  Cognition is the process of knowing. As carried out by a dynamical system, it
is the process by which the system absorbs information into its state. A
complex network of agents cognizes knowledge about its environment, internal
dynamics and initial state by forming emergent, macro-level patterns. Such
patterns require each agent to find its place while partially aware of the
whole pattern. Such partial awareness can be achieved by separating the system
dynamics into two parts by timescale: the propagation dynamics and the pattern
dynamics. The fast propagation dynamics describe the spread of signals across
the network. If they converge to a fixed point for any quasi-static state of
the slow pattern dynamics, that fixed point represents an aggregate of
macro-level information. On longer timescales, agents coordinate via positive
feedback to form patterns, which are defined using closed walks in the graph of
agents. Patterns can be coherent, in that every part of the pattern depends on
every other part for context. Coherent patterns are acausal, in that (a) they
cannot be predicted and (b) no part of the stored knowledge can be mapped to
any part of the pattern, or vice versa. A cognitive network's knowledge is
encoded or embodied by the selection of patterns which emerge. The theory of
cognition summarized here can model autocatalytic reaction-diffusion systems,
artificial neural networks, market economies and ant colony optimization, among
many other real and virtual systems. This theory suggests a new understanding
of complexity as a lattice of contexts rather than a single measure.
