Why Complicated Systems Have Short Theories and Complex Systems Do Not

The standard heuristic for separating the complicated from the complex — that complicated systems can be disassembled and reassembled while complex ones cannot — fails on its own terms. The criterion is observer-dependent: reassembly is a function of the skill brought to the task, not an intrinsic property of the system. A more rigorous distinction focuses on the nature of the components themselves. In complicated systems, components are stationary — they do not adapt, learn, or co-evolve. This stationarity is what allows theories of complicated systems to be compact and universal. Newtonian mechanics and general relativity apply to all masses at all scales; the Description Length of the theory does not grow as the system grows.

Complex systems exhibit what can be termed Extensivity of theory: as the system scales, the minimal description of its Generating Process must scale with it. This happens because adaptive components introduce contingency, path-dependence, and Broken Symmetry that cannot be compressed away. Each adaptation event adds information that the theory must encode. There is no Einstein equation for the economy or the brain precisely because the irreducible history of adaptive interactions defeats any fixed-length formalism.

This framing also cleanly separates complexity from chaos. A low-dimensional system of differential equations can produce trajectories that are effectively indistinguishable from randomness — but the Generating Process remains short. Chaos is complicated, not complex. Complexity science, properly understood, concerns systems where the Generating Process itself must expand to faithfully represent what the adaptive components have become. The richness is not in the output but in the irreducible growth of the mechanism.