This paper was written by Luis Bettencourt and published in 2024. It is part of an elaborate project of the Sante Fe Institute to chart the course of the development of complex-systems science by discussing eighty-nine revolutionary works originally published between 1922 and 2000. Bettencourt’s paper begins volume one by focuses on the papers that Alfred Lotka published in 1922. Below you will find an excerpt from his paper and a discussion of the project.
Excerpt
The reconciliation of evolution—the theory underlying all of biology and society—and physical theory, which explains energy and matter and underlies most current technology and engineering, remains one of the most important problems in science. A synthesis of these very different theories is essential for creating a general, predictive theory of complex systems (Mitchell 2009; Thurner, Hanel, and Klimek 2018). Some of the deepest unanswered questions in science, such as the origins of life or the sustainability of future human societies, also hinge on a theory that can articulate the physical and biological worlds and produce extrapolations to entirely new situations (Elmqvist et al. 2021).
An important step in this direction was taken a century ago by Alfred Lotka (1922a) with a very simple deductive observation that was then, and it is now, as powerful as it is intriguing. His insight, following closely on developments in statistical physics and specifically the work of Boltzmann and the second law of thermodynamics, is simple and direct. It first recognizes that 1) any living organism requires “available energy,” which must be harvested from its environment, to live and thrive. It follows that 2) organisms that can harvest more energy from their environment relative to others will do better in the sense of sustaining larger numbers of their kind and more mass. This putative advantage is then interpreted by Lotka as the physical instantiation of natural selection (Lotka 1922a, 1922b), equating evolutionary fitness to the ability to obtain energy inflows from the environment. In Lotka’s own words, this principle “may be expressed by saying that natural selection tends to make this energy flux a maximum, so far as compatible with the constraints to which the system is subject” (Lotka 1922a). This idea must be true because it follows from the laws of physics: This is what it makes it powerful.
Foundational Papers in Complexity Science
Foundational Papers in Complexity Science presents the first unified charting of the full territory of complexity science—an essential resource for navigating the modern world.
This project maps the development of complex-systems science through eighty-nine revolutionary works originally published between 1922 and 2000. Curated by SFI President David C. Krakauer, each seminal paper is introduced and placed into its historical context, with enduring insights discussed by leading contemporary complexity scientists.
These four volumes are a product of collective intelligence. More than a compilation, Foundational Papers represents large-scale collaboration within the SFI community—brilliant thinkers who have contextualized the work that shaped their own research, resulting in a sparkling demonstration of how complexity shatters the usual scientific divisions and a look back at the path we’ve followed in order to gain a clearer view of what lies ahead.
Volume I spans the turbulent years from 1922 to 1962. Across several decades of war, runaway technological invention, and economic upheaval, complexity science emerges through the integration of ideas from evolution, computation, dynamics, and statistical physics.
Volume 2 examines the utopian–dystopian years from 1962 to 1973: a decade of global instability, social revolution, space exploration, and growing ecological awareness. Complexity science challenges our understanding of prediction, control, and uncertainty.
Volume 3 describes the maturing of complexity science in the age of democratized computing. Mini-computers and personal computers supporting computer graphics, simulation environments, and numerical mathematics, intersect with nonlinear dynamics, evolutionary theory, and statistical physics. This culminates in new models and theories—from autopoiesis to synergetics, cellular automata to agent-based models—and their many applications, including ecological resilience, complex materials, the origin of life, and climate dynamics.
Volume 4 marks the era of the global internet, ubiquitous computing, and multiple network revolutions. As complexity science matures, unifying frameworks emerge, including connectionism, scaling theory, new models and theories of transmission and contagion, and various forms of biologically inspired computing. The application of mechanisms of decentralized knowledge production to society and culture transforms our understanding of socio-economic and cultural systems.
Luís M. A. Bettencourt. 2024. “Maximum Power as a Physical Principle Evolution.” Santa Fe Institute of Science.
Bibliography
Elmqvist, T., E. Andersson, T. McPhearson, X. Bai, L. Bettencourt, E. Brondizio, J. Colding, et al. 2021. “Urbanization in and for the Anthropocene.” npj Urban Sustainability 1 (6). https://doi.org/10.1038/s42949-021-00018-w.
Lotka, A. J. 1922a. “Contribution to the Energetics of Evolution.” Proceedings of the National Academy of Sciences 8 (6): 147–151. https://doi.org/10.1073/pnas.8.6.147.
Lotka, A. J. 1922b. “Natural Selection as a Physical Principle.” Proceedings of the National Academy of Sciences 8 (6): 151–154. https://doi.org/10.1073/pnas.8.6.151.
Mitchell, M. 2009. Complexity: A Guided Tour. Oxford, UK: Oxford University Press.