Complex Systems. Perspectives on General Theory, Germán de la Reza, 1st edition, Barcelona, Universidad Autónoma Metropolitana y Anthropos, 2010, 175 pp., ISBN 978-84-7658-964-9.

Complex systems and complexity are terms in vogue but the way these terms are used is often inappropriate or confusing. In this regard the book written by Germán de la Reza clarifies their meaning, and also explains how systemic thinking has evolved, presenting an application of complex systems in the field of economics. It is worth highlighting the extensive citing of authors and their works, and the clarity with which information is presented. For those unfamiliar with the topic, however, it may be difficult to follow the author at times.

The first part of the book addresses the development of systemic thinking a task that is far from easy. In its “itinerary of systemic hypotheses” the purpose of the first three stops is to present methodological arguments. To this end, without ignoring the contributions of thinkers from Ancient Greece, de la Reza begins with the image of a tree as a symbol of the system. Using the ideas developed around this image, especially worth mentioning is the contribution from Raymond Lull (Ramon Llull in Catalan, Raimundo Lulio in Spanish). An explanation is given of how Lullian systematization impacted the combinatorial theory developed by Wilhelm G. W. Leibniz. Moving beyond the combinatorial theory, the author develops the basic proposals from the doctrine of Leibniz nomads which, according to de la Reza, is a forerunner of the modern concept of a social system. Lastly, the author emphasizes the main aspects of rationalism and heuristics as research methods, and the connection between the latter and systemic thinking.

The last stops on the itinerary are aimed at addressing applications to real systems. The first application is a matter of sensitivity to initial conditions. The author connects the three-body problem studied by Jules H. Poincaré –which would lead him to establish the principles that are today known as non-linear dynamic systems or the theory of chaos– to the discovery of fractals by Edward N. Lorenz. In another section, the author reviews ideas from Immanuel Kant, Kurt Gödel and Niklas Luhmann, emphasizing their contributions to the advances made in systemic theory. He concludes this section by underscoring systemic study in economics, from Quesnay to the Santa Fe school, with a focus on equilibrium and cycles.

The second part of the book consists of a synthesis between “old and new proposals” in systems theory. As a prelude to addressing complex systems, de la Reza emphasizes two important points: the complementarity between analytical and systemic methods, and the need for building linguistic bridges between disciplines. The author then presents a brief introduction to the history of general systems theory, including its main aspects such as the presence of feasible laws or structures of study, the identification of similar laws among disciplines, the non-linear nature of complex systems, the existence of control parameters and the practicity of studying this theory through concepts of organization or order. The author also emphasizes the importance of isomorphism, which is “the formal correspondence or essential similarity between general principles and special laws” between two or more disciplines or fields of research. A section is dedicated to pointing to differences between closed, open and diffuse systems, in order to highlight an essential aspect: the limitations of predictions of social systems. Continuing with this point, the author reviews the principle of multi-finality, or the variations in trajectories on the basis of similar initial conditions and the role played by feedback in the evolution of a system. An interesting contribution made by de la Reza is the review of the notion of equilibrium in social systems, presenting this notion as a relationship between cooperation and competition.

The last part, dedicated to applications to complex systems, constitutes fundamentally an effort at experimental application in the social sciences, particularly in economics. It presents an entropic model of open economies–international trade–based on entropic relations (entropy, homeostasis, selection, restriction and feedback) and in basic components (exterior borders and sub-systems). The study of this model is divided into two levels: at the qualitative level, the author proposes conducting a general, multi-faceted diagnostic assessment of the system's entropy based on entropic relations, and at the quantitative level, the use of econometric techniques is proposed. While the author proposes qualitatively studying interactions through entropic relations, this could be enriched, using computational modeling based on cellular automaton, and models based on complex networks or agents–tools that also reinforce quantitative analysis.

De la Reza makes an important point regarding the need for debate between disciplines, or interdisciplinary debate. In this sense, the work reviewed here encourages building bridges and deepening dialogue between disciplines.

Paola Vera
Department of Accounting and Administration, unam
[ 1• ]