DOI：10.12201/bmr.202604.00096

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

• 摘要：中医数学化的根本困难在于，现有的数学语言大多基于实体本体论，以“物”及其属性为基本单位，而中医的核心概念——阴阳、五行、藏象、经络、气血——本质上是对“关系模式”的描述。本文提出“关系演算学”（Calculus of Relations），一套以“关系”为基本单位的数学框架，旨在为中医提供严格的数学语言。该框架由六个层级构成：基础层（范畴论+拓扑学+网络科学）定义关系宇宙的静态结构和网络拓扑；动态层（系统动力学+随机过程）为关系注入确定性与随机性的双重演化法则；尺度层（重整化群+多尺度建模）打通微观到宏观的涌现通道，确保跨尺度自洽；信息层（信息论）量化关系的不确定性与价值；计算层（可计算性理论+算法）提供理论实现的路径与边界；反思层（元数学+高阶逻辑）赋予体系自我审视与演化的能力。关系演算学以“生生唯物运动观”为本体论承诺，将“关系”确立为不可还原的基本单位，为中医的阴阳消长、五行生克、藏象功能、经络传感、辨证论治提供统一的数学表达。这一框架不仅为中医现代化提供了数学基础，也为复杂系统科学贡献了一种以关系为核心的新型数学语言。

  关键词： 关系演算学; 中医数学化; 范畴论; 涌现; 生生唯物运动观; 复杂系统

   

  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

  提交时间：2026-05-08

  版权声明：作者本人独立拥有该论文的版权，预印本系统仅拥有论文的永久保存权利。任何人未经允许不得重复使用。
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• 序号	提交日期	编号	操作
  1	2026-04-11	10.12201/bmr.202604.00096V1	下载

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