Why Not Fractal Geometry?

Abstract

This article argues that if axiology became a strict science it would over-simplify the human functions that lead to "knowing." All of those functions are needed in the very human realm of values. Hartman's hierarchy points to the ascendency of the intrinsic and the relatively low potential of the systemic. Yet, math and science are the tools of the systemic. Therefore, under Hartman's own construct, systemically-oriented science cannot "know" ethical truth better than the fully human individual who keeps all intrinsic identifications intact. The article goes on to advocate that the pursuit of axiology as though it were a science is the best way to demand clear thinking and to provide at least a modicum of freedom from personal bias. The pursuit of "value science" provides a North Star for the further development of Hartman's axiology. Having made those two assertions, the bulk of the article suggests that fractal geometry may provide a potent new metaphor for further explorations and innovative developments in wild new frontiers. It also suggests that a fractal model may hold benefits for those seeking personal growth. Finally, it compares and contrasts transfinite mathematics with fractal geometry and concludes that the two serve different and necessary functions.