Abstract
Two‐dimensional metric scaling is based on the relations of incidence and orthogonality and on the motion of reflection in a straight line. Together with a set of optional postulates concerning different types of orthogonality these primitives are sufficient for operationalizing the Cayley‐Klein geometries for use in the psychological laboratory. They include the three Riemannian geometries (elliptic, Euclidean and hyperbolic) as special cases. The representation refers to a vector space over an unspecified field. The advantage of this lies in the identifiability of the geometry present, before technical axioms have been invoked in order to secure a field of real numbers.The approach appears to be commendable because it yields new solutions to classical problems from monocular and binocular space perception as well as from colour vision. Extensions to derived measurement outside of psychophysics and to three and more dimensions of multidimensional scaling are reported.
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