Complex Mimetic Systems

The goal of science is to make the wonderful and complex understandable and simple—but not less wonderful.

—Herb Simon, The Sciences of the Artificial¹

1. Introduction

Complex systems theory stands for an approach in the social as well as natural and computational sciences that studies how interactions between parts give rise to collective behaviors of a system, and how the system interacts and forms relationships with its environment. A typical example is the market economy, in which the order is emergent: it is the result of human action, but not the execution of any human design.² Complex systems theory is currently a popular vehicle for understanding the complexities of the Internet; other examples of its application are as diverse as the stock market, ant colonies, epidemics, and the spread of business innovations. The focus in this article is on modeling social systems rather than physical or biological phenomena.

The mimetic theory developed by René Girard fits well with a systems perspective, as it has specific ideas about the drivers of human action (at the micro level) and cultural processes (at the macro level). The relationship has been explored earlier in several books and articles;³ in particular, in the work of the Centre de Recherche en Epistémologie Appliquée (CREA) in Paris. The systems perspective received a new stimulus in the 1990s in the form of complex adaptive systems (CAS),⁴ not least because of the agent-based computer simulations adopted at that time. The objective of this article is to introduce a special version of CAS, called complex mimetic systems (CMS), which builds on mimetic theory. The purpose of this article is twofold. On the one hand, the phrasing of mimetic theory in terms of CMS poses an interesting challenge to the theory to formalize its concepts and explicate possible limitations. On the other hand, CMS might be a useful contribution to the CAS field, as it incorporates concepts such as “social influence” that are very basic to but typically not spelled out in current CAS work.

The structure of this article is as follows. In section 2, I briefly review the CAS literature and introduce the idea of complex mimetic systems. Section 3 describes a straw-man agent architecture for CMS, whereas in section 4, I move to the macro level and formalize the culture reproduction cycle. To illustrate the applicability of the CMS framework, I discuss in section 5 Ingo Piepers’s recent CAS analysis of the European international system in the period 1490–1945, and comment on it from a CMS perspective.

2. Complex Mimetic Systems

The characteristic features of complex systems are as follows:

• • Nonlinear effects: a small perturbation may have a large effect.

• • Feedback loops: the effects of an element’s behavior are fed back to it in some way. The feedback can be positive (amplification, runaway) or negative (damping).

• • Openness: a typical complex system interacts with its environment.

• • Memory: the history of a complex system may be important. Prior states may have an influence on present states.

• • Nesting, hierarchy: a complex system may itself be an element of a larger complex system. For example, clans in a tribal society, nation-states in an international system, or divisions in a company.

• • Topology: the interactions of the elements are enabled and constrained by the network, or grid, of relationships between them.

Complex Adaptive Systems

Complex adaptive systems (CAS) are a modern variant of complex systems theory. The elements of a complex adaptive system are called agents, as CAS builds on computational research in the field of multiagent systems.⁵ Although there is not much difference in the overall objectives, the use of agent simulation opens up interesting research opportunities. Let me clarify this by means of an introductory example given by Miller and Page, the standing ovation problem.⁶

Standing ovations, in which waves of audience members stand up to express their particular appreciation of a performance, usually arise and evolve spontaneously. Suppose that we want to model this phenomenon. A starting point could be a simple mathematical model in which we distinguish N people, each receiving a signal...