Information, complexity, and dynamic depth

Why are computers so radically different than brains in terms of phenomenology? The difference is one of complexity but not complexity in mere numbers of elements, interactions, operations per time and space, or even generative difficulty. We argue that the difference is dynamical. We propose a measure of the complexity of a system that is largely orthogonal to computational, information theoretic, or thermodynamic conceptions of structural complexity. In contrast, we propose a complementary measure of system complexity that captures a system’s degree of internal causal convolutedness and hierarchic dynamical organization. We term this measure a system’s dynamical depth. This is assessed in terms of the degree to which it exhibits discrete levels of dynamical organization in which successive levels are distinguished by their inverse relationships to entropy production and constraint generation. A system with greater dynamical depth than another consists in a greater number of such nested dynamical levels. Thus a mechanical or thermodynamic system has less dynamical depth than an inorganic self-organized (e.g. morphodynamic) system, which has less dynamical depth than a living or mental (e.g. teleodynamic) system. Dynamical depth can provide a more precise and systematic account of the fundamental difference between computation (low dynamical depth) and cognition (high dynamical depth), or inorganic chemistry (low dynamical depth) and living chemistry (high dynamical depth) irrespective of their structural complexity. Taking both dimensions of complexity into account is necessary to clearly distinguish between information processing understood in merely structural terms and information understood semiotically