University of Wollongong Thesis Collections University of Wollongong Thesis Collection University of Wollongong Year 2009 Shadows of another dimension: a bridge between mathematician and artist Janelle Robyn Humphreys University of Wollongong Humphreys, Janelle Robyn, Shadows of another dimension: a bridge between mathe- matician and artist, Doctor of Creative Arts thesis, School of Art and Design - Faculty of Creative Arts, University of Wollongong, 2009. http://ro.uow.edu.au/theses/3079 This paper is posted at Research Online. Shadows of another dimension: A bridge between mathematician and artist A thesis submitted in partial fulfilment of the requirements for the award of the degree Doctor of Creative Arts from University of Wollongong by Janelle Robyn Humphreys BA (Mathematics and physics). Macquarie University Advanced Diploma of Fine Arts. Northern Sydney Institute TAFE NSW Master of Studio Art (hons.). Sydney College of the Arts Faculty of Creative Arts School of Art and Design 2009 1 CERTIFICATION I, Janelle Robyn Humphreys, declare that this thesis, submitted in partial fulfilment of the requirements for the award of Doctor of Creative Arts, in the Faculty of Creative Arts, School of Art and Design, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution. Janelle Robyn Humphreys 15 March 2009 2 TABLE OF CONTENTS List of figures……………………………………………………………………………5 List of tables……………………………………………………………………………..8 1 Introduction: A bridging course .............................................................................. 12 1.1 Rationalising ..................................................................................................... 12 1.2 Art and science / mathematics connection ........................................................ 15 1.3 Bridging the gap ................................................................................................ 16 1.4 Not all numbers and geometry .......................................................................... 17 1.5 Place value ........................................................................................................ 19 2 Topology: Reinterpreting Australian landscape paintings: A Möbius model ....... 23 2.1 Introduction: Bridging topic ............................................................................ 23 2.2 The features of the Möbius strip ....................................................................... 25 2.3 Ceramic Möbius strips: An introduction to the Möbius properties ................. 27 2.4 Möbius model and William Robinson .............................................................. 29 2.5 A mathematics lesson: The fourth dimension and topology ............................. 30 2.6 Robinson’s view: Topology or topography? .................................................... 35 2.7 Other artists and the Möbius strip ..................................................................... 41 2.8 Möbius curves “out there” ................................................................................ 45 2.9 Conclusion: Mathematics and art ..................................................................... 46 3 A twisted model ...................................................................................................... 48 3.1 Introduction: “The geometrical place” ............................................................. 48 3.2 Properties of the Möbius strip ........................................................................... 49 3.3 Nuances of binaries: Gaston Bachelard ........................................................... 50 3.4 “Extreme” model: Jean Baudrillard ................................................................. 52 3.5 Stationary points: TS Eliot on the still point .................................................... 53 3.6 Compressing time: Geomorphology and Kern ................................................ 55 3.7 Contracting time: Henri Bergson ..................................................................... 57 3.8 Compressing time in painting ........................................................................... 58 3.9 Depth-in-space and the Möbius model ............................................................. 61 3.10 Science / art dualism and the Möbius model .................................................... 62 3.11 The Klein factor: Four-dimensional space ....................................................... 63 3.12 Application: Painting in the twilight zones of London .................................... 68 3.13 Conclusion: Möbius common threads ............................................................. 70 4 The shadow of a shadow ......................................................................................... 73 4.1 Introduction: Möbius Strip and projections ..................................................... 73 4.2 (n-1)-Dimensional projections .......................................................................... 74 4.3 Mathematics in practice .................................................................................... 79 4.3.1 Translation ................................................................................................ 82 4.3.2 Dimensions and projections ...................................................................... 84 4.3.3 London watercolours revisited .................................................................. 86 4.3.4 Unfolding .................................................................................................. 87 4.3.5 Evolve ....................................................................................................... 91 4.3.6 Sketches .................................................................................................... 96 4.4 Summing up: Shadow of a shadow .................................................................. 99 5 The Sydney Harbour Bridge and the Möbius strip: The missing link to the fourth dimension in Australian painting .................................................................................. 105 3 5.1 Introduction: Bridging the gap ....................................................................... 105 5.2 Bridging Sydney: Meccano art ....................................................................... 106 5.3 Multiple perspectives ...................................................................................... 108 5.4 Revisiting the Möbius strip: Cross-section of the fourth dimension ............. 112 5.5 Fourth dimension: Unseen dimension ........................................................... 113 5.6 Maggie, the two Graces and mathematics ...................................................... 113 5.7 Möbius trope ................................................................................................... 118 5.8 Preston, the spiral and the Möbius twist: Cook’s books ................................. 123 5.9 Conclusion ...................................................................................................... 124 6 Rounding up: Conclusion ..................................................................................... 125 6.1 Summing up: Mathematics and meaning ....................................................... 125 6.2 Cyclical exegesis: Interconnections ............................................................... 127 6.3 Projections for the future: Art / science connection ....................................... 128 Bibliography………………………………………………………………….……….131 Appendix 1.…………………………………………………………………………...145 4 LIST OF FIGURES Figure 2.1 Möbius strip with vector arrows at right angles to the surface .................. 25 Figure 2.2 Maurits C. Escher. Möbius strip II. 1963 .................................................. 26 Figure 2.3 Mitsumasa Anno, I am a prisoner of my thoughts ..................................... 27 Figure 2.4 Janelle Humphreys. Double twist. 1970-1990. Ceramic. 8 x15 x 6 cm ..... 28 Figure 2.5 William Robinson. Moonlight landscape. 1987. Oil on linen. 147 x 193 cm. Private collection, Sydney .................................................................. 29 Figure 2.6 Mapping of Robinson’s 2-D painting Moonlight landscape, 1987 (left), onto the 3-D ceramic Möbius strip Double twist (right) with outline of the model also superimposed over the painting. .............................................. 30 Figure 2.7 Mitsumasa Anno. The shadow of the earth ............................................... 31 Figure 2.8 Detail (right) of the sieves from Marcel Duchamp. The bride stripped bare by her bachelors, even (The large glass). 1915-23. Oil, varnish, lead foil, lead wire, and dust on two glass panels. 277 x 176 cm (left) .................... 35 Figure 2.9 William Robinson. Creation night Beechmont. 1988. Oil on canvas. 143.5 x 193 cm. Private collection, Sydney ....................................................... 37 Figure 2.10 William Robinson. Creation landscape: Darkness and light v. Lost world landscape. 1988. Oil on linen. 147.2 x 193 cm. Art Gallery of Western Australia, Perth .......................................................................................... 40 Figure 2.11 Janelle Humphreys. Darkness and light (after Robinson). 2006. Acrylic, ink & tape on canvas. 35 x 45 cm .............................................................. 41 Figure 2.12 William Robinson: Grassy painting with William and Shirley