Based on the relationships described in the sources—particularly the cycle of structure, dynamics, and time found in the works of Paul Cilliers and Peter Allen—here is a diagram illustrating how these five concepts interlock to drive the evolution of a complex system.
graph TD A[<b>Constraint</b><br><i>Limits chaos to enable structure</i>] -->|Provides the framework for| B[<b>Hierarchy</b><br><i>Asymmetrical arrangement of parts</i>] B -->|Channels flow of energy/info| C[<b>Causality</b><br><i>Non-linear feedback loops</i>] C -->|Amplifies small deviations| D[<b>Speciation</b><br><i>Emergence of new identities/diversity</i>] D -->|Changes system composition irreversibly| E[<b>Non-Ergodicity</b><br><i>Path dependence & history</i>] E -->|Sediments history into new| A
Explanation of the Cycle
1. Constraint → Hierarchy: Constraints are not just negative limits; they are enabling conditions that reduce chaos[1][2]. By limiting infinite possibilities, constraints allow an organised, asymmetrical structure to emerge, which Cilliers identifies as a loose, interpenetrating Hierarchy[3][4].
2. Hierarchy → Causality: This asymmetrical structure directs the flow of information and energy. Instead of simple linear causes, the hierarchy facilitates Causality characterized by “recurrency” (feedback loops), where outputs feed back into inputs[5][6].
3. Causality → Speciation: The non-linear feedback loops amplify small variations (micro-diversity). When these variations allow a component to occupy a new niche or function, Speciation occurs—the creation of new identities or “structural attractors” that increase the system’s diversity to cope with the environment[7][8].
4. Speciation → Non-Ergodicity: Because new species (identities) are constantly emerging and changing the system’s makeup, the system never repeats its exact state. It becomes Non-Ergodic, meaning its future cannot be predicted by statistical averages of its past; the specific path taken matters[9][10].
5. Non-Ergodicity → Constraint: This irreversible history implies that the system is constituted by its past. The “traces” of history sediment into the system, forming new Constraints and structures that shape future possibilities, restarting the cycle[11][12].
References
[1] Cilliers - boundaries hierarchies and networks in complex systems.pdf [2] Cilliers 2010 - Difference Identity and Complexity.pdf [3] Cilliers - boundaries hierarchies and networks in complex systems.pdf [4] Cilliers - boundaries hierarchies and networks in complex systems.pdf [5] [Book] Cilliers - 1998 - Complexity and postmodernism - Routledge.pdf [6] [Book] Cilliers - 1998 - Complexity and postmodernism - Routledge.pdf [7] Cilliers 2010 - Difference Identity and Complexity.pdf [8] Cilliers 2010 - Difference Identity and Complexity.pdf [9] Cilliers - boundaries hierarchies and networks in complex systems.pdf [10] [Book] Cilliers - 1998 - Complexity and postmodernism - Routledge.pdf [11] [Book] Cilliers - 1998 - Complexity and postmodernism - Routledge.pdf [12] [Book] Cilliers - 1998 - Complexity and postmodernism - Routledge.pdf