Dimensionland: An Excursion into Spaces

Abstract

Scaling analysis is based on a geometric metaphor. This workshop paper examines how our understanding of the metaphor affects our use of scaling. Instances which appear to be multidimensional are shown to be unidimensional under other scaling models. Conversely, some apparently unidimensional cases are found to be better described as multidimensional. Particular attention is given to the difference between multidimensional scaling and factor analysis. The philosophical implication of our dependence on the definition of unidimensionality is that scaling seeks only partial images of a real world that may be fundamentally unknowable.