From a discussion about the mathematical properties of metrics, we identify three fundamental characteristics of distance, which are optimality, detour and break. We then explore the implications of these properties for transport planning, urbanism and spatial planning. We state that distances contain the idea of optimum and that any distance is associated to a search for optimisation. Pedestrian movements obey this principle and sometimes depart from designed routes. Local sub-optimality conveyed by public transport maps has to be corrected by interventions on public space to relieve the load on central parts of networks. The second principle we state is that detour in distances is most often a means to optimise movement. Fast transport systems generates most of the detour observed in geographical spaces at regional scale. This is why detour has to be taken into account in regional transport policies. The third statement is that breaks in movement contribute to optimising distances. Benches, cafés, pieces of art, railway stations are examples of the urban break. These facilities of break represent an urban paradox: they organise the possibility of a break, of a waste of time in a trip, and they also contribute to optimising distances in a wider network. In that sense break should be considered as a relevant principle for the design of urban space in order to support a pedestrian oriented urban form.