Decomposability

Decomposability is the property of a system whose behavior can be predicted from the behavior of its components in isolation. It is stronger than modularity: a system can be modular in structure — its components can be separated and recombined — without being decomposable in dynamics.

Decomposability fails when components interact through feedback loops that cross modular boundaries. The climate system has modular subsystems (atmosphere, ocean, cryosphere, biosphere) but is not decomposable: the behavior of the atmosphere in isolation is a poor predictor of the coupled system. The same is true of economies, ecosystems, and brains.

The assumption of decomposability underlies much of reductionism in science. When it fails, the appropriate methodology is not component-level analysis but systems modeling that preserves the feedback structure.