A homological foundation for scale problems in physics

First steps towards a discrete theory of observation are developed by using algebraic topological concepts, and are shown to account for finite limits of resolution. The cohomology ring on a basic simplicial complex is claimed as the natural language of physical theory. This is illustrated by specific examples and a complete set of generators for such a ring will be called theEddingtonian of a system.The concept of tensorial covariance is logically replaced by that of an isomorphism between base homologies induced by a bijective simplicial map. This is applied to velocity space to produce an abstract form of the Lorentz-Einstein relativity theory and also to discuss an experimental diffraction arrangement devised by Bohm and Aharonov. The latter is shown to be homologically equivalent to the problem of the red shift, and consequently throws light on the question of galactic recession.