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

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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. In A. Miller, Einstein, Picasso, Paris, 1907, Fig. 4.1, Page 90

Chapter 4 36 Pablo Picasso, Studies for Ceramic, Zoomorphic Forms, 1947. In Theil, 74 “Preliminary Drawings,” Picasso and Ceramics, page 103 37 Pablo Picasso, Large Bird on a Base, 1947. 71x40x24cm. In Theil, 75 “Preliminary Drawings,” Picasso and Ceramics, page 102 38 Pablo Picasso, Studies of Bull, 1946. In Theil, “Preliminary Drawings,” 76 Picasso and Ceramics, page 114 39 Pablo Picasso, The Bull, 1946, lithograph. In Theil, “Preliminary 77 Drawings,” Picasso and Ceramics, page 113 40 Pablo Picasso, ‘Bourrache Provenϛal’ with Woman, Child and Flower, 79 1952. 16x40x26cm. Child and Flower, 1946. In Theil, “Preliminary Drawings,” Picasso and Ceramics, page 245

viii

Fig. 41 Pablo Picasso, Pitcher with Open Vase, 1954, height 38cm. In Foulem 81 and Bourassa, “Ceramics: Sources and Resources,” Picasso and Ceramics, page 247 42 Peter Voulkos, In Glandale Avenue studio, Los Angeles, 1959. In 81 R.Slivka, Peter Voulkos, Fig. 50, page 78 43 Peter Voulkos, Covered Jar, height 43cm, 1953. In R. Slivka, Peter 83 Voulkos, Fig.3, page 7. Photography by Ferdinand Boesch 44 Peter Voulkos, Bottle, 1953. Height 53 cm. In R. Slivka, Peter Voulkos, 83 Fig.4, page 10. Photography by Joseph Schopplein 45 Peter Voulkos, Rocking Pot, 1956. Height 35.5cm. In R. Slivka, Peter 85 Voulkos, Fig. 19, page 36. Photography by Joseph Schopplein 46 Peter Voulkos, Covered Jar, height 43cm, 1956. In R. Slivka, Peter 87 Voulkos, Fig.13, page 28. Photography by Joseph Schlopplein 47 Peter Voulkos, Multiform Vase, 1956. Height 51cm. In R. Slivka, Peter 89 Voulkos, Collection unknown, Fig. 18, page 35 48 Peter Voulkos, Pot Sculpture, Red River, height 94, 1960. In R. Slivka, 91 Peter Voulkos. Plate 10, page 46 to 47. Photography by Bobby Hanson 49 Hans Coper. In T. Birks, Hans Coper, page 53 93 50 Hans Coper, Large Pot, 1953. In T. Birks, Hans Coper, page 94 96 51 Hans Coper, Jug, 1952. In T. Birks, Hans Coper, page 33 97 52 Cycladic Marble sculpture, c. 2500-2300 BC. In J. Lesley Fitton, 98 Cycladic Art, Fig. 85, page 68 53 Hans Coper, ‘a rare shape,’ 1975. Height 17cm. In T. Birks, Hans Coper, 98 page 182 54 Hans Coper, photograph of a Cycladic stone carving from the British 99 Museum which Hans kept in his studio. In T. Birks, Hans Coper, page 148 55 Hans Coper, Small Spade 14cm, Sainsbury Centre for Visual Arts. In T. 100 Birks, Hans Coper, page 172 56 Hans Coper, ‘flattened form,’ 1970. Height 18.5 cm. In T. Birks, Hans 101 Coper, page 164 57 Hans Coper, Cycladic forms, 1974. Height 28-32 cm. In T. Birks, Hans 102 Coper, London, page 196 58 Hans Coper, Coventry Cathedral Candlesticks, 1963. In T. Birks, Hans 104 Coper, page 49

ix 59 Hans Coper, Spade, 1972-75. In T. Birks, Hans Coper, dust jacket 105 60 Hans Coper, ‘standing form,’ 1970. Height 30 cm. In T. Birks, Hans 106 Coper, page 178 61 A predynastic Egyptian pot, unknown maker. In T. Birks, Hans Coper, 107 page 202 62 Hans Coper, ‘The burnished black globular shape on grey-green base,’ 108 c. 1975. Height 21 cm. In T. Birks, Hans Coper, page 183 63 George Ohr, Photo from the Ohr family album, c. 1890. In G. Clark, et al, 109 The Mad Potter of Biloxi, Fig. 116, page 138 64 George Ohr, The Potter and His Wares, c. 1897. In G. Clark, et al, The 110 Mad Potter of Biloxi, Fig.19, page 25 65 George Ohr, Footed Vase, c. 1895-1900, height: 18cm. In G. Clark, et al, 110 The Mad Potter of Biloxi, Plate 109, page 158 66 George Ohr, Teapot with Snakes, front and back views, c.1985-1900. 111 Height: 12cm. In G. Clark, et al, The Mad Potter of Biloxi, Plate 124, pages 168-169 67 George Ohr , Three - Handled Mug, c.1900, height: 20cm. In G. Clark, et 112 al, The Mad Potter of Biloxi, Plate 133, page 176 68 George Ohr, Vase, c. 1895-1900, height: c. 23 cm. In G. Clark, et al, The 114 Mad Potter of Biloxi, Plate 92, page 147 69 George Ohr, Bowl , c.1902-7, height: c. 11 cm. In G. Clark, et al, The Mad 115 Potter of Biloxi, Plate 79, page 116 70 George Ohr, Double-Handed Vase, c.1898. Height: 13,5 cm. In G. Clark 116 et al, The Mad Potter of Biloxi, Plate 4, page 43 71 George Ohr, Pitcher , c1898-1907. Height: 9 cm. In G. Clark, et al, The 117 Mad Potter of Biloxi, Plate 60, page 104 72 George Ohr, Pitcher , c.1985-1900. Height: c. 7.5 cm. In G. Clark, et al, 117 The Mad Potter of Biloxi. Plate 58, page 104 73 Edmund De Waal, Bottles,1997. Porcelain. In Ceramics: Art and 120 Perception. No 35, 1999, cover page 74 Edmund De Waal, Bowl, 2003. Stoneware, opaque tin glaze. In 121 Ceramics: Art and Perception. No 54, page 11 75 Edmund De Waal, Tristia, 2008. In Ceramics: Art and Perception, 122 No 82, 2010, page 30 76 Edmund De Waal, Installation, 2002 in the Geffrye Museum. In Ceramics: 123 Art and Perception No. 54, page 9

x Fig. 77 Edmund de Waal, A Thousand Hours, 2012. In Apollo, November 2013, 125 page 64

Chapter 5 78 Nora Moelle, Study of the Square Mouthed Pottery, 2008. Southern Ice 128 porcelain, deep etching, shellac resist. Photograph by Allan Chawner 79a Square mouthed beaker and bowl recovered from a woman’s stone burial 129 site of mid-fifth millennium B.C. Centre for study of archaeological finds, Trento. Photograph by author Nora Moelle, with permission 79b Stone Age Spoutless Jug. Photograph by author, with permission 131 79c Stone Age Lugged Pot. Photograph by author, with permission 131 80 Nora Moelle 2008, Southern Ice porcelain, unglazed, etched, 133 16x16x16cm. Photograph by Allan Chawner 81 Nora Moelle, Pintadera (clay seal), detail, 2008, Southern Ice porcelain, 134 unglazed, etched. Photograph by Nora Moelle 82 Nora Moelle, 2008. Installation of vessels in spiral form of decreasing 135 height (from the “Square Mouthed Vessels” series), Southern Ice porcelain, unglazed, etched; various heights. Photograph by Allan Chawner 83 “Construction of Parabola.” In: D.W. Henderson and D. Taimina, 137 Experiencing Geometry, 288 84 “Construction of Hyperbola.” In D. W. Henderson and D. Taimina. 138 Experiencing Geometry, 289 85 Nora Moelle, 2008. Horizon (from the “Square Mouthed Vases” series). 139 unglazed, carved; various heights. Photograph by Allan Chawner 86 Holomorphic images, Circle to Square, by Dr. Brailey Sims, Department of 141 Mathematics, The University of Newcastle

Chapter 6 87 Antonio Gaudi’ “Casa Mila” in Barcelona, 1906-1910. Fig. 90. In Clark, et 142 al, The Mad Potter of Biloxi, page 88 88 Salvador Dali, Crucifixion, 1954, Metropolitan Museum of Modern Art. In 143 L.D. Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Fig 7.5, page 505

xi Fig. 89 Les Blakebrough. University of Tasmania, 2005. Fitting a ‘setter’. 148 Photograph by Lynda Warner. In Jonathan Holmes, Les Blakebrough: Ceramics, 2005, Page 89 90 Nora Moelle, Stemmed Vessel, 2005. Southern Ice porcelain, clear glaze 149 deep etching, shellac resist, 16x12x12cm. Photograph by author 91 Merewether Beach, residual marine life. Photograph by author 151 92 Nora Moelle, Open Forms. The Merewether Beach Collection, 2007. 152 Unglazed, deep etched, shellac resist, 17x17x17cm. Photograph by Allan Chawner 93 Merewether Beach. “Ripple Marks.” Photograph by author 153 94 Nora Moelle, Sphere. The Merewether Beach Collection. 2007. Unglazed 154 Southern Ice porcelain; carving, 14x13x13 cm, Photograph by Allan Chawner 95 Nora Moelle, Bottle, 2010, unglazed, 23x15x13. Photograph by Allan 156 Chawner 96 Hispano-Moresque Albarello, early 15th century, Valencia. In Alan Caiger- 156 Smith. In Tin Glazed Pottery, 1973. Illustration F, page 48 97 Nora Moelle, Bottles, 2012. Various sizes. Photograph by Allan Chawner 158 98 Nora Moelle, Work in Progress. Photograph by author 158 99 The hyperbolic paraboloid. In Silvia Benvenuti, The Numbers of Beauty: 159 Can Maths Foster Creativity? In G. Darvas, ed., Symmetry: Culture and Science, page 431 100 George Ohr. Plate 78. Vase, c.1902-7. In Clark, et al, The Mad Potter of 160 Biloxi, Abbeville press, New York, 1989, page 116 101 Hyperbolic space. Negative curvature. Fig. 19-8. In B. Rich & C. Thomas, 160 Schaum’s Outline of Geometry, Mc Graw Hill, New York, 2013 102 Albarello, Raqqa, Mesopotamia late 12th or early 13th century (22.9 cm) 162 Victoria and Albert Museum, London. In World Ceramics: An Illustrated History, ed. R. Charleston, New York: Crescent Books,1990, Fig. 250, page 86 103 Albarello, inscribed MIDEA BELL, Faenza, circa 1500. Height 31cm. 163 Musée du Louvre. In A. Caiger-Smith, Tin-glazed Pottery in Europe and the Islamic World, Fig. 63, following page 80

xii Fig. 104 Nora Moelle, 2010. (First model of ‘non-Euclidean’ albarello). 166 Wheelthrown and manipulated albarello-type vessel. Southern Ice porcelain, unglazed, various sizes. Photograph by Allan Chawner 105 Nora Moelle, 2010. Wheelthrown and manipulated. Southern Ice 167 Porcelain, unglazed. 34 x 30x30cm. Photograph by Allan Chawner 106 Nora Moelle, 2010. Manipulated wheelthrown parts. Working Stages 167 107 Nora Moelle, 2010. Manipulated albarello inspired vessels, installation, 168 wheelthrown, unglazed, various sizes. Photograph by Allan Chawner 108 Janet De Boos. Computer-designed cup, Australian National University. 169 Photograph by author 109 Feng Te. Computer-designed images of albarello inspired vessel forms, 170 2012 110 Nora Moelle, 2012. Computer-designed vessels, wheelthrown, 171 manipulated and bisqued. Various sizes. Photograph by Allan Chawner 111 Nora Moelle, 2012. Computer-designed vessels, wheelthrown, 171 manipulated and bisqued. Various sizes. Photograph by author 112 Nora Moelle, 2012. Working stage 172 113 Nora Moelle, 2012. Working stage 172

Appendix The Square Mouthed Pottery

114 Map of Northern Italy showing present day regional and national frontiers 176 and main towns 115 Map of Northern Italy in Middle Neolithic times and centres of square 177 mouthed pottery culture. In Lawrence Barwick, Northern Italy: Before Rome. London:Thames and Hudson, 1971, Fig. 11, page 3

xiii ABSTRACT

Breaking Symmetry: The Structure and Dynamics of Form in Ceramics

This project examined how the structure and dynamics in ceramics could be made to implement energy and change in the vessel form. A key objective was to clarify how the initial concept of symmetry in Antiquity, concerned with beauty, harmony, rhythm, balance and proportional relationships, changed. In this diachronic study of the concept of symmetry from an aesthetic point of view, the traditional viewing of the concept of

‘harmony of proportion’ can have the limitations sometimes implicit in symmetry — sameness, repetitiveness and indifference. In contrast to this vague notion of the concept, the changed modern viewing of symmetry is strictly geometrical, and absolutely precise. Like symmetry, asymmetry has dual aspects of significance, such as change, motion, dynamics, incongruence, disorder, chaos; another aspect is contrast, non-uniformity, diversity, freedom, individuality. For artists the new kind of space (curved space) offered by science signified such a new freedom to depart from earlier constraints. Picasso utilised this freedom in his ceramics, while ceramicists such as George Ohr, Peter Voulkos, Hans Coper and Edmund de Waal took advantage of both the dynamics and the freedom. Their contributions are considered to have formed the background to my own practice through their breaking of symmetry.

This period of my ceramic practice was motivated by an exploration of various ways to continue to “break” symmetry to create new ceramic forms. My studio work ran in parallel with my theoretical research, influencing each other reciprocally in carrying out basic symmetry breaking operations as well as multiple operations for compound vessel forms. This body of work was inspired by fieldwork undertaken in Trento, Italy.

This project offers to today’s ceramic artists, a wider, updated perception of

xiv symmetry/asymmetry, a broader understanding of its reciprocity and studio methodologies to explore its application.

xv

BREAKING SYMMETRY:

THE STRUCTURE AND DYNAMICS OF FORM

IN CERAMICS

INTRODUCTION

In the practice of ceramics the wheelthrown vessel form is inextricably tied to ideas of symmetry, which have been crucial in this type of ceramics. The value of symmetry in art has been well established, however, in the twentieth century changes in science have led to a re-evaluation of many previously accepted ideas in art. From the beginning of the twentieth century ceramic art has seen a rapid shift of form, from the symmetrical to symmetry breaking (with a reduction of symmetry), to the outright asymmetrical. An examination of the literature reveals that little work has been done on the technical, historical and philosophical side of symmetry breaking, particularly in vessel forms. This provided my rationale for changing the dynamics and structure within ceramics, as the notion of “breaking” symmetry has not yet been fully explored or exploited. I resolved to break the symmetry of the wheelthrown base-pot to implement dynamics and change, in order to create new kinds of ceramic vessel forms, and thus extend its possibilities for others in this field.

Early in my project I was inspired by an archaeological find of Stone Age pottery near my hometown of Trento, where several round bowls and beakers with a square lip were unearthed; they were given the name of Square Mouthed Pottery. I was able to undertake fieldwork in this area to explore the unique and unexplained breaking of the initial circular shape for a square (of reduced symmetry). This action engaged my

1 enquiring potter’s curiosity, and eventually led to a body of work of white Southern Ice porcelain vessel forms, reflective of today’s ceramic practice.

I wanted to investigate ‘how the meaning of symmetry had changed over time from the stone age pottery of Trento to now?’ How did ideas of symmetry/asymmetry develop in the work of artists and ceramicists? Most importantly, how could this changed understanding become a prime mover for myself and others artists and ceramicists to reflect these ideas in their creative practice?

The aim of the analysis developed in my methodology was to unfold a vocabulary of terms, and a hierarchy of concepts that I could use to analyse my own work, and place it in a contemporary framework of ceramic art practice. This entailed understanding the geometry of vessel forms, the role of symmetry in wheelwork and the consequences of the reduction of symmetry by violation of the initial symmetrical state. This aspect of research encompassed a necessarily brief diachronic study of the concept of symmetry.

The scope/motivation of my research was to identify the prime movers which set into motion these radical changes in the concepts of symmetry/asymmetry. My core question was how can the breaking of symmetry and asymmetry become prime movers for my ceramic practice in order to implement a new dynamics and change in the vessel form? This relates to the idea of action research where the studio practice leads the project.1

While in essence Western ceramic practice is predominantly anchored in traditions from Greek and Renaissance concepts of symmetry, both science and other cultures have contributed to the development of ideas of non-symmetry. New mathematics and the fourth dimension have made their mark on contemporary ceramic practice, as have

1 See Barbara Bolt, “The Magic is in Handling,” Practice as Research: Context, Method Knowledge, ed. Estelle Barrett and Barbara Bolt, I.B. Tauris, 2007. 2 the traditions of Zen from Japan. Indeed the idea of “asymmetrical harmony,”2 as demonstrated in the tea ceremony, was an important aim in my ceramic practice.

Chapter 1 is a general consideration of early ideas of symmetry, and examines theories of symmetry, breaking symmetry and asymmetry as an initial exploration of terms and concepts. I began with considering how symmetry was synonymous with beauty, harmony, rhythm, balance, and proportional relationships in Antiquity. In contrast to this vague notion of the concept, the modern viewing of symmetry is strictly geometrical, ‘an absolutely precise concept.’3 From an aesthetic point of view, the duality of symmetry is also in its contrasting perception: proportionality, beauty, uniformity, charm, but also sameness, repetitiveness, indifference.

Like symmetry, asymmetry has dual aspects of significance: asymmetry as change, motion, dynamics, incongruence, disorder, chaos; a distinguishing aspect of asymmetry is contrast, non-uniformity, diversity, freedom, individuality. Weyl recognises this tension:

Seldom is asymmetry merely the absence of symmetry. Even in asymmetric designs one feels symmetry as the norm from which one deviates under the influence of forces of non-formal character.4

The early Pre-socratic philosophers believed in a cosmos ordered and kept in balance by the highest mathematical laws: in the beginning there was symmetry and simplicity.

But in fact, it soon conflicted with discrepant observations: the world is neither simple nor in static balance and harmony; there is also change, dynamics, random and chaos.

2 Allen S. Weiss, “Guinomi,” Gastronomica, (University of California Press, 2010) Vol.10, No 1 (Winter 2010), 136. http://www.jstor.org/stable/10.1525/gfc.2010.10.1.136 (Accessed 22/06/2015). 3 Hermann Weyl, Symmetry, (Princeton University Press, 1952), 3. See below in the ‘Introduction,” the full quotation on page 6. 4 Weyl, Symmetry, 13. 3

Thus, the observed variety and diversity of structures in nature could only emerge by a reduction of symmetry or symmetry breaking. Consequently I consider symmetry breaking to be the origin of dynamics and of change.

In Chapter 2, I consider that “symmetry breaking” is a scientific expression, which is taken from the physical sciences. I have “borrowed” examples of symmetry breaking from modern physics (thermodynamics, phase transitions), and from biology (the amoeba and the virus). The connection between art and science becomes clearer when, at the beginning of the 20th century, due to major discoveries in physics by Albert

Einstein, two separate geometries were attracting the attention of both scientists and artists. These were the non-Euclidean geometries, which included surface and space curvature, and the fourth dimension. The “new” geometries became prime movers, central not only to the interpretation of our physical world, but to artists who were also attracted by the idea of curved space and by the spatial possibilities of a fourth dimension, leading also to the rise of abstraction, a ‘fundamental revolution in art.’5

In Chapter 3 I explain how the new kind of space (curved space) signified a new freedom for artists. Cubist painters took the challenge onto themselves; as did the

“irreverent” artist Marcel Duchamp. Pablo Picasso absorbed and resolved the newest scientific ideas of his time and contributed significantly to a new vision of ceramic art by transmogrifying traditional, wheel-thrown forms into surprising art creations that disrupted symmetry.

A further perception of aesthetics opened up when oriental graphic art, especially

Japanese art became available to artists: immediacy, spontaneity and intuition were aesthetic principles, leading to imbalance and asymmetry, which had been propagated in Japan by the school of Zen masters, based on a Buddhist system of Taoist thought.

5 Mainzer, Symmetry and Complexity: The Spirit and Beauty of Nonlinear Science (New Jersey: World Scientific, 2005), 377. 4

While the asymmetry of Sixteenth century black raku tea bowls and the pitted and burnt surfaces of Bizen wares attracted ceramicists to Japanese ceramic practice, they did not understand that the “spontaneity” of Japanese ceramics was achieved through a long process of control and growth. This meant that some of their work was often furiously gestural and spontaneous, more so then in Japanese pottery.6 This spontaneity contributed as a prime mover, or mainspring, which triggered wide-ranging changes across all art forms. The new tendencies were eagerly absorbed by various artists, such as action painter Jackson Pollock, and by ceramic artists such as Peter

Voulkos.

In Chapter 4 I consider the specific contributions of Pablo Picasso, together with that of ceramicists such as George Ohr, Peter Voulkos, Hans Coper and Edmund de Waal, to current ideas around breaking symmetry. Their contributions, and other aspects of my research, form the background to my own ceramic practice.

Finally, Chapters 5 and 6 concerns my methodology and the interconnections of my research with my own work. To a great extent my studio work has been running side by side leading the progress of my theoretical research project, thus influencing each other. Significantly, the new knowledge of non-Euclidean geometry has broadened my perspective in my assessment of my own work. For example, the potter’s wheel is the ideal tool, and wet clay is the ideal plastic material for an almost instantaneous production of geometric objects associated with non-Euclidean geometry.

However, the initial wheel-thrown shape has been for me only the point of departure from which I carried out, at the beginning, basic symmetry-breaking operations, and later more dynamic multiple operations for the symmetry breaks of body parts of compound vessel forms, in order to create new forms and extend the possibilities of ceramic practice. Interestingly, in the investigations I have carried out in my research

6 Garth Clark, Shards: Garth Clark on Ceramic Art, (New York: Ceramic Art Foundation, 2003), 275. 5 project, and in particular in the assessment of my work, I have been taking into consideration the duality of symmetry talked about by Hermann Weyl speaking about the concept of symmetry, as stated in the following excerpt, i.e., the Antique meaning of the harmony of proportion as well as the modern conceptualisation of symmetry, inclusive of elements of non-Euclidean geometry:

If I am not mistaken the word symmetry is used in our everyday language with two meanings. In the one sense symmetric means something like well proportioned, well balanced, and symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is bound up with symmetry. The image of the balance provides a natural link to the second sense in which the word symmetry is used in modern times: bilateral symmetry, the symmetry of left and right. Now this bilateral symmetry is strictly geometric and, in contrast to the vague notion of symmetry discussed before, an absolutely precise concept.7

7 Weyl, Symmetry, 3. In 1952, Hermann Weyl, before retiring from the Institute for Advanced Study at Princeton, gave a series of public lectures on mathematics. His topic was Symmetry, which is also the title of a book that grew from his talks, that ‘no book that follows in its footsteps can ignore it’ (Ian Stewart & Martin Golubitsky, Fearful Symmetry: Is God a Geometer ? (New York: Dover, 1992), 27. 6

Nora Moelle 2012

7

CHAPTER ONE: The Establishment of the Nature of Symmetry in Early Western

Thought

Introduction

In order to “break” symmetry in ceramics it is important to understand how concepts of symmetry have been built up over time. These ideas have been embedded in ceramic practice and this chapter deals briefly with the early history and development of notions of symmetry to the end of Renaissance.

Symmetry is a subject that covers an extensive area, encompassing nature, human life, culture and technology. All known cultures have used symmetrical patterns in their crafts and in their constructions; symmetrical forms generally prove to be more solid, simpler, easier to reproduce and to pass on to future generations, as well as being aesthetically attractive.1

People took notice of the great cycles of nature, the alternation of the seasons, of day and night, low tide and high tide, of the randomness of abundance and lean times.

They best succeeded in their survival by their intuitive understanding of nature, by acting in accordance with those cycles, which were possibly the first consciously experienced symmetries of nature. Therefore it is not surprising that the ever-recurring natural phenomena, with their life-giving and destructive power were incorporated in their myths to provide a model for the early nature religions.2

Nature religions were replaced by a philosophy of nature when questions were asked about causality and the reasons for the changes in nature. An assumption was made

1 Klaus Mainzer, Symmetries of Nature: A Handbook for Philosophy of Nature and Science, (Berlin: de Gruyter,1996), 64. 2 Dorothy Washburn, ed., “Introduction”, in Embedded Symmetries: Natural and Cultural, (Albuquerque: University of New Mexico Press, 2004), 1-5. 8 that behind the great diversity, the ongoing changes and the great cycles of nature, there was an unchanging principle of order. Symmetry was an aspect of life that captured the human imagination.

Early History of Symmetry

The concept of symmetry, as it was understood by the early Greek philosophers, was entirely different from the abstract way it is perceived today. However, the initial interpretation had a long-lasting life, as it was accepted and adopted for over two thousand years of our history until modern times, and today it is still a fundamental concept.

The earliest Socratic philosophers of the sixth century B.C. focussed attention on the origin and nature of the physical world3. Thales of Miletus (625-545 B.C.) was the first

Greek philosopher to give a purely natural explanation of the origins of the world, free of all mythological elements. He assumed that water, or the wet, was the first element and the cause of all things coming into being. For his contemporary, Anaximander, the original matter was in a primordial state ‘boundlessly-indeterminable’, and therefore everywhere of the same character and without opposites. Consequently, it was in a condition of complete uniformity and symmetry. Interestingly, with Anaximander, the concept of symmetry breaking arises early, almost with foresight in philosophical thought, when he predicts that the condition of symmetry is followed by symmetry breakings from which the world arises with forces in opposition to each other

(opposites are hot and cold, wet and dry, etc...).4

3 Mainzer, Symmetries of Nature, 66.

4 Mainzer, Symmetries of Nature, 66-8. The fascination with Anaximander increases when one reads his theory of evolution. He assumes that the first human beings were born from sea animals whose young are quickly able to sustain themselves, as he had observed in the case of certain kinds of sharks. In Mainzer, 68. 9

Heraclitus of Ephesus in Anatolia (circa 500 B.C.) is of significance for the history of philosophy; he took over Anaximander’s doctrine of the struggle and the tension of the opposites in nature, as well as the Pythagorean principle of harmony that is hidden behind all disharmonies. For Heraclitus the original matter, the source of everything is itself change and therefore is identified with fire. The material world consists of opposite conditions and tendencies, which are nevertheless held in unity by hidden harmony.5 In Heraclitus’ own words (translated): ‘What opposes unites, and that the finest attunement stems from things bearing in opposite directions’.6 The hidden harmony of opposites is the cosmic law of Heraclitus that he called logos.

In this context it is interesting to see the association of ideas by a modern physicist,

Werner Heisenberg (1901-1976):

At this point we can interpose that in a certain way modern physics comes extraordinarily close to the teaching of Heraclitus. If one substitutes the word ‘energy’ for the word ‘fire’, one can view Heraclitus’ pronouncements almost word for word as an expression of our modern conception… Energy can be transformed into movement, heat, light and tension. Energy can be regarded as the cause of all changes in the world. 7

Pythagoras (circa 580-500) and his followers developed a geometry by constructing regular polygons using the compass and the ruler. Later Euclid (circa 300 B.C.) assembled all geometrical knowledge in his treatise the Elements; some of his theorems are an important part of mathematics today. Assumptions of symmetry were founded on plane and solid figure symmetries of Euclidean geometry, the circle, the sphere and the regular bodies.8

For Plato, the mathematical symmetries of Pythagorean geometry existed as an ideal form, independently of technical application. Plato introduced a mathematical model of

5 Mainzer, Symmetries of Nature, 69. 6 Mainzer, Symmetries of Nature, epigraph. 7 Mainzer, Symmetries of Nature, 70. 8 The five regular polyhedra, called also the Platonic solids, are the tetrahedron, hexahedron (cube), octahedron, dodecahedron, icosahedron. They have respectively 4, 6, 8, 12, 20 congruent faces, and the angles at the vertices are all equal. In Klaus Mainzer, Symmetry and Complexity: The Spirit and Beauty of Nonlinear science, (New Jersey: World Scientific, 2005), 33. 10 the microcosm that for the first time explained the ultimate building blocks of matter

(which he did not call “atoms”) by means of the geometric symmetries of regular bodies. (See Fig. 1) As illustrated in Fig. 2, regular bodies can be cut open along appropriate edges, and their surface elements can be unfolded as nets.

Fig. 1. The regular (Platonic) solids of Euclidean space. In Mainzer, Symmetry and Complexity, Fig. 6, page 33.

Fig. 2. Symmetries of Platonic physics. In Mainzer, Symmetry and Complexity, Fig. 16, page 47.

11

In his dialogue “Timaeus”, Plato established a correspondence between each regular body and a particular element (fire, earth, air and water). He asserted that each element is able to transform into another, according to geometric laws. In Mainzer’s view, we have here the first attempt in the history of science to explain matter and its states by simple mathematical laws of symmetry.9

Plato’s early interpretation of the elements has been linked to modern elementary particles physics by Werner Heisenberg, who made this observation about it: ‘The elementary particles have the form Plato ascribed to them because it is the mathematically most beautiful and simplest form. Therefore the ultimate root of phenomena is not matter, but instead mathematical form’.10

In Plato’s time a well-defined theory of the macro cosmos was developed, that postulated a centrally symmetrical universe, with the earth as a sphere in the centre, and the sun and planets rotating around the celestial axis: each planet in its circular motion generates musical notes, and the interaction of the sounds produce the harmony of the spheres (anticipating harmonic analysis). Celestial harmony was the central theme of Pythagorean astronomy.11

However these early assumptions of a perfect symmetry of the world were put to the test because of contradicting observations of the sky, and with the realisation that the breaks of symmetry are rather the rule in a world of diversity and change.

Two later major developments were the so-called Copernican revolution, with the reversal of the earth and the sun as central points, and Kepler’s change from the circular to the elliptical orbits of the planets. The construction of regular polygons with compass and ruler had its limitations; these were overcome several centuries later with the introduction of the Arabic algebra to solve mathematical problems. In modern

9 Mainzer, Symmetries of Nature, 78-81. 10 Mainzer, Symmetries of Nature, 81-82. 11 Mainzer, Symmetry and Complexity, 40. 12 times Plato’s mathematical model has become a useful tool for explaining crystals and atomic and molecular compounds by means of the concept of symmetry in both crystallography and stereochemistry.12

Symmetry in Early Art i The Golden Section

In Northern Europe great stone monuments were erected during the second and the first millennium B.C. The most famous of these megaliths is Stonehenge in England, which shows how the time of the summer solstice was determined.

Fig. 3. Heelstone (H), Stonehenge. In Doczi, The Power of Limits, Fig. 79, page 40.

12 Mainzer, Symmetries of Nature, 81. Stereochemistry is the branch of chemistry concerned with the three-dimensional arrangement of atoms in molecules . Concise Oxford English Dictionary, Soanes and Stevenson, ed., Concise Oxford English Dictionary, 11th Edition (Oxford: Oxford University Press), 2006. 13

It is also striking that at Stonehenge the diameter of the external stone circle and the width of the internal horseshoe-shaped stone circle seem to be related to each other in the proportion of the golden section.13

Fig. 4. Stonehenge. In Doczi, The Power of Limits: Proportional Harmonies in Nature, Art and Architecture (Boulder & London: Shambhala, 1981), Fig. 74, page 39.

The golden section, which Pythagoras is said to have taken over from the Babylonians or Zoroastrians (6th century B.C), was considered for centuries to be “the” aesthetic standard. It is an important concept in both ancient and modern geometrical and architectural design. The harmonic effects of the golden section have been researched in depth by psychological investigations. Together with intuitively familiar proportional ratios of the human body, there is probably also the perception that in the golden section two parts of different sizes form a unity; the smaller part is related to the larger one as the larger one is to the whole, and thereby the unequal parts are harmonised in the whole.14

13 György Doczi, The Power of Limits: Proportional Harmonies in Nature, Art and Architecture, (Boulder & London: Shambhala, 1981), 38-40. 14 Mainzer, Symmetry and Complexity, 358. 14

Image unavailable due to copyright restrictions

Fig. 5. The golden section with square within semicircle, Rectangles 1x0.618 and 1x1.618 are reciprocal golden rectangles. In Doczi, The Power of Limits, Fig. 5, page 3.15

ii Polykletus

A canon of proportions for the Visual Arts was first mentioned by the architect and sculptor Polykletus (4th century B.C.), who shared with the Greek philosophers and mathematicians the belief in a well-ordered world that could be expressed in proportions and harmonies. However we only have ancient acknowledgments of the existence of Polykletus’ canon of rules, and only fragments handed down through interpretations in later centuries.16 It is not clear if the mention of the golden section was included in his canon, but modern studies of Polykletus’ work show an understanding and knowledge of proportional relationships. Galen, a physician of the

2nd century A.C. observed that ‘health depends on the symmetry of the elements, and beauty depends on the symmetry of the limbs…as is written in the canon of

15 See reference on page 14, footnote 13. 16 Mainzer, Symmetry and Complexity, 359. 15

Polykletus.” 17 This understanding of art is inclusive, in the sense that man was literally the measure of all things, and anticipates a generally broader philosophical approach to the world. A further proof of the broadening of the antique doctrine of proportions from the laws of nature and aesthetics to jurisprudence, may be implied in the spirit of the letter of Aristotles’ statement: ‘This, therefore, is what is just: the proportional. And the unjust is the offence against the proportional. But the proportional is a middle way.’18

Architect and author G. Doczi has carried out a detailed study of dynamic symmetry with samples taken from nature, the crafts, ancient and modern art and architecture and modern technology, as well as from the constructs of some Eastern and Western literary works.19 His method employs the juxtaposing of graphic diagrams of the golden section to the outline of the objects of his study, in order to determine the corresponding proportional relationships. It also indicates the wide application of the rules diachronically, by intuitive perception or by applied mathematical and/or geometrical rules of proportion.

17 Mainzer, Symmetry and Complexity, 359. 18 Mainzer, Symmetry and Complexity, 38. 19 György Doczi, The Power of Limits 16

Polykletus’ spear-bearer (Doryphoros) Fig. 6, considered a sculptural showcase of balance and a symbol of beauty of the male body, is a valid example of matching proportional ratios.20

Fig. 6. Polykletus, Doryphoros, The Spear Bearer. In Doczi, The Power of Limits, Fig. 151, page 104.

Image unavailable due to copyright restrictions

In a similar study, the Aphrodite of Cyrene, Fig. 7, that embodies all the attributes of the beauty of the classical period, reveals similarly harmonious length relationships.

Remarkably, on close examination, the Aphrodite’s fluid body posture deviates from the narrow standards of the rigid archaic statues, as her knees are at different levels, only the left knee matching the distance to the vulva, and the right breast indicates a

20 Doczi, The Power of Limits, 104. 17 changed proportion to the navel. These slight deviations from the norm of proportions are the symmetry breakings, which in a masterly way, enhance the aesthetic and erotic charm of Greek classical sculpture. Symmetry breaking is needed to create individuality and personality; yet the attractive characteristic of the particular is realised only because it is viewed in reference to standard proportional relationships.21

Fig.7. Aphrodite of Syrene. In Doczi, The Power of Limits, Fig. 152, page 105.

Image unavailable due to copyright restrictions

iii Vitruvius

Vitruvius, the first century Roman architect and writer, named Polykletus as well as nine additional artists who were believed to have written about ‘rules of symmetry’.

Vitruvius begins his ten books about architecture (25 B.C.) by recommending that temples be built similarly to human anatomy, which, in his view, possesses a perfect

21 Doczi’s illustration of the Aphrodite of Cyrene and the juxtaposition to the scale of the golden section is reproduced in Mainzer, Symmetries of Nature, 121. 18 harmony of its parts: ‘…just as the quality of eurhythmics in human body results in forearm, foot, hand, finger and the other symmetrical component parts, it emerges in perfect works of art.’22 The idea here is of the carrying over into art and architecture, standards of proportions drawn from the measure of man, that is, organic not arbitrary, measures, considered in the framework of a wide understanding of nature. It should also be mentioned here that in Vitruvius’ opinion, an architect should not ignore the science of medicine - medicinae non sit ignarus - 23 encouraging once more the study of the body.

The Fibonacci Sequence

In 1202 a mathematician, Leonardo da Pisa, called also Fibonacci (filius Bonacci,

Bonacci’s son), published a book, Liber Abaci, in which he introduced into Europe

Hindu-Arabic numerals and the decimal system. He also disclosed a series of numbers, called the Fibonacci sequence, in which each number is the sum of the two previous ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc... Any number of this series divided by the following one approximates 0.618…, and any number divided by the previous one approximates 1.618…, these being the characteristic proportional rates between the minor and major part of the golden section. These numbers are

“irrational”, so called because they can only be approximated, never expressed fully in a fraction.24

The discovery of incommensurable straight-line proportions – presumed to have been made by the Pythagorean Hippasus of Metapontum in the 5th century B.C. – is said to have set off a shock in Pythagorean circles, because it called into question the assumption that all proportions of magnitude could be expressed in ratios of whole

22 Mainzer, Symmetries of Nature, 120. 23 Mainzer, Symmetries of Nature, 120. 24 Doczi, The Power of Limits, 5. 19 numbers. The discovery of proportions of magnitude that are not in the ratio of whole numbers was considered an incursion into the irrational, which according to legend, brings the punishment of the gods upon those who divulge it.25

In regard to this irrational relationship, an explanation suggested by Jay Hambidge in

The Elements of Dynamic Symmetry, may be of interest. Hambidge acknowledges the incommensurability of lines: the end and the side of a golden rectangle, when divided into the other, produce sometimes irrational numbers. However, the relationship between the end and the side of a root-five rectangle (golden section rectangle) is a relationship of area not line, he says, because as length one cannot be divided into the other, but the square constructed on the end of a root-five rectangle is exactly one fifth the area of the square constructed on the side: ‘The Greeks’, Hambidge concludes,

‘said that such lines were not irrational because they were commensurable or measurable in square’.26

Logarithmic Spiral

An application of the golden section is the golden rectangle used for the construction of the golden spiral: if a golden rectangle ABDF is drawn and a square ABCH is removed, the remaining rectangle HCDF is also a golden rectangle (Fig. 8). If this process is continued and circular arcs are drawn joining two opposite corner points of the squares in the manner of a clock dial, the curve formed, approximates the logarithmic spiral, a form found in nature. The golden spiral is an approximation of the logarithmic spiral.27

25 Mainzer, Symmetry and Complexity, 36. 26 Jay Hambidge, The Elements of Dynamic Symmetry (New York: Dover, 1967)18. 27 Mainzer Symmetries of Nature, 46. 20

Image unavailable due to copyright

restrictions

Fig. 8. Symmetry of the Golden Spiral. In Fig. 9. Logarithmic Spiral cross section Mainzer, Symmetry and Complexity, Fig. 8, of nautilus shell. In Doczi, The Power of page 36. Limits, Fig. 134 B., page 85.

The logarithmic spiral, with its curve winding in a continuous and gradually widening curve around a central point, is typical for the growth of some shells, like the chambered nautilus shell (Fig. 9). Here the shell rim provides a template on which new shell material is laid down, so that it maintains the same shape, but the rim is expanded in scale at a consistent rate. The growth is slightly faster on one side of the embryonic rim than the other; this imbalance is maintained proportionally as the shell grows and it curves into a spiral. The organism is building a shell that needs to keep pace with its own growth. The animal lives in the last of the chambers, up to a maximum of 36. The chambers are connected by a tube that absorbs gases, allowing the shell to act as a float.28 A logarithmic spiral, typical of shell growth, shows that each consecutive stage of growth is encompassed by a golden rectangle that is a square larger than the previous one.29 Fig. 10. and Fig. 11. In contemporary times the interest in logarithmic spirals has been enhanced by computer-assisted computability of this number sequence; this modern application reflects a long-standing interest in a development, stemming from Pythagorean time and continuing into present.30

28 Philip Ball, The Selfmade Tapestry: Patterns Formation in Nature (Oxford: Oxford University Press), 1999, 11-12. 29 Doczi, The Power of Limits, 54, 56. 30 Mainzer, Symmetry and Complexity, 204. 21

Fig.10. Abalone shell. Reconstruction of outline with Fibonacci numbers. In Doczi, The Power of Limits, Fig. 102, page 54.

Fig. 11. Dilated whelk of New Zealand. In Doczi, The Power of Limits, Fig. 103, page 56.

Spiral Phyllotaxis

The Fibonacci numbers31 are also exemplified by the botanical phenomenon known as spiral phyllotaxis. The arrangements of the whorls on a pinecone or of florets of a sunflower grow along logarithmic, equiangular spirals, moving in opposite directions.

Fig. 12. and Fig. 13. show the Deerhorn Cedar and garlic florets.

31 Artist Mario Merz has used Fibonacci numbers in his Arte Povera works. 22

Modern statistical studies, in Mainzer’s opinion, lead in fact to conclusions about such laws of proportion in growth of patterns of humans, animals and plants. But perfect symmetry in these cases, is ‘merely a human fiction that is projected on nature by abstraction. It is rather the structure of biological growth programs which are realised in the context of certain statistical deviations’32.

Fig.12. Pythagorean 3-4-5 triangle in plants, Deerhorn Cedar and garlic florets. In Doczi, The Power of Limits, Fig.12, page 7.

Fig.13. Pentagon, Pentagram, Pythagorean triangle and golden section. In Doczi, The Power of Limits, Fig.11, page 6 (detail).

Symmetry in the Renaissance

A well-known dictum of the Renaissance period was ars sine scientia nihil est. The strong link between science and art, however, was not first dictated by the

Renaissance; the great medieval architects had tried to base their designs on mathematics as well as on the philosophy of nature. However, the strong theological considerations underpinning symmetry, evident in the Romanesque and Gothic cathedrals, faded into the background in the Renaissance.

32 Mainzer, Symmetry and Complexity, 202. 23

As the Antique scientific authors became increasingly known, the classic texts of the

Antique art canon were studied again and in the Renaissance symmetry was based again on proportion of man and nature. Thus, Leon Battista Alberti (1404-1472), poet, architect and theorist argued in De re aedificatoria that beauty is a correspondence of parts according to a specific number - proportionality and order. He asserted that an art form designed in this way is the absolute and highest law of nature.33 Alberti also indicated that reflection symmetry was the natural law for humans and animals, and concluded that therefore, it must be applied in architecture.34

In reflection symmetry, the two parts have the same form and proportion, in the second half only the direction is reversed. Leonardo da Vinci sometimes used this economy by carefully executing only one reflection half of a drawing in his architectural sketch books.35

Another author of this period who endorsed the laws of reflection in architecture was

Giorgio Vasari (1511-1574), painter, architect and writer. In The Lives of the Most

Eminent Italian Architects, Painters and Sculptors..., published in Florence in 1550,

Vasari adopted his concept of symmetry (disegno) almost literally from Vitruvius: proportional relationships encountered in the bodies of humans and animals and plants have to be reflected in buildings, paintings and sculptures.36

The spirit of the Renaissance can be seen as crystallised in one person, Leonardo da

Vinci (1452-1519). One aspect of Leonardo’s architecture became significant for the development of the concept of symmetry. Leonardo emphasised central symmetry, and he systematically worked out the possibilities of central structures for churches, castles and other buildings. Octagonal floor plans and octagonal rooms were of

33 Mainzer, Symmetries of Nature, 128. 34 Mainzer, Symmetries of Nature, 128. 35 Mainzer, Symmetries of Nature, 128. 36 Mainzer, Symmetries of Nature, 128. 24 particular interest.37 Central symmetry, with its emphasis on the centre, would satisfy the princes with their requirements for display: they want to be the focal point and to be seen from all angles. Leonardo asserted that all the arts, not only architecture, should have a scientific base and be sourced from natural laws.38 In his Trattato della pittura, he stressed the importance of the study of the human body and its proportions in anatomy. He related the human body to the circle and the square, which has become an icon of the modern age. (See Fig. 14) Leonardo also reasserted the importance of the golden section and illustrated the book De divina proportione written by his contemporary, the mathematician Luca Pacioli and published in Venice in 1509.

Fig. 14. Leonardo da Vinci’s interpretation of Vitruvius with golden proportions added In Doczi, The Power of Limits, Fig. 42, page 93.

From the initial concept of symmetry that was understood in Antiquity and Renaissance described in this outline, there was a concern with beauty, harmony, rhythm, balance and proportional relationships, evident in geometrical and numerical proportions.

However there were limitations to this doctrine of harmony, such as sameness, repetitiveness and indifference. Science, technology and aesthetics had become independent and had gone their own way; the common base of science and art had

37 Leonardo, Architectural Studies, in Mainzer, Symmetries of Nature, 129. 38 Mainzer, Symmetries of Nature, 129. 25 broken apart 39 and this in turn had impact on ceramic practice. In the next chapter I discuss how mathematics conceptualises symmetry, while in later chapters I explain how artists again considered their geometry in their work.

39 Mainzer, Symmetries of Nature, 131-132. 26

CHAPTER TWO: New Understanding of Symmetry in Mathematics and in Natural

Sciences

In this chapter the importance of the impact of scientific thought and notions of symmetry/asymmetry are considered, for these have been radically transformed from the earlier concepts. Within the laws of nature in modern sciences there is an assumption of symmetry; this is part of the contribution to artists in recent times, so it is necessary to understand modern developments in mathematics, with algebra and group theory expanded at the end of the eighteenth century, in order to reveal these new ways of considering symmetry.

1. Symmetry in Modern Mathematics i Symmetry Breaking: Similarity Transformations1

In the last one hundred years, the study of mathematical symmetries has resulted in the formulation of an algebraic theory that has found application in all branches of mathematics, as well as in the natural sciences (physics, chemistry, biology).

In antiquity figures and bodies were called symmetrical when they possessed common measures. For instance, the five regular solids of Plato can be rotated and maintain the same measurements of sides and angles. The human body can be mirrored along the vertical axis without a change in its proportions. Therefore, figures and bodies have common proportions if they possess the same geometric form, that is, if they are similar. For example, the proportional relationships of a circle, square, rectangle, etc.,

1 ‘The modern scientific notion of symmetry begins with the geometric symmetries of objects, both mathematical and physical. A perfect snowflake rotated through 60° about its centre is indistinguishable from its original appearance. Rotating the snowflake transforms it relative to something external. Symmetry transformations of an object leave the initial and final states indistinguishable. Three developments are fundamental: 1., the extension of the concept to “physical symmetries,” 2., the development of “group theory” and its scientific applications, and 3., the increasing importance of “symmetry breaking”’ In: J.L. Heilbron, “Symmetry and Symmetry Breaking,” The Oxford Companion to the History of Modern Science (Oxford: Oxford University Press, 2003). Current Online Version: 2003. elSBN9780199891153. October 2014. 27 are retained, although the dimensions of these figures can be enlarged or decreased.

Therefore, one can say that the form of a figure is determined by the similarity transformations, that leave it unchanged.2 In order to illustrate the form invariance of two similar bodies, Gottfried Wilhelm Leibnitz (1646-1716) used the example of two temples, the temple building itself and a small model: each is indistinguishable from the other, without reference to an external unit of measure, the only difference being the scale.3

Author Ian Stewart, in Why Beauty is Truth: A history of Symmetry, proposes an alternative elucidation of similarity transformations: ‘Symmetry is not a number or a shape, but a certain kind of transformation – a way to move an object. If the object looks the same after being transformed, then the transformation concerned is a symmetry. For instance, a square looks the same if it is rotated through a right angle.’4

Mainzer elaborates: “What is meant by a transformation is a mapping that maps a set of points (for instance, the points of a circle) onto itself with one to one correspondence”.5 Symmetry is congruence to itself.

The similarity transformations that do not alter the size of a body are the transformations (movements) of “rigid” bodies in space, which geometrically are called congruences or isometries (Greek: isos = equal, metron = measure). On the other hand, automorphisms are transformations that leave the structure of space unchanged.

A set of elements (e. g., points, numbers, transformations) is called a group.

The application of group theory in geometry is a matter of locating invariant symmetry characteristics in figures and bodies in relation to groups of transformations, for example rotations, translations or reflections. An explanation of the relationship

2 Mainzer,Symmetries of Nature, 134. 3 Mainzer,Symmetries of Nature, 134. 4 Stewart”Preface” to Why Beauty is Truth, IX. 5 Mainzer,Symmetries of Nature, 134. Hermann Weyl, in his much praised work on symmetry, defines congruences as ‘one-to-one mappings or transformations.’ 28 between groups and symmetry is given by Ian Stewart and applied in the context of geometry. Stewart’s favourite group is the symmetry group of an equilateral triangle.

To the question: what is symmetry? Stewart suggests the substitution of the word symmetry to be reinterpreted as a symmetry [operation]. Objects, in his view, do not possess symmetry alone; they often possess many different symmetries. A symmetry of some mathematical object is a transformation that preserves the object’s structure.

A symmetry is a process rather than a thing – ‘Symmetries are permutations, a permutation is a way to rearrange things. Or better, it is the rule you apply to get the rearrangement’ 6.

Therefore the key words in the definition of a symmetry are: transformation, structure and preserve. In these terms, for an equilateral triangle, the structure has to be preserved, namely, the length of the sides and the size of the angles (60º) as well as the location in the plane. For instance, a rotation of the triangle through a right angle is not a symmetry:

However, a rotation through 120º is a symmetry of the equilateral triangle:

6 Stewart, Why Beauty is Truth, 118. 29

(dots are for reference only and are not part of the structure that is preserved)

An octahedron is inscribed into a cube in such a way that the corners of the octahedron meet the corresponding sides of the cube at the centrepoints of the six square surfaces. Every rotation that turns the octahedron back into itself also leaves the cube invariant and vice versa. Therefore, the group for the cube is the same as for the octahedron. Conversely, a cube can also be inscribed into an octahedron, and in similar way it can be shown that the dodecahedron and the icosahedron are described by means of the same group.

Fig. 15. Symmetry of Cube and Octahedron. In Manizer, Symmetry and Complexity, Fig. 21, page 71.

ii Symmetry and Group Theory

Evariste Galois (1811-1832), had the brilliant idea of applying to solutions of equations the characteristics of symmetry, which remain unchanged under specific transformations, and thereby obtain information on solutions and the solubility of equations. Galois was a French mathematician who, before his tragic death in a duel at the age of 20, had proposed structural and unifying concepts among the most important topics studied in modern algebra. He sought a deeper understanding of the

30 essential conditions that an equation must satisfy in order for it to be solvable by radicals. ‘He formed the group of automorphisms of the ‘field’, obtained by adjoining the roots of the equation.’7

Stewart admits that the Galois theory has severe limitations as it works not with coefficients but with the roots of an equation. In other words, it works with the unknowns, not the knowns. Today, one century later, he adds, you can go to a suitable website, input your equation and it will calculate the Galois group. But Galois had discovered what steps should be taken to solve the problem, that is, which properties of the roots made an equation solvable.8

In Mainzer’s view, the group theory methods conceived by Galois are revolutionary, even independent of equation theory, and ‘stand at the beginning of modern structural mathematics, which was fundamental for physics’. 9

In the decades before World War II, many physicists around the world did not embrace group theory. Stewart recalls that when Hungarian-born physicist Eugene Wigner

(1902-1995) first tried to pursue a career in the USA in the academic setting of

Princeton University, he was not successful:

Group theory was not then a standard part of a physicist training, and his main application was still to the rather specialised area of crystallography. To most physicists group theory looked complicated and unfamiliar, a fatal combination. The quantum physicists, appalled by what was invading their patch described the development as a ‘Gruppenpest’, or ‘group disease’. Wigner had triggered an epidemic and his colleagues did not want to catch it. But Wigner views were prophetic. Group-theoretic methods came to dominate quantum mechanics, because the influence of symmetry is all-pervasive. It predicts existence of particles.10

7 Irving Kaplansky, ed., “Galois, Evariste”, in “Macropaedia,” The New Encyclopaedia Britannica, (Chicago: Encyclopaedia Britannica Inc., 1974). 8 Stewart, Why Beauty is Truth, 117. 9 MainzerSymmetry and Complexity, 76. 10 Stewart, Why Beauty is Truth, 219-220. 31

During the war Wigner, like Heisenberg, von Neumann and Fermi, and other leading mathematical physicists worked on the Manhattan project to construct the atomic bomb. He was awarded the Nobel Prize in Physics in 1963.

2. Symmetry in Physics

The contribution initiated by the mathematicians such as Galois in the development of the group theory methods, have been fundamental in clarifying the symmetries of the laws and theories of the physical sciences in the 19th and 20th centuries. The key concept for a mathematical explanation was based on the invariance of certain groups of transformations underpinning the validity of the geometric laws.11 Similarly, unresolved problems concerning the symmetries of space and time were explained by group theory in mathematical form.

i Symmetry Breaking: Thermodynamics and Phase Transitions

It is a familiar observation that nearly all processes in nature have a preferred direction

– they go one way but not the reverse. Heat flows from hot to cold; an ink droplet disperses in water. These processes are said to be irreversible. Irreversibility is connected with the second law of thermodynamics. The study of thermodynamics investigates the relations between heat and other forms of energy involved in physical and chemical processes. According to the Second Law of Thermodynamics, closed systems without any exchange of energy and matter with their environment, develop to disordered states near thermal equilibrium. The degree of disorder is measured by a quantity called entropy. The entropy always increases to its maximum value. For instance, when a drop of milk is put into coffee, the milk spreads out to a finally disordered and homogeneous mixture of milky coffee. The reverse processes are

11 Mainzer,Symmetries of Nature, 223. 32 never observed.12 In this sense, processes according to the second law of thermodynamics are irreversible with a unique direction of time. In Mainzer’s view, with this law and the irreversible processes of nature assumed in the Second Law of

Thermodynamics, it became possible for the first time to explain a development in nature, as well as Darwin’s evolutionary theory of life.13

The thermodynamic arrow of time is explained by the global expansion of the whole universe leading from states of symmetry to symmetry breaking and diversity with increasing entropy. But ‘in a global sea of entropy, local islands of new order like, e.g., stars, planets and life emerge and disappear’.14

Fig. 16. Spiral Galaxy. In Doczi, The Power of Limits, Fig. 129, page 81.

The emergency of order is made possible by phase transitions of systems interacting with their environment. If equilibrium is understood as a state of symmetry, then phase transition means symmetry breaking. Phase transitions with symmetry breaking can be

12 Mainzer, Symmetry and Complexity, 154. 13 Mainzer, Symmetries of Nature, 224. 14 Mainzer, Symmetry and Complexity, 154. 33 illustrated in many physical systems by lowering their temperature. Water provides a simple example. Above 100 degrees Celsius the system has a high degree of symmetry, because the molecules can move completely freely without any distinction or direction. If the temperature is lowered below 100 degrees Celsius water droplets emerge by passing through a gas-liquid phase transition, and the symmetry is reduced.

If the temperature is lowered down to 0 degrees Celsius, the system passes through a liquid-water / solid-ice phase transition that is associated with a spontaneous decrease in symmetry.15 How do water molecules moving at random in the atmosphere, form a wonderful six-petalled snowflake?

In the framework of modern physics, the emergence of the structural variety in the universe, from elementary particles to stars and living organisms, is modelled by phase transitions and symmetry breaking of equilibrium states.16 For instance, when a liquid is heated uniformly from below, it will spontaneously develop a pattern of hexagonal circulating cells. In Fig. 17, the cells are made visible by metal flakes suspended in fluid.17

Fig. 17. A liquid heated from below develops hexagonal circulating cells. Photo:

M. Velarde, Universidad Complutense, Madrid. In Phillip Ball, The Self-Made

Tapestry, Plate 1, page 25.

15 Mainzer, Symmetry and Complexity, 148. 16 Mainzer, Symmetry and Complexity, 109-110. 17 Philip Ball, The Self-Made Tapestry, 25. 34

Of interest in my own field of ceramics is the observation by D’Arcy Thompson who claimed that if a mass of clay pellets is compressed, they will form shapes close to rhombic dodecahedra; but if they are first made wet, so that they can slide over one another, they show instead square and hexagonal facets like those of the tetrakaidekahedron (with14 faces).18

3. Symmetry in Biology

With living organisms, symmetries may be looked at by the point of view of their special functions. Sometimes new characteristics of symmetry and asymmetry arise as a result of life processes like metabolism, self-reproduction or mutation. Furthermore, the evolution of organisms is explained by biological phase transitions and symmetry breaking, generating the diversity of life.19 Viruses are a good example. They are composed of organic molecules and possess genetic information for self-reproduction.

Viruses are unable to replicate without relying on the nutrients and mechanisms found only in a living cell. The virus then invades the cell, forcing it to make more virus particles.

The model of the virus, (Fig. 18), illustrates the molecule of the so-called adeno-virus

(relating to glands). The shell has the form of a regular Platonic body (icosahedron), with twenty equilateral triangles. Projecting from the 12 corners are thin extensions, which do infect the host cells. The effects of a virus in mammals, produce infection and cancer. To participate in the life of a host cell and to reproduce, the virus particle must trigger an infection and thus give up its symmetry. Its ghostly beauty recalls a space

18 D’Arcy Thompson, “On Growth and Form”. In Philip Ball, The Self-Made Tapestry, 24. 19 Mainzer, Symmetry and Complexity, 199-200. 35 ship from an alien world. The virus particle is a clear example of the fact that the dynamics of life processes require symmetry breaking.20

Fig. 18. Model of virus and its symmetry. In Mainzer, Symmetry and

Complexity, Fig. 59, page 201.

Fig. 19. Amoeba (magnified). In Encyclopaedia Britannica (Chicago: Benton, 1974), Macropadia Vol 1, page 320.

20 Mainzer, Symmetry and Complexity, 200-201. 36

Another example is the amoeba. (Fig. 19) From the point of view of structural form, the amoeba is a single cell organism that is entirely asymmetrical. It has the capacity to form appendices called pseudopodia, or false feet. Motion occurs as an extension of cell fluid, which flows forward inside the advancing pseudopod. Food is taken in and excreted at any point on the cell surface. The amoeba symmetry lies in its perfect functionality, whereby ‘the functions of metabolism, motion and nutrient-transport, etc…, are perfectly adjusted to one-another. In contrast to a geometric, structural symmetry, we deal here with functional symmetry.’21 D’Arcy Thompson had already anticipated a path of research directed at the functional symmetry of living cells, and singled out the amoeba as an example:

In an organism great or small, it is not merely the nature of the motions of the living substance which we must interpret in terms of force (according to kinetics), but also the conformation of the organism itself, whose permanence or equilibrium is explained by the interaction or balance of forces, as described in statics.22

Ideas such as phase transition are important to symmetry breaking, while ideas of functional symmetry provide an extension of geometric structural symmetry. It is important to understand the changes that such new scientific discoveries in the twentieth century have brought about, not only in the interpretation of our physical world, but also in the development of modern art. Artists took ideas from higher- dimensional mathematics and from non-Euclidean geometry23 and used them to radically advance their work. Once again, art becomes another kind of “representation” with relation to scientific views.

In Chapter Three I consider the impact of these changes for artists in the early 20th century, and in Chapter Four I relate these to early ceramic practitioners.

21 Mainzer, Symmetry and Complexity, 201. See also Kirk, Biology Today, 66, 69. 22 D’Arcy Thompson, “Introductory”, in On Growth and Form, Abridged Edition (London: Cambridge University Press, 1961),16. 23 See ‘The Fourth Dimension and Non-Euclidean Geometry' in Chapter Three. 37

CHAPTER THREE: The Influence of the New Geometries in Modern Art and

Symmetry

Introduction

The impetus for an alternative way of considering symmetry was extended through the

“new” geometries such as the fourth dimension and non-Euclidean geometry.

The interconnection between the artists of the twentieth century with either of the new geometries have mostly been ignored or dismissed by art historians and critics; they may have misinterpreted the terms as purely mathematical or purely mystical, missing the variety of views in between.1

Leading to the major discoveries in physics by Albert Einstein, who revolutionised scientific theory with his Special Theory of Relativity in 1905 and the General Theory of

Relativity in 1916, these two separate geometries were attracting the attention of both scientists and artists: they were the non-Euclidean geometry and a new, multidimensional geometry. The curved space of non-Euclidean geometry and the spatial possibilities suggested by a fourth dimension, were initially formulated during the nineteenth century, as an outgrowth of developments in early nineteenth-century geometry.2

1 Linda Dalrymple-Henderson, “Introduction,” in The Fourth Dimension and Non-Euclidean Geometry in Modern Art, rev. ed. (Cambridge, Massachusetts: The MIT Press, 2013), 98. 2 L. D. Henderson, “Introduction,” 97. 39

The Spatial Fourth Dimension

Fig. 20. Claude Bragdon, A Primer of Higher Space: The Fourth Dimension (Rochester, N.Y.: The Manas Press, 1913) Pl.1 (detail). In L. D. Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Plate 1, page. 3.

While the geometries of four or more dimensions could never be identified with a specific historical moment, Henderson suggests that the earliest, most prominent person who brought the attention of the public to the fourth dimension was English philosopher Charles Hinton (1877-1907), who together with others, promulgated the idea that space might possess a higher, unseen fourth dimension. Hinton published his last major book by the title The Fourth Dimension in 1904, after he had settled in the USA.3 He is now perhaps best remembered for his visualisation of the (‘to us unimaginable’) four-dimension, the hypercube, or tesseract, as he called it.4

3 L. D. Henderson, “Introduction,” 97. See also Chapter 5, “The Nineteenth-Century Background,” 127-32. 4 Bragdon provides a striking illustration, or “symbolic representations” of the hypercube, beginning with the geometrical progression from line to plane to cube to hypercube: just as a line contains an infinite number of points or a cube an infinite number of planes, the visually elusive hypercube contains an infinite number of cubes, bounded by eight external cubes. L. D. Henderson, “Reintroduction,” The Fourth Dimension, 4. 40

The first major popularisation of the spatial fourth dimension was a popular fiction book written in 1884 by theologian and educator Edwin Abbot, Flatland: A Romance of Many

Dimensions by a Square, a powerful warning tale of the refusal of individuals in a two- dimensional world to a change of attitude in accepting the idea of higher dimensions.

In addition to popular literature, hyperspace philosophy, initiated by Hinton, was continued and expanded by the Theosophist Claude Bragdon, ‘later America’s foremost theorist on the fourth dimension.’5 And indeed, Theosophy considerably widened the interest in higher dimensions of space, contributing further to the concept’s popularity. In pre-revolutionary Russia, Hinton’s philosophy was developed in a more mystical direction by the writings of the Russian mystic Peter Ouspensky (1878-1947), who started an independent popular tradition of ‘the fourth dimension’. His book,

Tertium Organum, (1911), was the major source of information for members of the

Russian avant-garde interested in higher dimensions.6

In this interest by the avant-garde in the fourth dimension there is the beginning of the effect of this new understanding of science on the practice of artists.

Non-Euclidean Geometry

Non-Euclidean geometry was named for its opposition to Euclid’s parallel postulate, as set forth in the Elements (c. 300 BC), according to which, through a given point, there is only a single line parallel to a given straight line. In Germany the mathematician Karl

Gauss, like others before him, had stated that all attempts to find a proof of the postulate had been unsuccessful, and in 1824 he concluded that an alternative geometry to Euclid’s must be possible. However, he did not publish his findings, and the honour for this remarkable change in the perception of geometry was given to the

5 L. D. Henderson, “The Nineteenth-Century Background,” 127. 6 L. D. Henderson, “Transcending the Present,” 377-79. 41

Russian Nikolai Lobachevsky and to the Hungarian János Bolay, who independently formulated the first system of non- Euclidean geometry, in 1929 and 1932 respectively.

The Lobachevsky-Bolay non-Eucidean geometry formulation is as follows: Through a given point not on a given line, more than one line can be drawn not intersecting the given line. Similarly, the sum of the angles of a triangle will be less than the familiar

180° of Euclidean geometry.7

For several decades the Lobachowsky-Bolay research remained practically unknown.

The visualisation of their geometry was enhanced when in 1868 the Italian mathematician Eugenio Beltrami (1835-1900), proposed the pseudosphere as a model.

(Fig. 21) On this surface of constant negative curvature it is easier to imagine how a group of lines may be parallel, approaching but never intersecting the other, and how the angle sum of a triangle can be less than 180°.8

7 L. D. Henderson, “The Nineteenth Century Background,” 102. 8 L. D. Henderson, “The Nineteenth Century Background,” 102. 42

Fig. 21. Beltrami’s Pseudosphere for the Lobachevsky-Bolay Geometry. Lines M 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.

Karl Gauss, who supported the fundamental change in this extended understanding of geometry, which included surface and space curvature, gave new prestige to the non-

Euclidean geometry, capturing the interest of a younger generation of mathematicians.

Among them was Georg Riemann, who in 1854 at the University of Göttingen offered another alternative to Euclid’s system. He used the surface of the sphere with its constant positive curvature. On the surface of a sphere, space would be unbounded and yet finite. Once space is finite, (as Euclid’s parallel postulate assumes it will be) no

43 line can be drawn parallel to a given line. In fact, all lines will intersect at the poles of the sphere. Furthermore, the sum of the angles of a triangle will be greater than 180°.9

Fig. 22. Riemann’s Geometry Represented on a Sphere. Lines such as l, M and N will always meet. Angles ABC+BCA +CAB > 180°. In L. D. Henderson, Fig. 1.2, page 104.

Riemann’s geometry of positive curvature is thus the opposite of the Lobachevsky-

Bolay geometry on surfaces of constant negative curvature. The measure of curvature in this type of geometry however, has to be constant. But in Riemann’s broad view of geometry, he envisaged also the possibility of surfaces or spaces where curvature may vary. The idea that the appearance of objects moving about in an irregular space might vary, would be of great interest to artists of the early twenty century, such as the

Cubists and Marcel Duchamp.10 These two types of non-Euclidean geometry presume yet again a drastic change of orientation in the familiar physical model world: the possibility of curved space.

9 L. D. Henderson, “The Nineteenth Century Background,” 103. 10 L. D. Henderson, “The Nineteenth Century Background,” 103. 44

Impact of Changes in Science

The philosophical impact of non-Euclidean geometry in the nineteenth century had the effect to shake the underlying basis of mathematics and science that for two thousand years had depended on the truth of Euclid’s axioms. Consequently, the belief in the ability to acquire absolute truth gradually gave way to the recognition of the relativity of knowledge. A succession of scientific discoveries beginning in the 1890s, radically altered the conception of matter and space. They included the discovery of the

Röntgen X-ray (1895), Marie Curie’s isolation of radio-active elements (1898), radioactivity, the structure of the atom and wireless telegraphy. All these phenomena pointed to the existence of an invisible reality beyond the reach of the sense of perception, and it was the ideal ground in which possible higher dimensions could flourish.11

One additional interest in this context is ether physics, as it played a significant part in science and because of the role it acted in art. The concept of the invisible ether, a substance supposed to permeate all space, was often linked with the fourth dimension to explain a variety of phenomena. Attempts were made but failed to establish the existence of the ether, by measuring the relative motion of the earth through it (and thereby also determining a kind of absolute velocity of the earth). Ultimately, after 1919

Relativity Theory would eclipse it to a large degree. Ether had however a remarkable hold on the popular imagination, as it did on occultism, mysticism and theosophy.

Among artists interested in ether were Duchamp and Boccioni.12

11 L. D. Henderson, “Reintroduction,” 15-18. 12 L. D. Henderson, “Reintroduction,” 15-20. See also “Appendix A,” 512. 45

Time as the Fourth Dimension

The definition of time as the fourth dimension was to displace popular interest in higher spaces. The first suggestion that time could be considered to be a fourth dimension was apparently made by Jean-Baptiste d’Alembert, published in his 1754 article in the

Encyclopédie edited by Denis Diderot. In 1895 H. G. Wells used a temporal fourth dimension in his science fiction tale, The Time Machine, which Wells adopted to express his social theory on class struggle in the late nineteenth century.13

The importance of the concept of time in the framework of the fourth dimension was maximised when it became part of Albert Einstein’s Relativity Theory. Art historians have in the past mistakenly associated Cubism and Relativity Theory, by ‘reading back into Cubist literature of 1911 and 1912 the development in physics of a non-Euclidean space-time continuum that was not completed until 1915 or 1916.’14 Indeed, in 1905, when the principles of the Special Theory were published in an article, neither a fourth dimension nor non-Euclidean geometry played any part in the Special Theory. Only in

1908, Hermann Minkowski’s formulation of the space-time continuum created a four- dimensional, geometric representation of Einstein’s theory, with its redefinition of the fourth dimension as time instead of space.15 On the other hand, the non-Euclidean curvature described by Riemann was included in Einstein’s General Relativity Theory, published in 1916. The finite and unbounded universe that Einstein proposed was ‘a

13 L. D. Henderson, “The Nineteenth Century Background,” 111. 14 L. D. Henderson, “Appendix A: The Question of Cubism and Relativity,” 515. 15 L. D. Henderson, “Appendix A: The Question of Cubism and Relativity,” 512-13. In 1908 Minkowski delivered a lecture by the title “Space and Time” to the German Natural Scientists and Physicians at Cologne. Minkowsky first words were revolutionary: ‘The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.’ 513-14. 46 structure curved back upon itself, just as the spherical model of Riemann’s elliptic non-

Euclidean geometry had been’.16

These revolutionary scientific discoveries, over the first two decades of the 20th century were of great interest for many scientists globally, and caught the imagination of artists in Europe and in America because of the radical changes in the interpretation of the physical world. However, Henderson theorises that this new knowledge came to the attention of the public in a delayed manner, partly because of the hostilities of the First

World War, partly because they took place on German soil. Furthermore, Einstein gained great notoriety mainly in 1919, when the findings of an English astronomical expedition to photograph the eclipse were announced at the Royal Society of London.

Star displacement photographed at the rim of the sun had confirmed that light rays from stars were indeed bent by the gravitational mass of the sun. The General Theory of Relativity thus suddenly gained legitimacy and unexpected notoriety;17 in the words of author Henderson, Einstein became ‘the architect of a new world view.’ 18

Impact of Changes in Art

As a consequence of the delayed process of information in France, Einstein’s Relativity

Theories did not have much impact on French artists until the 1920s. Cubism was therefore well established before artists were influenced by Einstein’s temporal space dimension; instead of Relativity, Cubist theory was based on the notion of a higher, unseen fourth dimension of space, developed out of nineteenth century multidimensional geometry.

16 L. D. Henderson, “Appendix A: The Question of Cubism and Relativity,” 515. 17 L. D. Henderson, “Appendix A: The Question of Cubism and Relativity,” 512-15. 18 L. D. Henderson, “Appendix A: The Question of Cubism and Relativity,” 519. 47

The changes in the perception of the physical world, which were brought about by the new discoveries in physics and mathematics in the first decades of the twentieth century, were reflected in a powerful manner in the way artists detached themselves from tradition and embraced alternative kinds of visual expression. Non-Euclidean geometry and the fourth dimension were mainly a symbol of liberation for artists. Belief in the fourth dimension encouraged them to reject visual reality, and the one-point perspective system that had for centuries portrayed the world as three-dimensional.

The “invisible” fourth dimension was for the artist at the same time an attraction and a provocation in the visualisation of the “unimaginable” (Bragdon)19. As a result, one of the most interesting aspects in early 20th century art is the variety of ways in which the fourth dimension was understood and represented in visual terms by the various artists. The fourth dimension was a topic common to artists in nearly every major modern movement; to Cubists, as well as to Marcel Duchamp and Frank Kupka; to the

Italian Futurists, Russian Futurists, to Suprematists and Constructivists; to Dadaists and to members of De Stijl; even the Bauhaus was involved, with Theo van Doesburg lecturing there in 1921, and with Wassily Kandinsky, Paul Klee and Johannes Itten also interested, in their own ways, in the fourth dimension.20

Non-Euclidean geometry was not as popular as the fourth dimension, which had many more non-geometric associations. Artists interested in an alternative geometry were

Duchamp and the Cubists Jean Metzinger and Albert Gleizes, Russian influential poet

Velimir Khlebnikov and painter El Lissitzky. Non-Euclidean geometry, by offering an alternative kind of space (curved space), signified a new freedom from the established laws.

19 Claude Bragdon, A Primer of Higher Space: The Fourth Dimension, Plate 1, “Fig.4,” as shown in Fig. 20, page 33. 20 L. D. Henderson, “Conclusion”, 491-94 and 542, note 35. 48

The Contribution of Marcel Duchamp (1887-1968)

Marcel Duchamp was contemporaneous with many of the artists in the earlier part of the 20th century. His contribution was important to many of these artists.

Marcel Duchamp Portrait i Duchamp and the Cubist Artists

In Paris Duchamp became acquainted with Cubists Gleizes and Metzinger, and

Fernand Léger, and, together with other artists they would carry lively debates about the fourth dimension and the Cubist painting of Braque and Picasso, who were exhibiting their works in a separate gallery at Kahnweiler’s. Another important participant was Maurice Princet, who supplemented and explained the mathematical theories. 21

21 L.D. Henderson, “Marcel Duchamp and the New Geometries,” 233-237. 49

In an early attempt to apply the concept of the fourth dimension in his work, Duchamp created six drawings, which he produced for his canvas Portrait of Chess Players,

(1911) (Fig. 29). The method used was to place several chessboards and chessmen and a few heads in the sketch, representing the minds of the players at various stages of the game. In the final painting the chessmen are located between the heads of the two players and one in the hand of one player. In a 1964 lecture Duchamp explained his line of action: ‘Using the technique of demultiplication in my interpretation of cubist theory, I painted the heads of my two brothers playing chess, not in a garden this time, but in indefinite space.’22 The “indefinite space” was to be the embodiment of the fourth dimension.

Fig. 23. Marcel Duchamp, Portrait of Chess Players, 1911, oil on canvas. . In L.D. Henderson, Fig. 3.2, page 239.

By experimenting with the new visual vocabulary of Cubism, Duchamp turned his attention to ideas about movement and the mechanical, expressed with the faceting of planes found in Picasso and Braque’s paintings. The best attempt was the dynamic and fluid Nude Descending a Staircase, No.2, (Jan. 1912) Fig. 30. However, when

Duchamp tried to exhibit it at the Cubist-dominated Salon des Indépendantes, Albert

Gleizes, chairman of the hanging committee, refused to accept it, unless at least the

22 L.D. Henderson, “Marcel Duchamp and the New Geometries,” The Fourth Dimension, 241. 50 title, inscribed on the canvas, was changed. Duchamp refused to do so and withdrew the picture.23

Fig. 24. Marcel Duchamp, Nude Descending a Staircase, No.2, 1912, oil on

canvas, In L.D. Henderson, Fig. 3.3, page 243.

ii From the “Retinal” to the Conceptual

In 1913 Duchamp decided to abandon the traditional tool and techniques of painting to take the art-making process beyond the visual or “retinal,” as he called it. The

23 Ades, Cox and Hopkins, Marcel Duchamp, 49. Nude Descending a Staircase No.2, was, however, shown in March at an exhibition of Cubism in Barcelona, as well as in Paris at the Salon de la Section d’Or in October 1912. In: J. Turner, ed., “Duchamp Marcel,” Dictionary of Art (New York: Macmillan, 1996), 335. 51 transition from the pictorial to a “mechanical” composition was a radical change even for Duchamp, who had already made many transgressions within the sphere of traditional aesthetics. During this time he intensified his background research in the complex theories of geometries. There is a record of his careful consideration on the new geometries in a collection of notes called A l‘Infinitif (1966). The end result is the product of his ironical outlook and of his scholarship, as he explained to Cabanne, ‘I was interested in introducing the precise and exact aspect of science… It wasn’t for love of science that I did this; on the contrary, it was rather in order to discredit it, mildly, lightly, unimportantly. But irony was present.’24 Henderson summarises

Duchamp standing, ‘an irreverent artist for whom nothing is sacred delves into avant- garde mathematics and science in secret so as to discredit longstanding beliefs still held by the majority of the public.’ 25

iii Fourth Dimension and Non-Euclidean Geometry in Duchamp’s Major Works.

The Bride Stripped Bare by Her Bachelors, Even (The Large Glass), Fig. 31. is dated

1915 to 1923, after Duchamp had left war-torn Europe for New York. The understanding of the title is a love-making machine, made up by a ‘Bride in the upper part and a complex Bachelors Apparatus’ below.’ In connection with the preparation for The Large Glass, Duchamp created The Three Stoppages, in Henderson‘s view,

‘the purest expression of non-Euclidean geometry in early century art,’…but also,

‘playful physics’26.

24 L. D. Henderson, “Marcel Duchamp and the New Geometries,” The Fourth Dimension, 236. 25 L. D. Henderson, “Marcel Duchamp and the New Geometries,” 236. 26 L. D. Henderson, “Marcel Duchamp and the New Geometries,” 246-48. 52

Fig. 25. Marcel Duchamp, The Bride Stripped Bare by Her Bachelors, Even

(The 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.

Duchamp’s attempt to create a new standard metre measurement was based on the geometries of Riemann and Lobachevsky. Interestingly, Duchamp gives a clear definition of purpose for his work, when he was asked by museum curator Katharine

Kuh, which of his work he considered the most important; he replied: ‘The Three

Stoppages of 1913 that was really when I tapped the mainspring of my future. In itself it was not an important work of art, but for me it opened the way – the way to escape from those traditional methods of expression long associated with art’.27 In The Large

Glass, shadows, mirrors and virtual images were complementing the vocabulary of the new geometries, a stimulus to go beyond the traditional; something ‘deliciously subversive’ (Henderson), to challenge so many longstanding truths.

27 Katharine Kuh, “Marcel Duchamp,” in The Artist’s Voice:Talk with Seventeen Artists, 81. 53

Fig. 26. Marcel Duchamp, Three Standard Stoppages, 1913-1914. Three

threads 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.

Most of Duchamp’s work had been thought of as being ephemeral, but not the ideas.

Duchamp himself believed that an artist’s work would not last: ‘A work of art,’ he said,

’had a life of about forty years, after which it became art history.’28 Ephemerality was built into his Ready-mades; that led to the unwitting consignment of the original Bottle

Drier, Bicycle Wheel and of his Fountain (a porcelain urinal) to the dump, almost immediately, like any other obsolete household utensil ─ at odds with their fame.

Marcel Duchamp challenged and redefined the concept of art, and opened the floodgates to most of the post-war avant-garde movements.

28 Ades, Cox and Hopkins, Marcel Duchamp, 206. 54

Impact of Non-Euclidean Geometry and the Fourth Dimension on Surrealism,

Suprematism, Constructivism and Cubism.

In connection with non-Euclidean geometry and the fourth dimension it is appropriate to look at a body of work in the ceramic field produced in the early decades of the 20th century and which has remained little explored in the study of ceramics. Often ceramic pieces and clay sculptures were produced by artists, whose art practice was mainly devoted to painting, which was attracting the principal attention of the art historians. One possible reason for the apparent neglect is that not all the artists who were engaged with clay works were actually themselves potters, but used the works of others to investigate the spatial possibilities of the clay medium and/or wanted to illustrate the rejection of realism, a trend present in nearly every major movement of the period. The practice of ceramic art was prevalent particularly in Surrealism,

Suprematism, Constructivism and Cubism.

Surrealism

Under the guidance of André Breton, surrealist principles were based on the theories of

Sigmund Freud. Breton saw the unconscious as the wellspring of the imagination and sought to release the creative potential, involving a strong element of surprise and of unexpected juxtapositions.

Salvador Dalí (1904-1989)

One contribution by Salvador Dalí to ceramics was the decoration of a collection of porcelain plates on which his Surrealistic art seems in many ways to satisfy the principles set in Breton’s manifesto, which focused upon “dreams, childhood and madness as states in which the imagination was accepted and free of utilitarian 55 consideration29. Dalí’s porcelain plates convey his consummate draftsmanship and the usage of the double image, the unexpected juxtapositions and the ever present element of surprise.

Fig. 27. Salvador Dalí, Dance of the Flower Maidens, design by Dalí,

watercolour over pencil. ©Fundacion Gala-Salvador Dalí.

http://www.dali.com/blog/category/interpretations-of-dali/page/2/ (accessed

15.5.2015).

Figure 27, by the title ‘Dance of the Flower Maidens’, is an impressive surrealist example, originally created as a porcelain dinner plate design for E. Helman, president of the Castleton China Company of New York City.30 Dalí uses perspective from

29 Jane Turner, ed., “Surrealism”, in Dictionary of Art, (London: MacMillan, 1996), 17-24. 30 http:www.dali.com/blog/category/interpretations-of-dali/page/2/ (accessed 15.5.2015). 56 below, enhanced by the classic architectural columns leading the eye to the centre of the work, but then he breaks the symmetry by employing asymmetrical elements, like the uneven spacing, random posture, gesture and clothing of four revelling female maidens (rather than the classical three Graces). In the centre, birds are flying in a pattern that forms a human face, in the ambiguity of double-imagery that Dalí uses often in his surrealist compositions.

Constructivism

Constructivism was another avant-garde movement in 20th-Century visual arts, including painting, sculpture, design, architecture, and ceramics. The term was first coined by artists in Russia in 1921, but was inspired earlier by abstract geometric constructions of Vladimir Tatlin (1913-14).

Constructivism has been later used to evoke a continuing tradition of geometric abstract art that is ‘constructed’ from visual elements such as lines and planes, and is characterised by precision, clear order, absence of superfluous elements, and the use of contemporary materials.31 Early in the century in Russia a period of enthusiasm fostered high interest in the application of constructivist ideas in many fields of the visual arts, including ceramic art.

El Lissitzky (1890-1941)

Lissitzky was one of the most gifted representatives of Constructivism in Russia; he was an architect, painter, sculptor, designer, illustrator and also a ceramicist. Lissitzky’s life-time involvement with abstract art began in 1919 soon after he met artist Kazemir

31 Turner, ed., “Constructivism” in Dictionary of Art, 767-772. 57

Malevich, whose geometric system, Suprematism, was very influential at the time, and became a convert to its geometric forms.

The spatial fourth dimension was very popular among the Russian Futurist painters and poets before the 1017 Revolution, whereas non-Euclidean geometry was rarely mentioned. Applications of the curved spaces of the geometries of Lobachevsky and

Riemann did not appear in paintings until the early 1920s, mainly as symbols of freedom from the constraints of the past. Einstein’s General Theory of Relativity played a central part not only in reinterpreting the concept of spatial fourth dimension as time, but it also helped to popularise the concept of curved space, providing an incentive to El Lissitzky and others to explore it in their art. 32

Between the end of 1921 and 1924 Lissitzky lived and worked in Germany. Although

he was initially reluctant to apply his distinctive geometric planes to functional objects,

it was at this time that his abstract pictures known as ‘Prouns’ (an acronym In Russian

for ‘project for the affirmation of the new’), began to be applied to designs for a group

of ceramics.33

32 L. Henderson, “Transcending the Present: The Fourth Dimension in the Philosophy of Ouspensky and in Russian Futurism and Suprematism,” in The Fourth Dimension and Non- Euclidean Geometry in Modern Art, 374. 33 http://www.powerhousemuseum.com/collection/database/?irn=319607 |access date=15 May 2015| 58

Fig. 28. El Lissitzky, Plate. Unglazed earthenware, designed by Lissitzky in

Germany, about 1923. Depth 26 mm, diameter 119mm. © Images for research

only. http://www.powerhousemuseum.com/collection/database/?irn=319607

(accessed 15.5.2015).

The plate (Fig. 28) designed by El Lissitzky in Germany in 1923 is of unglazed

earthenware, made by an unknown potter. It is decorated in red enamel, sprayed in a

stensil like manner (shablonen décor), with geometric motifs. Three red circles of

different sizes decorate one side of the plate. The other side has two red curved

rectangular bands of two different lengths.34 Lissitzky positions his coloured

geometrical shapes in apparent asymmetry; and the curved lines of the rectangles as

34 http://www.powerhousemuseum.com/collection/database/?irn=319607 (accessed 15.5.2015) (publisher=Power house Museum, Australia). 59

well as the circles on the curved walls of the plate connect with the concept of curved

space, proposed by non-Euclidean geometry.

Suprematism

Suprematism was a Russian abstract art movement developed circa 1915, characterised by simple geometrical shapes. Sometimes confusion arises because several artists, formerly part of the Suprematist movement, like El Lissitsky or

Rodchenko, soon became also exponents of the culture of materials (Constructivism).

Art critic Jean Claude Marcadé35 states that Constructivism and Suprematism are

‘antagonists.’ Constructivism aims to employ material as foundation, it involves the cult of the object. On the other hand, Suprematism was born of an awareness of the insignificance of the object. “It is an active negation of the world of objects.”36

Kasimir Malevich (1878-1935)

Born in Kiev, Ukraine, Malevich was a Russian painter, printmaker, writer, and is considered one of the most important avant-gard ceramicists.37 For Malevich,

Suprematism remained a mystical experience associated with concepts of the fourth dimension, as explored in the mystical speculations of Russian mystic Uspensky.

Malevich said that the simple geometrical suprematist shapes, “are not an aerial view of the earth. Aerial vision has not given rise to new geometrical forms, abstractly conceived by viewing forms from above. It explains the suprematist liberation from the

(35 Jean-Claude Marcadé, Kasimir Malewitsch zum 100 Geburtstag (Köln: Wienand, 1978), 182- 195. 36Marcadé, 183. 37 Clark, Shards, 334-335. 60 terrestrial gravity of objects.”38 As a potter, Malevich produced functional ware in

Suprematist style, outstanding in their design.

Fig. 29. Kasimir Malevich, Design for a Platter (year not given). In

Kasimir Malewitsch zum 100 Geburtstag. Page 205.

‘Design for a Platter’, Fig 29, (oil on plate) has the geometrical shapes traced on a horizontal surface, within the framework of a Suprematist picture space. Symmetry is still present on the flat surface of the design (the large circles and some geometric

38 Marcadé, 189. 61 shapes), whereas on the curvature of a finished platter they belong to the realm of non-

Euclidean geometry.

Malevich experimented with plaster constructions called Architechtons, (cubes and parallelepipedes); it was an attempt to accomplish a dramatic move from the pictorial plane to spatial construction. Built in a similar distinctive quality, his iconic Suprematist

Teapot was Malevich first work in porcelain, built at the Russian State Porcelain

Factory in Petrograd. Constructed from contrasting geometric volumes (cylinder, cube, rectangles, sphere), the teapot may look very complex for a functional vessel. In a similar style he built the cups, of which the traditional vertical volume is slashed in half, and called “half cup;” the handle, a plane rectangle, is set in contrast with the partially round volume of the cup’s wall.39

39 Yevgenia Petrova, ed., Kazimir Malevich in the Russian Museum, trans. K MacInnes (State Russian Museum: Kiblitsky, 2000). For images, see Catalogue, 317-388. 62

Fig.30. Kasimir Malevich, Suprematist Teapot and Cups. Porcelain. In G.Clark, Shards, 334

Cubism and the New Geometries

Cubism is the movement that perhaps best tried to illustrate the essential qualities of a mathematical concept of the fourth dimension, and of the geometrical asymmetry of non-Euclidean geometry. In the ‘Introduction’ to A Cubist Reader, editors Mark Antliff and Patricia Leighten have clarified misconceptions common to last century’s historians of the movement. The origins of Cubism have been generally attributed to the efforts of artists Pablo Picasso and Georges Braque. This interpretation was the assumption of influential art critic Edward F. Fry, whose anthology of selected writings and

63 introductory text in Cubism, did much to shape the literature on Cubism by other scholars of modernism since its appearance in 1966.40

The premise that Picasso and Braque were “leaders” and “inventors” of the movement and the others were “followers”, had been postulated in 1915 by the art dealer Daniel-

Henry Kahnweiler (while residing in neutral Switzerland), in his book Der Weg zum

Kubismus 41(1920; published in English as The Way to Cubism in 1949). Kahnweiler’s postulate, privileging Picasso and Braque in light of the philosophy of Immanuel Kant, − and later adopting the neo-Kantian terminology of the so-called analytical and synthetic phases of their development – was accepted by critics and historians, including Alfred

Barr, Clement Greenberg and John Holding. This formalist interpretation of cubism was also taken up by Edward Fry and dominated the movement from the 1950s; it was widely used ‘for the reminder of the century.’42 Art historians have in the meantime rewritten the history of Cubism, whereby a very complex milieu of intellectual, artistic, political and social ferment in the early stages of the movement is taken into account, and all individual artists are examined in their own stylistic differences.43

In the context of my research, and in regard to the contribution of ‘the new geometries’ in the development of Cubism, Antliff and Leighten point out that Fry excluded and denied Gleizes and Metzinger’s claim that their innovations were related to the theories of non-Euclidean geometry and the fourth dimension; their references, as Fry notes,

‘served only to obscure the understanding of Cubism with a pseudo-scientific mysticism.’44 However, in the essay Du Cubism, published in 1912, authors Gleizes

40 Mark Antliff and Patricia Leighten, eds., “Introduction” to A Cubist Reader: Documents and Criticism, 1906-1914 (Chicago: The University of Chicago Press, 2008), 1-2. Formalism’s principal philosophical roots have been traced to the philosophy of Immanuel Kant, whose theory of aesthetics and legacy in the development of formalism were foundation to Edward Fry’s interpretation of Cubism. See Lucien Krukowsky, “Formalism,” in Encyclopedia of Aesthetics, ed. Michael Kelly (Oxford: Oxford University Press, !998), 213-16. 41 Antliff and Leighten, 2. 42 Antliff and Leighten, eds., “Introduction,” 2-6. 43 Antliff and Leighten, eds., “Introduction,” 5-11. 44 Antliff and Leighten, eds., “Introduction,” 5. 64 and Metzinger clearly identify the indebtedness of Cubism. ‘If we wished to tie the painters’ space to a particular geometry, we should have to refer it to the non-

Euclidean scholars; we should have to study, at some length, certain of Rieman’s [sic] theorems’ 45.

Information about multidimensional and non-Euclidean geometry was provided to the artists in Paris by three documented sources. A direct connection was through the

‘theoretician of mathematics,’ Maurice Princet, their insurance actuary friend. Linda

Henderson admits that documents prove that the geometry that Princet taught was the new geometry46. The most important written sources for the Cubists were the books of

Henri Poincaré, a renowned mathematician, whose popular scientific texts advocated non-Euclidean geometry and the possibility of higher dimensions. A textual comparison of Gleizes and Metzinger’s Du Cubism with Poincaré’s La Science et l’Hypothèse of

1902, demonstrate that the painters had studied closely Poincaré’s writings. Duchamp, who was also a friend of Princet, mentions several times the name of Poincaré in his notes for the Large Glass.47

The third source which provided the Cubists with scholarly information was by the geometer Esprit Jouffret’s Traité Elémentaire de Géométrie à Quatre Dimensions

(1903). Jouffret’s text explained the notion of higher dimensions of space, but he also incorporated the ideas of Poincaré48 and Hinton on how to obtain a representation of higher dimensions. Jouffret believed with conviction in the mathematical value of multi-

45 L. D. Henderson, “Cubism and the New Geometries,” The Fourth Dimension, 145. 46 L. D. Henderson, “Cubism and the New Geometries,” 171-73. 47 L. D. Henderson, “Cubism and the New Geometries,” 173-74. 48 Henri Poincaré (1854-1912), was one of intellectual giants of his era. He taught at the Université de Paris from 1881 to 1912; his courses ranged from pure mathematics to mathematical physics and celestial mechanics. In Henderson , “Notes to Chapter 2,’” note 69, The Fourth Dimension, 585. 65 dimensional geometry, but he was of the opinion that the visualisation of higher dimensions was impossible.49

Picasso and the Fourth Dimension

In this section Picasso’s contribution is examined, and in Chapter Four his ceramics are considered in terms of their influence on later ceramicists and the breaking of symmetry.

Linda Henderson proposes a considerably suggestive juxtaposition of Jouffret’s sophisticated analytical approach to multidimensional geometry (Fig. 31) and Picasso’s

Portrait of Ambroise Vollard (1909) (Fig. 32), indicating the possibility of a perceived

‘causal relationship’ (Henderson), between Jouffret’s diagram and Vollard’s portrait.

Images unavailable due to copyright restrictions

Fig. 31. Perspective Cavalière of Fig. 32. Pablo Picasso, Portrait of Sixteen Fundamental Octahedrons of Ambroise Vollard, 1910, oil on canvas. In an Ikosatetrahedroid, from E. Jouffret. L. D. Henderson, Fig. 2.4, page 161. In Traité Elémentaire de Géométrie à Quatre Dimensions. In L. D. Henderson, Fig. 2.3, page 160.

49 L. D. Henderson, “Cubism and the New Geometries,” 174-75. 66

Jouffret’s Perspective Cavalière, (Fig. 31) a see-through view of triangular shapes representing a variety of planes and angles seen from different points of view, displays an impressive correlation to Picasso’s Portrait of Ambroise Vollard, (Fig. 32). The shading of certain facets create ‘shifting relationships that contribute to a general shimmering quality of iridescence’50 in both Jouffret’s diagram as well as in Picasso’s portrait of Vollard.

Henderson however, denies categorically that ‘in no way is a causal relationship being suggested between n-dimensional geometry and the development of the art of Picasso and Braque. Picasso’s art was the product of his own artistic genius in its quest for alternatives to the classical figural tradition and to Renaissance perspective space.’51

In addition, Henderson joins the majority of the critics of the 1970s, by claiming that the origins of Cubism (including the conception of the painting Les Demoiselles d’Avignon), are to be found within art itself, particularly in tribal sculpture and in the work of Paul

Cézanne.52

In Henderson’s opinion, it is impossible to establish the exact time when the fourth dimension or the non - Euclidean geometry were first mentioned in the Cubist circle frequented by Picasso; likewise there is no accurate evidence to determine the influence of mathematician Princet on Braque and on Picasso’s art by way of the new geometries, although she agrees that ‘Princet was a member of the group around

Picasso by at least the middle of 1907, and probably earlier, and that the new

50 L. D. Henderson, “Cubism and the New Geometries,” 159. 51 L. D. Henderson, “Cubism and the New Geometries.” 150. 52 Henderson states: “Of course the multiple viewpoints in Cubism had a specific artistic source in the painting of Cézanne. Cézanne’s influence had prompted Picasso to combine several views in early paintings such as Les Demoiselles d’Avignon as an initial protest against perspective…as paintings of the years 1909 and early 1010 such as Seated Nude and the Portrait of Villard. From this stage of Cubism came Metzinger’s theory of the artist’s movement about his object and the visual inspiration for much of Puteaux Cubist painting. At this point, n- dimensional geometry intervened, providing visual parallels and the theoretical justification for a pictorial space based on tactile and motor sensations.” See: L. D. Henderson, “Cubism and the New Geometries,” 188. 67 geometries may well have served as a temporary stimulus for Picasso.’53 Henderson offers an avalanche of contrasting opinions of critics, dealers, theoreticians, as well as of artists themselves, admitting the difficulty in ascertaining the degree to which

Picasso and Braque were influenced in their art by Princet in the formative years of

Cubism.54

For Henderson, the most general usage of the fourth dimension for the Cubists was to indicate ‘a higher reality, a transcendental truth that was to be discovered individually by each artist,’ as Gleizes and Metzinger explain in Du Cubism (where the fourth dimension is implied but not mentioned). This new freedom for the artists was also confirmed by critic and poet Guillaume Apollinaire in 1912, who stated that ‘it is to the fourth dimension alone that we owe this new norm of the perfect.’55 The most frequent deformation or distortion in Cubist painting was the breaking up of a figure into facets, a technique related to the Cubist’s rejection of perspective in favour of multiple viewpoints, but also suggesting the complexity of a higher-dimensional body. By merging figure and space, often with faceting, the three-dimensional perception of the figure was also destroyed.

In the 2013 revised edition of her book, Henderson timidly revises her opinion in an endnote, by agreeing with a more recent critical evaluation, which recognizes Princet’s importance (with the new geometries) for the evolution of Picasso’s art. That is, in her view, only after 1909; therefore it does not include the act of conception of the germinal canvas of Les Demoiselles d’Avignon, completed in 1907. Henderson agrees that:

Despite Picasso’s denial of Princet (he made other contradictory statements as well), the fourth dimension was too ubiquitous for him not to have been well aware of it, and its impact, beginning in ca.1909, seems quite certain, along with that of contemporary science. I have thus removed the overly cautious

53 L. D. Henderson, “Cubism and the New Geometries,” 171-72. 54 L. D. Henderson, “Cubism and the New Geometries,” 162. 55 L. D. Henderson, “Cubism and the New Geometries,” 181-82. 68

tone about Picasso in two places in the original book (more characteristic of views of the artist in the 1970s).56

Arthur I. Miller, in his survey of the period, Einstein and Picasso, disagrees with

Henderson, by backdating the impact of the new geometries on Picasso’s art to the time of the elaborate and stressful conception of Les Demoiselles d’Avignon. Very helpful to sustain his thesis are some of the hundreds of preparatory drawings and paintings associated with the Demoiselles, from 1906 to 1908. Picasso’s own sketches, collected into Carnets or notebooks, are of great value because they provide an insight into the creative thinking of the artist, ‘with false starts and dead ends ’.57

In Fig. 33, Composition study with Seven figures for The Demoiselles d’Avignon, the original group of five women, a sailor and a student, are depicted in the very first sketch of winter 1906-1907. Miller draws our attention to the squatting demoiselle on the right- hand side, being the most challenging motif to interpret, because it went through the most far-reaching metamorphosis. She is seated, naked, in front of the sailor in a direct attempt to attract his attention, her head in profile.

56 L. D. Henderson, “Notes to Chapter 2,” note 61, 584. Picasso had emphatically denied Princet’s role in the development of his art, in answer to Alfred Barr’s questionnaire of October 1945. 57 Arthur I. Miller, “How Picasso Discovered Les Demoiselles d’Avignon,” in Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc (New York: Basic Books, 2001), 106-117. 69

Image unavailable due to copyright restrictions

Fig. 33. Pablo Picasso, Composition Study with Seven Figures for Les Demoiselles d’ Avignon. Garnet 2, winter 1906-1907. In A. Miller, page 107.

The major changes envisaged for the face of the squatting demoiselle are revealed through drawings in Picasso’s later sketchbooks, also illustrated in Miller’s study. The final version of the demoiselle’s face, Fig. 34, is the closest image to be transferred to the painting; it was, in Miller’s view, ‘a projection onto the plane of the canvas from the fourth dimension, as Picasso understood this term in 1907 through Poincaré’s writings.’58 In my opinion, if Picasso, at this stage of his work, had seen Jouffret’s diagrams, with their extreme faceting generated by rotating complex polyhedra in order to obtain different perspectives, they could have provided not only the idea for faceting the image, but also the clue as to how to inform geometrically his African-inspired masks/faces. In particular, the squatting demoiselle is in the final version placed in a

58 Miller, “How Picasso Discovered Les Demoiselles d’ Avignon,” 113. Poincaré suggested how ‘we may picture a world of four dimensions’ in the following way: The images of external objects are painted on the retina, which is a plane of two dimensions; these are perspectives. But as eye and objects are movable, we see in succession different perspectives of the same body taken from different points of view Well, in the same way that we draw the perspective of a three-dimensional figure on a canvas of three (or two) dimensions, so we can draw that of a four-dimensional figure from different point of view. This is only a game for the geometer. Imagine that the different perspectives of one and the same object succeed one another (Miller, 105). I must say however, that Picasso saw that the different perspectives should be shown not as a succession of perspectives, but in spatial simultaneity. 70 grotesquely impossible posture, with her back facing the picture plane and her head rotated 180 degrees as if on a swivel, eyes distinctly different and off line, and a face that is ‘shockingly hideous’ in comparison to the others (Fig 34).

Images unavailable due to copyright restrictions

Fig. 34. Pablo Picasso, Squatting Fig. 35. Pablo Picasso, Les Demoiselle (Study for Les Demoiselles d’ Avignon, 1907, the Demoiselles d’ Avignon), Paris, Museum of Modern Art, New York. spring 1907. In A. Miller, Fig. 4.11, In A. Miller, Fig. 4.1, page 90. page 113.

In order to emphasise asymmetry and movement, Picasso has efficiently accentuated light and shade areas, not in the traditional chiaro-scuro method but in an apparently erratic way − another dramatic innovation, a seeming act of rebellion to tradition and imposed rules. Stylised limbs and postures are off-balance and asymmetric. Picasso’s intent to represent realism transformed into geometries is a major revolutionary innovation in art; it is strongly evident already in his first Cubist canvas, Les 71

Demoiselles: the breast’s contours are semicircles, cones, squares and trapezoids.

Picasso’s geometric language, the key to his discovery, became the hallmark of

Cubism.

When the new geometries impacted on artists, these ideas flowed through into their ceramics disrupting the earlier traditions of symmetry. The influence of these art movements, together with the impact of other cultures, caused ceramicists to respond in ways that often lead to the breaking of symmetry, and which have connections to my own ceramic practice.

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CHAPTER FOUR – New Initiatives in Ceramics and Symmetry

Introduction

In this chapter I consider the work of Pablo Picasso, Peter Voulkos, Hans Coper and

George Ohr as recent leading ceramicists who have championed the spirit of innovation in ceramics by subverting the tradional concept of symmetrical form. They worked in times when clay aesthetics were prescriptive and tied closely to traditional symmetry rules of the harmony of proportions as described in Chapter One. These artists were chosen to be representative of their time.

The earliest is the American George Ohr (1857-1918), however, as his work was unknown until 1947, I will consider him last. Pablo Picasso (1881-1973), starting late in life in1947, invented a whole new approach to ceramics. Peter Voulkos (1924-2002) in

America and Hans Coper (1920-1981) in England were working at a similar period to

Picasso.

At the end of this discussion of the work of the 20th Century ceramicists, I consider the contemporary English ceramic artist Edmund de Waal.

Symmetry and the asymmetrical may be seen like two sides of a coin, they complement each other. Asymmetry, as defined by the dictionary, signifies a lack of symmetry, its dependence is revealed in the etymology. In wheelthrown pottery, symmetry is the starting point; if you like, a mechanical happening. The breaking of the symmetry is a deliberate resolve, a decision to impose a mark, a personal signature exerted on a perfect shape; the bending of a will.

73

Pablo Picasso

Harald Theil’s study of the “Preliminary Drawings for Picasso’s Ceramics” has provided a remarkable insight, with documentary illustrations, into the artist’s ceramic design process, as well as in the development of an idea, culminating in the final ceramic object and this explains the development of his use of the new geometry.1

Image unavailable due to copyright restrictions

Fig. 36 Pablo Picasso, Studies for Ceramic, Zoomorphic Forms, 1947. In

Theil, “Preliminary Drawings,” Picasso and Ceramics, 103.

1 Harald Theil, “The Preliminary Drawings for Picasso’s Ceramics,” in Picasso and Ceramics (Toronto, Ont.: Gardiner Museum of Ceramic Art, 2004), [91-117] 74

Image unavailable due to copyright restrictions

Fig. 37 Pablo Picasso, Large Bird on a Base, 1947. 71x40x24 cm. In Theil,

“Preliminary Drawings,” Picasso and Ceramics, 102.

In connection with my research, however, the most informative aspect is what Theil calls ‘a new formal language,’2 that is, Picasso was focussing on a system of signs based on a geometry characterised by curved lines, oval shapes and circles. This new formal language, which at first developed in the field of drawing and lithography, was soon extended to three dimensional sketches, including his preliminary drawings for ceramics. The use of ovoids for the basic shape of zoomorphic forms is extensive

(owl, large birds, reclining kid).3 For the stylised bull Picasso made use of a variety of forms, derived from symmetrical and asymmetrical basic shapes, from circular, oval, or irregular curvature, to the curvilinear trapezoidal and conical, the parabola (as in the

2 Theil, ‘A New Formal Language’ 112. 3 Concerning his use of ovoid structures, Picasso observed that ‘When you start with a portrait and work by a process of elimination towards purity of form, smoothness and economy of volume, you inevitably finish up with an egg.’ Theil, “Preliminary Drawings,’ 108-109. 75 shape of the horns), to elliptic and hyperbolic forms ─ in a word, all the gamut of the non-Euclidean geometric space. From the earliest beginnings of the Cubist period, it is assumed that Picasso was aware of the critical and provocative idea of curved space,

‘a natural appeal to early modern artists’4 and that he would be familiar with the concept of non-Eucliden geometry, which, together with the fourth dimension, was discussed at length with a mathematician friend, Maurice Princet5.

Image unavailable due to copyright restrictions

Fig. 38 Pablo Picasso, Studies of Bull,1946. In Theil, “Preliminary Drawings,”

Picasso and Ceramics, 114.

4 Linda Henderson, “Non Euclidean Geometry,” The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 105. 5 See section “Cubism and the New Geometries” of Chapter Tree of my exegesis. as well as the following section “Picasso and the Fourth Dimension.” 76

Image unavailable due to copyright restrictions

Fig. 39 Pablo Picasso, The Bull, 1946, lithograph. In Theil, “Preliminary

Drawings,” Picasso and Ceramics, 113.

Pablo Picasso has an unusual place in the history of ceramics, as he was not a potter in the traditional sense. In his work Picasso appropriated freshly-thrown basic forms of prepared containers for him by professional potters. With them he created a new identity in clay, by reinventing forms and surfaces, but also by handling volume and surface that transformed the object into a new image and a concept.

Picasso was not the first European to do so, and he was not alone. Basque artist

Francisco Durrio (1868- 1940), his first artist-mentor in Paris, showed the young

Picasso some of Paul Gauguin’s ceramics already in 1906, and encouraged him to

77 explore hand-built clay figures. He also showed him how ceramic jugs and vases could be turned into figurative sculptures.6

Picasso had used clay as a medium for sculptures and for small clay pieces prior to

1946; it was in that year that the artist, then 65, became very interested in ceramics, when he first visited Vallauris, a small town in the south of France, which since Roman times had been running a major pottery industry. One of the many potteries still working was run by Georges Ramié (1901-1976) and his wife Suzanne, who had called their business “Madoura”. When Picasso returned in Vallauris a year later, he was carrying with him many drawings and notes, showing sufficient experience and invention to attempt quite elaborate experiments.

At Madoura he reached a working agreement and was given Jules Agard, ‘the best thrower in the world,’ according to Picasso, to help with the making of the works.7

Agard would throw small bottles and Picasso did not waste any time in transforming them (the next morning), when they could be twisted in every direction without being broken, into birds or little statuettes of women. ‘A slight pressure is exerted and the woman is seated, crouching or kneeling.’8 Experimentation was a driving force in all the stages of his work; he was prolific as he was inventive. By exploiting the spatial possibilities of the medium and through the integration of form and decoration he eliminated the illusion of perspective: ‘a vase becomes a woman, a plate becomes a face, a dish becomes a bullring’.9 For the surface treatment Picasso explored methods and results with enamels, lustres and commercial glazes, in the end opting for the potter’s slips: clay thinned with water and coloured with metallic oxides, like manganese, iron copper and cobalt. “In four days he worked on a hundred or so

6 Paul Bourassa, “Encounters with Ceramics,” [25-87] in Picasso and Ceramics, trans. Charles Penwarden and John Tittensor, (Toronto, Ont.: Gardiner Museum of Ceramic Art, 2004), 27-35. 7 Foulem and Bourassa, “Ceramics: Sources and Resources,” [155-253], in Picasso and Ceramics, 164. 8 Foulem and Bourassa, “Ceramics: Sources and Resources,” 164. 9 Yvonne G.J.M.Joris,“Preface,” Pablo Picasso: Ceramics, trans. J. Tucker (Amsterdam: Waanders Uitgevers, Zwolle, 2006), 7. 78 plates, which was pretty much all there was,’ Jules Agard recalled. ‘ In the end a mould worker was taken on to appease the Master’s enormous appetite.’10

Image unavailable due to copyright restrictions

Fig. 40 .Pablo Picasso, ‘Bourrache Provençal’ with Woman, Child and Flower

(1952). 61x40x26 cm. In Picasso and Ceramics, 245. Musée d’Art Moderne,

Saint-Etienne. Photo Yves Bresson.

On a small vessel for olive oil, called Bourrache Provençal, Picasso used the negative space between the neck and its handle and incorporated it into the form to represent the back of the woman’s head. With this highly unusual ceramic design he introduced a new element into ceramic art.11

10 Foulem and Bourassa, “Ceramics: Sources and Resources,” 172. Picasso’s glazes overpainted with slips, would not be accepted by the purists and considered as defects; but for Picasso they broke the monotony of a surface he saw as too smooth, too perfect and too close to the mass-produced in appearance. In 1950 Picasso declared that he no longer had anything to learn from potters: “What could they teach me, because they knew nothing. Just a few recipes!’ Foulem and Bourassa, 188.. 11 Foulem and Bourassa, “Ceramics: Sources and Resources,” 244. 79

Similarly, with another masterpiece, Pitcher with Open Vase, Picasso’s inventive power created ‘the first truly conceptual work in the history of ceramics.’12 He used a sturdy, wheelthrown jug, and with a radical gesture he cut wide open the side of the jug to reveal the volume inside the vessel. By painting in black a part of the jug he would emphasise the silhouette of the bottle which had been cut out, against the white clay body of the interior volume. As a result of that, he was turning negative into positive,

‘opening the door to ceramic for ideas and concepts.’13

Image unavailable due to copyright restrictions

12 Foulem and Bourassa, “Ceramics: Sources and Resources,” 244. 13 Foulem and Bourassa, “Ceramics: Sources and Resources,” 244. 80

Fig. 41 Pablo Picasso, Pitcher with Open Vase 1954. H. 38cm. Private

collection. In Foulem and Bourassa, “Ceramics: Sources and Resources,”

Picasso and Ceramics, 247.

Peter Voulkos

Image unavailable due to copyright restrictions

Fig. 42. In Glandale Avenue studio, Los Angeles, 1959 In: R. Slivka, Peter Voulkos, Fig. 50, page 78.

81

The episode of Peter Voulkos in the history of ceramics arouses a certain interest because the invention of new expressions in ceramic is focussed on one small group of individuals headed by Peter Voulkos. The impact of their work however, does not remain an isolated episode (as in the case of George Ohr), but won respect beyond the small domain of craft, in the wide world of contemporary art. The breaking of the symmetry for Voulkos meant the breaking of traditions, transgressing artistic boundaries and inventing new expressions. Although the aesthetics of his work has not as yet been assessed in its own right, as an individual Voulkos may be considered one of the prime movers of symmetry breaking in the world of ceramics.

Peter Voulkos, is considered to be one of the most influential potters of the last one hundred years in the USA. His legacy is not limited to the outstanding body of work he produced, but derives also from his innovative (some say revolutionary) methods of using and handling of clay. Voulkos had opened a new avenue for the humble clay material in the field of aesthetics. He was a leading force among a group of young artists in Los Angeles who, in the mid-1950s, challenged studio pottery’s traditional focus on utilitarian ware by extending the traditional use of clay.

Even before his graduation from college, Voulkos was able to set up his own studio in a brick-making factory by the name of the Archie Bray Foundation in his native Montana.

With a colleague, Rudy Autio, he could practise and experiment with clay, mainly throwing functional vessel forms. Two examples of this early period are the albarello- style vessel, Covered Jar, 1953, Fig. 43, and Rice Bottle, 1952-53, Fig. 44.

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Fig. 43. Peter Voukos, Covered Jar. 1953. Height 43 cm. In R. Slivka, Peter Voukos, Fig. 3, page 7. Photograph by Ferdinand Boesch.

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Fig. 44 Peter Voukos, Bottle, 1953. Height 53 cm. In R. Slivka, Peter Voukos, Fig. 4, page 10. Photograph by Joseph Schopplein.

The Foundation was not a school, but an open workshop for ceramic arts; workshops were sponsored there for visiting ceramic artists, including British potter Bernard Leach who was at that time the most respected and influential ceramicist in Europe, and the

Japanese artist Shoji Hamada. Voulkos was very impressed and fascinated by

Hamada’s approach to pottery and his use of the accidental as a positive event in the creation of art. Autio recalled that at the time of the Hamada’s workshop in 1952, he and Voulkos had no real appreciation for Oriental ceramics. He said, ‘We had never,

83 ever heard about Zen.’14 They were however, moved and excited by Hamada’s artistry, by his intimate way of handling the clay, ‘sensing that there was a kind of spiritual connection to it, that it was more than just making a pot.’15 The accidental and the irregularities that were allowed to surface because of the potter’s unassuming restraint, and the concepts of asymmetry associated with the bowl of the tea ceremony were the seductive concepts of the Zen philosophy. The experience proved to be important for both artists. However, while most potters saw Japanese pottery as a destination reached through imitation, Voulkos saw it as a springboard. He responded to “the deliberate lack of control”16 and the desire for Japanese potters to produce a not regular surface, or even too regular a shape.17 Often “the stone like inertness of pottery is …made dynamic… as well as by its slightly refracting optical quality.”18 Similarly, irregular surface decoration was deliberately developed by Bizen potters through using marks through their firing process, to change the appearance of symmetry in their pots.

Voulkos would soon amalgamate a variety of traditions, styles and art movements in work that would revolutionise the ceramic medium.

The Otis Years

When Voulkos was invited in 1954 to set up a department of ceramics at the Los

Angeles County Institute (later renamed Otis College of Art and Design) he developed a program in ceramics which attracted a small group of very talented young artists, who each soon made their own mark in the art world. Paul Soldner, John Mason and Ken

14 Michael Duncan, “How Clay Got Cool: Setting the Stage for Peter Voulkos’s Radical Shift,’” in Clay’s Tectonic Shift: John Mason, Ken Price and Peter Voulkos, 1956-1968, ed. Mary Davis MacNaughton (Claremont CA: Scripps College, 2012), 61-63. 15 Duncan, “How Clay Got Cool,” 63. Also Notes 13, 14, 15, page 71. 16 Malcolm Haslam, “The Pursuit of Imperfection: The Appreciation of Japanese Tea-Ceremony Ceramics and the Beginning of the Studio-Pottery Movement in Britain, in The Journal of the Decorative Arts Society 1850 ─ the Present, No. 28, Arts & Crafts Issue (2004), 153. 17 Haslam, “The Pursuit of Imperfection, 154. 18 Allen S. Weiss, Gastronomica, (University of California Press), Vol. 10, No 1 (Winter 2010), 139. http://www.jstor.org/stable/10.1525/gfc.2010.10.1.136 (accessed 22.6.2015). 84

Price were the most prominent; each developed their own style, aligning themselves with the modernist movement that post-war avant-garde artists in Europe and Japan were also pursuing19. By breaking with tradition, by crossing artistic boundaries and by inventing new expressions in their work, they stepped over the threshold of symmetry into the asymmetrical.

In a 1966 dialogue with Voulkos, Soldner remembered the actual moment of breakthrough:

Do you remember when, probably for the first time, you broke with the symmetry of the bottle? Some good-looking girls came from Chouinard Art School and asked if you would throw a big pot for them. You threw the pot and they were impressed. I remember you kept looking at the pot. And after they left, you went over and cut the top off. Then you threw four or five spouts and started sticking them around the rim. That didn’t seem to work, because it was still the same old bottle lip. Then you pared that off. The pot was still soft. Then you recentered it on the wheel and gouged three huge definitions – the top third, the centre third, and the bottom third. In one afternoon, you went from one kind of thinking to something completely different.20

One of the most interesting pieces which Voulkos produced when he started to undermine his technique, and where his attitude is more visible, is Rocking Pot, 1956,

Fig. 46, a caricature of the tradition of function.

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Fig. 45, Peter Voulkos, Rocking Pot. 1956. Height 35.5 cm. In R. Slivka, Peter Voukos. Fig. 19, page 36. Photograph by Joseph Schopplein.

19 Frank Lloyd,‘“Vanguard Ceramics: John Mason, Ken Price, And Peter Voulkos,” in Clay’s Tectonic Shift: John Mason, Ken Price and Peter Voulkos, 1956-1968, ed. Mary Davis MacNaughton (Claremont, CA: Scripps College, 2012), 19-22. 20 Clark, Shards, 272-73. 85

Holes are cut in the sides of an inverted cylinder, and rocking feet replace the foot of the punctured vessel, no longer a container. Garth Clark described it ‘a pot, a sculpture, and a demented birdfeeder.’21 Rose Slivka, Voulkos’ biographer and editor of Craft Horizons, on the other hand, was more assured in her judgement, meaning perhaps to compliment the artist: Rocking Pot was ‘… one of Voulkos’ outright sculptures. The pottery technique is evident, while the pottery function is subverted to the formal invention.’22 But Voulkos unequivocally stated, ‘I claim this as a pot.’ By viewing this object in ceramic terms, it becomes more intriguing than by looking at it from a purely sculptural point of view. ‘Voulkos’, Clark says, ‘ adds an edge of surreal spatial violence.’23 This idea has been important to me in the development of my asymmetrical vessels. The explorations of symmetry and asymmetry, spatial violence, the validity of clay as an aesthetic material and his aesthetic principles are important to my work.

Pablo Picasso’s Influence

The ceramics of Pablo Picasso were a source of inspiration for Voulkos. He had illustrations of Picasso’s work hanging in his studio in Otis, ‘to live with,’ as Voulkos recalled, ‘until I had absorbed all he had to say to me.’24 That was against the feelings of the director of the Institute, Millard Sheets, who detested Picasso. Voulkos was fascinated by the painter’s approach to the clay work, and in particular the way in which

Picasso set up a competing vitality between surface and form, and manipulated and restructured the appearance of the form. Voulkos later expressed what he had learned from Picasso’s manipulated pots:

21 Clark, Shards, 227. 22 Rose Slivka, The Art of Peter Voulkos, 36. 23 Clark, Shards, 229. 24 Davis MacNaughton, “Unexpected Connections, 152. 86

I brush on colour to violate the form and it comes out a complete new thing

which involves a painting concept on three-dimensional surface, a new idea.

These things are exploding, jumping off. I wanted to pick up that energy.

That’s different from decorating. Decorating enhances form, heightens the

surface. I wanted to change the form, get more excitement going.25

Like Picasso, Voulkos made the thrown ceramic form not the finished work but the starting point for a composition, sometimes by relocating the central focus of the vessel with the stroke of his brush. (Fig. 107) Both Mason and Voulkos did follow the tradition of the wheel and of the vessel/container, but the real purpose was to use the pot’s surface as painting.

Image unavailable due to copyright restrictions

Fig 46. Peter Voulkos. Covered Jar, height 43 cm, 1956. In R. Slivka, Peter

Voukos, figure 13, page 28. Photographer: Joseph Schopplein.

25 Clark, Shards, 274. 87

Abstract Expressionism and Other Influences

By 1959 Voulkos was considered ‘an outstanding pioneer in large-scale ceramic sculpture,’ according to the director of the Pasadena Art Museum, Thomas Leavitt, who exhibited Voulkos work in a solo show.26 By this time The Otis artists were attracted by the spontaneous approach to painting of the action painters of Abstract Expressionism.

Voulkos was drawn in particular to the work of painter Franz Klein, who composed with stark contrasts of black and white lines27, while Robert Rauschenberg demonstrated how to blur artistic boundaries with his multifaceted creativity. Decoration became

‘aggressive violation with tearing, slashing and gouging – combined with brushwork that often recalled Kline’s beamlike strokes.’28 A specific turning point for Voulkos was seeing the sculptures of Fritz Wotruba, an Austrian artist, who exhibited his work in

1955; after studying Wotruba’s work, Voulkos began stacking and piling his own clay forms, one on top of the other to achieve the greater heights and mass he was seeking.29

The Breaking of the Symmetry

26 MacNaughton, “Unexpected connections”, 155. Voulkos’ place in the History of Art seemed to be assured, if one looks at the impressive record of exhibitions and awards he received between 1953 and 1995: seventy solo exhibitions and two hundred and ninety group exhibitions; four Honorary Doctor Degrees, were awarded to him by universities and art institutions; G. Muller and S. Sterling, compilers, “Solo and Selected Exhibitions,” in Slivka and Karen Tsujimoto, The Art of Peter Voulkos, 172-181. It may seem to be inappropriate to mention the price-tag for Voulkos work in the ceramic market. It certainly does not reflect a presupposed aesthetic evaluation. However, it may be of interest to know the informed data provided by Garth Clark, writer, curator, historian and gallerist: ‘Peter Voulkos early sculptures are inching toward a quarter million dollar price tag, and his early pots are over $100,000’. In Clark, “Porcelain and Gold: The Ceramic Marketplace in the 21st Century, Shards, 431. First published in Ceramic Art Review 5 (Autumn 2002). 27 Lloyd, “Vanguard Ceramics,” 25. 28 Roberta Smith, “Peter Voulkos, 78, a Master of Expressive Ceramics, Dies”, New York Times, February 21, 2002; in Frank Lloyd, “Vanguard Ceramics,” 25, Note 29. 29 Karen Tsujimoto, “Confluence: People, Ideas, and Art: Southern California, 1945-1970”, in Clay’s Tectonic Shift, 45. 88

By 1955-56 Voulkos and his students were producing markedly different type of pots.

Emphasis was on the asymmetrical; vessels were distorted, torn, cut and reshaped

(Fig.47). With this uncoventional method of using clay, Voulkos upset elements of the craft community, aggravated by increased use of epoxy paint and adhesives.

Therefore, the path of Voulkos’ radical experimentation was not free of criticism. Clay was also not taken seriously by the fine arts community, because in sculpture, clay was not a medium considered to be on a par with marble or stone or with timber. In fact, some initial disapprobation came right from Voulkos’ own mother. When Peter told her that he was going to be a potter, ‘What!’ she exclaimed, ‘make pots and pans! I thought you were going to be an artist.’ Rose Slivka, with informed insight commented,

‘in those days, art was art and craft was craft. She dreamed of an artist among her sons. To her it was the highest aspiration and the most noble of all callings.’ 30

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Fig. 47. Peter Voukos, Multiform Vase, 1956. Height 51cm. In R. Slivka, Peter Voukos, Collection unknown, Fig. 18, page 35.

In 1956, when Voulkos had his first solo exhibition at the Landau Gallery in Los

Angeles, it was a show that won him both the admiration and protest of potters and

30 Slivka, The Art of Peter Voulkos, 36. 89 artists. Voulkos’ deep incisions and the cut-outs of clay used extensively were anathema to the conservative art and crafts movement, along with his use of synthetic colours and industrial glues. Moreover, the great Bauhaus potter Marguerite

Wildenhein, who had emigrated before World War II and who had spent five weeks working and teaching with Voulkos at the Archie Braye Foundation, eight years later cancelled her subscription to Craft Horizons as a protest to the reproduction of Voulkos’ new work in the magazine.31

At the end of 1958 Voulkos left Otis and soon after he moved to Berkley, where he took a position in the well-established Art Department of the University of California. Here

Voulkos continued building moderately scaled, thick walled vessels and torn and glaze- splashed plates. In Clark’s view, the pots he made between 1958 and 1963 represent a golden period of his oeuvre.32

Voulkos’ vigorous resolve to violate all rules of the aesthetic tradition of clay, left a mark on my own work of the early 1990s. Indeed, the images available in the ceramic reviews of the time, with Voulkos’ torn, perforated and glaze-splashed large plates, challenged my instinctive inclination to question and experiment. At the time I was at the Technical College learning how to throw huge platters on the wheel - a challenge in itself. I did slash the wide rim on two opposite sides and gently pulled apart the two severed sides to highlight the two gaps. After the bisque firing, I splashed the platters with an interesting shino glaze I was developing at the time, most suitable for the asymmetrical form.

31 Slivka, The Art of Peter Voulkos, 38. 32 Clark, Shards, 294. Although Clark admired Voulkos’ individual clay sculpture pieces, his oeuvre was, ‘unresolved as a body of work, lacking a central theme and striving awkwardly for an effect that his pots, although more modest in scale, seemed to deliver with ease and confidence.’ Clark, Shards, 277. 90

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Fig. 48. Peter Voulkos, Pot Sculpture, Red River, 1960. Height 94. In R. Slivka, Peter Voukos. Plate 10, pages 46 to 47. Photograph by Bobby Hanson.

In 1957 an exchange of heated letters by angry subscribers was published in Ceramics

Monthly over a few months, complaining about Voulkos’ ‘sloppy technique;’ and,

‘pieces that demonstrated technical competence but were formed into bizarre shapes or decorated in a “cute” fashion…His work was badly thrown, badly glazed and badly crafted. Shame on one of our reputable potters for such performance.’33 Even his solo show at the Metropolitan Museum of Modern Art in New York in 1960, a dream for any potter at that time, did not bring acceptance on the part of the world of fine arts. In the words of Slivka: ‘The show went largely ignored…The New York art world failed to recognise the major statement of Voulkos’ massive work probably because they were in clay and New York was snobbish about the modesty of the material.’34 John

Coplans, a painter, art historian and editor of Artforum, contended that one of the reasons Voulkos turned to bronze was over anguish that his ceramic work was not taken seriously.35

33 Ceramic Monthly, May 1957, 4, 6. 34 Slivka, Peter Voulkos, 55. 35 Clark, Shards, 295. 91

Coda

An assessment of the revolution within the tradition of pottery itself, which occurred in

Otis in the late 1950s, has not taken place as yet. Clark has contended that Rose

Slivka’s book, Peter Voulkos, ‘… is a love poem, not an analysis of his work. It has charm, passion and without a question, value.’ Similarly, in the second book, The Art of Peter Voulkos, written by Slivka with co-author Karen Tsujimoto, in Clark’s view,

‘… they do more to present the artistic persona than they do to analyse his art.’36

Clark, in 2002, was asking for an honest reappraisal of the revolutionary years of the

Otis clay: ‘The time has come to re-evaluate this achievement on its own terms, thoroughly examining its aesthetic principles.’37 Likewise, Michael Duncan, a corresponding editor for Art in America laments once again in 2012, that ‘… a definite assessment of the role of modernist ceramics in the history of twentieth century art is yet to be undertaken.’ Duncan, not unlike Clark, perceives that this Western movement is well rooted in the Japanese tradition, whereby ‘ceramic sculpture might provide the link for this more global, inclusive perspective.’ 38

In terms of the focus of this project on symmetry/asymmetry Voulkos demonstrated the enormous potential for other ceramicists inherent in breaking symmetry. His connection to the Japanese aesthetic acknowledged that “irregularities in craftsmanship and accidents in firing, do not impair the beauty of a pot.”39

36 Clark, Shards, 324. 37 Clark, Ceramics: Art and Perception (December 2002), 50. 38 Duncan, “How Clay Got Cool: Setting the Stage for Peter Voulkos’s Radical Shift,” in Clay’s Tectonic Shift, John Mason, Ken Price and Peter Voulkos, 1956-1968, ed. Mary Davis MacNaughton (Claremont CA: Scripp College, 2012),70. See also Clark, Shards, 274-75. 39 Michael Cardew, A Pioneer Potter (London: Collins, 1988), 31. 92

Hans Coper

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Fig. 49. Hans Coper. In T. Birks, Hans Coper, page 53.

Hans Coper was able to invent, by way of his imagination and original ideas, a world- class of essential timeless forms; by transgressing the primal symmetry of wheelthrown shapes he established his own geometry. For Coper the breaking of the symmetry is the driving impulse leading to the new form: with skill he joins manipulated parts, maintaining the idea of the essence which determines character. For inspiration he is looking back to ancient, totemic shapes of past civilisations. In view of his aesthetic preferences, working methods and his source of inspiration I perceive there is a common ground with my own work.

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It appears that the destiny of Hans Coper as an artist had been sealed already on the bunks of this German-Jewish refugee, in the English internment camps of the 1940s.

He had escaped from persecution, but now, as an enemy alien he had also lost his freedom and was subjected to hard labour conditions that had major consequences for his health. After work however, he was able to fraternise with other German detainees, who had similar interests, and who in their free time would talk about painting, architecture and sculpture. Coper learned a great deal about modern art from Fritz Wolf, an artist from Breslau (who later changed his name to Howard

Mason); he had a great influence on Coper and remained a trusted friend throughout his life.40 Coper had a natural ability for drawing, which he did whenever possible; he was remembered for having been seated on his bunk doing hundreds of drawings of his colleagues − but in those early days his preferences were more for sculpture.41

Coper developed both symmetrical and asymmetrical forms throughout his career.

Surface asymmetry was sometimes used in a subtle way by applying abstract, fine, circling networks of lines, or through irregular patches of dark and light patina hues, in order to break the surface symmetry of a regular shape. Sometimes the form itself was the subject of manipulation, by way of indentations in the soft clay with circular and/or elliptic grooves. Many pots changed their symmetrical appearance when the artist applied vertical, linear pressure bilaterally, which not only indented the surface, but metamorphosed the shape of the vessel into a non-Euclidean geometrical complexity.

40 Howard Mason eventually qualified as an architect and remained Coper’s mentor and admirer. In Birks, Hans Coper, (London Collins, 1983), 49. 41 Birks, Hans Coper, 14-16. 94

Coper eventually became one of the most famous and influential potters in England in the twentieth century.42 However, he came to pottery without any knowledge of clay, and probably never thought about the clay’s potential in three-dimensional art and sculpture, despite, as it has been pointed out,43 he had been living with his family for a few years in Dresden, not many kilometres from the famous porcelain factory of

Meissen. Coper was now in London, discharged from the Pioneer Corps, not in good health and in great need of a job in order to sustain himself and two children. By means of a recommendation by the refugee support group in the city, he went to see a certain William Ohly, formerly a sculptor who ran an Art gallery near Berkeley

Square.44 Hans told Ohly of his ambitions to be a sculptor, as well as his need for a job. With inspired insight Ohly sent Hans to see Lucy Rie, a refugee potter from

Vienna, who had a small workshop in Albion Mews, Paddington, and often employed other refugees in need of help to make ceramic buttons.45 Coper was accepted into the small community of potters; and in the friendly and congenial environment, which also gave him a minimum of financial security, was able to develop his full potential as an artist in the ceramic field.

Beginnings as a Potter

At Albion Mews the routine for Hans was intense: making buttons in the morning, pots in the afternoon, drawing in the evening, with the assistants taking turns as models. At night he would experiment with his own shapes, reclaiming the empty workshop for

42 Tony Birks, Hans Coper, (London, William Collins. 1983), book dust jacket. In “Degrees of Influence, ” ceramics writer and critic, Peter Dormer, examines the way in which Rie and Coper have influenced the next generation of potters, in parallel and in opposition to the School of Bernard Leach; in Lucie Rie & Hans Coper − Potters in Parallel, (exhibition cat.), edited by Margot Coatts, (London, 1997), 9-16. 43 Birks, Hans Coper, 27. 44Cyril Frankel, Modern Pots: Hans Coper, Lucie Rie and their Contemporaries, The Lisa Sainsbury Collection, (London: Thames and Hudson, 2000), 16. 45 Birks, Hans Coper, 18-19. 95 himself. At first Coper’s own pots were quite small, soft in outline, but boldly decorated with linear, asymmetrical designs in white and dark brown. From those early works it is evident that his object was to attain maximum visual asymmetry on his symmetrical shapes, as in his pot, Fig. 50,46 but also on his jug, Fig. 51, with semi abstract designs of birds and fishes, each with a single fierce eye. Already a contemporary art critic of that time, Carol Hogben, noticed with excitement an important change in the air, ‘modernism…here and there a surprisingly small twist which leads to an actually new form, such as the round bowls with oval levelled brim

(sic)’, noticing the breaking of the symmetry and its transformation into a new geometry. She continues, ‘Madam Rie…occasionally uses delicate criss-cross sgraffiti work. Coper’s sgraffiti is free, slashing and effective, reminding one occasionally of near-Eastern prehistoric ware,’47 ─ one more unexpected incongruence for the Establishment of the time.

Fig. 50. Hans Coper, Large Pot, 1953. In T. Birks, Hans Coper, page 94.

46 In T. Birks, Hans Coper, London, Collins. 1983 (all numbers of figures of this book are not given). 47 Carol Hogben, Art News and Review, 1950, written for the occasion of Coper’s first exhibition, shared with Lucie Rie at the Berkeley Gallery; in Birks, 22-23. 96

Fig. 51. Hans Coper, Jug 1952. In T. Birks, Hans Coper, page 33.

In order to create dynamism, Coper threw bowls and jugs as vehicles, to be metaphorically altered by brushwork, with a firm hand in the style of Picasso. In the studio he only used the basic ingredients available in Rie’s workshop, only occasionally experimenting with new combinations of components for his glazes. The house-rule was for one firing only, a method which was maintained indefinitely.48 Rie introduced porcelain to the workshop for the first time in 1947. With Rie, Coper was throwing monochromatic, porcelain table wares that sustained her business.49

48 Birks, Hans Coper, 21. 49 Margaret Coatts, ed. Lucie Rie and Hans Coper: Potters in Parallel: An Introduction, 11. See also Edmund de Waal, The Pot Book, edited by de Waal (London: Phaidon Press, 2011), 65. 97

Historical References – Contemporary Imagery

Coper’s early bowls are remarkable evidence of his interest in the Cycladic art right from the beginning, as they are strikingly similar in shape and decoration to the clay vessels, still extant, of the islands’ Neolithic Age.

Fig. 52. Cycladic Marble sculpture (detail), c. 2500-2300 BC. In J. Lesley Fitton, Cycladic Art, London: British Museum, 1989, Fig. 85, page 68.

Fig. 53. Hans Coper , ‘A rare shape’, 1975, 17 cm. In T. Birks, Hans Coper, page 182.

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Cycladic art, especially the three feet tall, female, marble statues of the same era, have consistently inspired Coper. It is known that he spent many hours in the British

Museum, a stimulating, comfortable environment, especially in the English winter, where he became acquainted with Cycladic art, but also with Egyptian, Etruscan and

Mycenaean art. He had great admiration for the works of Giacometti and Brancusi

(whch he tried to see in Paris at the end of 1956). In Fig. 54, behind the pot, is a photograph of a Cycladic stone carving from the British Museum, which Hans kept in his studio. All the work that inspired Coper was minimalist in its outline, with clean, uncluttered profiles, bare, with no decorations; his ideal, seemingly, was Brancusi’s essential, timeless forms.

Fig. 54. Hans Coper, photograph of a Cycladic stone carving from the British Museum which Hans kept in his studio. In T. Birks, Hans Coper, page 148.

Refinement and Abstraction

In the early 1950s open, decorated bowls were phased out and replaced by a single, unaltered, thrown shape. Coper’s interest was focussed on the development of a new 99 technique of surface finish, dispensing altogether with the use of glazes. By applying slips and oxides thickly to the surface and by firing the pots at high temperatures, he obtained a vitrified finish, more like a patina given by time, like the scarified surfaces of archaeological vessels. It was the result of many hours of hard and patient work by scraping and scoring repeatedly the surface with steel wool and metal tools, with fine circling networks and webs of lines to achieve a refined and subtle finish.50

Fig. 55. Hans Coper small Spade, 1970-72, Sainsbury Centre for Visual Arts, 14 cm. In T. Birks, Hans Coper, page 172.

Pots soon were becoming increasingly oval-shaped as the volume was compressed into flattened areas; bowls were attached rim to rim, others were compound forms of two or three parts of various geometrical manipulated shapes. The breaking of the symmetry of the single parts emphasised the overall asymmetry of the compound form.

50 Edmund de Waal. 20th Century Ceramics (London: Thames & Hudson, 2003), 124-127. In this context, Donald Brooks, recalling his conversations with Hans at Digswell in the early 1960s, commented, ‘It was a strong point that his pots had this immense subtlety of surface. This glaze that was not a glaze, and colour that was not a colour…’ in Birks, Hans Coper, 42. 100

Fig. 56. Hans Coper, flattened form based on a cylinder. 1970. Height 18.5 cm. In T. Birks, Hans Coper, page 164.

Coper was very much aware of the ambiguity of the vessel and its function; function is not limited to mere utility – a cup can be used for ritual purposes, as for instance is the chalice on the altar, which has its own scope. Some of Coper’s shapes, especially the so called Cycladic pots, named for their resonance with Cycladic figures standing on drums or plinths, with their vestigial wings give a feeling of almost totemic significance.

101

Fig. 57. Hans Coper, Cycladic forms. 1974, 28-32 cm. In T. Birks, Hans Coper, page 196.

The one existing statement Coper made about his work, written for the catalogue of the exhibition at the Victoria and Albert Museum in 1969, discloses more than a philosophical approach to his vocation as a potter of functional vessel forms:

The wheel imposes its economy, dictates limits, provides momentum and continuity. Concentrating on continuous variations of simple themes I become part of the process; I am learning to operate a sensitive instrument which may be resonant to my experience of existence now. 102

Practising a craft with ambiguous references to purpose and function one has occasion to face absurdity, somewhat like a demented piano-tuner, one is trying to approximate a phantom pitch.51

It has been reported by friends and former students that Coper never spoke to them about his work and his working methods.52 Some general technical details are commonly known to most practising potters. However, the method, developed to perfection, of joining and sealing diverse manipulated parts to form one unit and later, the interlocking of two forms, was a self-taught technical method of refinement and precision which he developed during long, solitary hours in his workshop. Even Lucie

Rie, who worked side by side with him for many years, was hesitant about saying how some forms were made.53

Performance and Recognition

The years Coper spent at Digswell, a community centre for artists, from 1959, were promising, because of the possibility of gaining collaborative work with architects, which was very appealing. But commercial considerations aborted the projects after three years. Of great satisfaction however, was his most prestigious commission to date – the design of six huge candlesticks for Coventry Cathedral, (Fig. 58), a project more consonant with his intimate connection with clay work.

51 Catalogue of the exhibition at the Victoria and Albert Museum, 1969. 52 Birks, Hans Coper, 57. 53 Birks, Hans Coper, 57. 103

Fig. 58. Hans Coper, Coventry Cathedral Candlesticks, 1963. In T. Birks, Hans Coper, page 49.

The responsibility of working for important exhibitions and prized commissions motivated Coper in the maintenance of the highest standard of craftsmanship and refinement; only the very best pieces were retained. Ralph Brown, one of the resident artists, recalled that at Digswell ‘the discards were colossal.’54 Shapes were often leading to new, related forms; echoes of earlier pots reappeared in later formats. In

54 Birks, Hans Coper, 52. 104

1967 he introduced the so-called “spade” shape (as seen in Fig. 59), which became one of his most popular and distinctive forms.

Fig. 59. Hans Coper Spade, 1972-75. In T. Birks, dust jacket of Hans Coper.

In these pots the mouth of the vessel has been compressed to a width of only one inch, and on the spade section he developed his remarkable surfaces, with skillfully placed turning lines, marking the asymmetry of the flattened wall. The most original and

105 powerful forms of Hans’s last years were ovoid pots with vertical, bilateral grooves, generating an inward curved number-eight-shaped mouth.

My own preference amongst his works, now in the Victoria and Albert Museum in

London, is the anthropomorphic composite form, with sensual, deep anatomic grooves, lively animated by the form and light.

Fig. 60. Hans Coper. Standing form, 1970. Height 30 cm. In T. Birks, Hans Coper, page 178.

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An Object of Complete Economy

The description of an archaic pot (as seen in Fig.61), which was given to Hans Coper by a friend, is very significant, for the sense of the ‘complete economy’ Coper was trying to achieve with his own ceramic forms, linking him with sculptural traditions of pre- classic times:

A pre-dynastic Egyptian pot, roughly egg-shaped, the size of my hand: made thousands of years ago, possibly by a slave, it has survived more than in one sense. A humble, passive, somehow absurd object – yet potent, mysterious, sensuous. It conveys no comment, no self-expression, but seems to contain and reflect its maker and the human world it inhabits, to contribute its minute quantum of energy – and homage. An object of complete economy made by MAN; Giacometti man; Buckminster Fuller man. A constant. This is the only pot which has really fascinated me. It was not the cause of my making pots, but it gave me a glimpse of what man is.55

Fig. 61. A predynastic Egyptian pot, unknown maker. In T. Birks, Hans Coper, page 202.

Coper’s choice of two iconic figures of the time, a sculptor and an engineer, cited in the above description, is very telling, invoking this connection between the modern and the archaic. The Cycladic pots Coper made in his final years, were small in size and were

55 Hans Coper, in De Waal, 20th Century Ceramics, 125. 107 mounted on a small drum-like, thrown base; they were cemented together on a piece of steel, knitting needle, with the point of contact reduced to two or three millimetres.56 An example is Fig. 62 below. The fact that they were designed to stand rather than to be held in the hand, was underscoring their totemic significance, glorified by a perfect balance between the asymmetrical parts and by means of the counterpoint of contrasting geometries.

Fig. 62. Hans Coper, The burnished black globular shape on grey- green base, c. 1975. Height 21 cm. In T. Birks, Hans Coper, page 183.

56 Birks, Hans Coper, 66. 108

George Ohr

Fig. 63. George Ohr, photo from the Ohr family album, c.1990 In G. Clark, et al., The Mad Potter of Biloxi, Fig. 116, page 138.

Ohr was a craftsman, now recognised not only for his manual skills, but also for his eclectic imagination in designing. He worked with conviction, feeling free to innovate, formally by subverting the rules of convention, and conceptually by devising completely new forms. Ohr was intrigued by the notion of function as a source of irony, made clear with his cups with several handles. He was dismissed as a curiosity by most, as he wore the mask of a jester, while feeling frustrated by his rejection as an artist. He had little impact in his own time, but he anticipated much of the innovation in our own time.

109

Fig. 64. George Ohr, The potter and his wares, c.1897 In G. Clark, et al, The Mad Potter of Biloxi, Fig. 19, page 25.

Fig. 65. George Ohr, Footed Vase, c. 1895-1900. Height: 18 cm. In G. Clark, et al., The Mad Potter of Biloxi, Plate 109, page 158.

110

George Ohr was an American studio art potter who, more than any other individual in the history of modern ceramics, dedicated his life to the creation of asymmetrical vessels. His method was to manipulate skilfully wheelthrown symmetrical pots, transforming them into unprecedented abstract configurations. Ohr, however, remained true to the vessel form, even after making radical changes that almost erased the original shape.

Fig. 66. George Ohr, Teapot with snakes, front and back views, c.1985-1900. Height: 12 cm. In G. Clark, et al., The Mad Potter of Biloxi, Plate 124, pages 168,169.

Ohr’s forms were at the outset very close to the traditional, largely standardised shapes and proportions handed down by centuries of pot making, not only in America but also in Europe. His innovation consisted largely of an abstract three-dimensional decoration, based on the manipulation of the form itself, thereby pushing it far beyond mere functionality to the point of abstraction. This set Ohr apart from all other potters of the period, thrusting his work into an unknown aesthetic territory. Ohr was very aware of not fitting into the expected mould; in a colourful expression, befitting his eccentric personality, he wrote in his short autobiography: ‘Suppose 5 hen eggs were put under a brood and somebody somewhere made a mistake and got a duck egg in 111 the job lot, that duck is going to be in some very hot aqua.’57 Not many of Ohr’s personal records exist, because, according to hearsay, all his paperwork was wantonly destroyed by his eldest son, Leo, who had a grudge against his father for being forced in his youth to do much manual work around the pottery.58

Fig. 67. George Ohr , Three-handled mug, c.1900. Height: 20 cm. In G. Clark, et al, The Mad Potter of Biloxi, Plate 133, page 176. Private collection, of artist Jasper John, New York City.

Dynamics of Form in Ohr’s Ceramics

For George Ohr, symmetry was always present in his manipulated vessel, either in its entirety or partially. The roots of his learning process were entrenched in the imperatives of tradition. Ohr’s breaking of that symmetry was greatly misunderstood

57 George Ohr, “Some Facts in the History of a Unique Personality, Autobiography of George E. Ohr, the Biloxi Potter,” printed in Crockery and Glass Journal 54 (12 Dec.1901), reprinted in “Appendix A” (hereafter mentioned as Ohr, “Autobiography”); in Garth Clark, Robert Ellison, Eugene Hecht, The Mad Potter of Biloxi: The Art and Life of George E. Ohr,( Abbeville Press: New York, 1989), 177. 58 Hecht, quoted from “Mississippi Trace,” in Studio Potter, 10:2 (1981-82), 83; in “The Time and Life of G. E. Ohr,” 9-64, in The Mad Potter of Biloxi, 179. 112 and disapproved in his time. The dominant aesthetic force came, then, from the Arts and Crafts Movement,59 which valued fine craftsmanship above creativity. Ohr’s distortion of the vessel was for his peers an act of destruction while, paradoxically, it gave a new life to his creations. Ohr’s oeuvre did not fit the simplicity required by the

Arts and Crafts Movement’s philosophy, although, by virtue of his doing all the work involved in making an artist’s pot – from digging the clay to throwing and forming, from glazing to the final firing – Ohr was in spirit the quintessential Arts and Crafts potter.

Ohr began to alter and recreate his exquisite wheelthrown vessels in all manners of unprecedented shapes, breaking the symmetry produced by the wheel and by implication, the history of ceramic form. There are no contemporary eyewitness descriptions of how Ohr proceeded when he altered his shapes in his studio.60 Ohr may have chosen his approach by observing how the clay twisted and often collapsed, as he sought to throw pots with extra thin walls. Paul Cox, a contemporaneous ceramist and a member of the Arts and Craft Movement wrote, ‘He (Ohr) could throw wares of considerable size with walls much thinner than any other potter ever has accomplished. It is quite probable that George Ohr was the most expert thrower that the craft has ever known.’61 No other potter had turned this incidental event into an aesthetic vision for a lifetime’s work.

59 The Arts and Crafts Movement, founded by William Morris in the late nineteenth century in England, evolved out of a desire to reform design and counter the decay of taste resulting from industrialisation. 60 Robert A. Ellison, George Ohr, Art Potter, 107. 61 Paul E. Cox, “The Mad Potter of Biloxi”, Ceramic Age, 1935; 125-26. 113

Fig. 68. George Ohr, Vase, c. 1895-1900. Height: c. 23 cm. In G. Clark, et al, The Mad Potter of Biloxi, Plate 92, page 147.

Ohr intuitively developed various techniques for the metamorphosis of his pieces.

Amongst his most frequently used procedures were ‘ruffling, twisting, crinkling, indenting, off-centering, folding and lobing’.62 This repertoire provided him with an infinite capacity to create the variations he sought in his lifelong quest to make unique pieces: ‘The twisted, crinkled clomerations (sic) in my Art Pottery stand alone on earth

– I cannot duplicate such myself.’63 Ruffling was often used by itself on the mouth of the vessel, with subtle variations, without changing the overall symmetry. Ohr’s exploration of this technique was sometimes eccentric and extreme: ruffled strips were added, covering the whole wall in a circular rhythm. Twisting was applied on the neck, the belly or on the foot. Indenting, often in a repetitive manner, would bestow on the

62 Ellison, George Ohr, Art Potter, 107. 63 Ohr, “Concerning the Biloxi Potteries,” in The China, Glass and Pottery Review 4 (April 1899) :47; in Ellison, George Ohr, Art Potter, 105. 114 walls a tree-dimensional surface. Often the neck was wrapped or flopped over by folding.

The vessels which more than any others lead to extreme asymmetry formed a body of work which was left in the bisque or unglazed state. The most striking examples were made from marbleised clay (two or more colours of clay blended together) These asymmetrical, self-contained designs expose new geometries that interact with the remaining parts of the original symmetrical profile, creating surprising spatial relationships and asymmetry. In Fig. 69, the vessel with terracotta slip and tilting at an angle, creates a dramatic abstract form, with only the base reminding us of its potter’s wheel origin.

Fig. 69. George Ohr, Bowl , c.1902-7. Height: 11 cm. In G. Clark, et al., The Mad Potter of Biloxi, Plate 79, page 116.

115

Fig. 70. George Ohr, Double-Handled Vase, c.1898. Height: 13.5 cm. In G. Clark, et al., The Mad Potter of Biloxi. Plate 4, page 43.

A handle on a symmetrical body may confer an element of asymmetry, encompassing the whole form. However, Ohr succeded in placing handles, at times extremely unconventional in shape, as a visual counterpart to the main volume, in a masterful balance of spouts and profiles. As a new vision he created severe asymmetry by transforming a bowl into a jug with a handle integral with the body. His technique was to throw a bowl on the wheel, pinch one side of the bowl together to form a flat, vertical protrusion, cut out a finger hole in it, pinch a small spout on the side opposite the handle and flare the rim outward. 64 Two examples are reproduced in Fig. 71 and Fig.

72.

64 Ellison, George Ohr, Art Potter, 95. 116

Fig. 71. George Ohr, Pitcher, c1898-1907. Height: 9 cm. In G. Clark, et al., The Mad Potter of Biloxi, Plate 60, page 104.

Fig. 72. George Ohr, Pitcher, c.1985-1900. Height: 7.5 cm. In G. Clark, et al., The Mad Potter of Biloxi, Plate 58, page 104.

Ohr could not envisage that anybody else would be able to take to the extremes the innovations he had accomplished :

117

My pottery life-work is only one collection as I alone created it – and if there is a greater variety of pottery on this earth emenating (sic) from one creature that is and has more extreams (sic) for poor and high quality shapes sizes – ugly, pretty, odd, queere (sic) etc. etc., than I have – I want to see the same and lle (sic) swim and wear out shoe leather to get there.65

Through the work of Ohr there is a demonstration of the new geometries. Not in his time, but in his own country two generations later, Voulkos revolutionised the way in which the humble clay was thrown on the wheel and would be manipulated, in a way

Ohr could not have imagined.

Edmund de Waal : Contemporary Ceramicist

In the field of contemporary ceramic art I have selected Edmund de Waal as a representative of several artists who have chosen the violation of symmetry for wheelthrown porcelain vessels. Technically, a simple way to disrupt the symmetry is to use gentle manual or tool pressure on the freshly thrown pot. Vice versa, the joining of the cut and the manipulated, asymmetrical parts of a porcellaneous clay body needs considerable skill and experience - it is a time consuming exercise. Edmund de Waal has chosen the cylinder as his basic ceramic form: he uses them in great numbers, sometimes in the hundreds or even in the thousands, for his now famous installations.

For a long time his adopted method has been to break the symmetry by exerting gentle thumb pressure on the wall or by stamping it to disrupt the perfection of the freshly thrown cylinder. Other possible violations include, among others, uneven heights, partly torn rims or visible throwing rings, all of these actions challenge ideas of perfection implicit in symmetry.

The artist I have selected, and who in my view, best represents a trend in contemporary ceramics, relevant to my research project, is English potter Edmund de

Waal. This choice is prompted by a suitable criterion of comparison between his

65 Ohr, Crockery and Glass Journal, in Ellison, George Ohr, Art Potter, 105. 118 ceramic work and my work: the common chosen material is porcelain, the working method is wheelwork and the common way to exhibit works of related vessels is in groups or collections. My focus is principally directed to the intentional violation of the symmetry of de Waal on his freshly wheelthrown vessels. His way of breaking the symmetry deviates from mine; with my method I induce structural changes to the initial symmetric form, both, in the square mouthed vessels, as well as in the albarello- inspired forms.66 A common feature of both groups of my pots is that elements of the initial symmetry are maintained to enhance the contrast between symmetrical perfection and the violation of it.

Japanese Influences

De Waal began to work with porcelain in 1998, during a year in Japan working with ceramists outside the studio tradition while researching Bernard Leach,67 whose ultra- conservative tuition was well entrenched in the formal training of de Waal, carried out in London.

First-hand experience of Japanese aesthetics left a definite mark on the form of his pots, a cylindrical shape, remarkably stripped of all ornamentation and free of all superfluous features. Many of the early shapes were touched lightly while wet, in a way that they would easily fit into the hand, as in Fig. 73. De Waal viewed this light breaking of the symmetry as a feature of function: ‘I would like to make porcelain

66 See my Square Mouthed Vessels, pages 133 and 139, the albarello inspired vessels, pages 166 and 168 and the computer-designed variations, page171. 67 Paul Laity, “Edmund de Waal: A Life in Arts,” The Guardian, Saturday 12 February, 2011, http://www.theguardian.com/books/2011/feb/12/edmund-de-waal-life-profile-interview (accessed 1.7.2015). In fact, in his book, Bernard Leach (1998), de Waal dismantled Leach’s authority, exposing, among other things, his limited understanding of Japanese culture. De Waal also confronted the legacy of Japonisme, the misreading of Japanese culture by the West, which had dominated the way of looking at Japanese arts and crafts for one hundred years. 119 vessels that can be used,’ he said, ‘because handling them daily expands the range of that significance.’ 68

Fig. 73. Edmund De Waal, Bottles, 1997. Porcelain. In Ceramics: Art and Perception. No 35, 1999, cover page.

The subtle violation of the symmetry became one of de Waal’s distinctive characteristics, from his early porcelain vessels onwards. It was sometimes achieved by pressing small dot-shaped depressions into the freshly-thrown clay and by applying small scraps of porcelain 69 to the smooth surface. Although that could be seen as accidental, de Waal says that he plans these things. ‘When a pot is finished, it is too perfect. I just touch it then.’70 Clearly, violating perfection seems to be for de Waal a primal mover for the breaking of the symmetry, and relates to aspects of Japanese ceramic practice.

Although there is a certain mannerism in this slight use of the decorative, de Waal is open about the source of his inspiration and to his debt to the Japanese aesthetics.

Marking with stamps carry engraved texts ‘about myself, where I’m coming from, ideas about work.’ He continues, ‘Ancient Japanese pots always had texts on them. The

68 Gaby Dewald, “Fruits of the Spirit,” 4. 69 Peter Voulkos used to apply small scraps of fresh white porcelain to mark the dark clay body of his slashed plates and of his huge bottles. 70 Dewald, “Fruits of the Spirit,” 6. 120 characters of the text that I use are illegible to other people − it is a conversation with myself. Pots are essentially closer to me than people.’71

Change of Direction

In 2002 a change of direction in de Waal’s work also found a corresponding way in the method of breaking the symmetry. For a period he abandoned the use of a porcelain clay body (usually Limoge) in favour of white stoneware. The thrown and assembled forms had been covered with a white opaque tin glaze; but he was also moving away from objects that could be seen as merely related to function. Although de Waal maintained the overall cylindrical shape, the rims were flattened and cut or thrown asymmetrically. The main violation of symmetry was “inflicted” inside the vessel, where a “false” bottom was produced by a shelf of clay, ripped or torn into a roughly shaped circle, partially covering the brightly coloured base of the vessel, as in Fig. 74.72

Fig. 74. Edmund De Waal, Bowl, 2003. Stoneware, opaque tin glaze. In Ceramics: Art and Perception, 54, page 11.

71 Dewald, “Fruits of the Spirit,” 6. 72 Emmanuel Cooper, “Hidden Depths: The Ceramics of Edmund de Waal,” Ceramics: Art and Perception, No 54, 2003, 11. 121

Installation Aesthetics

In 1999 de Waal started to “install” his ceramics as considered groups in specific locations. By placing pots in unlikely and often surprising places and only partly visible, he seems to be tempting the viewer to consider thoughtfully the revealed and the concealed: ‘I hope it is ambiguous,’ he said. 73 One installation, called ‘Tristia,’ seems to be particularly effective in partially hiding 31 thrown cylinders glazed in yellow and cream, close-packed between two white boxes which look heavy on top of each other, yet only 7 or 8 cm apart as can be seen in Fig. 75.

Fig. 75. Edmund De Waal, Tristia, 2008. In Ceramics: Art and Perception, No 82, 2010, page 30.

Obviously de Waal considers the display, presentation and framing of ceramics as vital to the ceramic experience; preference for the ensemble means the de-emphasis of the importance of the single piece. The ensemble is a group of items viewed as a whole, sometimes they are bound together by inspiration in the conception, or it is the casual taste of the viewer or the collector who assembles individual units to form a whole.

73 Cooper, “Hidden Depths,” 10. 122

The way de Waal displays his work is closely connected with his writing, but not “by chance.” His interest in the history of ceramics, linked with that of porcelain, became the topic of his book 20th Century Ceramics.74 References include the technical, social, economic and aesthetic history of his chosen medium. Tracing back to the 18th century

‘porcelain rooms’ where the wealthy families of Europe had assembled their precious collections of ceramics in ostentatious displays of wealth and power, de Waal started to produce hundreds of cylinders, thrown in series and covered with a delicate celadon glaze. He called them ‘Cargoes,’ and displayed in crowded shelves, shadowing the frantic trade of porcelain, known as the Eastern white gold. One example is the following installation in Fig. 76.

Fig. 76. Edmund De Waal. Installation in the Geffrye Museum, 2002. In Ceramics: Art and Perception, No. 54, page 9.

74 Edmund de Waal, 20th Century Ceramics, London: Thames & Hudson, 2003. 123

De Waal’s latest book, The Hare with Amber Eyes,75 which deals with the traumatic saga of the loss of the possessions of his extended family during World War I, and with the “discovery” of his Jewishness, opens a new chapter in the life of the artist. The new knowledge, which he acquired through years of painstaking research, has also filtered down in the way he feels compelled to exhibit his latest work. Concepts like collecting, exhibiting, hiding and displaying are revisited and revalued. De Waal relates how he spent the first twenty years of his life as a potter trying to convince people in museums and galleries to take his pots out of the glass cases. ‘They die, I’d say.

Vitrines were a sort of coffin…‘Out of the drawing room into the kitchen!’ I wrote in a sort of manifesto.’76 But in de Waal’s revised opinion, the vitrine ─ as opposed to the museum’s case ─ is for opening. ‘The moment of looking, then choosing, reaching in and then picking up the object is a moment of great seduction,’ he said. He described the instant of contact between the hand and the object as electric.77

In 2012 the Fitzwilliam Museum of Cambridge invited the potter to curate an exhibition of Chinese and European white porcelain ceramics of the museum’s extensive permanent collection. At one end of the exhibition de Waal installed his own work, the largest ever, called “A Thousand Hours.” It was comprised of two massive vitrines containing a thousand pots, only partly visible, as evident in Fig. 77.

75 Edmund de Waal, The Hare with Amber Eyes: A Hidden Inheritance (London: Vintage, Random House, 2011). 76 De Waal, The Hare, 65. 77 De Waal, The Hare, 66. 124

Fig. 77. Edmund de Waal, A Thousand Hours, 2012. In Apollo, November 2013, page 64.

De Waal’s work remains to this day focused on wheelthrown porcelain vessels; he uses clear or very pale coloured glazes, like celadon or various hues of white. His preferred form remains the cylinder, thinly thrown and rather tall in relation to the small diameter. The breaking of the symmetry is, as usual, unobtrusive, but mostly present in every collection: a gentle knock or impression on the wall of the vessel, occasionally facetted walls, with slices of clay removed seemingly by wire; visible throwing rings, uneven or partly torn rims.

In this chapter I have examined in depth the work of Picasso, Voulkos, Coper, Ohr and de Waal in order to contextualise the methods and concepts that have driven my ceramic practice. All these ceramicists had a traditional background in ceramics practice in throwing symmetrical containers. As the clay needs to be wet when thrown,

Ohr and de Waal change the pliable shape, wheras Voulkos and Coper throw different parts and assemble them in an asymmetrical compound form. All of these ceramicists

125 maintain a container form. Ohr tried to create a new beauty while Voulkos wanted to create new sculptural structures in order to move into the more respected field of fine art. The next chapter begins with the field research that inspired my own breaking of symmetry.

126

CHAPTER FIVE: The Square Mouthed Pottery: My Inspiration.

Fig. 78. Nora Moelle. Study of the Square Mouthed Pottery, 2008. Southern Ice porcelain, deep etching, shellac resist. Photograph by Allan Chawner.

Introduction to My Ceramic Practice

At the time I was considering ways of altering the shapes of my vessels by breaking the initial symmetrical form, I received news from my brother Pietro in Italy, announcing that very interesting clay vessels had been unearthed from Stone Age burial sites recently discovered near the city of Trento.1 The location is called La Vela, on a hill on the right side of the river Adige, at a walking distance from my former high school. From the description, these archaeological findings were of great interest to me because of the shapes of the clay vessels (cups, bowls and larger containers), hand-built from the base up in circular form, but the upper section (the mouth) has a square finish. This peculiarity

1 A more extensive discussion of this field work is in Appendix, page 176-185. 128 gives them the name of the Square Mouthed Pottery (Vasi a bocca quadrata).2 (Fig. 69) I perceive this procedure to be the breaking of the initial circular symmetry for a symmetry of a lower order of transformations, the square.3

Fig. 79 a. Square mouthed beaker and bowl recovered from a woman’s stone burial site of mid-fifth millennium B.C. Centre for study of archaeological finds, Trento. Photo by author, with permission.

Symmetry breaking is the origin of dynamics and of a variety of forms and patterns.4 My interest, however, is not exclusively of an aesthetic nature. The “phenomenon” of the

2 For details, see the homonymous section in my Appendix. 3 I deal extensively with the mathematical concept of transformation in Chapter Two by the title “Symmetry in Modern Mathematics,” page 27-32. 4Symmetry breaking was a concept already present in the theoretical thinking of the Pre-socratic philosophers, such as Anaximander and Heraclitus. See my Chapter One, section “Symmetry in Early Art,” pages 13-17. In my Chapter Two with sub-headings “Symmetry in Modern Mathematics,” “Symmetry in Modern Physical Sciences,” and “Symmetry in Biology,” I have explained (and given examples) the conceptualisation of symmetry breaking in modern sciences. 129 square-mouthed pottery is a unique happening, in one single region of the world (Northern

Italy, south of the arc of the Alps). This ceramic practice lasted for about one thousand years during the Neolithic period, starting approximately halfway through the fifth millennium B.C. But, why “square,” when in this region and everywhere else all other pots were circular?

My enquiries in the museum of Trento clarified the wide-ranging connections of the

Northern regions of Italy with the entire Mediterranean area. By way of archaeometric studies carried out since the oldest archaeological findings of the 1960s, it was possible to determine that the ceramic industry, already well advanced in the regions of the eastern

Mediterranean sea, had been “exported” via the sea, together with agriculture, and introduced first to the populations of the Ligurian shores in the north-west of Italy (to the west of the modern city of Genova), in the first centuries of the sixth millennium B.C. From there, over the following centuries, agriculture and ceramic practices (among them the square mouthed pottery) spread over many areas of Northern Italy.5 Fragments of seeds of grapes (Vitis vinifera) and of pears (Pyrus sp.) and of bones of domestic animals (not present in chronologically older findings) were also part of the grave goods found in the fifteen burial sites of La Vela.6

5 See maps of the region and of the archaeological sites to date, in the Appendix. 6 Mauro Rottoli, “I Resti Archeobotanici,” in: Spirali del Tempo, Meandry del Passato: Gli Scavi Archeologici a La Vela di Trento dal 1960 al 2007. Provincia Autonoma di Trento (Trento: Soprintendenza per i Beni Archeologici, 2007). Number of pages is not given. 130

Fig. 79 b. Stone Age Spoutless jug. Photo by author, with permission.

Fig. 79 c. Lugged pot. Photo by author, with permission.

131 This distant past is of great importance to me, both as a potter and because of my connection with the land. The recent discovery of the ancient “culture” of the square mouthed pottery, marked by unique ceramic pieces found in funerary stone cists and in rock shelters, traces back my interest for the earthy clay to a tradition which was valuable for the living and for the dead, and vital for the development of civilisation. Of equal importance was the introduction of agriculture to the sparse population at the feet of the

Alps, a signpost of the transition from a primordial lifestyle of hunters and gatherers to the dawn of a civilised society.

According to A. Pedrotti, author of recent studies of the prehistory of Northern Italy, the origins of the square mouthed pottery Culture could not be ascertained because of lack of evidence, although many data indicate ‘ a local genesis, probably stimulated by external influences.’7 The gradual replacement of round vessels with the squared version has been only tentatively explained by Pedrotti, ‘perhaps because the form may be more practical’, or ‘for having a particular symbolic significance’.8

My contribution as a potter was to try to unravel the mystery of this pre-historical, intentional breaking of the symmetry of these clay vessels, hand built upon a circular foot and round body, but beautifully and gently squared at the top, with the corners slightly thinned and pulled-out. My conjecture is, perhaps predictably, based on functionality. It may have been an attempt to create a proto-spout, or better, a four-spout vessel, in order to facilitate the pouring action of substances and liquids. My preliminary enquiries confirm my observations in the museum of Trento about the absence of the familiar spout among all Neolithic pottery in Northern Italy.

7 Annaluisa Pedrotti, “Il Neolitico,” in “La Storia del Trentino,” Vol.1, La Preistoria e la Protostoria, M. Lanzinger, et al, eds. (Bologna: Il Mulino, 2000), 119-182. 8 A Pedrotti, “Il Neolitico,” 140. For details, and for an extended survey, see Appendix, page 176. 132 The vessels of the square-mouthed pottery have inspired my development of two groups of vessels within a framework of contemporary aesthetics, and, obviously, with the use of modern materials and techniques. Throughout my work I have maintained the resolve not to use any glazing in order to avoid a gloss finish, but rather to bring about a natural,

“satin” surface appearance by the method of burnishing with the finest sand paper. This method seems to reflect best the raw (unglazed) finish of all Stone Age pottery of northern

Italy, and it seemingly enlivens the pristine white Southern Ice porcelain body. White clay was chosen for the absence of colour, the translucency and the purity of form. This allows any breaking of symmetry to be revealed without distraction of colour and to emphasise the form of the vessel. The first body of work consists of vessels initially round in shape; while still wet on the wheelhead I individually squared their rim by using my fingers and my eyes as the only tools for reshaping and measuring, not unlike my earliest predecessors would have done. (Fig. 80)

Fig. 80. Nora Moelle 2008, Southern Ice porcelain, unglazed, etched, 16x16x16cm. Photograph by Allan Chawner.

133 By employing the use of a shellac resist method (a technique which involves gently sponging away the clay surrounding the section that has been painted with shellac), I have been breaking the symmetry again, by etching on one of the pot’s wall part of a double spiral, akin to the fragment of the pintadera, a clay stamp found in one of the excavation sites of La Vela. My etched clay seal is reproduced in Fig. 81.

Fig. 81. Nora Moelle, Pintadera (clay seal), detail, 2008, Southern Ice porcelain, unglazed, etched. Photo by author.

Symmetry Breaking – Dilations

Symmetry breaking is a fascinating example of how abstract mathematics can be transferred and applied to distinct physical problems, which may obey identical mathematical rules. In my study of symmetry in nature I found one such rule called dilation. A dilation is a change of scale: uniform expansion or shrinkage about some specific fixed point, the centre. Dilations are non-rigid symmetries of space. I came across dilation symmetry in association with the logarithmic spiral of the Nautilus and the

134 Abalone shells, as well as with the rule of the growth of plants that put outside-shoots at regular angles as they grow.

From a geometrical point of view, the simplest object with dilational symmetry is a cone. If you shrink it to half its size (or any smaller size) it looks exactly the same; or if you double it or expand it to any size, it also looks exactly the same. The cone is invariant under all dilations centred on its tip.9 In my studio work I have applied dilational symmetry of the cone when I planned the vessels inspired by the squared mouthed pottery. I threw on the wheel a cone section with the objective of making a mould; I then used the mould as a template for a series of slip-cast circular vessels of decreasing height, which I subsequently squared manually about the rim. By using a progressing variation of heights for a body of work of over a dozen pieces, I exhibited them as an installation in spiral form as in Fig. 82 (the spiral itself is symmetric under a suitable combination of rotations and dilations and translations).

9 Ian Stewart and Martin Golubitsky, Fearful Symmetry, 264. 135 Fig. 82. Nora Moelle 2008 Installation of vessels in spiral form of decreasing height (from the “Square Mouthed Vessels” series). Southern Ice porcelain, unglazed, etched; various heights. Photograph by Allan Chawner.

Wheelthrowing as a Symmetry Operation

The work of a potter is intimately connected with a “presence”, be it on the mind or in the actual object the potter is making – that is form. The material used is plastic clay, wonderfully adaptable to give body in a tangible way to the idea of the form the potter has envisaged. The main tool the thrower uses, the wheelhead, can also be part of the creative operation, as are the hands. The clay is centred on the wheelhead, thereby creating the invisible but essential vertical axis of the virtual symmetrical vessel in the making.

To create the vessel you need to pull up the clay. To do so you start a depression at the centre point and by pulling up the clay outwards you follow a virtual parabola – on the wheelhead an open curve, controlled from the outside by the fingers of the other hand, which likewise pull up the clay in an upward direction. The parabola, when rotated about its axis, forms a paraboloid.

By exerting pressure from the bottom of the axis outwards, some clay is removed and driven toward the side, creating a flat surface (a base for the next form). A combined action from the inside and the outside would shift the clay upward in a vertical direction, by thinning the wall to the desired thickness and creating therewith a cylindrical form. The cylinder is considered to be the generator of most geometric forms in clay. By gradually increasing the pressure upwards and outwards from the inside, you obtain a positive curvature and the expansion of the vessel and the related elliptic geometry; whereas inward pressure applied from the outside leads accordingly to negative curvature and to hyperbolic geometry. The combination of the two actions, applied in sequence outwards

136 and inwards by the experienced potter’s hands, will result in the formation of a globular form, the sphere, with all the attributes of spherical geometry.

The illustration of the method mathematicians use to draw the geometrical figure of a parabola, Fig. 83, gave me the idea for the method I have employed for the wheelthrowing of the solid cone I utilised to build the mould for my conic sections. By turning the graphic image of the parabola upside-down, the dilational symmetry of the cone becomes visually clear: the cone is invariant under all dilations centred on its tip. This method gave me the possibility to use one only conic section as a mould for over a dozen conic vessels of varying heights; I subsequently manually squared their rims and added a carving for my square mouthed pots. (See Chapter 6, “Ceramic Practice”, Section “Symmetry Breaking –

Dilation,” 9.)

Fig. 83. “Construction of Parabola,” in D .W Henderson and D. Taimina, Experiencing Geometry: Euclidean and Non – Euclidean with History, 288.

137 Similarly, the mathematician’s geometric method for the construction of the hyperbola is graphically sketched in Fig.84.

Fig. 84. “Construction of Hyperbola,’ in D.W. Henderson and D. Taimina, Experiencing Geometry, 289.

Squaring of the Circle as a Symmetry Operation

By following the same production process I created a new body of work also inspired by the Ice Age square mouthed pottery, however informed by contemporary art design, and dissimilar in shape and size from the previous group. The vessels are tall, of various heights and initially round. While the clay was still damp I manually squared the rim and carved a horizontal, gently undulating line, suggesting a horizon of distant hills or dunes when displayed next to each other. (Fig. 85)

138

Fig. 85. Nora Moelle, 2008. Horizon (from the “Square Mouthed Vases” series). Southern Ice porcelain, unglazed, carved; various heights. Photograph by Allan Chawner.

The breaking of the initial symmetry (circular) and its replacement (square) is a symmetry reduction, a scaling down from an infinite order of symmetry (rotations and translations) around the centre, to a symmetry of degree eight for the square (four rotations and four reflections). We need to recall the definition suggested by K. Mainzer (2005): what is meant by a transformation is a mapping that maps a set of points (e.g. the points of a circle) onto itself with one to one correspondence.10 In Foundation of Science, mathematician Henri Poincaré explains that, in geometry, all conclusions are drawn as if geometric figures behave in just the same way as solid bodies. How for instance, can one prove the definition of the equality of two figures. ‘Two figures are equal,’ Poincaré writes,

10 Mainzer, Symmetry and Complexity, 64. Map, mapping (in mathematics) means ‘associate each element of a set with an element of another set.’ In Concise Oxford English Dictionary, eleventh ed., revised (Oxford University Press, 2006). 139 ‘when they can be superposed; to superpose them one must be displaced until it coincides with the other; but how shall it be displaced? If we should ask this, no doubt we should be told that it must be done without altering the shape and as a rigid body’.11

Ambiguity

The operation of breaking the circular symmetry of the “mouth,” replaced by a square rim, has engendered an interesting outcome on the vessel’s wall: a zone of ambiguity between the two geometrical entities, the circular and the square. The transition, due to the plastic, soft state of the clay during the operation, has left a zone of geometrical ambiguity, with no marks of definite borderline between them. In Paolo Fenoglio’s words, ‘a structure is ambiguous when it belongs on the side of symmetrical indiscernibility, while at the same time presenting a breaking of symmetry’.12

The continuous deformation of a circle in to a square results in the symmetry being broken the instance the circle is distorted. Successive horizontal cross-section define a homotopy

(continuous deformation) between the circle and the square. Interestingly, the infinite symmetry of the circle is broken to the eightfold symmetry of the oval the instant after deformation commences.13 (Fig. 86)

11 Henri Poicaré, Foundation of Science, citation in Herbert Molderings, Duchamp and the Aesthetics of Chance: Art as Experiment (New York: Columbia University Press, 2010), 41-42. 12 Paolo Fenoglio, “Preface,” in Giuseppe Caglioti, The Dynamics of Ambiguity, (Berlin: Springer- Verlag, 1992), XV. Caglioti’s definition of ambiguity is ‘coexistence, at a critical point, of two aspects or schemes of reality which are mutually exclusive.’ 17. 13 I acknowledge the appreciated elucidations and holomorphic images by Dr. Brailey Sims, Department of Mathematics, The University of Newcastle. 140

Fig. 86. Holomorphic images, Circle to Square, by Dr. Brailey Sims.

Square mouthed pots14 are a unique happening that provided for both the living and the dead and were an introduction into the new world of settled civilisation. These pots were important to me in developing two groups of vessels that use contemporary Southern Ice porcelain body. But also the idea of dilation from abstract mathematics generated the spiral installation of these conic sections (Pintadera). In the final chapter I describe my initial Introduction to ceramics and explain the ways in which my research into symmetry has informed my studio practice.

14 See Appendix Field Work: The Square Mouthed Pottery. 141 CHAPTER SIX – My Ceramic Practice

Introduction

The use of geometry as a technical tool is obvious for disciplines like architecture and design; it is not always clear that geometry can be a very creative tool for artists. One instance where this creative spirit is easily perceived is in the works of the Catalan architect Antonio Gaudí, a pioneer in the use of curved, non-Euclidean surfaces: ‘The straight line belongs to man,’ he said, ‘the curved line belongs to God.’1 Gaudí also made use of clay in a most creative fashion, as part of his innovative architectural constructions.

Fig.87. Antonio Gaudí, Casa Mila in Barcelona,1906-10. Fig. 90, In Clark, et al., The Mad Potter of Biloxi, New York, Abbeville, 1989, page 88.

1 Silvia Benvenuti, “The Numbers of Beauty: Can Maths Foster Creativity?” in G. Darvas ed., Asymmetry 429. 142

Not so expected, perhaps, was the attitude of Salvador Dalí, one of the most visionary artists of his time, who in his book Fifty Secrets of Magic Craftsmanship (1948), recommends to the young artist:

You have to use geometry as a guide to the symmetry in the composition of your works. I know that the romantic painters argue that these mathematical frameworks kill the artist’s inspiration, giving him too much to think about. Do not hesitate a moment to reply that, on the contrary, it is exactly not to have to think and reflect on certain things, that you use them2.

Dalí himself gave free rein to his creativity in his interpretation of the fourth dimension, by nailing his crucified Christ, to the representation of a four dimensional hypercube.

Fig. 88. Salvador Dalí, Crucifixion,1954, Metropolitan Museum of Art. In Linda D. Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 2013.

2 Salvador Dalí, Fifty Secrets of Magic Craftsmanship(1948), in Silvia Benvenuti, “The Numbers of Beauty: Can Maths Foster Creativity?” in G. Darvas, ed.,Symmetry: Culture and Science, Vol. 24, Numbers 1-4, 2013, 427. 143

I have found that breaking symmetry has given me a great impulse towards a freer expression of creativity.

Beginnings

I became involved with ceramics almost by chance soon after my arrival in Australia.

Originally it was supposed to give me the opportunity “to do something interesting,” while I had the chance to improve my oral communication in the new country. I am still grateful being taken to the Technical College in Wollongong, the largest populated area near the coal mines and the steelworks of Port Kembla. Here, my husband, a geologist, started his working life. For me, working with clay was the beginning of a lifelong active interest, a fascination that gives me the opportunity to fulfil my inclination for learning and for experimentation. At the college I was soon prompted to look at the attractive wheelwork on a kick-wheel, which, comparing with hand-building without mechanical tools, was promising a more speedy production technique. Following the visual instructions of centuries’ old tradition, I began my career as a wheelthrowing potter.

From day one wheelwork has focussed my interest in the concept of symmetry in a very tangible way. I still have my first hand-built pot with the visible and attractive thumb marks joining each coil for structural strength; but it always annoyed me that it was not quite perfectly symmetrical. The aesthetic of the hand-made was, at that time, overlooked by striving for precision.

A change of tack in my husband’s career took us north to the city of Newcastle. I continued to frequent pottery classes at the local College in order to improve my throwing skills, by experimenting with the iron-rich stoneware clays available at that time, and by developing my own stoneware glazes. At the end of my course, at the last student exhibition at the college, I saw for the first time several small, thin vessels made by one of the students who used a beautiful translucent porcelain clay body, not

144 available before. It was easy to make up my mind to continue my learning process by enrolling in Fine Arts at the University of Newcastle.

Discovering Porcelain

My mind was set to the task of handling the porcelain clay body, notoriously much more difficult to control than the coarser coloured clays. The fine, silky texture of raw porcelain clay, a sensuous pleasure to the touch and to the eye, has to be rigorously kept separate from all other clays; even the dust in the studio could affect its pristine whiteness. During my undergraduate studies I embarked upon a self-directed program of experimentation using several manufactured porcelain clay bodies as an exercise in studying and comparing the plasticity of the clays for wheelthrowing, whiteness and translucency, as well as their behaviours during the firing process. Porcelain requires attention and care at every stage of production; it has a greater shrinkage than earthenware and stoneware and a propensity for slumping, warping and distorting in the kiln. I set out to select the best among six or seven types available to me, which I threw and fired, including a new one, not long on the market, developed in Tasmania and produced later in Victoria by Les Blakebrough, after ten years of research in the

1990s, both in Australia and overseas.

The results were, without any doubt, in favour of Southern Ice developed by

Blakebrough, for its high plasticity and whiteness and for the high degree of translucency. However, I was confronted with a major problem − a high rate of failure caused by warping when firing thin open vessels.

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Beginning Post-Graduate Research and Studio Work 3

Considerations about symmetry, the breaking of symmetry and asymmetry are the prime movers for both my practical studio work and also for the theoretical nature of the topic of my research. On the practical side, symmetry is the starting point for any wheelwork, because the vertical axis of the wheel head determines the equal distance to the rotating pot’s wall. Years of experimentation and experience have been fairly satisfactory in the pursuit of vessel forms, reflecting the traditional canons of aesthetics.

However, to achieve a balance of parts and an overall harmony of proportions is not an easy task. Wheelwork, in particular, is a physical activity, which requires the concentration of controlled muscle power of the arms and a rigid upper body, in order to maintain firm control of hands and fingers in the shaping of the pot. To control your progress you may stop the wheel head and view the shape from the side. For an overall view, you walk away and judge from a certain distance. The potter’s aesthetic judgment is subjective, and may be guided by contemporary trends. Early, in the learning process, I made enquiries about established rules or measurements for the asymmetrical proportions of the vessel form; however, it was only later in my research studies that I obtained a partial answer to these questions, through my in-depth research on symmetry. Jay Hambidge, in Dynamic Symmetry: The Greek Vase, provides a very detailed study of form for the vessels of the classic period in Greece

(from circa the sixth century B.C.), by looking at proportional relationships. The practicality of implementation of such rules is however limited, because it cannot be easily transposed to other vessel forms, and the study is burdened by complex geometrical and mathematical operations.4

3 I started my postgraduate studies as a M.Phil student. By doing my work part-time I was able to dedicate more time to my studio work, which I regularly did by devoting three or four months each year to wheelthrowing, hand manipulation, decoration (carving, deep etching and shellac resist), burnishing and firing. At Confirmation, my Master degree was upgraded to a PhD. 4 Jay Hambidge, Dynamic Symmetry: The Greek Vase, (New Haven, Connecticut: Yale University Press, 1920).. 146

My earliest probing of literature into the field of symmetry, with a view to it being a possible topic for my postgraduate research project, was rather disconcerting, as the text I had was written for a highly specialised audience: Symmetry and Complexity:

The Spirit and Beauty of Nonlinear Science, (2005) by Klaus Mainzer.5 However I persisted with it, as I could read “between the lines”, the winding course taken by the concept of symmetry throughout the ages, not only in the western world, but as a worldwide, universal representation of the human mind. Moreover, Mainzer’s emphasis on the operation of symmetry breaking in all physical and natural processes was of particular interest to me because it would give me the driving force and the motivation to carry out, in a more knowledgeable manner, my plan to break the symmetry of my wheelthrown vessels, by converting it to a symmetry of a different order, or outright into the asymmetrical. On the practical side I wanted to know how far I could take variations of the proportional relationships between the parts of a vessel, but within certain aesthetic parameters. By and large, Mainzer’s treatise was essential reading for an informed overview of symmetry in nature, in science and in art, and also crucial for my understanding and for evaluating subsequent literature on the topic.

A unique opportunity came my way when in 2005 Clayworks Potters Supply advertised

Master Classes conducted by Les Blakebrough to demonstrate throwing and forming, and the shellac deep etching process using Southern Ice Porcelain.

Blakebrough displayed a disciplined approach and high standards of craftsmanship that were inspiring and challenging; he worked with ingenious tools, essential for the success of throwing and turning the fine clay. Most importantly, he offered a solution to the problem of distortion during the firing process, by adopting preventative measures.

They consisted of the additional throwing of a setter, Fig. 89, made from the same

5 In 2005 Klaus Mainzer was Professor of Philosophy and Science Theory at the University of Augsburg, Germany; In 2014 Mainzer has been working in Munich at TUM (Technische Universität München), Faculty of Education and Research, Department of Philosophy of Science. 147 porcelain body to fit the bowl and then to fire it upside down. This method greatly reduced distortion problems.6

Fig. 89. Les Blakebrough, Universty of Tasmania, 2005. Fitting a “setter.” In Jonathan Holmes, Les Blakebrough: Ceramics (Fishermans Bend, Vic: Thames and Hudson, Australia, 2005, 89. Photograph by Lynda Warner.

The works I had chosen for the exhibition of my studio work for my Honours degree were symmetrical, white porcelain, glazed and unglazed pieces, decorated with deep etching and carving, seeking to optimise the inherent qualities of translucency of the

Southern Ice clay body, as can be seen in Fig. 90.

6 The technique of stocking ware on its rim to reduce the risk of warping was pioneered in Northern China early in the 8th Century. The point of contact between the setter (chuck) and the pot has to be free of glazing material to prevent fusion. This explains why the Chinese sometimes fitted a ring of copper, silver or gold to cover the rough edges of the rim, and this, coincidentally, enhanced the status of the vessels. 148

Fig 90. Nora Moelle, Stemmed Vessel, 2005. Southern Ice porcelain, clear glaze, deep etching, shellac resist. 16x12x12 cm. Photograph by author.

My research project has been like a voyage into the unknown, but with unexpected treasure troves along the way. As it is for most people, the concept of symmetry was for me limited to its most popular understanding, i.e., bilateral symmetry, or the symmetry of left and right, like an object and its mirror image, or two identical parts; and central symmetry, as in the rosette windows of Medieval cathedrals. In addition to

Mainzer’s book Symmetry and Complexity, I was trying to complement my approach to symmetry with another work by Mainzer, Symmetries of Nature, (1988 – English translation 1994), a comprehensive treatise on the philosophy of nature and science.

My way of handling the complex material, that is, my methodology, was to extract from my readings the most salient theoretical principles relating to my topic, not only in order to clarify my understanding, but also for later reference in respect to my own studio work. The essential features of this background information are part of my exegesis, collected in the preceding chapters.

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Research and Studio Work: Reciprocal Influences

This ongoing interchange between the growing understanding of the nature and manifestation of symmetry and the development of the studio work was not one of

“illustrating” these ideas but was inspired by my growing excitement about the potential for breaking symmetry. This relates to the Japanese tradition of ‘losing control’ through changing the potential sameness, repetitiveness and indifference’ that sometimes mark ceramics that are inspired by earlier concepts of symmetry.7

During my candidature, a few months every year are dedicated to the planning and making of my ceramic work; this was usually related to and inspired by the particular research direction I was involved in at that time. My first body of work in ceramics was created while I was trying to accommodate Mainzer’s theoretical principles of symmetry in nature (and its links to the Golden Section), with the applied study of biology by

D’Arcy Thompson, and Philip Ball’s informative dissertation on pattern formation in nature. I should add here that since my early reading and my interest in the function of symmetry in natural phenomena, the role and the importance of the golden proportional symmetry, the Golden Section,8 has soared dramatically (as author Scott Olsen has stated in a recent publication), ‘playing a formidable, in fact a striking role in a variety of the most provocative scientific developments. 9

7 See final paragraph of Chapter One, 25-26. 8 For the Golden Section, see my Chapter 1, “Symmetry of Early Art,” 7-8. 9 Scott A Olsen,” The Golden Section’s Pivotal Role in Modern Science,” in György Darvas, ed., Symmetry: Culture and Science, (Budapest: Symmetrion, 2013), Vol. 24, Nos. 1-4, 257-274. Author Olsen in his study states that The Golden Section, which was considered an ‘outmoded, pseudo-scientific subject,’ can no longer be ignored, due to the ‘stunning advances with Golden Section consequences’ in physics, chemistry, biology and cosmology. In particular, among others, he mentions DNA structure, Fibonacci regularity in the periodic table, the function of the heart, division of biological cells, quantum mechanics, black holes, and even cosmogenesis – the very origin and structure of the Universe. 150

The Merewether Beach Collection

The inspiration to transpose to my ceramic vessels objects of nature, which bear the imprint of the symmetrical rules of growth, came from a variety of marine detritus during my daily walk along the sand of Merewether Beach, a south eastern suburb of

Newcastle, an example is shown in Fig. 91.

Fig. 91. Merewether Beach, residual marine life. Photograph by author.

I frequently come across marine plants like seaweed washed ashore, and shells of widely differing forms, each one displaying, in its own asymmetrical shape, a rhythm of growth, which conforms with exact, proportional relationships.10 On a winter morning it is not rare to come across a shell similar to that of Doczi’s Abalone (Haliotis asinina), which unfolds in a logarithmic spiral, in the combination rotation-plus-dilation. Doczi’s diagram shows that each consecutive stage of growth is encompassed by a golden rectangle which is by a square larger than the previous one. Successive stages of

10 Architect György Doczi, in The Power of Limits, has created a collection of remarkable studies on the proportions of nature, art and architecture − from plants and animals to the crafts and hieroglyphs, from the proportions in buildings to the rhythms of music and to Dante’s constructions in his poem La Divina Commedia. 151 growth of shells are Fibonacci’s numbers.11 Shells collected along the shoreline which have been used as a template for delicate carvings on the translucent walls of my symmetric porcelain vessels. (Fig. 92)

Fig. 92. Nora Moelle, Open Forms. The Merewether Beach Collection, 2007. Unglazed Southern Ice porcelain, deep etched, shellac resist, 17x17x17 cm. Photograph by Allan Chawner.

The waves of the sea, the little ripples on the shore, the outline of the hills, the shape of the clouds, all these are so many riddles of forms, so many problems of morphology, and all of them the physicist can more or less easily read and adequately solve. D’Arcy Thompson, On Growth and Form.

After a windy night the sandy beach has lost all marks of human footprints; ripples of sand glitter, in apparent symmetry, in the light of the morning sun in a tapestry of parallel wavy ridges and furrows, similar but not identical. In Fig. 93, ripple marks are engraved by the wind. When the wind blows persistently, the sand is shifted upwind.

But if by chance a tiny bump appears, more grains impact the windward (stoss) side.

11 Doczi, The Power of Limits, 54. For the details of the Fibonacci sequence, see my Section “Early History of Symmetry,” Chapter One, page 19. Doczi’s Abalone shell and diagram (Fig.22) illustrating the Fibonacci sequence. 152

They do not simply sit where they strike, the grains bounce. Each grain scatters others from the surface as it strikes and travels downwind in a series of short hops, a process called saltation. The grains accumulate at the slope crest; the leeward foot of the slope therefore receives fewer new grains, and so it begins to hollow out into a depression.

At the top of this new slope grains begin to accumulate by saltation, developing into a new, downwind stoss slope and a new ripple is formed.12

Fig. 93. Merewether Beach. “Ripple Marks”. Photograph by author.

12 Ball, “Shifty Sands,” in The Self-Made Tapestry, 216-222. 153

Fig. 94. Nora Moelle, Sphere. The Merewether Beach Collection. 2007. Unglazed Southern Ice porcelain; carving, 14x13x13 cm. Photograph by author.

The appearance of small-scale sand ripples on a flat surface, blasted with a continuous flow of wind-blown grains, is an example of growth instability. Although the superficial appearance of sand ripples is symmetrical, two ripples are never identical and they are not at exactly repeating intervals in space. Their asymmetry is due, among other reasons, to the varying size and weight of the single sand grains and to the changing strength and direction of the wind, as well as to the fluctuations in the topography.

As an example of a spontaneous pattern process, I have chosen the complex system of transformations of the ripple marks because it is visually attractive, and the mechanics of the process are intriguing. Hermann Weyl suggested that asymmetry probably results more effectively in beauty when the underlying symmetry upon which it is built is still apparent.13

13 Weyl, Symmetry, 13. 154

As I am walking, I let the coastal and marine environment inspire the shapes of my vessels on which the asymmetrical wavy ripples of sand will mark indelibly the pristine white background of the Southern Ice porcelain as can be seen in Fig.84.

Occasionally, I stop and use the sandy beach as a drawing surface, in order to evaluate the visual impact of a curve, or to assess the proportional relationship of the pot’s spherical shape and the winding lines of the ripple marks. And the gentle sweep of the frothy water will brush away the lines in the sand.

Identifying the New Geometries in My Work after the Breaking of Symmetry

The research I have carried out in connection with my Chapter Three on the “new geometries” has been critical for me in identifying the qualifying elements of the particular geometries which inform the shapes of my related groups of vessels. One body of work which I completed in 2009-2010 consists of several globular bottles (Fig.

95), which I threw on the wheel, each in two composite parts, and then manipulated in order to radically change their geometry. Following the group of bottles, I planned a series of vessel forms inspired by the shape of an ancient jar, used for millennia to transport spices and precious substances across continents; it is known by the name of albarello (Fig. 96). As I grew up in Northern Italy, the albarello “drug” jar was a common sight in the pharmacies; today some are still there, perhaps only for decorative purposes. In my family’s country house there was a battery of albarello jars, with a mysterious Latin inscription, on the sideboard of our dining room. However, before I deal individually with the geometric forms of these groups of vessels (characterised by many elements of non-Euclidean geometry), I will recall the essential distinguishing properties of Euclidean and the Non-Euclidean geometry.

155

Fig. 95. Nora Moelle, “Bottle”, 2010, Southern Fig. 96. Hispano-Moresque Ice Porcelain, unglazed, 23x15x13 cm. Albarello, Valencia, early 15th Photograph by Allan Chawner. century. Height 38 cm, in Victoria and Albert Museum. In Alan Caiger-Smith, Tin Glazed Pottery, 1973. Illustration F, page 48.

Euclid’s Fifth Postulate (or Parallel-Lines Postulate) states that through a given point not on a given line, one and only one line can be drawn parallel to a given line. With this assertion, it can be deduce that in

Euclidean geometry

• Planes are infinite in area and flat

• Lines are infinite in length

• The angles of triangles always sum to 180°

In the 19th century, however, after many centuries of controversy about the dependence / independence of the fifth postulate, and by accepting the possibility of

156 curved space, mathematicians finally established that there are another two basic types of planar geometry besides Euclidean Geometry. These are:

Elliptic Geometry14. In elliptic geometries:

• Planes are positively curved, like spheres, finite in area15

• Lines are great circles, finite in length16

• Angles of a triangle add up to more than 180°

Hyperbolic Geometry17. In hyperbolic space

• Planes are negatively curved and infinite in area

• Lines are infinite in length

• The angles of a triangle add up to less than 180°

Geometry is Symmetry 18

1. The Globular Bottle

The outline of my globular bottle, Fig. 97 and Fig. 98, shows bilaterally two opposing curvatures, one is positive, i.e., the globular body (elliptic geometry); and one of negative curvature, corresponding to the “inward” curving of the neck (hyperbolic geometry).

14 Elliptic = Spherical; or Riemannian = Positively curved space 15 See “Riemann’s Geometry Represented on a Sphere” in my Chapter Three, “The New Geometries,” page 44, Fig.22. 16 Great circles on a sphere are intrinsically straight lines which divide the sphere into two equal- size pieces. Additional information in this section has been taken from: B. Rich and C.Thomas, “Non-Euclidean Geometry”, in Schaum’s Outline of Geometry, fifth edition (New York: McGraw- Hill, 2013), 3-9. 17 Beltrami’s Pseudosphere is hyperbolic. See my Chapter Three “The New Geometries,” Pages 42-43, Fig.21. 18 “Geometry is Symmetry” is the Title of a section of Chapter 2 in Stewart and Golubitsky, Fearful Symmetry, 43-46. 157

Fig. 97. Nora Moelle, Bottles, 2012. Fig. 98. Work in progress. Photo by Photograph by Allan Chawner. author.

The long curve of the neck bears combined elements of curvature which is called a saddle;19 or hyperbolic paraboloid, as seen in Fig 99. Hyperbolic surfaces are sometimes frilly, like crocheted hyperbolic planes with different radii,20 or like certain kinds of seaweed (the word hyperbolic has roots meaning excessive and exaggerated) as seen in Fig. 101.

19 “Saddle,” a place on a surface where one cross-section is convex and another concave, like a mountain pass or a horse’s saddle. 20 “Crocheted Hyperbolic Planes,” in David Henderson and Daina Taimina, Experiencing Geometry: Euclidean and Non-Euclidean with History (Upper Saddle River, NJ:Pearson Prentice Hall, 2005), 72. 158

Fig. 99. ‘The hyperbolic paraboloid.’ In: Silvia Benvenuti, The Numbers of Beauty: Can Maths Foster Creativity? In G. Darvas, ed., Symmetry: Culture and Science, Vol. 24, Numbers 1-4, 2013 (Budapest: Symmetrion, 2013), page 431.

An example of hyperbolic and elliptic geometries is embodied dramatically in the shapes of some of the outstanding pottery forms of George Ohr, as seen in Fig. 100.21

21 See the section of my Chapter Four, “George Ohr,” 110-119. 159

Fig. 100. George Ohr. Plate 78, Vase, c.1902-7 In: Clark, et al., The Mad potter of Biloxi, Abbeville press, New York, 1989, page 116.

Fig. 101. Hyperbolic space Negative curvature, Fig. 19-8. In: B. Rich & C. Thomas, Schaum’s outline of Image unavailable due to copyright Geometry, McGraw Hill, New York, 2013. restrictions

The “induced” symmetry breaking in my globular bottles has occurred by shifting the vertical axis of the neck off centre and by tilting it to the side. In order to join the tilted neck to the body, an elliptic opening had to be cut diagonally across the shoulder of the bottle, adjusted to fit with the elliptic base of the neck. The hovering curved handle may visually enhance the tilting of the neck. Moreover, I have carved a vertical line on one side (only) of the handle of three bottles to add a further element of asymmetry in

160 relation to the individual vessel; but when the bottles are viewed (exhibited) together in a row, the carving becomes a complementary element of translational symmetry of the installation.

Planning my Next Project (Studio Work)

Towards 2010, I became more confident due to the additional theoretical information I had found in my research and by gaining more experience on the practical level of handling porcelain clay. I therefore planned the next body of work with more complex forms by breaking the symmetry and by manipulating some individual components towards non-Euclidean geometrical variations (i.e. curved surfaces, elliptical and hyperbolic planes). Furthermore, almost in defiance of ancient rules of symmetry, that is of balanced, proportional relationships’ required by century old canons of aesthetics,

I decided to experiment by introducing a variation of lengths and widths of the single parts, which altered the proportional relationships.

The point of departure for this latest project (2010-2012) is a “classical” vessel form, the iconic shape of the centuries old albarello drug jar.’ 22 An early example, originally from Mesopotamia, Fig. 102, as well as the Spanish-Moresque albarello, seen as above in Fig. 96, and its Renaissance “descendant”, Fig. 103, exhibit prominent hyperbolic planes, i.e., a continuous negative curve of the vessel’s wall, used by the

(anonymous) painter as a canvas. In fact, the albarello, in its oldest, primeval version, is believed to have been a storage vessel made from a section of the woody, hollow stem of the bamboo, a common tree in the regions of the Far East of Asia. The timber

22 The etymology of albarello is uncertain. In Lo Zingarelli: Vocabolario della Lingua Italiana (Bologna: Zanichelli, 2005). 161 container, being light and durable, has been used from ancient times to store and transport food, spices and herbs, often fitted with a lid made of leather.23

Fig. 102. Albarello, Raqqa, Mesopotamia late 12th or early 13th Century (22.9 cm) Victoria and Albert Museum, London. In World Ceramics: An Illustrated History, ed. R. Charleston. New York: Crescent Books, 1990, Fig. 250, page 86.

2. The Albarello. Brief Historical Background

The history of the ceramic albarello may be closely associated with that of tin-glazed pottery, a white glaze developed in Mesopotamia in the ninth century. The tin-glaze was originally used as a white background to cover coloured (iron) clays, as a canvas for painting exquisite decorations with lustres and enamels. It was exported to Syria and Egypt. Over the next two centuries, with the expansion of Islam, its technical

“secrets” were carried by itinerant Egyptian craftsmen and potters across Northern

23 Walter Dexel, Keramik Stoff und Form (Berlin: Kilnkhart und Biermann, 1958), 21. 162

Africa and into Spain; from there it reached Europe, where it was adopted and used for the next 300 years.24

Fig. 103. Albarello. Inscribed MIDEA BELL. Faenza, c 1500. Height 31 cm. Musée du Louvre. In A. Caiger-Smith, Tin-glazed Pottery in Europe and the Islamic World, Fig. 63, following page 80.

At the time, the albarello ceramic container was used for the transportation of spices across the continents. China was the only country which was manufacturing porcelain wares, with beautiful decorations and glazes. From the late eighth century the Chinese were exporting porcelain wares to the Middle East and South-East Asia, most appreciated and sought-after everywhere they went. Many attempts were made over the centuries to reproduce Chinese porcelain wares; their failure prompted people to develop white slips or glazes, like the white tin glaze, to conceal the dark clay bodies.

Similarly, the albarello container was also covered with white tin-glaze as a background for the spectacular oriental lusters and enamel decorations.25

24 Alan Caiger-Smith, Tin-Glazed Pottery in Europe and the Islamic World: The Tradition of 1000 Years in Maiolica, Faience & Delftware, (London: Faber and Faber,1973), 50. 25 Caiger-Smith, Tin-Glaze Pottery in Europe and the Islamic World, 50. 163

The journey of tin-glaze on the albarello continued its long march to Spain. From there tin-glazed wares were shipped from the southern ports of Spain to Italy, to a great extent by Majorcan traders. The term maiolica in Italy came to denote all tin-glazed wares. The slightly inward curve (hyperbolic curve) of the albarello’s tall body, coming to an abrupt change of direction at the foot and shoulder, made a clearly defined area also for the Renaissance painter to explore, in harmony with the ideals expressed in fine arts, using line drawing and a wide range of colours.26

The Albarello and My Studio Work

My albarello-inspired form has gone through a series of dramatic changes, closely integrated with the theoretical framework that I have developed in the exegesis. My intention was to follow a path of symmetry breaking operations, which has been experimented before, during the last one hundred years of ceramics, albeit, at first only by a few potters and with strong opposition on the part of the ruling “authorities” on entrenched aesthetic principles.27 I planned a deliberate change of the initial symmetry for a geometry of non-Euclidean, unconventional variations. Obviously, the plastic composition of wet clay material is an ideal medium for innumerable transgressions, e.g., for the breaking of the initial symmetry dictated by the action of throwing.

In order to structure my plan of action I had to set certain parameters, defining the limits in which to work. Wheelwork is the point of departure, as it gives me the initial symmetric unit. Normally I would throw the albarello shape in one consecutive action

26 Caiger-Smith, Tin-Glaze Pottery in Europe and the Islamic World, 83. 27 In the last century the Arts and Craft Movement, in England first, but also in the United States and Australia, among other countries, had a major impact in dictating ceramic practices, which were followed by the majority of ceramic teachers and practitioners. Prominent non-conformists potters were, in USA, George Ohr, whose work had been utterly rejected during his lifetime and forgotten for half a century after his death (but now a museum has been built to exhibit his work). The nonconformist work of Hans Coper, who worked in England, was also rejected at first; and equally Peter Voulkos’s working methods in the USA were initially dismissed. To these three representative potters of the asymmetrical I have dedicated Chapter 4 of this exegesis. 164

(a ceramic lid was, historically, a later, optional addition). Changing the shape means manipulating the single parts of the vessel (foot, wall, neck, lid), hence they have to be thrown separately. Within my plan was also the intention to maintain the “functional” vessel form, a container − my work-option all along − as I wanted to retain the primeval functional container form of wheelthrown pots. By comparison, of the three most representative potters, whose asymmetrical work I have chosen for a study in my exegesis (George Ohr, Hans Coper and Peter Voulkos), it is Hans Coper’s working method which could best be associated with my own methods and ceramic techniques

(albeit by using fundamentally different materials and firing methods).

For the first set of four of these altered vessels I decided to maintain the overall proportions and measurements of the original albarello, in order to highlight the “blood- relationship.” (Fig. 104) I broke the symmetry by setting the neck off-centre, and by making the neck’s base curved and inclined, at an angle to the vertical axis. The neck itself is symmetrical and vertical, and bears the potter’s “signature” by displaying the undisguised finger marks of the throwing process; this was to avoid the symmetry implicit in most industrial pots.

165

Fig. 104. Nora Moelle. 2010. (First model of “non-Euclidean” albarello), Wheelthrown and manipulated albarello-type vessel. Southern Ice porcelain, unglazed, various sizes. Photograph by Allan Chawner.

For the subsequent units of the albarello-inspired body of work I have applied the basic operational elements of symmetry violations described above, but the proportions of the composing parts have been severely altered to varying degrees, affecting each single unit in a different way. (Fig. 105) For the purpose of placing an inclined upper plane, the thrown cylinder defining the main body had to be cut diagonally, resulting in an elliptic (oval) opening. (Fig. 106) Consequently, the curved base and the lower part of the neck had to be adjusted accordingly. This symmetry breaking operation resulted in a change of the geometry, from circular to elliptic, from Euclidean to non-Euclidean geometry.

166

Fig. 105. Nora Moelle 2010. Wheelthrown and manipulated. Southern Ice Porcelain, unglazed. 34 x 30x30 cm. Photograph by Allan Chawner.

Fig. 106. Nora Moelle. 2010. Manipulated wheelthrown parts. Working stages. Photograph by author.

167

Fig. 107. Nora Moelle Manipulated albarello inspired vessels, installation. Southern Ice Porcelain, wheelthrown, unglazed, various sizes. Photograph by Allan Chawner.

The presentation of this group of vessels in the final exhibition has to take into account the altered proportional relationships (heights and widths) applied to each vessel; therefore, this body of work might be best exhibited in an installation of a corresponding asymmetrical set-up, Fig. 107, perhaps with each vessel sitting comfortably in the shade of its “mate”.

3. Computer-Designed Variations of the Albarello Form

My next body of work was prompted by an interesting ceramic vessel I saw in the

Canberra school of Art Gallery in the Australian National University, on the occasion of a Ceramic Symposium held in August of 2012. It was a special “cup,” wheelthrown by potter Janet de Boos, but computer-designed by Dutch potter Jeroen Bechtold, who

168 was at that time a visiting artist in the Ceramic Department at the Australian National

University. (Fig. 108)

Fig. 108. Janet De Boos. Computer-designed cup, Australian National University . Photograph by author.

In the design of my albarello-inspired vessel, the idea of extending the violations of symmetry − short of being “off balance” − was an attractive option. At the symposium, I was lucky to meet a fellow participant, Feng Te, an art student in China, who had the skill and was willing to try and use his expertise to computer-design my next body of work. (Fig. 109)

169

Fig.109. Feng Te, 2012. Computer designed images of albarello-inspired vessel

forms.

My idea, prompting the project, was to exploit the process of translation from one geometrical system to another (i.e., from Euclidean to non-Euclidean geometry), and to amplify the characteristic of each system. This becomes evident in the conversion of the straight vertical and inclined planes of the main body into curved, hyperbolic and elliptic planes. The lid has also been dramatically transmogrified, by magnifying the proportional relationships of the parts, and by a drastic conversion, from the straight horizontal plane of the lid, to a curved, hyperbolic, but also inclined and swivelling

170 surface, as seen in Feng Te photogram. My realisation of the computer designed vessels in bisqued Southern Ice porcelain are reproduced in Fig. 110 and Fig. 111.

Fig. 110. Nora Moelle, 2012. Computer-designed vessels, Southern Ice Porcelain, wheelthrown, manipulated, bisqued. Various sizes. Photograph by Allan Chawner.

Fig. 111. Nora Moelle, 2012. Computer-designed vessels, Southern Ice Porcelain, wheelthrown, manipulated, bisqued. Various sizes. Photograph by author.

171

Working Stages

Fig. 112.

Fig. 113

172

Coda

My journey in the world of symmetry has been interesting, complex, puzzling and illuminating; and indeed, there have been interesting treasure troves along the way.

Sometimes tasks are demanding and daunting; but, as Italian writer Italo Calvino points out,

in the urge to look for a way out, there is always a certain amount of love for the labyrinth in itself; and a certain zeal in looking for the way out, plays a part in the game of losing oneself in labyrinths. 28

Italo Calvino, 1962.

28 The English translation of Calvino’s excerpt is in Giuseppe Caglioti’s The Dynamics of Ambiguity, (Berlin: Springer, 1992), 135. 173

CONCLUSION

My resolve in undertaking this project was to break the symmetry of the wheelthrown base pot in order to implement dynamics and change in the vessel form. This led to a series of ceramic projects: the first body of work is comprised of translucent, open vessel forms, engraved with sea-shore objects that I have called “The Merewether

Beach Collection”, including spherical vessels carved with ‘ripple marks’, following a series of globular bottles marked by combined and reduced symmetries. The point of departure for the next three projects was the albarello shape, familiar to me from childhood. I have progressively altered its shape by breaking the original symmetry and by manipulation of the parts. Subsequent changes were variations in lengths and widths of single parts, which altered the proportional relationships.

Lastly, I created a computer designed variation of the manipulated albarello shape, thereby I intended to extend the violations of symmetry through the identification of the prime movers for contemporary practice. While my intention was to break symmetry, I consider that the ceramic works in this project still contain elements of harmony, rhythm, balance and proportional relationships. In Antiquity beauty was seen as implicit within proportion. By manipulating proportion, I sought to discover new ideas of beauty that formed, not through cannons of proportion, but through new juxtapositions of relationships. Through my research and understanding of the limitations sometimes implicit in symmetry – sameness, repetitiveness and indifference – the contribution of the new geometries, and the work of previous ceramicists, have helped me to reframe these limitations to break symmetry and so implement new dynamics and change in the vessel form. The non – Euchlidean geometry and the fourth dimension enable the reframing of these limitations by introducing motion, dynamics, incongruity, disorder and chaos.

174

The impact of the new geometries had a powerful effect in the world of art. My research contributes both to the understanding of these influences, and to provide strategies such as dilations, conic sections and curvature of space, so that such insights might be used by other ceramic artists. This project provides a way of seeing and using these revolutionary changes in the aesthetic perception of symmetry within ceramic practice.

175

APPENDIX

Field Work: The Square Mouthed Pottery

The degree of competency in the production of prehistoric square mouthed pots appear surprisingly high. A background knowledge of the society and of the times in which the pottery was produced has thrown some light on an age for which little information is available. Obviously the archaeological finds collected in the strata of the earth, accumulated and untouched for millennia, give the best clues and guide for a meaningful interpretation. Archaeometric studies of the area have identified the chronology of square mouthed pots, dating to the latter part of the Stone Age, the Neolithic.

Fig.114. Northern Italy showing present day regional and national frontiers and main towns.

176 The Neolithic era is believed to have spread to the northern regions of Italy at about the middle of the sixth millennium BC, after the first groups of farmers had arrived via the sea on the shores of the Liguria region in the west, about 5800 BC.1 Over the centuries they replaced the groups of hunters and food gatherers of the Mesolithic and introduced agricultural methods and animal farming, as well as the basic technologies for the manufacture of ceramics. 2

Fig. 115. Northern Italy in Middle Neolithic times. In Lawrence Barwick, Northern

Italy: Before Rome. London: Thames & Hudson, 1971. Fig. 11, page 34.

1 Pedrotti, “Il Neolitico”, 122-23. 2 Pedrotti, “Il Neolitico”, 122, 124-5. The transition from the stage of hunter-gatherer to that of farmer happened independently at different times and in different parts of the world. Generally the Near East is recognised as the centre for domestication (after 9000 BC); vegetal species were introduced, like wheat, barley, leguminous plants, as well as animals as sheep, goat ox, pig, from which the “colonisation” of the Mediterranean coasts is believed to have started via the sea, and via land along the river Danube. Pedrotti, “Il Neolitico,” Endnote 35, 179. 177 Indications of the spreading of agriculture and of improved lithic tools for cutting and carving stone and timber, as well as widespread making of clay vessels have been confirmed in many archaeological sites of the Early Neolithic, predominantly in rock shelters. However it was during the Middle Neolithic (first half of the fifth millennium BC) that major changes in the lifestyle of the population took place. With the expansion of agriculture, people occupied more flatlands and lived in more durable dwellings; pottery was used for cooking food, for storage and for funeral rites; the practice of weaving was also introduced.3

The unearthing of ceramic pieces, together with other related findings in bone and stone, were of great interest to archaeologists; with the help of modern technologies and methods, they were able to recreate the paleo-environment of the region, which they called The Square Mouthed Pottery Culture.4 It covers a period of time of about one thousand years, from approximately 4900 to 3900 BC.5

Archaeological sites indicating the presence of artefacts belonging to the Square Mouthed

Pottery Culture extend from the Liguria region in the north-west to the southern fringes of the Po Plain, as well as to the far north-eastern region of Friuli. However the most prolific sites to date are those unearthed in the Trentino-Alto Adige region in the central north-east area of the Alps. Two of these sites are located on the outskirts of the city of Trento; one called the Gaban rock shelter shows evidence of protracted habitation from the Mesolithic

Period down to Roman times. The other site, La Vela, almost incorporated into the city by

3 Elisabetta Mottes, “Le Prime Scoperte”, in Spirali del Tempo, Meandri del Passato. (Page numbers not given.) 4 Analysis of stratigraphic sequences in the excavation sites, as well as comparative studies of styles preceded more accurate methods of determining the age of findings. A breakthrough occurred with the discovery of radiocarbon dating in 1949 by W.F. Libby. Best known as carbon 14, it is the ‘best known example of an atomic clock based upon radio-active decay; applied to an organic material such as charcoal, grain seeds, twigs and bones…these reveal traces of carbon 14, thereby helping date whatever inorganic objects were associated with them.’ Marija Gimbutas, “Chronology”, The Language of the Goddess, (Harper and Row: San Francisco, 1989), 330. 5 Pedrotti, “Il Neolitico”, 128. 178 the sprawling suburbs (and within walking distance from my high school), has revealed the most comprehensive finds of the Middle Neolithic in the Province.6 It is situated on a large alluvial fan build up over millennia by the torrent Vela at its confluence with the Adige river.

Excavations at La Vela have brought to light evidence of structures for habitation, and of holes for supporting timber poles and also relatively large areas of pebbles and gravel, indicating a likely means to stabilise spaces and assist with drainage; included are the remains of a structure for a fireplace.7 Since excavations started in 1960 (now covering an area of 800 metres), fifteen stone cist graves have been unearthed; the burial area was originally situated outside the village site. The cists contained the skeletal remains of men, women and children that were placed in a crouched position and in most cases were supplied with grave goods.8

Some aspects of these funerary rituals are highly codified and witness an ideological common ground shared within the Square Mouthed Pottery Culture.9 The burial sites were usually individual; the bodies were always placed on their left side, legs tucked up; the skull facing north and the face turned to the east. Some parts of the body and in particular the skull were often sprinkled with red ochre or cinnabar. Square mouthed pots were usually placed next to the bodies of women or children; the original content and intended use can only be speculated. Their personal ornamental objects were shells (Spondylus gaederopus) used for forming beads for necklace, bracelets or belts; sometimes there were bone bodkins used probably to hold together their clothing.

Bodies of males were often buried with objects characteristic of the image of the hunter – warrior, generally associated with polished stone axes and scalpels, flint arrowheads and

6 Pedrotti, “Il Neolitico”, 132. 7 Pedrotti, “Il Neolitico”, 145. 8 Mottes, “I Riti Funerari della Cultura dei Vasi a Bocca Quadrata”, in Spirali del Tempo. 9 Mottes, “I Riti Funerari della Cultura dei Vasi a Bocca Quadrata”, in Spirali del Tempo. 179 bladelets. Other objects found in the graves were millstones and a fragment of a loom weight.10

From prehistoric times the Adige Valley has been one of the main arteries for communication between the Italian peninsula and central Europe, with access, by way of the river Danube and the Balkans, to the Near Eastern countries. There is evidence that with the onset of the Square Mouthed Pottery Culture the local communities of Northern

Italy fostered relationships of trade and shared skills within the groups, but that they also developed intercultural associations and commercial intercourse with people far afield.

In the southern Alpine area the archaeological sites of Gaban and La Vela have revealed many objects of exotic origin; at La Vela these were mostly wares of prestige which were deposited in the stone cists with the body, thereby underlining the person’s social status: a skilfully shaped and polished dark green axe made of jadeite, believed to have originated in the Western Alps; a polished scalpel of actinolite schist believed to be of north Alpine provenance. The shell used for the jewellery pieces found in the burial site of women and children is that of the bivalve mollusc Spondylus gaederopus, which lives only in the waters of the Mediterranean Sea; its usage is also documented over a large area along the river Danube.11 A strong ideological association with the Balcanic - Mediterranean area is evidenced by the presence of two small female figurines believed to represent the symbolic image of the Earth / Goddess; they were unearthed in the Gaban rock shelter.12

The existence of cultural contacts between the communities of the north and Neolithic groups of southern Italy has been suggested after a globular vase with a short neck and a square handle was found in a rock cist at La Vela; this ceramic form imitated models of

10 Mottes, “I Riti funerari della Cultura dei Vasi a Bocca Quadrata”, in Spirali del Tempo. 11 Mottes, “Oggetti da terre lontane” in Spirali del Tempo. 12 Pedrotti, “Il Neolitico”, 138. See also Gimbutas, Fig. 168 (3), 103, and Fig. 139, 85. 180 peninsular tradition in the style of the Sierra d’Alto Culture (fifth millennium BC) of the south-eastern region of Puglia.13 Likewise at La Vela a fragment of an S-shaped clay stamp or seal has been found, with an operative face carved to form an antithetic spiral, a decorative design pattern feature which also finds matching models in the Sierra d’Alto tradition.14

The significance of archaeological finds acquires a new dimension through the analysis and interpretation of symbols and images that have appeared repeatedly in design patterns; they are believed to be the expression of a basic world view and spirituality of ancient European peoples.15

A remarkable study in this field has been carried out by the archaeologist and pre-historian

Marija Gimbutas in The Language of the Goddess.16 In this research, illustrated with nearly 2,000 artefacts collected over a vast area from the Near East to the Mediterranean, from Europe’s eastern and central areas to the northern and western regions, Gimbutas has documented a shared pool of related basic patterns and images:

The amazing repetition of symbolic associations through time and in all of Europe on pottery figurines and other cult objects has convinced me that they are more than ‘geometric motifs’; they must belong to an alphabet of the metaphysical.17

In a bold and imaginative reconstruction Gimbutas has not only confirmed a matriarchal order of thought and life in pre-historic times; she has also been able to establish, on the

13 Mottes, “Peninsular cultural influences in the Square Mouthed Pottery Culture in Trentino,” in Preistoria Alpina, Vol.33 (1997), (Trento: Museo Tridentino di Scienze Naturali, 2001), 63-67. 14 Pedrotti, “Il Neolitico”, 144. According to Gimbutas, the spiral as a design on pottery emerged in the second half of the 7th Millennium B.C. in south-eastern Europe (Thessaly); it spread to the Danube basin and to the eastern Balkans between 6000 and 5500 B.C. and became very common in the next two millennia. Gimbutas, The Language of the Goddess, 279. 15 Dorothy Washburn & Donald Crowe eds., “Introduction”, Symmetry Comes of Age: The Role of Pattern in Culture, (Seattle: University of Washington Press, 2005), ix–xxx. 16 Gimbutas, The Language of the Goddess, see footnote 5. 17 Gimbutas, The Language of the Goddess, 1. 181 basis of these interpreted signs, the main themes of a “religion” of worship of the universe as the living body of a Goddess – Mother creator.

In her view the images and symbols of a parthenogenetic (creating from herself) Goddess are the most persistent feature of the Palaeolithic era around 25,000 BC, when the first sculptures of bone, ivory or stone appeared together with their symbols – streams, triangles, nets, chevrons (double or triple Vs), zigzags, cup marks (or dots), meanders –

(graphically a pubic triangle is most directly rendered as a V).18 These hieroglyphs relate primarily to life-giving water, and by association, to the Goddess’s breasts, eyes, mouth and vulva.

The major aspects of the Goddess of the Neolithic, the birth-giver, the fertility giver, the dispenser of nourishment can be traced back to agricultural people’s beliefs concerning sterility and fertility, the fragility of life, the fear of destruction and the periodic need to renew the generative processes of nature.

The main theme of the Goddess’ symbolism is the mystery of birth and death and the renewal of life, not only human but the whole cosmos. In art this is expressed by signs of dynamic motion: whirling and twisting, spirals, coiling snakes, circles, horns, sprouting seeds and shoots.19

The Goddess-centred art with a notable absence of images of warfare and male domination reflects, in Gimbuta’s view, a peaceful existence and a true ‘florescence and sophistication of art and architecture’ reaching its heights in the 5th millennium BC.

However a very different Neolithic culture with the domesticated horse and lethal weapons emerged in the Volga basin of southern Russia and spread to the south-west, changing

18 Gimbutas, “Introduction,” The Language of the Goddess, xix. 19 Gimbutas, The Language of the Goddess, xx. 182 the course of European pre-history. Invasion and encroachment by Proto-Indo-European people put an end to the old European culture between 4,300 and 2,800 BC, changing a matriarchal society to a patrilineal and androcratic system. Western Europe, in Gimbuta’s view, escaped the process of those significant changes to the social fabric the longest: here images and symbols continued to play a prominent role for more than a thousand years after central Europe was thoroughly transformed; and indeed they have remained a vital part of the cultural heritage of Europe.20

The opinion of the archaeologists who have studied the Square Mouthed Pottery Culture in

Italy seems to coincide in general terms with Gimbuta’s assessment of the troubled transitional period occurring in Western Europe towards the end of the Neolithic period. In particular Bagolini, (quoted by Pedrotti), who is considered to be an authority on the study of pre-historical archaeology of Northern Italy, wrote in 1980 that at about the middle of the fifth millennium BC ‘a profound turmoil caused a radical transformation to the cultural texture of the northern regions of Italy, marking the last phase of the Neolithic cycle in these regions. The unification of the territory brought by the peoples belonging to the

Square Mouthed Pottery Culture collapsed under the thrust of new groups mainly from

Western Europe, the regions of the Adriatic Sea and also, in part, from the area north of the Alps’.21

Bagolini, who recognised an evolutionary process of growth and expansion within the

Square Mouthed Pottery Culture, was also able to identify a concurrent development in both the lithic and in the ceramic industry; therefore he proposed a subdivision of the

20 Gimbutas, The Language of the Goddess, xx-xxi. 21 The idealistic concept of a “peaceful existence” proposed by Gimbutas may be challenged by a less optimistic view, especially after the discovery at Tahlheim in Germany of a mass grave with the remains of 34 people (18 adults and 16 children) who had died by a violent death: 22 of them had been brutally killed by scalpel blows, as evidenced by fractures inflicted on their skulls. Pedrotti, “Il Neolitico”, 151-152. 183 Culture in three phases based on stylistic components of ceramic objects, namely surface design patterns and the related technique methods of execution.

The first stage, characterised by plain geometric motifs in the graffito technique is peculiar to the earliest period and has been defined as the linear-geometric style. It is followed by design patterns of dynamic motifs such as spirals, meanders and serpentines, carried out by means of graffito and excision techniques. This period coincides with the maximum development of the Culture and the first appearance of square mouthed vessels. The last phase is represented by design patterns of zigzags, nets and cupmarks, imprints of fingernails dragged on clay, as well as cuneiform marks obtained by way of incision and impression of north-alpine influence, marking the decline of the culture.22

The hieroglyphs on round and square mouthed vessels are all present in Gimbutas’ study of context and association of the language of the Goddess: zigzags, nets, parallel lines, meanders and spirals are marked on the clay surface in an apparent irregular, asymmetrical mode. Equally, the objects in bone, horn or stone of the earlier period (the

Gaban Group) display anthropomorphic and zoomorphic images related to the Goddess; in particular two female figurines, one on a pebble, the other on a bone plaque are equipped with breasts, vulva, chevrons and net- patterned lozenges.23

Gimbutas’ Goddess is a superhuman being in an existential sense, one related directly to human experience and practicality rather than a strictly metaphysical one. Gerda Lerner, author of The Creation of Patriarchy, said: ‘The dominance of [Gimbutas’] Great Goddess can never be proven, but that it may have been is enough to challenge, inspire and

22 Mottes, ‘I vasi a bocca quadrata’, in Spirali Del Tempo. For a definition of graffito and incision, the following: Graffito: decoration on dry raw clay (or leather-hard), but mainly after clay has been fired, obtained by scratching the surface with a pointed tool. Incision: decoration obtained by the same process as before the firing. Very often the edges of the graffito scratchings are serrated, whereas the lines obtained by incision indicate that the clay has been carried forwards. (My translation). Pedrotti, Endnote 20, 178. 23 Gimbutas, The Language of the Goddess, Fig.139, 85; and Pedrotti, “Il Neolitico” Fig.14, 138. 184 fascinate’.24 The origins of the Square Mouthed Pottery Culture could not, in Pedrotti’s view, be ascertained because of lack of sufficient evidence, although many data indicate a local genesis, probably stimulated by external influences.25 The gradual replacement of round ceramic vessels with square mouthed pottery has been only tentatively explained by

Pedrotti, the replacement having ‘perhaps more practical forms’, or ‘because of a particular symbolic significance’. 26

My own study of the square mouthed pots, both in my studio practice and in a preliminary survey of early Neolithic ceramics, has persuaded me that the change in shape was an attempt to create a proto-spout, or rather a four-spout vessel, for the obvious reason of facilitating the pouring action of substances and liquids. When I visited the archaeological museum in Trento I realised that the collection of Neolithic pottery did not include one single vessel that had the familiar spout. Similarly, spouts are absent in Gimbutas’ illustrated volume of Old Europeans vessels.

Yet, some square mouthed pots have the four corners slightly elongated and thinned out, in my view, in order to delay and direct the flow, and therefore to ease the pouring action.

Another revealing detail is the squaring of the spout itself on each of the four corners of the vessel’s mouth, as it may be observed in one particular extant sample. On the empirical level, the squaring of a round vessel is, with practice, a manageable and practical solution.

24 Quotation on the dust jacket of The Language of the Goddess. 25 Pedrotti, “Il Neolitico”, 127, “…una genesi locale probabilmente stimolata da apporti esterni”. 26 Pedrotti, “Il Neolitico”, 140, “…forse perche’ piu’ pratiche, o per un loro particolare significato simbolico”. 185 BIBLIOGRAPHY

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