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The Golden Mean and the Physics of Aesthetics

A horizon is perspectival. There are no horizons without perceivers. One sense of the word 'environment' has that logic, noticing the modifiers. My environment is rather like my horizon. I take it with me as I move through the world. Horizons require an attention span. Analogously, my environment has an owner. We can spell this 'environment' with a lower case e. Arnold Berleant concludes: 'This is what environment means: a fusion of organic awareness, of meanings both conscious and unaware, of geographical location, of physical presence, personal time, pervasive movement. . . . There are no surroundings separate from. | Archive of Physics physics 0411195 2004 The Golden Mean and the Physics of Aesthetics Subhash Kak Louisiana State University Baton Rouge Abstract The golden mean o has been applied in diverse situations in art architecture and music and although some have claimed that it represents a basic aesthetic proportion others have argued that it is only one of a large number of such ratios. We review its early history especially its relationship to the Mount Meru of Pingala. We examine the successive divisions of 3 7 and 22 notes of Indian music and suggest derivation from variants of the Mount Meru. We also speculate on the neurophysiological basis behind the sense that the golden mean is a pleasant proportion. Dedicated to the memory of José Maceda 1917-2004 Introduction Two and a half years ago in 2002 the celebrated Philippine composer José Maceda organized a Symposium on A Search in Asia for a New Theory of Music in Manila. His objective was to explore Asian mathematical sources that may be helpful in providing a direction to world music everywhere. The papers at the Symposium have since appeared as a book Buenconsejo 2003 . At this meeting Maceda had many conversations with me regarding what he called the aesthetics of Asian court musics which seek permanence with little change. I told Maceda that I considered the dhvani-approach to aesthetics particularly insightful since it made the audience central to the process of illuminating the essential sentiment behind the artistic creation e.g. Ingalls et al 1990 . According to this view the permanence being sought is the universal that can only be approached and never quite reached by the diverse paths that represent different cultural experiences. Maceda appreciated the fact that physiological geometry plays in perception and aesthetics but he was emphatic that there was a cultural component to it and that there could be no unique canon of beauty in art. I take this thought as the starting point of my discussion of the .