About
Cliodynamics is a transdisciplinary area of research integrating historical macrosociology, cultural and social evolution, economic history/cliometrics, mathematical modeling of long-term social processes, and the construction and analysis of historical databases. Cliodynamics: The Journal of Quantitative History and Cultural Evolution is an international, peer-reviewed, open-access journal that publishes original articles advancing the state of theoretical knowledge in this transdisciplinary area. In the broadest sense, this theoretical knowledge includes general principles that explain the functioning, dynamics, and evolution of historical societies and specific models, usually formulated as mathematical equations or computer algorithms. Cliodynamics also has empirical content that deals with discovering general historical patterns, determining empirical adequacy of key assumptions made by models, and testing theoretical predictions with data from actual historical societies. A mature, or ‘developed theory’ thus integrates models with data; the main goal of Cliodynamics is to facilitate progress towards such theory in history and cultural evolution.
This journal is available for sharing and reuse under a Creative Commons Attribution (CC BY) 4.0 International License which means that all content is freely available without charge to users and their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author.
Cliodynamics is a member of the Directory of Open Access Journals (DOAJ) and Scopus.
Volume 17, 2026
Issue 2
Articles
- Doomsday: Friday, 13 November, A.D. 2026. Demographic-Technological Positive Feedback, Hyperbolic Acceleration of the Global Complexity Growth, and the 21st Century Singularity
This paper examines the striking mathematical correspondence between two independently derived hyperbolic equations describing global evolutionary dynamics: Panov's time series of "biospheric revolutions" spanning 4 billion years of biological and cultural evolution, and von Foerster's famous "Doomsday" equation for world population growth (1960). Both phenomena are governed by equations of the form y = C/(2027 − t), with singularity dates converging on the third decade of the 21st century (R² = 0.9991 and 0.996 respectively). The analysis demonstrates that this correspondence is not coincidental but reflects the operation of a nonlinear second-order positive feedback mechanism between demographic growth and technological development, formalized through the coupled differential equations of the Verhulst-Pearl logistic model and the Taagepera-Kremer technological growth equation. The mathematical singularity – the point at which equations project infinite values – should not be interpreted literally. Within social system, just as in physical and chemical systems exhibiting "blow-up" regimes (autocatalytic reactions, thermal explosions, gelation), other mechanisms intervene before infinity is reached. For world population, this transition began in the early 1970s with the fertility decline phase of the global demographic transition; evidence suggests a similar deceleration has commenced in global techno-scientific and economic growth rates. Thus, the 21st century can be called "singular" not because it will witness infinite growth, but because it marks the transition of global complexity evolution from the hyperbolic trajectory that has characterized it since the emergence of life on Earth to a qualitatively different evolutionary regime. The enduring significance of von Foerster's discovery lies in demonstrating that the most complex social system known to humanity can be described with extraordinary accuracy by astonishingly simple mathematical equations, revealing deep structural patterns beneath the apparent chaos of historical events.