Epistemology Diagrams : Geometric Representation of Knowledge Management of Financial Engineering

The purpose of this paper is to advance a geometric representation of knowledge spaces and demonstrate their utility in the field of epistemology visualization using the epistemology diagrams (epistemigrams) framework as a prototype. In the presence of excessive mutations of scientific fields and disciplines, epistemic knowledge management is needed to identify emerging fields and support innovation. The basic idea of the order of science is introduced first to build up the higher dimensional knowledge spaces. The idea of a questive operator and questive space are introduced in this paper. Instantiations of primary, dyadic, triadic and higher-order spaces of sciences are proposed. Examples from the dyadic space of mathematical physics and the quartic space of quantitative finance is given as an example. Examples from the classical fields of hard sciences are examined since they are most intuitive. Examples from quantitative finance and financial engineering are provided to disambiguate the two disciplines in their epistemic positioning. Epistemology visualization via an epistemigram is developed as an exemplar for the emerging field of financial engineering with sixteen dimensions of fields of knowledge. It demonstrates that the epistemigram can discover directions of competitive education, resource management and identifying emerging scientific challenges in a technology and knowledge-driven enterprise