Article ID: CBB001320409

Helmholtz, Riemann, and the Sirens: Sound, Color, and the “Problem of Space” (2013)

unapi

Emerging from music and the visual arts, questions about hearing and seeing deeply affected Hermann Helmholtz's and Bernhard Riemann's contributions to what became called the 'problem of space [ Raumproblem],' which in turn influenced Albert Einstein's approach to general relativity. Helmholtz's physiological investigations measured the time dependence of nerve conduction and mapped the three-dimensional manifold of color sensation. His concurrent studies on hearing illuminated musical evidence through experiments with mechanical sirens that connect audible with visible phenomena, especially how the concept of frequency unifies motion, velocity, and pitch. Riemann's critique of Helmholtz's work on hearing led Helmholtz to respond and study Riemann's then-unpublished lecture on the foundations of geometry. During 1862-1870, Helmholtz applied his findings on the manifolds of hearing and seeing to the Raumproblem by supporting the quadratic distance relation Riemann had assumed as his fundamental hypothesis about geometrical space. Helmholtz also drew a 'close analogy ... in all essential relations between the musical scale and space.' These intersecting studies of hearing and seeing thus led to reconsideration and generalization of the very concept of 'space,' which Einstein shaped into the general manifold of relativistic space-time.

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Authors & Contributors
Darrigol, Olivier
Polak, Paweł
Malloy, Vanja V.
Zanarini, Gianni
Wittje, Roland
Schmidt, Michael J.
Concepts
Physics
Music
Senses and sensation; perception
Acoustics
Auditory perception
Mathematics
Time Periods
19th century
20th century, early
21st century
20th century
18th century
Places
Germany
United States
England
Cracow (Poland)
Ukraine
Poland
Institutions
IMAX Filmed Entertainment
Uniwersytet Lwowski (Lwów, Poland)
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