"The Art of Painting" by Johannes Vermeer depicts a painter at an easel, capturing a young woman dressed as the muse Clio. The studio setting showcases a map, chandelier, and draped curtain. This masterpiece celebrates artistic creation, with the woman symbolizing history and fame through her trumpet and book.

Cliodynamics and Mathematical Models in History. Part 1

What is Cliodynamics?

Peter Turchin's pioneering work in cliodynamics uses mathematical modeling to investigate deterministic patterns in historical processes, balancing social predictability with inherent randomness.

The term “cliodynamics” was proposed in 2003 by Peter Turchin, an American physicist of Russian descent. Such refers to an interdisciplinary field of research on long-term historical processes, which are based upon the development of diverse mathematical models whilst employing differential equations as a tool. As a basis for construction, Turchin formed models on the notion of “asabiyyah”, which was established in the XIV century by the Arab philosopher Ibn Khaldun. Ibn Khaldun considered the term "asabiyyah" to mean the degree of social solidarity in a community and the extent to which that society is capable of collective action to preserve its state and itself.

Immanuel Kant once wrote – “In any special doctrine of nature there can be only as much proper science as there is mathematics therein”. Mathematical calculations, however, entail rigorous determinism, in other words, the result of which is always predetermined, hence, rising important questions. Do historical processes have the properties of determinism? Is it feasible to employ mathematical instruments to formalise these processes?

To what extent will the components of high stochasticity (randomness) of historical processes impact the final results of a calculation? Peter Turchin chose to investigate the issue by employing medieval agrarian societies as an example, presuming their mathematical framework is far less complex than it would be if they were modelling the historical dynamics of later, industrial states of the New Age. Turchin rightly noted that more than 95% of written history is the history of agrarian societies. That is to say, as per time and geographical framework for research, he chose the history of Europe in the period 500-1800.

During the development of modelling approaches, Turchin opted to focus on the usage of multi-agent modelling, which is distinguished by the presence of the properties of autonomy, limited representation, and decentralisation. Autonomy denotes agents' total or partial independence; limited representation indicates agents' lack of comprehensive awareness of the system due to its complexity. Finally, decentralisation implies that none of the agents have the ability to manage the entire system as a whole. As previously stated, the modelling language was based on differential equations.

Turchin explored various forms of dynamic processes of state expansion for the mathematical study of geopolitical models, among which he defined the following patterns of growth: linear (limitless) (a), exponential (b), asymptotic (c), logistic (d), "rise and fall" (e), as well as undamped fluctuations (f). As per rightful belief, that the nature of the dynamics of the natural historical process cannot be of unlimited or exponential type of growth, due to limited resources as well as the constant influence of some states on others, he came to the conclusion that it is inevitable to introduce a negative feedback component into the models. This, in turn, leads to models that assume either an asymptotic equilibrium of growth or oscillatory conceptions of "rise and fall".

Dynamic patterns of growth: linear (limitless), exponential, asymptotic, logistic, "rise and fall", undamped fluctuations

Read the second part following this link.

Contribute to Historica's blog!

Learn guidelines, requirements, and join our history-loving community.

Become an author
Don't miss out on the latest news!
Thank you! Your submission has been received!
Oops! Something went wrong while submitting the form.

People also read

Man is writing about history and AI

Evaluating history, or solving it? Thoughts on the epistemology of historical “discoveries”

This article starts from a recent paper on the application of large language models to mathematical problems, to ask how far “evaluating” and “solving” are conceptually useful in understanding the past. It explores whether the idea of knowledge as “discovery” can be applied to history, and, if so, what that would mean for the parameters invoked by, and applied to, machine learning.
angus russell
Angus Russell
February 1, 2024
min read
Generative AI
Historical Research
Historical Processes
Mathematical Models
Researches discuss art history and ai axioms

Art, History, AI, and Axioms

Discover the impact of AI on art and history through insightful axioms. Explore ethical considerations, AI's role in historical research, and the balance between human and AI capabilities.
Anastasia Serbinova
Anastasia Serbinova
January 22, 2024
min read
Historical Processes
Historical Research
The team is working on ontology using AI

Is it possible to create an ontology that could serve as the basis for describing the history of humanity using AI?

Developing an ontology for AI in human history, crucial for a digital footprint, involves interdisciplinary challenges: diverse data, multiple interpretations, expanding datasets, language barriers, standardization issues, and ethical considerations.
Anastasia Serbinova
Anastasia Serbinova
December 23, 2023
min read
Generative AI
Digital Humanities
Ontological Bridges


How can I contribute to or collaborate with the Historica project?
If you're interested in contributing to or collaborating with Historica, you can use the contact form on the Historica website to express your interest and detail how you would like to be involved. The Historica team will then be able to guide you through the process.
What role does Historica play in the promotion of culture?
Historica acts as a platform for promoting cultural objects and events by local communities. It presents these in great detail, from previously inaccessible perspectives, and in fresh contexts.
How does Historica support educational endeavors?
Historica serves as a powerful tool for research and education. It can be used in school curricula, scientific projects, educational software development, and the organization of educational events.
What benefits does Historica offer to local cultural entities and events?
Historica provides a global platform for local communities and cultural events to display their cultural artifacts and historical events. It offers detailed presentations from unique perspectives and in fresh contexts.
Can you give a brief overview of Historica?
Historica is an initiative that uses artificial intelligence to build a digital map of human history. It combines different data types to portray the progression of civilization from its inception to the present day.
What is the meaning of Historica's principles?
The principles of Historica represent its methodological, organizational, and technological foundations: Methodological principle of interdisciplinarity: This principle involves integrating knowledge from various fields to provide a comprehensive and scientifically grounded view of history. Organizational principle of decentralization: This principle encourages open collaboration from a global community, allowing everyone to contribute to the digital depiction of human history. Technological principle of reliance on AI: This principle focuses on extensively using AI to handle large data sets, reconcile different scientific domains, and continuously enrich the historical model.
Who are the intended users of Historica?
Historica is beneficial to a diverse range of users. In academia, it's valuable for educators, students, and policymakers. Culturally, it aids workers in museums, heritage conservation, tourism, and cultural event organization. For recreational purposes, it serves gamers, history enthusiasts, authors, and participants in historical reenactments.
How does Historica use artificial intelligence?
Historica uses AI to process and manage vast amounts of data from various scientific fields. This technology allows for the constant addition of new facts to the historical model and aids in resolving disagreements and contradictions in interpretation across different scientific fields.
Can anyone participate in the Historica project?
Yes, Historica encourages wide-ranging collaboration. Scholars, researchers, AI specialists, bloggers and all history enthusiasts are all welcome to contribute to the project.