  The rise of AI in human contexts places new demands on automated systems to
be transparent and explainable. We examine some anthropomorphic ideas and
principles relevant to such accountablity in order to develop a theoretical
framework for thinking about digital systems in complex human contexts and the
problem of explaining their behaviour. Structurally, systems are made of
modular and hierachical components, which we abstract in a new system model
using notions of modes and mode transitions. A mode is an independent component
of the system with its own objectives, monitoring data, and algorithms. The
behaviour of a mode, including its transitions to other modes, is determined by
functions that interpret each mode's monitoring data in the light of its
objectives and algorithms. We show how these belief functions can help explain
system behaviour by visualising their evaluation as trajectories in
higher-dimensional geometric spaces. These ideas are formalised mathematically
by abstract and concrete simplicial complexes. We offer three techniques: a
framework for design heuristics, a general system theory based on modes, and a
geometric visualisation, and apply them in three types of human-centred
systems.
