Causal models find application in almost all areas of science, and they often support the development of theories that are straightforward and testable. Yet scientists also observe things that surprise them. Fascinated by such observations, they learn to admire the playful aspects of life, as well as its creativity and diversity. Under these circumstances, a compelling question arises: Can causal models explain life’s creativity and diversity? Some life scientists say yes. However, other humanities scholars cast doubt, positing that they reached the end of theory. Here, I build on common empirical observations as well as long-accumulated modeling experience, and I develop a unified framework for causal modeling. The framework gives special attention to life’s creativity and diversity, and it applies to all sciences including physics, biology, the sciences of the city, and the humanities.

"What is life?" and Erwin Schrödinger's answer, "negative entropy", inspired researchers in the 20th century to unite physics, chemistry, and physiology into a new synthesis that many believe to be an important foundation for life science today. Decades after Schrödinger, life scientists are still fascinated by the riddle that entropy can only accumulate in physical systems, which often leads to biological deterioration and death, but life finds ways to persist and prevail. So to say, life "negates" entropy. Can this fascination and research concept be broadened even further to human culture? Short after Schrödinger's publication, Claude Shannon coined the term "information entropy." Information entropy accumulates when noise interferes during communication. Eventually, all useful information is lost. Yet, from this observation, something surprising can be inferred. Not only biological life but also cultural life has the ability to persist and prevail in spite of the accumulation of entropy. Does this insight mean that cultural life also negates entropy, in Schrödinger's sense? These questions guided me over several years of research during which I developed and tested a new theory of culture based on variation-selection processes and homeostatic regulation. My contribution is to discover that these two processes not only make statements about biological life. They also explain some of the most important phenomena of culture: returning fashions, polarization, diversification, cycles of growth and reform, and the formation of common ethos across entire bodies of knowledge. With access to big data and supercomputing, I tested my theory against hundreds of thousands of news, magazine articles, books, and TV transcripts as well as textual content collected from the social media. Historical, institutional, and geographical information was extracted from these data using a new method; and new interactive tools were created to interpret the results. What should not be missed when reading this article is that the theory proposed here reveals a striking equivalence between nature and culture. The article states this equivalence in mathematical terms, and contextualizes it in the history of science. The mathematical breakthrough is relevant because it aligns the humanities to science while also allowing for live evaluation of what I call "cultural diversification cycles."

A large body of research across science and humanities has come to deal with diversity, which, as a scientific concept, has proved immensely relevant in helping researchers understand anything from ecosystems and natural habitats to cities and culture. Here, we develop a first method to quantify and map urban diversity. Our article begins with a concrete example through which we demonstrate how to apply a basic version of our method to create a diversity map for a given urban area. This map is easy to interpret and can be used to accurately locate the most diverse centers of urban activity. We then go on to show how our basic method can be expanded to quantify many different types of urban diversity, and how it can be used to create regional and global diversity maps. Such diversity maps are relevant in both studying diversity and modeling the dynamics of diversification in urban environments. We conclude the article by making a bridge to other scientific disciplines, and by proposing six key steps that may serve as a foundation for a general framework for the evaluation and mapping of diversity across all fields of science.

People have a "right to the city", at least if one is to agree with French philosopher Henri Lefebvre. But if cities are places that everyone has a right to, they must be places for diverse people, and hence, places for diversity. This insight makes it all the more relevant to quantify and map urban diversity, which has become an emerging field of research. In this present article, we build on past and ongoing research, and we expand diversity mapping to the mapping of commuter diversity, specifically. As a case study, we map commuter diversity in New York City, and we discover a correlation between diversity and tall buildings. We show that urban areas that have many tall buildings are most diverse. As a rule of thumb, the height of the tallest building in many such areas can be taken as rough estimate of how diverse the area is. The opposite is not necessarily true. Urban areas without tall buildings do not necessarily lack diversity, although they rarely are the most diverse. These findings suggest that diversity and vertical growth may form a positive feedback loop. The article comes with a GitHub repository that provides data and code that makes it easy for anyone interested to replicate the results.

In earlier articles we developed and applied a method to map urban diversity. This preprint contains additional maps of urban diversity, and it also contains simulations and proposed applications. The preprint will be expanded and updated over time.