Complexity Science
Complexity science studies how macroscopic properties and dynamics arise from interactions among components of a system. It uses many subfields like graph theory, dynamical systems, statistical mechanics, information theory, probability and computational modeling.
Studies of interest:
Emergence and self-organization
Criticality, scaling laws, and phase transitions
Robustness, resilience, and cascading failures
Collective computation and distributed information processing
Evolution of complexity itself
Applications to real systems (politics etc.)
Dimensions of Systems
Useful dimensions to classify the complexity of a system.
Dynamics: static ↔ dynamic
Does the system's state change over time?
Dynamical sensitivity: stable ↔ chaotic
How sensitive is the system's evolution to small changes in its initial state?
Behavior: non-emergent ↔ emergent
What properties arise at the system level that are not directly specified by the component-level rules?
Determinism: deterministic ↔ stochastic
Does the current state uniquely determine the future state, or are transitions probabilistic?
Mathematical behavior: linear ↔ nonlinear
Do effects combine linearly, or can interactions produce nonlinear effects?
Algorithmic complexity
Rules: fixed ↔ self-modifying
Can the rules governing state transitions change as a consequence of the system's evolution?
Adaptation: non-adaptive ↔ adaptive
Can the system change its behavior in response to its environment or experience? (self-modification with goal / intent)
Boundary: closed ↔ open
Does the system exchange matter, energy, or information with its environment?
Representation: continuous ↔ discrete
Are relevant states and/or transitions continuous or discrete?
Thermodynamics: equilibrium ↔ far-from-equilibrium
How far is the system from thermodynamic equilibrium?
Modularity: Hierarchical / modular organization
Scale: few-body ↔ many-body
How many interacting components or degrees of freedom does the system contain?
Organization: centralized ↔ decentralized
Is coordination primarily concentrated in a central component or distributed across the system?
Interactivity: Local ↔ long-range interactions