The role of a synthetic geometry in representational measurement theory (Q1368398)

The author describes a framework for viewing the construction of analytic numeric models of empirical data. Of particular interest is the ability to infer order relationships for numerical data from an embedding of the data in some ordered space. Thus embedding data in a vector space allows for the construction of many linear orderings via projections. When embedding in a linear space is not possible it is sometimes possible to embed the data in a more general structure such as an ordered n-quasigroup. The author abstracts this process into one in which the data is embedded into a synthetic geometry generated by an abstract geometric space.