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Melencolia I ITEM NO: 1950795 Bound by BOOKBINDING PABBEY & PRINTING Unit 3 Gabalfa Workshops Excelsior Ind. Est. Cardiff CF14 3AY Tel: (029) 2062 3290 Fax: (0291 2062 5420 Email: [email protected] Web: www.abbeybookbmding.co.uk FOR REFERENCE ONLY I INFORMATION •• '^'r • Geraint James Davies Numbers, Dimensions, Perceptions: Resonances from Diirer's MELENCOLIA I VOLUME I K 0; LIBRARY £ AND -01 ? INFORMATION ~> SERVICES ^V> CAERLEON Geraint James Davies, BA (Hons) Numbers, Dimensions, Perceptions: Resonances from Diirer's MELENCOLIA I Submitted for PhD University of Wales, Newport School of Art, Media and Design 2012 This thesis was submitted in partial fulfilment of the requirements of the University of Wales for the degree of Master/Doctor of Philosophy. DECLARATION This work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree. Signed ^(candidate) Date STATEMENT 1 This thesis is the result of my own investigations, except where otherwise stated. Where correction services have been used, the extent and nature of the correction is clearly marked in a footnote(s). Other sources are acknowledged by footnotes giving explicit references. A bibliography is appended. (candidate) STATEMENT 2 I hereby give consent for my thesis, if accepted, to be available for photocopying and for inter-library loan, and for the title and summary to be made available to outside organisations. (candidate) Acknowledgements Before I mention some of the many who have assisted me or who were influential in the development and completion of this practice based thesis, I must, first and foremost, thank my wife, Christine, for her encouragement, great forbearance and patient support, particularly as our house and home had to take on the additional functions of library, study, studio and workshop. However, the principal debt I owe to my supervisory team: to Prof. Mark Durden - my lead supervisor, and Director of Studies at University of Wales, Newport (UWN) - not only for his very close and detailed academic over-viewing of this thesis, but also for his huge personal support and encouragement; to Peter Finnemore - Ty Gwendraeth, Pontiets (Gwendraeth House, Pontyates) - also for his most crucial personal support, encouragement and advice, including his insights on practical and curatorial matters; and to Dr. Barry Plummer, my external advisor - thanks also for his most valuable insights. I also owe a debt of gratitude for contributions by: Emeritus Prof. David Smith, my initial lead supervisor; Prof. Howard Riley, in examining my transfer report; Dr. Robert Newell for his previous influences and for offering his considerable expertise and availability as potential examiner; Dr. Ceri Thomas for initially making Orielau y Bont, at University of Glamorgan, available as venue for the exhibition but where his illness necessitated a late change; and to Dr. James Edmundson for over-viewing the vast majority of the mathematical content of this thesis. Thanks also to Russell Roberts, at UWN, for taking such great interest and offering advice. There were many others who also listened and offered support and advice, but who have not been mentioned here, and to them I also extend my gratitude. However, among many administrative personnel, a special thanks must go to Joan Fothergill, Research & Knowledge Exchange Administrator at UWN: thanks also to Ellie Dawkins, Collections Assistant at the Glynn Vivian Art Gallery, Swansea; Angie Dickinson, Manager of Oriel Lliw Gallery, Pontardawe; and Carol Rowden, Events Manager at Swansea Grand Theatre. The technical support of Wayne Stephens and Matthew Harris at UWN was also most valuable, particularly at the beginning practical stages of the thesis development, as was the excellent library support at Swansea University, Swansea Metropolitan University and at UWN, throughout my researches. I'm indebted also to Paul Duerinckx, for taking a professional photographic record of my final exhibition at Swansea Grand Theatre, and where the curatorial advice and practical assistance given (again) by Peter Finnemore towards this final exhibition must particularly be acknowledged, as has been (again) the advice of Prof. Mark Durden towards this same end. Thanks also to Luke Illingworth for his technical support and to Jonathan Anderson for his independent assistance during the 'setting up'. Finally, I wish to thank Prof. John Harvey and Geraint Cunnick for their examination of this thesis, together with their evaluation of its further visual dissemination through, and as, my final exhibition. [The kind assistance afforded by Valeric Davies in the printing of this document is also acknowledged.] Abstract This PhD combines theory and practice in order to explore how art can express fundamental scientific truths, principally through an understanding of numerical harmony and its expression in and through geometric form. Consequently, in making accommodation and finding concomitance between Art and Science, this thesis intends to address, on the one hand, some quite broad and difficult philosophical questions within the truth paradigm. A number of dual relationships are investigated, this principally through a central and more clearly defined dichotomous relationship between 'the literary' and 'the mathematical', where the one is imbued with the uncertainty and difficulties in interpretation and understanding of 'word', the other being the more rationally dependable and more consistent language of 'number', principally expressed through and within examples of proportional and geometric harmonies. All this encompasses an important 'human' condition, that of the 'believer'/'rationalist' duality, that then indicates the biologically based problem of psychological accommodation. On the other hand, in order to further elucidate the ontological/phenomenological divide as a precursor to understanding (the most) difficult issues within the truth paradigm, and ultimately the relationship between perception and consciousness, an in-depth investigation is made into the mathematical properties of perfect and imperfect harmonic relationships, taking the enigmatic polyhedron in Diirer's MELENCOLJAI as a central focus of a wider locus that encompasses also some related properties of Islamic two-dimensional patterning as well as important numerical relationships within three-dimensional geometric space. This is a practice based thesis and, therefore, the parallel practical and artistic nature of this investigation is seen as important in enabling the acquisition of further knowledge and in helping to underpin the theoretical, as well as in corroborating a number of innovative mathematical propositions. Lastly, the bilingual nature of this document and the difficulties encountered in attempting to obtain as closely similar nuances and meaning within each language as it is possible to do through word and syntax - these being culturally different and contextually, experientially acquired - only serves to highlight and accentuate one of the central issues concerned; in that although thinking (as a cognitive process) may well happen in and through an internalized verbal language, the potential presence of ontological realities that are outside our ability to perceive and to comprehend may best be indicated by a further understanding of mathematical and essentially numerical truths. These may be indicated visually through geometry and, it is contended, can therefore best be disseminated culturally as included within a form of artistic representation, either overtly or covertly. Contents VOLUME I Acknowledgements Abstract Thesis Thesis List of Plates Introduction .............................................. Chapter 1 Certitude and Belief A. Metaphysics 1.1 Viewing Perception and Consciousness .................................. 8 1.2 Philosophy and mathematical foundations ............................... 11 1.3 A mathematical proof of God? ............................................. 13 1.4 The Dialectic .................................................................. 15 1.5 The phenomenological/ontological divide ............................... 18 1.6 The theological God and metaphysics .................................... 21 B. Physics 1.7 The School of Empiricism ................................................. 24 1.8 Mind as tabula rasa ....................................................... 24 1.9 Objects of the mind ......................................................... 28 1.10 Human nature .............................................................. 31 1.11 Towards a conclusion .................................................... 35 Chapter 2 The Power of Word: the Beauty of Number A. Language 2.1 Historical context .......................................................... 37 2.2 The language of fear ...................................................... 37 2.3 The climate of fear ......................................................... 39 2.4 The artist's contribution ................................................... 43 2.5 Purer's polyhedron as symbol ........................................... 43 B. Mysticism 2.6 CorneliusAgrippa ......................................................... 44 2.7 Melancholy in context .................................................... 46 2.8 Standard research .......................................................... 48 2.9 The further significance of melancholy ....................................... 48 2.10 Durer's polyhedron as
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