From reductionism to complexity

The field of “complex systems” physics was identified by P.W. Anderson, winner of the Nobel Prize for Physics in 1977. At first it referred to the physics of matter, but more recently it has expanded beyond the boundaries of physics itself. This area of physics is in a sense complementary to that of elementary particles, which is based on a reductionist approach. The traditional approach of physics, in fact, is to consider the simplest systems and study them in detail. This approach focuses on the elementary “building blocks” that are the constituent elements of matter. This reductionist view can be applied to many situations and necessarily implies the existence of characteristic length scales: the size of an atom, a molecule, or some macroscopic object.

Anderson’s article originated as the response of a physicist in the field of condensed matter to a physicist in the field of elementary particles. For example, the first director of the European Organisation for Nuclear Research, CERN, Victor Weisskopf, divided science into ‘intensive’ (elementary particles) and ‘extensive’ (everything else). This view implied the concept that elementary particle physics would be the only real intellectual challenge and that the other fields would be ‘just chemistry’, i.e., a simple application of fundamental laws to increasingly complex systems. This hierarchical view was accepted to a certain extent by Anderson, who however subverted its terms: One cannot assume that the laws of a given science are only consequences of those of another.

From the reductionist approach, it was in fact possible to derive general laws extending from the scale of the atomic nucleus to that of galaxies. It is easy, however, to realise that, as soon as the degree of complexity of structures and systems increases, and when these are composed of many interacting elements, one finds oneself faced with new situations, in which knowledge of the properties of individual elements (e.g. particles, atoms, molecules, up to astronomical systems such as planets, etc.) is no longer sufficient to describe the system as a whole.

The point is that, when interacting with each other, these elements form complex structures and develop collective motions that have little to do with the properties of the individual elements in isolation: the individual elements have relatively simple behaviour, but their interactions lead to new emerging phenomena. This is why the behaviour of the whole is fundamentally different from any of its elementary components. We can represent this situation as the study of the ‘architecture’ of matter and nature, which depends to some extent on the properties of the ‘building blocks’, but which then displays fundamental characteristics and laws that cannot be linked to those of the individual elements.

Using a metaphor, we can represent this situation as the psychology of the masses, which studies the influence of the collective psychological phenomena of a mass on the behaviour of people that cannot be traced back to that of the individual elements. In other words, one can easily observe that sometimes people, if taken individually, assume behaviours that are diametrically opposed to those that are often assumed in a collective situation such as, for example, the fans inside a football stadium.

According to Anderson, reality has therefore a hierarchical structure and at each level of the hierarchy it is necessary to introduce concepts and ideas that are different from those used in the previous level. In other words, from the knowledge of the fundamental laws that regulate the interaction between elementary particles it is not possible to understand the formation or in other words the emergence of many of the phases of condensed matter and, even more so, of increasingly complex systems, right up to biological systems and social aggregates.

The concept of “emergence” was borrowed from biology in relation to the emergence of life from matter, but this concept has since been exported to the field of physics and generalised. For example, all the properties that characterise solids—such as crystal structure, metallic or insulating properties, elasticity and macroscopic coherence—do not make sense in a world of individual atoms. Instead, they develop naturally as emergent properties of a system with many interacting atoms.

Anderson’s aim was to demonstrate the intellectual autonomy of higher-level phenomena with respect to the ‘tyranny’ of the fundamental equations that were supposed to constitute the ‘theory of everything’ (a term introduced later). There are no absolute fundamental laws that, starting from the smallest scale, allow (at least in principle) the derivation of all other properties at all other scales. There are different levels and fundamental laws for each of them that allow the passage to the next level. From this perspective, the various scientific disciplines become part of the same global system with many more possibilities to be integrated with each other, which is why the field of complex systems is naturally interdisciplinary.  The complexity approach is not an alternative to the reductionist approach, but complementary, opening avenues of exploration and new and unexpected connections.

Today, the study of complex systems refers to the emergence of collective properties in systems with many interacting parts. These parts may be atoms or macromolecules in a physical or biological context, but also people, machines, or companies in a socioeconomic context. Complexity science seeks to uncover the nature of the emergent behaviour of complex systems, often invisible to the traditional approach, by focusing on the structure of interconnections and the overall architecture of systems, rather than on individual components.

This is a fundamental change of perspective in the mindset of scientists rather than a new scientific discipline. Traditional science is based on reductionist reasoning whereby, if you know the basic elements of a system, you can predict its behaviour and properties. It is easy to realise, however, that for a cell or for socioeconomic dynamics we are faced with a new situation in which knowledge of the individual parts is not sufficient to describe the overall behaviour of the structure. Starting with the simplest physical systems, such as phenomena in which order and disorder compete, these emergent behaviours can be identified in many other systems, from ecology to the immune system to social behaviour and economics. Complexity science aims to understand the properties of these systems. What rules govern their behaviour? How do they adapt to changing conditions? How do they learn efficiently and how do they optimise their behaviour?