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Bernhard Riemann, the ear, and an atom of consciousness

by A. Bell and B. Davies and H. Ammari

(Report number 2021-20)

Abstract
Why did Bernhard Riemann (1826–1866), arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from them to build a broad picture of what he might have been driving at. Our interpretation is that Riemann was a committed idealist and from this philosophical standpoint saw that the scientific enterprise was lame without the “poetry of hypothesis”. He believed that human thought was fundamentally the dynamics of “mind-masses” and that the human mind interpenetrated, and became part of, the microscopic physical domain of the cochlea. Therefore, a full description of hearing must necessarily include the perceptual dimensions of what he saw as a single manifold. The manifold contains all the psychophysical aspects of hearing, including the logarithmic transformations that arise from Fechner’s law, faithfully preserving all the subtle perceptual qualities of sound. For Riemann, hearing was a unitary physical and mental event, and parallels with modern ideas about consciousness and quantum biology are made. A unifying quantum mechanical model for an atom of consciousness – drawing on Riemann’s mind-masses and the similar “psychons” proposed by Eccles – is put forward.

Keywords: Bernhard Riemann; hearing; manifold; mind-mass; psychon; consciousness; quantum mechanics

@Techreport{BDA21_962,
  author = {A. Bell and B. Davies and H. Ammari},
  title = {Bernhard Riemann, the ear, and an atom of consciousness},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-20},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-20.pdf },
  year = {2021}
}

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