Mathematical Conversations

In 1976 Dennis Sullivan gave an example of a smooth vector-field on a compact (Riemannian) 5-dimensional manifold in which all the orbits are closed but for which there is no upper bound to the length of a closed orbit. (At first this doesn't even seem possible...) Sullivan explained his proof to me at IHES in 1992 and I still remember his beautiful visual argument - except perhaps for some very fine points. The whole thing boils down to an interesting "clock-like" isotopy of a smooth loop on the 2-sphere. In this talk I'll try to convey the construction in non-technical terms and with a lot of pictures and waving of the arms.