Current status of mathematical foundations of the Gestalt concepts in psychophysics

Eileen Kowler was a member of the team of cognitive scientists that was assembled over a half a century ago by Robert M. Steinman. This team had grown and spanned several institutions in this country, as well as in Europe. The mechanisms governing the movements of the eyes were always at the center of Eileen's attention, but her research, as well as the research of our interdisciplinary group, is best understood by realizing its roots in Gestalt psychology. In the first part, this paper describes perspectives of two of the authors from the point of view of Eileen Kowler's collaborators. The second part provides a new look at the origins of Gestalt psychology, pointing out the scientific context of what has been referred to as the Gestalt revolution. The Gestalt revolution closely followed similar revolutions in mathematics and in physics, and it gave rise to new questions and challenges that have received recognition only recently.