Usefulness and limitation of spatial representation

What discussed herein is not an “open problem” in the sense of mathematics. It is a problem that psychologists should keep in mind when presenting a formal model. A model will be useful for phenomena on which the model has been formulated. However, the model may contain a number of remaining properties that not necessarily represent related psychological phenomena adequately. The situation is analogous to that the particle model of light does not represent diffraction whereas the wave model of light is not adequate for the Compton effect. When presenting a model, mathematical psychologists should be especially keen about this point. The problem is discussed with a concrete example.