Geometrical Analysis of Geum-Won Era Prescriptions : A Novel Approach to Traditional Asian Medicine's Basic Theory

금원사대가 처방운용패턴의 기하학적 분석 : 한의학 기초이론에 대한 새로운 접근

Throughout history, Traditional Asian Medicine (TAM) has accumulated diverse theories and extensive knowledge from different medical scholars and schools of thought. While numerous qualitative studies have explored the unique theoretical and prescriptive characteristics of each scholar and school of thought, quantitative research with complementary roles remains limited. This study seeks to explore the potential of geometric data structure analysis as a novel quantitative method to enhance understanding of the basic theories of TAM. Specifically, by analyzing the prescriptions of the four noted scholars of Geum-Won era, we evaluated the similarity of representation of herbs and analyzed the topological properties of prescription networks. Our results suggest that there are both subspaces that are significantly shared among scholars and unique subspaces that are not aligned by linear transformation. From the constructed prescription networks, we found a pattern of continuous variation among the prescriptions, which generates a specific directional trajectory on the herbal manifold. Furthermore, we can derive specific directions for future research from the analysis results. Our study highlights that the analysis of TAM theories using mathematical methods can contribute to the modernization of the theories and allow the existing theories to be understood from a novel perspective.