  Traditionally, Euclidean geometry is treated by scientists as a priori and
objective. However, when we take the position of an agent, the problem of
selecting a best route should also factor in the abilities of the agent, its
embodiment and particularly its cognitive effort. In this paper we consider
geometry in terms of travel between states within a world by incorporating
information processing costs with the appropriate spatial distances. This
induces a geometry that increasingly differs from the original geometry of the
given world as information costs become increasingly important. We visualise
this "cognitive geometry" by projecting it onto 2- and 3-dimensional spaces
showing distinct distortions reflecting the emergence of epistemic and
information-saving strategies as well as pivot states. The analogies between
traditional cost-based geometries and those induced by additional informational
costs invite a generalisation of the notion of geodesics as cheapest routes
towards the notion of infodesics. In this perspective, the concept of
infodesics is inspired by the property of geodesics that, travelling from a
given start location to a given goal location along a geodesic, not only the
goal, but all points along the way are visited at optimal cost from the start.
