50 Color science historical notes
Suggestions of all kinds for this book draft are welcome — whether it’s fixing small errors, raising bigger questions, or offering new perspectives. Please share comments through GitHub Issues. To make feedback easier to address, please point to the section you have in mind — by section number or a short snippet of text.
These are notes, many of which are based on Mollon’s excellent chapter in the Shevell book. Also some other notes that I want to remember about Helmholtz and trichromacy.
50.1 Did Palmer “really know” about trichromacy?
Mollon’s reading of Palmer’s 1777 tract (Theory of Colours and Vision) and his subsequent 1781/1786 writings reveals a mix of prescient biological intuition and physical error:
What Palmer actually asserted: Palmer proposed that the retina possesses three distinct types of particles, fibres, or membranes (corresponding to red, yellow, and blue), and that equal stimulation of all three gives rise to the perception of white. In 1781 (writing under the pseudonym Giros von Gentilly), he extended this to argue that color blindness occurs when one or two of these three molecular classes are missing or inactive—which Mollon notes as arguably the earliest proposal of an inherited receptor-level defect.
The caveat: Palmer did not deduce trichromacy from quantitative color matching, nor did he realize that physical light is a continuous distribution of wavelengths. Palmer believed that light itself physically consists of only three types of rays. Young’s later advance was realizing that physical light is a continuum, making trichromacy strictly a limitation of the eye’s physiological sensors.
50.2 Waller
I think John credits Waller too much. That author wrote that the primary colors cannot be created from other colors, but all others can be created from the primaries. That is false about lights. Any three lights will do as primaries. It has a bit (only a bit) more validity for subtractive matches because if you throw light away there isn’t much that can be done. But subtractive color mixing is a plague that should be avoided, certainly in the case of initial teaching.
50.3 Color Matching Before Maxwell: Empirical Craft vs. Additive Tests
Before Maxwell’s quantitative colorimetry in the 1850s, the notion of three-dimensionality existed primarily as an industrial rule of thumb, along with a handful of qualitative optical experiments:
- The Practical / Subtractive Tradition: Early printers and painters knew empirically that a small palette of pigments could span the gamut of hues. Jacob Christoph Le Blon (1710s–1720s) commercialized three-color mezzotint printing using red, yellow, and blue inks. Tobias Mayer (1758) and Johann Heinrich Lambert (1772) later formalized pigment mixtures into triangular color solids. However, these subtractive mixtures conflated pigment physics with light mixture, entrenching the mistaken belief that green light was physically composed of yellow and blue light.
- Christian Ernst Wünsch (1792): As John Mollon has documented, Wünsch conducted the first decisive additive mixture experiments using prisms to isolate and superimpose spectral bands. He proved that spectral red and spectral green additively produce yellow, and identified red, green, and violet as the true fundamental lights.
- Thomas Young (1801–1802): Young took the critical step of shifting trichromacy from an assumed property of light to a property of human physiology. Because light spans an infinite physical spectrum, the eye cannot possess infinite resonators; Young asserted that the retina contains three types of sensitive nerve fibers (red, green, violet). Young’s hypothesis, however, remained an untested physical-physiological conjecture; he performed no systematic color-matching experiments to prove that all colors could be represented in a 3D linear space.
Remember that Brewster still thought color was a physical property. Maxwell did some simple, decisive experiments by interposing a filter on metamers to show that they transmitted differently and thus the lights were not the same. They only appeared to be the same and thus the color matches were biological, not physical.
50.4 Helmholtz’s 1852 Logic: Segmenting the Spectrum
I am very fond of this logical error on Helmholtz’ part.
When Hermann von Helmholtz took up the problem in his 1852 paper (Über die Theorie der zusammengesetzten Farben), he set out to test Newton’s color circle and Young’s hypothesis using a V-shaped slit and prism apparatus to superimpose pairs of narrow spectral bands:
- The Stepping Procedure: Rather than attempting three-variable color matching, Helmholtz fixed one spectral wavelength and gradually moved a second wavelength further away along the spectrum, mixing them to see whether intermediate spectral hues could be reproduced.
- The Failure of Two-Wavelength Segments: As soon as the two wavelengths were separated by more than a certain interval, their mixture could no longer match the appearance of the wavelengths between them. By continuing this “stepping” across the visible range, Helmholtz partitioned the spectrum into five distinct segments: red, yellow, green, blue, and violet.
- The Flawed Premise: Underlying Helmholtz’s reasoning was the assumption that each primary sensation operated essentially in isolation—that a pure, monochromatic wavelength was detected by one primary element at a time. If mixing the end-points of a segment failed to capture the sensations inside the next, he concluded that Young’s three-receptor scheme was insufficient and that the eye must require at least five primary sensations (or a continuum of them).
50.4.1 Spectral overlap
It is useful that the spectral sensitivities of the different receptors overlap. If the spectra were purely block spectra, non-overlapping, we would have 1-dimensional color vision in each of the bands. We might know which band we are in, but different wavelengths within the band would just differ in intensity -like scotopic vision. We would have multidimensional representation if the signal is broadband, informing us about the relative excitation from the broadband signal. But if the spectral sensitivities overlap, then we can still discriminate the color of narrow band signals.
50.5 Grassmann’s Mathematics and Maxwell’s Resolution
Poor Grassmann.
The breakthrough came from abandoning Helmholtz’s assumption of independent, segmented primary channels:
Hermann Grassmann (1853): Grassmann recognized that Helmholtz’s experimental logic violated basic linear geometry. Grassmann showed theoretically that if color matching obeyed three basic rules (superposition, homogeneity, and transitivity), any human color sensation could be represented as an element in a three-dimensional vector space. Grassmann argued that Helmholtz’s failure to reproduce spectral colors with two-primary steps did not disprove trichromacy; rather, it arose from treating color mixture as piecewise combinations rather than simultaneous vector mixtures of three primaries.
Maxwell’s Coterminal Curves (1855–1860): Maxwell grasped what Helmholtz had missed: the eye’s sensitive elements must have broad, overlapping spectral sensitivities. Under this framework, light at any single wavelength (such as 580 nm) simultaneously stimulates multiple receptor classes in a fixed ratio. Mixing a spectral red and a spectral green stimulates those same classes in that exact same ratio, producing a complete perceptual match to 580 nm.
Maxwell’s Quantitative Metric: Using spinning tops and his calibrated color box, Maxwell carried out the world’s first true quantitative color-matching experiments, determining the linear color-matching functions and proving that human color vision is strictly three-dimensional.
Helmholtz’s Conversion: Convinced by Grassmann’s linear formulation and Maxwell’s empirical measurements, Helmholtz retracted his five-primary interpretation. In his Handbuch der physiologischen Optik (1860), he embraced Young’s three-receptor framework combined with Maxwell’s overlapping broadband sensitivities, synthesizing it with Johannes Müller’s law of specific nerve energies into the modern Young–Helmholtz theory.