Introduction to Complexity Science

by Antonio Caperna


The epistemological reformulation is based on two elements: the science of dynamic complex systems and the Copernican revolution, which is occurring in the life sciences.

Biourbanism aims to reformulate the epistemological foundation of architecture and urbanism, according to the science of dynamic complex systems and science of life.

The first aspect implies a passage from a reductionistic methodology to science of complexity, that is structured on a model of interdisciplinary study of the adaptive complex systems and of the relevant emerging phenomena.

In complex systems the features are not described by the constituting elements, but by the dynamic relations and interconnections intervening both within the internal components and  between the latter and the external environment.

One of the particular features of complex systems is the concept of emergence.

Generally we can say that we consider those phenomena as “emerging”, which occur in complex systems due to the interaction established within the different impredictable levels or components of the system.

Francisco Varela defines “the emergentism as that perspective, according to which “a great number of elementary agents endowed with simple properties can be put together, also accidentally, in order to create something that appears to an observer as an integrated and significant whole, without the need of a central supervision”.

In his book La Nature de la Nature, Edgar Morin writes: “emergence is a new quality regarding the constituents of the system. Hence, it has the status of event, since it arises in a discontinuous manner as soon as the system is constituted; of course, it has a character of irreducibility, it is a non-decomposable quality  and it cannot be deducted by the prior elements. […] What does this mean? First of all, that the emergence imposes itself as a fact, as a phenomenical data which the intellect has first to verify. The new properties emerging on a cellular level are not deductible from the molecules intrinsically considered. Even when one can predict it, starting from the conditions of its appearance, emergence constitutes a logical leap and opens in our intellect a passage through which the irreducibility of the reality gets in”.

The analysis of the evolutional dynamics of a complex system can be described through the network science. The study of the nets, in mathematical form as a graph theory, is one of the fundamental pillars of the discrete mathematics. Thus, a network is a discrete set of knots connected by links. Better yet, we can say that a network is a system of which it is possible to formulate an abstract  mathematical representation through a graph, whose knots (or vertexes) identify the elements of a system, and in which the set of connections (links) stands for the presence of relations or interactions between these elements.

So, the network becomes an essential element to understand the fundamental principles not only of the ecological and social sciences, but also of other scientific branches, where these organizational principles, structured around the mathematics of complexity (fractals, theory of chaos, etc.), can be applied: from biology to IT, from economics to social sciences, eventually reaching urbanism.

Regarding this topic, by now there are many studies, starting from those pioneering ones of Jane Jacobs in the sixties of the last century, getting to those of Christopher Alexander, of Micheal Batty, Bill Hillier and Nikos Salingaros opened new scenarios in the study of urban dynamics.

These works have proved that the city, as a highly complex system, is characterized by a high number of relations and interconnections occurring within their components and between the latter and the external environment. The result is ruled by an evolutional non-linear dynamic, that characterizes all the relational processes and interconnections of the system.

The exposition of this thesis implies that each urban environment lives, works and organizes itself through its networks of connections. An example for this is the network of streets or walkways, whose interactions and connections determine the degree of livability of the urban districts, as well as its overlapping with other networks, such as the energetic, the informational (augmented city), the ecological, the social, the one concerning economical flows, etc.