An algebraic interpretation of multilayer networks is introduced in relation to conscious experience, brain and body. The discussion is based on a network model for undirected multigraphs with coloured edges whose elements are time-evolving multilayers, representing complex experiential brain-body networks. These layers have the ability to merge by an associative binary operator, accounting for biological composition. As an extension, they can rotate in a formal analogy to how the activity inside layers would dynamically evolve. Under consciousness interpretation, we also studied a mathematical formulation of splitting layers, resulting in a formal analysis for the transition from conscious to non-conscious activity. From this construction, we recover core structures for conscious experience, dynamical content and causal efficacy of conscious interactions, predicting topological network changes after conscious layer interactions. Our approach provides a mathematical account of coupling and splitting layers co-arising with more complex experiences. These concrete results may inspire the use of formal studies of conscious experience not only to describe it, but also to obtain new predictions and future applications of formal mathematical tools.
Mathematical Formulation of Multilayer Networks
