“Understanding” the behaviour of a system depends on projection from the space of manifest phenomena to a distinct conceptual space. These projections can take many forms, corresponding to different types of understanding, such as analogy, metaphor, and mechanism. This project will explore how the abstract mathematical spaces resulting from dynamical

systems models provide new sets of explanatory structures, distinct to those provided by specifying the components of the system. In dynamical systems models, a given system composition (the components, and their modes of interaction) corresponds to an abstract configuration space, or phase space, each point of which corresponds to a possible state of the system. I will use specific models of developmental and physiological processes to explore how system-level behaviour (and the propensities for significant changes in behaviour) can be understood in terms of the natural descriptors of configuration space. I will use the results of these mathematical studies as concrete examples of how a process-based understanding can give novel mechanistic insight into the emergence of developmental and physiological behaviours, and their evolution.