The Calculus of Relations: A Mathematical Framework for the Mathematization of Traditional Chinese Medicine

DOI: 10.12201/bmr.202604.00096

•  

  Abstract: The fundamental difficulty in the mathematization of Traditional Chinese Medicine (TCM) lies in the fact that existing mathematical languages are predominantly based on substance ontology, taking “things” and their properties as basic units, whereas the core concepts of TCM—yin-yang, five phases, visceral manifestation, meridians, qi and blood—are essentially deions of relational patterns. This paper proposes the “Calculus of Relations,” a mathematical framework that takes “relations” as its fundamental units, aiming to provide a rigorous mathematical language for TCM. The framework consists of six layers: the foundational layer (category theory + topology + network science) defines the static structure of the relational universe and real-world network topology; the dynamic layer (system dynamics + stochastic processes) injects dual evolutionary laws of determinacy and randomness into relations; the scale layer (renormalization group + multi-scale modeling) opens the emergence channel from micro to macro, ensuring cross-scale consistency; the information layer (information theory) quantifies the uncertainty and value of relations; the computational layer (computability theory + algorithms) provides implementation paths and boundaries for translating theory into practice; and the reflective layer (metamathematics + higher-order logic) endows the system with the capacity for self-examination and self-evolution. The Calculus of Relations takes the “Sheng-Sheng Materialist Movement View” as its ontological commitment, establishing “relations” as irreducible basic units, and provides a unified mathematical expression for TCM concepts such as yin-yang ebb and flow, five-phase generation and restraint, visceral functions, meridian transmission, and pattern differentiation. This framework not only provides a mathematical foundation for the modernization of TCM, but also contributes a novel relational-centered mathematical language to complex systems science.

  Key words: Calculus of Relations; mathematization of Traditional Chinese Medicine; category theory; emergence; Sheng-Sheng Materialist Movement View; complex systems

  Submit time: 8 May 2026

  Copyright: The copyright holder for this preprint is the author/funder, who has granted biomedRxiv a license to display the preprint in perpetuity.
• html

• 图表

• Zheng Jianyu. The Ontology and Boundaries of Relational Calculus under the Sheng-Sheng Materialist Movement Perspective. 2026. doi: 10.12201/bmr.202604.00101

  ZHENG Jianyu. A Study on the Theoretical Boundaries and Falsifiability of Traditional Chinese Medicine under the Heaven-Human Systems Medicine Framework. 2026. doi: 10.12201/bmr.202604.00099

  ZHENG Jianyu. The Primacy of Relations over Entities: The First Principle of Heaven-Human System Medicine——On the Xing-Qi Synthesis of Traditional Chinese Medicine and Systems Medicine. 2026. doi: 10.12201/bmr.202604.00102

  ZHENG Jian Yu. "Proof" and "Treatment" from the Perspective of Category Theory: Searching for the Underlying Structure of Traditional Chinese Medicine. 2026. doi: 10.12201/bmr.202603.00073

  ZHENG Jian yu. From Yin-Yang and Five Elements Theory to Dynamical System Cybernetics: Modern Mathematical Reconstruction of Traditional Chinese Medicine Theory. 2026. doi: 10.12201/bmr.202603.00075

  ZHENG Jianyu. A Classification Model of TCM Syndrome Based on Algebraic Moduli Space and Rigid Degeneration. 2026. doi: 10.12201/bmr.202604.00098

  Zheng Jianyu. The Redefinition and Reconstruction of Qi in the Medicine of Heaven-Human System. 2026. doi: 10.12201/bmr.202604.00097

  SHI Shenghui, YOU Mao, LI Rui feng, TIAN Xue qing, REN Ping, ZHENG Qiu ying, WU Lan tao. Analysis of the content of Chinas basic medical insurance policy for Traditional Chinese Medicine from the perspective of policy instrumentSHI Sheng-hui,LI Rui-feng,YOU Mao,TIAN Xue-qing,REN Ping,WU Lan-tao,ZHENG Qiu-ying. 2024. doi: 10.12201/bmr.202405.00004

  zhengxiaoyan, xiasudi, xiejing. Research on the Current Situation of Traditional Chinese Medicine Health and Elderly Care Policies in China-- Analysis based on the three-dimensional framework of topic - tool - effectiveness. 2026. doi: 10.12201/bmr.202601.00075

  胡铁骊. Research on the Construction of Catalogue System in Traditional Chinese Medicine Data Resources. 2023. doi: 10.12201/bmr.202312.00025

• ID	Submit time	Number	Download
  1	2026-04-11	10.12201/bmr.202604.00096V1	Download

• Public  Anonymous  To author only Submit Comments