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Mathematics and music : models and morals
Get PDFThe intimate association between mathematics and music can be traced to the Greek culture. It is well-represented in the prevailing Western musical culture of the 18th and 19th centuries, where the traditional cycle of fifths provides a mathematical model for classical harmony that originated with the well-tempered, and later the equal-tempered, keyboard. Equal-temperament gives equivalent status to all twelve tonal centres in the chromatic scale, leading to a high degree of symmetry and an underlying group structure. This connection seems to endorse the Pythagorean concept of music as exemplifying an ideal mathematical harmony. This paper examines the relationship between abstract mathematics and music more critically, challenging the idealized view of music as rooted in pure mathematical relations and instead highlighting the significance of music as an association between form and meaning that is negotiated and pragmatic in nature. In passing, it illustrates how the complex and subtle relationship between mathematics and music can be investigated effectively using principles and techniques for interactive computer-based modelling that in themselves may be seen as relating mathematics to the art of computing - a theme that is developed in a companion paper (viz. paper #082 in this directory)
Radical Empiricism, Empirical Modelling and the nature of knowing
No full textThis paper explores connections between Radical Empiricism (RE), a philosophic attitude developed by William James at the beginning of the th century, and Empirical Modelling (EM), an approach to computerbased modelling that has been developed by the author and his collaborators over a number of years. It focuses in particular on how both RE and EM promote a perspective on the nature of knowing that is radically different from that typically invoked in contemporary approaches to knowledge representation in computing. This is illustrated in detail with reference to the modelling of several scenarios of lift use. Some potential implications for knowledge management are briefly reviewed. This paper considers the potential significance of William James's philosophic attitude of 'Radical Empiricism (RE)' [13] in relation to contemporary problems of knowledge representation in the information sciences. Current trends in computer technology and use provide a strong motivation for reviewing RE in this light. For instance, as Gooding relates in [11], our understanding of how scientific knowledge relates to interaction with the natural world and with our peers is challenged by the development of virtual reality environments, and the role that virtual experiments have come to play in science. Such considerations have prompted a reappraisal of the fundamental assumptions that inform the logicist approach to knowledge representation in AI, and called into question the extent to which knowledge is mediated by language rather than engagement with the world (cf. Cantwell-Smith [9], Turner [16]). In this connection, the relevance of RE stems from the priority it ascribes to 'pure experience', and its contention that (to paraphrase William James) the whole of the nature of knowing can ..
DoNaLD : a line-drawing system based on definitive principles
Get PDFThe DoNaLD line-drawing system has been designed to illustrate how a generalised spreadsheet (or "definitive notation") can provide a simple medium for interactive graphics. Novel features of DoNaLD are: the use of variables based upon the recursive specification of a line-drawing as a union of points, lines and subdrawings, and a complementary user interface based upon windows of definitions
Empirical modelling and the foundations of artificial intelligence
No full textAbstract. This paper proposes Empirical Modelling (EM) as a possi-ble foundation for AI research outside the logicist framework. EM offers principles for constructing physical models, typically computer-based, by construing experience in terms of three fundamental concepts: ob-servables, dependency and agency. EM is discussed in the context of critiques of logicism drawn from a variety of sources, with particular reference to the five foundational issues raised by Kirsh in his pape
Computing applications from an empirical modeling perspective: Progress, projects and prospects
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