher the given puzzles and riddles. Like a mathematician who reads a mathematical text with pen and paper to verify theorems or to do the inevitable exercises at the end of a chapter, the reader of La Princesse Hoppy must answer 79 questions to verify whether s/​he has properly “understood” the tale.

One of Roubaud’s problems for the reader happens at the very beginning, when Hoppy is worried about her four king uncles who are plotting against each other. In an analogous situation to Queneau’s x prend y pour z, Roubaud’s algebraic group consists of x complote avec y contre z (Oulipo, 1981d, p. 338). For all four kings to plot with another against a third, “[t]‌here are 16 possible combinations of visiting situations and 4 plotting possibilities, which result in 4^16 =​4,294,967,296 possible plots” (Laskowski-​Caujolle, 2001, p. 78). The resulting “règle de Saint Benoît” is a literary translation of the notion of algebraic group that I outlined above, referring to associative laws (in the first part), the identity element (in the second), and invertibility (in the third part).8 The Princess then wonders 8

Laskowski-​Caujolle has also noticed this detail and described it at length in Die Macht der Vier.

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if the group is commutative (if one uncle pays a visit to another, do the two plot against the third king as if the second had visited the first?), her trusty dog claiming: “un oue a uatre éléents est orcéent coutati” (a group of four elements is necessarily commutative) (Roubaud, 2008, p. 13). In her articles and book, Laskowski-​Caujolle proves that Roubaud’s four-​ element group in the king problem is in fact the Klein group of order four, which is isomorphic to the symmetric group of order 3. Laskowski-​Caujolle points out several examples of Roubaud playing with the alphabet in La Princesse Hoppy, the first of which parodies a math question Gustave Flaubert wrote to his sister. His question appears at first glance to be a standard mathematical problem to solve, providing his sister with information about a ship sailing from Boston to Le Havre, and then asking her to answer an unrelated question about how old the captain is. Unlike Flaubert, who does not provide his sister with any figures that could help her discover the age of the captain, Roubaud’s novel contains of list of geographical names whose initials provide the answer: “qcuaapriatnatienuens” (the bolded letters spell the word “capitaines” and the remaining ones provide the age: quarante (et) un) (Laskowski-​Caujolle, 2001, p. 79). Roubaud’s La Princesse Hoppy is a complex novel that operates based on a great number of constraints, and it is beyond the scope of this book to reveal them all. What is important to note, however, is that Roubaud plays with different types of basic elements –​letters, words, numbers, and characters –​to create a ludic yet pedagogical tale for the reader to solve. Roubaud’s compositional constraints not only draw from the prior Oulipian work discussed in this chapter, but combine them in such a way as to move beyond the simplistic nature of some of the earlier constraints. Etymologically and homophonically playing with the term “conte/​compte/​ comte,” Roubaud uses a genre that had famously been mathematized in Propp’s morphological study to foster mathematical thinking on the part of the reader, who must actively translate, answer questions, and solve problems. Building upon the already established relationship between letters and numbers, Oulipo is aware of the long and intertwining history of the two. This chapter has demonstrated the various ways in which the group

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has taken advantage of this intersection and to what ends, revealing a trajectory of increasing mathematical and literary complexity. By reducing language to its basic units, the members manipulate those units to various effects. Beginning with simple counting, then moving on to operations and abstract mathematics, Oulipo has investigated to an impressive degree the mathematical nature of reading and its analytic and synthetic nature. For the analytic cases, Oulipo’s results demonstrate the artificiality of language and literature, calling the reader’s attention to the constituent parts of both language and literature that create meaning and forcing him or her to question that meaning. For instance, the S+​7 depends upon a reader’s familiarity with a pre-​written text in order to defamiliarize it, emphasizing through a mechanical process what is artificial about literature itself. This affords an Oulipian reader a more nuanced conception of Oulipo’s mathematical project: all literature can be understood as the product of constraint, yet Oulipo’s potential literature is rather a subset that is produced by a conscious and conscientious reflection on the nature of constraints. With this heightened understanding of literature as the product of constraints, Oulipo gradually shifted to purely synthetic examples, producing texts without recourse to what was already written and relying on more abstract developments in mathematics. For such synthetic cases (such as the more complex texts produced by Braffort and Roubaud), the authors encourage the reader to deconstruct them according to the rules by which they were created. This heightened involvement of the reader is key, for he/​she must continually recognize patterns, fostering connections that were put in place by the author.

Puzzle Theorem of the Four Colors, designed by OuPeinPo member Eric Rutten. Reproduced with the artist’s permission.

Chapter 3

Combinatorics

Combinatorics, Raymond Queneau’s favorite branch of mathematics, studies countable, discrete structures and their combinations. Combinations of even a small number of discrete elements have the potential to produce very large numbers and a study of how they function is central to fields of applied mathematics such as probability, a study that attempts to quantify the likelihood that certain events will occur. If mathematics is the study of abstract patterns, probability theory is the branch of mathematical work that most directly confronts the true enemy of mathematics: chance, or the lack of all pattern. As with the other mathematical fields of inquiry that have been discussed in this study, combinatorics deals primarily with mathematical objects, or anything that can be formally defined. It should be noted that in the history and philosophy of mathematics, there is a longstanding debate on the nature of mathematical objects. While some mathematicians believe that mathematics is a human creation, others believe that mathematical objects exist independently of humans and that mathematical truths are simply “discovered.” This philosophy is known as mathematical platonism,1 and is loosely related to mathematical structuralism, which holds that it is not the internal nature of mathematical objects that counts, but rather the relations between those objects. As we have seen, some key texts in structural linguistics, Russian formalism (specifically Propp’s Morphology of the Folktale), and structuralism also considered the mathematical potential of combinations of finite elements, but in this case, elements of language and literature. The underlying 1

The name is a misnomer, as mathematical platonism (with a lowercase P) does not necessarily have any connection to Plato. Platonism (with a capital P) refers to Plato’s philosophy, yet few modern mathematicians would consider themselves Platonists.

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notion that language and literature are composed of semi-​fixed elements that can be shuffled was neither radical nor new, but using mathematics as a tool for producing or analyzing literature represents an original interdisciplinary development, especially when one considers using combinatorics to exhaust all possibilities as Oulipo does. Oulipo goes a step beyond Propp and other similar combinatorial literary studies in that the group not only recognizes the existence of patterns in literature, but additionally proposes to use mathematics as a tool to produce literature. Considering the goals of mathematics itself, the early Oulipo’s combinatorial impulse had the explicit goal of reducing the role of chance, as Claude Berge concisely declared in April 1962: “Nous aurons fait un grand pas vers nos définitions si nous admettons, par exemple, ce qui est mon avis, que nous sommes essentiellement anti-​hasard” (Bens, 2005, p. 146). In Chapter 1, I outlined the theoretical groundwork the founding members of Oulipo created and its historical, social, and mathematical influences, while Chapter 2 dealt with an evolution in the group’s procedural or algebraic constraints. These changes corresponded with a parallel development in terminology, as the notion of “experimental literature” (used by Le Lionnais in the postface of Cent mille milliards de poèmes) was progressively abandoned in favor of a more standardized vocabulary of “potential.” Terms such as “method,” “structure,” and “procedure” were also condensed into the more umbrella-​like term of constraint (Bloomfield, 2014, p. 34). This shift in lexicon is representative of a larger aesthetic evolution from purely procedural production to the more structural work produced by second-​generation members. These theoretical shifts occurred around the time of the first recruitment of new members, with the co-​opting of Jacques Roubaud in 1966, followed by Georges Perec in 1967 and Italo Calvino in February of 1973 (although he had been in contact with the group much earlier, as the first half of his first “explicitly” Oulipian text, Il castello dei destini incrociati, was published in 1969) (p. 34). These new additions had very tangible effects on the group’s public face, and several years later these members would make some of the most famous contributions to the group’s key anthologies: La Littérature Potentielle (1973) and Atlas de littérature potentielle (1981). With the publication of these collective volumes as well as the appearance of these

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authors’ Oulipian chef-​d’œuvres –​Roubaud’s ∈ (1967), Calvino’s Il castello dei destini incrociati (1969), and Perec’s La vie mode d’emploi (1978) –​came a profound shift in the notion of Oulipian constraint. Perec and Calvino in particular also developed the corresponding notion of clinamen, or the purposeful deviation from constraint on aesthetic grounds. This chapter examines Oulipo’s treatment of combinatorics, which is integral to understanding the complementary notions of patterns and chance. The first Oulipian text, Queneau’s Cent mille milliards de poèmes (1961), depends upon the principles of combinatorics and a few supplementary constraints to generate one hundred thousand billion poems from ten original sonnets. Roubaud, Calvino, and Perec, on the other hand, do not simply apply basic procedures to pre-​existing texts and structures as we saw in Chapter 2. Instead, they absorb notions of combinatorial potential and use them as a creative force, engaging with both the combinatorial literary criticism of the time as well as with parallel developments in mathematics and science. An examination of three key texts from these second generation Oulipians that depend largely on combinatorics and games of chance elucidates fundamental elements of Oulipian aesthetics: the role of chance and its countermeasure, the clinamen.

I. Raymond Queneau, Cent mille milliards de poèmes Raymond Queneau’s Cent mille milliards de poèmes (1961) is the first published Oulipian text and considered by scholars and Oulipians alike to be of great importance in the definition of the group’s aesthetics. For instance, Warren Motte (2006, p. 47) has claimed that it is the “seminal Oulipian text” while Jacques Roubaud has emphasized that it represents the first public display of the power of constraint and more specifically an illustration of literary potential (Roubaud, 2004, p. 101). It is also one of the few documents that Oulipo released in its first decade of existence apart from the Dossier 17: Exercices de littérature potentielle that Oulipo published in the same year in the Cahiers du Collège de ‘Pataphysique. Since the genesis of Cent mille milliards de poèmes predates Oulipo’s

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creation, standard Oulipian vocabulary such as potential or constraint is noticeably absent from the text, even though it is clearly a preliminary example of the potential of constrained writing. In an interview with Georges Charbonnier, Queneau (1962, p. 116) acknowledges this timeline while also confirming the importance of this text within Oulipo: J’avais écrit cinq ou six des Cent mille milliards de poèmes, et j’hésitais un peu à continuer, enfin je n’avais pas beaucoup le courage de continuer, plus cela allait, plus c’était difficile à faire naturellement, quand j’ai rencontré Le Lionnais, qui est un ami, et il m’a proposé de faire une sorte de groupe de recherches de littérature expérimentale. Cela m’a encouragé à continuer mes sonnets ; ce recueil de poèmes est, en quelque sorte, la première manifestation concrète de ce Groupe de recherches.

The fact that Queneau had been working on these poems since 1959 at the latest and that it was published in early 1961, mere months after the creation of Oulipo, explains why the group’s name does not appear in the volume. Le Lionnais’s post-​scriptum as well, “À propos de la littérature expérimentale,” indicates that the volume had gone to print while the group still referred to itself as the Séminaire de Littérature Expérimentale (Sélitex) until December 1960 (Bens, 2005, p. 28). Cent mille milliards de poèmes consists of an epigraph by Alan Turing, a curious preface by Queneau (called a mode d’emploi), 10 sonnets with the verses printed on individual strips of paper so the main body of poetry looks as if it exploded, and Le Lionnais’s post-​scriptum. In short, this is not a “traditional” volume of poetry by any means, and a reader must develop new reading strategies. This study forges its own approach, first through a preliminary analysis of the paratextual material and then a “close reading” of the text itself (in spite of the inherent difficulties in reading an exponential quantity of poems, most of which were produced by a combinatorial machine rather than a living author), which demonstrates the various influences on the early Oulipo, such as mathematics (more specifically, Bourbaki’s axiomatic method and the field of combinatorics), computer science, and surrealism. Although Cent mille milliards de poèmes illustrates the potential contribution of mathematics to literature through its combinatorial constraint, the epigraph is a direct reference to computers: “Seule une machine peut

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apprécier un sonnet écrit par une autre machine. –​Turing” (Queneau, 1961, p. 331). Gérard Genette (1987, pp. 145–​149) signals four main uses of the epigraph: as commentary on the title; as commentary on the text itself; as commentary on the identity of the author; and as commentary on the intellectual or cultural nature of the work. Queneau’s epigraph fulfils all of these uses, commenting on the exponential nature of the title, the poems contained within, and indicating an intellectual alliance with the logical, mathematical, and scientific work of Alan Turing. It also serves an additional purpose that is not theorized by Genette: it is a warning, for the reader is not a machine and will therefore (according to Queneau, at least) be incapable of appreciating this volume. Alan Turing (1912–​1954) was a British mathematician and one of the founders of computer science. In addition to his technical work, his theoretical understanding of computers and their capabilities were ahead of his time, as he demonstrated in a London Times interview, stating a slightly different version of Queneau’s epigraph: … I do not see why [a computer] should not enter any one of the fields normally covered by the human intellect, and eventually compete on equal terms. I do not think you can even draw the line about sonnets, though the comparison is perhaps a little bit unfair because a sonnet written by a machine will be better appreciated by another machine. (Quoted in Hodges, 2012, p. 420)

Queneau was an experienced English translator at Gallimard and is clearly not translating Turing directly, but paraphrasing his Times interview to suit his purpose. Turing’s original statement can be interpreted as a criticism of his contemporaries who maintained that computers would never be able to replicate human creativity. However, Queneau’s misquoting takes this to its logical extreme: not only can a machine produce a sonnet, but only a machine can appreciate a sonnet written by another machine. This interesting conflation of reading and appreciation is indicative of Queneau’s aesthetic goals. While it is true that a human reader would be unable to read all the potential poems, he or she would certainly be able to appreciate a certain subset and the potentiality of the collection. Indeed, the mere suggestion that machines are better able to appreciate

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a canonical Western poetic form can also be understood as a provocative commentary on the nature of poetry itself. Cent mille milliards de poèmes begins with a preface, unconventionally called a mode d’emploi. Genette’s (1987, p. 194) theorization acknowledges that a preface can function as a user’s manual, though he avoids reducing the nature of this paratext to a set of instructions: “ ‘La préface, disait Novalis, fournit le mode d’emploi du livre.’ La formule est juste, mais brutale. Guider la lecture, chercher à obtenir une bonne lecture, ne passe pas seulement par des consignes directes.” Queneau’s use of the term mode d’emploi is of an explicit nature, ostensibly telling the reader how to approach a text that has already been declared problematic. The use of this term is a provocative continuation of the epigraph’s mention of computers, as a mode d’emploi is a technical guide that traditionally accompanies a machine and teaches the user how to operate it. The implication is that Queneau’s text as well is mechanical and the reader needs specific instructions on how to use it. The use of this term is reminiscent of Nicolas Bourbaki’s textbook, Éléments de mathématique (1939), which also began with a mode d’emploi that was more concerned with the theoretical conception of the volume than with providing the reader with specific instructions. Likewise, Queneau’s user’s manual does not begin with rules for the reader to follow, but recounts the genesis of his text, claiming that it is inspired more by a children’s game called Têtes folles (where one creates dolls by recombining the parts) than surrealist games such as cadavre exquis. The cadavre exquis was a collective game practiced by André Breton’s surrealist group that assembled either words or images. To produce the image in Figure 3.1, several members of the group would draw a part of the image beginning with the end of a previous participant’s drawing. No single member would look at what had been drawn before, yet knew what body part their contribution was supposed to be.

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Figure 3.1.  An example of a surrealist cadavre exquis. Reproduced with permission from the Association Atelier André Breton and the photographer. See Bibliography for full citation.

On the other hand, the children’s game, Têtes folles, is similar in scope but mathematically regulated. It offers a child a booklet divided into three parts: head, torso, and legs. The child can flip the pages and create a complete body from a finite number of provided parts, as pictured in Figure 3.2.

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Figure 3.2.  An example of the children’s book Têtes folles. Reproduced with permission from Pascal Kummer. See Bibliography for full citation.

Queneau’s choice to compare the surrealist cadavre exquis to a children’s game could be seen as a provocative attack, especially given that Queneau himself had been kicked out of the group by his former brother-​in-​law, founding member André Breton. However, this confrontation could also be understood as an explanation of two opposing models for literary creation: on the one hand, a mathematical approach indicated by the reference to Bourbaki and the combinatorial approach of the Têtes folles; on the other hand, the counter-​example of surrealism, which hinges on the notion of artistic inspiration. Which model could prove more fruitful for literary creation? The emphasis on games inscribes this volume in a larger history of ludic literature, which has been defined and theorized by Warren Motte and Kimberly Bohman-​Kalaja as “Play-​Texts.”2 Bohman-​Kalaja (2007, p. 7) 2 See Playtexts by Warren Motte (1995) and Reading Games by Kimberly Bohman-​ Kalaja (2007).

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defines “Play-​Texts” as those in which “… the formal devices involved in the process of literary creation are foregrounded as aesthetic issues, especially as they complicate questions of reception and interpretation.” Queneau’s (1961, p. 333) text as explained in the mode d’emploi operates through a formal device in the process of literary creation, or in the author’s words, it is a “machine à fabriquer des poèmes, mais en nombre limité ; il est vrai que ce nombre, quoique limité, fournit de la lecture pour près de deux cent millions d’années (en lisant vingt-​quatre heures sur vingt-​quatre).” By creating a formal device to produce more poems than can be read in a human lifetime, Queneau complicates issues of reception and interpretation, rendering any formal analysis of the volume in its entirety impossible. As with the early procedural production of Oulipo introduced in Chapter 2, Cent mille milliards de poèmes has both analytic and synthetic elements, drawing from previous examples of constraint to produce something new. The method is reminiscent of the practices of the Renaissance poets known as the Grands Rhétoriqueurs, which were mentioned several times in early meetings by specialist Albert-​Marie Schmidt. Queneau’s system has much in common with Jean Molinet’s fifteenth-​century Sept rondeaux sur un rondeau, which even includes a few instructional verses that allude to the potential of the system: “Sept rondeaux en ce rondeau/​Sont tissus et cordellés,/​Il ne fault claux ne cordeaux/​Mettés sus, se rondellés” (Gray, 1999, p. 16). The following poem through its internal rhymes and specific syntactic structure can be read as seven different poems, all of which conform to the specifications of a rondeau. Cent mille milliards de poèmes produces more poems, but operates on a similar principle, making this volume an ideal illustration of both Oulipian tendencies: analytically, it respects the tradition of constrained literature (and specifically the sonnet) that precedes it; synthetically, it builds on the mathematical potential of combinatorics. The sonnet is a poetic form that depends upon a series of rules that determine the number of verses and stanzas, the types of rhymes, and the versification. The rest of Queneau’s mode d’emploi explains how he produced so many sonnets by adding a few new rules: first, he varied the vocabulary to eliminate monotony, specifying that the rhymes could not be too banal and that he had imposed a rule of using at least 40 different

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words in the quatrains and 20 in the tercets; second, each poem had to have a thematic continuity, while the poems formed by the combinatorial machine “n’auraient pas eu le même charme”; finally, the grammatical structure of the verses remained constant, which allows for their permutation: La structure grammaticale, enfin, devait être la même et demeurer invariante pour chaque substitution de vers. Une solution simple aurait été que chaque vers formât une proposition principale. Je ne me suis permis cette facilité que dans le sonnet nº 10 (le dernier !). J’ai veillé également à ce qu’il n’y eût pas de désaccord de féminin à masculin, ou de singulier à pluriel, d’un vers à l’autre dans les différents sonnets. (Queneau, 1961, pp. 333–​334)

This final constraint is the hardest, especially given the grammatical structure of the French language. To write lines that will grammatically recombine is an impressive linguistic achievement, much more difficult than finding interesting rhyming words. The fact that any verse in any sonnet rhymes with the corresponding verse in any other, coupled with these grammatical considerations allows Queneau to interchange the verses, producing 1014 potential sonnets. Queneau (1961, p. 334) then invites the reader to create, and not to read poetry: “… il est facile de voir que le lecteur peut composer 1014 sonnets différents, soit cent mille milliards.” Contrary to Queneau’s earlier insistence that this volume was inspired more by a children’s game than by surrealist practices, the effect of his poetic machine does indeed seem surrealist. However, the combinatorial principle at play rejects the role of chance, which is central to a cadavre exquis. Despite the aleatory nature of such surrealist practices, it is useful to note that practitioners of surrealism were similarly concerned with preserving grammar: “But as Aragon admits, surrealism is not a refuge against style. On the contrary, in the best of their works the surrealists’ grammar is impeccable. The most incomprehensible sentence could be parsed, for it is not the structure that is ambiguous but … the mating of words and the incongruous image that results” (Balakian, 1959, p. 164). Indeed, a text such as a cadavre exquis only functions because it is grammatical. Queneau’s insistence on preserving the grammatical structure in his sonnets and then shuffling the verses can be understood as an answer to surrealism using its own tools, as Queneau is able to produce incongruous

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poetry automatically, but through a mechanical process that was produced by an initial conscious reflection. After reading the paratextual material, the reader opens the volume and observes the unorthodox physical conception of this unique volume of poetry. Designed by Robert Massin, the volume itself is a visualization of the combinatorial possibility of the collection: the sonnets are printed on only one side of each page, and then cut above and below each verse, producing a set of “languettes” or strips (Figure 3.3). Such a design also touches upon what Queneau is doing to the sonnet, and to the book in general. It is only by ignoring the integrity of each of the original 10 sonnets and literally chopping them up that the collection functions as intended.

Figure 3.3.  A photograph of Robert Massin’s design for the Cent mille milliards de poèmes, beautifully executed by Maxime Fournier of SAE Institute Paris and reproduced with his permission.

Queneau’s mode d’emploi does not advise the reader on how to read the sonnets and can be best described as an attempt by the author to recount the genesis of his text a posteriori. In doing so, Queneau privileges

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the system he created to the content of the poems, which has had unfortunate consequences for the text’s critical reception. Most literary critics do not discuss the content of the 10 poems or any of their potential recombinations, but focus –​like Queneau –​on the physical conception of the volume and its implications. The conspicuous lack of more “traditional” forms of literary analysis such as close readings has two explanations: first, Queneau’s volume resists traditional literary analysis, as it is impossible to read in its entirety; second, the original volume as designed by Massin3 makes reconstructing Queneau’s original 10 sonnets (which do lend themselves to a close reading) tedious. A closer look at Queneau’s original 10 poems reveals certain commonalities between them. Each, for instance, exhibits the distinguishing features of Queneau’s writing: a sense of humor and an oddly antiquated (and sometimes foreign) vocabulary. Furthermore, more than half of them deal with themes relating to a particular part of the world, which results in individual verses that contain culturally specific vocabulary: the first recounts a trip to South America (using words like pampa, taureaux, gauchos, L’Amérique du Sud); the second talks about Greece and London (Parthénon, lord Elgin, climat londonien, la Tamise, Platon, Socrate, marbre); the third has a maritime feel (marin, poissons, requin, port, homards, etc.); the fourth is about colonial India (cinq o’clock, indigène, Du Gange au Malabar, Chandernagor, les Indes); the fifth moves from Italy to Avignon; and the sixth has a metropolitan setting (Queneau, 1961, pp. 335–​340). The final four poems speak more generally about poetic themes: the eighth deals self-​referentially with poetry and language while the tenth is a reflection on endings and death (Queneau, 1961, pp. 344–​342). The verses of these poems are thus tagged with specific terms, facilitating their identification as belonging to a particular poem. The final poem speaks directly to the reader, who has been agonizing to finish these poems:

3

In printing Queneau’s original 10 poems and not cutting between the verses, the Pléiade edition facilitates such a reading today. However, by printing each page recto verso, the editors have also prevented readers (even those who would consider taking scissors to a Pléiade edition) from producing their own recombined poems.

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Cela considérant ô lecteur tu suffoques Comptant tes abattis lecteur tu te disloques Toute chose pourtant doit avoir une fin (Queneau, 1961, p. 344)

This exhausted reader breaks to pieces (disloquer), counts his limbs, and resigns himself to the fact that everything must come to an end. However, Queneau’s poems do not end here. The reader can dislocate (disloquer) the individual verses from their respective poems, breaking the volume to pieces to have enough poetry to read forever. When shuffled, this specific vocabulary produces odd juxtapositions, for instance, resulting in a poem that includes gauchos and the leaning tower of Pisa with no logical continuity between them. While in the mode d’emploi, Queneau had facetiously claimed that the recombined poems do not have the “charm” of the originals, they are intentionally nonsensical due to this specific vocabulary.4 Indeed, as with the procedural constraints discussed in Chapter 2, semantic dissonance draws the reader’s attention to the artisanal labor that goes into crafting a text, making the artificiality of the form more visible. While Queneau might have conceivably defined an additional constraint, forcing him to write each poem about the same theme, he chose not to do so. I do not consider Queneau’s insistence on the grammatical and poetic rules of sonnets rather than on the content a mere oversight. Indeed, his choice of extremely specific subject matter for each poem demonstrates a desire to produce humorous, logically impossible, and geographically destabilizing results. The fact that the potential poems exhibit a lack of meaning that is antithetical to traditional poetry risks alienating the reader who, according to the paratextual material, makes the entire process possible. However, Queneau’s insistence on the impossibility of reading the volume in its entirety problematizes any notion of interpretation. Without being able to read all the poems, it is impossible to make a claim that no worthwhile poetry exists in the volume. While the vast majority of the poems in the 4

See my article in Digital Humanities Quarterly, “Digital Oulipo: Programming Potential Literature” (available online at ) for a discussion on how replacing Queneau’s sonnets with Shakespearean love poems results in less jarring substitutions.

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collection have no author, theme, or continuity and read like surrealist cadavres exquis, it is impossible to express a final judgment on the collection. Furthermore, an explication de texte or close reading of a single poem produced in this manner seems impossible, as one cannot speak of authorial intent or coherent themes. Though perhaps the fact that Queneau’s Cent mille milliards de poèmes resists traditional analysis can be understood as a commentary on the methods themselves, which might indeed blind readers to certain aspects of text by focusing on others. It must be mentioned that Cent mille milliards de poèmes is not a perfect system. In the mode d’emploi, Queneau mentions that he had taken the repetition of rhyming words into consideration when writing his base poems: “Il eût été, d’ailleurs, sans importance que de mêmes mots se trouvassent à la rime au même vers puisqu’on ne les lit pas en même temps ; je ne me suis permis cette licence que pour ‘beaux’ (substantif et anglicisme) et ‘beaux’ (adjectif )” (Queneau, 1961, p. 333). Even though he was conscious of this difficulty, there are actually three repetitions of this type: the A-​rhyme, marchandise; the B-​rhyme, beaux; and the E-​rhyme, destin. At these three places where the possible rhymes are identical (no verse is identical to any other individual verse), two of those repeat in the same verse, meaning that if substituted, they would not be identical to any other rhyme in the new poem. The rhyme “marchandise,” however, repeats in two separate verses, creating one instance where the new sonnet would have the same rhyme twice. Keeping those two verses constant and allowing for the permutation of the other verses creates 1012 “potential poems” that are not sonnets in the strict sense, as one rhyme repeats the same word twice. The glitch is not particularly disruptive for two reasons: first, this only constitutes 1 percent of the collection; second, the title (Cent mille milliards de poèmes) still holds, given that these invalid sonnets are still poems. Given the relatively small percentage of invalid sonnets, a reader of a digital edition of this text would be statistically unlikely to encounter a poem that did not conform to the rules of a sonnet. Rather than understand this as a failure, this glitch is indicative of a possible strategy for reading a volume that Queneau maintains is impossible to read. In the physical book, once the reader is aware of which rhyme disrupts the system, he or she can immediately see all the potential disruptions by purposefully choosing both marchandise verses.

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Like a machine, this critical attitude toward a glitch allows the reader to acknowledge the brilliance of the program while potentially improving it. Such a reader would have succeeded in reading like a machine, appreciating this collection for the technical capacity of the system. Bohman-​Kalaja (2007, p. 24) comments on Oulipo’s obsession with machine production: “The fundamentally ludic nature of Oulipian formal experimentation flirts with the mechanization of creative production. In an age of artificial intelligence and cybernetics, the group’s efforts and successes have pressing ethical implications concerning the production, reception, and interpretation of literary texts.” In the specific case of Queneau’s Cent mille milliards de poèmes, this mechanization of creative production can be understood as a commentary on three different types of automatism: computers, surrealist automatic writing, and mass production. The Turing epigraph, the volume’s design, and the glitch produced by the repetition of the rhyme marchandise imply a certain sensitivity to computers, which were very much on the minds of the founding members of Oulipo (see Chapter 4). In the 1960s as computers were being developed and quickly becoming a ubiquitous aspect of modern life, this new type of automatism had recently begun to supersede the surrealist use of the term, automatic writing as an expression of the unconscious mind. By creating a formal system reminiscent of computers to produce sonnets automatically, Queneau’s system produces poems that sound as though they could have been produced by surrealist automatic techniques. In this sense, the semantic dissonance created by the intentional shuffling of specific references is not only a joking critique of surrealist practices, but actually rivals it. Queneau’s recombined poems sound remarkably like surrealist writing without making claims about the nature of the unconscious or art itself. Through mathematical permutations, he proves that there is no need for recourse to the unconscious or dreams or collective writing to produce surrealist imagery, but that it can be reproduced mechanically through craft and cleverness. Furthermore, Queneau’s machine is far more efficient than surrealist practices, producing an exponential quantity of poems from a limited number of originals. The efficiency of Queneau’s system brings to mind mass production, a highly politicized concept in post-​war France, where American consumerist

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culture was proposed as a way to combat communism, ironically capitalizing on the same tools used in Nazi death camps for mass murder. While the ubiquitous nature of American products after World War II is not thematized in Cent mille milliards de poèmes, it could not have been far from Queneau’s mind after the recent publication and success of Zazie dans le métro (1959), in which the title character is obsessed with “bloudjinnzes” and “cacocalo.” Queneau’s sonnet-​producing machine is also reminiscent of mass production, devaluing the worth of the poetic form and reducing it to a set of arbitrary rules that, when manipulated correctly, can be exhausted. Furthermore, as properties of large numbers are often counterintuitive for those who do not study combinatorics, it is difficult to understand the sheer amount of poetry in this collection and how long it would take to read. When faced with the volume, the reader has the impression that the combinatorial results are cheapened poetry, uninteresting and nonsensical. This notion seems to have been predicted by Queneau as well, who used the rhyme marchandise not once, but twice, ironically creating a glitch in the collection. Since this is the foundational Oulipian text, a comprehensive reading is integral in understanding the group’s conception of its goals. By beginning with a highly constrained and prestigious literary form, the sonnet, Queneau constrains it further, unleashing the potential of the form itself. Combinatorics allows one to calculate the exact number of potential poems using exponents, adding a mathematical meaning to potential. This automatism, however, is to be distinguished from surrealist automatic writing. The resulting poems –​impossible to read in a human lifetime and written by no one –​have the status of “found poetry.” This is reminiscent of mathematical platonism in the sense that Queneau has created a system in which poetry is to be found. As with mathematics, one can study Queneau’s collection forever and never see the end. Taking these elements into account, this first Oulipian text provides an initial example of constraint, a demonstration of what this rhetorical strategy can accomplish, and emphasizes the peculiar nature of the reading experience. It is precisely the role of the reader that is developed through the group’s subsequent activities, and particularly by the second generation Oulipians Jacques Roubaud, Georges Perec, and Italo Calvino.

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II. Jacques Roubaud, ∈ (Signe d’appartenance) In 1967, Jacques Roubaud published a collection of poetry and received his doctorat d’état in mathematics. He had already been teaching mathematics at the Université de Rennes since 1958 after having abandoned his literary studies. A disciple of Bourbaki, he was also attracted to fixed forms in poetry and opposed to strict exams and concours. However, he kept his passion for poetry, composing a volume that is in part mathematical, in part an ode to the sonnet, and finally a game of Go. The volume, unconventionally titled ∈ (a mathematical symbol meaning element of or belonging to, commonly pronounced in French as signe d’appartenance), caught the attention of Queneau, who had it published by Gallimard and invited the young poet/​mathematician to join Oulipo, as Roubaud seemed the perfect confluence of mathematical and poetic thought. Roubaud’s interest in combining mathematics and poetry was predicated on the interrelated nature of both. As poetry depends upon the repetition of rhyming words, rhythmic counting, and organization of syllables, it is already inherently mathematical. Furthermore, the concept of fixed form poetry depends upon mathematical abstraction, which allows poets to generalize various types of poetry into categories based on their common structures. As Queneau demonstrated with the sonnets in his Cent mille milliards de poèmes, the rigorous definition of such common structures allows one to treat poetry mathematically, manipulating the form to exploit the combinatorial potential of language. The fact that Roubaud was also concerned with the sonnet and its poetic potential was a fortuitous coincidence, as it not only provided the impetus for his invitation to join Oulipo, but also created an important precedent for the incipient group that was already experimenting with various forms. Such experimentation with fixed form poetry elucidated the interrelated nature of Oulipo’s analytic and synthetic goals. While Roubaud’s treatment of the sonnet in this volume builds on a much longer tradition of fixed form poetry, his use of the game of Go is exceptional given the time and place in which this collection was composed. Go is an abstract strategy board game that has a long, illustrious history in

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Asia, where it was first invented in ancient China more than 2,500 years ago and then popularized in Japan, making it “the oldest game still played in its original form” (A Brief History of Go). Despite this enduring popularity in the East, it remained relatively unheard of in the West, where its practice was mostly restricted to Chinese-​American communities from the mid-​1800s onward. In 1960s France, it was equally obscure, known only to a handful of mathematicians, who appreciated its elegant nature and exotic origins. Indeed, the game of Go depends upon the increasingly complex combinatorial possibilities of a finite number of playing pieces (called stones) on a playing board of intersecting lines (known as the go-​ ban, of which the official size is 19 × 19, however smaller boards can be used for beginners or for those who prefer shorter games). Accompanying these simple materials, the game of Go is also regulated by a set of simple rules. However, as with the field of combinatorics and axiomatic thought in general, rule-​based combinations of a finite set of elements can lead to complex results. Given the complexity of this text, the following analysis is restricted to three facets of the volume: the mode d’emploi and its implications; a mathematical reading of the organization of the volume; and finally, an example of how to read excerpts in parallel with the game of Go. While the volume, by its combinatorial nature, is inexhaustibly rich, these three aspects of Roubaud’s poetics are important indications of Oulipo’s continued development of its mathematical ideals. The use of Go in particular opens new avenues for second-​generation Oulipian writers to compose longer texts that also attempt to play games with the reader, inviting him or her to participate in a new type of abstract thought. As Roubaud writes in his co-​authored treatise on the game: “Il n’existe qu’une seule activité à laquelle se puisse raisonnablement comparer le GO. On aura compris que c’est l’écriture” (Lusson et al., 1986, p. 42). Like Queneau’s Cent mille milliards de poèmes, ∈ begins with a mode d’emploi that serves as both introduction and instruction manual, a Chapter 0 that is divided numerically into five parts. The numbering system Roubaud introduces in the mode d’emploi, unlike Queneau’s which is not divided into subsections beyond individual paragraphs, applies to the rest of the volume as well, serving a critical organizational purpose. As with

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Queneau, Bourbaki is an important reference. The title of the volume, ∈, is itself a set-theoretical symbol introduced on the first page of part 1 of the first volume of Bourbaki’s (1939, p. I.14) Eléments de mathématique. On the first real page of the text, the first printed symbol before any alphabetic signs is §, which is identical to what Bourbaki used to designate the primary sections of his treatise. The first title of part 1, for instance, is printed “§1. TERMES ET RELATIONS” (I.14). Finally, Roubaud’s mode d’emploi is called Mode d’emploi de ce livre, an even more explicit import from Bourbaki’s Mode d’emploi de ce traité (Roubaud, 1967, p. 7; Bourbaki, 1939, p. I.3). Furthermore, Roubaud’s numbering system is reminiscent of the one introduced by Bourbaki in the Mode d’emploi de ce traité, but Roubaud’s structure serves a rhetorical purpose and is self-​contained, as it is restricted to a single volume. Roubaud’s mode d’emploi is divided numerically: 0.1 discusses the composition of the book and its contents; following that, 0.2–​0.5 propose four possible ways to read the text. The following poems are also divided into five parts which would indicate some sort of correspondence between the poetry and the five sections of the mode d’emploi. In 0.1, Roubaud explains: “Ce livre se compose, en principe, de 361 textes, qui sont les 180 pions blancs et les 181 pions noirs d’un jeu de go …” (Roubaud, 1967, p. 7). 361, it should also be noted, is the square of 19 as well as the number of intersections on a go-​ban. Roubaud’s explanation is true, but a deception, as his texts are more meaningful than just individual pieces in a game of Go. Each text belongs to various categories: sonnets, short sonnets, interrupted sonnets, prose sonnets, short sonnets in prose, citations, illustrations, grids/​tables, whites, blacks, poems, prose poems, categories that can be divided further based on types of rhymes or meters. Finally, the pieces also have different meanings, successions, or positions between them. The specific game of Go of which these poems are meant to be taken as pieces is reproduced in part in an annex (Figure 3.4).

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Figure 3.4.  The game of Go represented in Jacques Roubaud’s poetry collection, ∈ (p. 151). Reproduced with the permission of the publisher. © Éditions Gallimard. Tous les droits d’auteur de ce texte sont réservés. Sauf autorisation, toute utilisation de celui-ci autre que la consultation individuelle et privée est interdite.

The following four sections of the mode d’emploi introduce Roubaud’s four proposed “modes de lecture,” which the poet claims are independent of the preceding categorizations and subdivisions: “… les pions entretiennent entre eux différents rapports de signification, de succession ou de position. Ce sont certains de ces rapports (ou absence de rapports) que nous proposons au lecteur, selon quatre modes de lecture, explicités aux numéros

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suivants” (Roubaud, 1967, p. 7). The first of these reading strategies (0.2) encourages the reader to read certain diagrams of groupings of pieces in isolation, with the texts belonging to that group reproduced at the end of the diagram in a specific order. The second (0.3) suggests that texts can be read according to their “paragraph” divisions defined in the table at the end, each paragraph having a mathematical sign as a title, taken by the author “dans un sens non mathématique dérivé” even though Roubaud does provide definitions of these mathematical symbols immediately following the mode d’emploi (Roubaud, 1967, p. 8). Each of these numbered paragraphs is preceded by the same symbol as the mode d’emploi (designated as §0), implying a larger structural relationship between the six primary sections of the volume. However, Roubaud indicates that the system is merely an illusion of order, as the volume itself is incomplete: “Les paragraphes doivent être considérés comme ouverts: certains textes ne sont pas donnés, certains le sont fragmentairement, tous pourront être ultérieurement modifiés, partiellement ou totalement” (Roubaud, 1967, p. 8). This proposed reading privileges the reader’s freedom to draw personal associations between the paragraphs and their corresponding mathematical symbols. The third mode de lecture (0.4) challenges the reader to treat the book as a specific game of Go, reproduced in the appendix, but left unfinished (only the first 157 moves are given), the order of the moves indicated by the black and white circles in the text and a table at the end. Finally, the last option (0.5) is the lack of all rules: “On peut enfin, sans tenir compte de ce qui précède, se contenter de lire ou d’observer isolément chaque texte” (Roubaud, 1967, p. 9). This final strategy is a resignation that despite the author’s best intentions, the reader is free to read as he or she wishes. While Roubaud appears to offer the reader several ways to read the text, each mode de lecture comes with its own specific challenges. While 0.2 and 0.3 are at least approachable, helping the reader divide the text into smaller sections and find meaning in isolated excerpts, the third option in particular would have been nearly impossible given the obscurity of the game of Go in France at the time. Within this introduction, Roubaud provides no information about the rules or materials necessary to a game of Go. In the mode d’emploi, the only information provided about the game of Go is that there are 361 stones in a complete game and that this volume

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only concerns the first 157 moves in an unfinished game of Go. Should the reader wish to know the result of this game, he or she would have to find the cited edition of the Go Review (p. 8). Unbeknownst to the reader, however, Roubaud falsified this model for aesthetic reasons (Kiraly, 2016, p. IV). An honest attempt to follow Roubaud’s reading recommendations in 0.2 and 0.4 would require the reader to learn to play Go, the rules of which are briefly sketched out in an appendix following the poetry, which further indicates that: “Il n’entre pas dans notre propos de décrire complètement le jeu de go et nous renvoyons le lecteur qui ne connaît pas encore ce jeu aux traités spécialisés (cf. Bibliographie)” (Roubaud, 1967, p. 149). The bibliography, however, does not reference a single introduction to Go in French, as none existed at the time. Two years later, Roubaud collaborated with Perec and Pierre Lusson to publish the first French-​language guide to the game, Petit traité invitant à la découverte de l’art subtil du go (1969), a useful intertext when approaching this specific type of reading. Roubaud’s mode d’emploi can be understood on multiple levels. First, the mathematical division into paragraphs (0.2) provides a set-theoretical basis for the combinatorial possibilities contained within. Furthermore, the various groupings of texts and their relation to the game of Go set the stage for a game of combinatorial play between author and reader. On a pedagogical level, Roubaud’s modes de lecture serve as a critical introduction, effectively teaching the reader how to read. Finally, Roubaud’s use of the mode d’emploi is illustrative of a greater Oulipian tendency. Introducing mathematical or otherwise formal rules into the composition of a text compels an Oulipian to explain (or hide) certain aspects of those compositional methods. Roubaud’s use of the mode d’emploi can therefore be viewed as a second, more complex, development in Oulipo’s pedagogical aesthetics. Roubaud does not only recount the composition of his text and offer various strategies for reading in a literary adaptation of Bourbaki, but more importantly, he acknowledges the paradoxical nature of constrained literature: it sets up a literal game between author and reader of which the rules pre-​ exist the reading of the text; on the other hand, the reader is free to follow the rules or read as he or she likes. This creates multiple possible readings that coexist within a larger structure designed by the author, regulated by the mathematics of combinatorics. Akin to the role of the mathematician

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within the philosophy of mathematical platonism, the reader of Roubaud’s text must therefore discover the various possibilities within. Roubaud’s mathematical reading (0.3) depends on five mathematical symbols that are meant to be taken in a non-​mathematical way. The first, ∈ (both the title of the novel and §1), is described as “Signe substantifique de poids 2. En théorie des ensembles, signe figurant dans la relation d’appartenance. On écrit a ∈ A et on lit: a ‘élément de A’ a ‘appartient à A’ (Bourbaki, première partie, livre I, chap. II, § 1). Par extension, symbole de l’appartenance au monde de ‘l’être au monde’ ” (Roubaud, 1967, p. 11). To a reader unfamiliar with abstract mathematics, this definition would be incomprehensible, as it does not define key terms such as weight. While this mode de lecture does not require the reader to understand the mathematical meaning of the symbol, the mere act of choosing to follow this particular strategy plunges the reader into paratextual elements, explanations of non-​poetic symbols with referents that must be searched for elsewhere. In mathematics, “Signe substantifique de poids 2” indicates that this symbol refers to the nature or substance of two objects. However, Roubaud’s use of the sign in a non-​mathematical context gives it an added, poetic notion: that this symbol represents belonging to the world. This poetic meaning of a non-​poetic, mathematical symbol can be understood through Roubaud’s mode d’emploi as a key to reading the subsequent poetry, a theme that applies to the content of this numbered section, §1. For instance, one of the early poems begins as follows: “j’appartiens à tout non pas hier au feu demain à l’ongle à tout simultanément j’ai ce pouvoir qui n’est pas ce que je peux non ce que je suis j’appartiens …” (Roubaud, 1967, p. 17). This lyric je is a recurring narrative figure in most poems in the first section of this paragraph (1.1), with a few notable exceptions: 1.1.5, 1.1.10, and 1.1.14 are empty poems; 1.1.8 is a self-​reflexive rumination on abstract structures and the relationship between the parts; 1.1.9 and 1.1.11 do not use the first person, but instead address a second person, tu; 1.1.12 and 1.1.13 refer to either a singular, formal second-​person subject, vous, or multiple subjects; 1.1.16 refers to both the subject and his interlocutor using the first-​person plural, nous; 1.1.17 is a narrative description of someone’s life, but with no indication as to whose.

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It is therefore not simply a question of whether the poet belongs, but also the reader, who is just as much a participant in this strange game, separated from the lyric je narratively, physically on the page, and potentially even by the black and white stones of the developing game of Go. However, it is not just the game that is in question, but poetry itself, for the reader must decipher these “vingt-​neuf sonnets en prose, composant deux sonnets de sonnets suivis d’un pion isolé: ces deux sonnets sont séparés par un pion noir, les quatrains et tercets de chaque sonnet de sonnets par des pions blancs” (Roubaud, 1967, p. 4). The issue is more complicated than whether the poet and reader belong in the world, but additionally whether the poems in this “paragraph” belong to this general category. The symbolic title of the following paragraph, §2, is that of a proper subset: ⊃. This symbol designates one category as a “proper” subset of (or rather, part of but not equal to) another. However, Roubaud does not indicate a metaphoric understanding of this particular symbol. Given the orientation of this symbol in Roubaud’s volume, the set that follows would be the proper subset, or contained within what precedes, which could orient a reader in two ways. First, the reader could understand the entire section, §2, as a proper subset of the §1, or that the first contains all the elements of the second and more. Second, the meaning of this symbol could direct a reading of the contents of this part, for the sonnets in §2 form subsets of larger patterns, which the author already indicated could be taken as specific instances in Go. The mathematical symbol for the following §3, , is a logical symbol that Roubaud claims: “désigne les occurrences. Par extension, symbole de l’éventuel” (Roubaud, 1967, p. 11). It is used in both logic and mathematics to designate something that is provable, obligatory, or believed. The corresponding paragraph is: “… un sonnet court de sonnets courts en prose” (p. 90). While this short paragraph is supposed to symbolize the potential, the following §4 is indicated by the symbol, τ. This is known as “Hilbert’s tau,” a specific symbol to Bourbaki’s set theory that can be regarded as the result of some particular choice among all possible solutions. By extension, this symbol of choice follows a similar model to §2 in that it also contains certain poem patterns in which one can choose how to read. However, the content of this part is fragmentary, often reproducing poems in other

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languages that are cited in the Bibliography at the end, such as: William of Ockham’s Summa logicae (Roubaud, 1967, p. 112); citations of illustrations (as in Illustration de La petite marchande d’allumettes by Andersen (Roubaud, 1967, p. 113)); encyclopedia entries (Roubaud, 1967, p. 120); and a dialogue between J. C. Shaw and his computer (Roubaud, 1967, p. 124). It is up to the reader to choose which to prioritize: the poet’s text, fragments from other texts, or establishing relations between them. The mathematical symbol for §5 is even more disconcerting, as Roubaud invented it (Le grand incendie de Londres §195). The combination of two inverted ∈’s is a “symbole de la réflexion” (Roubaud, 1967, p. 11). This last paragraph, like the first, consists of prose sonnets. This symmetry highlights Roubaud’s intentional organization. Each paragraph contains various “species” of sonnets (likely a reference to Bourbaki’s “species of structures”) and the mathematical symbols taken in their metaphoric, derived senses allow the reader a vocabulary with which to treat these new subsections of forms. Taken as a whole, the poems in the volume are all elements of the larger, fixed form of sonnets; §2 is a proper subset thereof, demonstrating a great variety of typography and rhyme schemes; §3 is a prose sonnet composed of prose sonnets, a mise en abyme that represents the potential of the form; §4 represents choice, including some of the only “traditional” sonnets in the volume as well as excerpts from other poems and texts; finally, the unfinished prose sonnet in §5 allows the reader to reflect on which elements belong to each category. In his comprehensive reading of ∈, Jean-​Louis Kiraly hypothesizes why no academic work on this collection follows the two modes de lecture that depend upon a knowledge of Go: La force de ce préjugé vient sans doute du fait qu’il apporte le sentiment d’une difficulté extratextuelle, donc irréductible, qui ne saurait être surmontée par un seul effort de pénétration du poème, de la langue, ou d’éléments qui entreraient dans un champ de compétence purement littéraire. Il faudrait apprendre les règles d’un jeu, y jouer, et parvenir au moins au même niveau de compréhension du jeu que pouvait avoir l’auteur au moment de la composition ! La tâche apparaît alors d’autant plus ardue qu’elle se double parfois d’un contresens des plus dommageables : l’illusion que les règles elles-​mêmes seraient d’une difficulté redoutable. (Roubaud, 1967, p. 9)

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While it is understandable that literary critics who are not already experts in the art of Go would feel intimidated by the prospect of learning a new game, Roubaud’s volume helps introduce it to the reader by means of the first mode de lecture, 0.2, and offering the final strategy, 0.4, as an advanced task for experienced players. Indeed, the rules of Go are simple to learn, albeit difficult to master. Roubaud, Perec, and Lusson open their Petit traité with this encouraging notion: “Les règles sont simples et nous les graverons aisément dans notre mémoire” (Lusson et al., 1986, p. 38). Roubaud admitted his dissatisfaction with the critical response in his correspondence with Kiraly: Un tel écart entre la publication et une réaction telle que la vôtre montre que j’ai échoué dans une partie (qui me semblait importante) de mon projet en composant ce livre. Car la totalité des lectures critiques qui en ont été faites considèrent l’intervention du jeu de go comme un élément purement décoratif. Certes, peu de mes lecteurs (pas très nombreux de toute façon) sont des joueurs de go. Mais, si on prend au sérieux ce que je dis dans ma présentation, on peut envisager de confronter, comme vous, la représentation de la partie à l’original. J’en indique la provenance. Sans rien connaître du jeu lui-​même, des bizarreries apparaissent, qui suscitent, il me semble, des interrogations. Donc des questions à poser à l’auteur. Qui aurait répondu. (Kiraly, 2016, p. IV)

Fortunately, Roubaud found an ideal reader in Kiraly, whose pioneering work provides a close reading of the text in parallel with the corresponding unfinished game of Go as Roubaud suggests in 0.4. This study aims instead to illustrate the strategy proposed in 0.2 of the mode d’emploi, a pedagogical attempt on the part of Roubaud to introduce the reader to the game by considering groupings of texts: “dont l’organisation est symboliquement représentée par un diagramme, placé immédiatement en dessous du titre. Ce diagramme indique une position des pions sur la table de jeu. Cette disposition peut être une figure de go (Cf. Notamment page 64)” (Roubaud, 1967, p. 8). The overall game of Go as explained by Kiraly exhibits a dialogue between the experienced player (the white stones) and his novice opponent (the black stones). While the expert plays the first move, the novice is ultimately victorious due purely to the handicaps accorded to him by the expert at the outset of the game (Aoki, 1965, p. 14). In my view, Roubaud

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selected a game with this balance of players and outcome in order to mirror the structure he envisioned providing the reader. In this analogy, Roubaud expects an inexperienced reader to face off against a poet who is an expert not only in his artistic craft, but also in the art of Go. Roubaud’s modes de lecture can therefore be read as the equivalent of the handicaps, allowing the novice reader to read the volume successfully and win the game set up for him by the poet. A concrete example of how a reader can follow Roubaud’s instructions outlined in 0.2 can be found in the passage titled “situation de seki,” in which the relationship between the text and the game of Go becomes more clear (Roubaud, 1967, p. 65). The grouping has the title “Elégies et jardins” and defines seki as followed: “Les positions respectives des blancs et des noirs sont telles qu’aucun camp ne peut prendre l’avantage sur l’autre” (Roubaud, 1967, p. 65). ⚫ élégie: l’âge ⚫ (Rilke) ⚫ Deuxième élégie ⚫ (Samivel) ⚫ troisième élégie ⚫ troisième élégie

⚪ un loup ⚪ un jardin à Moret ⚪ un jardin ⚪ ensuite la nuit ⚪ dans l’horloge de fleurs ⚪ le dieu … ⚫ cinquième élégie

⚫ jets d’eau et soir ⚫ huitième élégie ⚫ huitième élégie ⚪ jardin second ⚫ sixième élégie

This rare occurrence in Go is better described in the Petit traité: “C’est une situation d’impasse … Le SEKI a lieu lorsque chaque joueur est dans la situation suivante: quel que soit le coup qu’il voudrait jouer pour prendre un groupe adverse, ce coup permettrait à l’adversaire de lui prendre son groupe. Dans ce cas, les deux groupes blanc et noir sont saufs, et les intersections vides ne sont à personne (et personne n’est obligé au coup suicidaire)” (Lusson et al., 1986, p. 71). Each stone in this diagram corresponds with one of the following sonnets. The opening of the first poem in the series, corresponding with “élégie: l’âge,” begins: “et chacun de vous se retourne sur son Eurydice de fumée/​qui du regard même se brouille évanouissante sans surseoir”

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(Roubaud, 1967, p. 65). Compared to the lovers Orpheus and Eurydice, these two lines have the opposite problem. Were one to move toward the other as Orpheus turned toward Eurydice, it is that player who risks everything. The following elegy, following an excerpt from Rainer Maria Rilke’s Die Sonette an Orpheus (which can be seen as a coda to the first elegy), ends with another reference, to Yzengrin the wolf, the mortal enemy of Renart, followed by a blank space referencing a “dessin de Samivel pour Le roman de Renart” (Roubaud, 1967, p. 67). The black stones (with the Rilke and Samivel codas, which speak about the same subject and offer the reader an alternate image) are all elegies as well as traditional verse sonnets whose scansions and rhyme schemes may vary, but which adhere to the traditional structure of two quatrains and two tercets. On the other side, the white stones and their corresponding sonnets are less regular, two of which (“dans l’horloge de fleurs …” and “un jardin à Moret”) are even suspiciously in prose, the only two prose poems that figure in a pattern within the volume. Another one, entitled “un jardin” is nothing but a series of dots, a blank in what otherwise would have been approximately the center of the pattern. The organization of these sonnets according to a particular situation in Go allows a reader to consider both Roubaud’s variations on the sonnet and the board game through a new lens. Pedagogically, Roubaud’s grouping of texts suggests that the reader can follow a linear path across these pages, examining each poem in the order Roubaud has placed them, and then read in other ways to determine possible relations between them, shedding new light on Roubaud’s interpretation of the malleability of the sonnet form. Looking at the thematic content of the poems forces the reader to consider the impossibility of couples in the seki situation, instructing a reader through poetry about the nature of this aspect of Go. By engaging with these small passages and musing over the meanings of individual poems, their relationships with one another, and how they represent a particular case in Go or the governing mathematical symbol, a reader is ready for the ultimate mode of reading, understanding the totality within a particular game as Kiraly has done. Roubaud’s work ultimately establishes a game between author and reader, in which the reader is afforded various handicaps by way of an instruction manual. While Roubaud does not focus on his compositional

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method, his mode d’emploi is a compelling paratextual addition that is illustrative of an evolving trend in Oulipian authorial intent between the first and second generations. While Queneau’s inaugural text insists on the impossibility of reading, the first generation’s early procedural constraints concern themselves exclusively with disrupting a reader’s familiar reading strategies through mechanical procedures. Roubaud’s mode d’emploi is the first Oulipian instance of an author explicitly indicating a pedagogical intent in the meta-​commentary, a strategy reprised and developed by Calvino and Perec.

III. Italo Calvino, Il castello dei destini incrociati5 Italian author Italo Calvino arrived in Paris in 1967 in the midst of a literary excitement for combinatorics, just two years after the publication of Tzvetan Todorov’s Théorie de la littérature and the belated French translation of Vladimir Propp’s Morphology of the Folktale and at a time when French literary theorists such as Algirdas Julien Greimas and Claude Bremond were beginning to elaborate on this work, broadening its scope to include the rest of literature. Having already engaged with such theories and incorporated them into his own work earlier in his literary career,6 during his time in Paris, Calvino sought to integrate himself into 5

6

This section represents a modified excerpt of an article I published in MLN 135 (2020), entitled “Italo Calvino’s Oulipian Clinamen.” For a more comprehensive understanding of Calvino’s approach to the clinamen, please consult this article, which also discusses the use of this device in Le cosmicomiche, Le città invisibili, and Se una notte d’inverno un viaggiatore in addition to the discussion of Il castello dei destini incrociati that is reproduced in a slightly modified version below. Upon his arrival, Calvino was already aware of such trends, having worked on the 1966 Italian edition of Propp’s Morphology of the Folktale at Einaudi and having reviewed his Historical Roots of the Wonder Tale (1946) as early as 1949. Calvino’s readings of Propp influenced his rewriting of Italian folktales in the 1956 collection Fiabe italiane, which the author indicates in his Introduzione of 1956 and in his Nota dell’autore all’edizione 1971 (XI, L).

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Parisian theoretical circles. He attended Roland Barthes’s structuralism lectures at the École des hautes études en sciences sociales (EHESS), published an article in A. J. Greimas’s Actes sémiotiques, and was co-​opted to Oulipo in 1973. Calvino (1980a, p. 210) notes in his essay “Cibernetica e fantasmi” that the world was increasingly understood as discrete rather than continuous: “Il processo in atto oggi è quello d’una rivincita della discontinuità, divisibilità, combinatorietà, su tutto ciò che è corso continuo, gamma di sfumature che stingono una sull’altra.”7 The emphasis on mathematics and more specifically combinatorics is no coincidence, as both Oulipo and theoretical schools such as structuralism had common origins in the structural linguistics of Ferdinand de Saussure and Russian formalism, as seen in Chapter 1. What distinguished Oulipo, however, was its explicit use of mathematics as a tool for literary composition through the notion of constraint. However, Oulipo devised an escape hatch from strict constraint known as the clinamen, defined by the group as follows: “For Oulipians, the clinamen is a deviation from the strict consequences of a restriction. It is often justified on aesthetic grounds: resorting to it improves the results … (A number of Oulipians, notably Italo Calvino, have felt that the clinamen plays a crucial role in Oulipian theory and practice)” (Oulipo, 1998, p. 126). Within Oulipo, Calvino attempted to apply notions of formal constraint and clinamen to his own work. The texts he produced under this Oulipian influence have clearly articulated, geometric structures that, while not generative, are often thematized within the texts themselves. In Atlas de littérature potentielle, Calvino classifies three texts –​Piccolo sillabario illustrato8 (1978), Il castello dei destini incrociati (1973), and Se una notte d’inverno un viaggiatore (1979) –​as either rigorously or partly Oulipian. However even Le città invisibili (1972) has Oulipian elements, notably a well-​formed geometric structure that Calvino presented at an Oulipo 7 8

“The ongoing process today is the triumph of discontinuity, divisibility, and combinatoriality over all that is in flux, or a range of nuances following one after the other.” (my translation) This is a short text published in the Bibliothèque Oulipienne that is a creative translation of Georges Perec’s Petit abécédaire illustré (1969).

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meeting (see Chapter 5). Each of these texts is composed of fragmentary units that are then arranged in a mathematical structure, which illustrates Calvino’s particular understanding of Oulipian work as providing a rigorous structure for recombinations of basic elements. Long before Italo Calvino or Oulipo, the term clinamen was first used by Lucretius, Epicurean philosopher and author of the first-​century bce poem, De Rerum Natura. The basic matter of Epicurean physics as described by Lucretius has two components: atoms (infinite in number but finite in shape and size) and void (within which the atoms combine). The atoms fall through the void and it is the swerve (clinamen) that allows for the creation of matter: Here too is a point I’m eager to have you learn. Though atoms fall straight downward through the void By their own weight, yet at uncertain times And at uncertain points, they swerve a bit –​ Enough that one might say they changed direction. And if they did not swerve, they all would fall Downward like raindrops through the boundless void; No clashes would occur, no blows befall The atoms; nature would never have made a thing. (Lucretius, 1977, II v. 216–​224)

For Epicurus, the clinamen is a distinctive factor: the atom that swerves does so of its own accord, not due to any external force, allowing for the concept of free will. Warren Motte (1986, p. 264) explains the most original facet of Lucretius’s clinamen: In his account, the mechanism of the clinamen is unclear, because its intervention seems to be largely unmotivated: “at uncertain times /​and at uncertain points.” And yet this is necessarily so, it is a deliberate tactic, insofar as the Epicurean-​Lucretian strategy depends precisely upon the injection of the aleatory into the motivated, upon the insertion of an element of chaos into a determinist symmetry.

The term was adopted first by the Collège de ‘Pataphysique, before being inherited by Oulipo while it was still a subgroup of the Collège. The ‘pataphysical clinamen is “the smallest possible aberration that can make the greatest possible difference” (Bök, 2002, pp. 43–​45). The

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Oulipian definition of clinamen as a deviation from strict constraint on aesthetic grounds seems to combine Lucretius’s original vocabulary with the ‘pataphysical clinamen, adapting this proposal that atoms can be combined in an infinite number of ways to language and literature, understanding the latter as discrete and combinable. It is worth noting that the definition of clinamen in the Oulipo Compendium quoted above is purposefully vague, neither discussing the origin of the term nor the way it was practiced by individual members of Oulipo. Furthermore, this explanation runs contrary to the group’s previous theorizations of constrained literature, paradoxically claiming that a deviation from strict constraint can improve the result. Independently of his work in Oulipo,9 Calvino (1988, p. 10) speaks of Lucretius in the first of his Lezioni americane with respect to his concept of “lightness”: “Al momento di stabilire le rigorose leggi meccaniche che determinano ogni evento, egli sente il bisogno di permettere agli atomi delle deviazioni imprevedibili dalla linea retta, tali da garantire la libertà tanto alla materia quanto agli esseri umani.”10 He continues to relate the Lucretian understanding of the universe to the combinatorial potential of letters in the alphabet,11 defining his personal clinamen in opposition to 9

According to Dennis Duncan (2012, p. 105), “We should also treat with caution the suggestion that Calvino’s understanding of the concept was mediated by Jarry, the Oulipo, or indeed any of the others who have adopted it, since he writes explicitly and admiringly of Lucretius, both as a poet and as a philosopher. It is of course possible that Calvino did learn of the clinamen from the Oulipo and subsequently traced the concept to its source, where he found much else to admire.” 10 “At the moment of establishing the rigorous mechanical laws that determine each event, he feels the need to allow atoms to deviate unpredictably from the straight line, so as to guarantee freedom both for matter and for human beings.” (my translation) 11 “… già per Lucrezio le lettere erano atomi in continuo movimento che con le loro permutazioni creavano le parole e i suoni più diversi; idea che fu ripresa da una lunga tradizione di pensatori per cui i segreti del mondo erano contenuti nella combinatoria dei segni della scrittura …” (“… already for Lucretius letters were atoms in continuous movement that, through their permutations, created more diverse words and sounds; an idea that was taken up by a long tradition of philosophers for whom the world’s secrets were contained in the combinatorics of the characters in writing”; 27; my translation).

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strict rules and aligning it with freedom, intrinsically linked to language and its potentiality. For Paul Harris (2012, pp. 74–​75), “… Calvino’s use of the clinamen involves a literalizing of the metaphor whereby it is incorporated into his textual dynamics as an underlying principle … Calvino sees the clinamen as the moment in the text which breaks the repetitive or closed code and generates new narrative lines …” As Calvino’s writing was explicitly influenced by the development and application of strict rules, we can understand these comments as reflective of the author’s attitude toward Oulipian constraint –​while he is intrigued by both implicit and explicit rules of literature, he is nevertheless skeptical of an overly scientific approach, necessitating the use of a clinamen. Calvino understands the term as a purposeful disruption of the structures of his texts. Nowhere is this oscillation between strict structure, combinatorial potential, and clinamen more apparent in Calvino’s œuvre than in his first full-​length Oulipian novel, Il castello dei destini incrociati, which is illustrative of a structural revolution in Oulipo’s mathematical project provoked by the members of the second generation as well as a clear example of the aesthetics of the Oulipian clinamen. As with the other texts in this chapter, Calvino’s text is filled with paratextual indications of how to read it: pictures of tarot cards line the margins, two full pages are devoted to the overarching arrangement of these cards in each section of the novel, and finally, Calvino recounts the genesis of this novel in an explanatory note that follows the text. An analysis of this paratext as well as the self-​referential language of the text demonstrates Calvino’s theoretical understanding of Oulipian constraint as fundamentally structural as well as his development of the clinamen. Il castello dei destini incrociati is a fragmentary novel told in two independent parts that are further divided into short stories, which draw from great classics of the western literary canon. While the individual elements that make up each half are distinct, the two parts have similar framing stories: a group of travelers, having lost their way in a forest and found shelter (in a castle for the first half, and tavern in the second), decide to kill time by telling their personal stories. However, they have lost the ability to speak and must use a deck of tarot cards to “tell” their tales. While Calvino’s approach to producing a coherent narrative made of shorter stories

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is reminiscent of a larger Italian tradition (such as Boccaccio’s Decamerone), it is distinguished through two primary aspects: Calvino’s individual tales are each accompanied by a series of tarot cards, through which the stories are told; the complete set of tales recounted in each half form a corresponding structure of tarot cards, also reproduced in two full-​page images within the text. Inspired by Paolo Fabbri’s presentation at a conference in Urbino ( July 1968) on “Il racconto della cartomanzia e il linguaggio degli emblemi,” Calvino had the idea to write a novel based on the combinatorial power of tarots. He began to experiment writing stories based on various combinations of cards in a deck of Marseilles tarot cards,12 which later became the second part of the novel, “La taverna dei destini incrociati.” While Calvino was only officially co-​opted in 1973, his interactions with Oulipo had begun much earlier and were probably informing this first attempt at constrained literature. Unsatisfied with his progress, Calvino began a new project at an invitation from publisher Franco Maria Ricci, similar in scope but with the Visconti tarot deck.13 The resulting text, “Il castello dei destini incrociati,” was published in part in 1969 as a contribution to the volume Tarocchi, Il mazzo visconteo di Bergamo e New York. Calvino eventually completed “La taverna” and published it alongside “Il castello” in the form that is most well known today, the novel Il castello dei destini incrociati (1973). Calvino’s explanatory note to this volume recounts this tortuous genesis and serves as a paratextual indication as to how to approach this unconventional volume: “This book is made first of pictures –​the tarot playing cards –​and secondly of written words. Through the sequence of 12 13

The Marseilles tarot card deck, very popular in southern France, was most likely invented in northern Italy in the fifteenth century. The Visconti tarot card deck was originally commissioned in the fifteenth century by the influential Visconti family of Milan. The design of the cards is generally attributed to Bonifacio Bembo, an Italian fresco artist. “The deck includes eleven trump cards, six court cards, including the King, Queen, Male Knight, Female Knight, Male Valet, and Female Valet, as well as the unusual addition of the three Theological Virtues, Faith, Hope and Charity. The unique addition of the female knight and valet may be an indication that this set was intended to be used by a female member of court” (Visconti Tarot | Beinecke Rare Book & Manuscript Library).

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the pictures stories are told, which the written word tries to reconstruct and interpret”14 (Calvino, 1979, p. 123). Because the number of cards at the characters’ disposal is limited to the 78 of the Visconti deck and 56 of the Marseilles, these narrators must construct their tales in such a way as to intersect with the cards already played. The cards in “Il castello” are assembled in intersecting rows and columns, with each row or column representing two stories (depending on whether it is read forward or backward), while the design of “La taverna” is less regular with individual stories forming odd blocks. In both cases, the tarot cards serve as building blocks whose various combinations create stories. Within the greater design, individual cards do not have fixed meanings, but the meaning depends upon the current story being read, allowing Calvino to consider them the equivalent of Propp’s functions (basic elements of narrative).15 While Calvino classified Il castello dei destini incrociati as Oulipian, it is clear from this paratextual commentary that he designed his tarot card structure with the end result in mind, making this far less strict than first-​generation Oulipian procedures, and certainly not generative, as Calvino (1992b, p. 1277) explains: “… cambiavo continuamente le regole del gioco, la struttura generale, le soluzioni narrative.”16 14 The Italian and English translations are slightly different, so I quote the English only when the Italian has less explanation. 15 “Bisogna tenere presente che alle carte corrispondono le funzioni del racconto, le quali sono in maggioranza (controllare su Propp) nefaste (l’ostacolo, la mancanza, la trasgressione ecc.) solo che l’astuzia retorica del racconto popolare (e ciò che la contraddistingue p. es. dalla tragedia, dall’histoire larmoyante ecc.) è che le carte faste sono disposte alla fine, come in una divinazione truccata (propiziatoria) mentre invece nella tragedia, nel romanzo larmoyant ecc. è il contrario (per scongiuro?)” (“It is necessary to remember that the cards correspond to the functions of the tale, which are mostly (verify in Propp) ill-​fated (obstacles, lack, transgression, etc.). Only that the rhetorical trick of the popular tale (and that which distinguishes it from tragedy, from the ‘larmoyante’ story, etc.) is that the cards put into play are laid out at the end, as in a rigged divination (propitiatory), whereas with tragedy or in a ‘larmoyant’ novel, it is the opposite (to conjure?)”; Fabbri; my translation). 16 “… I continually changed the rules of the game, the general structure, the narrative solutions.” (my translation)

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Calvino’s hybrid narrative complicates the reading experience by introducing various obstacles between the author and the reader, who are separated by multiple surrogates: each part is recounted by a narrator who is also a character and whose job it is to interpret the card-​based storytelling of the other characters. In this hierarchy, each element simultaneously carries out the parallel tasks of recounting and interpreting. For instance, the narrator of an individual story always begins by choosing the card that most closely resembles him and placing it on the table while the other potential narrators observe and interpret the wordless tale. The narrative unfolds as the “player” lays down a sequence of cards, which is reproduced in the margin of the text. The interpretation of each sequence is never the true story being told by any individual narrator, but is rather a “reading” of the cards by the narrator of the framing story. The narrators here are both readers and writers, trying to tell their own stories while simultaneously interpreting the tales of the others. At the end of “Il castello,” the narrator is unable to find his story in the mess of cards; in “La taverna,” on the other hand, the narrator has a moment when he too tries to tell his tale. The link between the author and narrator reaches an apex at the precise moment when the structures become apparent (Figure 3.5).

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Figure 3.5.  The completed tarot card design of the first half of Italo Calvino’s Il castello dei destini incrociati (p. 538).

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Calvino’s clinamen, which is programmed into the space itself, is best understood by taking each part individually. According to Calvino (1979, p. 126), “Il castello” was more successful than “La taverna:” “I succeeded with the Visconti tarots because I first constructed the stories of Roland and Astolpho, and for the other stories I was content to put them together as they came, with the cards laid down.” These two stories from Ludovico Ariosto’s classic, Orlando Furioso, occur just before the reader sees the completed tarot card structure and the final chapter, entitled “Tutte le altre storie.” In fact, immediately preceding the story of Orlando is the first explicit narrative description of the (still incomplete) tarot card structure: “Adesso i tarocchi disposti sul tavolo formavano un quadrato tutto chiuso intorno, con una finestra ancora vuota al centro” (Calvino, 1992a, p. 527).17 Orlando is the last of the characters to put any cards into play, with his tale of being driven to insanity filling in the previously empty center of the tarot card design. The conclusion of his tale emphasizes the importance of combinatorics and chance: “Era [La Giustizia] dunque l’immagine della Ragione quella bionda giustiziera con spada e bilancia con cui lui doveva in ogni caso finire per fare i conti? Era la Ragione del racconto che cova sotto il Caso combinatorio dei tarocchi sparpagliati?” (Calvino, 1992a, p. 531).18 Orlando believes he has understood: “Ho fatto tutto il giro e ho capito. Il mondo si legge all’incontrario. Tutto è chiaro” (Calvino, 1992a, p. 532).19 Naturally, the next story (that of Astolfo), is read backward, from the bottom to the top. The question of why Ariosto is central to this design draws from Calvino’s editorial work at the time. In 1967, Calvino retells this classic on the radio, a version which was published by Einaudi (without his 17

“Now the tarots placed on the table formed a square all closed on the edges, with a window still open in the center.” (my translation) 18 “Was it the image of Reason, that blond dispenser of justice with her sword and scales with whom in any event he would finally have to settle the score? Was she the Reason of the story, lurking under the combinatorial Chance of the scattered tarots?” (my translation) 19 “I have come full circle and I understand. The world must be read backward. Everything is clear.” (my translation)

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participation) in a volume entitled Orlando Furioso di Ludovico Ariosto raccontato da Italo Calvino (1970). A few years later, he writes a critical essay entitled “La struttura dell’Orlando Furioso” (1974). In both the essay and rewriting of Orlando, Calvino lauds Ariosto on the ingenious open structure, with which the author leaves space in the poem to follow whichever character he wants rather than another. To speak of the structure of Orlando Furioso is impossible, Calvino (1991a, p. 80) writes, “… perché non siamo di fronte a una geometria rigida: potremmo ricorrere all’immagine d’un campo di forze, che continuamente genera al suo interno altri campi di forze. Il movimento è sempre centrifugo; all’inizio siamo già nel bel mezzo dell’azione, e questo vale per il poema come per ogni canto e ogni episodio.”20 Ironically, to rewrite this classic tale in his Oulipian-​inspired text, Calvino must use it as a structural tool. Kerstin Pilz (2005, pp. 141–​142) argues that “it is the chaos which is symbolically introduced into the order of the square: the empty centre of the square is completed by the story of ‘Orlando pazzo per amore,’ who descends into ‘il cuore caotico delle cose, al centro del quadrato dei tarocchi e del mondo, al punto d’intersezione di tutti gli ordini possibili’21 …” While the subject matter alone could justify Orlando’s position in the center of the structure, the use of Ariosto’s open structure to complete the empty center of his own can be understood as an attempt at a clinamen: a way to destabilize his own geometrical structure with an unexpected chaotic element, Orlando’s madness (Figure 3.6).

20 “… because we are not faced with a rigid geometry: we could resort to the image of a force field, which continuously generates other force fields within it. The movement is always centrifugal; at the beginning we are already in the middle of the action, and this applies to the poem as well as to every canto and every episode.” (my translation) 21 “… the chaotic heart of everything, at the center of the square of tarot cards and of the world, at the point of intersection of all possible orders.” (my translation)

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Figure 3.6.  The completed tarot card design of the second half of Italo Calvino’s Il castello dei destini incrociati (p. 590).

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Whereas Orlando’s tale fills in the empty center in Il castello, La taverna’s has an empty center. The writing of La taverna is even more inferential than the first half, because the characters in La taverna tell their stories simultaneously, all reaching for the same cards. The young man who goes first must protect the cards he places down, complicating the reading of his story and the writing of new ones. The production of the final tarot arrangement is much less certain, almost chaotic, until halfway through when it is finally completed: Gli avventori della taverna si dànno spintoni intorno al tavolo che s’è andato coprendo di carte, sforzandosi di tirar fuori le loro storie dalla mischia dei tarocchi, e quanto più le storie diventano confuse e sgangherate tanto più le carte sparpagliate vanno trovando il loro posto in un mosaico ordinato. È solo il risultato del caso, questo disegno, oppure qualcuno di noi lo sta pazientemente mettendo insieme? (Calvino, 1992a, p. 582)22

The question of chance necessitates a clinamen, and as with the central story of Orlando in “Il castello,” this has a tangible effect on the writing, as the narrator now questions who really assembles the cards. At a certain point, Faust and Parsifal construct their stories simultaneously, using the same cards to discuss Alchemy and the search for the Grail. Unlike the clearly demarcated tales in “Il castello,” Faust begins laying cards at the bottom center while Parsifal begins at the center of the left-​hand side. At the spot where they should meet, there is a gap. Faust is a pessimist about the combinations of cards: “-​Il mondo non esiste … non c’è un tutto dato tutto in una volta: c’è un numero finito d’elementi le cui combinazioni si moltiplicano a miliardi di miliardi, e di queste solo poche trovano una forma e un senso e s’impongono in mezzo a un pulviscolo senza senso e senza forma; come le settantotto carte del mazzo di tarocchi nei cui

22

“The patrons of the tavern shove each other around the table that has been covered with cards, forcing themselves to get their stories out of the mess of tarot cards, and the more the stories become confused and disorganized, the more the scattered cards find their place in an orderly mosaic. Is this design just the result of chance, or is one of us patiently putting it together?” (my translation)

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accostamenti appaiono sequenze di storie che subito si disfano” (Calvino, 1992a, p. 589).23 Parsifal offers a different interpretation: “-​Il nocciolo del mondo è vuoto,24 il principio di ciò che si muove nell’universo è lo spazio del niente, attorno all’assenza si costruisce ciò che c’è, in fondo al gral c’è il tao, -​e indica il rettangolo vuoto circondato dai tarocchi” (Calvino, 1992a, p. 589).25 For Calvino, the fact that a destabilizing element is programmed into the center of the structure of both halves is telling. Whereas the center of “Il castello” was filled with a destabilizing force, in “La taverna,” it is precisely the refusal to fill this space –​the insistence on leaving a void in the center of the pattern –​that gives meaning to the chaotic text. While not truly generative as were the procedural constraints of the first-​generation “The world does not exist … there is not an all given all at once: there is a finite number of elements whose combinations multiply into billions of billions, and of these only a few find a shape and a meaning and impose their presence in the midst of a senseless and formless dust cloud; like the seventy-​eight cards of the tarot deck in whose combinations appear sequences of stories that immediately unravel.” (my translation) 24 The language of this quote bears a strong resemblance to Calvino’s preface to Cecchi’s Messico in 1985: “Quando una donna Navajo sta per finire uno di questi tessuti, essa lascia nella trama e nel disegno una piccola frattura, una menda: ‘affinché l’anima non le resti prigioniera dentro al lavoro.’ Questa mi sembra una profonda lezione d’arte: vietarsi, deliberatamente, una perfezione troppo aritmetica e bloccata. Perché le linee dell’opera, saldandosi invisibilmente sopra se stesse, costituirebbero un labirinto senza via d’uscita; una cifra, un enigma di cui s’è persa la chiave. Per primo, s’irretirebbe nell’inganno lo spirito che ha creato l’inganno.” (“When a Navajo woman is finishing one of these textiles, she leaves a small hole in the center of the design: ‘so that the soul does not remain a prisoner inside the work.’ This seems to me to be a profound artistic lesson: to forbid yourself, deliberately, from having a perfection that is too arithmetical and blocked. Because the lines of the work, invisibly soldered above itself, would constitute a labyrinth without an exit; a code, an enigma of which the key has been lost. For starters, the spirit that created the deception would be trapped within it himself ”; “Prefazione” xv–​xvi; my translation) 2 5 “‘The world’s core is empty. The principle of all that moves in the universe is the space of nothing. Around the absence, that which exists is built. Inside the grail is the tao,’ and he indicates the empty rectangle surrounded by the tarot cards.” (my translation) 23

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members, Calvino’s conception of constraint as a structural principle to be used not only in the composition of the text, but additionally to direct the reader in a new type of interpretive act is in line with the precedent set by Roubaud. Furthermore, the two halves of this text are elegant visual examples of the principle of clinamen. I would even argue that as Calvino’s most explicit illustration of the clinamen in his only novel-​length Oulipian text, Il castello dei destini incrociati was a pioneering force in the development of this aesthetic principle. However, Calvino’s use of constraint and clinamen is threatening in a number of ways to Oulipo’s original mathematical project: first, Calvino’s tarot card structure may be a narrative device, but it is not a generative constraint; second, his visually appealing spatial clinamens brought about by either literal or metaphorical destabilizations at the center of his structures cannot possibly be considered a deviation from a strict constraint, because the constraint itself was not strict; finally, his tarot card narrative device (regardless of whether it is generative) is in dialogue with various theoretical discourses outside of Oulipo,26 potentially contaminating the group’s legitimate intellectual inheritance of mathematical developments with formalist theories that only indirectly make use of mathematical thought. However, this novel entered into the Oulipian canon through its use of combinatorial play to create a fictional exploration of literary theory 26 For instance, Calvino admitted in a personal correspondence with Fabbri that his presentation had inspired him to use tarot cards as a way to experiment narratively with Propp’s formalism: “Bisogna tenere presente che alle carte corrispondono le funzioni del racconto, le quali sono in maggioranza (controllare su Propp) nefaste (l’ostacolo, la mancanza, la trasgressione ecc.) solo che l’astuzia retorica del racconto popolare (e ciò che la contraddistingue p. es. dalla tragedia, dall’histoire larmoyante ecc.) è che le carte faste sono disposte alla fine, come in una divinazione truccata (propiziatoria) mentre invece nella tragedia, nel romanzo larmoyant ecc. è il contrario (per scongiuro?).” (“It is necessary to remember that the cards correspond to the functions of the tale, which are mostly (verify in Propp) ill-​fated (obstacles, lack, transgression, etc.). Only that the rhetorical trick of the popular tale (and that which distinguishes it from tragedy, from the ‘larmoyante’ story, etc.) is that the cards put into play are laid out at the end, as in a rigged divination (propitiatory), whereas with tragedy or in a ‘larmoyant’ novel, it is the opposite (to conjure?)”; Fabbri; my translation)

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and Oulipian aesthetics. Regardless of the lack of a generative constraint, it is useful to consider Il castello dei destini incrociati as an imaginative visualization of the Oulipian conception of chance. In that sense, specific elements of Calvino’s technique including a playful combination of basic elements, a strict mathematical structure, and a destabilizing factor in an intentional location contribute to a more general theorization of constraint and clinamen. In this interpretation, a new question arises: did Calvino’s influence on Oulipo broaden its approach too much, derailing its mathematical project and leading to the subsequent development of less rigorous constraints that rely only on a metaphorical understanding of mathematical structures? While this may indeed be true, one could argue the opposite: that by freeing the group from the necessity of purely generative constraints, Calvino allowed for a more flexible understanding of the group’s synthetic goals. For the purposes of this study, it is important to acknowledge that Roubaud, Calvino, and Perec each disrupt the prior rigor of Oulipian constraints to varying degrees, and that Calvino’s infractions are clearly the most severe. However, it is equally true that Il castello dei destini incrociati is perhaps even more apt at fostering mathematical thought in an Oulipian reader than purely procedural operations, as it teaches the reader to recognize abstract patterns within a larger structure, employing a formal narrative mechanism to discern familiar stories in various combinations of basic elements. In this sense, Calvino’s text is a reinvention of mathematical platonism for literature, suggesting that classic stories are of an elemental nature, interspersed in modern literature and meant to be discovered by a reader.

IV.  Georges Perec, La Vie mode d’emploi Georges Perec was co-​opted by Oulipo in 1967, two years after the publication of his first novel, Les Choses (1965). While the sociological nature of this novel appealed greatly to critics and won the author the prestigious Renaudot prize, Perec’s subsequent Oulipian production was of an entirely different nature. Within Oulipo, Perec excelled at finding the

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most difficult constraints and exhausting them, publishing his famous La disparition in 1969 without the letter E and then a peculiar sequel to this constraint (but not to the novel), entitled Les Revenentes (1972) in which E was the only vowel used. Within the group’s two collected volumes of that period, La littérature potentielle (1973) and Atlas de littérature potentielle (1981), Perec was also an enthusiastic and prolific contributor not only of constrained texts, but also of theoretical essays such as his Histoire du lipogramme. La Vie mode d’emploi (1978) is not only Perec’s best-​known novel, but also his most ambitious in terms of the underlying Oulipian constraints, which, unlike in the preceding works by Queneau, Roubaud, and Calvino, do not overtly manifest themselves in the reading of the text. Indeed, one can read the entire novel without any knowledge of the compositional constraints that generated it, enjoying the overarching plot as well as a great number of interrelated tales. The eccentric millionaire protagonist of the novel, Percival Bartlebooth, devises an intricate but ultimately useless life project, meant to exhaust his entire fortune. This project involves the participation of several inhabitants of his building: he spends a decade learning the art of watercolors under the instruction of painter Serge Valène; another 20 years traveling the world with his faithful servant Mortimer Smautf, painting watercolor landscapes of ports; upon completion, Bartlebooth has each painting cut into a puzzle by artisan Gaspard Winkler; Bartlebooth then devotes the rest of his life to reassembling the puzzles; once completed, each puzzle is subjected to a chemical process designed by Georges Morellet to eliminate all traces of the cuts; finally, the completed and restored watercolor is destroyed. The puzzles become more difficult, however, and Bartlebooth grows older, becoming blind. He might have completed his task were it not for the antagonistic Winkler, who set his revenge into motion early on. While this main plot makes for an enjoyable read, the reader does not get the facts in the order I have just provided. Instead, the story is told out of order, describing every room of a fictional Parisian apartment located at the imaginary address, 11 rue Simon-​Crubellier, in great detail: the objects within, the decorations, the history of their ownership, and the stories of the inhabitants. As with Calvino’s Il castello dei destini incrociati, the

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fragmentary nature of Perec’s work and the ostensibly disorganized reading experience attest to the novel’s unique compositional methods. Indeed, Perec envisioned it as a complex layering of structural and thematic constraints (of which some Perec chose to reveal and others he kept to himself ), the totality of which constituted a machine for writing stories. While the sheer number and variety of constraints that went into the composition of this novel seems intimidating, Perec’s machine worked, allowing him to produce an Oulipian novel, the first of its length and narrative complexity. Perec’s multiple compositional constraints find a parallel in the reading experience, as a reader can choose to read in a variety of ways. Perec even provided a thematic index, which allows the reader the possibility to read individual narratives linearly. It is precisely the complex relationship between the compositional constraints of the author and the freedom of the reader that is central to this combinatorial discussion. A linear reading of La Vie mode d’emploi is somewhat jarring at first. The descriptions of individual locations in the apartment building are filled with details, most of which have little to nothing to do with the main story of Bartlebooth. La Vie mode d’emploi was initially conceived as a response to a challenge by Jacques Bens in an Oulipo meeting: could Oulipian constraints be used to produce a longer text, a large novel? Perec’s solution, first proposed on November 8, 1972, was to compound the initial problem with more constraints that would determine the content of the text as well as its organization (Bellos, 1993, p. 513). To determine the content, Perec devised a mathematical system, described below; to determine which order to proceed through the building, Perec wanted a constraint that would appear random to the reader, but that would actually be mathematically organized by a particular solution to a famous problem in chess, the knight’s tour.27 It is worth noting that Perec often hesitated between 27 There are multiple reasons for which Perec might have used the Knight’s Tour. By the time he had joined Oulipo, co-​founder François Le Lionnais was mostly senile and had little to do with the group. However, perhaps as an homage to this chess grand master, Perec chose a spatial constraint dealing with chess. Le Lionnais, a chemical engineer, spent the Cold War studying the art of chess, even publishing the Que sais-​je? volume on the subject in 1974. Marcel Duchamp as well, foreign correspondent to Oulipo, was often inspired to represent chess in his artwork, a

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revealing the compositional means of his works and keeping them hidden. After La disparition, his fear was that once the reader knows the constraint, he or she sees only the constraint. For La Vie mode d’emploi, that oscillation between hiding the constraint and boasting of his accomplishments is further complicated by two texts: an issue of L’Arc in which Perec published an article entitled “Quatre figures pour La Vie mode d’emploi” that explains the basic constraints he used to produce the text; and the Cahier des charges de La Vie mode d’emploi, a posthumously published edition of Perec’s manuscripts. The knight’s tour problem seeks to answer the simple question: is there a path that the knight can take in which it would hit every square on a traditional 8 × 8 chessboard once and only once? A knight in chess can move in eight possible ways, each a jump that places it one square in one direction and two in a direction perpendicular to the first. The knight’s tour is an ancient problem with many solutions, each of which exhibits mathematical properties whose study leads to a greater understanding of combinatorics. There are two main types of tours: those that are circular (ending at the same place they begin) and those that are not. However, Perec’s apartment building is larger than a traditional chessboard and can be represented as a 10 × 10 grid with the façade removed. Perec therefore had to find his own solution, succeeding “… par tâtonnements, d’une manière plutôt miraculeuse” (Perec, 1981b, p. 390). None of his work on finding a particular solution can be found in his preparatory documents. While his solution (depicted in Figure 3.7) is not circular and not particularly elegant by mathematical standards, it takes on an added significance within the context of the novel.

passion that led him to befriend Le Lionnais and Raymond Roussel. Perec was also a lover of games, though not particularly fond of chess, as evidenced by the language in the Petit traité invitant à la découverte de l’art subtil du go, in which he deplores: “la fâcheuse popularité de ce jeu minable en France” (Lusson et al., 1986, pp. 23–​24).

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Figure 3.7.  The knight’s tour problem solved by Perec for determining the chapter order of La Vie mode d’emploi, as reimagined by OuPeinPo member Philippe Mouchès. Reproduced with the artist’s permission.

Perec’s novel starts in the staircase, grid number (6,6) and proceeds to exhaust the board. However, the square that should have been the 66th move is missing, representing the clinamen and making it impossible for a reader to reconstruct the knight’s tour from the book alone. Whereas Calvino’s clinamen was literally central to the structure, Perec’s is found in the basement, in the bottom left-​hand corner. The similarity between the number of this skipped move, 66, and the grid location of the starting square, (6,6), indicates that Perec had planned this clinamen from the very beginning. It is also the inversion of the number of chapters (99), and may be a reference to Queneau’s 99 variants in Exercices de style. Furthermore, the location of this absence is thematized within the novel, when right before the missing room, a little girl bites the corner of her “petit-​beurre” cookie

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(Perec, 2017b, p. 365). The knight’s tour offers the reader a non-​sequential path through an apartment building that would otherwise be impossible to navigate as it has no depth, no corridors, and no courtyard. Perec’s chosen method of navigating through this flat space is equally impossible, given one cannot move through an apartment building like a knight would on a chessboard –​only a novelist can. However, the “petit-​beurre” cookie example is indicative of how Perec uses this mathematical constraint to generate a self-​reflexive narrative. A careful reader must remain alert to Perec’s method to understand the subtle interplay between form and content. Once Perec settled on the organizational principle for the chapters, he needed to devise a system through which he could order everything else. A Latin bi-​square of order 10 determined the placement of various elements in response to fellow Oulipian Claude Berge’s challenge: to use a recently discovered property of Greco-​Latin bi-​squares to direct the content in a way that would appear random but was in fact regulated. A Greco-​Latin bi-​square is a way to order two distinct sets of elements, such that every row and column contains each element of both sets exactly once and no two cells contain the same combination of elements. Until 1959, mathematicians had thought that a bi-​square of order 10 (10 rows and 10 columns) could not exist, but it had recently been proved that such a bi-​square was possible. For Perec, this was an excellent method for shuffling a predetermined number of elements to create the impression of randomness to any reader who did not have the system at his or her disposal. Given that Perec had a total of 420 “things” to distribute throughout his novel, he sorted them into 21 bi-​squares, each containing two lists of 10 elements. Rather than using the same bi-​square 21 times, Perec chose to use a variant based on Queneau’s mathematical work on the sestina. As mentioned in the introduction, Queneau had devised a way to generalize the sestina permutation, rewriting this medieval poetic form in a formalized, mathematical language, discovering that it worked for numbers other than 6. This discovery led Queneau to create “quenines,” or variants on the original form with a different number of stanzas and verses. This is how Perec was able to vary his orthogonal bisquares, by grouping into sets of four and subjecting them to a sestina-​like rotation using a “pseudo-​ quenine” based on Queneau’s generalized sestina, a permutation of elements

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that did not change the pairs of elements, but rather their respective positions within the table. The result of this is that Perec’s structure is more complex, less rigidly determined, and therefore less predictable. While these constraints are interesting, they may seem arbitrary to a reader who is unfamiliar with Oulipo. Perec alluded to several inspirations in Espèces d’espaces (1974), citing “Le Diable boiteux,” a scene of a game of Go in Gengi monogatori emaki, and Saul Steinberg’s illustration in The Art of Living (1952) of a building with the façade removed as inspirations for the overall project (Perec, 2017a, p. 589). He describes Steinberg’s drawing in great detail, explaining that “Un examen un peu plus attentif du dessin permettrait sans peine d’en tirer les détails d’un volumineux roman …” (Perec, 2017a, p. 86). He also makes some general comments about the nature of apartment buildings that could be understood as the beginnings of the theoretical foundation of La Vie mode d’emploi. However, Perec does not explain his more complex constraints nor how he chose them, and the number of lists, 42, does not appear to have any additional meaning. The “Quatre figures” article is the only place where Perec explicitly and publicly lays out the constraints in writing, but there are also three “secret” constraints not contained within and not accounted for by the Cahier des charges, which he explained orally at a meeting of the Cercle Polivanoff on May 17, 1978, but “… he regretted having done so, and said he would never be so indiscreet again” (Bellos, 1993, p. 593). Nevertheless, we now know that (1) each chapter inscribes within itself its own grid location (usually given in digits, not literals–​although most numbers in the novel are written in literals), leading to an inscription of the novel’s own arithmetical plot; (2) each chapter contains an allusion to one other work by Perec, including texts not yet published in 1978 or future projects; (3) each chapter contains a reference to something that happened to Perec during the writing of it. These secret rules formalize the self-​referential aspect of the novel, inscribing the author’s life (in details known only to him) and work within this novel, appropriately titled La Vie mode d’emploi. The only constraint that Perec adhered to without fail was the organizational principle of the chapters. However, the subsequent levels of constraints had to be methodically documented as well. The novel’s plurality of tales and styles is rooted in part in these constraints, demonstrating the

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writer’s narrative skills as well as in non-​narrative forms of writing. For instance, two of his lists force him to cite other authors, reproducing (but not necessarily citing) excerpts from works by: Kafka, Borges, Flaubert, Leiris, Roussel, Verne, Sterne, Queneau, Mathews, Proust, Lowry, Roubaud, Rabelais, Stendhal, Joyce, Butor, Mann, Freud, Nabokov, and Calvino (Perec, Cahier des charges de La Vie mode d’emploi). The variety produced by this intertextuality complicates the notion of style, as much of the content was not written by Perec. With so many elements determined in advance by mathematical, combinatorial shuffling –​the place of each chapter in the novel’s sequence, the position of the room in the apartment building, and the 42 different things to say about each room –​Perec expected the novel to write itself. However, the primary plot about Bartlebooth and his puzzles does not appear in these preparatory documents. The intense combinatorial nature of La Vie mode d’emploi as evidenced by its knight’s tour ordering mechanism and its Greco-​Latin Orthogonal bi-​square facilitated the writing of the novel to a certain extent, but the true substance of the work is unrelated to the rules that supposedly generated it. La Vie mode d’emploi begins with two epigraphs that seem to contradict one another. The first epigraph, to the novel itself, reads: “Regarde de tous tes yeux, regarde ( Jules Verne, Michel Strogoff)” (Perec, 2017b, p. 5). When taken in full knowledge of Perec’s published and secret generative constraints, this seems to be an authorial invitation for the reader to uncover them. However, the epigraph to the preamble says the opposite, implying that the reader of the novel will be invisibly guided by an authorial hand: “L’œil suit les chemins qui lui ont été ménagés dans l’œuvre. –​Paul Klee, Pädagogisches Skizzenbuch” (Perec, 2017b, p. 7). The combination of these two epigraphs holds with the previous analyses of Queneau’s, Roubaud’s, and Calvino’s texts. Intentionally constrained literature creates a system that guides the reader, who must be at least implicitly aware of his role. The resulting role of the reader is reminiscent of mathematical platonism, implying that he or she should search for those intentional paths created by the author. Vladimir Nabokov’s The Real Life of Sebastian Knight, indicated by Perec in the “Quatre figures” essay as one source of inspiration for La Vie mode d’emploi, discusses an author’s unknown, lost book. At one point, the

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narrator declares: “It is not the parts that matter, it is their combination” (Nabokov, 1959, p. 176). This holds true for Perec’s novel as well, which has multiple paths whose combinations lead to the instant fatal where Bartlebooth, hunched over an incomplete puzzle, has just died. While the reader might have only noticed a few oblique signs about Bartlebooth’s illness throughout the novel, all the necessary information to process such a conclusion was provided earlier, hidden among a great mass of information. Through a repetition of the date and time –​“C’est le vingt-​trois juin mille neuf cent soixante-​quinze et il sera dans un instant huit heures du soir …”28 (Perec, 2017b, p. 576–​578) –​the reader understands at last that everything has taken place in one instant, the instant of Bartlebooth’s death. As with a mathematical theorem, such a revelation is supported by everything that came before it. A mathematical demonstration contains only that which is necessary, whereas Perec’s text is filled with superfluous information. The difficulty lies in constructing Bartlebooth’s story from the unsorted pieces that precede the revelation, of which even seemingly innocuous references can play a large role. For instance, the tiny detail of an ostensible proof of Goldbach’s Conjecture in chapter LXXVIII –​“… note sur le problème de Goldbach, proposant que tout nombre n soit la somme de K nombres premiers …” (Perec, 2017b, p. 427) –​is applicable to this final moment. Goldbach’s Conjecture is a heuristically observable and demonstrable mathematical notion, true for all observable cases, but seemingly impossible to prove: any even number is the sum of two primes. Bartlebooth dies without quite finishing the 439th puzzle, which means 61 of the 500 total puzzles remain unsolved. However, the number 61 also refers to the location of the room within the apartment building, indicating that Perec had planned this from the start. Since both 439 and 61 are prime numbers, this clin d’œil is a demonstration of the Goldbach Conjecture. While not a proof, its appearance at the end of the novel feels like a eureka moment that the mathematician has at the end of a theorem. 28 This date and time have a personal meaning for Perec, as it marks the beginning of his relationship with Catherine Binet: “Don’t you see, Perec later explained to Catherine, it’s when the old man died” (Bellos, Georges Perec: A Life in Words, chap. 54).

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La Vie mode d’emploi is missing a chapter, the notion of space, the third dimension, and yet somehow still manages to communicate a story. It is filled with a number of interrelated stories, told out of order, yet regulated by an intricate network of constraints. It contains multiple paratextual and intertextual elements, including epigraphs, excerpts from other literature, diagrams, mathematics, and even an index. These generative jumbles create a “network of connections,” the sensation of an infinitely varied but nonetheless self-​contained object, and that is what makes the book so powerful and gives the reader the impression of exhaustiveness. And yet, knowledge of how the book was created is entirely unnecessary to reading, understanding, and enjoying the novel. In the Perecquian (and indeed, Oulipian) debate of whether to conceal or reveal the underlying constraints, La vie mode d’emploi occupies a precarious position. It has an impressive documentation about the genesis of the novel, but that documentation has almost nothing to do with the novel. As with chess, one only needs to know the basic rules in order to enjoy it, whereas mathematically speaking, there is much more to be discovered in the combinatorial potential of the board and its pieces. Oulipo’s theoretical framework as defined by Le Lionnais in the manifestos grounded itself in set theory, aiming to create an analogous project in literature. Meanwhile, the majority of Oulipian production for the first two decades was procedural in nature, offering various mechanical methods to apply to literature through a set-theoretical understanding of language. Equally important in the early conception of the group was Queneau’s interest and expertise in combinatorics, which he inscribed into the group’s mathematical project by way of Cent mille milliards de poèmes. While Le Lionnais was responsible for penning the explicit goals of the group in the manifestos, Queneau’s role as co-​founder was to set these abstract goals into motion through the creation of a literal example of potential literature. In this sense, compared to Le Lionnais’s set-theoretical manifestos, this reading of Queneau’s Cent mille milliards de poèmes situates combinatorics as the second pillar upon which the group’s mathematical project was based. This foundational text therefore sets important precedents for all subsequent Oulipian creation, most notably a pedagogical imperative through the unconventional use of the mode d’emploi. While Queneau’s mode d’emploi can be read as a coy warning to the reader that the volume

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is impossible to read, for Oulipian authors, this meta-​commentary opens a crucial debate on whether or not it is necessary to explain the constraint to the reader. Individual members of Oulipo have taken sides, and some (such as Perec) have oscillated between these two poles, but at the heart of this debate is a focus on the reader, who is central to Oulipian aesthetics. As with mathematics, one does not simply read linearly on the page to discern meaning, but one must actively work to understand the solution. Queneau’s Cent mille milliards de poèmes demonstrates an implicit understanding of this pedagogical intent, which was then reprised by later generations of Oulipians. Through his continued use of the mode d’emploi, Roubaud expands upon this precedent, making his pedagogical intent more explicit and literally instructing the reader how to read while continuing to reference Bourbaki. This marriage of Le Lionnais’s theoretical objectives and Queneau’s practical results solidified Roubaud as the successor to Le Lionnais in terms of the definition and clarification of Oulipo’s mathematical project. Indeed, Roubaud has continued to combine both founders’ goals theoretically and in his individual texts. However, while Roubaud’s ∈ and its mode d’emploi share similarities with Queneau’s, his text does not contain an explicit meta-​commentary on its compositional methods and focuses instead on the finished product and how the reader should use it. In his explanatory note to Il castello dei destini incrociati, Calvino returns to Queneau’s side of the debate by explaining his compositional methods. However, the methods he uses are at odds with Oulipian techniques that came before it: first, he deviates from any sort of generative constraint, breaking from the prior Oulipian emphasis on rigor; second, his increased emphasis on the destabilizing role of the clinamen in the text sets a new aesthetic precedent; finally, Calvino’s integration of formalist French and Russian theories of the time introduces a potential contamination of the pure mathematical thought that was at the heart of the group’s initial project. This is a decisive rupture from the original mathematical project put forth by Le Lionnais and first-​generation members, with two main consequences: it makes the mathematical aims and products far less rigorous going forward; on the other hand, it pushes the strict boundaries implied by the group’s initial goals, making Oulipo more flexible and open.

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Thus Calvino was able to fail at strict mathematical constraint, yet still be inspired by mathematical structure. Perec’s use of constraint and clinamen was similar, but more rigorously applied, leading to the impression of chaos despite the fact that La Vie mode d’emploi was meticulously ordered from the start. This creates a puzzle (a metaphor commonly used by Perec within the novel) for the reader to solve. However, Perec’s partial sharing of constraints and use of the clinamen thwart the reader in any attempt at grasping the full complexity of the novel’s genesis. Like mathematical platonism or Bourbaki’s image of mathematics as structure, Perec’s novel can never be exhausted by a reader and, in one sense, it even exhausted its author through its combinatorial potential. These three authors of the second generation of Oulipo bend the rules of mathematically constrained literature to varying degrees, changing the nature of the group’s mathematical project. This aesthetic shift can be criticized as cheapening the intellectual project first envisioned by François Le Lionnais in the early 1960s, one that situates Oulipo as an intellectual inheritor of Bourbaki. However, this second-​generation shift also allowed for more flexibility in the group, in the selection of members and in individual approaches to constrained literature. Indeed, this opening resulted in some of the most well-​known and beloved Oulipian texts. This greater flexibility is also a potential reason for Oulipo’s continued presence and success.

Self portrait as Les Demoiselles d’Avignon, designed by OuPeinPo member Helen Frank. Reproduced with the artist’s permission.

Chapter 4

Algorithms

Computer science is fundamentally different from pure mathematics. While its theoretical underpinnings lie in abstract mathematics and logic, computer science involves mechanical devices that facilitate calculations and problem solving by way of algorithms. An algorithm is a sequence of unambiguous, mechanically executable, elementary instructions: a logical division of a problem into its constituent parts and reduced to binary choices that are also mutually exclusive. In short, algorithms break up how to do something into a step-​by-​step procedure. In its most trivial form, an algorithm is just a linear sequence of actions, but more complex problems require the conditional future. In computer science, a conditional statement depends upon an if/​then construct: should the condition following the “if ” (which must be Boolean, meaning it is either true or false) hold, the action following the “then” is executed; otherwise, the program searches for another branch (generally designated as “else”). By way of conditional statements, an algorithm increases in complexity from a simple sequence of steps to a diagram with iterations known as a flowchart. Oulipo’s initial mathematical project insisted on approaching literature logically, inventing procedures –​which they would later call constraints –​to follow during the composition of a text to reduce the role of chance. In this sense, the group’s overall project had much in common with algorithms, producing procedures that also divide complex literary and linguistic objects into constituent parts and manipulating them. Even longer Oulipian texts such as those produced by second-​generation Oulipians, while likely impossible to reduce to an algorithm, share a tendency to organize individual elements mathematically. Considering that one purpose of Oulipo’s constrained literature is to avoid the influence of chance, computers were of interest to the group, as computers are incapable of true randomness.

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Indeed, algorithms can only at best produce pseudo-​random numbers. By that logic, computerized procedures were the perfect solution to Oulipo’s wariness of chance, and a timely one, since Oulipo’s founding in 1960 coincided with critical stages in the development of modern-​day computing. Even at their earliest meetings, Oulipo members sought out computing professionals to try their potential literature out on actual computers, which helped them nuance their notion of potential literature, leading to the important discovery that a willing reader is imperative in Oulipian aesthetics. While data structures and algorithms offer an excellent model within which to conceive of Oulipian work, the question of how exactly the group used computers in its mathematical project has two main answers: first, as a conceptual tool for the creation of potential literature; second, as a literal machine for literary creation. Oulipo engaged in both simultaneously from its founding in 1960 to the early 1980s, with individual members adapting the theoretical and logical underpinnings of computer work to produce texts, and others engaging more directly with programming those texts on literal computers. Given the logical, mathematical basis of computer programming and the fact that several of Oulipo’s founding members were mathematicians who were also getting involved in computers in the 1960s, it would have been extraordinary if the group had not considered issues of logic and algorithms. Through a detailed analysis of Oulipo’s archives as well as close readings of specific texts, this chapter retraces the evolution of Oulipo’s engagement with computers. Just as the early members of Oulipo were interested in procedural production (see Chapter 2), so too were they engaged with how to program those procedures on computers, resulting in their first collaborative partnership with a computer scientist at Bull Computers that ended in 1963; given the skepticism produced by this first programming endeavor, members of the second generation then began to consider new ways of combining literature with machines, culminating in a second computer initiative at the Centre Pompidou in 1977 that further nuanced the group’s understanding of constraint, automatic procedures, and the role of the reader. This sort of work brought the members of Oulipo into close contact with the structure of computing and programming, since to use a computer in the 1960s or 1970s meant dividing a problem into its simplest, logical components and writing

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a solution in a specific coding language. If the group ultimately abandoned the idea of computers, it is because it failed to align the methodical nature of programming with the axiomatic method the members wished to create for literature. Programming greatly appealed to Oulipo for its highly formalized nature; however, algorithms are designed to solve specific problems, whereas Oulipo considers the creation of constraints to be an end itself.1

I. Programming Procedural Production In its early days, the fledgling Oulipo was primarily concerned with defining itself and its goals. The name alone changed a number of times: in a September 1960 letter from Le Lionnais to Queneau, the Président-​ Fondateur refers to the nascent group as the “Atelier de Littérature Expérimentale” (Fonds Oulipo, 1963); in the meeting minutes of the first meeting on November 25, 1960, the title names the group the “Séminaire de Littérature Expérimentale” (Fonds Oulipo, 1963); it was only during the second meeting on December 22 that the group finally settled on “Ouvroir de Littérature Potentielle (O. Li. Po.)” (Fonds Oulipo, 1963). However, it was not until the following meeting that they eventually settled on the acronym OuLiPo (Fonds Oulipo, 1963). This evolution of the group’s name represents a pronounced shift from discussion to action –​ rather than a seminar where one tends to discuss, the group preferred the antiquated ouvroir, a type of workshop where women share sewing patterns. However, it is even more telling that at the same meeting, the members decided to seek out new tools for the analysis and creation of this as yet undefined potential literature, declaring in a “TOP SECRET”2 annex to their second meeting in December 1960: 1 2

This conclusion is supported not only by my archival research, but also by my own attempt at exploratory programming. See: Berkman [2017] in Digital Humanities Quarterly (see Bibliography for full reference). Curiously, this annex does not appear in the archives, but only in Jacques Bens’s reproduction of the first three years of meeting minutes, published in Genèse de l’Oulipo (see Bibliography for full citation).

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chapter 4 Deux de nos membres les plus dévoués se sont donné pour tâche d’intéresser les sociétés IBM et BULL à nos travaux. Leur but est de tenter d’utiliser des machines électroniques pour différents travaux d’analyse littéraire, dans le cadre des activités de l’OLiPo. Nous souhaitons à ces vaillants tractateurs le plus grand succès dans leurs entreprises. (Bens, 2005, p. 32)

Through the first 10 years of Oulipo’s monthly minutes (the first three years having been published by Jacques Bens in 2005 with the remainder of the archives now available through Gallica), it is clear that the first decade of Oulipo’s production was marked by an emphasis on definitions (not only the group’s name, but also key terms such as potential, constraint, and chance), a clear interest for procedural constraints that were both inspired by and carried out on computers, and finally a pronounced skepticism toward the results of such work. Such skepticism would result in the concretization of some of the pillars of Oulipian aesthetics and influence the group’s further collaborations with computer scientists in their second decade of existence. The subsequent meeting minutes do not mention the results of this “top secret” task, yet do include definitions of Oulipo,3 Oulipians,4 as well as readings of historical examples of constrained literature and discussions of new constraints. Computers were not mentioned again until the minutes from April 28, 1961, during which the members engaged in a heated discussion which they titled “CRITIQUE ET RECHERCHE D’UNE DÉFINITION” immediately following the unanimous induction of computer scientist, Paul Braffort (Bens, 2005, p. 47). When Albert-​Marie Schmidt questions the use of the word scientific in the group’s definition, Jacques Bens insists on the term method,5 as evidenced by the group’s use of pre-​existing texts upon which they apply “… un certain nombre de traitements systématiques et prévus par avance. C’est la démarche même 3

4 5

“Organisme qui se propose d’examiner en quoi et par quel moyen, étant donnée une théorie scientifique concernant éventuellement le langage (donc: l’anthropologie), on peut y introduire du Plaisir esthétique (affectivité et fantaisie)” (Fonds Oulipo, 1963). “Rats qui ont à construire le labyrithe dont ils se proposent de sortir” (Fonds Oulipo, 1963). For all italicized words in this paragraph, the emphasis is not mine, but in both the original meeting minutes and the Bens anthology, Genèse de l’Oulipo.

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de toute expérience scientifique” (Fonds Oulipo, 1963). While Schmidt is concerned that they are transforming potentialités into réalités through their methods, Noël Arnaud was only concerned with the practical aspects of Oulipian work: “Je voudrais insister à mon tour sur les faits. C’est de là que nous partons. C’est pourquoi, je crois qu’il serait bon d’éliminer de notre définition ‘les théories scientifiques’. Il vaut mieux nous en tenir au matériau concret. Et puis, ne pas oublier les machines” (Bens, 2005, pp. 55–​56).6 Queneau, on the other hand, contends that their methods can be applied to works that do not yet exist and that the goal of Oulipo is one of discovery, situating Oulipians as one iteration in a longer history of such mathematical literature. To this, Lescure responds : “Du boulier à la machine Bull !” While “la fin de la discussion se perd dans le tumulte et l’anarchie,” this oscillation between theory and practice is indicative of the still developing nature of Oulipo’s mathematical project: while Le Lionnais was primarily concerned with the pure mathematics of Bourbaki, other members gravitated toward computers, or applied mathematics (Bens, 2005, p. 56). That said, even Le Lionnais seems to have been fascinated by computers around this time. Indeed, after first announcing the idea of poetry based on a programming language in the January meeting, he finally debuts his “poème algolique” (a pun on “alcoolique”): ALLER AU RÉEL POUR FAIRE VRAI TANDIS QUE FAUX PERSISTANT … TABLEAU ! … (Bens, 2005, p. 61)

6

While the term ordinateur was first invented by Jacques Perret and introduced by IBM France, the company retained an exclusive copyright on the term until 1965, upon which it became a common term in the French language (Azan). Prior to this point, however, the term was not yet a recognized French word for computers, and computeur remained a serious rival. Thus, the Oulipian use of the word “machine” in these early meetings can refer to their own devices as well as to computers. However, many of these mentions are immediately followed by discussions of the products of their collaboration with Bull, removing some of this ambiguity.

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Short for “Algorithmic Language,” ALGOL is a family of computer programming languages, originally developed in the 1950s. While distinct from the most common languages in use today, ALGOL greatly influenced computer programming, even more so than similar languages of the time such as Fortran. As Le Lionnais (1973a, pp. 215–216) explains in the preface to his “Ivresse algolique” of the group’s 1973 collected volume, La Littérature Potentielle, ALGOL is an intermediary language, allowing for humans and computers to communicate more efficiently: “Il se caractérise par un vocabulaire très réduit –​comportant peu de mots, mais des mots humains –​et par une grammaire très stricte, composée d’un petit nombre de règles sans exceptions”. As Le Lionnais explains, the purpose of literature is also to combine words according to various rules. As ALGOL did not exist in French, Le Lionnais’s vocabulary is the result of a translation of the basic terms necessary to this programming language, which I have translated back with explanations for convenience (Backus et al., 1962, p. 7).7

7

This list was published in Le Lionnais’s preface to “Ivresse algolique” in La Littérature Potentielle (1973), and therefore does not conform perfectly to the vocabulary in the poem cited above (which dates to 1961). Specifically, I suspect that in Le Lionnais’ original poem, “tandis que” would refer to “While” and “Persistant” would likely be “Own.” However, I am relatively certain that I have found the proper English equivalents for the list provided in La Littérature Potentielle, as the translations for the word order in Le Lionnais’s list are in perfect alphabetical order.

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Algorithms Table 4.1.  Le Lionnais’s translations of ALGOL commands into French 1.

Tableau

Array

Indicates a type of data, an n-​dimensional table.

2.

Début

Begin

Indicates the start of a block of code.

3.

Booléen

Boolean

Name of the Boolean data type.

4.

Commentaire Comment Indicates that start of a comment.

5.

Faire

Do

Indicates the end of a for clause.

6.

Sinon

Else

Separates the else from the then in a conditional statement.

7.

Fin

End

Indicates the end of a block of code.

8.

Faux

False

One of the Boolean data types.

9.

Pour

For

Indicates the start of a loop.

10.

Aller à

Goto

Indicates an unconditional transfer of control to a label.

11.

Si

If

Starts a selection statement of conditional expression.

12.

Entier

Integer

Name of a fixed point data type.

13.

Étiquette

Label

Indicates a label parameter.

14. Rémanent

Own

Indicates a variable with static life time but local scope.

15.

Procédure

Procedure

Indicates a sub-​program or function.

16.

Réel

Real

Name of a floating point type.

17.

Pas

Step

Used in a for clause to indicate an increment.

18.

Chaîne

String

A type of character string data type.

19.

Aiguillage

Switch

Declares a variable that is something like an array of labels.

20. Alors

Then

Separates a condition from the true part of a selection.

21.

True

A Boolean value.

22. Jusqu’à

Vrai

Until

Indicates the final value in a for clause.

23.

Value

Indicate pass by value in a parameter.

While

Indicates a conditional loop part of a for clause.

Valeur

24. Tant que

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While the terms in this table have extremely specific meanings in the context of a programming language, Le Lionnais’s use of them suggests new, metaphorical interpretations. However, for a computer, his original poem might be understood as a command to go to the realm of real numbers to find truth, as long as an unspecified case is false. While for a human reader, the final word, tableau, might indicate a painting, for such a computer, it could be understood as an array in which to organize the results. Oulipo members at the meeting where Le Lionnais presented this poem did not consider an interpretation of the text, whether metaphorical or otherwise. Instead of pondering the theoretical use of a programming language for poetic creation, they were distracted by the punctuation and disappointed that the poem did not constitute a functional program: F. Le Lionnais ne nous a pas indiqué si les … et le ! font partie du vocabulaire ALGOL. Mais il a affirmé que ce poème a l’allure des programmes que l’on soumet aux machines algologlottes –​non sans préciser, toutefois, que ce programme-​là n’a que peu de chances de correspondre à un problème soluble. À quoi Paul Braffort ajoute qu’il est parfaitement possible de composer des poèmes constituant un programme réellement cohérent. Nous attendons, avec curiosité, de telles communications. (Bens, 2005, p. 61)

It is a shame that this rare example of Le Lionnais’s textual production was overlooked by Oulipo at this stage, as it is much more in line with the aims the group developed over time. Indeed, Le Lionnais finds the poetic potential of programming language, producing a semantically rich poem from this highly restricted vocabulary that in turn speaks about the nature of computer science. While his poem is not a literal algorithm as fellow members would have preferred, it raises an essential question: is there a poetics of the algorithm? Algorithms (as well as mathematics) are characterized by their simplicity, elegance, and logical flow. This could be understood as a poetics which the early Oulipo aimed to reproduce in literature. By August 1961, the group had succeeded in its “top secret” objective and set up a partnership with Dmitri Starynkevitch, a Russian-​born computer programmer at IBM-​Bull Computers, who worked on the SEA CAB 500 computer. Developed by the French company SEA (Société

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d’Electronique et d’Automatisme) in 1956 and launched in 1960, the CAB (Calculatrice Arithmétique Binaire) 500 was designed to be a low-​cost, easy-​to-​use computer for primarily scientific calculations. In an article, Starynkevitch (1990, p. 23) notes that it could be viewed as a forerunner to the personal computer. It could perform arithmetical and logical operations, which were entered on a typewriter keyboard that had been designed specifically for the use of the PAF (Programmation Automatique des Formules) programming language, allowing for direct communication with the machine (Starynkevitch, 1990, p. 24). Starynkevitch called PAF a “high-​level programming language,” mainly oriented toward working with mathematical formulae. Designed for mathematicians who were less familiar with programming and reticent to type on a keyboard, the language was simple to learn (Starynkevitch, 1990, pp. 26–​27). Using this computer, Starynkevitch had generated excerpts from Cent mille milliards de poèmes. While no record of Starynkevitch’s code survives and neither do the excerpts he sent to Queneau, it is not difficult to infer how he must have accomplished this. In computer science terms, a sonnet is an array of 14 verses that can each be attributed a numbered index (the first verse, the fourteenth verse, and everything in between). The data structure of Cent mille milliards de poèmes is slightly more complicated, an array of arrays: 10 sonnets of 14 lines each. Each individual verse for Queneau’s text can thus be attributed two indices: the first indicating in which poem the verse can be found (0 being the first of Queneau’s base sonnets and 9 being the last); the second indicating which numbered line it occupies in that sonnet (a number between 1 and 14). To create a program to generate random sonnets using the PAF language, Starynkevitch would have input these verses into the computer’s memory and constructed a data structure within which they could be swapped. The distinguishing feature of Starynkevitch’s program would have come from the pseudo-​random number generator (PRNG), of which the answer was lost with the code.8

8

In my personal correspondence with him, Starynkevitch’s son, Basile, claimed that his father was no expert in random number generators and would have simply used a rudimentary one.

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The reaction of Oulipo members to these computer-​generated excerpts was not very enthusiastic: “On souhaita que M. Starynkevitch nous précise la méthode utilisée; on espéra que le choix des vers ne fut pas laissé au hasard” (Bens, 2005, p. 79). While Starynkevitch’s method could not have been random given the incapacity of computers to generate true random numbers, the method Starynkevitch used to generate the excerpts would have been entirely invisible when members of the group were confronted with just the excerpts. However, there was something disconcerting for the early Oulipo about the appearance of chance in the computer-​generated poems, resulting in the members’ insistence on seeing the underlying method, rather than just the results, in an attempt to avoid le hasard (the first appearance of this key concept in Oulipian aesthetics). Even early on, the members knew that Starynkevitch’s computer-​generated poems were not representative of their aesthetic aspirations due to the fact that a reader confronted with a seemingly random selection of poems has less autonomy than one who can manipulate the physical volume. Almost a year later in April 1962, the question of chance was once again broached by Noël Arnaud: “Il faudrait enfin parler des machines. Il est difficile d’en parler. Mais comment ne pas en parler?” (Bens, 2005, p. 145). Berge declared: “Nous aurons fait un grand pas vers nos définitions si nous admettons, par exemple, ce qui est mon avis, que nous sommes essentiellement anti-​hasard” (Bens, 2005, p. 146). Queval then brought the conversation back to machines: “La notion du hasard est délicate. Il ne faudrait pas substituer à l’automatisme psychique des surréalistes un automatisme mécanique où le hasard aurait autant de part” (Bens, 2005, p. 146). Oulipo’s definition of its project in opposition to chance eventually became a central focus of the group, and the fact that this aesthetic distinction was first developed in response to the group’s computer collaborations is particularly significant. While the early Oulipians considered themselves opposed to randomness, which they understood as a central facet of surrealist writing, computers represented a different, yet equally problematic type of randomness. Cent mille milliards de poèmes parodies surrealist automatic writing, but is produced by a different combinatorial process. However, generating poems using an actual computer presented

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a real danger: this new automatism had to avoid letting chance play a role in the selection. At the following meeting in May 1962, Arnaud still insisted on the role of machines: “Arnaud parle des machines” (Bens, 2005, p. 150). While his discussion was not recorded, later in that same meeting, Queneau shared Starynkevitch’s newest accomplishment, a fake telephone book produced by a machine, which elicited the following reaction: “L’intéressant, c’est que ce n’est pas ‘intéressant’. Je veux dire: ni bizarre, ni drôle, etc” (Bens, 2005, p. 158). Despite the methodical nature of computer programming, it is clear that Oulipo was still skeptical about the aleatory nature of computer-​assisted literature, as Mark Wolff notes: “They sought to avoid chance and automatisms over which the computer user had no control” (Bens, 2005, p. 5). Indeed, even in its first year, the group was more concerned with the computer user than the computer itself. By December 1962, Oulipo had begun preparations for a conference in Liège to be held on October 2, 1964, organized by Le Lionnais on the topic of “Machines LOGIQUES et ELECTRONIQUES et LITTERATURE” (Viridis Candela, 2004, p. 37). When discussing potential topics for the program, Starynkevitch’s Cent mille milliards de poèmes program was suggested, provoking another discussion on the word “automatic” and its respective meanings in surrealism and computer science (Bens, 2005, p. 182). To resolve the issue, Le Lionnais argued that “… la naissance des machines électroniques a modifié le sens courant d’‘automatique’ … Le mot ‘structure’ contient tout ce qu’il y a dans le mot ‘automatique.’ ‘Contrainte’ également” (Bens, 2005, p. 185). Le Lionnais’s publication history with Bourbaki and appreciation for the collective mathematician’s structural image of the discipline gave Le Lionnais a preference for set theory over algorithmic computer science. He therefore insisted upon Oulipo’s use of an abstract mathematical vocabulary of structures and constraint, rather than applied mathematical terms such as automatic. The following month, Starynkevitch was an invited guest, speaking first about the Cent mille milliards de poèmes program and second about the difficulties of programming the S+​7 method: Toute la difficulté vient, évidemment, de la quantité de matériau dont vous avez besoin –​donc : à introduire en machine. Il nous est possible de travailler sur quelques

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In addressing these questions, Starynkevitch had to do a great deal of work by hand, which he details in a letter to François Le Lionnais in February 1963: N’ayant pas de dictionnaire élémentaire, j’ai pris au hasard quelques centaines de substantifs, qui ont été enregistrés dans la machine. Pour des questions d’accord, j’ai distingué les substantifs masculins et féminins et effectué les substitutions d’après le genre du mot original. Il subsiste quelques fautes d’orthographe, notamment dans les pluriels et les articles. Quelques règles de grammaire ont été introduites, mais je n’ai pas tenu compte des exceptions. Les textes obtenus me paraissent néanmoins quelquefois intéressants. (Fonds Oulipo, 1963)

Despite these difficulties, by the following meeting, Starynkevitch had programmed the S+​7 method and sent Queneau examples of the program applied to Exercices de style, Genesis from the Bible, Shakespeare, and Hugo. Although the S+​7 method should have lent itself to computers given its procedural nature, Starynkevitch’s frustrations indicate that carrying it out on an actual computer was more trouble than it was worth. And while some of these issues were resolved by the time Oulipo collaborated with the Centre Pompidou, at that point, the group had lost interest in the S+​7 method, preferring to focus on more complex substitutional constraints. Bloomfield (2017, p. 127) notes that the group’s disappointment with the S+​7 method is indicative of its incompatibility with Oulipo’s aesthetic goals: “La méthode S+​7, dont le succès, pour Queneau, ‘est une catastrophe’, doit sa célébrité à sa facilité de mémorisation et d’application, ainsi qu’à sa dimension ludique, mais n’étant pas exactement caractéristique de l’Oulipo, elle est à la fois fort pratiquée et critiquée au sein du groupe.” In contrast, Alison James believes that the arbitrary nature of the constraint has “… a liberating effect, opening up possibilities that can then be harnessed to the aesthetic purposes of a particular author. While S+​7 texts owe their uncanny impact (as well as their humor) to their exploitation

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of the machine-​like dimension of language, in other respects the apparent absence of the human subject is an illusion. The author lurks behind the scenes as the inventor of the constraint and the manipulator of its applications” ( James, 2006, p. 123). While both scholars’ points of view are valid, the insights Oulipo gained from attempting to program S+​7 on computers in these early years perhaps solidified the group’s ambivalent stance toward this constraint. Indeed, in subsequent computer projects such as ARTA, they did not reattempt to create an S+​7 program. While the determinism of computers appealed greatly to the early Oulipo, the members experienced first-​hand the technological limitations of the time, which in turn influenced the group’s future production and aesthetics. Indeed, they saw through Starynkevitch’s work that there was little potential to be found in random number generators and that computers at best only facilitate generating texts to read given a set of basic elements. Nevertheless, this collaboration produced important results on both sides: for Oulipo, although the practical results were underwhelming, the group refined its core terminology of potential and chance and began to conceptualize the role of the reader; for Starynkevitch, who was doing mostly mathematical work at IBM at the time, this was a rare occasion to understand the potential of computing for natural language through a creative partnership with a unique literary group. While this was the last time that Oulipo as a group would program procedural constraints in such a way, a few years later, new member Georges Perec would pretend to program these procedures on a fictional computer in a very popular German radio play (Hörspiel) 9called Die Maschine (1968), which he produced in collaboration with his German translator, Eugen Helmle. After an initial meeting with Helmle and his literary circle in Saarbrücken, Perec had the idea of writing a characterless play for the radio, where a lone voice, “… that of a computer, [tries] to answer the first question Descartes asked of himself in his Discourse on Method: How do I know I exist?” (Bellos, 2005, p. 5). He quickly abandoned that idea for another: What is poetry? As Perec had been learning in Oulipo meetings 9

To this day, Die Maschine has not been translated into French, which is an obvious reason for the shocking lack of French criticism on this text.

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at the time, the rise of computational linguistics was making it possible for computers to answer scholarly questions about literature. With this in mind, Perec devised a new project that would impersonate a computer analysis of one of the most famous German poems, Johann Wolfgang von Goethe’s Wandrers Nachtlied. While similar to other fictional manipulations of machines (such as HAL from 2001: A Space Odyssey),10 Perec’s creation is in line with Oulipo’s early approach toward computers, engaging rather in a fictional experiment to discover how one can influence the other. The introduction claims that the titular machine consists of a repertoire of procedures (a catalogue of Oulipian procedural constraints) and a memory or database of sorts (including the poem itself, data about the author, a multilingual dictionary, several alphabets and a phonological key to form new words, a grammar, and a wide selection of poetry from world literature) (Perec, 1972, p. 4). The basic understanding of syntax and structure coupled with an extensive vocabulary allows the computer to carry out analytic procedures on the poem; furthermore, literary criticism would not be complete without biographical information of the author and historical context. Goethe’s Wandrers Nachtlied is an excellent choice for such a project given its extremely recognizable nature in the German-​speaking world. As with the S+​7 method, applying computer-​like procedures to such a famous text disorients a reader. The commands are given by a harsh female voice known only as “Kontrolle,” who “… löst in bestimmter Reihenfolge die von den Programmen fixierten Operationen aus und überprüft ihre Abfolge. Die Kontrolle hat absoluten Vorrang vor den Speichern und kann ihnen Befehle erteilen wie: halt, warten, vor, zurück, umkehren, anschließen, weitermachen, rekapitulieren usw” (Perec, 1972, p. 4).11 Three other voices in Die Maschine dutifully carry out the system control’s commands. Contrary to the listener’s expectations, however, the system control’s voice is not entirely unemotional. For instance, she is often polite, preceding orders with 1 0 A name produced by a quasi Oulipian procedure, as HAL =​the letters of IBM –​1. 11 “… activates the operations designated by the programs in a certain sequence, and examines their progress. The system control has absolute priority over the processors. It can give them commands such as: stop, wait, forward, backward, return, connect, continue, repeat, etc.” (Perec, 2009, p. 34).

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“bitte,” and also sounds exasperated in response to various results. The other three voices, however, are often monotonous and emotionless. Given the nature of the Hörspiel, Perec is obligated to create a speaking machine, an idea that was in the air at the time of Perec’s short trip to America in July 1967, when “… he must have seen or been told about [the University of Michigan’s] famous speech-​synthesis machine, one of only two or three in the world at the time” (Bellos, 2005, p. 5). Before the programs can begin, perforated cards upload basic information onto the computer. The “Kontrolle” asks the three speaking memory units to recite the title, date, and author of the poem, the original language, and the poem itself, information that a student might use to carry out a traditional literary analysis. Then, the programs begins: “Die Programme, mit den notwendigen Instruktionen gefüttert, die eine korrekte Ausführung der verschiedenen Operationen gewährleisten, sind in fünf Protokolle eingeteilt, welche den fünf fundamentalen logischen Kategorien entsprechen, die die Maschine nacheinander anwenden wird, um das Gedicht zu analysieren”12 (Perec, 1972, p. 4). After this preliminary information, Protokoll 0 is a literal breakdown of the poem into numerical categories: number of verses, number of words, words per verse, number of metrical feet, distribution of those metrical feet, average metrical feet per verse, rhyming structure, number of letters, number of letters per verse, average number of letters per verse, average number of letters per word, frequency of letters, lipogrammatic index, distribution of punctuation marks, distribution of syntactic elements (such as prepositions, adjectives, nouns, verbs, pronouns, adverbs, and articles) (Perec, 1972, pp. 7–​9). While some of these elements might be useful in a traditional literary analysis, this quantitative analysis quickly turns into a parody, and even the computer notes that some of the categories are “ohne Belang” or “n/​a” (for instance, the number of letters per verse, average number of letters per verse, average number of letters per word, frequency of letters, and lipogrammatic index) (Perec, 1972, p. 8).

12

“The programs containing the necessary instructions guaranteeing the correct execution of the various operations are divided into five protocols, which correspond in turn to the five fundamental logical categories that the machine uses in turn in order to analyse the poem” (Perec, 2009, p. 34).

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The following two protocols apply Oulipian constraints to the poem, gleaning hilarious, but not totally unexpected results: Protokoll eins (innere Operationen) ist im wesentlichen linguistischer Natur: es geht von dem vorgegebenem Wortmaterial des Gedichts aus. Protokoll zwei (äußere Operationen) ist im wesentlichen semantischer Natur: es verändert das Gedicht durch von außen kommende Einschränkungen und Modifikationen.13 (Perec, 1972, p. 8)

Protocol 1 begins with recitations of the poem using groups of words of various lengths (from one word at a time to all 24) for the express purpose of the “deformierung der rhythmischen bewegungen ohne veränderung der wörter und der reihenfolge” (Perec, 1972, p. 9).14 The composite nature of the integer 24 allows for this plurality of divisions into 1, 2, 3, 4, 6, 8, 12, and 24 words at a time, dividing the poem not into verses or stanzas, but simply integer values. The final group of all 24 words at once is read so fast that it is barely comprehensible: “DAS GEDICHT WIRD SEHR SCHNELL UND OHNE BETONUNG VON EINER EINZIGEN STIMME AUFGESAGT” (Perec, 1972, p. 13).15 In an exasperated tone, the “Kontrolle” says “stop.” The program then reads the poem backward, verse by verse; from top to bottom; with the verses in a different order; and with a “random” word order. Next, by an “aleatorische neuschöpfung die programmierung der vokalischen, konsonantischen und syntaktischen Leitungen ermöglicht es den speichern, das gedicht zu rekonstruieren, revealing unexpected associations” (Perec, 1972, p. 16).16 For instance, “über alles” gives way

13

“Protocol one (internal operations) is essentially linguistic in nature: it operates on the lexical material of the poem. Protocol two (external operations) is essentially semantic in nature: it changes the poem through externally determined restrictions and modifications” (Perec, 2009, p. 34). 14 “deformation of rhythmic inflections without changing the words and sequence” (Perec, “The Machine” 39). 1 5 “THE POEM IS READ VERY FAST AND WITHOUT STRESS BY ONE SINGLE VOICE” (Perec, 2009, p. 42). 16 “aleatory recreation the programming of the vocalic, consonant, and syntactical strands enable the processors to reconstruct the poem” (Perec, 2009, p. 44).

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to “über alles in der welt,” a German propaganda film from 1941. There is no time to linger over these associations, however, as the machine proceeds relentlessly. Arriving at “ruh,” the machine produces “ruhe ist die erste bürgerpflicht” (Perec, 1972, p. 20).17 A common aphorism meaning that peace is the citizen’s first obligation, Ruhe also means silence (the main theme of Goethe’s poem). Preceded by the reference to Über alles in der Welt, this literal meaning of a common aphorism can be understood as a critique of the silent collaboration of many German citizens during the Holocaust. Other associations are of a literary nature, for instance, “warten” leads to “warten auf godot” (Perec, 1972, p. 28).18 These mechanical associations are ostensibly derived automatically by the computer, as if these twentieth-​century cultural references were innate in this eighteenth-​century poem. While Protocol 1 experimented with basic units of language, the constraints in Protocol 2 are more sophisticated: anagrams; slight letter changes which result in new words with their own meanings; a translation into “javanais” (where every syllable is separated by a v); isomorphisms (including fixing the vowels, consonants, replacing all nouns with common words from fairy tales, S+​n with n =​5, 10, 15; v +​n with n =​3 and 12); translations; generation of proverbs using various words in the poem; a reduction of the poem into logical sentences; and replacing words with their synonyms. Following these first two protocols, which parody reading and writing poetry, Protocol 3 deals with the role of the literary critic: “Protokoll drei ist im wesentlichen kritischer Natur: es untersucht die möglichen Beziehungen und Querverbindungen zwischen dem Gedicht und seinem Autor” (Perec, 1972, p. 5).19 However, rather than analyzing specific elements of Goethe’s biography, it simply lists various events in Goethe’s life, judgments about Goethe by other authors, and an alphabetical list of associated topics (such as “Goethe und Schiller” for S, or “Goethe und der Tabak” for T) (Perec, 1972, p. 64). The program then finishes with a dictionary of

1 7 Note: The translator did not attempt to reproduce this in English. 18 Waiting for Godot, a reference to a play by Samuel Beckett. 19 “Protocol three is essentially critical in nature: it examines the possible relationships and cross-​references between the poem and its author” (Perec, 2009, p. 34).

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Goethe quotations. However, as with Protocol 0, this information would be mostly useless for a literary analysis of the poem. The explanation of Protocol 4 is extraordinarily ambitious: “Protokoll vier schließlich (die Zitatenexplosion) ist im wesentlichen poetischer Natur: es konfrontiert zunächst das Gedicht mit der Dichtung der Weltliteratur, um am Ende das aus ihr herauszuziehen, was man den Wesenskern der Dichtung nennen kann” (Perec, 1972, p. 5). 20Perec’s explosion of quotations searches through the fictional computer’s imaginary bank of world literature to inundate the listener with poetic reflections on these same themes. Many citations are in languages other than German, some come with corresponding translations, and others occur in the wrong language. The voices in this part are no longer monotonous repetition machines. Instead, they recite poetry in an emotional performance that relentlessly pushes forward from one to the next, not allowing the audience to process. Finally, the play dissolves in a chorus of “peace” in various translations until it fades away to a whisper, or last breath. The final words of the introduction had declared that: “Dem aufmerksamen Hörer kann somit deutlich werden, daß dieses Spiel über die Sprache nicht nur die Arbeitsweise einer Maschine beschreibt, sondern auch, wenngleich verborgener und subtiler, den inneren Mechanismus der Poesie aufzeigt” (Perec, 1972, p. 5).21 However, when encountered in the introduction, this grand claim seems either ironic or provocative, as a listener of the 1960s most likely did not believe that a machine –​or perhaps even Perec –​could describe the “inner mechanism of poetry.” But by the end, the play has indeed said something profound about Perec’s idea of poetry and mortality. Through this final protocol, Perec locates the “essence of poetry” in the relationship between the most perfect lyric poem in the German language and other poetry, which share a common reflection on human mortality.

20 “Finally, protocol four (explosion of quotations) is essentially poetic in nature: it confronts the poem with the poetry of world literature in order to identify, ultimately, what one might call the essence of poetry” (Perec, 2009, p. 34). 21 “To the attentive listener it may become clear that this play about language not only describes the functioning of a machine, but also, though in a more concealed and subtle manner, the inner mechanism of poetry” (Perec, 2009, p. 35).

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In the 1960s, scholars were beginning to use computers to analyze text in the fledgling field of computational linguistics, a study that was limited at the time by the technological capacities of early computing (a hindrance that also adversely affected Oulipo’s experimental work on computers). Perec’s radio play parodies this new type of work by using an imaginary computer to tear apart a classic German poem in the guise of an analysis. Yet, Perec’s creative imagining of what a machine can do with language also results in a refreshing and unexpected understanding of what poetry is. Die Maschine is not only the most performed German radio play of all time, but is the best-​ known work produced by Oulipo in Germany. What is not often considered in scholarship on Oulipo, however, is that this radio play is the most commercially successful production (just not in France) of the group during this period. Nevertheless, Die Maschine is an excellent example of how the basic functions of a computer can inspire not only literary creation, but provoke a more serious reflection on literature and mortality and its marginalization in France22 (and even within Oulipo) is a major disappointment.

II. Programming Choice: Arborescent Narratives As I mentioned in the introduction to this chapter, computers depend on algorithms, and those procedures can be represented graphically in what is called a flowchart, where each node (step in the procedure) has mutually exclusive paths, or edges (the alternatives). The study of these and other graphs belongs to the mathematical subfield of graph theory, which has notable intersections with Oulipo. Indeed, one of the founding members of the group, mathematician Claude Berge, greatly contributed to this field later in his career and seems to have inspired a parallel interest 22

For instance, Olivier Salon is the Oulipian who has most publicly dealt with Perec’s L’Art et la manière and subsequent theatrical adaptation, but has never mentioned Die Maschine. Furthermore, in the new Pléiade edition of Perec’s work, while the German adaptation of L’Art et la manière is mentioned briefly in the notes following the text, Die Maschine does not appear even once.

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for graphs among members of Oulipo, including most notably Raymond Queneau and Georges Perec. The foundations for the field of graph theory were laid by Leonard Euler in 1736 when he solved the famous bridges of Königsberg problem, which seeks to know if it would have been possible for Immanuel Kant to cross every bridge in his hometown in only one walk, with no repetitions. The town is intersected by the Pregel River and contains two large islands, which are connected to both banks by seven bridges as pictured in Figure 4.1. According to Euler’s proof, the choice of a route inside each land mass is totally irrelevant. The problem can be abstracted to its most basic elements: the nodes and edges of the graph.

Figure 4.1.  A visual illustration of the Bridges of Königsberg problem in graph theory, beautifully reimagined as Immanuel Kant’s face by OuPeinPo member Helen Frank. Reproduced with the artist’s permission.

To enter a node via an edge, one also must leave that node via an edge. If every bridge must be crossed exactly once, the number of bridges touching each land mass (except for the start and finish) must be even (to get to and from that land mass). However, all four land masses are touched by an odd number of bridges, making such a route impossible. This first

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result generated an entire mathematical subdiscipline to study properties of graphs and their nodes and edges and Oulipo applied it to literature. In the first phase of Oulipo’s computer work, the members primarily wrote texts that were inspired by or which imitated the functioning of computers. Indeed, the S+​7 method and Cent mille milliards de poèmes could be said to reproduce the number crunching capacities of computers and it was precisely for this that they could be programmed so easily. Between this first phase in Oulipo’s computer work and the second, certain members began to capitalize on computers’ algorithmic nature, specifically through Queneau’s Un conte à votre façon (1967) and Perec’s L’art et la manière d’aborder son chef de service pour lui demander une augmentation (1968). These texts would not only pave the way toward the group’s next phase of computer experiments in which the members tried to use computers to assist them in both the reading and writing of texts, but they would also become a genre in their own right, indirectly paving the way for interactive fiction as well as video games. Queneau published Un conte à votre façon in 1967, just two years after the delayed French translation of Propp’s Morphology of the Folktale. In the original Russian text, Propp (1965, p. 122) defines a specific type of Russian folktale that was primarily an oral form, which was then translated into French as “conte merveilleux,” described in the following language: La constance de la structure des contes merveilleux permet d’en donner une définition hypothétique, que l’on peut formuler de la façon suivante : le conte merveilleux est un récit construit selon la succession régulière des fonctions citées dans leurs différentes formes, avec absence de certaines d’entre elles dans tel récit, et répétitions de certaines dans tel autre.

The sequences Propp describes do not imply as strict an order as an algorithm requires. He groups his 31 functions into three main groups: a preparatory sequence (functions 1–​7); a first sequence of actions (functions 8–​18); and a second sequence (functions 19–​31). While Propp insists that these 31 functions always follow the same order, all of them do not necessarily appear in any individual tale. Given Queneau’s use of the word “conte” in his title, it seems logical to conclude that his algorithmic tale plays with Propp’s basic idea that stories

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can be broken down into their constituent parts, as the text takes the form of a numbered list of potential elements. The rest of the title, à votre façon, refers to a potential reader, who can compose this story as he or she sees fit. However, Queneau’s tale is structurally very different from Propp’s study in that its sequence of possible paths creates a literal algorithm, defining a strict series of events from which any deviation on the part of the reader is impossible. The algorithmic nature of this text is made explicit in an introductory note: “Ce texte … s’inspire de la présentation des instructions destinées aux ordinateurs ou bien encore de l’enseignement programmé. C’est une structure analogue à la littérature ‘ en arbre ’ proposée par F. Le Lionnais à la 79e réunion” (Queneau, 1973e, p. 77). Largely considered to be one of the earliest examples of the choose-​your-​own-​adventure story genre, Queneau’s Un conte à votre façon therefore has wide reaching implications for both the composition and analysis of other arborescent narratives. Queneau initially gives the reader a choice between the story of three little peas, three big skinny beanpoles, or three average mediocre bushes,23 any of which can ostensibly be read by means of a step-​by-​step procedure, a literal algorithm: 1-​Désirez-​vous connaître l’histoire des trois alertes petits pois ?     

Si oui, passez à 4.

    

Si non, passez à 2.

2-​Préférez-​vous celle des trois minces grands échalas ?     

Si oui, passez à 16.

    

Si non, passez à 3.

3-​Préférez-​vous celle des trois moyens médiocres arbustes ?

23

    

Si oui, passez à 17.

    

Si non, passez à 21. (Queneau, 1973e, p. 277)

Hélène Campaignolle-​Catel (2006, p. 139) notes that the botanic imagery of the bean poles and the shrubs illustrates the arborescent nature of the tale, which is also reminiscent of the genre itself, as the conte and Propp’s analysis call to mind bifurcating paths around several common basic elements.

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As with algorithms, the choices in Queneau’s text are all binary oppositions, providing mutually exclusive alternatives so as not to be contradictory. Either the reader chooses to read the tale of the three peas or does not. Should the reader prefer not to read this first option, opting instead for the beanpoles or the bushes, he or she will find that the two alternatives offer meagre results: 16-​Trois grands échalas les regardaient faire.     

Si les trois grands échalas vous déplaisent, passez à 21.

    

S’ils vous conviennent, passez à 18.

17-​Trois moyens médiocres arbustes les regardaient faire.     

Si les trois moyens médiocres arbustes vous déplaisent, passez à 21.

    

S’ils vous conviennent, passez à 18. (Queneau, 1973e, p. 280)

Grammatically speaking, these false paths are cleverly constructed –​by using the plural direct object “les,” Queneau allows the node to have indefinite antecedents of any type or gender. Should the reader arrive at this node after following a more complete path through the algorithm, he or she will realize that “les” refers to the “petits pois.” However, arriving at this node immediately after the incipit creates an insurmountable interpretive challenge for the reader: either the “trois grands échalas” or “trois moyens médiocres arbustes” “les regardaient faire.” Who are they watching and what are they doing? These questions can only be answered by paths the story did not take. Alternatively, should the reader refuse all three initial options, the program terminates after only three nodes with the problematic statement: “21-​Dans ce cas, le conte est également terminé” (Queneau, 1973e, p. 280). To what, in this case, could the “également” refer? In order to find out, the reader must forsake the logic of the flowchart and look at the preceding choice 20: “Il n’y a pas de suite, le conte est terminé” (Queneau, 1973e, p. 280). By referring to other choices within individual nodes that are unconnected in any scenario (it is impossible to have both 20 and 21 if one follows the algorithm), Queneau uses a traditional, linear mode of reading to disrupt his algorithmic structure. Furthermore, these

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preliminary disruptions indicate to the reader that there is only one “real” story to read, and that the reader must cooperate if he or she does not wish to arrive at unsatisfying dead ends and contradictory conclusions. If the reader chooses the proper beginning and advances in the tale, the first few choices determine mere descriptive aspects of the story –​whether the peas dream, what color gloves they wear, and whether they roll around on a highway before turning in for the night. These superficial elements have nothing to do with the story, which the reader soon notices is limited. For Campaignolle-​Catel (2006, p. 140), this indicates the extent to which Queneau is respecting Russian formalism: “Le Conte à votre façon obéit ici à la logique décrite par Cl. Brémond à propos du conte russe : les alternatives proposées, les déviations possibles sont des leurres …” I would argue, however, that Queneau is not respecting Russian formalism, but playing with these principles. In a traditional conte, proposed alternatives may be decoys, but there is still an overarching narrative that forces the reader to imagine alternatives. The majority of Queneau’s alternatives are offered to the reader in an effort to deny him or her the autonomy promised by the title: both the pointless alternatives and the unsatisfying dead ends indicate that there is only one story to read. These bifurcations exist for one other reason as well: to complicate Queneau’s graphical representation of the tale (Figure 4.2), first published in La Littérature Potentielle in an article by Claude Berge (1973, p. 55).

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Figure 4.2.  The graphical representation of Raymond Queneau’s Un conte à votre façon, taken from La Littérature Potentielle (p. 51). Reproduced with the permission of the publisher. © Éditions Gallimard. Tous les droits d’auteur de ce texte sont réservés. Sauf autorisation, toute utilisation de celui-ci autre que la consultation individuelle et privée est interdite.

According to Berge (1973, pp. 55–​59), this graph represents “… une imbrication de circuits, Chemins convergeants, etc…, dont on pourrait analyser les propriétés en termes de la Théorie des Graphes …” This graph is indeed exceptional for several reasons. First, Propp’s study provides the foundation for understanding the conte genre as combinatorial rearrangements of basic elements that always follow a basic sequence. The spatial aspect of Queneau’s graph therefore distinguishes what Queneau is doing from Propp’s style of thinking about narrative structure by emphasizing a strict order. Second, the layout of Queneau’s graph is aesthetically rich. Queneau provides a literal frame, composed of the first three options on the left edge (1, 2, and 3, the choice between the peas, beanpoles, and shrubs), just as “once upon a time” might begin an ordinary conte at the top left corner of the first page. Choices 4 and 9 on the top edge of the frame represent an initial description of the peas (the reader has two options

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here), and choice 21 at the bottom, right corner is one of the two endings, the one containing “également.” It is visible from the graph that this ending always results from a case of uncooperativeness on the part of the reader. As long as the reader in the final options (17, 18, 19) chooses to read “la suite,” he or she will arrive at the “proper” ending node, number 20. Mathematically speaking, any graph with these same nodes and edges is equivalent to Queneau’s.24 However, Queneau constructed a graph that mirrors the story itself: one can remain on the edges, musing over inconsequential details and eventually finishing without reading about the three little peas; or one can follow the path Queneau has set out, providing a few bifurcations, but ultimately resulting in the same story and ending. The choice promised to the reader in the title is an illusion, as Queneau maintains full control of the text through the structure he created. The story’s graphical representation is informative, its algorithmic layout on the page is unique, and its theoretical underpinnings are apparent. However, the tale is relatively meagre and the narrative often contradicts the logic of the binary choices provided should one faithfully follow the procedure, as previously noted with the case of the “les regardaient faire” and the false ending. In another case, the text’s playfulness surrounding alternatives creates an interpretative glitch. In node 5, the narrator describes the peas in their slumber: “Ils ne rêvaient pas. Ces petits êtres en effet ne rêvent jamais” (Queneau, 1973e, p. 278). Queneau then gives the reader a choice: either the reader would prefer that the peas dream, or not. Should the reader choose the latter, he or she has to read an explanation and interpretation of the dream anyway and on the way is referred to a dictionary to learn the definition of the word “ers.”25 In this scenario, a reader could read the sentence “Ils ne rêvaient pas” and the story of the dream they were having in the same story (Queneau, 1973e, p. 278). This contradictory 24 See Berkman (2017) in the Bibliography for an explanation of another equivalent graph and what it shows about Queneau’s narration. 25 This instance is particularly interesting as it forces the reader to leave the tale and consult a dictionary. While not an impasse (in the sense that the reader returns to the story after having learned the meaning of the word “ers”), forcing the reader to leave the program seems contrary to the idea that the computer or program of the text should be doing the bulk of the work.

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narrative, as with the “les regardaient faire” node is an impediment to interpretation, rather than a “glitch” in the strict sense of the word (the algorithm functions as expected, regardless of the continuity of the story). Regardless of the path the reader takes, there is only one “real” story. There are even two choices that are not even choices at all: node 13 asks the reader if he or she wishes to know how long one brother has been analyzing dreams, and the alternative option is “si non, passez à 14 tout de même, car vous ne le saurez pas plus” (Queneau, 1973e, p. 279). The following node promises the analysis of the dream, but the alternative proposition affirms: “si non, passez également à 15, car vous ne verrez rien” (Queneau, 1973e, p. 279). In short, this conte is not at all à notre façon. The reader must read a certain subsection of the story as Queneau wrote it and in reality has very little freedom compared to what was promised in the title. Campaignolle-​ Catel (2006, p. 141) notes: “Le texte façonné porte ainsi les traces d’une confection défectueuse où les chemins s’appellent les uns les autres dans une cacophonie plaisante. L’ensemble des choix offerts par la structure du Conte figure une arborescence autant lacunaire que parodique.” While it lacks any and all of Propp’s functions, Queneau’s text has been reduced to its bare elements and presented in a way that implies a certain freedom, but does not deliver. The true pleasure in this text comes from the realization that the system, while possible to program on a computer, is fundamentally incompatible with such a design. In this sense, this text is a useful illustration of Oulipo’s relationship with computers in general. While it is initially tempting to take advantage of a computer’s incompatibility with the notion of chance, a rigorous application of computer procedures to literature results in a diminished role of the reader. While this lack of freedom on the part of the reader may have been compatible with the group’s early procedural production, by the time second-​generation members were producing more complex texts that reorient the reader in a different style of reading, the strict nature of the algorithm had become incompatible with the group’s aesthetic goals. Georges Perec had a day job in the Laboratoire de neurophysiologie médicale at the CNRS, for which he developed his own organizational system, an algorithm of sorts: “It was not a purely mechanical job; an elementary grasp of the contents was a sine qua non, for a Flambo system

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was no different from a computer: if you put garbage in, you got garbage out” (Bellos, 1993, p. 255). In order to perfect his system, “Perec read his way into the field through the work of a distinguished mathematician who happened to be French, Claude Berge. He could have had no idea at the time that Berge had recently joined a discreet little group that called itself the … OuLiPo” (Bellos, 1993, pp. 253–​254). Given the monotony of Perec’s job, the author amused himself by writing pseudo-​scientific articles and experimenting with incremental indentations on the typewriter to produce texts in various shapes26 (Bellos, 1993, pp. 261–​262). Through this work, Perec was not only exposed to mathematical and scientific principles that he would not have otherwise known, but also parodied them; not only was he working on typewriters and other mechanical precursors to the modern computer, but he was developing an organizational system similar to the way early computers worked; finally, he was making steady money doing mind-​numbing tasks that in turn impacted his authorial voice. L’art et la manière d’aborder son chef de service pour lui demander une augmentation (1968) began as a commission by the Humanities Computing Centre of the CNRS. Jacques Perriault (a researcher at the Maison des Sciences de l’Homme) gave Perec a humorous flowchart by an anonymous programmer at the Laboratoire Électronique, of which the central idea was: … la possibilité de souligner l’importance du rôle des facteurs humains dans les PROBLÈMES DE COMMUNICATION dans l’entreprise. Approcher un client, un chef de service, un employé relève de techniques différentes : le fond du problème est toujours le même : d’une façon ou d’une autre, CONQUÉRIR UN HOMME, LE CONVAINCRE. (Salon, 2015, p. 12)

Perec’s text, based on a refurbished flowchart of his own design, appeared in the December 1968 issue of the revue L’Enseignement programmé, published by Dunod-​Hachette. Perec transformed the text a few months later into a German-​language Hörspiel, which was later translated and performed in France as a stage play entitled L’Augmentation (November 26 This might have influenced the typographical nature of some of Perec’s earlier Oulipian endeavors, such as the poem “Rail” in the volume La littérature potentielle (see Chapter 2).

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12, 1969). While at first glance, Perec’s flowchart has the appearance of a serious computer program, it is filled with unexpected and humorous scenarios: a trash can, disease, unlucky fish bones, T60 issues, and more. While each fork in the road technically represents a binary choice (either the boss has red spots on his face or he does not, for instance), the scenarios obey a different kind of logic –​not that of a computer algorithm, which would not foresee the consequences of a cafeteria serving fish during Lent, but rather the unspoken rules of a bureaucratic office. Perec’s text presents itself as an ironic user’s manual for asking for a raise, as evidenced by the title and the second-​person narration. While Un conte à votre façon could be represented as a flowchart, Perec’s tour de force lies in the unexpected way he translated the content and structure of a flowchart into text. For a computer to proceed through an algorithm, it must choose one single path based on the data it is given. Perec’s remastered flowchart, however, is structured in such a way that each path leads either to a trash bin in the center of the text or back to the beginning, allowing Perec to reinitiate the algorithm at the end of every failed attempt. This creates multiple iterations in the program, allowing it to repeat itself indefinitely. While Perec does not take every possible path through the flowchart, his exhaustive rewriting of multiple iterations produces a 65-​ page sentence that, while perfectly regular in syntax, contains no punctuation or capital letters. Perec’s narration takes advantage of the repetitive nature of iterations rhetorically in a variety of ways, first and foremost in his adoption of the term, l’augmentation (the original flowchart was titled simply L’art et la manière d’aborder le chef de service). “Augmentation” refers to a raise in the main character’s salary, but also to the augmentation of the text itself through multiple attempts to achieve this raise. Bellos explains a third meaning: “The plot itself is a pun, since the French word for a pay raise or increment (augmentation) also signifies ‘incrementation’, the procedure used by a computer to mark its path around an algorithm” (Perec, 2017c, p. 911). While the expression L’art et la manière evokes the idea of rhetoric in the traditional sense, the thought of composing such a long single sentence hardly seems to be a standard rhetorical move. However, upon closer inspection, it is clear that the lack of capital letters and punctuation is nothing

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more than a typographical distraction, as the text is still grammatically correct, reproducing a logical progression through the flowchart. While the text is syntactically repetitive due to the repetition of the logical propositions that allows Perec to proceed through the algorithm,27 one could easily reconstruct the individual propositions that make up each clause, adding in punctuation and capital letters for clarity. The lack of typographical divisions therefore forces the reader to pay more attention, reading the text side-​by-​side with the corresponding flowchart to ensure that the proper sequence is indeed being followed. The uniform nature of each line and lack of punctuation resembles computer tape, but with words instead of numbers. The resulting text simulates computer outputs of the day,28 but also creates a sense of confusion that the reader is caught in a machine and has no idea where it begins or ends. The text begins in medias res with the perfect participle construction describing a ground situation which leads to a (1) proposition, at which point there is a branch in the flowchart, which results in a choice between two (2) alternatives: either the (3) positive hypothesis or the (4) negative hypothesis. Since the negative hypothesis turns out to be true according to the narration, a (5) choice is made for the character, which would lead to a (6) solution in an ordinary algorithm, but which Perec interrupts with a conditional reprise, leading back to the initial proposition and beginning the next iteration: (1) [a]‌yant29 mûrement réfléchi ayant pris votre courage à deux mains vous vous décidez à aller trouver votre chef de service pour lui demander une augmentation (2) vous allez donc trouver votre chef de service … (3) là de deux choses l’une (4) ou 27 In the subsequent radio play adaptation, Perec divides these logical elements into six voices and a joker: “1. La proposition; 2. L’alternative; 3. L’hypothèse positive; 4. L’hypothèse négative; 5. Le choix; 6. La conclusion La Rougeole” (Perec, 1981a, p. 10). 28 Many of Perec’s early manuscripts are typed like this, with no uppercase letters. This is also reminiscent of the poetry of e. e. cummings. 29 In the original publication, all letters are lowercase, however the Pléiade edition capitalized the first letter. I have corrected this here. Furthermore, all the numbers in the text which correspond with the logical elements cited above are mine, added for the sake of clarity.

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bien mr x est dans son bureau (5) ou bien mr x n’est pas dans son bureau (6) si mr x était dans son bureau il n’y aurait apparemment pas de problème mais évidemment mr x n’est pas dans son bureau vous n’avez donc guère qu’une chose à faire guetter dans le couloir son retour ou son arrivée mais supposons non pas qu’il n’arrive pas en ce cas il finirait par n’y avoir plus qu’une seule solution retourner dans votre propre bureau et attendre l’après-​midi ou le lendemain pour recommencer votre tentative … (Perec, 2017c, p. 911)

Perec seems to have understood the algorithm as a machine for producing conditional clauses, and his text can therefore be considered a pastiche of algorithmic language in literature. The simplicity of this six-​part structure is complicated by Perec‘s use of the conditional. Furthermore, as he continues throughout the text, Perec varies these six steps so that the reader is never quite sure as to what is coming next. The logical propositions necessary to Perec’s chosen path through the flowchart result in repeated words and turns of phrase, which in essence allow the reader to understand the text’s syntactic structure without traditional division into sentences, capital letters, or punctuation. For this reason, reading Perec’s narration is not a true equivalent of reading the flowchart that generated it, which is reproduced at the end of the text. The beauty of algorithms lies in their simplification, a reduction of complex problems to a series of logical steps. Perec’s text plays with this notion, often repeating the clause: “car il faut toujours simplifier.” One way Perec plays on this formalized nature of algorithms is by creating placeholders, reducing several characters to algebraic variables. The first time, the author reduces “votre chef de service” to “monsieur xavier” and finally to “mr x.” The choice of x for the substitution implies basic algebra, as it is the most common choice for the unknown in basic algebraic equations. The reduction of monsieur xavier to x allows for abstraction. The boss is no longer a unique individual and can be easily replaced by any other chef de service. This gesture is an excellent illustration of the formalization of mathematical language: an algebraic variable is not only an unknown to find through the manipulation of the problem, but in more abstract mathematics, such abstractions can be used to find global solutions. Perec performs a similar substitution with mr x’s boss, Zosthène, or mr z. With the boss’s secretary, on the other hand, Perec reverses the direction, replacing

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the placeholder “mlle y” with Yolande. Perec’s use of algebraic variables interchangeably with real named characters indicates the replaceable nature of the individual cogs in the bureaucratic machine. Furthermore, the substitutions allow a reader to treat the text as a user’s manual, replacing mr x with the name of his or her own boss and following the instructions in order to pursue a raise. While Perec’s use of the flowchart and his creation of an algorithmic language is interesting, the key to this text lies in what escapes the rule. As with Die Maschine, Perec begins with an entirely anti-​humanist game –​ using a computer to solve a problem –​and turns it into a very human kind of work. Not only does the text seem to be a conventional left-​wing tale of the small, dispensable worker within a large and impersonal bureaucracy, but the various obstacles the protagonist encounters are often incompatible with machines, such as disease, food, and emotions. What is least compatible with computing is the element of time, since computers make calculations almost instantaneously. At each augmentation of the text signaled by the return to the beginning, the repetitions (of words, situations, and scenarios) function as an incrementation in the algorithm, marking the path that has been taken. The variations indicate the passage of time, a signal to the reader that the algorithm is not a human solution to this problem. For instance, the main character spends an unprecedented amount of time doing the following activities: “guetter dans le couloir” (Perec, 2017c, p. 911), “attendre l’après-​midi ou le lendemain” (Perec, 2017c, p. 911), “le lendemain ce qui est un samedi et que le samedi vous ne travaillez pas mais ceci est un problème délicat que nous nous proposons d’envisager de plus près tout à l’heure” (Perec, 2017c, p. 917), “pendant quarante jours ouvrables” (should the boss have the measles) (Perec, 2017c, p. 923), etc. The ending as well returns the reader to the beginning: “… efforcez-​vous à nouveau de le convaincre” (Perec, 2017c, p. 945). The text does end eventually, leading the reader back to the beginning of the flowchart, which appears on the next page, implying that the reader can carry out this same process him or herself. Mark Wolff (2017, p. 87) notes that Perec was wary of computers: “Indeed, Perec recognised the computer’s ability to perform many operations systematically without error, but he believed that error in a

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system was required for freedom and creativity, and that programming a computer to err would be very difficult to achieve.” This reading of L’Art et la manière is in line with mine, as Perec’s algorithmically inspired text forces both author and reader to become obsessively conscious of time. The result is a lamenting of the inevitability of time and death, a traditional poetic topic that is incompatible with the algorithmic procedure. Humans do not function in the same way that computers do. They simply do not have the time. In this sense, Perec uses the constraint of an algorithmic procedure to emphasize the incompatibility of algorithms and literature, marking a high point in Oulipo’s use of algorithmic procedures as generative constraints for producing potential literature.

III. Programming Reading and Writing A decade after its initial collaborations, Oulipo participated in a research group at the Centre Pompidou known as the Atelier de Recherches et Techniques Avancées (ARTA), directed by computer scientist Paul Braffort. The goal was to create a foundation for “un possible accord entre l’informatique et la création littéraire” (Fournel, 1981, p. 298). The intent of the project was to demonstrate that computers could assist in both reading and writing literature and was divided into two main categories: first, “La lecture assistée,” which resulted in the programming of an example of “littérature combinatoire” (Cent mille milliards de poèmes) and “littérature algorithmique” (Un conte à votre façon); and “La creation assistée,” which dealt with interventions by the author, reader, and computer (Fournel, 1981, pp. 298–​301). The results were presented at a conference entitled “Écrivain-​ordinateur” in June 1977 by Paul Fournel, Italo Calvino, Jacques Roubaud, and Paul Braffort. In Atlas de Littérature Potentielle, Fournel reproduced his presentation, which details the goals and results of this collaborative endeavor. The first experimental text treated by Braffort’s project was Queneau’s Cent mille milliards de poèmes, ostensibly due to the physical volume, which complicates the selection of which verses to read: “Le recueil imprimé

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est très joliment conçu mais la manipulation des languettes sur lesquelles chaque vers est imprimé est parfois délicate” (Fournel, 1981, p. 299). While it is true that certain manipulations of the set of poems are cumbersome, for instance reading Queneau’s original 10 sonnets, the physical design of the volume is visually compelling and informative regarding the combinatorial aspects of the text and one risk of programming it on a computer is to lose this original object. Nevertheless, Fournel (1981, p. 299) claims in his article that a computer facilitates this reading process: “L’ordinateur, lui, opère une sélection dans le corpus à partir de la longueur du nom du ‘lecteur’ et du temps qu’il met à le dactylographier sur le terminal puis édite le sonnet qui porte la double signature de Queneau et de son lecteur”. This method responds to Oulipo’s earlier question to Starynkevitch regarding the selection of the poems, determining the poem based on the reader’s name and typing speed and therefore according to the reader a limited role in the selection of the sonnets while also bestowing on this reader the title of co-​author. Wolff (2007, p. 6) comments on this increased role of the reader: The program’s algorithm provides a certain degree of interaction between the user and the machine, and the results of running the program are theoretically reproducible if a user types the same name in the same amount of time. The algorithm therefore has potential, but only insofar that it accelerates the production of poems … The original algorithm preserves an active role for the user, even if that role requires the minimal engagement of typing one’s name in order to sustain the creative process.

However, while the ARTA program does indeed have more potential than Starynkevitch’s, which generated sonnets without any reader involvement, it is still restrictive. The physical edition affords the reader endless possibilities to read in different ways, but the ARTA program only produces a single poem using a method that is never explained to the reader. Even though the program does require some form of reader involvement, it is doubtful that a willing reader would find any amusement in reading more than one or two poems produced in this manner. Furthermore, as the reader is not privy to the selection process, he or she has little to no conscious control over the results. Ironically, programming

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a computer-​inspired text deprives the reader of an essential part of the reading experience –​manipulating the physical object. Like Starynkevitch’s program, the ARTA program for Cent mille milliards de poèmes is not accessible today, and likely obsolete given the nature of programming languages. That said, Fournel did propose an unexpected interpretive use for the program: “L’auteur lui-​même peut faire son profit d’une telle édition: lorsque les combinaisons sont aussi nombreuses, il peut procéder à des contrôles par sondage. L’ordinateur joue dans ce cas un rôle d’assistant à la mise au point définitive du texte” (Fournel, 1981, p. 299). The thought that the author could use a computer as a computational tool to organize an exponential quantity of poems could be viewed as contrary to the Oulipian project, as it represents simple calculations instead of a creative, generative device. However, this sampling idea could be viewed as an important precursor to digital humanities work, proposing an authorial equivalent to Franco Moretti’s distant reading30 that would enable an author to deal with the exponential results of combinatorial literature. In humanities scholarship today, this method could help literary scholars approach Queneau’s text by allowing for educated statistical inferences about a body of poetry that the author has designed to be impossible to read in a human lifetime. Through ARTA, Oulipo also programmed Un conte à vôtre façon with the help of Dominique Bourguet. The resulting program guides the reader through the text, node by node, prompting him or her for choices to advance in the story: “L’ordinateur, dans un premier temps, ‘dialogue’ avec le lecteur en lui proposant les divers choix, puis dans un second temps, édite ‘au propre’ et sans les questions, le texte choisi. Le plaisir de jouer et le plaisir de lire se trouvent donc combinés” (Fournel, 1981, p. 299). As with Cent mille milliards de poèmes, the use of the computer to read Un conte à vôtre façon is reductive in terms of reader interaction. Queneau’s simultaneous display of all possible options allows the reader to understand the potentiality of the short tale, its contradictory nature, and his 30

In his award-​winning essay collection of the same name, Moretti outlines his vision of “distant reading,” or a professional reading method that relies heavily on computer programs. (Moretti)

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or her own limited role. This program, however, only allows the reader to see one step at a time, requiring the reader to read the tale multiple times in order to gain any insight into the system itself. Furthermore, the editing process that the computer carries out risks generating a “clean” text that first claims the peas do not dream and then explains the dream they had. While the example provided in Atlas de littérature potentielle does not contain this contradictory set of nodes, the chance that a reader would stumble upon this contradiction during a reading is far more likely than the Cent mille milliards de poèmes program generating a poem that repeats the rhyme marchandise. The second goal of the ARTA project was to determine new methods for computers to assist in literary creation at three levels: first, the simplest case examined how a computer could assist the author in the composition of a text; the second chain of intervention allowed the computer to intervene in the composition, and then again in the reading of the text; the third level was technically the most complex, requiring input from both the author and the reader to generate texts to read. The participants in the project explored each of these three cases using specific examples: Calvino’s “L’incendio della casa abominevole,” Roubaud’s La Princesse Hoppy, and Marcel Bénabou’s “aphorismes artificiels.” No evidence is provided as to which chapter of Roubaud’s novel was written “… avec l’aide de la machine..” and “… que le lecteur devra lire avec cette même machine” (Fournel, 1981, p. 301), while the case of Bénabou’s aphorisms is elaborated with more detail and Calvino gave his own presentation on “L’incendio della casa abominevole.” Bénabou’s aphorisms31 are ostensibly the most complex case investigated during the ARTA project, but in reality they are simply another example of Oulipian substitutional constraints such as those discussed in Chapter 2: “l’auteur donne un stock de formes vide et un stock de mots destinés à les remplir; le lecteur vient ensuite formuler une demande et selon cette demande, la machine combine mots et formes et produit des 31

Mark Wolff has reconstituted the code from this project and used it to generate his own aphorisms. His website allows readers who have a background in programming to load his file into an APL interpreter and do the same. (Oulipian Code | Mark Wolff)

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aphorismes” (Fournel, 1981, p. 301). Like the S+​7 method, Bénabou’s aphorisms seem inherently programmable given their reproducible syntactic structures and a given vocabulary with which to make substitutions. However, as with the S+​7 method, the most amusing aphorisms are more likely to be generated by a human being than by a computer, as the human author can select the substitutions that would produce the most humorous effects on a human reader. Ironically, the simplest case in this half of the ARTA project produced the most interesting results. The text in question was Calvino’s “L’incendio della casa abominevole,” a 1973 text that represents this foreign member’s attempt to consider computers creatively. This short story was written in response to a rather vague question first proposed by IBM, according to a preface by Esther Calvino: “C’era stata una richiesta, piuttosto vaga, della IBM: fino a che punto era possibile scrivere un racconto con il computer?” (Calvino, 1993a, p. 4).32 A short version of the story, “L’incendio della casa abominevole,” was first published in Playboy Italia in 1973, and Calvino hoped to expand on it to produce a longer novel entitled L’ordine del delitto. While a legitimate programming experiment did indeed accompany the composition of Calvino’s short story, influencing the author’s conception of literature in the process, the actual extent to which the text produced drew from tangible results of this project is questionable. “L’incendio della casa abominevole” takes the form of a detective story, in which a computer scientist narrates his role in solving a complicated crime. Following a suspicious fire that burned down a villa and killed all four of its inhabitants, the only evidence in this crime is a book found at the scene entitled: “Relazione sugli atti abominevoli compiuti in questa casa”33 that lists 12 abominable acts in alphabetical order: “Accoltellare, Diffamare, Indurre al suicidio, Legare e imbavagliare, Minacciare con pistola, Prostituire, Ricattare, Sedurre, Spiare, Strozzare, Violentare”34 32

“There had been a rather vague request from IBM: to what extent was it possible to write a story with a computer?” (my translation) 33 “Report on the abominable acts performed in this house.” (my translation) 34 “Stabbing, defaming, inducing suicide, binding and gagging, threatening with a gun, prostituting, blackmailing, seducing, spying, choking, raping.” (my translation)

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(Calvino, 1993a, pp. 176–​177). Hired by an insurance agent, Skiller, to reconstruct the events that led to the fire, this unnamed narrator must use his computer’s number-​crunching power to determine which crime can logically be attributed to the dwellers of the house and in which order the crimes were committed. The insurance company must learn the true nature of these events if it is to fulfil its obligations to the owner of the house, the life insurance policy of the widow of one of the victims, and the owner of an insured wig collection that was destroyed in the fire. Mathematically speaking, each of the 12 crimes listed had to have been committed by a single character on a single victim, and the four characters can be grouped into pairs in 12 different ways. Since there are 12 crimes that were committed before the arson and 12 possible pairs, combinatorics allows one to calculate 1212 possible combinations, a daunting number of possibilities even considering that it is 91,083,899,551,744 less than the number of poems in Queneau’s Cent mille milliards de poèmes. Just as Queneau insisted that it would be impossible for a reader to read all his poems, it is likewise impossible for Calvino’s narrator to consider this exponential number of possibilities alone. However, the problem Calvino devised runs contrary to Queneau’s text as it is inherently anti-​combinatorial, forcing the computer scientist protagonist to use a computer’s combinatorial power to reduce the number of possible scenarios. In this sense, Calvino’s choice of the detective fiction genre is especially appropriate, as it depends upon logical deduction. His innovation is to introduce a computer to solve a problem that is far too complicated for a human detective to tackle. In the explanatory essay, “Prose et anticombinatoire,” that Calvino published in Atlas de littérature potentielle, the author concludes: “Cela montre bien, pensons-​nous, que l’aide de l’ordinateur, loin d’intervenir en substitution à l’acte créateur de l’artiste, permet au contraire de libérer celui-​ci des servitudes d’une recherche combinatoire, lui donnant ainsi les meilleurs (sic) possibilités de se concentrer sur ce ‘clinamen’ qui, seul, peut faire du texte une véritable œuvre d’art” (Calvino, 1981, p. 331). However, beyond the author’s use of combinatorics to create such a large number of possibilities that would necessarily have to be solved by a computer, there is little evidence in the story itself that Calvino’s computer experiment succeeded in allowing him to answer his own combinatorial problem. His text

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neither cites literal programs nor tangible results, but rather recounts the computer scientist’s imaginative musings on the nature of the crime: “Non posso impedire ai lenti tentacoli della mia mente d’avanzare un’ipotesi per volta, d’esplorare labirinti di conseguenze che le memorie magnetiche percorrono in un nanosecondo. È dal mio elaboratore che Skiller aspetta una risposta, non da me” (Calvino, 1993a, p. 180).35 While the human programmer must use deductive reasoning to provide more constraints (a character could not have killed another after having been killed himself, for instance), his wild imagination begins to introduce unintentional bias into the task. Susie Cronin (2017, p. 4) notes this facet of the text as well, claiming: “The narrator nonetheless feels his methodology oscillating between ‘modelli algebraici’ and ‘un cinematografo mentale’: between careful, systematic deduction and wildly creative sensationalism.” Attempting to narrow the list, the programmer introduces the insurance man as a new element in his program. While a reader might recognize this development as a conventional twist in a traditional detective story, this new variable causes the machine to crash (Calvino, 1993a, p. 188). He then imagines a more complicated scenario: that the insurance agent is the true criminal, who, with the help of another programmer, devised an elaborate plot to incite the inhabitants of the villa to commit these crimes, knowing that it would be mathematically impossible to resolve and absolving the insurance company of its obligation to honour the insurance claims. The text ends with a knock at the door and the now paranoid computer programmer is convinced that Skiller is there to kill him, as he has seen through the insurance company’s perverse scheme, leading the reader to wonder if the programmer has accurately assessed the situation or rather descended into madness due to the unsolvable nature of the problem. Irrespective of any literal computer experiments that coincided with Calvino’s publication of this text, “L’incendio della casa abominevole” depends upon a primarily theoretical understanding of how computers function. Furthermore, the published text does not contain 35

“I cannot prevent the slow tentacles of my mind from advancing one hypothesis at a time, from exploring mazes of consequences that magnetic memories travel in a nanosecond. It is from my computer that Skiller expects an answer, not from me.” (my translation)

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any legitimate proof that the work carried out in the context of ARTA had a tangible effect on the plot. Rather, it is the possibility of using algorithms to solve an impossibly complicated literary problem that fuels the writing of the story. Just as Il castello dei destini incrociati was constructed around a destabilizing factor, the computer itself is a disruption that Calvino likens to the Oulipian clinamen, despite the fact that there is no strict generative constraint at the heart of either text. That said, this text is indicative of the Oulipian approach to computers in the second decade of its existence. Rather than using literal procedures to produce text, Calvino’s experiment derives the heart of his story from a rudimentary understanding of computers. The resulting text can therefore be read as Calvino’s unease about this new technology, which he considered an unanticipated disruption in the way human beings interact and behave. In Calvino’s presentation at the conference, entitled “Prose et anticombinatoire,” the author delves into far more technical aspects of programming a computer to limit the combinatorial potential of the difficult situation, presenting two types of “contraintes objectives” that he used to reduce the number of total possibilities: “compatibilité entre les relations … pour les actions de meurtre … pour les actions sexuelles … pour les appropriations d’un secret … pour les appropriations de volonté” and “ordre des séquences” such that the order of the acts of murder do not prevent the logical succession of other crimes (Calvino, 1981, pp. 323–​324). These constraints are akin to the type of logic a detective might engage in, but in Calvino’s project become parameters for the program to limit possibilities. Calvino then introduces necessary “contraintes subjectives” that take into account the attributes and capabilities of the characters in question, constraints that do not stem from a mathematical impossibility, but rather from the human dimension of such a tale. For instance, one character is an innocent young boy scout, who would vomit immediately upon taking any drugs (Calvino, 1981, pp. 326). Calvino recognizes an additional complication associated with this category, in that “Chaque personnage pourrait changer dans le déroulement de l’histoire (après certaines actions accomplies ou subies): perdre certaines incompatibilités et en acquérir d’autres !!!!!!!! Pour le moment on renonce à explorer ce domaine” (Calvino, 1981, pp. 327). The final category Calvino explored in his presentation was

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that of “contraintes esthétiques (ou subjectives du programmeur),” complicated by the preferences of the programmer for “l’ordre et la symétrie” (Calvino, 1981, pp. 327). Some of these aesthetic preferences fall into the realm of common sense, for instance that commutativity is not possible in the case of murder: “si A tue B, B ne pourra pas tuer A” (Calvino, 1981, pp. 327). Others, however, have the potential to eliminate viable scenarios due to a lack of aesthetic charm, for instance Calvino’s programmer proposes a model according to which “les 12 actions soient également distribuées entre les 4 personnages, à savoir chacun d’eux perpètre 3 actions (une sur chacun des autres) et est victime de 3 actions (chacune perpétrée par un des autres)” (Calvino, 1981, pp. 327). The theoretical elaboration of these three categories of constraints by Calvino in his presentation offers insight into the types of programs that Braffort and others were designing for this facet of the ARTA project, but also fails to explain the finished product. It is clear that the work Calvino participated in through ARTA was more inspirational than generative, leading to the publication of an imaginative short story that does not take into account the actual results of the programming. And while Calvino might indeed have intended to return to this project, expanding on the short story to create a longer work that discussed the computer’s actual results, the fact remains that Calvino’s computer experiments seem to have been a failed project for the author, considering his ambitious initial goals. Indeed, Calvino learned through this project that computers of the time were simply incapable of replacing the author’s creative role, as Cronin (2017, p. 15) suggests: “The truth is much simpler: computer technology, in 1977, was at a much more modest stage than that which would demonstrate the machine’s autonomy to reach inaccessible dimensions of potential literature”. Cronin’s conclusion is optimistic, claiming that Calvino was simply ahead of his time and that computer-​assisted literature needed time to develop the capabilities that Calvino sought. However, I would argue that Calvino’s “failed” experiment is in fact a promising development for humanities research. While computing technology has made great strides since the 1970s, Calvino’s project is a strong indication that there is a preeminent human element that makes literature what it is, and that computing, while useful, can never replace that.

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IV.  An End to Oulipian Programming After ARTA, Oulipo definitively abandoned its organized collaborations with computer scientists. To continue these explorations, Braffort and Roubaud created a new group in 1981, which they called ALAMO (Atelier de littérature assistée par les mathématiques et les ordinateurs) (Braffort, 2000, p. 102). The founding members, like those of Oulipo, bridged a gap between humanistic and scientific work and included many who had already collaborated with Oulipo.36 The group’s three main areas of interest were combinatorial literature, substitutional constraints, and the creation of an algorithmic language for the computer to assist in literary production. Predictably, the first item on ALAMO’s combinatorial agenda was Queneau’s Cent mille milliards de poèmes, creating its own program that was similar to efforts mentioned above: “Pour ce type d’application, l’outil informatique fonctionne essentiellement comme un éditeur: c’est ainsi qu’un lecteur est évidemment incapable de reconstituer effectivement les cent mille milliards de sonnets de Queneau. En revanche, l’ordinateur peut en produire un nombre aussi grand que l’on veut” (Braffort and Roubaud). However, the group’s programmed version for this text does not appear on the website. Instead, a number of similar combinatorial texts are available in digital formats. Two are historical examples that could be considered plagiarism by anticipation of Queneau’s text, including the fifteenth-​century Litanies de la Vierge of the Grand Rhétoriqueur Jean Meschinot and the seventeenth-​century Les Baisers d’Amour de Quirinus Kuhlmann. Others are new creations by individual members, including a dizain by Bénabou inspired by Queneau’s Un conte à votre façon in which the verses can be permuted, as well as a musical example by Braffort, six triolets that can be recombined in order to generate 65 or 7,776 (ALAMO). These examples, 36

Simone Balazard, Jean-​Pierre Balpe, Marcel Bénabou, Mario Borillo, Michel Bottin, Paul Braffort, Paul Fournel, Pierre Lusson, and Jacques Roubaud, with Anne Dicky, Michèle Ignazi, Josiane Joncquel, Jacques Jouet, Nicole Modiano, Héloïse Neefs, Paulette Perec and Agnès Sola joining later. (Braffort and Roubaud)

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while interesting analytic and synthetic explorations of combinatorial poetry, do not represent a particular challenge to program on a computer. The process would be much the same as that of programming Cent mille milliards de poèmes. The group’s second interest in substitutional constraints also had much in common with Oulipo’s original algorithmic procedures and programming attempts, but made use of different types of syntactic structures: Alexandrins au greffoir is a program created by Bénabou and Roubaud, who selected hemistiches from some of the most famous alexandrine verses in the French language and then shuffled them to produce new ones; Aphorismes à votre façon is similar to the previous aphorisms developed in the context of ARTA, but are accompanied by an additional example of Locutions introuvables that performs the same procedure on popular sayings (ALAMO). Wolff asserts that Oulipo’s and ALAMO’s computer work on such combinatorial and substitutional constraints demonstrates incredible potential: “The potential of these computer programs resides in the way fragments of words and verses are recombined according to a set of well-​defined rules. Poetic forms can thus be understood as algorithms for creating meaning with language” (Wolff, 2007, para. 7). However, the idea that poetic forms are algorithms is questionable, as writing fixed-​form poetry is hardly a step-​by-​step procedure. Rather, the examples of poetic forms and recognizable syntax that allow for combinatorial and substitutional constraints are indicative of the generalizable nature of language, which allows it to be treated on a computer. While these programs are interactive and amusing, they do not result in anything more than a few additional examples of the potential of substitutional constraints for literary creation, though the “Rimbaudelaire” program does produce some particularly amusing examples by emptying Arthur Rimbaud’s “Le dormeur du val” of its nouns, adjectives, and verbs, and replacing them with words borrowed from Charles Baudelaire’s vocabulary (Alamo | Programmes /​Rimbaudelaires). This is a particularly fruitful example of a substitutional constraint due to the fact that “Le dormeur du val” is one of the most recognizable poems in the French language with a memorable syntactic structure. Replacing meaningful words in that poem with vocabulary common to Baudelaire’s poetry creates results

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that sound rather odd to anyone who knows the poems. While a feeling of déjà lu or vague familiarity was common to many of Oulipo’s substitutional constraints, the specific choice of stuffing one of Rimbaud’s most famous poems with Baudelaire’s vocabulary can be understood as a commentary on nineteenth-​century poetry in general, suggesting that this computer program is capable of generating an exponential amount of symbolist poetry. The final aspect of ALAMO’s production was a program called LAPAL (Langage Algorithmique pour la Production Assistée de Littérature), which allows the user to create his or her own program following some simple instructions: first, on paper, the user determines a corpus (a set of similar terms that one wishes to define), a schéma (an algorithmic mechanism for producing elements from the corpus), and eventually contraintes (rules imposed on the schéma); then, the reader inputs these three elements into the LAPAL system, which automatically produces a text. While ALAMO’s website allows a user to create an account and experiment in this type of literary programming, the interface is unfortunately rather complicated and riddled with internal errors. For instance, it is currently impossible to visualize examples of schémas or contraintes, which would greatly hinder a novice programmer. The textual production feature as well is dysfunctional, making it impossible to evaluate the quality of the program. If the program accomplishes what it purports to do, then it is an early iteration in natural language processing and deserves greater attention in the historiography of digital humanities and computational linguistics. In short, while ALAMO built upon the previous experiments carried out by Oulipo, it does not seem to have succeeded where Oulipo failed, namely in a truly productive creative enterprise that investigates the potential of computing for literary production. There are two ways to understand the role ALAMO has played in this critical history of Oulipo’s engagement with mathematics. First, ALAMO represents an abject failure of Oulipo to continue its exploratory programming initiatives, which were some of the first of their kind and represent a critical moment in the historical development of computer science, computational linguistics, and digital humanities. Had Oulipo maintained control of its programming objectives rather than relegating this activity to a subsidiary, the group might have remained at the cutting edge of these fields, which are no less

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relevant today. Alternatively, ALAMO could be understood as the confirmation that computers are incompatible with Oulipo’s mathematical objectives, depriving the reader of an important role in the creation of potential literature. While ALAMO marks the end of organized experiments on computers by Oulipo or a subsidiary, it would be erroneous to suggest that the members of the group did not continue to evolve with the times and work on computers on an individual level or as a group. For instance, in 1999, Oulipo engaged in a subtly different commercial exercise when the group created a CD-​ROM, Machines à écrire, a mass-​produced and widely available digital interactive collection of Oulipian texts, including: an interactive biography of Raymond Queneau; a “galaxie combinatoire” that allows the reader to learn more about combinatorics and literature; a digital edition of Un conte à votre façon; another of Cent mille milliards de poèmes that offers the reader four different ways to generate pseudo-​random poems, as well as the possibility of reproducing Queneau’s original 10; an interactive edition of Perec’s L’art et la manière d’aborder son chef de service pour lui demander une augmentation; and finally, Perec’s postcards to Calvino (Gauthier, 2009). As this was a commercial and editorial endeavor rather than an organized project in exploratory programming, I do not consider this CD-​ROM to be indicative of the group’s evolving relationship with computers. Furthermore, the technology is already out of date and it is very difficult to find a computer that can run this (admittedly delightful) CD-​ROM. Additionally, with the induction of Valérie Beaudouin to the group, Oulipo not only found a talented webmaster, but a digital humanist whose work with computers is analytic in nature. For instance, in “L’outil qui démasque: l’usurpation littéraire” published in the Tangente volume Mathématiques et littérature, Beaudouin (2006, p. 16) details her work on stylometry: “… un ensemble de méthodes statistiques qui ont pour vocation d’apporter, par la mesure, des éclairages à la stylistique. Le presupposé de cette discipline est qu’il y aurait dans les textes des traits quantifiables qui signeraient la marque d’un auteur, d’un genre, d’un texte”. Beaudouin’s article discusses the potential uses of stylometry to find the relative “distance” between famous seventeenth-​century French theatrical texts

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of Corneille and Molière. However, her conclusion is practically Oulipian in nature: “Enfin, ces méthodes d’attribution peuvent avoir d’autres lieux d’application plus paisibles que les grands textes de la littérature, ne serait-​ ce que pour repérer les plagiats, les textes non authentiques, les textes écrits par des machines …” (Beaudouin, 2006, p. 19). Claude Berge as well continued his work finding literary examples of graph theory, even using it as the solution to a detective story, which he published in the Bibliothèque Oulipienne under the title “Qui a tué le duc de Densmore?” (1994) Berge’s text constructs a narrative of which the solution can be best illustrated by a specific mathematical theorem in the field of graph theory. In this seemingly traditional “whodunit,” the protagonist, Detective Ralston, attempts to solve the mystery of a grisly murder that took place at a lovely retreat on the Isle of White, the castle of the Duke of Densmore. When the burned bodies of the Duke, his butler, and a crocodile are found in a tower, it becomes apparent that this was no accident. The two men and the crocodile were killed in an explosion, most likely by one of the eight visitors who had come to see the Duke in the past year. Luckily, Detective Ralston is able to interview these eight visitors, all women who do not remember the dates of their visits, but who do remember who else was on the island at the time:

1. Felicia (F) met Emily (E) and Ann (A) 2. Cynthia (C) met Diana (D), Emily (E), Ann (A), Betty (B), and Helen (H) 3. Georgia (G) met Ann (A) and Helen (H) 4. Diana (D) met Cynthia (C) and Emily (E) 5. Emily (E) met Felicia (F), Cynthia (C), Diana (D), and Ann (A) 6. Ann (A) met Felicia (F), Cynthia (C), Georgia (G), Emily (E), and Betty (B) 7. Betty (B) met Cynthia (C), Ann (A), and Helen (H) 8. Helen (H) met Cynthia (C), Georgia (G), and Betty (B)

While this information is insufficient for a detective, it is plenty for his acquaintance, Oxford mathematics professor Turner-​Smith. As with the Bridges of Königsberg, this information can be represented as a graph,

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simplifying the analysis and making the missing information (the dates of each woman’s visit) irrelevant. While according to the testimonies of each of these women, the detective had declared the butler the killer with his own death being an accident, Professor Turner-​Smith sees from the graph that one of the women was lying, and therefore the killer. Using only the data provided by the women, it is possible to construct what is called an interval graph (since each woman stayed only once on the island, and each edge therefore corresponds to the intersection of two intervals) (Berge, 2000, p. 145) (Figure 4.3).

Figure 4.3.  The graphical representation of who met whom upon visits to the Duke’s island, taken from Claude Berge’s “Qui a tué le duc de Densmore?” (p. 145). Reproduced with Oulipo's permission.

On this graph, the eight women are represented as nodes, each labelled with the first letter of her first name. The edges that link them represent whether two women had corresponding stays on the island. While the graph corresponds perfectly to the data provided by these eight women, the professor notes that, given a theorem about interval graphs, one must be lying. The concept of the interval graph first came about in 1957 when Hungarian mathematician, György Hajós, began to ask mathematical questions about what sort of graphs could be obtained by considering the intersection of intervals. Hajós’s theorem defines these interval graphs and

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determines various properties, which turn out to be the keys that can solve the mystery of the Duke of Densmore. Hajós states that an interval graph cannot contain a cycle of length four or more without a chord, but the professor notes that this graph contains the cycle ACHG in which there is no chord. Hajós’s theorem also demonstrates that a proper interval graph cannot contain a triangle inscribed within a hexagon (which this graph does contain, in the set ABCDEF). Therefore, this is not a proper interval graph, leading the professor to conclude that one of the eight women lied about her time spent on the island, possibly hiding in the castle’s cellars on multiple occasions to carry out her evil plan. Since these two anomalies have only one point in common, the vertex A, and given that the removal of this point would make it an interval graph, the professor determines that the node A is the culprit and that Ann Laybourn must have been the killer (Berge, 2000, p. 147). Berge’s major contribution to graph theory was to give it a prominent place in mathematics by emphasizing its connections to set theory and applications in other relevant sub-​disciplines, fitting it into the overall architecture of mathematics perpetuated by Bourbaki in texts such as “L’architecture des mathématiques” (Toft, 2007, p. 7). In “Qui a tué le duc de Densmore?” Berge applies graph theory to detective fiction, a genre that other Oulipians including Calvino and Le Lionnais37 had also examined within the context of Oulipo. In Berge’s approach, not only is the information provided only sufficient for solving the crime in a mathematical sense, but the specific solution depends upon a mathematical theorem within this larger field. In this sense, Densmore is not unlike Braffort’s Mes Hypertropes or Roubaud’s La Princesse Hoppy, finding a literary problem that can be solved using a specific theorem. Indeed, Berge’s application of mathematics to detective fiction is especially appropriate, given that the genre itself implies a logical, mathematical approach to problem solving that is reflected in Berge’s literal fashioning of this text around a legitimate mathematical proof. Furthermore, the fact that both Calvino and Berge chose the detective fiction genre to illustrate a mathematical or technological idea is intriguing, 37

Le Lionnais had even created a spinoff group devoted to examining the potential of the genre, called the Ouvroir de Littérature Policière Potentielle or OuLiPoPo.

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as it implies that both considered this genre inherently mathematical as it depends upon finding a solution to a particular problem. Algorithms are created with a goal in mind: to solve a problem. Algorithmic texts therefore require that the author and reader both solve the problems of the text through reading and writing, a quintessential feature of the texts and programs produced by Oulipo in its various engagements with computers. Whether the problem makes use of a restricted vocabulary set (as with Le Lionnais’s ALGOL poems) or converts flowcharts into narratives or vice versa (as Perec and Queneau demonstrated), this type of literary production requires a corresponding algorithmic mentality on the part of the reader. Ironically, programming these algorithmic texts on computers forced Oulipo to return to a human domain and re-​evaluate the role of the reader in its mathematical project. While the Oulipian author has an explicit role in the production of constrained literature, the group’s practical forays into computer science allowed the members to realize that a willing reader is imperative to the group’s mathematical aesthetics. Oulipo’s computer experiments represent some of the first digital humanities work, falling under the category of exploratory programming and producing electronic literature. Understanding why the group abandoned these computer efforts is therefore key to a more critical understanding of the potential and limitations of digital humanities scholarship today. If Oulipo chose to distance itself from computer science in later years, it is because algorithms are not constraints, but rather procedures meant to solve problems. Oulipo, however, was interested in the potential of pure mathematics to literature, rather than applied mathematics. This predilection for abstract mathematics and its effects is illustrative of a possible strategy to bridge the two-​culture divide in our scholarship, pedagogy, and literary production.

Vocalocolorist portraits of Michèle Audin and Italo Calvino by OuPeinPo member George Orrimbe. Reproduced with the artist’s permission.

Chapter 5

Geometry*

Geometry comes from the ancient Greek roots “geo” or earth and “metron” meaning measurement. The desire to measure the earth is a natural byproduct of mankind’s innate ability for mathematical reasoning. While pre-​modern mathematics understood geometry in precisely these terms (using it to find lengths, angles, areas, and volumes), Euclid’s Elements proposed a new approach to geometry that was not concerned with actual, physical space, but studied properties of abstracted, ideal shapes. In this sense, the history of geometry straddles a fine line between mathematical abstraction and practical applications, deducing properties of an abstracted space in order to apply them to the world in which we live. Geometry, with its historical oscillation between abstracted and real space, is evidence of a greater debate about the nature of mathematical work: does the study of mathematics allow one to understand the rules that govern the world in which we live; or is it rather a reflection of the way humans understand the world? The work of a geometer is merely one instance of the human tendency to generalize, look for models, and apply them to the world. In humanistic scholarship as well, scholars often have recourse to structures, plot diagrams, and definitions in order to theorize larger categories of cultural objects. Digital humanities scholarship in particular makes use of computing power to understand larger trends in literary genres, with a recent example being the work of Matthew Jockers, who has created mathematical models of six archetypal plot shapes derived from tracking words with emotional charges (Piepenbring, 2015). While such methods can be viewed as ambitious *

This chapter represents an expanded and English-language version of an article recently published in the revue Etudes littéraires (2021), entitled “L’OuLiPo et la géométrie : l’étrange utilité de la table des matières.”

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attempts to extend the results of humanistic research from studies of individual texts or restricted corpora by means of computing power, they can also be understood as contrary to the reading experience. In Se una notte d’inverno un viaggiatore (1979), for instance, Italo Calvino questions such technology with his portrayal of Lotaria, who claims to be able to replace traditional reading with frequency lists generated by a computer: “Cos’è infatti la lettura d’un testo se non la registrazione di certe ricorrenze tematiche, di certe insistenze di forme e di significati? La lettura elettronica mi fornisce una lista delle frequenze, che mi basta scorrere per farmi un’idea dei problemi che il libro propone al mio studio critico” (Calvino, 2008, p. 795).1 When read in the light of the preceding chapter’s analysis of Calvino’s experimental computer project and “L’incendio della casa abominevole,” this passage can be understood as a warning from Calvino about relying too heavily on computers for literary production and reception. On the other hand, considered in the context of Oulipo’s mathematical project, Lotaria’s understanding of reading as the recognition of recurring themes and insistence on forms and meaning could be understood as a reference to the formal aspects that constrained literature makes explicit to its reader. This chapter considers two specific examples of Oulipian structural practices, their effects on the reading experience, and their larger implications for literary studies. In Le città invisibili (1972), Calvino groups a series of fragments into thematic categories, which he then organizes according to a geometrical principle which can be derived from the table of contents. The resulting text teaches the reader to reconcile the form and content by means of self-​reflexive language and mises-​en-​abyme. Similarly, Michèle Audin’s Mai quai Conti (2014) uses a table of contents as an organizational and generative device that determines everything from the relationship between characters to individual linguistic constraints. Both authors use such organizational constraints to broach similar topics of structure, science, politics, and language. Furthermore, considering these two case studies in parallel elucidates the role of the reader in Oulipian aesthetics. 1

“In fact, what is the reading of a text if not the recording of certain thematic recurrences, of certain insistences of forms and meanings? Electronic reading provides me with a list of frequencies, which I just have to scroll through to get an idea of the problems that the book proposes to my critical study.” (my translation)

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I. Geometric Structure As both Calvino and Audin use the table of contents as a pedagogical tool in the enunciation of their structural constraints, a brief introduction to this literary phenomenon is a necessary starting point. As with mathematical models, the table of contents represents a reduction of the contents of a written text (chapter titles, for instance, or other subdivisions). Throughout literary history, there exist tables of contents of varying degrees of complexity. In Gérard Genette’s Seuils, not much time is devoted to the table of contents, which is considered a consequence of intertitres or divisions within the body of the text. For the case of narrative fiction, Genette covers a variety of historical examples: ancient examples of which the divisions were imposed later by editors; Renaissance classics like the Decameron or Canterbury Tales, which are divided according to the framing narrative; a classical tradition of numbered divisions; and an opposing recourse to thematic divisions that are descriptive in nature (seemingly predicated on medieval traditions). The thematic divisions, Genette (1987, pp. 171–172) claims, became a sort of norm, continuing into the nineteenth and twentieth centuries in works by Dickens, Melville, Thackeray, France, Pynchon, and Eco. Even considering this long, diverse tradition of editorial practices, the tables of contents that open both Calvino’s and Audin’s novels are extraordinary exceptions to any rule. Indeed, while Genette’s understanding of tables of contents is inextricably linked to dividing up a text that has already been written, both Calvino and Audin constructed the table of contents before finishing their novels, using geometry as a structural tool that directs and divides the content while guiding the reader through the text. This paratextual object that Genette leaves more or less undefined is the first step to understanding Calvino’s and Audin’s constraints, objectives, and pedagogy. Calvino’s obsession with literary structure developed throughout his career as he came into contact with a number of influences: through his work at Einaudi, he learned about editorial structures; from his work on the Fiabe italiane, he became interested in structural commonalities within

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the folktale genre; in France, he dabbled in various literary circles that promoted structural theories; finally, his participation in Oulipo gave him a more nuanced understanding of structure as a mathematical concept (see Chapter 1). The structure of Le città invisibili could be understood as a synthesis of all of these disparate influences, but owes its strict mathematical nature especially to Oulipo. In a lecture at Columbia University,2 Calvino (1974a, p. V) explained that he had composed Le città invisibili in fragments, out of order, as the ideas came to him: “et ce n’est que plus tard, après avoir composé plusieurs villes, que j’ai eu l’idée d’en écrire d’autres”. However, he did not consider his collection complete until it had a structure: Mais toutes ces pages mises ensemble ne formaient pas encore un livre : un livre (c’est mon opinion) doit avoir un début et une fin (même s’il ne s’agit pas d’un roman au sens strict), c’est un espace dans lequel le lecteur doit entrer, errer, voire se perdre ; mais vient le moment où il lui faut trouver une issue, ou même plusieurs, la possibilité de se frayer un chemin pour en sortir. (Calvino, 1974a, p. II)

In essence, what Calvino wished to create was a framing device, landing on a series of dialogues between Marco Polo and Kublai Khan. The resulting novel does not necessarily have an overarching plot, but is meant to be interpreted as an extended conversation between these two protagonists, with the Italian emissary recounting his travels throughout the Khan’s vast empire, and describing each individual city. Given these structural and thematic considerations, Le città invisibili grounds itself in a broader classical literary tradition, rewriting Marco Polo’s Il milione but in the form of the Arabian Nights; through Marco Polo’s words, the reader is granted at once an image of Thomas More’s Utopia and Dante’s Inferno; furthermore, the use of a framing narrative in order to cohere a series of fragments is in keeping with the broader Italian literary tradition of composite works like the Decameron.

2

This French translation of Calvino’s personal Italian translation of the original English-​language talk is taken from the preface to the 2002 French edition of Les villes invisibles. To the best of my knowledge, this is the only place where this talk has been published.

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While Calvino did not classify Le città invisibili as Oulipian in Atlas de littérature potentielle, he did present the geometric structure as indicated in the Table of Contents in an Oulipo meeting on October 24, 1974, claiming that: “ce qu’il y a d’oulipien d[an]s les Villes Invisibles: la table des matières; sur le plan sémantique, pas de rigueur oulipienne” (Costagliola d’Abele, 2014, p. 102). The existence of such a strict structure is not necessarily exceptional in Calvino’s œuvre, as many of his texts are composed of fragments arranged in a somewhat ordered way: for instance, Marcovaldo tells a series of vignettes to describe a southern Italian factory worker living in the north and his dissatisfaction with modernity; Le cosmicomiche are all narrated by Qfwfq, a strange and indescribable narrator who has ostensibly borne witness to the literal scientific landmarks in the history of the universe; and Il castello dei destini incrociati has both a framing narrative and two literal structures (see Chapter 3). Le città invisibili distinguishes itself from these prior examples in the fact that the structure is for the most part invisible when reading the text and is not explicated by the author in any of his published writing. This secrecy runs contrary to Calvino’s two “Oulipian novels” as classified in Atlas: Il castello dei destini incrociati (1973) contains an explanatory note by the author explaining the novel’s composition, and Calvino published an explanatory article in both the Bibliothèque Oulipienne and Actes sémiotiques, which allegedly revealed the underlying structural constraints he used to produce Se una notte d’inverno un viaggiatore (1979). Le città invisibili has no preface,3 no postface, no footnotes, no index. Therefore, aside from the title, the only paratextual indication that there is a geometric structure is the table of contents itself. To emphasize the importance of what would ordinarily be a common, unremarkable addition to narrative fiction, Calvino insisted on putting the Indice4 before the text as opposed to the traditional Italian editorial practice of placing it after.5 3 4 5

With the small exception of the 2002 French edition. In Italian, this is the standard editorial word for table of contents, but can also mean “sign” or “clue.” In America, since all Tables of Contents are found at the beginning, the novelty of the gesture is negated. In the French edition, the Table of Contents is found at the end, once again making any preliminary interpretation more difficult.

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The Indice is atypical, reflecting Calvino’s unconventional division of his novel into nine numbered (but not titled) chapters, each of which begins and ends with a dialogue between Polo and Khan (indicated in the table of contents by ellipses) and contains a selection of fragments (10 for the first and last, and 5 for the others) that are not titled, but rather divided into 11 categories (each followed by a number from 1 to 5). The fact that the relationship between the ellipses and category names in the Indice and the corresponding dialogues and city descriptions in the body of the narrative is never explicitly stated coupled with the Indice’s appearance before the text itself complicates interpretation for a reader who has not yet begun to read the book. The numbers in the Indice seem to have been intentionally chosen, as 11 categories of five cities each yields 55 cities in total, or one more than the number of cities in Thomas More’s Utopia. Add that to the nine pairs of dialogues to get 64, the number of squares on a chessboard (toward the end of the novel, the protagonists engage in a game of chess). While within the text, each city description is given a woman’s name, they are nowhere to be found in the Indice, which lists only which category each fragment belongs in, preceded by a page number and followed by a second number indicating the iteration of the category. Arranging each category vertically, the pattern becomes a two-​dimensional geometrical figure, a parallelogram, as pictured in Figure 5.1.

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Figure 5.1.  The parallelogram created using the numbers in the Indice of Italo Calvino’s Le città invisibili, artistically imagined by OuPeinPo member Philippe Mouchès. Reproduced with the artist’s permission.

Calvino’s parallelogram is based on a regenerative pattern: the first numbered chapter introduces 4 of the 11 categories (1, 21, 321, 4321) and the last ends the series in the opposite order (5432, 543, 54, 5). The chapters in the middle are a simple regenerative sequence, each of which has the pattern (54321), terminating the first category in the sequence (the number 5 indicates the last appearance of a particular category) and introducing a new one (the number 1 indicates the first appearance of a category). Calvino’s pattern, while hidden, is rather simple: “Le système selon lequel les séries alternent est le plus simple qui soit, même si certains ont beaucoup travaillé pour lui trouver une explication” (Calvino, 1974a, pp. V–​VI).

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Scholars disagree on strict interpretations of the figure. Laura Chiesa (2006) discusses Invisible Cities in quasi-​mathematical terms without elaborating on the geometrical structure while Laura Marello (1986) provides an interpretation of the constraint culminating in Hubble’s theory of the universe. Carolyn Springer (1985) addresses the structure briefly before continuing her geographical reading of the novel, emphasizing its “formidable symmetries” and musical modality. Paul Harris (1990, p. 79) defines the table of contents as an “algorithm for running the Invisible Cities program, for it simulates a self-​generative system looping back on itself …” Martin McLaughlin’s (1998) biographical study provides an explanation of the structure, as does Claudio Milanini’s (1990) L’Utopia discontinua and a more recent study on the names of Polo’s cities, Le città e i nomi (Giudicetti et al., 2010). In contrast to most scholars, who take the table of contents to be an important facet of the book, Els Jongeneel (2007, p. 595) has a more negative interpretation: “Au contraire, la macrostructure régulière du texte contraste avec la microstructure fragmentaire et ouverte des esquisses urbaines. En outre, la structure ingénieuse du texte ne correspond pas à un développement thématique parallèle.” While some critics have admired the symmetries of Calvino’s Indice, the parallelogram exhibits a false symmetry given the numbers that compose it cannot be inverted without reversing the sequence. This avoidance of absolute perfection in art is a recurring theme in his critical writings, resulting in his choice of the crystal as a metaphor for the type of structure he seeks. Calvino (1995, pp. 261) first used the crystal as a metaphor for describing the fantastic: “Al centro dalla narrazione per me non la spiegazione d’un fatto straordinario, bensì l’ordine che questo fatto straordinario sviluppa in sé e attorno a sé, il disegno, la simmetria, la rete d’immagini che si depositano intorno ad esso come nella formazione d’un cristallo”.6 This idea had evolved by the time he wrote the text of the Six Memos (the posthumously published text essays should have been delivered at Harvard University’s annual Norton Lecture):7 “Il cristallo, con la sua esatta sfaccettatura e la sua capacità di rifrangere la luce, è il modello di perfezione che ho sempre tenuto come un 6

7

“For me, at the center of the narration is not the explanation of an extraordinary event, but rather the order of things that this extraordinary event produces in and around itself; the pattern, the symmetry, the network of images deposited around it, as in the formation of a crystal.” (my translation) I choose to quote the Italian edition of this text, called Lezioni americane, due to the fact that Calvino wrote his lecture notes in Italian, intending to translate

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emblema …” (Calvino, 1988, p. 71).8 Between these two definitions, Calvino’s conception of the crystal and its properties had been influenced by its use in the linguistic debate between Noam Chomsky and Jean Piaget, specifically in Massimo Piattelli-​Palmarini’s (1980, p. 6) introduction,9 which refers to a biological debate on two opposing models of life: the crystal (invariance –​illustrated by the recently discovered DNA) and the flame (steady state, dynamic equilibrium –​or statistical disorder, represented by Schroedinger’s notion that life feeds on both order and random atomic vibrations and collisions).10 This debate provided a necessary foil to Calvino’s original theorization of the crystal, which he elaborated on in the Six Memos: … i modelli per il processo di formazione degli esseri viventi sono “da un lato il cristallo (immagine d’invarianza e di regolarità di strutture specifiche), dall’altro la fiamma (immagine di costanza d’una forma globale esteriore, malgrado l’incessante agitazione interna)” … Cristallo e fiamma, due forme di bellezza perfetta da cui lo sguardo non sa staccarsi, due modi di crescita nel tempo, di spesa della materia circostante, due simboli morali, due assoluti, due categorie per classificare fatti e idee e stili e sentimenti … Io mi sono sempre considerato un partigiano dei cristalli, ma la pagina che ho citato m’insegna a non dimenticare il valore che ha la fiamma come modo d’essere, come forma d’esistenza.11 (Calvino, 1988, pp. 71–​72) them into English at a later date. His unexpected death in 1981 prevented him from carrying out this translation and presenting the talks. 8 “The crystal, with its exact facets and its ability to refract light is the model of perfection that I have always taken as an emblem …” (my translation) 9 Harris (1990, p. 77) notes that: “While Calvino remarks that he appropriates these terms from Massimo Piattelli-​Palmarini’s introduction (1980) to the debate between Noam Chomsky and Jean Piaget over models for language acquisition, it is clear from works like Invisible Cities (1972), that he had intuited the resonance of these images some years before the debate.” 10 Similar metaphors were used by Henri Atlan in his book Entre le cristal et la fumée, in which he describes self-​organizing systems. Atlan (1979, p. 5) is critical of the reduction of biology to the simple idea of genetic recombination, arguing instead that while the crystal represents pure order and the smoke dynamism, neither is sufficient for life, which grows between the two, where order emerges in chaos. 11 “… the models for the process of formation of living things are ‘on the one hand the crystal (image of invariance and regularity of specific structures), on the other the flame (image of regularity of an external global form, despite ceaseless internal agitation)’ … Crystal and flame, two forms of perfect beauty from which the gaze cannot detach itself, two modes of growth over time, of expenditure of the matter surrounding them, two moral symbols, two absolutes, two categories to classify facts and ideas and styles and feelings … I have always considered myself a partisan

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Calvino gravitated toward the structural aspects of this debate, finding in these two structural models a scientific illustration of the Oulipian predilection for constrained writing in opposition to chance. Piattelli-​ Palmarini (1980, p. 7) explains that the “crystal” model depends upon two primary assumptions: “(1) that specific visible patterns are always, at least in principle, traceable to the microscopic world, where they correspond to specific molecular patterns, and (2) that the crystalline (or molecular) underworld can only change according to its own rules. There is no symmetry of determinism between the two worlds; the microscopic dictates its laws to the macroscopic.” In the context of Le città invisibili, this is reminiscent of the interaction between the macroscopic structure of the novel as a whole and the individual elements that make it up, except that the direction is reversed for Calvino’s text, in which it was the development of the macroscopic structure that determined the individual elements. Following his brief survey of the Chomsky-​Piaget debate in the Six Memos, Calvino (1988, p. 71) draws from these two metaphors a third, the city: Un simbolo più complesso, che mi ha dato le maggiori possibilità di esprimere la tensione tra razionalità geometrica e groviglio delle esistenze umane è quello della città. Il mio libro in cui credo d’aver detto più cose resta Le città invisibili, perché ho potuto concentrare su un unico simbolo tutte le mie riflessioni, le mie esperienze, le mie congetture; e perché ho costruito una struttura sfaccettata in cui ogni breve testo sta vicino agli altri in una successione che non implica una consequenzialità o una gerarchia ma una rete entro la quale si possono tracciare molteplici percorsi e ricavare conclusioni plurime e ramificate.12

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of crystals, but the page I just cited teaches me not to forget the value of the flame as a way of being, as a form of existence.” (my translation) “A more complex symbol, which has given me the greatest possibility of expressing the tension between geometric rationality and the tangle of human existences is that of the city. My book in which I believe I have said the most is Invisible Cities, because I was able to concentrate all my reflections, my experiences, my conjectures on a single symbol; and because I built a multifaceted structure in which each short text is close to the others in a succession that does not imply a consequentiality or hierarchy but a network within which multiple paths can be traced and multiple and branched conclusions can be drawn.” (my translation)

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The city represents a tension between geometrical rationality and human randomness, making it a complex combination of the crystal and flame metaphor, reflected in the structure of the text itself. Therefore, while it is true that Calvino is comparatively silent in his critical writing and interviews about the structure of Le città invisibili, its appearance is not to be taken for granted. The Indice gives the reader a tool with which to navigate and interpret, but is useless to a reader who wants to find a particular city or idea. It suggests different ways to read the novel (in the linear order, category by category, privileging the short city descriptions to the dialogues, etc.), and also hints at Calvino’s own scientific and mathematical inspirations for the text. Michèle Audin was born in Algiers in 1954 and is arguably one of the most important female mathematicians of our time, as well as an active author and historian. A former student at the École Normale Supérieure (Sèvres), she has since served as a mathematician at the Université de Genève (1979–​1980), the Université Paris-​Sud (Orsay, 1980–​1987), and the Université de Strasbourg (1987–​2014). Her mathematical research deals mainly with the fields of algebraic topology, symplectic geometry, and integrable systems. On her personal webpage on the Université de Strasbourg’s website, one can find her published mathematical articles, as well as her books on mathematical and historical topics (Audin, Michèle Audin). In recent years, Audin’s work has tended to favor the vulgarization of mathematical topics and historical work on the discipline.13 One of the main facets of her historical and popular work on mathematics is to help mathematics regain its place in general culture. This is exemplified first and foremost by her unique blend of mathematics, historical work, and literary and Oulipian writing. By providing the reader with mathematical subjects told in a non-​mathematical way, she allows for a more ludic and pedagogical introduction into abstract thought. 13

For instance, she has worked on mathematicians Henri Cartan and André Weil and their correspondence as well as the larger relationship between Bourbaki and Oulipo. She has also written a historical text (Souvenirs sur Sofia Kovalevskaïa, 2008) about the same historical figure who becomes central to the plot and proof of Mai quai Conti. Additionally, she directs the section “Mathématiques ailleurs” for the online revue Images des mathématiques, which publishes articles about mathematics in the world, not just in textbooks and professional settings.

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Audin’s novel shares important similarities with Calvino’s: both make use of a geometric device and unusual table of contents to write about historical figures. Mai quai Conti was originally written in 2010, but was not well received by publishers (according to the author, it has been refused by at least 15). Given this lack of enthusiasm, Audin chose to release the novel in serialized instalments for the 140th anniversary of the Commune de Paris (the historical event at the heart of the novel) on Oulipo’s blog in the spring of 2011, and then again in 2014 with major revisions. The current version was modified with the help of Audin’s friend Yves Cunat who is denoted “le lecteur” in the text. An enthusiast of both history and science like the author, this “lecteur” helps identify a falsified document at a crucial moment in the novel. It is difficult to place Audin’s work within a particular genre: while its subject matter is historical and rigorously backed by archival documents, it does not read like historical academic work; while the book deals with mathematical and scientific thoughts, it recounts the story of the Paris Commune of 1871 as seen by the members of the Académie des Sciences; while the novel is organized and determined by a strict mathematical constraint that is thematically tied to the story, it was composed using a variety of shorter constraints, pastiches, and references. In short, Mai quai Conti is a fictional exploration of archival records of the Académie des Sciences during a particularly intense historical moment. To reflect the interdisciplinary nature of her topic, Audin’s approach is threefold: scientific, recounting 13 meetings of the Académie des Sciences; historical, considering the important context and ramifications of the Paris Commune on these scientist characters; and literary, as Audin makes use of a repertoire of literary and Oulipian techniques to compose the novel, which is then organized according to a mathematical principle. Audin had originally envisioned writing a novel about the Commune de Paris. Knowing that the Communards held the sciences in high esteem, she reread the meeting minutes of the Académie des Sciences, which met as scheduled during the political unrest. What she found was peculiar: during the Commune, mathematician Michel Chasles discussed and proved a number of theorems on conic structures. With this in mind, Audin devised her table of contents, a particular theorem on conic sections proved

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by Michel Chasles during the period that serves as both a generative, structural constraint as well as a mise-​en-​abyme of the story of Chasles’ unlikely obsession with conic structures amid political conflict. She writes: “Cette table des matières est une sorte de coquetterie : elle regroupe les indications figurant sous les figures au cours du texte, ce qui constitue (aussi) un énoncé et une démonstration du théorème de Pascal” (Mai Quai Conti Présentation) (Figures 5.2 and 5.3).

Figure 5.2.  An illustration of the notion of the cross-​ratio superimposed over Michel Chasles’s portrait, designed by OuPeinPo member ACHYAP. Reproduced with the artist’s permission.

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Figure 5.3.  The table of contents of Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

The mechanism that allowed Audin to write Mai quai Conti has entered into the repertoire of Oulipian constraints, defined on Oulipo’s website: “La contrainte de Pascal consiste à écrire un texte … dans lequel les relations entre les personnages sont dictées par les positions des points dans une figure de géométrie, tirée du Théorème de Pascal” (“Contrainte de Pascal”). An explicitly geometrical constraint, it forces the author to carry out the sort of creative activity suggested by Queneau in Les fondements de la littérature d’après David Hilbert and construct a plot scenario that conforms to a geometrical shape. Audin has provided a simpler example of the concept based on the Euclidean rule that given two points, one can construct one and only one line: “Xavier et Yvette sont follement amoureux l’un de l’autre, et leur amour est si exclusif qu’ils ont cessé de voir qui que ce soit d’autre” (Oulipo, 2014a, p. 72).

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The content of Mai quai Conti is not mathematical, but organized using Pascal’s Theorem, which appears in full in the table of contents, and progressively through a series of geometric figures at the end of each chapter. While either form (the formal language of the table of contents or the geometric constructions within each chapter) is sufficient to prove the theorem, the separation of the mathematical language from its illustration forces a reader who is not a geometer to reconcile the two, constantly referring back to the table of contents at the close of each chapter. Furthermore, just as the progression of the figure in the theorem is integral in the thematic development of the novel, it also directs stylistic points, making each chapter a literary illustration of the mathematics involved. Understanding the history in novel form therefore helps a non-​mathematical reader understand the mathematics of projections, bringing to life what would otherwise be a dry and incomprehensible collection of formal language. Given that the reader must continually refer to the table of contents, the blog format has unenvisaged advantages. With the “sommaire” available on the left-​hand side of the screen, the reader can flip between the table of contents and the individual chapters, referring to certain diagrams to accompany mathematical points. Audin’s table of contents provides a visual form to the novel, defining its characters and their respective positions from the outset. The historical matter of the book, its compositional techniques, and the mathematical structure seamlessly interact, allowing one discipline to explain and illustrate the other and vice versa.

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II. Language Having a well-​defined structure is just the beginning for these two authors, who then use their respective mathematical tables of contents as a generative tool, adapting their writing to the form. As with Perec’s La disparition, in which the constraint of the lipogram determined the number of chapters and the thematic content of the work, both Calvino and Audin use the constraint to determine the literary language of the text in a way that both justifies the structure while also teaching the reader how to understand it. For Calvino, this means speaking of the organizational principle of Le città invisibili at key moments throughout the novel in the framing dialogues between Marco Polo and Kublai Khan. These five separate mises-​ en-​abyme not only describe the structure of the novel within its pages, but also serve to illustrate an evolving relationship between reader and writer as mirrored by the protagonists. Marco Polo, an author surrogate within the text, directs Kublai Khan in his readings of the structure of his empire, forcing him not to stop at the crystalline surface, but to dig deeper, understanding the fragments’ relationship to the whole. This rhetorical move is pedagogical, mirroring Calvino’s expectations for the real reader of his novel. In the case of Audin, not only does the overall figure correspond directly to the characters and setting of the novel, determining plot developments, but the formal way in which the proof is constructed through the figures determines a series of localized rhetorical constraints, allowing Audin to demonstrate her constrained writing skills, which she developed as a member of Oulipo. For the Oulipian reader, these further constraints act as an indication about how to understand the structure as a whole, alerting him or her to the mathematical significance of the theorem in conjunction with the historical significance of the textual elements. While Le città invisibili has a relatively meagre plot for a traditional piece of narrative fiction, the first sentence could be understood as a standard introduction of the main characters, their relationship, and the general premise: “Non è detto che Kublai Kan creda a tutto quel che dice

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Marco Polo quando gli descrive le città visitate nelle sue ambascerie …”14 (Calvino, 1972, p. 5). While Polo’s credibility as a storyteller is thus compromised by the Khan’s skepticism, the final sentence of this introduction demonstrates that the Khan nevertheless relies on Polo’s tales due to the patterns that arise from his travel narratives: “Solo nei resoconti di Marco Polo, Kublai Kan riusciva a discernere, attraverso le muraglie e le torri destinate a crollare, la filigrana d’un disegno così sottile da sfuggire al morso delle termiti” (Calvino, 1972, pp. 13–​14).15 While Kublai Khan has many messengers reporting on various affairs throughout his empire, it is Marco Polo’s narrative descriptions that allow him to make sense of the chaotic nature of human life. This statement can therefore be understood as a challenge to the reader: while the contents of the novel are meticulously ordered according to a pattern, the reader (or termite) can devour every word and still have the subtleties of the pattern escape him or her. Turning the page, the reader passes from this first italicized framing section to the first city description, which takes the form of one block paragraph with the heading Le città e la memoria. From the vantage point of the individual city descriptions in chapter I, it is possible for the reader to gain an implicit sense of Calvino’s pattern by paying specific attention to the poetic themes of memory, desire, and signs as indicated by three of the four categories. For instance, the third city (Le città e il desiderio 1), Dorotea, can be described in two ways: first, in enumerations of what it contains and how it can be divided; and second, as a representation of the multiple paths one can pursue: “… ma ora so che questa è solo una delle tante vie che mi si aprivano quella mattina a Dorotea” (Calvino, 1972, p. 17).16 While Calvino has offered the reader a specific path from city to city, it is impossible to discern the overall pattern from within. As with many of the individual city descriptions, Calvino’s explanation of Dorotea 14

“Kublai Khan does not necessarily believe everything that Marco Polo says when he describes the cities visited in his empire …” (my translation) 15 “It was only in Marco Polo’s accounts that Kublai Khan managed to discern, amidst the walls and towers destined to crumble, the filigrane of a pattern so subtle that it could escape the termites’ gnawing.” (my translation) 16 “… but now I know that this path is only one of many that opened before me that morning in Dorothea.” (my translation)

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can be understood as a meta commentary on the novel itself and how to read it. The following city description, Zaira (Le città e la memoria 3), recounts a city of high bastions which consists of “… relazioni tra le misure del suo spazio e gli avvenimenti del suo passato …” (Calvino, 1972, p. 18).17 Following this advice, the reader must consider the novel from its structure and enumerations in the Indice as well as from within. However, the introduction of the next category, Le città e i segni, ruminates on the problematic nature of interpretation of such signs: “L’occhio non vede cose ma figure di cose che significano altre cose …” (Calvino, 1972, p. 20).18 Recall that in the Six Memos for the Next Millennium, Calvino (1988, p. 70) reflected on the implications of his structure, claiming that it was the multifaceted structure of Le città invisibili that allowed the reader to draw multiple conclusions. Indeed, Calvino’s thematic categories combined with the corresponding reflections on those themes and their interrelated nature in each city description provoke a greater reflection on patterns that was already indicated at the close of the first italicized framing narrative of Marco Polo and Kublai Khan, surrogates for both the author and reader. In his role as reader, Kublai hopes that by understanding each piece, he might understand the whole in a structural or formalist sense, but Polo is less convinced that such a comprehensive understanding is possible: “Sire, non lo credere: quel giorno sarai tu stesso emblema tra gli emblemi” (Calvino, 1972, p. 30).19 The second mise-​en-​abyme occurs at the opening pages of chapter IV. Kublai Khan is conflicted about how he should understand his empire and what information he needs from Marco Polo’s accounts. Rather than describing in detail the various problems facing each individual city in his empire, Polo insists on recounting fable-​like descriptions of non-​existent cities that cannot help the Khan in his role as emperor. On the other hand, Kublai believes in the progress implied by the structure of his empire, comparing it to a crystal: 17 “… relationships between the measurements of its space and the events of its past …” (my translation) 18 “The eye doesn’t really see things, but rather signs of things that mean other things …” (my translation) 19 “Sire, do not believe it: on this day, you will be an emblem among emblems.” (my translation)

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–​Eppure io so, –​diceva, –​che il mio impero è fatto della materia dei cristalli, e aggrega le sue molecole secondo un disegno perfetto … Perché le tue impressioni di viaggio si fermano alle delusive apparenze e non colgono questo processo inarrestabile? Perché indugi in malinconie inessenziali? Perché nascondi all’imperatore la grandezza del suo destino?20 (Calvino, 1972, p. 66)

This oscillation between the perfect, abstract structure of an inherently dysfunctional conglomeration of cities is reminiscent of the nature of geometry. Furthermore, in light of the geometrical design of the Indice that produces a parallelogram that resembles a crystal, this metaphor also speaks to the nature of the novel as a whole. The Khan insists on the geometrical perfection of his empire rather than brooding over the imperfections within. Whereas Kublai’s view rests on the surface, Polo plays devil’s advocate: “–​Mentre al tuo cenno, sire, la città una e ultima innalza le sue mura senza macchia, io raccolgo le ceneri delle altre città possibili che scompaiono per farle posto e non potranno piú essere ricostruite né ricordate” (Calvino, 1972, p. 66).21 His philosophical discourse contradicts Kublai’s insistence on superficial perceptions and he implores the Khan to pay heed to the individual parts and their imperfections. Kublai prefers to see in the construction of his empire a utopia, already indicated by the number of cities; Polo hints that it might indeed be the opposite. The Khan’s insistence on the crystalline perfection of his empire speaks to Calvino’s compositional practices. Calvino’s regenerative pattern is reminiscent of crystal formation: the beginning chapter grows organically; the middle chapters maintain a constant size through a recurring series that allows for the organic elimination and introduction of categories; finally, the last chapter terminates the series in a mirror image of the first. Albert Sbragia (1993, pp. 297–​299) has noted Calvino’s use of mise en abyme as an 20 “ ‘Yet I know,’ he said, ‘that my empire is made of the stuff of crystals, and assembles its molecules according to a perfect pattern … Why do your travel impressions stop at disappointing appearances and not capture this unstoppable process? Why do you linger over inessential melancholies? Why are you hiding from the emperor the greatness of his destiny?’ ” (my translation) 21 “While, at a sign from you, sire, the unique and final city raises its stainless walls, I am collecting the ashes of the other possible cities that vanish to make room for it, cities that can never be rebuilt or remembered.” (my translation)

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“… attempt to transmit the order found in simple systems to the complex universe …,” claiming that Calvino employs this strategy to “to illustrate the generative lesson of the crystal.” He argues that Calvino uses synecdoche to counteract these mises-​en-​abyme and thereby combat the ungraspable notion of chaos. On a rhetorical level, it is true that the mises-​en-​abyme and synecdoche counteract one another; on a structural level, Calvino makes use of the non-​Euclidean center (discussed below) to counteract the rigidity of his design. These opposing rhetorical and structural models allow Calvino to create a novel that exists between the crystal and the flame, providing a literary solution to a troubling scientific debate. Chapter V can be understood as a central bridge between the two halves of the novel, beginning with a discussion of the embedded city, Lalage, during the opening framing dialogue and ending with a discussion of a bridge. In the geographical center of the structure, Le città e gli occhi 3 describes the city of Bauci, built on stilts from which its residents simply observe the earth little by little from above using telescopes. The bridge metaphor that follows further underscores the importance of understanding the individual pieces composing a structure: Marco Polo descrive un ponte, pietra per pietra. –​Ma qual è la pietra che sostiene il ponte? –​chiede Kublai Kan. –​Il ponte non è sostenuto da questa o quella pietra, –​ risponde Marco, –​ma dalla linea dell’arco che esse formano. Kublai Kan rimane silenzioso, riflettendo. Poi soggiunge: –​Perché mi parli delle pietre? È solo dell’arco che m’importa. Polo risponde: –​Senza pietre non c’è arco.22 (Calvino, 1972, p. 89)

Following the bridge, Kublai Khan interrogates Marco Polo about his origins, and why he has never described the city where he was born, Venice. At this point, Polo reveals that “Ogni volta che descrivo una città

22 “Marco Polo describes a bridge, stone by stone. ‘But which is the stone that supports the bridge?’ Kublai Khan asks. ‘The bridge is not supported by one stone or another,’ Marco replies, ‘but by the line of the arch they form.’ Kublai Khan remains silent, reflecting. Then he adds: ‘Why are you talking to me about the stones? It is only the arch that matters to me.’ Polo replies: ‘Without stones there is no arch.’ ” (my translation)

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dico qualcosa di Venezia” (Calvino, 1972, p. 94).23 The following fragment, Smeraldina (Le città e gli scambi 5), seems to be a description of Venice: “… città acquatica, un reticolo di canali e un reticolo di strade si sovrappongono e s’intersecano” (Calvino, 1972, p. 96).24 Etymologically linked to the Italian word for emerald, smeraldo (which is a type of crystal), the name Smeraldina indicates this city’s singularity, which has been noted by several scholars already. For instance, Pierre Laroche (1998, p. 66) discusses the metaphor of the city as a way to bridge Calvino’s fiction and critical work, claiming that Calvino’s “implicit cities” are Turin, Paris, and New York: “Mais il faut faire aussi une place à part à Venise et, bien entendu, aux villes de Ligurie.” This interpretation is reminiscent of Kerstin Pilz’s claim that the mathematical structure of Le città invisibili is a reflection of Calvino’s admiration for the regularity of New York. In her article, Reconceptualizing thought and Space: Labyrinths and Cities in Calvino’s Fictions, Pilz (2003, p. 234) makes an interesting point that “Venice is of course also the Renaissance centre of cartography. And ironically it is this aquatic city that defies definite mapping …” She contrasts the labyrinthine Venice with Calvino’s preferred city, New York, as a Model of an “emblematic … embodiment of mastery and imposition of order” (Pilz, 2003, p. 235). Calvino’s central mise-​en-​abyme, the bridge, gives way to a prolonged discussion of Venice, its significance for Marco Polo, and its resulting intertextual role in every one of Polo’s city descriptions. The importance of the city of Venice for Calvino could be explained due to the city’s architectural significance, explained by Calvino (1974b, p. 2689) in an essay: “La forza con cui Venezia agisce sulla immaginazione è quella d’un archetipo vivente che si affaccia sull’utopia”.25 The description of Smeraldina, however, implies an additional, mathematical interpretation through its insistence on the anti-​Euclidean nature of the city, where “… la linea più 23 “ ‘Every time that I describe a city, I am saying something about Venice.’ ” (my translation) 24 “… aquatic city, a network of canals and streets that overlap and intersect.” (my translation) 25 “The force with which Venice acts on the imagination is that of a living archetype that overlooks utopia.” (my translation)

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breve tra due punti … non è una retta ma uno zigzag che si ramifica in tortuose varianti …” (Calvino, 1972, p. 95).26 Furthermore, the revelation that Polo has only been talking about Venice immediately after the central chapter’s insistence on examining the individual components of a structure can be understood as analogous to the destabilizing factor that Calvino includes at the geographical center of the tarot card design in the first half of Il castello dei destini incrociati (Chapter 3). In this sense, every city in this otherwise Euclidean geometric pattern is a variant on the fundamentally non-​Euclidean city of Venice, enforcing the irreconcilable nature of geometric patterns and the entropy of human life. Like Oulipo, Calvino (1988, pp. 69–70) is skeptical of the role of chance in literature, writing in the Six Memos: “La poesia è la grande nemica del caso, pur essendo anch’essa figlia del caso e sapendo che il caso in ultima istanza avrà partita vinta”.27 Calvino (1988, pp. 46–47) admits that his preference is for geometric regularity: “Perché io non sono un cultore della divagazione; potrei dire che preferisco affidarmi alla linea retta, nella speranza che continui all’infinito e mi renda irraggiungibile”.28 However, he understands that chance is an essential element of the human experience, despite his mathematical predilections, which is why he includes it as a sort of clinamen, inserting into an otherwise regular structure a city which resists this type of organization. At the beginning of chapter VIII, Kublai Khan and Marco Polo play a game of chess, which the Khan considers a parallel activity to understanding his empire: “Pensò: ‘Se ogni città e come una partita a scacchi, il giorno in cui arriverò a conoscerne le regole possiederò finalmente il mio impero, anche se mai riuscirò a conoscere tutte le città che contiene’ ”29 (Calvino, 26 “… the shortest distance between two points … is not a straight line, but a zigzag that branches off in tortuous variations.” (my translation) 27 “Poetry is the great enemy of chance, even though it is also the daughter of chance and knows that chance will ultimately prevail.” (my translation) 28 “Because I’m not a lover of digressions; I could say that I prefer to rely on the straight line, in the hope that it will continue indefinitely and make me unreachable.” (my translation) 29 “He thought: ‘If each city is like a game of chess, the day when I have learned the rules, I shall finally possess my empire, even if I shall never succeed in knowing all the cities it contains.’ ” (my translation)

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1972, p. 117). Kublai Khan understands the rules of the chess game to be analogous to those that govern his empire, which constitute an invisible order. However, he realizes that it is not a perfect metaphor: “Alle volte gli sembrava d’essere sul punto di scoprire un sistema coerente e armonioso che sottostava alle infinite difformità e disarmonie, ma nessun modello reggeva il confronto con quello del gioco degli scacchi” (Calvino, 1972, p. 118).30 As with geometry, his method discerns inherent properties of an abstracted entity, rather than being reduced to a single game or city. However, the Khan’s enthusiasm wanes toward the end of the game, when he wonders what the use is if a victory only results in an illusory conquest: Allo scacco matto, sotto il piede del re sbalzato via dalla mano del vincitore, resta un quadrato nero o bianco. A forza di scorporare le sue conquiste per ridurle all’essenza, Kublai era arrivato all’operazione estrema: la conquista definitiva, di cui i multiformi tesori dell’impero non erano che involucri illusori, si riduceva a un tassello di legno piallato: il nulla …31 (Calvino, 1972, pp. 118–​119)

Since the numbers in the Indice imply that the novel can be reduced to a chessboard, does reading also result in nothing more than a temporary possession of a void? Marco Polo then teaches Kublai Khan to read the story of the empty square, recounting the life of the tree that provided a knotted piece of wood. Kublai marvels at “… la quantità di cose che si potevano leggere in un pezzetto di legno liscio e vuoto …” (Calvino, 1972, p. 140).32 The reader as well can understand this as a metaphor for the novel itself, in that every fragment is not only a philosophical reflection, 30 “At times, he thought he was on the verge of discovering a coherent, harmonious system underlying the infinite deformities and discords, but no model could stand up to the comparison with the game of chess.” (my translation) 31 “At checkmate, beneath the foot of the king that was knocked aside by the winner’s hand, a black or a white square remains. By disembodying his conquests to reduce them to only the essential, Kublai had arrived at the other extreme: the definitive conquest, of which the empire’s multiform treasures were only illusory envelopes. It was reduced to a square of planed wood … the void.” (my translation) 32 “… the quantity of things that could be read in a little piece of smooth and empty wood …” (my translation)

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but a piece in a larger whole. Polo’s story of the chess square echoes the city of Olinda (Le città nascoste 1) that precedes it. It is a city that grows “in cerchi concentrici,”33 which blossom within each other, only visible through a magnifying lens (Calvino, 1972, p. 136). While the pattern created at the outset was reminiscent of Thomas More’s Utopia, the idea of concentric circles refers to Dante’s Inferno, evidence of a degeneration from mathematical ideals of space to the reality in which humans coexist. Kublai’s perfect utopian structure has disintegrated through the tales of Marco Polo. The final mise-​en-​abyme, the Atlas, includes modern cities each with a different philosophy as well as fictional utopian and dystopian cities. Kublai Khan, as could be expected, prefers his Atlas to the actual cities, while Polo remarks that the differences categorized in the Atlas are not as obvious (Calvino, 1972, p. 135). The Atlas implies the work of a geometer, classifying forms by their differences and allowing for a more abstract understanding, while Marco Polo claims the position of an artist, assembling pieces to create a new city: “… partendo di lí metterò assieme pezzo a pezzo la città perfetta, fatta di frammenti mescolati col resto, d’istanti separati da intervalli, di segnali che uno manda e non sa chi li raccoglie”34 (Calvino, 1972, p. 169). Le città invisibili has elements of both of these methods in the way Calvino’s various fragments are categorized and assembled within a larger pattern. This interest in classification and society is also reminiscent of the early nineteenth-​century social theorist, Charles Fourier, on whom Calvino penned a series of essays beginning in 1971. In the selections of Fourier’s writings that were published and introduced by Calvino, the organization of working life in the phalanx occupies a prominent position. This fascination with order is reminiscent of the crystalline aspects of Le città invisibili, but the social aspects of Fourier’s work bring out a more subtle, political connection: communism.

33 “… in concentric circles …” (my translation) 3 4 “… setting out from there, I will put together, piece by piece, the perfect city, made of fragments mixed with the rest, of instants separated by intervals, of signals that one sends out without knowing who receives them.” (my translation)

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In his youth, Calvino was an engaged communist, abandoning his affiliation with the party in 1957, and publicly declaring in L’Unità that the reason stemmed from his disapproval of the 1956 Soviet Invasion of Hungary. While Calvino’s Paris period is often characterized by scholars as a refusal of the more political writings of his youth, Le città invisibili is filled with utopian themes that seem in part inspired by Calvino’s readings of Fourier in the years preceding its publication. In his essays on Fourier, Calvino (1980b, p. 232) notes that Fourier can be seen as a precursor to Marx and Engels, and that even Marx and Engels considered the contrast between Fourier’s “systematic form” and “real content” of systems to be a key aspect of his work. His musings on Fourier oscillate between the practical and the theoretical, situating this utopian socialist thinker in a longer intellectual history. This conception of Fourier as providing a practical framework to follow for intentional collective living finds its echoes in Le città invibili, a novel that fashions imaginative cities out of the architectural or theoretical developments of the era.35 This political, theoretical impulse directly mirrors Calvino’s use of science and mathematics, creating a geometrically rigorous shell to house the messy, fragmented nature of communal human life. Le città invisibili is an œuvre non-​oulipienne, not generated by a constraint, but which developed organically from a series of fragments to a crystalline structure with a framing narrative. This Oulipian influence orients the reader, much like the invisible mathematics directs the content of the book. While the Indice is not a proper constraint, the gesture is still Oulipian and adheres to both of Roubaud’s (1981a, p. 90) principles: “1. Un texte écrit suivant une contrainte parle de cette contrainte; 2. Un texte écrit suivant une contrainte mathématisable contient les conséquences de la théorie mathématique qu’elle illustre”. To address the first “principle,” Calvino’s text speaks explicitly of the constraint at several key moments. As for the second proposition, geometrically speaking, the text is an excellent illustration of the paradoxical nature of geometry itself: mathematical abstraction of that which is, by definition, imperfect. Like Calvino, Michèle Audin’s choice of both content and design can be understood in terms of her political background. Audin is the daughter 35

See Letizia Modena, Italo Calvino’s Architecture of Lightness [2011].

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of mathematician, Maurice Audin, who is primarily known not for his mathematical work, but for the unfortunate circumstances of his death. As a Frenchman born in the French Protectorate of Tunisia, Maurice Audin was transferred with his family to France and then to Algiers. After renouncing a brief military career in favor of mathematical scholarship, he earned his undergraduate degree at the Université d’Alger in June 1953 and a DES that same July. From that point on, he became an assistant at the Faculté des sciences while working on his doctoral dissertation which he defended in absentia due to his untimely disappearance, which became known as the “affaire Audin.” The Audin Affair, which finally came to a close in September 2018 with an official recognition from French president Emmanuel Macron, began with Maurice Audin’s arrest on June 10, 1957 by parachutists of General Jacques Massu (Chrisafis, 2018). Given his strong ties to the Algerian Communist Party and his militant anticolonialism, he was tortured and disappeared. The last person to have seen him alive was Henri Alleg, author of La Question, one of the most important texts dealing with the issue of torture during the war in Algeria. Audin’s body was never recovered, and despite numerous pleas and formal requests from his widow, Josette Audin, and famous mathematician Laurent Schwartz, who had been supervising his dissertation, the authorities never revealed what happened to him. While the only information given at the time indicated that he might have escaped, an investigation by Pierre Vidal-​Naquet established that Audin died under torture on June 21, 1957. Michèle Audin has long disagreed with the national response to her father’s death36 and has honored her father’s memory in her own way, by refusing to accept former French President Sarkozy’s offer of the order of the Legion of Honor. Her reason, she explains in a letter, was Sarkozy’s refusal to respond to her mother’s letter requesting further information about her husband’s disappearance (Béguin, 2012). 36 At the time of the affair, Audin was honored in the form of a prize for mathematicians, the Prix de mathématiques Maurice Audin, which was awarded between 1957 and 1963, and then reestablished more recently. Additionally, the Place Maurice Audin in the fifth arrondissement of Paris was officially inaugurated on May 26, 2004. There is also a Place Maurice Audin in Algiers, as he is considered a martyr of the war of independence.

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The disappearance of Maurice Audin remains a terrible stain on the French government, and his daughter’s subsequent political engagement has a biographical connection to this Affair. Concerning Mai quai Conti, her choice of the moment of the Commune as the time period of this historical, archive-​based novel can also be understood as a political gesture. Structuring the novel with a mathematical theorem, however, seems to be an attempt at rationalizing an exceedingly messy event. Like her father, Audin is a believer in communist ideals and values the Commune for its ideology, treatment of women, and reverence toward science. The bloody reality, however, is more difficult to grasp. By prioritizing the positive aspects of the Commune through a portrayal of science and specifically the female mathematician, Sofia Kovalevskaïa, Audin is able to capture what she considers to be important historical lessons. Superimposing a strict, mathematical structure is an attempt to take possession of this event, using it as a pretext for the vulgarization of mathematics and science and also to make a political statement, despite the failed nature of the Commune. As with Calvino’s Le città invisibili, geometry is used as a strategy to speak about the apparent disconnect between ideal politics and the messy nature of human events. In these cases, Oulipo has captured an essential element of geometry itself, using the table of contents as a liminal space between geometric perfection and the real world in which we live. Audin’s novel begins five days before the start of the Commune on Monday, March 13, 1871. The first part of the first chapter speaks about the setting, the quai Conti, where the Académie des Sciences is located. However, the setting in this first chapter is devoid of traditional descriptive elements, as the author is temporally removed from the period in which the story takes place and can only hypothesize about what this building was like during the Commune and speak more generally about its architectural properties. Instead, the setting is an abstract, empty geometrical figure, filled with possibility: “Soit C une conique propre d’image non vide …” (Audin, 2011, Lundi 13 mars) (Figure 5.4).

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Figure 5.4.  The first mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

Since Audin has no real first-​hand knowledge of this setting from the year in question, she relies on rhetorical questions and hypothetical statements about the light and heating that the building might have had, since the weather during the Commune was well-​documented. What were their conversations, she wonders: did they speak about battles, politics, the weather? Finally, she speaks of what is certain: the scientific discussion and the list of members who were present. This information, documented in the meeting minutes, is incomplete. The real story about how these scientists reacted to the historical event taking place outside is omitted from the meeting minutes, and Audin can only speculate. The following chapter, Lundi 20 mars, introduces the primary characters. Since they are permanent members of the Académie, Audin places them on the ellipse as six fixed points: A. Charles Hermitte; B. Joseph Bertrand; C. Michel Chasles; D. Charles Delauney; E. Léonce Élie de Beaumont; F. Hervé Faye (Figure 5.5).

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Figure 5.5.  The second mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

Audin describes these characters’ appearances, social and political positions, their lives, and scientific contributions. She imagines how they might have arrived at the meetings, inventing itineraries based on their addresses and issues during the Commune that might have affected normal routes. Audin distinguishes Chasles: “Et puis Michel Chasles qui, si ceci était un roman, un roman banal avec un héros, serait ce héros” (Audin, 2011, Lundi 20 mars). This preliminary information in the first two chapters does not only introduce the setting and main characters, but the premise that every element of this novel is predicated on archival research, verifiable and objective facts, reinforced by the insistence on a rigorous, mathematical structure. In Calvino’s novel, the reader and writer surrogates were a crucial part of reading the novel with the constraint in mind. Audin’s text also contains an explicit relationship between the author and her reader, Yves Cunat. Thanking him for his help, Audin describes “… le plaisir rare de faire intervenir un lecteur dans le texte …,” using his expertise to clarify one of her sources (Audin, 2011, 20 mars (l’interruption, et après)). This gesture serves two purposes: first, it provides a concrete example of the type of engaged reader Audin hopes for; second, it teaches the reader an important truth about the novel’s mathematical constraint, as neither Audin nor Cunat is pictured on the accompanying diagram like the other

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characters. This hint allows the reader to understand the mathematical method: the rigorous structure applies only to the historical characters. The following chapter, Lundi 27 mars, introduces a new character, Simon Newcomb, who is placed at one of the two foci of the ellipse, linked to the letters A, E, D, and F by intersecting lines. Not a member of the Académie des Sciences, Newcomb has relationships and commonalities with the characters that have already been introduced, but is first and foremost an implant, brought from a faraway land into an unfamiliar setting.

Figure 5.6.  A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

This position is only part of Audin’s use of her constraint. She further incorporates the mathematics into the writing using tautograms, texts in which every word (or in this case, most of the words) begin with the same letter, to signal the relationship between Simon Newcomb and the characters to which he is linked by Figure 5.6: Simon Newcomb, astronome américain, amateur d’algèbre, actif et aguerri, accueilli par l’Académie et accoutumé à ses alentours, affolé par l’ampleur de l’anarchie, accablé, familier de Faye, aux peu fictives facilités, fuyant frileusement la foison des fédérés faméliques, les farandoles de farouches fantassins fourbus, les fangeux et funestes faubourgs, fuyant la France. (AF)

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Ensuite … Simon Newcomb, un expert, éreinté par l’écriture de son éblouissante ébauche, ému par l’envahissement des églises, effarouché par l’effervescence égalitaire, effrayé par l’émeute et les émeutiers, les directives douteuses, la discorde dramatique, le durable durcissement, la domination de la domesticité, les drôlesses dynamiteuses, décidant de disparaître, la dissolution donc la disparition. (ED)37 (Audin, 2011, Lundi 27 mars)

These passages employ the mathematical substitution of characters for lettered points to write tautograms. The first citation links Newcomb (N) to both A (Hermitte) and F (Faye) whereas the second links him to both E (Élie de Beaumont) and D (Delaunay). Newcomb is not only the mathematical intersection between these four characters, but also a metaphorical one, determined by historical fact and the narration. While Audin’s tautograms alone might come off as superfluous rhetorical acrobatics, combining them with the structural constraint of Pascal’s theorem narrativizes mathematics. Based on the parameters Audin chose at the outset, the characters and the relationships between them are determined by the figure and its development within the theorem, but the writing of the passage is additionally determined by the figure and its properties. Even more, this type of writing illustrates mathematical properties that might not have been immediately obvious to a non-​mathematical reader. While points and their intersections mean something specific within the context of this proof, Audin’s narration illustrates the mathematics that govern the proof without speaking about mathematics directly. For the remainder of the text, Audin continues to use this same constraint for every projection, indicating her satisfaction with the effectiveness of this device.

37 The parenthetical indications are mine and do not appear in the original text. I have added them to facilitate matching each paragraph with its respective chord in Figure 5.6.

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Figure 5.7.  A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

For the following chapter and figure, Lundi 3 avril, Audin introduces the narratrice who is distinguished from the auteure: “Car il y a un ‘ je ’, qui apparaît ici, je c’est moi. Attention, ce ‘ moi ’ n’est pas l’auteure, qui parle d’elle-​même à la troisième personne, il y a désormais quelqu’un d’autre qui raconte cette histoire, une narratrice qui dit je, moi, qui regarde Hermite et Bertrand, qui admire Chasles et Delaunay. Elle est la lettre M de la figure, M comme ‘ mathématicienne ’, comme ‘ mystère ’, comme ‘ moi ’ …” (Audin, 2011, Lundi 3 avril). This is not a theoretical discourse about the difference between the author and narrator. A cursory glance at Figure 5.7 indicates that the two are indeed distinct, as the auteure does not appear on the figure at all, whereas the narratrice appears outside of the ellipse, designated by the letter M. This implies that she is a character who watches from afar, connected to the action by mathematical projections, continuations of pre-​existing lines: Following this introduction is a sort of homage to Perec’s Je me souviens (1978), a novel in which every sentence attests to a particular memory of a specific historical moment. Like Perec’s novel, Audin’s appropriation of Je me souviens touches upon the collective memory of the Commune, and in one particular case, also exhibits a univocalic constraint in the style of Perec’s Les revenentes (1972):

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je me souviens que les institutrices recevaient le même salaire que les instituteurs (et je célèbre les femmes de ce temps • femmes de légende • telle excellente et ses textes révérés de ses élèves • telle revêt veste, béret et bretelles • telle est même sergente et défend ses frères • de venelle en venelle elles se pressent vers le Tertre • ensemble fédérés et fédérées se dressent • cernées échevelées blêmes • blessées lèvres desséchées • éventrées démembrées enchevêtrées enterrées • échec de ce bref présent • en cet enfer en même temps de cet éphémère été • et le ferment de l’éternel) … (Audin, 2011, 3 avril (suite, je me souviens))

These constraints are hints about the identity of this mysterious narrator as well as a valorization of the feminine, as the repetition of the vowel E accompanies a discussion of women and their rights as they were recognized by the Commune. Even though the narrator was not there, it is easy for her to imagine. Furthermore, this homage to Perec references a sentence from Les revenentes that is also the epigraph of ­chapter 99 of La Vie mode d’emploi: “Je cherche en même temps l’éternel et l’éphémère” (Perec, 2017b, chap. 99). Perec was particularly fond of this sentence, though the use of the terms éternel and éphémère together has a background in surrealist art and Dada theater, as it was the title of a Dada play by Michel Seuphor, L’Ephémère est éternel, for which Louis Mondrian designed models for the three acts (All The World’s A Stage Set By Piet Mondrian). For Perec and Audin, these structural constraints seem to be a way to capture both the ephemeral and the eternal, an inherent dichotomy in the study of geometry. The meeting of Lundi 17 avril is the moment of alignment of the three characters who have been introduced thus far: L, M, and N; Lissagaray the journalist, “moi” or the narrator, and Newcombe, the American visitor. Their alignment is due to their existence on a common plane, which is not only useful for the mathematical proof, but also for the narration. To be able to speak about a scientist, a journalist, and a narrator in the same sentence is convenient and made possible by literary language. But this alignment is also a property of Audin’s particular combination of disciplines: “Notre livre, mieux notre lutte, mêlera nombres, lettres, manuscrits, notices, liberté, méthodes neuves, lumineuses, modernes, novatrices. Ligne, magique notion!” (Audin, 2011, Lundi 17 avril) A line can be drawn between them, as follows (Figure 5.8).

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Figure 5.8.  A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

However, even at this critical point of alignment, the narrator is still shrouded in mystery: “Qui suis-​je, moi ? Qui suis-​je, pour pouvoir raconter cette histoire ? Parler en même temps, presque d’une même phrase, de Prosper-​Olivier Lissagaray et de Simon Newcomb ? Du journaliste, historien de la Commune, communard lui-​même, et de l’astronome américain fuyant Paris ?” (Audin, 2011, Lundi 17 avril) Lundi 1er mai is the day of chaos, and the most notable effect of this political development is the disappearance of the narrator. The indication that this is a turbulent moment is objectively described using the passé simple, indicating a historical development rather than a literary one: Soudain le chaos fut. Sous la Commune. Fusillades sauvages. Les capitaines fourbes. Sommations, longs coups frappés. Bris, bandits, brigands, barricades, bal, babil, baril, blanc, banc, bec, bloc, bluff, barouf, bref. (Audin, 2011, Lundi 1er mai)

The first three sentences indicate the projection SLCF, mathematically created by the projections of BS, BL, BC, and BF (designated again with a series of tautograms). To justify speaking of these projections, Audin discusses the absent Bertrand (B), the secret secretary (S), Chasles (C), and Faye (F). We have therefore: [S,L,C,F] =​[BS, BL, BC, BF], or visually (Figure 5.9).

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Figure 5.9.  A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

The following meeting of Lundi 8 mai, the narratrice speaks of Bertrand (B) who is present with Élie de Beaumont (E) and Chasles (C), but not Hermite (A) and Faye (F) (otherwise, [BA, BE, BC, BF] =​[DA, DE, DC, DF]). The following week (lundi 15 mai) was the last meeting of the Académie before the “semaine sanglante” and final attack. In preparation, the lines BC and BF disappear and BA and BE (which were red before) are now drawn in black. On Lundi 22 mai, a new character is introduced: Sophie Kowalevski (K). This (unofficial) mathematics student in Berlin bravely ventured to Paris during the Commune (Audin, 2011, Lundi 22 mai). K is the intersection of projections LN and AB, but there is also an entertaining anecdote that connects Sophie and Michel Chasles, a story of manuscripts of Gauss and Pascal. The final two meetings describe the climax of the Commune and resolve the theorem. The first, Lundi (28+​1) mai, describes the “semaine sanglante,” which ended on Sunday, May 28. To describe such a devastating historical event, Audin chooses the most canonical Oulipian text to imitate, La disparition. In addition to paying homage to Perec and his contributions to constrained literature, she uses this constrained text to describe her own constraint. In this case, it is Sophie “… qui imagina (mais trop tard) un roman communicatif, allusif, sur nos amis communards” (Audin, 2011,

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Lundi (28+​1) mai). Audin’s lipogram borrows many of Perec’s techniques for writing without the most common vowel of the French language (she uses alphabetical lists of Parisian sites, for instance). The mathematical construction of the theorem dictates that: “La perspective de centre K envoyant CF sur AF envoie S sur A, L sur N et F sur F. L’image de C est donc T” (Audin, 2011, Lundi (28+​1) mai). Likewise, Audin’s lipogrammatic text projects each of the corresponding characters onto another, interrogating their relationships in a chaotic, violent clash (Figure 5.10).

Figure 5.10.  A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

The final meeting begins with a discussion of the preceding chapter: “Il y avait donc eu ce 29 mai, après ces jours dont on eut du mal à parler normalement” (Audin, 2011, Lundi 5 juin). The chapter is narrated by a “je,” but the M does not return in the figure. Instead, this “je” is finally revealed: Je n’ai jamais rencontré Michel Chasles, cet éminent géomètre. Des lettres de cinglés, ça oui, j’en ai eu ma part, on me connaissait comme mathématicienne, alors, sur le postulat d’Euclide, celui-​là, même Joseph Bertrand s’y était laissé prendre qui en avait communiqué une démonstration à l’Académie des sciences, il faut dire qu’il ne connaissait pas Lobatchevski, sur la quadrature du cercle aussi, même après Lindemann, pourtant, si π est transcendant, la quadrature est impossible, ou sur Fermat, des démonstrations fausses, oui j’en ai vu quelques-​unes. Delaunay non plus,

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le pauvre, noyé au cours d’une promenade en bateau, même pas au large mais dans la rade même de Cherbourg, deux ans plus tard il était mort, et bien sûr, non je ne l’ai pas connu. (Audin, 2011, Lundi 5 juin)

Mathematically, K is equivalent to M, concluding both the proof and the novel with the revelation that the mysterious narrator was none other than Sophie (Figure 5.11).

Figure 5.11.  A mathematical image from Michèle Audin’s Mai quai Conti. Reproduced with the author’s permission. See Bibliography for full citation.

In the epilogue, Audin returns to a discussion of the book itself: “pas un roman, même pas, surtout pas, un roman historique, et (sauf erreur de ma part et sauf à un endroit précis où je l’ai signalé explicitement) j’ai essayé de n’écrire que du sûr, de l’avéré” (Audin, 2011, Lundi 1er mai encore). Indeed, Mai quai Conti is not a historical novel and is even less a historical study. It is neither history of mathematics nor a novel. Rather, it is a little of all of it. The structural constraint requires the reader to engage more actively with the content of the novel, reading in parallel with mathematical diagrams to understand the cast of historical figures, their points of view, and the relationships between them. This compositional method produces a great variety of narrative styles, pastiches, and constraints, creating a heterogeneous text that demands a lot of effort on the part of the reader. While this interdisciplinarity may be part of the reason behind the

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author’s lack of success in finding a publisher, the primary reason seems to lie in Audin’s use of a mathematical constraint as opposed to the subject matter of the plot. That said, while Mai quai Conti may not be a literary masterpiece, it should nevertheless be considered one of the most successful attempts by an Oulipian author to create a truly mathematizable constraint. Indeed, Michèle Audin is able to turn a mathematical proof into a plot resolution, carrying the historical significance of the Commune de Paris in its very language. Mai quai Conti thus satisfies both of Audin’s goals of vulgarizing mathematical concepts and presenting an accurate history of the discipline. The table of contents, as I have demonstrated, coupled with the writing of the book, not only fosters general abstract mathematical thought in the reader as do some of the other Oulipian texts and devices we have seen in this study, but actively allows the reader to make explicit connections between the text and a specific mathematical theorem. Audin’s work allows the reader a literary entry point to the literal work of a mathematician, teaching him or her how to read a mathematical theorem. In this sense, Audin’s project is more ambitious and I would argue more successful than another novel in this genre, Cédric Villani’s Théorème Vivant, which walks the reader through the stages in a mathematician’s development of a theorem, but does not offer the reader the tools to participate in this creative process. Unfortunately, Audin’s project has a far more limited readership than Villani’s (especially since he was awarded the Fields Medal in 2010). That said, through Mai quai Conti’s explicit compositional methods and pedagogical nature, this novel accomplishes a feat similar to what is proposed in Roubaud’s La Princesse Hoppy –​it teaches a willing reader how to read mathematically. Geometry aims to apply forms to the world, to abstract reality and discern its properties. By understanding the properties of such ideal forms, one can imitate it as one does in architecture, art, and even in literature. These two facets of geometrical work –​the ideal and the reality from which it is abstracted –​are difficult to reconcile. Situated in this debate are Calvino and Audin, who also alternate between the abstract idea of applying geometrically abstracted forms to literature and using them to speak about reality.

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Calvino uses a geometrical structure to represent the city. The divide between the crystal and flame as two metaphors for literature elucidates the oscillation between the perfection of the form and the messiness of reality. Since in Calvino’s geometrical understanding, the crystal cannot be too perfect, he uses clinamen as asymmetry, a way to program the imperfections he knows are there. Audin, on the other hand, uses a rigorous geometrical structure to represent the history of the Commune, mathematicians and their place in politics, and female mathematicians and their relative absence. This political statement is elegantly contained within and determined by the corresponding steps of Pascal’s theorem. One could argue that Audin forces history to coincide too perfectly with the theorem by the façade of her writing, but this criticism underscores the fact that this fundamental contradiction is at the heart of geometry itself. The impossibility of reconciling the human propensity for abstraction and the world in which we live is precisely the reason mathematics can be used as a tool for literary invention –​literature as well is an abstracted, human-​ invented version of reality, distinct from the real world in which we live, but of which careful study can inform our understanding of the non-​ideal, literal space in which we live. It is not a literary tendency that pushes authors to structure their stories, but rather a human tendency for abstraction. This quality allows one to translate reality, understand it, and to speak about it with others. By choosing geometry, these authors understand that space and the abstraction thereof are two facets of the same problem. With abstraction as the point of departure, the resulting work draws attention to how we process literature, mathematics, and reality, revealing the critical role of the reader. In every mathematically constrained work discussed in this study, Oulipo plays with structures and form, but the work does not end there. Indeed, Oulipian invention forces the reader to understand the critical relationship between the structure and the content, fostering connections between the composition of the text and the equally important act of reading. While Calvino’s and Audin’s geometrical examples are exceptionally fine examples of the strategies Oulipian authors employ to communicate this heightened role to a reader, they are additionally representative of the non-​ trivial nature of Oulipian work. While some critics have considered Oulipo

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to be conceptually interesting, but ultimately failing to produce objects that are worthy of further study, this analysis suggests that the opposite is true –​Oulipian work, precisely due to its use of mathematics, renders explicit certain properties of literature and how they act upon a reader.

Conclusion

On November 12, 2020, in the midst of a global pandemic, Oulipo celebrated its 60th birthday with a public reading1 livestreamed on the website of the Bibliothèque nationale de France. Just a few weeks later, on the 30th of that same month, the group’s current president Hervé Le Tellier, became the first Oulipian to win the Prix Goncourt with his novel L’Anomalie (2020), demonstrating the group’s continued relevance in French literary circles as well as in the public sphere. Oulipo has even infiltrated English scholarship, most recently with the publication of The Penguin Book of Oulipo: Queneau, Perec, Calvino and the Adventure of Form (2019), edited by Philip Terry, a Times Literary Supplement book of the year. Given its continued presence, importance, and accolades, this book can be considered yet one more attempt to elucidate the public’s fascination with constrained literature and mathematical inside jokes. This study has attempted to trace the longevity and popularity of Oulipo to its origins with a somewhat Bourbachian emphasis on foundations, demonstrating the rise and fall of Oulipo’s mathematical project and its lingering presence in the group’s production and reception. At the outset, I highlighted three main questions underlying this project: first, why did Oulipo use mathematics; second, how did the group propose to use mathematics (and how has that goal changed over time); and finally, what is the effect of this use of mathematics on the reading experience? By dividing this work according to the different types of mathematical work that have influenced Oulipo’s project and individual members and texts, certain trends in the group’s intellectual influences and the evolution and results of its project have come to light, which this conclusion seeks to reconstruct chronologically. In so doing, I wish to emphasize the results 1

This was part of its monthly readings series at the Bibliothèque nationale de France that had been moved entirely online during the pandemic.

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of Oulipo’s mathematical project and its greater implications for literary scholarship, history of science, and the digital humanities at large.

I. Oulipo’s Mathematical Project: Intellectual Genealogy and Evolution While Oulipo and its members have recounted their genealogy in many published works, their version of events must be taken with a grain of salt (much like their other texts). This work, on the other hand, has retraced the group’s intellectual history and evolution through a meticulous analysis of its meeting minutes and earliest publications. The following paragraphs therefore represent a reconstituted history of Oulipo’s mathematical project, based on the various readings provided in the preceding chapters according to mathematical disciplines. As seen in Chapter 1, Oulipo’s mathematical project can be traced back to the late twentieth-​century crisis of mathematics that led to the development of set theory, of which Nicolas Bourbaki was an important popularizer in France beginning in the 1930s. Bourbaki, a unique collective of mathematicians, defined a mathematical project that would prove a lasting influence on Oulipo’s, one which depended simultaneously on extreme formalism (in the use of the language of set theory) in the study and classification of mathematical structures. As demonstrated by Leo Corry, due to an overlap in Bourbaki’s use of the term structure in his technical and popular writing, however, his mathematical project has often been confused with the group’s overall conception of mathematics as a structure in which various disciplines are connected in a larger architecture, with formalism and axiomatization as the foundations. While Bourbaki’s structural image of mathematics enjoyed a wide-​ spread interdisciplinary popularity in the intellectual debates of postwar France,2 I have argued that Bourbaki’s greatest legacy outside of mathematics 2

Termed by David Aubin as a “cultural connector.” (See Chapter 1.)

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is in Oulipo’s mathematical project. Indeed, in Oulipo, Bourbaki found an attentive group of readers and a visionary group of writers, who brought Bourbaki’s group culture, mathematical project, and disciplinary vision into the realm of literature. This influence is present on a sociological level, determining to a certain extent the group culture of Oulipo. On a more profound level, the mathematical project of the founding members of Oulipo constitutes a legitimate intellectual inheritance of Bourbaki’s mathematical project. The main difference between the two, however –​ and a possible reason for Oulipo’s success and longevity –​is that Oulipo’s membership is far more heterogeneous than Bourbaki’s, which was composed uniquely of mathematicians. Oulipo, in contrast, brought together mathematicians and writers, as well as individuals who dabbled in both. As a result, some members were prolific creators of constrained writing while others contributed to the theoretical underpinnings of the group. Such an understanding of Oulipo’s connection to Bourbaki situates the group not only as an interdisciplinary endeavor, but furthermore as an actor in the history of mathematics itself. François Le Lionnais was not only the instigating factor in the creation of Oulipo, but was instrumental in the theorization of the group’s mathematical project primarily through his Oulipian manifestos, which allow us to better understand this co-​founder’s vision for the group’s interdisciplinary endeavor. While the genre of Le Lionnais’s Oulipian manifestos likens the group’s activity to a number of avant-​garde and experimental movements before them, an unusual yet critical intertext is Bourbaki’s Eléments de mathématique. In the first manifesto, Le Lionnais defines a possible literary equivalent of mathematical structures, in other words objects that can be studied through systematic applications of constraints. In the second, Le Lionnais distinguishes the work of Oulipo from structuralism, inscribing the group’s mathematical project into the history of Bourbaki’s use of the term. This use, according to Le Lionnais’s drafts for a third manifesto, is twofold: first in the systematic creation of constraints to apply to these literary structures, allowing for their creative study; second, in the classification of these structures in a table in the style of Bourbaki’s Architecture des mathématiques. While Le Lionnais was not a writer, many of his contributions to the group confirm that this theoretical basis was his primary

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concern, including: his set-theoretical considerations of the number of words in poetry; his Boolean projects; and even his restricted vocabulary usage in the ALGOL poetry. My analysis of these documents allows us to situate Oulipo’s project within a greater intellectual history and understand how it positions itself with other groups and theoretical movements. While Le Lionnais did not often succeed in applying constraints to create texts, his co-​founder, Raymond Queneau did. Indeed, the only volume Queneau published in the Bibliothèque Oulipienne, “Les fondements de la littérature d’après David Hilbert” is a quintessential example of a practical Oulipian application of Le Lionnais’s theorizations. In this text, Queneau considers literature as sets of words, sentences, and paragraphs, proposing both analytic and synthetic explorations of the generalizable nature of language. Queneau’s subsequent mathematical explorations of language and literature such as “x prend y pour z” make use of this same set-theoretical tendency, defining the simple elements that comprise everything we read. My readings of Queneau’s pioneering Oulipian texts demonstrate his practical contributions to Le Lionnais’s theoretical project, highlighting the importance of both co-​founders in the definition of the group’s overall mathematical project. Beginning with Le Lionnais’s set-theoretical conception of the Oulipian mathematical project, the founding members began work on a great variety of procedural constraints, of which Jean Lescure’s S+​7 is one of the earliest examples. Ubiquitous in Oulipo scholarship and criticism, this type of constraint depends on the inherent structure of language in order to allow for substitutions, resulting in a somewhat arbitrary mechanical replacement of certain words. While this type of work results in the immediate production of texts that are often amusing renditions on well-​ known literary excerpts, it is not representative of what the group would become. This procedural genre, predicated in the formal properties of mathematical language that allow for abstraction and substitution, serves a primarily analytic purpose in the sense that it reveals properties inherent in certain texts, grammatical constructions, and literature itself. For the Oulipian author who produces an S+​7, the procedure leads first and foremost to greater understanding of the source text through the production of a new text that remains largely dependent on the first. The Oulipian

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reader, on the other hand, has a different experience of such a text, as he or she is forced to consider what might be behind the S+​7 and why such replacements create such an unexpected effect. Concurrently with its procedural production (which was often inspired by the functioning of computers), Oulipo was also beginning to engage directly with computers in the 1960s, programming Cent mille milliards de poèmes and the S+​7 method on the CAB 500 computer and considering the aesthetic merit of the results. Ironically, the determinism of computers revealed to the founding members of Oulipo that such procedures, when applied mechanically, were reductive in terms of reader involvement. While Cent mille milliards de poèmes offers a reader a plethora of ways to read what Queneau maintained was an unreadable text, computers of the 1960s were not sufficiently complex to allow the reader any freedom in the selection of the poems. It is precisely at this moment that the group discovered the true enemy of mathematically constrained literature, namely chance. And while computers were and continue to be incapable of aleatory production of any kind, the effect of such programmed texts on a human reader gives the impression of randomness, denying the Oulipian reader the possibility of discovering the mathematical patterns programmed into the text by the Oulipian author. While the group’s computer activities became more varied in the 1970s with the ARTA project at the Centre Pompidou and its continuation within ALAMO, the group has nevertheless ceased all activity in these proto digital humanities efforts in pursuit of a greater focus on reader involvement, which as we have seen, varies with each Oulipian author. With the co-​opting of new members such as Jacques Roubaud, Georges Perec, and Italo Calvino (from 1966 to 1973), the mathematical project of Oulipo was put to work creating longer texts that have since become modern classics. In order to produce Oulipian novels (or longer poetry collections, in the case of Roubaud), these authors observed that mathematics can be understood as a collection of patterns and rules that determine everything we know in the world. As a response, these second-​generation members used the mathematical field of combinatorics to organize and structure their work, resulting in the construction of longer texts from various fragments, organized on a foundation of constraints. In this literary equivalent to the mathematical platonism, the reader is immersed in a

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fictional space filled with hidden secrets just waiting to be found, set up in advance by an author. However, these Oulipians also realized that the key to art is precisely that which escapes the rule, defining the clinamen (or the purposeful deviation from constraint on aesthetic grounds) to counteract the logical effect of truly strict constraint and dooming the reader to fail at the game they created. While the clinamen was in many cases built on a foundation of sand in the sense that it presupposes a strict, generative constraint that may indeed not have played a legitimate role in the creation of the text, as an aesthetic principle, it has remained an essential aspect of Oulipo’s mathematical project. The development of the clinamen represents a turn from the more rigorous and ambitious mathematical project originally proposed by Le Lionnais. Indeed, the various texts written by Roubaud, Perec, and Calvino and discussed in Chapter 3 do not necessarily reflect the various rules that were used in their composition, which in turn were not purely mathematical or generative. Specifically, in the case of Calvino, texts such as Il castello dei destini incrociati and Le città invisibili have the impression of mathematical rigor through an explicit structure, but seem to derive from a structural aesthetic inspired by Oulipo rather than being the products of strict constraint. This deviation from strict mathematical rigor has serious implications for the present-​day group, which does not currently include many mathematicians3 and, aside from Michèle Audin, no longer produces the same caliber of mathematical constraints. While this could be considered a failure of Le Lionnais’s original mathematical project, it nevertheless represents a newfound flexibility for the group, allowing it to persist and remain relevant in French literary and intellectual life, which leads to the next question: what are the results of Oulipo’s mathematical project? 3

With the notable exceptions of second-​generation member Jacques Roubaud, who is still an active member of the group today. Among more recent coopts, Pierre Rosenstiehl (who recently passed away in October 2020) and Olivier Salon have advanced degrees in and have taught mathematics. However, Rosentiehl was not particularly active in the group and Olivier Salon’s most important contributions to the group have been of a more theatrical nature. As mentioned previously, Michèle Audin is the only current member who is actively continuing the group’s mathematical project.

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II. Results of Oulipo’s Mathematical Project While Oulipo’s original mathematical project as conceived and theorized by Le Lionnais may not have been feasible for literature, it has proved to be quite fruitful. In addition to the numerous examples of procedural constraints, computer experiments, and longer structural works discussed in this book, Oulipo has been the site of literary production for more than 60 years and has become a visible feature in French literary, intellectual, and popular culture (contrary to its original desire to be a semi-​secret society). This study has observed the role that the group’s mathematical project played in this reception and argued that the group’s mathematical foundations have several important results on its readers, academic scholarship, the group’s longevity and reputation, and even computer science and mathematics. As demonstrated in the close readings of the mathematically constrained texts included in this study, Oulipo’s use of mathematics creates a new kind of reader. The Oulipian reader, confronted with a text of which the compositional methods are unconventional, must read in a new way. While this is true for much experimental literature, the unique aspect of Oulipian reading is that the reader is confronted with a text that may be the result of a mathematical constraint. Just as one must read a theorem with a pen and paper, reproducing the logical steps in order to understand the mathematical object in question, a reader of an Oulipian text must exert a mathematical effort that is parallel to that employed by the author to compose the text. Such a reader, implicated in the creation of the text by the very act of reading, engages in mathematical thought, a search for abstract patterns that resulted from the constraints that produced the text. The pedagogical nature of the Oulipian mathematical project results in a body of paratextual and extratextual instructions, references and commentaries that the reader can use in his or her reading. However, the author’s intentions are only the first step of the process, and a willing reader must accomplish the rest. In addition to the effect on the reader, Oulipo’s mathematical project can be considered a possible reason for the group’s popularity, longevity,

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and reputation. Given the promotion of scientific disciplines following World War II, it is natural that Oulipo, which makes intentional use of mathematics and science in the production of literature, has found a large audience, as it responds to a growing concern in education. Indeed, the French educational system in particular is strictly divided into sciences and lettres, so Oulipo’s ability to mix the two challenges this two-​culture distinction. It is nevertheless surprising that such an interdisciplinary group originated in France, given an educational system that forces students to specialize even before they begin their undergraduate work. Oulipo was founded by a restricted group of much older erudites, many of whom had ventured outside of their disciplinary confines during World War II. In fact, Queneau and Le Lionnais even met during the war and discussed their respective interests in mathematics and literature, creating a lasting partnership that could be viewed as the first step in the creation of Oulipo (Salon, François le Lionnais, le disparate, p. 120). Early on, the group changed its name from séminaire to ouvroir, as the members were wary of academia. By breaking from this tradition, Oulipo represents a particularly important non-​academic initiative in the blending of disciplines, and a surprisingly early one. Its continued relevance and popularity in France especially highlights the erroneous nature of the educational system’s strict division of academic disciplines. While Oulipo is certainly a major object of study in literature, it has remained relatively unacknowledged in other disciplines, whereas the work it accomplished in the 1960s and 1970s belongs, in theory, in studies of history of science and mathematics. The lack of scholarship in the history of science and mathematics on Oulipo is perhaps linked to the fact that most of the group’s production is of a primarily literary nature; however this study has shown that the value of Oulipo’s production is not purely literary. For instance, the group’s computer experiments were on the cutting edge of informational technology at the time, and Oulipo was therefore an important historical actor in the development of computer science and computational linguistics. Indeed, a renowned computer scientist such as Dimitri Starynkevitch was able, through his partnership with Oulipo, to code literature on a forerunner of the personal computer, a machine that, at the time, was designed exclusively with calculations in mind. The ARTA

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project as well fostered interdisciplinary connections, putting a famous author such as Italo Calvino in conversation with computer programmers, leading both sides to question the potential of one discipline for another and constituting an early precursor to what is known today as digital humanities scholarship and electronic literature. An even more impressive interdisciplinary result of Oulipo is that the group’s mathematical exploration of literature has even contributed to mathematics itself. While Cent mille milliards de poèmes represents an adaptation or creative use of combinatorics for literature, Queneau in fact published a mathematical study, his “Note complémentaire sur la sextine,” in the Subsidia Pataphysica in 1963. Of Queneau’s multiple published theorems, this one stands out because the mathematical discovery is derived from a medieval poetic form. Queneau’s article generalized the repetition of the sestina’s six rhyming words to determine other n’s for which the spiral permutation of Arnaut Daniel’s original sestina could operate, inventing a new structure of fixed-​form poetry in the process. While Oulipo has produced examples of this new type of poetry and its applications (for instance, Perec used this result to organize the contents of each room in La Vie mode d’emploi as discussed in Chapter 3), further mathematical studies have been carried out to learn more about these potential n’s and their properties, most notably by Jacques Roubaud, Jean-​Guillaume Dumas, and Monique Bringer, as discussed in the introduction. Several aspects of these mathematical studies on the sestina are exceptional. First, rather than taking the rhyming words as meaningful signifiers that fit into a larger poem, Queneau’s original study abstracts them in a mathematical sense. Instead of reading the poem, Queneau looks only at these permuting elements and the way they move, generalizing their pattern. Additionally, the permutation Queneau uncovered has an elegant spiral pattern, which resembles the logarithmic spiral which was inscribed on Ubu’s stomach in Alfred Jarry’s Ubu roi and which later became the symbol of the Collège de ‘Pataphysique from its founding in 1948 (S. Harris, p. 12). While the spiral permutation as represented by the sestina is not drawn as a logarithmic spiral, this ‘pataphysical understanding of the spiral shares much with the sestina, whose rhymes remain unchanged yet permute in a way that does not imply hierarchy or importance. Queneau

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even includes at the end of his ‘Pataphysics article Bernoulli’s “éloge de la spirale logarithmique” (Note complémentaire sur la sextine, p. 80). In addition to connections with ‘Pataphysics, there is an obvious correlation with the work of Oulipo. Queneau published his sestina work in 1963, three years after the founding of the group. Seeking to apply mathematical principles to literary production, the work of the troubadours (a favorite topic of Jacques Roubaud) is an obvious subsection of their analytic branch of research, as both are defined by strict constraints. Furthermore, attempting a formal definition of the sestina’s permutational constraint is in keeping with the group’s synthetic goal. By fostering mathematical thinking in the development of constraints, Oulipo created a new family of constraints, the quenine, but also turned literature into mathematics. As far as is known, this is the only case of literature creating a mathematical study, contrary to the vision perpetuated by mathematical platonism that mathematics exists independently of humans. In this sense, Oulipo’s work on the sestina is a crowning achievement: not only does the group use mathematics to enrich literature, but its members have actually created mathematics from literature.

III. Implications for Scholarship In La Littérature Potentielle, Oulipo defines itself by what it is not: “1. Ce n’est pas un mouvement littéraire. 2. Ce n’est pas un séminaire scientifique. 3. Ce n’est pas de la littérature aléatoire” (p. 7). This study has demonstrated the following: first, while Oulipo is not a literary movement, its group practices, textual production, and results contribute to the study of literary history in a variety of ways; second, while Oulipo is not a scientific seminar, it engaged in important literary and scientific projects that contribute to academic scholarship; finally, Oulipo refuses to produce random literature precisely due to the fact that chance is the absence of all pattern and therefore anti-​mathematical. In other words, while Oulipo defines itself in opposition to traditional or mainstream literary

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phenomena, creative practices, and academic work, its results contribute to our understanding of all of the above. The theoretical framework I have built regarding Oulipo might very well apply to other experimental trends in literature and more specifically, to other studies of intersections between mathematics and literature. While Oulipo represents a culturally and historically specific appropriation of Bourbaki, it simultaneously recognizes its place in a long line of constrained literature and mathematical literature. Therefore, the vocabulary I have used in speaking of the group’s constraints, structures, and procedures can provide a useful lens for analyzing similar trends in experimental literature, especially with those Oulipo deems plagiarists by anticipation. Furthermore, the methodology I have used has further applications in reader reception theory and can therefore be replicated when considering readerly responses to experimental literature. That said, much is also to be learned from the work that Oulipo abandoned along the way. For instance, the group’s ground-​breaking work on computers was not only a precursor to digital humanities work, but foreshadows interrogations into computer-​assisted text generation and analysis, both of which are becoming increasingly important today. Indeed, with the advent of machine learning and artificial intelligence, computers are participating actively in writing, reading, and even mathematics. Furthermore, Queneau’s and Perec’s flowchart narratives represent the beginning of a new genre of arborescent literature, which has since been developed greatly by practitioners of electronic literature and most importantly video games. In this sense, Oulipo’s pioneering work has now escaped the confines of literature and belongs to the realm of the audiovisual. This is not to say that the group and its individual members have not pursued audiovisual productions: for instance, Le Lionnais was a radio personality; Perec, as we have seen, published his German radio plays which were commercially successful; and even to this day many members including Jacques Bens, François Caradec, Paul Fournel, Jacques Jouet, Hervé Le Tellier, Ian Monk, and recent recruit Clémentine Mélois participated on France Culture’s longrunning literary quiz show, Des Papous dans la tête (1984–​ 2018); of course, we cannot forget the group’s 1999 CD-​ROM, Machines à écrire. That said, the group’s contribution to interactive literature is often

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mentioned, yet rarely studied in detail, likely due to the fact that these arborescent pursuits were abandoned in their infancy. On the other hand, Oulipo and its mathematical project (whether one considers it successful or not) should be lauded for its impressive and perhaps unparalleled productivity. Indeed, the group itself is prolific, but has given rise to its own mathematically substituted spinoff groups, the OuXPo. These distinct groups that specialize in reproducing Oulipo’s constraint-​ based writing in other fields –​music, cooking, art, and more –​have extended the group’s methods and can be considered a particularly interesting effect of the group’s mathematical project. They demonstrate just how fruitful such an approach can be, even outside the realm of literature. Their works, such as the numerous illustrations throughout this book by members of OuPeinPo, the Ouvroir de Peinture Potentielle,4 also capitalize on the mathematical search for patterns, creating new types of “writers” and “readers” for new disciplines. Furthermore, as Dennis Duncan (2019, p. 151) mentioned in his recent book, The Oulipo and Modern Thought, Oulipo’s constrained writing principles have also inspired a great number of American and Canadian writers and, following a 2005 conference, the creation of a loose collective of practitioners of a “new Oulipo” or “noulipo” for short. An obvious outcome of Oulipo’s transdisciplinary endeavor is that creative practices are inherently fruitful when structured properly. While Oulipo was created as an explicitly anti-​academic endeavor, the results of its mathematical project are irrefutably beneficial to scholarship in a variety of academic disciplines, including (but not limited to): literary studies, literary history, history, history of science, history of mathematics, computer science, digital humanities, and cultural studies. To verify this list or find new results, one need only look to the titles included in Virginie Tahar’s Bibliographie des études oulipiennes, which extend across disciplines and find unexpected conclusions to be drawn from the work of Oulipo. In academia today, interdisciplinarity is often considered a solution to the two-​culture 4

See appendix for more information about this group as well as the artists’ own explications of the beautiful visual contributions they made to this volume, including the cover.

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debate, and many steps are currently being taken to bridge disciplines in research and pedagogy. In this investigation of the genealogy and evolution of Oulipo’s mathematical project, I have identified the following aspects as key to the success of this endeavor: the rich, interdisciplinary backgrounds of the group’s members; the group’s openness and desire to solicit experts when necessary (such as their computer collaborations and other invited guests at their monthly meetings); the proper balance between theory and practice; and finally, the importance of creativity to interdisciplinary work.5 By taking Oulipo as a particularly successful example of interdisciplinary work, we can adapt these aspects into our research and pedagogy, perhaps developing equally interesting results for scholarship and education.

5

In digital humanities especially, the need for more creative approaches could be a way to put an end to the longstanding debate about what this work truly is. What distinguishes excellent digital humanities scholarship is similar to what distinguishes top academic or artistic production in general –​namely, an important yet previously unaddressed research question coupled with innovative methods to answer it.

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Presentation

• An Ouvroir or workshop In other words, a place where we work. It is not a laboratory in that it is not a place of labor; nor is it a learned society, because the advancement of science is not its purpose; neither is it a sect, because no doctrine is followed; nor is it a school, because it has neither teachers nor pupils. It has nothing in common with an academy, a museum, a lodge, a police station, an institute or any kind of institution. If we can find some connection with a workshop, it is to the extent that we actually devote ourselves to many tasks. • of Peinture, or painting but by synecdoche, because the OuPeinPo in no way restricts painting to the art of applying pigments. On the contrary, it extends the definition of “painting” without scruples to all graphic or plastic arts and, recommends the painter’s brush as well as the draftsman’s pencil, the engraver’s tip, the sculptor’s chisel, the stucco-​maker, the graffiti artist’s aerosol, the odds and ends of the installer, the videographer’s camera, even the mouse of the graphic artist. The photographer’s camera and the printer’s press are not unknown to us. The OuPeinPo strives to promote the needle and the scalpel, the bacon and the chopper, the jet and the compressor, the pie server and the mechanical shovel, the laser and the rolling mill, the field gun (if necessary the bomb), or even the bare hand and digital agility. Extending the range of what is available to the painter in the way of material as well as of materials, supports, techniques, processes, subjects,

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points of view, theories, etc., offered to the “painter” is one of the objectives of OuPeinPo. • Potentielle, or potential because the OuPeinPo, as such, does not produce any “real” painting. It applies itself not to works, but to methods, devices, manipulations, structures, formal constraints with the help of those which past, present, and future painters have been able, can, and will be able to use to create their art. The OuPeinPo certainly does not devalue the act of painting or its results, but asserts rather that this is the business of the artists, sponsors or the viewing public. The OuPeinPo’s role is to propose “forms” or transformations in which the works exist as possibilities. Let us hasten to add that its members strive to be the first users of the forms the group develops so that they do not remain empty but are manifested by examples. The OuPeinPiens thus provide, with the constraints they invent, proofs of feasibility. Hence an appearance of production which gave rise to exhibitions and publications. However, the examples produced represent only a tiny proportion of OuPeinPian inventions, and if certain works present themselves with the ambition and the finish of “artwork,” it is the result of the individual authors, not of the Ouvroir as a group. A first OuPeinPo was created on November 5, 1964 and relaunched on May 9, 1966. Aline Gagnaire, Jean Dewasne, and Jacques Carelman participated during this period. The group was inactive from January 1968, but then brought back to life on December 12, 1980 by François Le Lionnais, Jacques Carelman, and Thieri Foulc, joined on January 14 the following year by Aline Gagnaire and Jean Dewasne. The following years saw the addition of new members: Tristan Bastit (December 21, 1985), Jack Vanarsky ( January 20, 1990), Olivier O. Olivier and Brian Reffin Smith (both on September 10, 1999), Guillaume Pô (March 23, 2002), George Orrimbe (2007), Philippe Mouchès (2009), Eric Rutten (2013), Achyap (2013) André Stas (2013), Helen Frank (2016). The biological death of some members has no effect on their membership in the Ouvroir (which is by right), nor on their influence, which is always noticeable over the sessions. The exact number of OuPeinPiens

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remains difficult to determine, however, due to quasi-​members with less certain statuses. For instance, Suzanne Allen participates in the sessions as an “active witness,” as does the dog Virgule and Mrs. Cassette, who provided the recording as long as the sessions were held at Carelman’s. Foreign correspondents take part or have taken part in certain works or in certain demonstrations (Brunella Eruli, Aldo Spinelli in Italy; Alastair Brotchie in Great Britain). Finally, documents attest to the involuntary but real participation of Hieronymus Bosch, Leonardo da Vinci, Giuseppe Arcimboldo or Andy Warhol.

Expositions of the OuPeinPo

• May 1989 –​Gallery of the Université du Québec à Montréal (UQAM), exposition on ‘Pataphysics. • February–​March 1990 –​Centre Culturel Les Chiroux, Liège (Belgium). • April 1991 –​Publication of the first volume of OuPeinPien works, • May 1991 –​Chiostro di San Marco, Florence (Italy), at the conference Attenzione al potenziale ! • June–​July 1991 –​Presentation at the Centre national d’art et de culture Georges-​Pompidou, Paris, in the context of the Revue parlée. • October 1991 –​Presentation of the Tableau des Cent Fleurs at the Marraine du Sel, Paris. • October 1992 –​Presentation of the OuPeinPo at Thionville (France), at the Raymond Queneau Conference. Exposition at the city’s cultural center. • May 1996 –​Exposition at Sophia Antipolis. • March 1997 –​Exposition at the University of Poitiers with the publication of the corresponding volume, Nouveaux aperçus sur la potentialité restreinte (Publications de la Licorne).

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• October 1997 –​Presentation of the OuPeinPo at Cristina Martinez’s workshop. This marked the beginning of the group’s monthly publication, Les Séances de l’Oupeinpo. • May 1999 –​Collective participation with the Oulipo and other OuXPo groups, at the Centre Georges-​Pompidou. • October 2000 –​Exposition in Capri at the conference La regola è questa and of the Premio Capri dell’Enigma. Reading of L’Hôtel de Sens, by Jacques Roubaud and Paul Fournel, with 28 “paintings” created by the OuPeinPo. Public tearing and digraphage. Speech on La Contrainte contre, by Thieri Foulc. • October–​November 2000 –​Resumption of the Capri exhibition at the Artoteca Alliance, Bari (Italy). • Presentation of the book and exhibition at the Mouvements bookstore; performance by the OuTraPo on December 12 at Jussieu at one of the Oulipo’s monthly performances. • May 2003 –​Seminar of the Collège de ’Pataphysique at CAMAC (Centre d’Art Marnay Art Center), Marnay-​sur-​Seine, invited by Frank Ténot and his Foundation. Presentation of OuPeinPian work. Zombie art performance by Brian Reffin Smith. Pictée, by Carelman. • March 2005 –​Retrospective at the Nicaise bookstore in Paris. • May–​June 2011 –​Exposition Oueinpo (Pictée by J. Carelman), LA BOX Gallery, Bourges. • September–​October 2011 –​Certain works of the Oupeinpo on exhibit at the conference “L’Oulipo a 50 ans” at the Karpeles Manuscript Library Museum, Buffalo (USA). • April–​May 2014 –​Exposition of Oulipian Portraits at Lagny-​sur-​ Marne, in the context of Olivier Salon’s residence at Marne-​et-​ Gondoire, with works by Achyap, Thieri Foulc, Philippe Mouchès, George Orrimbe, Éric Rutten, Brian Reffin Smith, André Stas, Jack Vanarsky (Pictée by E.Rutten and Pushy-​poulies by B. R. Smith) • January–​April 2014 –​ Peintures de mots, by Thieri Foulc, at Vieille Charité (cipM), Marseille, displaying 27 black background frames with the potential artwork to be listened to with an audio guide.

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• May 2014 –​Conference of Anne-​Maya Guérin on the Oupeinpo at the Matisse du Cateau-​Cambrésis Museum, for the Dewasne Exposition, with Thieri Foulc. • November 2014–​February 2015 –​Presentation of the Oupeinpo in the context of the Oulipo, la littérature en jeu(x) exhibition at the National Library of France (bibliothèque de l’Arsenal). Catalogue: Ouvroir de littérature Potentielle, edited by Camille Bloomfield and Claire Lesage, édition BNF and Gallimard, 2015 • Janvier 2015 –​Portraits de tous les membres de l’OuLiPo de George Orrimbe, exposition Galerie Weiller, Paris • April–​July 2018 –​exposition Art et Maths, at the Technische Universität, Berlin, with work by Thieri Foulc, Brian Reffin-​Smith, George Orrimbe, Philippe Mouchès, Achyap, Eric Rutten, André Stas, and Helen Frank. • March–​July 2020 –​Exhibition L’OUPEINPO en vient aux maths at the Institut Henri Poincaré, Paris with work by George Orrimbe, Philippe Mouchès, Achyap, Eric Rutten, and Helen Frank.

Publications Collective Works Prenez garde à la peinture potentielle! Cymbalum Pataphysicum, nº21. September 1991. OuPeinPo (Ouvroir de Peinture Potentielle): nouveaux aperçus sur la potentialité restreinte. Exposition, Poitiers, 24–​28 mars 1997. La Licorne. Du potentiel dans l’art, par l’Oupeinpo, éditions du Seuil. 2005. Oulipo compendium, H. Mathews, A. Brotchie, 1998, 2005, Atlas Press London, Make Now Press.Los Angeles Roubaud, Jacques and Paul Fournel, L’Hôtel de Sens, with 41 paintings by the OuPeinPo. Au crayon qui tue, 2002

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Selected Individual Works Thieri Foulc, Le Morpholo, Cymbalum Pataphysicum, 1985. Tristan Bastit, Toto à la rhétorique, éditions du Sel & Couëdic réunis, 2001. Philippe Mouchès, Contrepicterie, 2011,Bibliothèque Oupeinpienne, N° 17 Paul Fournel, Formes cyclistes, avec quatre dopages visuels par Thieri Foulc, Au crayon qui tue, éditeur, 2012. Paul Fournel, Le Lagarde et Panard, illustré par Philippe Mouchès, Dialogues, 2015. George Orrimbe, Portraits vocalocoloristes de tous les membres de l’OuLiPo. 2016, Forêt secrète éditions. Paris Math de l’Oulipo illustré par Achyap, 2017.

Achyap Achyap is a mathematician and an artist who joined the OuPeinPo in 2013 and who likes to explore potentialities at the threshold of mathematics and art. Constraints lie at the heart of mathematics, and guide mathematicians in their research. The art of a mathematician is to transgress the frontiers of a theory in order to explore new fields of research while respecting some constraints which ensure the coherence of the extended theory. The beauty of a mathematical theory emerges when the constraints melt into it, turning out to be so natural that they become invisible. The power of a constraint is then to provide a framework, a canvas for explorations whether artistic or mathematical, and to vanish once it has served its purpose to produce a work of art. ACHYAP explores the power of constraints in art and mathematics.

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Cover Stokes’ formula, depicted on the front page in its elegant modern form ∫ dω = ∫ ω offers an ideal battleground for a confrontation of art and X

δX

mathematics. It is the main protagonist of a novel that Michèle Audin, an Oulipo member who is portrayed in the background, dedicated to its long sinuous and fascinating history. The acrobats clinging onto it relate its various building blocks, the manifold X, its boundary δ X , the differential form ⍵, and its exterior differential d ω . The form ⍵ relates to the boundary δ X in a similar manner to how its coboundary d ⍵ relates to X. Cover of Chapter 1 A mathematical formula can also be portrayed using a dictionary which provides a graphic representation of the protagonists, links and assemblers. The formula A ∩ (B ∩ C) =​(A ∩ B) ∪ (A ∪ C) borrowed from set theory, reflects the distributivity of the intersection ∩ with respect to the union ∪. It comprises three sets A, B, C linked by the union «∪», the intersection «∩» and the identity « =​» which is a relation, organized by the assemblers which correspond to the parentheses. Without aiming at a faithful translation which would enable a full reconstruction of the initial formula from the portrait, the dictionary aims at making «visible» the distributivity of the intersection with respect to the union. It should nevertheless be faithful enough so as to distinguish a correct transcription from an incorrect one. Setting up a dictionary is where art comes into play, whereas the constraints lie in the realization of the portrait of the formula following the rules set by the dictionary. Other Images The famous formula of Pythagoras a +​ b2 =​c2 that we all know from school (see Figure 1.1), can be proven pictorially as illustrated in Figure 1.2

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making poor Pythagoras feel rather dizzy! The cross-​ratio, which goes back to Pappus of Alexandria was later used by Michel Chasles, so much so that his eyes crossed while following the intersecting lines as depicted in Figure 5.2. Transposing mathematical syntax pictorially is a never-​ending challenge, which has kept many OuPeinPo members busy!

Helen Frank Helen Frank has been a member of the OuPeinPo since 2016. As an artist, she explores the visual potential of graph theory and topology with the intent of turning abstract elements, uncannily, into something figurative. Cover image: Still taken from an animation: Graph Isomorphism Escape Plan

  [or : HelenMF] This animated portrait of Raymond Queneau is the result of separating his face into 10 pieces and assigning each feature to a node of a Petersen graph. His facial features are rearranged as the graph follows a cycle of 7 specific isomorphic configurations. To ensure the correlation between facial feature and node is constant, the 10 nodes were labelled A to J and the facial features labelled A to J –​feature A placed at node A, B to B, etc.

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Ear = A Left eyebrow = B Right eyebrow = C Cheek = D Mouth, lower = E Glasses = F Left ear = G Right eye = H Nose = I Mouth, upper = J

  Figure 4.1: A visual illustration of the Bridges of Königsberg problem. Still taken from an animation: Kant as Königsberg, a Problem.

  [or : HelenMF] This animated portrait of Immanuel Kant was made according to Leonard Euler’s abstraction of the Bridges of Königsberg problem; four land masses became four nodes, and seven bridges became seven edges. Euler’s reformulation removed all unnecessary features as they had no bearing on how he would come to solve the problem. The key elements remain here in this portrait; however, an emphasis has been placed on the position of the nodes and the length of the edges so that it forms the features of Immanuel Kant.

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Using a graph coloring system, the animation shows Euler (represented by a red circle) on his various attempted and failed routes across Königsberg: the first route “Euler” takes, each bridge he crosses turns yellow, when he gets to a repeated bridge, he turns back and tries another route, each subsequent bridge crossed, turns from yellow to green. Again, when he reaches a repeated bridge, he turns back, and each subsequently crossed bridge turns from green to pink.

Philippe Mouchès Philippe Mouchès, who joined the OuPeinPo in 2009, works readily around the potential offered by figurative painting, from Lascaux to Picasso. He became interested in reversible and bi-​reversible images and tried to find pictorial correspondences to certain literary games such as the contrepèterie or the anagram. He particularly practices pastiche, the diversion of heritage works, and mystification. Works willingly contributed according to the theme of figurative potentials. Cover 1. Portrait of Jacques Roubaud This portrait belongs to the OuPeinPian genre of the “Reading multiplier” in which two images can be read simultaneously: the face of Jacques Roubaud and a game of Go. 2. Portrait of Jean Lescure This portrait is an anapict, in reference to the anagram. We take an image, stylize it and then divide it into n pieces that we recombine in order to generate another (or more).

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Chapter 2, Cover 8+​1=​9, Nature morte arithmétique “The mathematician put down his hat and his operation.” This is a zeugme for the scholar, but for OuPeinPian, it is an invitation to go further in the exploration of what he calls “reading multipliers.” Besides, don’t we talk about “mathematical objects?” So, if we can lay hats like operations, let’s lay down operations with hats, candles, umbrellas, or sewing machines. Chapter 3, Figure 3.7 The puzzle game is one of the obvious keys in Georges Perec’s masterpiece, the movement of the knight is, on the contrary, one of the hidden keys; hence the idea of bringing the two together, in what is more an illustration than an OuPeinPian production. Chapter 5, Figure 5.1 Jasper Johns once had the brilliant idea of using numbers as a subject of painting. The OuPeinPian, who is less of an artist but more of a mathematician than Jasper Johns, grants himself the right to Jasper-​Johnify any arithmetical enunciation he sees.

George Orrimbe Coopted by the OuPeinPo in 2007, George Orrimbe works on the transposition of words into plastic objects in two or three dimensions according to the constraint named “vocalocolorism” by Jacques Carelman. This constraint consists of using the vowels of a word to make way for a visual transposition of the word itself. Orrimbe makes use of two

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codes: one defining the color (A=​black; E=​yellow; I=​red; O=​blue; U=​ green, courtesy of Jean-​Nicolas Arthur Rimbaud) and the other defining the shape (if a word contains one vowel, it will be transposed as a circle; two vowels, a rectangle; three, a triangle; four, a square; five, a five-​pointed star or regular pentagon; etc.). A vocalocolorist portrait, which is the true portrait of the author because it comes directly from his works, is constructed from a chronological list of 10 titles of his works. Cover The vocalocolorist constraint is applicable to two portraits on the cover, G. Perec et P. Braffort, with each title transposed using the vocalocolorist method, the oldest for the hair, the others follow, in chronological order for each part of the face; hair, forehead, nose, eyebrow (2), eye (2), ear (2), mouth, cheek (2), chin and neck. Thus for G. Perec, the hair is derived from his first novel, Les Choses, as a series of yellow circles (Les) with each one followed by a blue rectangle (Choses). The forehead transposes the title Quel petit vélo à guidon chromé au fond de la cour as a green rectangle, (Quel), followed by a yellow rectangle for (Petit), and so on. Finally, the neck comes from Je me souviens: yellow circle (je), yellow circle (me), blue square (souviens). The date of the portrait is that of the publication of the last opus transposed for the neck. The name of the portraiture gives the general shape of the face on which the different parts are glued for Perec, a yellow rectangle (E). For G. Perec, The portrait is supported by a cube, each of the five visible faces of which represents a view of the face; front, right profile, left profile, top view, neck view; the quality of the cubic portrait was therefore essential. Introduction, Figure 0.2 Vocalocolorism can also be applied to text, such as the sestina table on pp. 3, where the words of column 1 are each represented by a rectangle (two vowels) according to the color code:

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–​ intra, red, –​ ongla, dark blue (to account for the other word containing an E) –​ arma, light gray, –​ verja, yellow –​ oncle, light blue –​ cambra, dark gray.

Chapter 5, Cover The portraits of Michèle Audin and Italo Calvino are produced under the same constraints as those of G. Perec.

Eric Rutten Eric Rutten, who joined OuPeinPo in 2013, has a strong taste for blue, yellow, red, and spirals, or gidouilles. He practices a somewhat punk geometric abstraction, in the thickness of the line between clarity of ideas and vanity of virtuosity. He takes polyptych, polyhedral, abstract or figurative forms (bestiary, painting the giraffe, portraits and figures, landscapes), visible here: . He practices with certain classical constraints of OuPeinPo (particularly the measured color, then declined in blue, yellow, red of course), and experiments with what could become other constraints, with the force of illustration. Cover, “Projection of the Galaxy of Oulipo Members on a Logarithmic Spiral according to the subgroup considered by NB” The cover art is composed with portraits of Oulipo members designed by different Oupeinpo members, arranged in a leftward spiral, structure

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of both the galaxy of the OuLiPo from which it is an extract, and of the Gidouille, a symbol commonly associated with the College of ‘Pataphysics. It therefore falls under Gidouillism. Cubism had its cubes, pointillism its points, and tachism its spots: gidouillism has its gidouilles. This approach to painting composes images by assembling gidoullic forms. In particular, it uses, in its n-​angularist movement, spirals presenting angles, at each turn to the number of n (cf. from the same author, Gidouilles n-​angulaires, Viridis Candela, Collège de ‘Pataphysique, no. 21, pp. 65–​78, vulg. oct. 2012) (see: . Among the different Oulipian portraits can be found the “Portrait of Etienne Lécroart (according to himself ) prime gidouilliste” (EL), who is himself an example of gidouillisme. Another portrait in the Galaxy is “Portrait of Claude Berge as a graph Q-​6” (CB), composed by retracing his face (including mustache and glasses) on a Q6 graph, dedicated by CB to Raymond Queneau, and of which the Oulipian qualities were described on a 1996 postcard from INRIA. Introduction, Figure 0.2 The “6-​angled sestina,” whose classic spiral is here revised in an angular manner, constitutes another example of gidouillisme. Chapter 3, Cover The “Puzzle Theorem of the Four Colors” demonstrates the application of the Four Color Theorem to the coloring of the pieces of a puzzle, cut by hand by the Wilson brand. This theorem, which consists in constructing flat images using four colors (typically: blue, yellow, red, and white or black), asserts that it is possible, using only four different colors, to color any map divided into related regions, so that two adjacent (or bordering) regions, that is to say sharing a whole border (and not just a point), will always be painted in two distinct colors.

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Index

2001: A Space Odyssey  186 Abbott, Edwin  12 abstraction  23, 40, 63, 111, 133, 203, 223, 247, 261, 266, 285, 289 Académie des Sciences  3, 20, 234, 249, 252 Actes sémiotiques  14, 146, 227 ALAMO  214–​217, 267 Albarès, René-​Marie  67 Albert-​Marie Schmidt  9, 125, 176–​177 alexandrine 63, 75, 77–​78, 215  ALGOL  177–​180, 221, 266 anoulipisme  12, 54, 73, 77, 93, 97 Anthologie de l’Oulipo  53 Apollinaire, Guillaume  75 Aragon, Louis  126 Ariosto, Ludovico  154–​155 Aristotle  88 arithmetic  19, 23, 60, 70, 86, 103, 107, 158, 166, 181, 289 Arnaud, Noël  10, 90, 177, 182–​183 ARTA  185, 205–​215, 267, 272 Atlas de littérature potentielle  14, 17, 52, 59, 75, 78, 91, 93, 96, 97, 109, 118, 146, 161, 205, 208, 210, 227 Aubin, David  38, 44, 46, 48–​52, 264 Audin, Michèle  49, 224–​225, 233–​238, 247–​261, 268, 289 Mai quai Conti  20, 224, 233–​237, 249–​260 automatism  78, 131, 132, 181–​183 axiom  18, 23–​24, 29–​36, 39–​43, 45, 48–​ 49, 59–​61, 68, 97, 102, 111–​112, 120, 134, 175, 264

Barthes, Roland  7–​8, 146 Baudelaire, Charles  215–​216 Beaudouin, Valérie  86, 217–​218 Beckett, Samuel  189 Bellos, Alex  27 Bellos, David  66, 92, 162, 166, 168, 185, 187, 200, 201 Bénabou, Marcel  7, 51, 92–​93, 208–​209, 214–​215 “aphorismes artificiels”  208 Aphorismes à votre façon  215 Poésie antonymique  93 Bens, Jacques  9–​10, 50, 74, 76, 162, 175, 176, 273 Sonnet irrationnel  76 Berge, Claude  10, 17, 20, 49–​50, 118, 165, 182, 191, 196–​197, 200, 218–​ 220, 290 Qui a tué le duc de Densmore ?  218–​220 Bible  87, 184 Bibliothèque Oulipienne  14, 30, 44, 52, 53, 146, 218, 227, 266 Binet, Catherine  168 Bloomfield, Camille  15, 51, 53, 118, 184, 281 Boccaccio, Giovanni  150 Boole, George  66 Borges, Jorge Luis  15, 167 Boule et Bill  66 Bourbaki, Nicolas  10, 13, 15, 18, 24, 37–​63, 68–​69, 111–​112, 120, 122, 124, 133, 135, 138, 139, 140, 141, 170, 171, 177, 183, 220, 233, 264–​ 265, 273

306 Index Eléments de mathématique  37–​41, 44, 46, 52, 55, 56, 57, 111, 122, 135, 265 Éléments d’histoire des mathématiques  38, 40 “L’Architecture des mathématiques”  40, 45, 55 La Tribu  52 Mode d’emploi de cetraité  40 “Notice sur la vie et l’œuvre de Nicolas Bourbaki”  38 Bourguet, Dominique  207 Braffort, Paul  10, 17, 19, 62, 72, 93, 94, 103–​108, 114, 176, 180, 205, 213, 214, 220, 288 Mes Hypertropes  19, 62, 72, 103–​108 Brébeuf, Jean de  64 Bremond, Claude  145, 196 Breton, André  52–​54, 122–​124 Bringer, Monique  5, 271 Bull Computers  174, 176, 180 Butor, Michel  167 cadavre exquis  122–​124, 126 Calvino, Italo  7, 11, 14, 19, 20, 118, 119, 132, 145–​160, 161, 164, 167, 170–​171, 205, 208–​262, 267, 268, 271, 289 Fiabe italiane  145, 225 Il castello dei destini incrociati  19, 118, 119, 145–​160, 161, 170, 212, 227, 244, 268 “La struttura dell’Orlando Furioso”  155 Le città invisibili  20, 145, 146, 224, 226, 227, 232, 233, 238–​262, 268 Le cosmicomiche  145, 227 Lezioni americane  148, 230 L’incendio della casa abominevole  208–​213, 224 Orlando Furioso di Ludovico Ariosto raccontato da Italo Calvino  155

Se una notte d’inverno un viaggiatore  14, 146, 224, 227 Six Memos for the Next Millennium  232, 240 Campaignolle-​Catel, Hélène  194, 196, 199 Cantor, Georg  37 Carroll, Lewis  12, 109 Cartan, Henri  38, 233 Centre Pompidou  174, 184, 205, 267 Cercle Polivanoff  166 chance  15, 19, 20, 23, 117–​119, 126, 154, 157, 160, 173, 174, 182, 183, 185, 199, 232, 233, 244, 267, 272 Charbonnier, Georges  120 Chasles, Michel  234, 235, 250, 251, 254, 256, 257, 258 chess  162, 163, 169, 228, 244, 245, 246 Chevalley, Claude  38, 50 Chomsky, Noam  42, 231 clinamen  10, 19, 20, 119, 145–​149, 155, 157, 159, 160, 164, 170, 171, 210, 212, 244, 261, 268 Collège de ‘Pataphysique  3–​5, 10, 13, 52, 53, 63, 119, 147, 271, 280, 290 Commune de Paris  20, 234, 249–​261 computational linguistics  186, 191, 216, 270 computer  20–​21, 85, 120–​122, 173–​224, 267, 269–​271, 273–​275 computer science  17, 20, 120–​121, 173, 180–​183, 216, 221, 269–​270, 274 constraint  11–​19, 50, 54, 56, 57, 60–​68, 72, 73, 74, 75, 78, 81, 82, 85, 86, 88, 89, 90, 91, 93, 96, 97, 103, 107, 113, 114, 118, 119, 120, 125, 126, 129, 132, 145, 146, 148, 149, 158, 159, 160, 161, 162, 163, 165, 166, 167, 169, 170, 171, 173, 174, 175, 183, 184, 185, 186, 188, 189, 205, 208, 211, 212, 213, 214, 215, 216, 221, 224, 225, 227, 230, 234, 235, 236,

307

Index 238, 247, 251, 252, 253, 254, 255, 257, 259, 260, 265, 266, 267, 268, 269, 272, 273 conte  109–​113, 193–​197, 199, 201, 205, 207 content  20, 28, 62, 68, 85–​86, 89, 128–​ 129, 144, 154, 162, 165, 167, 201, 224, 238–​240, 249, 261, 263 Corneille, Pierre  64, 218 Corry, Leo  30, 39, 42–​45, 264 Croisot, R.  95 Cronin, Susie  211, 213 Cunat, Yves  234, 251 Daniel, Arnaut  1–​5, 14, 271 Dante  1, 5, 226, 246 Descartes, René  12, 185 Devlin, Keith  23, 44 Dickens, Charles  225 Dieudonné, Jean  45 digital humanities  13, 16, 17, 20, 21, 207, 216, 221, 223, 264, 267, 271–​275 Dossier 17  63, 119 Du Bellay, Joachim  7 Duchamp, Marcel  9, 162 Duchateau, Jacques  64 Dumas, Jean-​Guillaume  5, 271 Duncan, Dennis  8, 148, 274 Eco, Umberto  225 Einaudi  145, 154, 225 electronic literature  17, 20, 221, 271 Euclid  24, 25, 27, 29, 30, 31, 40, 223, 258 Fabbri, Paolo  150, 151, 159 Féval, P.  55 Fibonacci sequence  103–​107 fixed form  58, 133 Flaubert, Gustave  113, 167 flowchart  20, 173, 191, 195, 200, 201, 202, 203, 204, 221, 273 form  4, 18, 20, 40, 59, 64, 74, 76, 89, 94, 125, 129, 132, 133, 134, 140, 141,

144, 150, 165, 173, 193, 194, 226, 237, 238, 239, 247, 248, 261, 271 formalism  19, 23, 35–​36, 42, 43, 52, 62, 159, 196, 264 formalization  34, 42–​43, 63, 78, 203 foundations  19, 23, 31, 33, 34, 41, 44, 54, 68, 192, 263, 264, 269 Fourier, Charles  246–​247 Fournel, Paul  17, 84, 85, 205, 206, 207–​ 209, 214, 273, 280–​282 La liseuse  84–​85 France, Anatole  225 Freud, Sigmund  167 Gallimard  10, 121, 133, 281 Genette, Gérard  121, 122, 225 Go  133–​138, 140–​144, 166 Goethe, Johann Wolfgang von  186, 189, 190 Goldbach’s Conjecture  168 Grands Rhétoriqueurs  9, 12, 125 graph theory  10, 191, 192, 218, 220, 284 Greco-​Latin bi-​square  165, 167 Greimas, Algirdas Julien  14, 145 Grothendieck, Alexandre  38 Hajós, György  219, 220 Harris, Paul  149, 230, 271 Hilbert, David  29–​34, 38, 40, 47, 108, 140, 295, 296, 301 homomorphisms  90 Hugo, Victor  63, 73–​74, 77–​78, 84, 184 Jarry, Alfred  3, 52, 106, 148, 271 Jockers, Matthew  223 Joyce, James  167 Kafka  167 Kiraly, Jean-​Louis  138, 141, 142, 144 Klee, Paul  167 knight’s tour  162–​167

308 Index Kovalevskaïa, Sofia  233, 249 Kuhlmann, Quirinus  214 La Fontaine, Jean de  89 La littérature potentielle  52, 53, 74, 87, 88, 89, 90, 91, 93, 96, 118, 161, 178, 200, 272 La Littérature Sémo-​Définitionnelle  92 La Rochefoucauld, François de  88 LAPAL  216 Laskowski-​Caujolle, Elvira Monika  109–​113 Latis  10 Le Lionnais, François  7, 10, 12, 13, 20, 45, 46, 53, 54, 55, 56, 57, 58, 59, 60, 64, 68, 75, 78, 79, 81, 90, 118, 120, 162, 163, 169, 170, 171, 178, 180, 183, 184, 194, 220, 221, 265, 266, 268, 269, 270 ALGOL poetry  266 “À propos de la littérature expérimentale”  120 Ivresse algolique  178 La LiPo (Le Premier Manifeste)  10, 12, 53 Les Grands Courants de la pensée mathématique  10, 45 Poèmes Booléens  64 “Raymond Queneau et l'amalgame des mathématiques et de la literature”  30 “Théâtre booléen”  64 troisième manifeste  53 Le Tellier, Hervé  14, 263, 273 Lécroart, Étienne  11, 17, 64–​65, 79–​83, 290 Leiris, Michel  167 Leroux, Gaston  92 Lescure, Jean  11, 63, 86, 87, 88, 89, 90, 177, 266, 286 Levin Becker, Daniel  14 Lévi-​Strauss, Claude  7, 41, 48, 50, 101 Li Po  51

lipogram  11, 12, 60, 66–​68, 161, 187, 238, 258 logic  15, 23, 24, 36, 54, 94, 102, 140, 173, 174, 195, 198, 201, 212 Lowry, L. S.  167 Lucretius  147–​148 Lusson, Pierre  134, 138, 142, 143, 163, 214 Mad Libs  87 Mallarmé, Stéphane  9, 64, 75, 100 Mandelbrojt, Szolem  38 Mann, Thomas  167 Marx and Engels  247 Massin, Robert  127, 128 mathematical platonism  117, 132, 139, 160, 167, 171, 267, 272 Mathews, Harry  14, 72, 96, 97, 98, 99, 100, 101, 102, 167 Melville, Herman  225 Meschinot, Jean  214 Mesures  75–​76, 81 metamathematics  33 method  20, 24, 29, 31, 40, 41, 42, 56, 60, 63, 64, 67, 78, 81, 82, 84, 86, 87, 88, 89, 90, 91, 93, 98, 102, 109, 112, 118, 120, 125, 145, 165, 175, 182, 184, 186, 206, 207, 209, 245, 252, 259, 267 mode d’emploi  40–​43, 51, 111, 119, 120, 122, 125, 127, 129, 130, 134, 135, 136, 137, 138, 139, 142, 145, 160, 162, 163, 169, 170, 255 Molinet, Jean  9, 125 More, Thomas  226, 228, 246 Moretti, Franco  207 Motte, Warren  14, 97, 119, 124, 147 Nabokov, Vladimir  167–​168 natural language processing  216 number theory  19, 23, 103 Oedipus  95 Oulipo Compendium  14, 148

Index PAF  181 Pascal, Blaise  12, 235–​237, 253, 257, 261 pattern poetry  73 patterns  2–​4, 9, 12, 18, 23, 36, 44–​45, 55, 85, 98, 101–​103, 107, 114, 118–​119, 140, 144, 158, 160, 175, 228–​230, 232, 244, 246, 267, 269, 271–​ 272, 274 Perec, Georges  11, 15, 19, 20, 62, 66–​68, 76, 92, 96, 118–​119, 132, 138, 142, 145, 146, 160–​171, 185–​191, 192, 199–​205, 214, 217, 221, 238, 254, 255, 257, 258, 267, 268, 271 Cahier des charges de La Vie mode d’emploi  163, 166–​167 Die Maschine  185–​191, 204 Espèces d’espaces  166 Histoire du lipogramme  161 La disparition  11, 52, 62, 66–​68, 78, 161, 163, 238, 257 L’art et la manière d’aborder son chef de service pour lui demander une augmentation  193, 199–​205, 217 L’Augmentation  200 La vie mode d’emploi  19, 160–​171, 271 Les Choses  160, 288 Les Revenentes  161, 254–​255 “Quatre figures pour La Vie mode d’emploi”  163, 166–​167 “Rail”  76, 200 permutation  4–​5, 59, 63, 100, 126, 130–​ 131, 148, 165, 271–​272 Petit traité invitant à la découverte de l’art subtil du go  138, 142–​143, 163 Petrarch  1 Piaget, Jean  231–​232 Piattelli-​Palmarini, Massimo  231–​232 Pisano, Leonardo  see Fibonacci sequence Poincaré, Henri  38, 281 potential  9–​11, 19, 21, 39, 57, 60, 62, 66, 81, 93, 114, 117–​120, 125–​133, 140, 141, 149, 152, 169–​171, 174,

309 177, 185, 194, 205–​206, 212–​217, 220–​221 probability  19, 23, 117 procedure  11, 12, 17–​19, 20, 24, 54, 63, 73, 86, 87, 89, 92, 93, 96–​103, 118–​ 119, 145, 151, 173, 174, 186, 191, 194, 198, 199, 201, 205, 212, 215, 221, 266, 267, 273 Propp, Vladimir  101, 102, 112, 113, 117, 118, 145, 151, 159, 193, 194, 197, 199 Proust, Marcel  32, 84, 167 puzzle  112, 116, 161, 167, 168, 171, 287, 290 Pynchon, Thomas  225 Queneau, Raymond  5–​10, 14, 19, 20, 27–​ 37, 40, 52, 59–​64, 71, 72, 77–​100, 108–​112, 117, 119–​135, 145, 161, 164, 165, 167, 169–​184, 192–​199, 205–​207, 210, 214, 217, 221, 236, 266, 270–​272 Cent mille milliards de poèmes  9, 19, 20, 63, 77, 118, 119–​132, 133, 134, 169, 170, 181, 182, 183, 184, 205, 207, 208, 210, 214, 215, 217, 267, 271 Exercices de style  27, 35, 88, 89, 94, 95, 164, 184 “La cimaise et la fraction”  89 La littérature définitionnelle  91 La Redondance chez Phane Armé  64 Les Enfants du Limon  90 Les Fondements de la littérature d’après David Hilbert  30, 71, 95, 111, 236, 266 “Note complémentaire sur la sextine”  5, 271–​272 “Science and Literature”  7 Un conte à votre façon  193–​198, 201, 205, 207, 214, 217 x prend y pour z  72, 93, 96, 108, 112, 266 Zazie dans le métro  132

310 Index quenine  6, 165, 272 Queval, Jean  77, 182 Rabelais, François  84, 167 randomness  see chance Ricci, Franco Maria  150 Rilke, Rainer Maria  143–​144 Rimbaud, Arthur  106, 215, 216, 288 Robbe-​Grillet, Alain  67 Roubaud, Jacques  5, 11, 14, 17, 19, 50, 53, 59, 60–​62, 67–​68, 72, 75, 84, 103, 109–​114, 118–​119, 132–​145, 159–​ 161, 167, 170, 205, 208, 214, 215, 220, 247, 260, 267, 268, 271, 272 ∈  19, 111, 119, 133–​145, 170 “Deux principes parfois respectés par les travaux oulipiens.”  59, 61 “La mathématique dans la méthode de Raymond Queneau”  14, 59 La Princesse Hoppy  19, 62, 72, 109, 112, 113, 208, 220, 260 Le Grand incendie de Londres  50, 141 “Un certain disparate”  53, 58 Roussel, Raymond  163, 167 Russell, Bertrand  35–​37 Russian formalism  6–​7, 24, 47, 49, 101, 102, 117, 146, 196 S\\+​7  11, 63, 72, 86–​90, 97, 100, 114, 183–​186, 209, 266, 267 Salon, Olivier  191, 200, 268, 270, 280 Saussure, Ferdinand de  6–​7, 23, 47–​ 48, 146 Schmidt, Albert-​Marie  9, 125, 176–​177 Schwartz, Laurent  9, 38, 50, 248 Sélitex  8, 120 Serre, Jean-​Pierre  38 Sestina  1–​5, 12, 64, 85, 165, 271, 272, 288, 290 Shakespeare, William  129, 184 Snow, C. P.  6, 8 snowball  73–​75

sonnet  1, 19, 75–​77, 100, 119–​121, 125–​132, 133–​144, 181, 184, 206, 214 Starynkevitch, Dmitri  180–​185, 206, 207, 270 Steinberg, Saul  166 Stendhal  167 Sterne, Laurence  167 structural linguistics  6, 47–​48, 117, 146 structuralism  7, 8, 18, 24, 38, 56, 101, 117, 146, 265 structure  19, 20, 41, 43–​48, 54–​58, 72, 75, 85–​91, 103, 104, 107, 108, 118, 125, 126, 135, 138, 143, 144, 146, 147, 149, 150, 151, 154, 155, 159, 160, 164, 166, 171, 181, 183, 186, 187, 193, 194, 195, 197, 198, 199, 201, 203, 215, 224, 225, 226, 227, 230, 232, 233, 237, 238, 240, 241, 243, 244, 246, 247, 249, 251, 252, 261, 264, 266, 268, 271 Subsidia Pataphysica  4, 5, 271 substitution  30, 33–​34, 59, 72, 86–​93 surrealism  7, 9, 10, 13, 49, 53, 54, 78, 98, 120, 122, 123, 124, 126, 130, 131, 132, 182, 183, 255 synthoulipisme  12, 54, 73, 77, 81, 97 table of contents  20, 224–​260 Tavera, Antoine  4–​5 Têtes folles  122–​124 Thackeray, William Makepeace  225 Todorov, Tzvetan  101, 145 Tubbs, Robert  32–​33, 107–​108 Turing, Alan  120, 121, 131 Verne, Jules  167 Weil, André  38, 48, 233 Wolff, Mark  183, 204, 206, 208, 215 Wright, Ernest Vincent  66 Zeckendorf, Édouard  104–​107

Modern French Identities

Edited by Jean Khalfa

This series aims to publish monographs, editions or collections of papers based on recent research into modern French Literature. It welcomes contributions from academics, researchers and writers worldwide and in British and Irish universities in particular. Modern French Identities focuses on the French and Francophone writing of the twentieth and twenty-first centuries, whose formal experiments and revisions of genre have combined to create an entirely new set of literary forms, from the thematic autobiographies of Michel Leiris and Bernard Noël to the magic realism of French Caribbean writers. The idea that identities are constructed rather than found, and that the self is an area to explore rather than a given pretext, runs through much of modern French literature, from Proust, Gide, Apollinaire and Césaire to Barthes, Duras, Kristeva, Glissant, Germain and Roubaud. This series explores the turmoil in ideas and values expressed in the works of theorists like Lacan, Irigaray, Foucault, Fanon, Deleuze and Bourdieu and traces the impact of current theoretical approaches – such as gender and sexuality studies, de/coloniality, intersectionality, and ecocriticism – on the literary and cultural interpretation of the self. The series publishes studies of individual authors and artists, comparative studies, and interdisciplinary projects and welcomes research on autobiography, cinema, fiction, poetry and performance art and/or the intersections between them. Editorial Board Contemporary Literature and Thought Martin Crowley (University of Cambridge) Francophone Studies Louise Hardwick (University of Birmingham) Jean Khalfa (University of Cambridge) Gender and Sexuality Studies Florian Grandena (University of Ottawa) Cristina Johnston (University of Stirling) Language and Linguistics Michaël Abecassis (University of Oxford) Literature and Art Peter Collier and Jean Khalfa (University of Cambridge) Literature and Non-fiction Muriel Pic (University of Bern) Poetry Nina Parish (University of Stirling) Emma Wagstaff (University of Birmingham) Zoopoetics and Ecocriticism Anne Simon (CNRS/Ecole normale supérieure, Paris)

Volume 1

Victoria Best & Peter Collier (eds): Powerful Bodies. Performance in French Cultural Studies. 220 pages. 1999. ISBN 3–906762-56-4 / US-ISBN 0–8204-4239-9

Volume 2

Julia Waters: Intersexual Rivalry. A ‘Reading in Pairs’ of Marguerite Duras and Alain Robbe-Grillet. 228 pages. 2000. ISBN 3–906763-74-9 / US-ISBN 0–8204-4626-2

Volume 3

Sarah Cooper: Relating to Queer Theory. Rereading Sexual Self-Definition with Irigaray, Kristeva, Wittig and Cixous. 231 pages. 2000. ISBN 3–906764-46-X / US-ISBN 0–8204-4636-X

Volume 4 Julia Prest & Hannah Thompson (eds): Corporeal Practices. (Re) figuring the Body in French Studies. 166 pages. 2000. ISBN 3–906764-53-2 / US-ISBN 0–8204-4639-4 Volume 5 Victoria Best: Critical Subjectivities. Identity and Narrative in the Work of Colette and Marguerite Duras. 243 pages. 2000. ISBN 3–906763-89-7 / US-ISBN 0–8204-4631-9 Volume 6 David Houston Jones: The Body Abject: Self and Text in Jean Genet and Samuel Beckett. 213 pages. 2000. ISBN 3–906765-07-5 / US-ISBN 0–8204-5058-8 Volume 7 Robin MacKenzie: The Unconscious in Proust’s A la recherche du temps perdu. 270 pages. 2000. ISBN 3–906758-38-9 / US-ISBN 0–8204-5070-7 Volume 8 Rosemary Chapman: Siting the Quebec Novel. The Representation of Space in Francophone Writing in Quebec. 282 pages. 2000. ISBN 3–906758-85-0 / US-ISBN 0–8204-5090-1 Volume 9 Gill Rye: Reading for Change. Interactions between Text Identity in Contemporary French Women’s Writing (Baroche, Cixous, Constant). 223 pages. 2001. ISBN 3–906765-97-0 / US-ISBN 0–8204-5315-3 Volume 10 Jonathan Paul Murphy: Proust’s Art. Painting, Sculpture and Writing in A la recherche du temps perdu. 248 pages. 2001. ISBN 3–906766-17-9 / US-ISBN 0–8204-5319-6 Volume 11 Julia Dobson: Hélène Cixous and the Theatre. The Scene of Writing. 166 pages. 2002. ISBN 3–906766-20-9 / US-ISBN 0–8204-5322-6

Volume 12 Emily Butterworth & Kathryn Robson (eds): Shifting Borders. Theory and Identity in French Literature. 226 pages. 2001. ISBN 3–906766-86-1 / US-ISBN 0–8204-5602-0 Volume 13 Victoria Korzeniowska: The Heroine as Social Redeemer in the Plays of Jean Giraudoux. 144 pages. 2001. ISBN 3–906766-92-6 / US-ISBN 0–8204-5608-X Volume 14 Kay Chadwick: Alphonse de Châteaubriant: Catholic Collaborator. 327 pages. 2002. ISBN 3–906766-94-2 / US-ISBN 0–8204-5610-1 Volume 15

Nina Bastin: Queneau’s Fictional Worlds. 291 pages. 2002. ISBN 3–906768-32-5 / US-ISBN 0–8204-5620-9

Volume 16 Sarah Fishwick: The Body in the Work of Simone de Beauvoir. 284 pages. 2002. ISBN 3–906768-33-3 / US-ISBN 0–8204-5621-7 Volume 17 Simon Kemp & Libby Saxton (eds): Seeing Things. Vision, Perception and Interpretation in French Studies. 287 pages. 2002. ISBN 3–906768-46-5 / US-ISBN 0–8204-5858-9 Volume 18 Kamal Salhi (ed.): French in and out of France. Language Policies, Intercultural Antagonisms and Dialogue. 487 pages. 2002. ISBN 3–906768-47-3 / US-ISBN 0–8204-5859-7 Volume 19 Genevieve Shepherd: Simone de Beauvoir’s Fiction. A Psychoanalytic Rereading. 262 pages. 2003. ISBN 3–906768-55-4 / US-ISBN 0–8204-5867-8 Volume 20 Lucille Cairns (ed.): Gay and Lesbian Cultures in France. 290 pages. 2002. ISBN 3–906769-66-6 / US-ISBN 0–8204-5903-8 Volume 21 Wendy Goolcharan-Kumeta: My Mother, My Country. Reconstructing the Female Self in Guadeloupean Women’s Writing. 236 pages. 2003. ISBN 3–906769-76-3 / US-ISBN 0–8204-5913-5 Volume 22 Patricia O’Flaherty: Henry de Montherlant (1895–1972). A Philosophy of Failure. 256 pages. 2003. ISBN 3–03910-013-0 / US-ISBN 0–8204-6282-9 Volume 23 Katherine Ashley (ed.): Prix Goncourt, 1903–2003: essais critiques. 205 pages. 2004. ISBN 3–03910-018-1 / US-ISBN 0–8204-6287-X Volume 24 Julia Horn & Lynsey Russell-Watts (eds): Possessions. Essays in French Literature, Cinema and Theory. 223 pages. 2003. ISBN 3–03910-005-X / US-ISBN 0–8204-5924-0

Volume 25 Steve Wharton: Screening Reality. French Documentary Film during the German Occupation. 252 pages. 2006. ISBN 3–03910-066-1 / US-ISBN 0–8204-6882-7 Volume 26 Frédéric Royall (ed.): Contemporary French Cultures and Societies. 421 pages. 2004. ISBN 3–03910-074-2 / US-ISBN 0–8204-6890-8 Volume 27 Tom Genrich: Authentic Fictions. Cosmopolitan Writing of the Troisième République, 1908–1940. 288 pages. 2004. ISBN 3–03910-285-0 / US-ISBN 0–8204-7212-3 Volume 28 Maeve Conrick & Vera Regan: French in Canada. Language Issues. 186 pages. 2007. ISBN 978–3-03-910142-9 Volume 29 Kathryn Banks & Joseph Harris (eds): Exposure. Revealing Bodies, Unveiling Representations. 194 pages. 2004. ISBN 3–03910-163-3 / US-ISBN 0–8204-6973-4 Volume 30 Emma Gilby & Katja Haustein (eds): Space. New Dimensions in French Studies. 169 pages. 2005. ISBN 3–03910-178-1 / US-ISBN 0–8204-6988-2 Volume 31 Rachel Killick (ed.): Uncertain Relations. Some Configurations of the ‘Third Space’ in Francophone Writings of the Americas and of Europe. 258 pages. 2005. ISBN 3–03910-189-7 / US-ISBN 0–8204-6999-8 Volume 32 Sarah F. Donachie & Kim Harrison (eds): Love and Sexuality. New Approaches in French Studies. 194 pages. 2005. ISBN 3–03910-249-4 / US-ISBN 0–8204-7178-X Volume 33 Michaël Abecassis: The Representation of Parisian Speech in the Cinema of the 1930s. 409 pages. 2005. ISBN 3–03910-260-5 / US-ISBN 0–8204-7189-5 Volume 34 Benedict O’Donohoe: Sartre’s Theatre: Acts for Life. 301 pages. 2005. ISBN 3–03910-250-X / US-ISBN 0–8204-7207-7 Volume 35 Moya Longstaffe: The Fiction of Albert Camus. A Complex Simplicity. 300 pages. 2007. ISBN 3–03910-304-0 / US-ISBN 0–8204-7229-8 Volume 36 Arnaud Beaujeu: Matière et lumière dans le théâtre de Samuel Beckett: Autour des notions de trivialité, de spiritualité et d’ « autre-là ». 377 pages. 2010. ISBN 978–3-0343-0206-8

Volume 37 Shirley Ann Jordan: Contemporary French Women’s Writing: Women’s Visions, Women’s Voices, Women’s Lives. 308 pages. 2005. ISBN 3–03910-315-6 / US-ISBN 0–8204-7240-9 Volume 38 Neil Foxlee: Albert Camus’s ‘The New Mediterranean Culture’: A Text and its Contexts. 349 pages. 2010. ISBN 978–3-0343-0207-4 Volume 39 Michael O’Dwyer & Michèle Raclot: Le Journal de Julien Green: Miroir d’une âme, miroir d’un siècle. 289 pages. 2005. ISBN 3–03910-319-9 Volume 40 Thomas Baldwin: The Material Object in the Work of Marcel Proust. 188 pages. 2005. ISBN 3–03910-323-7 / US-ISBN 0–8204-7247-6 Volume 41 Charles Forsdick & Andrew Stafford (eds): The Modern Essay in French: Genre, Sociology, Performance. 296 pages. 2005. ISBN 3–03910-514-0 / US-ISBN 0–8204-7520-3 Volume 42 Peter Dunwoodie: Francophone Writing in Transition. Algeria 1900–1945. 339 pages. 2005. ISBN 3–03910-294-X / US-ISBN 0–8204-7220-4 Volume 43 Emma Webb (ed.): Marie Cardinal: New Perspectives. 260 pages. 2006. ISBN 3–03910-544-2 / US-ISBN 0–8204-7547-5 Volume 44 Jérôme Game (ed.): Porous Boundaries: Texts and Images in Twentieth-Century French Culture. 164 pages. 2007. ISBN 978–3-03910-568-7 Volume 45 David Gascoigne: The Games of Fiction: Georges Perec and Modern French Ludic Narrative. 327 pages. 2006. ISBN 3–03910-697-X / US-ISBN 0–8204-7962-4 Volume 46 Derek O’Regan: Postcolonial Echoes and Evocations: The Intertextual Appeal of Maryse Condé. 329 pages. 2006. ISBN 3–03910-578-7 Volume 47 Jennifer Hatte: La langue secrète de Jean Cocteau: la mythologie personnelle du poète et l’histoire cachée des Enfants terribles. 332 pages. 2007. ISBN 978–3-03910-707-0 Volume 48 Loraine Day: Writing Shame and Desire: The Work of Annie Ernaux. 315 pages. 2007. ISBN 978–3-03910-275-4

Volume 49 John Flower (éd.): François Mauriac, journaliste: les vingt premières années, 1905–1925. 352 pages. 2011. ISBN 978–3-0343-0265-4 Volume 50 Miriam Heywood: Modernist Visions: Marcel Proust’s A la recherche du temps perdu and Jean-Luc Godard’s Histoire(s) du cinéma. 277 pages. 2012. ISBN 978–3-0343-0296-8 Volume 51 Isabelle McNeill & Bradley Stephens (eds): Transmissions: Essays in French Literature, Thought and Cinema. 221 pages. 2007. ISBN 978–3-03910-734-6 Volume 52 Marie-Christine Lala: Georges Bataille, Poète du réel. 178 pages. 2010. ISBN 978–3-03910-738-4 Volume 53

Patrick Crowley: Pierre Michon: The Afterlife of Names. 242 pages. 2007. ISBN 978–3-03910-744-5

Volume 54 Nicole Thatcher & Ethel Tolansky (eds): Six Authors in Captivity. Literary Responses to the Occupation of France during World War II. 205 pages. 2006. ISBN 3–03910-520-5 / US-ISBN 0–8204-7526-2 Volume 55 Catherine Dousteyssier-Khoze & Floriane Place-Verghnes (eds): Poétiques de la parodie et du pastiche de 1850 à nos jours. 361 pages. 2006. ISBN 3–03910-743-7 Volume 56 Thanh-Vân Ton-That: Proust avant la Recherche: jeunesse et genèse d’une écriture au tournant du siècle. 285 pages. 2012. ISBN 978–3-0343-0277-7 Volume 57 Helen Vassallo: Jeanne Hyvrard, Wounded Witness: The Body Politic and the Illness Narrative. 243 pages. 2007. ISBN 978–3-03911-017-9 Volume 58 Marie-Claire Barnet, Eric Robertson and Nigel Saint (eds): Robert Desnos. Surrealism in the Twenty-First Century. 390 pages. 2006. ISBN 3–03911-019-5 Volume 59 Michael O’Dwyer (ed.): Julien Green, Diariste et Essayiste. 259 pages. 2007. ISBN 978–3-03911-016-2 Volume 60 Kate Marsh: Fictions of 1947: Representations of Indian Decolonization 1919–1962. 238 pages. 2007. ISBN 978–3-03911-033-9

Volume 61 Lucy Bolton, Gerri Kimber, Ann Lewis and Michael Seabrook (eds): Framed!: Essays in French Studies. 235 pages. 2007. ISBN 978–3-03911-043-8 Volume 62 Lorna Milne and Mary Orr (eds): Narratives of French Modernity: Themes, Forms and Metamorphoses. Essays in Honour of David Gascoigne. 365 pages. 2011. ISBN 978–3-03911-051-3 Volume 63 Ann Kennedy Smith: Painted Poetry: Colour in Baudelaire’s Art Criticism. 253 pages. 2011. ISBN 978–3-03911-094-0 Volume 64

Sam Coombes: The Early Sartre and Marxism. 330 pages. 2008. ISBN 978–3-03911-115-2

Volume 65 Claire Lozier: De l’abject et du sublime: Georges Bataille, Jean Genet, Samuel Beckett. 327 pages. 2012. ISBN 978–3-0343-0724-6 Volume 66 Charles Forsdick and Andy Stafford (eds): La Revue: The Twentieth- Century Periodical in French. 379 pages. 2013. ISBN 978–3-03910-947-0 Volume 67 Alison S. Fell (ed.): French and francophone women facing war / Les femmes face à la guerre. 301 pages. 2009. ISBN 978–3-03911-332-3 Volume 68 Elizabeth Lindley and Laura McMahon (eds): Rhythms: Essays in French Literature, Thought and Culture. 238 pages. 2008. ISBN 978–3-03911-349-1 Volume 69 Georgina Evans and Adam Kay (eds): Threat: Essays in French Literature, Thought and Visual Culture. 248 pages. 2010. ISBN 978–3-03911-357-6 Volume 70 John McCann: Michel Houellebecq: Author of our Times. 229 pages. 2010. ISBN 978–3-03911-373-6 Volume 71 Jenny Murray: Remembering the (Post)Colonial Self: Memory and Identity in the Novels of Assia Djebar. 258 pages. 2008. ISBN 978–3-03911-367-5 Volume 72 Susan Bainbrigge: Culture and Identity in Belgian Francophone Writing: Dialogue, Diversity and Displacement. 230 pages. 2009. ISBN 978–3-03911-382-8

Volume 73 Maggie Allison and Angela Kershaw (eds): Parcours de femmes: Twenty Years of Women in French. 313 pages. 2011. ISBN 978–3-0343-0208-1 Volume 74 Jérôme Game: Poetic Becomings: Studies in Contemporary French Literature. 263 pages. 2011. ISBN 978–3-03911-401-6 Volume 75 Elodie Laügt: L’Orient du signe: Rêves et dérives chez Victor Segalen, Henri Michaux et Emile Cioran. 242 pages. 2008. ISBN 978–3-03911-402-3 Volume 76 Suzanne Dow: Madness in Twentieth-Century French Women’s Writing: Leduc, Duras, Beauvoir, Cardinal, Hyvrard. 217 pages. 2009. ISBN 978–3-03911-540-2 Volume 77 Myriem El Maïzi: Marguerite Duras ou l’écriture du devenir. 228 pages. 2009. ISBN 978–3-03911-561-7 Volume 78 Claire Launchbury: Music, Poetry, Propaganda: Constructing French Cultural Soundscapes at the BBC during the Second World War. 223 pages. 2012. ISBN 978–3-0343-0239-5 Volume 79 Jenny Chamarette and Jennifer Higgins (eds): Guilt and Shame: Essays in French Literature, Thought and Visual Culture. 231 pages. 2010. ISBN 978–3-03911-563-1 Volume 80 Vera Regan and Caitríona Ní Chasaide (eds): Language Practices and Identity Construction by Multilingual Speakers of French L2: The Acquisition of Sociostylistic Variation. 189 pages. 2010. ISBN 978–3-03911-569-3 Volume 81 Margaret-Anne Hutton (ed.): Redefining the Real: The Fantastic in Contemporary French and Francophone Women’s Writing. 294 pages. 2009. ISBN 978–3-03911-567-9 Volume 82 Elise Hugueny-Léger: Annie Ernaux, une poétique de la transgression. 269 pages. 2009. ISBN 978–3-03911-833-5 Volume 83 Peter Collier, Anna Magdalena Elsner and Olga Smith (eds): Anamnesia: Private and Public Memory in Modern French Culture. 359 pages. 2009. ISBN 978–3-03911-846-5 Volume 84 Adam Watt (ed./éd.): Le Temps retrouvé Eighty Years After/80 ans après: Critical Essays/Essais critiques. 349 pages. 2009. ISBN 978–3-03911-843-4

Volume 85 Louise Hardwick (ed.): New Approaches to Crime in French Literature, Culture and Film. 237 pages. 2009. ISBN 978–3-03911-850-2 Volume 86 Emmanuel Godin and Natalya Vince (eds): France and the Mediterranean: International Relations, Culture and Politics. 372 pages. 2012. ISBN 978–3-0343-0228-9 Volume 87 Amaleena Damlé and Aurélie L’Hostis (eds): The Beautiful and the Monstrous: Essays in French Literature, Thought and Culture. 237 pages. 2010. ISBN 978–3-03911-900-4 Volume 88 Alistair Rolls (ed.): Mostly French: French (in) Detective Fiction. 212 pages. 2009. ISBN 978–3-03911-957-8 Volume 89 Bérénice Bonhomme: Claude Simon: une écriture en cinéma. 359 pages. 2010. ISBN 978–3-03911-983-7 Volume 90 Barbara Lebrun and Jill Lovecy (eds): Une et divisible? Plural Identities in Modern France. 258 pages. 2010. ISBN 978–3-0343-0123-7 Volume 91 Pierre-Alexis Mével & Helen Tattam (eds): Language and its Contexts/ Le Langage et ses contextes: Transposition and Transformation of Meaning?/ Transposition et transformation du sens? 272 pages. 2010. ISBN 978–3-0343-0128-2 Volume 92 Alistair Rolls and Marie-Laure Vuaille-Barcan (eds): Masking Strategies: Unwrapping the French Paratext. 202 pages. 2011. ISBN 978–3-0343-0746-8 Volume 93 Michaël Abecassis et Gudrun Ledegen (éds): Les Voix des Français Volume 1: à travers l’histoire, l’école et la presse. 372 pages. 2010. ISBN 978–3-0343-0170-1 Volume 94 Michaël Abecassis et Gudrun Ledegen (éds): Les Voix des Français Volume 2: en parlant, en écrivant. 481 pages. 2010. ISBN 978–3-0343-0171-8 Volume 95 Manon Mathias, Maria O’Sullivan and Ruth Vorstman (eds): Display and Disguise. 237 pages. 2011. ISBN 978–3-0343-0177-0 Volume 96 Charlotte Baker: Enduring Negativity: Representations of Albinism in the Novels of Didier Destremau, Patrick Grainville and Williams Sassine. 226 pages. 2011. ISBN 978–3-0343-0179-4

Volume 97 Florian Grandena and Cristina Johnston (eds): New Queer Images: Representations of Homosexualities in Contemporary Francophone Visual Cultures. 246 pages. 2011. ISBN 978–3-0343-0182-4 Volume 98 Florian Grandena and Cristina Johnston (eds): Cinematic Queerness: Gay and Lesbian Hypervisibility in Contemporary Francophone Feature Films. 354 pages. 2011. ISBN 978–3-0343-0183-1 Volume 99 Neil Archer and Andreea Weisl-Shaw (eds): Adaptation: Studies in French and Francophone Culture. 234 pages. 2012. ISBN 978–3-0343-0222-7 Volume 100 Peter Collier et Ilda Tomas (éds): Béatrice Bonhomme: le mot, la mort, l’amour. 437 pages. 2013. ISBN 978–3-0343-0780-2 Volume 101 Helena Chadderton: Marie Darrieussecq’s Textual Worlds: Self, Society, Language. 170 pages. 2012. ISBN 978–3-0343-0766-6 Volume 102 Manuel Bragança: La crise allemande du roman français, 1945– 1949: la représentation des Allemands dans les best-sellers de l’immédiat après-guerre. 220 pages. 2012. ISBN 978–3-0343-0835-9 Volume 103 Bronwen Martin: The Fiction of J. M. G. Le Clézio: A Postcolonial Reading. 199 pages. 2012. ISBN 978–3-0343-0162-6 Volume 104 Hugues Azérad, Michael G. Kelly, Nina Parish et Emma Wagstaff (éds): Chantiers du poème: prémisses et pratiques de la création poétique moderne et contemporaine. 374 pages. 2013. ISBN 978–3-0343-0800-7 Volume 105 Franck Dalmas: Lectures phénoménologiques en littérature française: de Gustave Flaubert à Malika Mokeddem. 253 pages. 2012. ISBN 978–3-0343-0727-7 Volume 106 Béatrice Bonhomme, Aude Préta-de Beaufort et Jacques Moulin (éds): Dans le feuilletage de la terre: sur l’œuvre poétique de Marie- Claire Bancquart. 533 pages. 2013. ISBN 978–3-0343-0721-5

Volume 107 Claire Bisdorff et Marie-Christine Clemente (éds): Le Cœur dans tous ses états: essais sur la littérature et l’art français. 230 pages. 2013. ISBN 978–3-0343-0711-6 Volume 108 Michaël Abecassis et Gudrun Ledegen (éds): Écarts et apports des médias francophones: lexique et grammaire. 300 pages. 2013. ISBN 978–3-0343-0882-3 Volume 109 Allison and Imogen Long (eds): Women Matter / Femmes Matière: French and Francophone Women and the Material World. 273 pages. 2013. ISBN 978–3-0343-0788-8 Volume 110 Fabien Arribert-Narce et Alain Ausoni (éds): L’Autobiographie entre autres: écrire la vie aujourd’hui. 221 pages. 2013. ISBN 978–3-0343-0858-8 Volume 111 Leona Archer and Alex Stuart (eds): Visions of Apocalypse: Representations of the End in French Literature and Culture. 266 pages. 2013. ISBN 978–3-0343-0921-9 Volume 112 Simona Cutcan: Subversion ou conformisme ? La différence des sexes dans l’œuvre d’Agota Kristof. 264 pages. 2014. ISBN 978–3-0343-1713-9 Volume 113 Owen Heathcote: From Bad Boys to New Men ? Masculinity, Sexuality and Violence in the Work of Éric Jourdan. 279 pages. 2014. ISBN 978–3-0343-0736-9 Volume 114 Ilda Tomas: Arc-en-ciel: études sur divers poètes. 234 pages. 2014. ISBN 978–3-0343-0975-2 Volume 115 Lisa Jeschke and Adrian May (eds): Matters of Time: Material Temporalities in Twentieth-Century French Culture. 314 pages. 2014. ISBN 978–3-0343-1796-2 Volume 116 Crispin T. Lee: Haptic Experience in the Writings of Georges Bataille, Maurice Blanchot and Michel Serres. 316 pages. 2014. ISBN 978–3-0343-1791-7 Volume 117 Ashwiny O. Kistnareddy: Locating Hybridity: Creole, Identities and Body Politics in the Novels of Ananda Devi. 208 pages. 2015. ISBN 978–3-0343-1814-3

Volume 118 Michaël Abecassis et Gudrun Ledegen (éds): De la genèse de la langue à Internet: variations dans les formes, les modalités et les langues en contact. 278 pages. 2015. ISBN 978–3-0343-1798-6 Volume 119 Peter D. Tame: Isotopias: Places and Spaces in French War Fiction of the Twentieth and Twenty-First Centuries. 592 pages. 2015. ISBN 978–3-0343-0837-3 Volume 120 Daniel A. Finch-Race et Jeff Barda (éds): Textures: Processus et événements dans la création poétique moderne et contemporaine. 242 pages. 2015. ISBN 978–3-0343-1898-3 Volume 121 Hélène Sicard-Cowan: Vivre ensemble: éthique de l’imitation dans la littérature et le cinéma de l’immigration en France (1986–2005). 149 pages. 2016. ISBN 978–3-0343-1944-7 Volume 122 Mercedes Montoro Araque et Carmen Alberdi Urquizu (éds): L’entre- deux imaginaire: corps et création interculturels. 216 pages. 2016. ISBN 978–3-0343-1926-3 Volume 123 Maureen A. Ramsden: Crossing Borders: The Interrelation of Fact and Fiction in Historical Works, Travel Tales, Autobiography and Reportage. 191 pages. 2016. ISBN 978–3-0343-1995-9 Volume 124 Jean Khalfa: Poetics of the Antilles: Poetry, History and Philosophy in the Writings of Perse, Césaire, Fanon and Glissant. 388 pages. 2017. ISBN 978–3-0343-0895-3 Volume 125 Mathilde Poizat-Amar: L’Eclat du voyage: Blaise Cendrars, Victor Segalen, Albert Londres. 252 pages. 2017. ISBN 978–1-78707-296-1 Volume 126 Philippe Willemart: L’Univers de la création littéraire: Dans la chambre noire de l’écriture: Hérodias de Flaubert. 160 pages. 2017. ISBN 978–1-78707-458-3 Volume 127 Margaret Atack, Alison S. Fell, Diana Holmes and Imogen Long (eds): French Feminisms 1975 and After: New Readings, New Texts. 276 pages. 2018. ISBN 978-3-0343-2209-6 Volume 128 Matt Phillips and Tomas Weber (eds): Parasites: Exploitation and Interference in French Thought and Culture. 284 pages. 2018. ISBN 978-3-0343-2266-9

Volume 129 Zoe Angelis and Blake Gutt (eds): Stains / Les taches: Communication and Contamination in French and Francophone Literature and Culture. 274 pages. 2019. ISBN 978-1-78707-443-9 Volume 130 Michaël Abecassis avec Marcelline Block, Gudrun Ledegen et Maribel Peñalver Vicea (éds): Le Grain de la voix dans le monde anglophone et francophone. 332 pages. 2019. ISBN 978-1-78874-107-1 Volume 131 Philippe Willemart: L’écriture à l’ère de l’indétermination: Études sur la critique génétique, la psychanalyse et la littérature. 232 pages. 2019. ISBN 978–1-78874-631-1 Volume 132 Augustin Voegele: De l’unanimisme au fantastique: Jules Romains devant l’extraordinaire. 382 pages. 2019. ISBN 978-1-78874-513-0 Volume 133 Maggie Allison, Elliot Evans and Carrie Tarr (eds): Plaisirs de femmes: Women, Pleasure and Transgression in French Literature and Culture. 278 pages. 2019. ISBN 978-1-78874-383-9 Volume 134 Aaron Prevots: Bernard Vargaftig: Gestures toward the Sacred. 144 pages. 2019. ISBN 978-1-78997-357-0 Volume 135 Susie Cronin, Sofia Ropek Hewson and Cillian Ó Fathaigh (eds): #NousSommes: Collectivity and the Digital in French Thought and Culture. 184 pages. 2020. ISBN 978-1-78874-767-7 Volume 136 Anaïs Stampfli: La coprésence de langues dans le roman antillais contemporain. 456 pages. 2020. ISBN 978-1-78874-578-9 Volume 137 Philippe Willemart: Les mécanismes de la création littéraire: Lecture, écriture, génétique et psychanalyse. 214 pages. 2020. ISBN 978-1-78997-737-0 Volume 138 Maureen A. Ramsden: The Evolution of Proust’s ‘Combray’: A Genetic Study. 152 pages. 2020. ISBN 978-1-78997-785-1 Volume 139 Charlène Clonts: Gherasim Luca: Texte, image, son. 454 pages. 2020. ISBN 978-1-78997-916-9

Volume 140 Polly Galis, Maria Tomlinson and Antonia Wimbush (eds): Queer(y)ing Bodily Norms in Francophone Culture. 304 pages. 2021. ISBN 978-1-78997-514-7 Volume 141 Natalie Berkman: OuLiPo and the Mathematics of Literature. 338 pages. 2022. ISBN 978-1-78997-780-6 Volume 142 David Gascoigne and Ana de Medeiros (eds): Marie Nimier: Le Sujet et ses écritures / The Self in the Web of Language. 312 pages. 2021. ISBN 978-1-80079-195-4 Volume 143 Carole Bourne-Taylor and Sara-Louise Cooper (eds): Variations on the Ethics of Mourning in Modern Literature in French. 332 pages. 2022. ISBN 978-1-78997-273-3 Volume 144 Sophie Large and Flora Valadié (eds): Le Fanon des artistes. Perspectives transaméricaines 288 pages. 2022. ISBN 978-1-80079-630-0