Emergence and self-organization in chemistry and biology

Complex systems display two key properties that distinguish them from systems that are merely very, very complicated: emergence and self-organization. Emergence is the appearance of behaviour at system level that is not implicit in the properties of the system's components; self-organization implies the increase of a system's internal order without the imposition of external control. Competing definitions of emergence and self-organization have led to confusion. Here, we follow the idea proposed by Anderson, that emergence and self-organization are signalled by symmetry-breaking. In general, a steady-state configuration of matter must exhibit the same symmetries as the equations that govern its dynamics. However, while this might apply to the component parts of a system in isolation, the whole system might display less symmetry because of the interactions between its individual parts. Here, we will explore several systems where microscopic symmetry is broken by the interaction between the component parts of the system. These examples show that macroscopic symmetry-breaking is an important factor in the formation of system level order from chemical reactions through to the organization of ecosystems.