  We propose a new way to measure the balance between freedom and coherence in
a dynamical system and a new measure of its internal variability. Based on the
concept of entropy and ideas from neuroscience and information theory, we
define \emph{intricacy} and \emph{average sample complexity} for topological
and measure-preserving dynamical systems. We establish basic properties of
these quantities, show that their suprema over covers or partitions equal the
ordinary entropies, compute them for many shifts of finite type, and indicate
natural directions for further research.
