The notion of dimension in geometry and algebra

Abstract

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are invoked and compared. Glenn Gould disapproved of his own recording of Goldberg variations. "There is a lot of piano playing going on there, and I mean that as the most disparaging comment possible. " NYRB, Oct. 7, 2004, p. 10.