Causal Models, Creativity, and Diversity

The paper begins by highlighting the widespread use of causal models in science, which often lead to straightforward and testable theories. However, the inherent creativity and surprising diversity observed in life pose a challenge to these models. The central question is whether causal models can adequately explain these aspects of life. While some life scientists suggest a positive answer, humanities scholars have expressed skepticism, arguing that we have reached the limit of theoretical explanation. This paper seeks to bridge this gap by building on empirical observations and existing modeling experience to propose a unified framework for causal modeling. This framework will specifically address life's creativity and diversity, demonstrating its applicability across various scientific fields, from physics and biology to urban studies and the humanities. The author uses the work of Gottfried Semper, an architect who attempted to explain the evolution of artistic styles using mathematics, as a starting point for this exploration.

The paper draws upon a range of existing theoretical frameworks and empirical observations. It references the work of Gottfried Semper, whose attempt to explain artistic styles through mathematical modeling serves as a historical precedent. The author cites works on biological evolution, particularly the theories of quasispecies evolution and perturbation theory, which provide insights into the mathematical modeling of creative processes. Other relevant literature includes studies on Simpson's diversity index, Lotka-Volterra equations in ecology and virology, game theory, and compartmental models used in various disciplines. The author also touches upon relevant works in the humanities, including studies of artistic styles, literary genres, and social fields, to illustrate the broad applicability of the proposed causal framework. The work of Bejan on the constructal law, Lotka on the law of evolution, and Boccioni on the relationship between necessity and speed in art and architecture also inform the author’s approach.

The methodology is primarily theoretical and mathematical. The author starts by formulating a general formula of causality, expressing it mathematically and graphically as a causal flow model. This initial model is then refined by introducing addition signs to create a general model of creativity. This model is further developed to account for the emergence of diversity by incorporating multiplication signs, leading to models of interplay. The author uses Simpson's diversity index as a basis for introducing the concept of multiplication in the model. The paper examines the interplay between creativity and interplay, culminating in a general model of 'creative play,' which unifies the previous models. The author analyses basic models with a small number of variables, gradually expanding the complexity to encompass multi-level interplay. Mathematical equations are provided for the different models, including differential equations to describe continuous changes. These models are illustrated through various diagrams and figures, including causal flow models, Venn diagrams, and representations inspired by geometry. The models are applied to various case studies, including ecosystems, epidemics, the evolution of fashions and trends, the development of HIV, urban development, and the historical development of scientific disciplines.

The paper's key findings center on a unified framework for causal modeling that integrates creativity and diversity. The author proposes that: 1. A general model of causality can be represented by differential equations, transforming the past into the present. 2. Adding (addition signs) in the model represents creativity and leads to the emergence of ‘creative groups’ of related entities. 3. Multiplication (multiplication signs) in the model signifies interplay and the emergence of diversity. 4. The integration of addition and multiplication leads to a model of ‘creative play’, explaining the dynamic interplay between creativity and diversity. 5. This model reveals the emergence of short-term growth waves and long-term cycles of growth and reform, observable in various domains, including science, urban development, and cultural trends. 6. The proposed framework suggests a multi-level architecture of life, progressing from basic building blocks to creative groups and finally to diverse, interacting systems. 7. The model explains the emergence of diversity in various fields, including biology, virology, ecology and the humanities. The mathematical operations of addition and multiplication are interpreted geometrically, with additions corresponding to linear extension and multiplications representing the creation of multidimensional spaces. The analysis is supported by various diagrams and figures that visually depict the causal models and their applications.

The proposed unified framework for causal modeling offers a significant contribution by addressing the limitations of previous models in explaining creativity and diversity. The framework integrates diverse theoretical and empirical findings from various scientific fields, highlighting the underlying similarities in the processes of creation and diversification. The integration of mathematical concepts, such as addition and multiplication, provides a rigorous and quantitative approach to analyzing these phenomena. The application of the framework to different case studies demonstrates its versatility and broad applicability across disciplines. The findings emphasize the interconnectedness of creativity and diversity and their fundamental role in the evolution of complex systems, from ecosystems to human cultures. The framework's capacity to predict short-term waves and long-term cycles of growth and reform provides valuable insights for understanding the dynamics of these systems.

This paper presents a unified framework for causal modeling that successfully integrates creativity and diversity, bridging the gap between life sciences and humanities. The model, utilizing additions for creativity and multiplications for interplay leading to diversity, provides a versatile tool for analyzing complex systems across various disciplines. Future research could focus on further refinement of the models, exploring the implications for specific fields, and developing more sophisticated tools for data analysis and prediction within this framework. The historical context provided by Semper’s work serves as a reminder of the power and potential of applying mathematical models to the understanding of human creativity and cultural evolution.

The primary limitation of this paper is its theoretical nature. While the proposed framework is supported by existing empirical observations and theoretical frameworks, further empirical validation across diverse fields is needed to fully assess its generalizability. The mathematical models presented are simplified representations of complex real-world phenomena, and their parameters often need further empirical calibration for accurate prediction. While the paper attempts to connect these models across disciplines, some aspects might require further refinement in specific contexts.