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

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 Riemann’s critique of Helmholtz’s work on hearing led Helmholtz to respond and study Riemann’s then-unpublished lecture on the foundations of geometry.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.     

Rotational Analysis of the B2Σ+-X2Σ+ Bands of 12C18O+

The emission spectrum of the B²Σ⁺-X²Σ⁺ (First Negative) system of the molecular ion ¹²C¹⁸O⁺ have been photographed at a resolution sufficient to observe the spin splitting of the lines with N > 18. Four bands, 0-1, 0-3, 1-4 and 2-5, have been rotationally analyzed and the molecular constants of the B²Σ⁺ , v = 0,1, 2 and X²Σ⁺ , v =1, 3, 4, 5 have been obtained.     

Identification of the amino acid labionin and its desulfurised derivative in the type-III lantibiotic LabA2 by means of GC/MS

A GC-MS method for the rapid and unambiguous identification of the amino acid labionin (Lab) occurring in type-III lantibiotics is presented. This method will constitute a valuable tool for the characterisation and structure elucidation of labyrinthopeptins and their differentiation from lanthionine-type lantibiotics.