Article ID: CBB084267730

Helmholtz and the geometry of color space: Gestation and development of Helmholtz’s line element (2023)


Modern color science finds its birth in the middle of the nineteenth century. Among the chief architects of the new color theory, the name of the polymath Hermann von Helmholtz stands out. A keen experimenter and profound expert of the latest developments of the fields of physiological optics, psychophysics, and geometry, he exploited his transdisciplinary knowledge to define the first non-Euclidean line element in color space, i.e., a three-dimensional mathematical model used to describe color differences in terms of color distances. Considered as the first step toward a metrically significant model of color space, his work inaugurated researches on higher color metrics, which describes how distance in the color space translates into perceptual difference. This paper focuses on the development of Helmholtz’s mathematical derivation of the line element. Starting from the first experimental evidence which opened the door to his reflections about the geometry of color space, it will be highlighted the pivotal role played by the studies conducted by his assistants in Berlin, which provided precious material for the elaboration of the final model proposed by Helmholtz in three papers published between 1891 and 1892. Although fallen into oblivion for about three decades, Helmholtz’s masterful work was rediscovered by Schrödinger and, since the 1920s, it has provided the basis for all subsequent studies on the geometry of color spaces up to the present time.

Citation URI

Similar Citations

Article Wise, M. Norton; (2007)
What Can Local Circulation Explain? The Case of Helmholtz's Frog-Drawing-Machine in Berlin (/isis/citation/CBB000931384/)

Article Finger, Stanley; Wade, Nicholas J.; (2002)
The Neuroscience of Helmholtz and the Theories of Johannes Müller - Part 2: Sensation and Perception (/isis/citation/CBB000340361/)

Book Reichardt, Hans; (1976)
Gauss und die nichteuklidische Geometrie (/isis/citation/CBB000027166/)

Article Abardia, Judit; Reventós, Agustí; Rodríguez, Carlos J.; (2012)
What Did Gauss Read in the Appendix? (/isis/citation/CBB001251202/)

Article Chen, Huiyong; (2011)
Study on the Approach to Realize the Thought of Gauss' Non-Euclidean Geometry (/isis/citation/CBB001210056/)

Book Gray, Jeremy J.; (2004)
János Bolyai, Non-Euclidean Geometry, and the Nature of Space (/isis/citation/CBB000750880/)

Article Amanda Paxton; (2021)
The Hard Math of Beauty: Gerard Manley Hopkins and "Spectral Numbers" (/isis/citation/CBB150662150/)

Article Christiansen, Andreas; (2009)
Bernt Michael Holmboe (1795--1850) and His Mathematics Textbooks (/isis/citation/CBB000931934/)

Article Capelo, António Cândido; Ferrari, Mario; (1982)
La “cuffia” di Beltrami: Storia e descrizione (/isis/citation/CBB000000126/)

Article Martins, Roberto de Andrade; (1995)
A influência das geometrias não-euclidianas no pensamento físico de século XIX (/isis/citation/CBB000068213/)

Article Stump, David; (1991)
Poincaré's thesis of the translatability of Euclidean and non-Euclidean geometries (/isis/citation/CBB000052800/)

Article Fuller, Steve; (1999)
Authorizing science studies: or, Why we have never had paradigms (/isis/citation/CBB000079981/)

Chapter Freguglia, Paolo; (2002)
Giuseppe Veronese's Studies on Four-Dimentional Descriptive Geometry (/isis/citation/CBB000430145/)

Authors & Contributors
Reichardt, Hans
Paxton, Amanda
Lorenat, Jemma
Wise, M. Norton
Wade, Nicholas J.
Stump, David J.
Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)
VIET: Voprosy Istorii Estestvoznaniia i Tekhniki
Victorian Studies
Revista da Sociedade Brasileira de Historia de Ciência
The MIT Press
Non-euclidean geometry
Spherical geometry
Gauss, Carl Friedrich
Helmholtz, Hermann Ludwig Ferdinand von
Poincaré, Jules Henri
Beltrami, Eugenio
Hopkins, Gerard Manley
Bolyai, Janos (Johann) von
Time Periods
19th century
United States
British Isles
Berlin (Germany)
Great Britain
Deutsche Physikalische Gesellschaft (DPG)

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment