Complex systems, their philosophy, and the models we use to study them
A system is complex when its parts interact in ways that shape the behavior of the whole. Because parts affect one another, the system can develop feedback, thresholds, memory, adaptation, cascades, resilience, fragility, and collective behavior.
A landscape is a space, a value function, a neighborhood, and a search process. By progressively relaxing assumptions, each unit reveals why adaptation, search, emergence, and complexity are inseparable.
Emergent patterns press on older ideas about reduction, causation, objectivity, explanation, intervention, and responsibility.
A model starts with a pattern, proposes a mechanism, turns that mechanism into interacting agents, and tests what the simulation can responsibly claim.
Decomposition is the default strategy for understanding anything: break it into parts, study them separately, add the results. This course asks when that strategy works, when it fails, what formal tools detect the failure, and what the failure reveals about the relationship between wholes and parts. It also asks the opposite question: when does holistic language overreach, mistaking mere relation or explanatory convenience for genuine non-decomposability? The recurring signatures of non-decomposable systems are intensive properties (properties that do not add under combination, like temperature or density) and nonlinear couplings (interactions where each part's behavior depends on the states of the others).