Riemann and the Sound of Space
Peter D. Pešić · The MIT Press eBooks · 2014
The separate works of Bernhard Riemann and Hermann von Helmholtz reflected their shared concern with hearing in the context of the problem of space and the physical foundations of geometry. Riemann had established a new conception of multidimensional curved space; his final, uncompleted work critiqued Helmholtz’s account of hearing. Helmholtz read Riemann’s work on hearing even before his ideas about space, toward which Helmholtz had been independently working. After Riemann’s death, Helmholtz argued that geometry rested on physical facts rather than hypotheses (as Riemann held). Helmholtz drew these arguments from findings about visual perception, but later extended them to the manifolds of simple tones and of time. Einstein later acknowledged Helmholtz and Riemann’s work as essential sources for general relativity. Einstein considered Helmholtz’s connection of geometric hypotheses with empirical facts absolutely crucial for the general theory of relativity, whose field equations epitomize that connection. To reach that point, Helmholtz connected his work in music and vision, hearing and seeing, whose comparison lay at the grounds of his synthetic understanding. Throughout the book where various sound examples are referenced, please see http://mitpress.mit.edu/musicandmodernscience (please note that the sound examples should be viewed in Chrome or Safari Web browsers).