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Quick summary

Complex systems are composed of a hierarchy of subsystems. The complexity of a system can be characterized by how many layers of hierarchical subsystems exist. A system is nearly-decomposable when the subsystems at different hierarchies only loosely interact.


Four aspects of complexity discussed in this paper:

  1. Frequency of hierarchy forming within a complex system
  2. Relationship between structure of a complex system and the rate at which that system emerges through evolution
  3. Dynamic properties of hierarchical systems
  4. Relation between complex systems and their descriptions

Hierarchy is defined as a system that is composed of interrelated subsystems.

At each level of hierarchy an elementary unit is defined. For example, in social systems a family might be the elementary unit that belongs to a village, which belongs to a community, etc. If traversing the scale of subsystems in the opposite direction, a family consists of people, which are made up of tissue, which are made by cells, etc.

The relation between units at each level of hierarchy can be defined by their interactions.

In a formal hierarchical system each subsystem is managed by a another system acting as “boss.” However, this paper focuses on those subsystems with more complex or unrelated dynamics to the higher level systems they are subordinates of.

The span of a system refers to the number of subsystems that it can be divided into at a specific hierarchic level. For example, the diamond has a wide span at the crystal level because a crystal is composed of many carbon atom subsystems.

Social systems

In fact, even in human organizations, the formal hierarchy exists only on paper; the real flesh-and-blood organization has many inter-part relations other thaffasn the lines of formal authority

Biological and physical systems

Compounds, like diamond, have a structural hierarchy of crystals, formed by carbon atoms, which are formed by protons, neurons, and electrons. The hierarchy of a diamond crystal is considered to be flat because the number of first-order systems (carbon atoms) that can belong to a crystal is - in theory - infinitely large.

Symbolic systems

Evolution of complex systems

Two approaches to systems building are compared using the story of two watchmakers. One builds a highly complex system made of individual parts, and the other builds a complex system created from composable subsystems.

Group problem solving benefits from frequent feedback on whether the decisions result in positive, negative, and intended outcomes. This helps keep the group aligned and focused on the right aspect of the problem.

In nature feedback takes the form of successful creation of a stable building block through a process of experimentation and evolution. These building blocks are subsystems - cells, tissue, organs, human, family, community, society, etc.

Frequency and evolution

The speed and frequency that a stable, loosely coupled system can form within a system directly impacts the rate of evolution possible in that system.

The reason for this is new combinations of composable parts can be tested until the most adaptable survives, providing a stepping stone for the next iteration.



  1. Simon, Herbert A.. 1962. “The Architecture of Complexity”. Proceedings of the American Philosophical Society 106 (6). American Philosophical Society:467–82. https://www.jstor.org/stable/985254.