In some areas of cognitive science we are confronted with ultrafast cognition, exquisite context sensitivity, and scale-free variation in measured cognitive activities. To move forward, we suggest a need to embrace this complexity, equipping cognitive science with tools and concepts used in the study of complex dynamical systems. The science of movement coordination has benefited already from this change, successfully circumventing analogous paradoxes by treating human activities as phenomena of self-organization. Therein, action and cognition are seen to be emergent in (...) ultrafast symmetry breaking across the brain and body; exquisitely constituted of the otherwise trivial details of history, context, and environment; and exhibiting the characteristic scale-free signature of self-organization. (shrink)