Based on the sources, the various authors establish that complexity does not arise in a vacuum; it requires specific physical, structural, mathematical, and cognitive conditions to exist. These conditions and circumstances can be categorized into several distinct paradigms:
1. Thermodynamic and Physical Conditions (Far-From-Equilibrium)
For complexity scientists and systems theorists focusing on the material world, complexity requires specific energetic and thermodynamic circumstances.
• Non-Equilibrium and Energy Flux: Alicia Juarrero, James Ladyman, and Paul Cilliers establish that complex systems are strictly “open systems” that must operate far from thermodynamic equilibrium[1]. They require a continuous exchange of energy and matter with their environment to survive[2][3]. If a system is closed or reaches equilibrium, it ceases to be complex and degrades into entropy (death)[1][3].
• The Four Base Conditions: Ladyman specifically outlines that physical complexity requires four conditions: numerosity (many interacting parts), disorder (a lack of central top-down control), non-equilibrium (openness to energy flux), and feedback loops[4].
• Bifurcation and Autocatalysis: Juarrero notes that when systems are pushed far from equilibrium by environmental gradients, they require positive feedback loops (autocatalysis) to reach a critical threshold of instability[9]. Under these circumstances, they undergo “bifurcations” (discontinuous phase transitions), spontaneously self-organizing into new, complex structures[12][13].
2. Structural Circumstances: “The Middle Numbers” and Interdependence
Complexity emerges in a specific structural zone between perfect order and total randomness.
• Organized Complexity: Relying on Warren Weaver, authors like Christopher Alexander, David Spiegelhalter, and Alex Ryan locate complexity in the “middle numbers”[14]. This is the circumstance where a system has too many interacting variables to be mapped by simple deterministic mechanics (like a clock), but possesses too much structure to be averaged out by statistical mechanics (like a randomized gas)[15].
• Dimensionality plus Interdependence: John Flach establishes that complexity requires two interacting dimensions: high dimensionality (a near-infinite number of variables or degrees of freedom) and high interdependence (where these variables are mutually coupled in non-linear ways rather than simple, additive chains)[18].
• Hierarchical Elaboration: Tim Allen strictly distinguishes complexity from mere “complicatedness.” Complicatedness is structural elaboration (adding more parts, which increases degrees of freedom)[21][22]. True complexity requires organizational elaboration—adding hierarchical depth which actually constrains degrees of freedom to enable new emergent behaviors[21][23].
3. Mathematical and Computational Conditions (Incompressibility)
For mathematical biologists and information theorists, complexity is a condition that defies computational modeling.
• Non-Simulable Models: Robert Rosen establishes that a system is complex if it possesses “non-computable” or “non-simulable models”[3][11]. Under these conditions, the system admits multiple, non-equivalent encodings, meaning no single algorithm or finite-state machine can completely capture it[24].
• Impredicativity: Rosen states that complexity requires closed loops of efficient causation (impredicativities)[25][28]. A complex system (like a living cell) internally entails its own catalysts for repair and replication, breaking linear cause-and-effect[2][29].
• Algorithmic Incompressibility: Paul Cilliers and David L. Abel define complexity mathematically as algorithmic incompressibility[30][31]. A complex system cannot be represented by a model simpler than the system itself without losing vital, non-linear information[31].
4. Temporal and Dynamic Circumstances
Complexity arises under specific conditions of time, delay, and environmental turbulence.
• Dynamic Complexity vs. Detail Complexity: Peter Senge and Donella Meadows establish that true complexity is dynamic. It occurs in circumstances where cause and effect are subtle, non-linear, and distant in time and space[30]. It requires conditions where the same action yields vastly different effects in the short term versus the long term, driven heavily by systemic delays[5].
• Turbulent Fields: Fred Emery notes that complexity arises in “Type IV” environments (Turbulent Fields). This is a circumstance where dynamic properties and uncertainties are generated by “autochthonous” (self-generating) processes in the environment itself, creating deep interdependence and making the “ground” constantly shift[34].
5. Epistemological and Cognitive Circumstances (The Observer’s Mind)
Several authors establish that complexity is not an objective state of the world, but a condition that arises within human cognition and social interaction.
• Cognitive Overload: John Warfield establishes that complexity resides entirely in the human mind[33][37]. It is the subjective condition of frustration and cognitive overload experienced when a human observer faces a situation with too many variables to hold in short-term memory, leading to an inability to comprehend it[38][39].
• Nontrivial Machines and Wickedness: Horst Rittel and Peter Checkland establish that complexity arises when a situation involves human actors. Because humans are “nontrivial machines”—meaning their internal states, memories, and values continuously change—their behavior cannot be predicted analytically from their inputs[12]. This creates conditions of “wicked problems” or “messes” characterized by conflicting subjective interpretations and no definitive formulation[37][41].
References
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