Breaking Symmetry: The Structure and Dynamics of Form in Ceramics Eleonora A. B. Moelle MA (HONS) Class 1 Italian, BFA (Hons) Class 1, BFA Doctor of Philosophy July 2015 Statement of Originality The thesis contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to the final version of my thesis being made available worldwide when deposited in the University’s Digital Repository, subject to the provisions of the Copyright Act 1968. Signed: Dated: In the Memory of Konrad H. R. Moelle Acknowledgements I would like to thank my principal supervisor, Associate Professor Pam Sinnott for her support and her confidence in my capabilities; for securing special equipment and good supervision. Also thanks to Professor Emeritus Liz Ashburn, my associate supervisor, for her professional expertise and encouragement and for her intellectual engagement with my work. I wish to also acknowledge Dr. Angela Philp for coming along the journey and offering me highly valued opinions, support, resources and encouragement. I would also particularly acknowledge the assistance of Professor George Willis and Associate Professor Brailey Sims from the Department of Mathematics of the University of Newcastle who gave their time in transferring their enthusiasm and their passion for numbers, and know that art and mathematics are entwined and compatible. Thank you to photographer Dr Allan Chawner for his expertise and professionalism, and to Werner Wurz for his assistance on technical matters and for his encouragement. Thanks also to the talented editor Nola Farman. A special thank you to my children David, Martin and Barbara for their enthusiastic road and crash testing of my functional pots and for rescuing me from numerous computer entanglements. i Contents Acknowledgements i Figures vi Abstract xiv Introduction 1 Chapter 1 The Establishment of the Nature of Symmetry in Early Western Thought 8 Introduction 8 Early History of Symmetry 9 Symmetry in Early Art 13 i. The Golden Section 13 ii. Polykletus 15 iii. Vitruvius 18 The Fibonacci Sequence 19 Logarithmic Spiral 20 Spiral Phyllotaxis 22 Symmetry in the Renaissance 23 Chapter 2 New Understandings of Symmetry in Mathematics and in Natural Sciences 27 1. Symmetry in Modern Mathematics 27 i. Symmetry Breaking: Similarity Transformations 27 ii. Symmetry and Group Theory 30 2. Symmetry in Physics 32 i. Symmetry Breaking: Thermodynamics and Phase Transitions 32 3. Symmetry in Biology 35 ii Chapter 3 The Influence of the New Geometries in Modern Art and in Symmetry 39 Introduction 39 The Spatial Fourth Dimension 40 Non-Euclidean Geometry 41 Impact of Changes in Science 45 Time as the Fourth Dimension 46 Impact of Changes in Art 47 The Contribution of Marcel Duchamp (1887-1968) 49 i. Duchamp and the Cubist Artists 49 ii. From the ‘Retinal’ to the Conceptual 51 iii. Fourth Dimension and Non-Euclidean Geometry in Duchamp’s Major Works 52 Impact of Non Euchlidean geometry and the Fourth Dimension on Surrealism, Suprematism, Constructivism and Cubism 55 Surrealism 55 Salvador Dali (1904-1989) 55 Constructivism 57 El Lissitzky (1890-1941) 57 Suprematism 60 Kasimar Malevich (1878-1935) 60 Cubism and the New Geometries 63 Picasso and the Fourth Dimension 66 Chapter 4: New Initiatives in Ceramics and Symmetry 73 Introduction 73 Pablo Picasso 74 iii Peter Voulkos 81 The Otis Years 84 Pablo Picasso’s Influence 86 Abstract Expressionism and Other Influences 88 The Breaking of the Symmetry 88 Coda 92 Hans Coper 93 Beginnings as a Potter 95 Historical References – Contemporary Imagery 98 Refinement and Abstraction 99 Performance and Recognition 103 ‘An Object of Complete Economy’ 107 George Ohr 109 Dynamics of Form in Ohr’s ceramics 112 Edmund de Waal. Contemporary Ceramist 118 Japanese Influences 119 Changes of Direction 121 Installation Aesthetics 122 Chapter 5 The Square Mouthed Pottery: My Inspiration 128 Introduction to My Ceramic Practice 128 Symmetry Breaking – Dilations 134 Wheelthrowing as a Symmetry Operation 136 Squaring of the Circle as a Symmetry Operation 138 Ambiguity 140 iv Chapter 6 My Ceramic Practice 142 Introduction 142 Beginnings 144 Discovering Porcelain 145 Beginning Post-Graduate Research and Studio Work 146 Research and Studio Work: Reciprocal Influences 150 The Merewether Beach Collection 151 Identifying the New Geometries in My Work After the Breaking of Symmetry 155 Geometry is Symmetry 157 1. The Globular Bottle 157 Planning My Next Project (Studio Work) 161 2. The Albarello. Brief Historical Background 162 The Albarello and My Studio Work 164 3. Computer-Designed Variations of the Albarello Form 168 Coda 173 Conclusion 174 Appendix Field Work: The Square Mouthed Pottery 176 Bibliography 186 v FIGURES Chapter 1 Fig. 1 The regular (Platonic) solids of Euclidean space 11 In Mainzer, Symmetry and Complexity, Fig. 6, page 33 2 Symmetries of Platonic physics 11 In Mainzer, Symmetry and Complexity, Fig. 16, page 47 3 Heelstone (H), Stonehenge 13 In Doczi, The Power of limits, Fig. 79, page 40 4 Stonehenge 14 In Doczi, The Power of limits: Proportional Harmonies in Nature, Art and Architecture (Boulder & London: Shambhala, 1981), Fig. 74, page 39 5 The golden section with square within semicircle. Rectangles 1x0.618 and 15 1x1.618 are reciprocal golden rectangles. In Doczi, The Power of Limits, Fig. 5, page 3 6 Polykletus, Doryphoros, The Spearbearer. In Doczi, The Power of Limits, 17 Fig. 151, page 104 7 Aphrodite of Cyrene. In Doczi, The Power of Limits, Fig. 152, page 105 18 8 Symmetry of the Golden Spiral. In Mainzer, Symmetry and Complexity, 21 Fig. 8, page 36 9 Logarithmic Spiral, cross section of nautilus shell. In Doczi, The Power of 21 Limits, Fig. 134 B, page 85 10 Abalone shell. Reconstruction of outline with Fibonacci numbers. In Doczi, 22 The Power of Limits, Fig.102 page 54 11 Dilated whelk of New Zealand; whorls share the same golden relationship. 22 In Doczi, The Power of Limits, Fig, 103, page 56 12 Pythagorean 3-4-5 triangle in plants, Deerhorn Cedar and Garlic florets. In 23 Doczi, The Power of Limits, Fig. 12, page 7 13 Pentagon, Pentagram, Pythagorean triangle and golden section detail. In 23 Doczi, The Power of Limits, Fig.11, page 6 14 Leonardo da Vinci’s with golden proportions added. In Doczi, The Power of 25 Limits, Fig. 142, page 93 vi Chapter 2 Fig. 15 Symmetry of Cube and Octahedron. In Manizer, Symmetry and 30 Complexity, Fig. 21, page 71 16 Spiral Galaxy. In Doczi, The Power of Limits, Fig. 129, page 81 33 17 A liquid heated from below develops hexagonal circulating cells, 34 Photograph: M.Velarde, Universidad Complutense, Madrid. In: Phillip Ball, The Self-Made Tapestry, Plate 1, page 25 18 Model of virus and its symmetry. In Mainzer, Symmetry and Complexity, 36 Fig. 59, page 201 19 Amoeba (magnified). In Encyclopaedia Britannica (Chicago: Benton, 36 1974), Macropadia Vol 1, page 320 Chapter 3 20 Claude Bragdon, A Primer of Higher Space: The Fourth Dimension 40 (Rochester, N.Y.: The Manas Press, 1913) Pl.1. In L. D. Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Plate.1, page 3 21 Beltrami’s Pseudosphere for the Lobachevsky-Bolay Geometry. Lines M 43 and N through point P approach line “l” but will never intersect it. Angles ABC+BCA+CAB <180°. In L. D. Henderson, Fig. 1.1, page 104 22 Riemann’s Geometry Represented on a Sphere. Lines such as l, M and N 44 will always meet. Angles ABC+BCA +CAB > 180°. In L. D. Henderson, Fig. 1.2, page 104 23 Marcel Duchamp, Portrait of Chess Players, 1911. Oil on canvas. In L. D. 50 Henderson, Fig. 3.2, page 239 24 Marcel Duchamp, Nude Descending a Staircase, No.2 , 1912, oil on 51 canvas. In L. D. Henderson, Fig. 3.3, page 243 25 Marcel Duchamp, The Bride Stripped Bare by Her Bachelors, Even (The 53 Large Glass), 1915-1923. Oil, varnish, lead foil, lead wire, and dust on glass panels encased in glass. In L. D. Henderson, Fig. 3.5, page 247 26 Marcel Duchamp, Three Standard Stoppages, 1913-1914. Three threads 54 glued to three painted canvas strips, each mounted on a glass panel and three wooden slats. In L. D Henderson, Fig. 3.6, page 249 27 Salvador Dali, Dance of the Flower Maidens. Design by Dali, watercolour 56 over pencil. Foundation Gala – Salvador Dali, vii http://www.dali.com/blog/category/interpretations-of-dali/page12/ (accessed 15.5.2015) 28 El Lissitzky, Plate. Unglazed earthenware, designed by Lissitzky in 59 Germany about 1923. Depth 26mm, diameter 119mm. © Images for research only 29 Kasimir Malevich, Design for a Platter. (year not given). In Kasimir 61 Malewitsch zum 100 Geburtstag, page 205 30 Kasimir Malevich, Suprematist Teapot and Cups. Porcelain. In G. Clark, 63 Shards, 334 31 Perspective Cavalière of Sixteen Fundamental Octahedrons of an 66 Ikosatetrahedroid, from E. Jouffret. In Traité Elémentaire de Géométrie à Quatre Dimensions. In L. D Henderson, Fig. 2.3, page 160 32 Pablo Picasso, Portrait of Ambroise Vollard, 1910, Oil on canvas. In L. D 66 Henderson, Fig. 2.4, page 161 33 Pablo Picasso, Composition Study with Seven Figures for Les 70 Demoiselles d’Avignon. Carnet 2, Winter 1906-1907. In A. Miller, Einstein, Picasso, page 107 34 Pablo Picasso, Squatting Demoiselle (Study for Les Demoiselles 71 d’Avignon), Paris, Spring 1907. In A. Miller, Einstein, Picasso, Fig. 4.11, Page 113 35 Pablo Picasso, Les Demoiselles d’ Avignon, 1907, The Museum of 71 Modern Art, New York.