Abstract

The approximation of a high-dimensional, discrete or continuous, quantified or even non-quantified system by a lower-dimensional well-quantified system occurs in multiscale numerics, cf. Ames (1969), in lower-dimensional representations and in modelling, cf. Murray (2008). In particular in modelling, the small system is interpreted as a model for the larger system, oftentimes a real-world problem. Here, we discuss basic ideas by hands of finite dimensional specifications in order to find a conceptual framework that describes the approximation of a system by lower-dimensional sub-systems. We investigate the link between this framework and the process of modelling.