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Interdisciplinary research consists of many levels and pathways. One research level that has emerged since the early 21st century is called integration science. Specifically, we focus on a research pathway that structurally integrates social sciences with theoretical physics from perspectives of dynamic analysis. Building on nearly 20 years of prior work, this paper proposes a basic theory of integration science, laying the theoretical foundation for its subsequent development. The significance of integration science operates on three levels. First, identifying structural connections between different disciplines helps in our holistic understanding of natural and social phenomena. Second, generally speaking, the current level of conceptualization and modeling in natural sciences, especially physics, is ahead of social sciences. Integration science research can help elevate the level of conceptualization and modeling in social sciences. Third, the structural similarity across different disciplines reflects the shared thinking of scientists from various fields. Integration science is not simply a synthesis of knowledge from different disciplines. The standard of integration science is to enable social sciences and natural sciences to share the same mathematical structures, thereby possessing a unified mathematical language for description. The empirical basis of integration science is discussed, proposing a unified theory of interdisciplinary scientific observation. This includes concepts like the directionality of scientific observation and the orthogonal principle, the concept of observational disturbance and the diagonal law, defining low and high disturbance quadrants, and discussing why different disturbance quadrants follow their respective mathematical paths. The basic theory of integration science is proposed. The application of category theory in integration science is introduced, along with the necessary semantic supplements. The fundamental concepts of integration mathematics are proposed, defining concepts like integration points, lines, plans, and bulks, and discussing their algebraic and functional analysis methods, thereby laying the mathematical foundation for the integration science. The structural force hypothesis is proposed, along with an axiomatic system of structural forces, thereby laying the philosophical foundation for integrative science. Based on prior work, specific cases of integrative points, lines, plans, and bulks are provided.
Yingrui Yang (Fri,) studied this question.