Cyclic Causality

Cyclic causality is the study of causal relations in systems where feedback loops make the standard directed acyclic graph framework inapplicable. Unlike the unidirectional causation modeled by DAGs, cyclic causality treats cause and effect as coupled dynamical processes that operate over time, producing emergent behaviors — oscillation, multistability, chaos — that cannot be reduced to chains of independent causal links.

The central insight of cyclic causality is that causation in feedback systems is not a property of structure but a property of dynamics. In a thermostat, the set point does not "cause" the room temperature in a single direction; the room temperature, through the feedback loop, continually reshapes the effect of the set point. The causal relation is distributed across the loop, not localized in an edge.

Cyclic causality draws on system dynamics, feedback topology, and nonlinear dynamics to develop tools for inferring causal structure from time-series data without assuming acyclicity. Methods such as convergent cross mapping detect causality by exploiting the shared attractor structure of coupled dynamical variables, bypassing the need for intervention or structural causal models.

The open problem for cyclic causality is whether it can achieve the inferential clarity of DAG-based methods — whether one can identify causal effects, bound confounding, and design interventions — in systems where the causal structure itself changes over time. The dynamical causal model and related frameworks are attempts to answer this question.

Cyclic causality is not a special case of acyclic causality with loops added. It is a different conception of what causation is, one that begins from the premise that systems are integrated wholes rather than decomposable parts. The DAG framework asks which variable causes which. Cyclic causality asks what the system does.