What relationship does the inverse spectra of Goethe’s theory of colours have to the duality of projective geometry?

In Goethe’s theory of colour we find two spectra: the rainbow spectrum (Newton’s spectrum) with green in the middle, and the “inverted spectrum” with magenta in the middle, which is also called the “inverse spectrum” or “Goethe’s spectrum”. In today’s optics, it is known that the two spectra are mutually dependent as complements that are — at least phenomenologically — equivalent.

At about the same time the duality principle in geometry was formulated, thereby founding projective geometry. Rudolf Steiner repeatedly pointed out the importance of projective geometry for understanding life processes, and he coined the term “counterspace” in this context. Research was done on both fields since decades, often also in local and inner proximity, like in the case of Michael Wilson and George Adams at Sunfield. Yet, both research questions were not often addressed together. Against this background, the question arises as to the relationship between the optical complementarity of the inverse colour spectra and the duality of projective geometry. Can the physical-mathematical description of light and colour be extended by a view and/or description of counterspace?

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About Dr Mattias Rang

Matthias Rang studied physics in Freiburg, Germany and Berlin before becoming a visiting researcher in the field of nano-optics at the University of Washington, Seattle. He received a PhD from the University of Wuppertal, Germany. At the Goetheanum in Dornach, Switzerland, where Rang co-leads the Natural Science Section, he carries out research on Goethe’s theory of color in relation to physical optics..

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