Turning a Sphere Inside Out

Turning a Sphere Inside Out opens with a discussion of the problem of turning a sphere inside out by passing the surface through itself without making any holes or creases. Mathematicians believed that the problem was insoluble until 1958 when Stephen Smale proved otherwise. However, no one could visualize the motion, called a regular homotopy. The homotopy in this film was developed by Bernard Morin, a blind mathematician. It is illustrated with a sequence of chicken-wire models, built by Charles Pugh, showing the crucial stages in the motion. Mathematicians Nelson L. Max, Stephen Smale, and Charles Pugh, and physicist Judith Bregmann provide the commentary. The film closes with several different sequences of computer animation revealing the continuous motion of the sphere. Supplemental information and images are available by clicking here.