Numbers, dimensions, perceptions : resonances from Dürer's Melencolia 1

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 Dürer's MELENCOLIA I 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