Relations Between Modern Mathematics and Poetry: Czesław Miłosz; Zbigniew Herbert; Ion Barbu/Dan Barbilian
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Relations between Modern Mathematics and Poetry: Czesław Miłosz; Zbigniew Herbert; Ion Barbu/Dan Barbilian by Loveday Jane Anastasia Kempthorne A thesis submitted to Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy Victoria University of Wellington 2015 Abstract This doctoral thesis is an examination of the relationship between poetry and mathematics, centred on three twentieth-century case studies: the Polish poets Czesław Miłosz (1911-2004) and Zbigniew Herbert (1924-1998), and the Romanian mathematician and poet Dan Barbilian/Ion Barbu (1895-1961). Part One of the thesis is a review of current scholarly literature, divided into two chapters. The first chapter looks at the nature of mathematics, outlining its historical developments and describing some major mathematical concepts as they pertain to the later case studies. This entails a focus on non-Euclidean geometries, modern algebra, and the foundations of mathematics in Europe; the nature of mathematical truth and language; and the modern historical evolution of mathematical schools in Poland and Romania. The second chapter examines some existing attempts to bring together mathematics and poetry, drawing on literature and science as an academic field; the role of the imagination and invention in the languages of both poetics and mathematics; the interest in mathematics among certain Symbolist poets, notably Mallarmé; and the experimental work of the French groups of mathematicians and mathematician-poets, Bourbaki and Oulipo. The role of metaphor is examined in particular. Part Two of the thesis is the case studies. The first presents the ethical and moral stance of Czesław Miłosz, investigating his attitudes towards classical and later relativistic science, in the light of the Nazi occupation and the Marxist regimes in Poland, and how these are reflected in his poetry. The study of Zbigniew Herbert is structured around a wide selection of his poetic oeuvre, and identifying his treatment of evolving and increasingly more complex mathematical concepts. The third case study, on Dan Barbilian, who published his poetry under the name Ion Barbu, begins with an examination of the mathematical school at Göttingen in the 1920s, tracing the influence of Gauss, Riemann, Klein, Hilbert and Noether in Barbilian’s own mathematical work, particularly in the areas of metric spaces and axiomatic geometry. In the discussion, the critical analysis of the mathematician and linguist Solomon Marcus is examined. This study finishes with a close reading of seven of Barbu’s poems. The relationship of mathematics and poetry has rarely been studied as a coherent academic field, and the relevant scholarship is often disconnected. A feature of this thesis is i that it brings together a wide range of scholarly literature and discussion. Although primarily in English, a considerable amount of the academic literature collated here is in French, Romanian, Polish and some German. The poems themselves are presented in the original Polish and Romanian with both published and working translations appended in the footnotes. In the case of the two Polish poets, one a Nobel laureate and the other a multiple prize-winning figure highly regarded in Poland, this thesis is unusual in its concentration on mathematics as a feature of the poetry which is otherwise much-admired for its politically-engaged and lyrical qualities. In the case of the Romanian, Dan Barbilian, he is widely known in Romania as a mathematician, and most particularly as the published poet Ion Barbu, yet his work is little studied outside that country, and indeed much of it is not yet translated into English. This thesis suggests at an array of both theoretical and specific starting points for examining the multi-stranded and intricate relationship between mathematics and poetry, pointing to a number of continuing avenues of further research. ii Acknowledgements I owe the greatest gratitude to my supervisors, Dr Marco Sonzogni from the School of Languages and Cultures, and Dr Peter Donelan from the School of Mathematics, Statistics and Operations Research at Victoria University of Wellington. As primary supervisor, Marco was irreplaceable for his much-needed enthusiasm in welcoming me to the university, his consistent intellectual openness to a free exploration of the topic and for motivating and guiding me through the thesis. Equally, Peter has always provided excellent suggestions, thoughtful and detailed criticism, and constant encouragement. I have enjoyed many coffees with each of them, and the three of us together, and remain deeply grateful. I have also very much appreciated the multi-faceted support of Victoria, including the helpful staff in both Schools; the always obliging university librarians; the pleasant campus environment; the travel and archival research grants from both Faculties; and the full and generous doctoral scholarship from the Faculty of Graduate Research. Without that scholarship, I would not have been able to undertake this thesis. A most important service has been the university crèche. My daughter began at nursery, has moved through toddlers, and is now about to finish at preschool, ready and excited to be starting her proper school years. The crèche community has been flexible, supportive and reliable. On my floor, I have enjoyed the calm, friendly and dedicated company of my fellow students, Nobuko, Sian, Lily, Mitsue, Alina, Mukta and Janette. Their friendship has been essential. As always, I am reliant on the encouragement and wisdom of my parents, Penelope and Renatus, of my friends, of little Hattie, and of course my husband Roberto. Wellington, September 2014 I would also like to acknowledge the detailed questions and comments from my three examiners – Rebecca Priestley, Brian Boyd and Iggy McGovern – during the period after submission, as their suggestions have begun a much valued process of clarification of ideas that I hope will continue. February 2015 iii Contents Abstract i Acknowledgements iii INTRODUCTION Making sense of a conundrum 1 PART I THEORETICAL DISCUSSION AND LITERATURE REVIEW 9 CHAPTER ONE 11 The Nature of Mathematics: ‘Why are numbers beautiful? […] I know numbers are beautiful’ Abstract 11 Introduction 11 Evolution of mathematics 12 Historiography of mathematics 18 Mathematical truth and language 24 Mathematics in Poland and Romania 30 Poland 30 Romania 33 Concluding remarks: the multiple nature of mathematics 35 CHAPTER TWO 37 Mathematics and Poetry: ‘a delicate, beautiful explanation of the world’ Abstract 37 Introduction: “Mathematics and poetry” as an academic discipline 37 Mathematical poetry 40 Poets attracted to the structure and aesthetics of mathematics 41 Poetic Symbolism: Novalis; Mallarmé; Valéry; Norwid; Belyj; Khlebnikov 44 An American comparison: Dickinson and Stein 53 Oulipo: constructing mathematical literature 55 The nature and representation of knowledge: towards a common aesthetic 58 Ambiguity and truth: imagination as a highpoint between senses and intellect 59 Two types of language 67 Metaphor in mathematics and poetry 74 Solomon Marcus: metaphor, inventiveness and language 79 Concluding remarks: imagination and method 86 v PART II CASE STUDIES 89 CHAPTER THREE 91 ‘I sigh and think of a starry sky, of non-Euclidean space, of amoebas and their pseudopodia’: Science in the society of Czesław Miłosz Abstract 92 Introduction 92 Ethics and religion 94 Scientism in Nazism, Marxism, Western Capitalism 96 Rationalism, Newton and Darwin 98 Twentieth-century science: Albert Einstein ‘via’ Oscar Milosz 102 Mathematics and modernist poetry: symbolism, formalism and order 109 Concluding remarks: Marxist science and twentieth-century morality 119 CHAPTER FOUR 123 ‘I felt my backbone fill with quiet certitude’: Zbigniew Herbert and a Poetic Interaction with Mathematics Abstract 123 Introduction 124 Biographical background 124 Herbert’s exposure to mathematics 124 Human Ethics and the Political 126 Opposites and Duality 128 Language and Metaphor 129 Translations into English 131 Mathematical Poetry 134 Counting 135 Zero and Infinity 138 Amorality of Mathematics 141 Mathematics as Certain Knowledge 145 Geometry, Clarity and Exactness 148 Uncertainty 154 Non-Euclidean geometry, parallel lines and multiplicity 157 A Scientific Theory of Poetry 159 Concluding remarks: ‘a dangerous assertion for the theory of poetry’ 161 vi CHAPTER FIVE 167 Ion Barbu’s “Ut algebra poesis”: the Mathematical Poetics of Dan Barbilian Abstract 168 Introduction: the Mathematical Zeitgeist of 1920s Göttingen 168 Barbilian the adult mathematician 174 Barbilian and his mathematical literary theory 180 Geometry meets poetry 180 Mathematical humanism 187 Barbu’s poetry viewed by his critics 189 Barbu’s hermetic poetics: approaching the mathematical 189 Mathematical critics 199 Joc secund 205 [DIN CEAS, DEDUS…] 206 GRUP 209 ÎNECATUL 211 MOD 213 DIOPTRIE 215 PARALEL ROMANTIC 217 UT ALGEBRA POESIS 220 Conclusions: Barbilian’s highly depersonalised ideal 223 CONCLUSION ‘Creative transposition’ 229 WORKS CITED 239 vii INTRODUCTION Making sense of a conundrum Stéphane Mallarmé 1 Ca și în geometrie, înțeleg prin poezie o anumită simbolică pentru reprezentarea formelor posibile de existență. […] Pentru mine poezia este o prelungire a geometriei, astfel încât, rămânând poet, n-am părăsit niciodată domeniul divin al geometriei. Dan Barbilian 2 3 1 One hundred years ago, in 1914, “Un coup de dés jamais n’abolira le hasard” (A throw of the dice will never abolish