Pehr Sällström
GOETHE AND THE BOUNDARY COLOURS
Version date 2022-11-25
Video at https://youtu.be/MDBE0dn_t9E
Goethe searched for general rules governing the appearance of colour in nature.
Coming across the prismatic colours, he thought he had found what he was looking for.
His observations boiled down to four types of colour spectra which taken together supply material for a complete colour system with promising features, such as complementarity and polarity, and where each colour gets its proper place between white and black.
When he presented his finding to contemporary physicists, they told him that these spectra were well-known and explainable in terms of Newton's theory of rays of different refrangibility.
They apparently didn't see the possibility of the colour system Goethe had in mind. Which is a shame, because it is a beautiful piece of theory, even from a purely physical point of view. Let me repair their mistake and give due credit to Goethe, by presenting the system of ideal colours, he anticipated.
ANALYSIS OF THE GOETHE-SPECTRA
Let me remind you of Goethe's procedure. He studied black-and-white pictures through a prism, under ordinary daylight conditions. Looking, for instance at a black square on white background, holding the prism horisontally, he saw this:
At the upper and lower boundary there appear spectra - a blue and a yellow one respectively. Looking instead at a white square on black ground, you get the inverse image white yellow and red at the upper boundary and cyan and blue at the lower. Always the same transition between white and black - a passage from light to darkness.
If you look at a sufficiently narrow black stripe, the black in the middle disappers and instead a purple colour appears, and in the inverse case - with a thin white stripe on black - green.
<
THEORETICAL ANALYSIS
In order to explain how these spectra come about, we consider the visual situation -- a person looking through a prism at an image on the wall -- and apply geometrical optics, with the inclusion of Newton's concept of "rays of different refrangibility".
Note. In geometrical optics the heuristic concept of "ray" represents the rectiliniear propagation of light together with the principle of superpostion of light intensities. (And by superposition is meant that the light fluxes do not interact or in any way disturb each other. Their separately measured intensities simply add.)
Looking through the prism at a white wall you see no colours (to Goethe's astonishment, at the first moment). Any point on the diffusely reflecting surface reflects light rays in various directions - some of which arrive at the pupil of the eye of the observer along his line of gaze. Rays of different refrangibility then come from different spots on the wall, but they all join along the sight-ray, thus making up the full spectrum of white (i.e. uncoloured) light.
But in the vicinity of a black area it may happen that blue type of rays cannot reach the eye along this line of sight. But still green and red rays are available, so the impression will be yellow.
Finally only red rays are avaliable:
In the case of a narrow stripe of black on the white wall, it happens for a particular line of sight that there are no green rays available (from reflections at the white surrounding area) with the result that a superposition of red and blue light appears in the direction of this line of sight, appearing as a purple colour, for instance magenta.
Let me illustrate how this modulation of the white illumination proceeds along any of these spectral images. I will use a newtonian spectrum (the ordered series of light-sorts, according to degrees of refrangibility) to illustrate the spectral composition of the light reaching the eye. (See note #3 in the appendix!)
Going from white to black, we successively cut away more and more of the rays, starting with those of greatest refrangibility.
The similar is true for the blue boundary spectrum, but in this case we cut away more and more from the red side, i.e. the rays of least refrangibility. Observe that to each colour in the yellow boundary spectrum there is a corresponding colour in the blue boundary spectrum. They are additive complementaries, since superimposed they constitute the full spectrum.
When it comes to the spectral image with purple, the modulation rather consists in cutting away a part in the middle of the full spectrum. A part that can be more or less wide, resulting in purples of various lightness and saturation, from light rose to deep red-violet.
The complementary light, given by the darkened area in the middle of the full spectrum, turns out as variants of green.
What have we done so far? By expressing the boundary spectra in terms of spectral compositions, we have taken Goethe's investigation a step further. The analysis helps us to design an optical device - a so called spectral integrator - by help of which we can dive into each of the spectra, experience it in detail and follow the lawful transformation of hue, typical for each kind.
THE SPECTRAL INTEGRATOR
By help of the spectral integrator individual ideal colours (i.e. idealized boundary colours) can be visually compared with colours produced by other means, for instance by help of colour filters, coloured solutions, or reflecting pigmented surfaces.
The geometry of the set-up is like this:
As light source I used a low voltage incandescent lamp. Slit S1 is projected as a sharp spectrum at S3 and the opening S2 is projected as a homogeneously illuminated image on screen S4. To begin with white. With sliding screens at S3 you can cut away more or less of the spectrum, from the shortwave side, as well as from the long-wave side. Thus producing single colours from the boundary spectra as well as from any central part of the full spectrum.
An improvement is to make the screens out of plexiglas in the shape of thin prisms, so that the light, cut away, is not absorbed but redirected and separately displayed. Which means that you always see the complementary pairs of colours, being the two halves into which the original white light is cleaved. In the particular set-up, I once constructed, the crucial component at S3 looks as follows:
The spectrum is projected onto the transparent thin prisms, for instance like this:
Leading to a double image on the screen, in this case looking somewhat like this:
Observe that the spectral integrator shows us that colours come in pairs. Any possible colour has its complementary. Simply because they are the two parts into which the original full-spectrum light has been divided. Consequently they do not have any wavelength in common. They are both opponent and complementary.
This way of displaying ideal colours is preferable. Namely as an image containing both the two colours belonging together and the white reference. This to avoid "the trap of the dark chamber". Presenting only a green spot in dark surround would not give sufficient information to the perceptual system for the observer to be able to identify the colour, in the sense of finding its place in the colour system, between the poles black and white.
WHAT ABOUT GREY?
Playing with the spectral integrator, you will take pleasure in being able to produce colours that are more brilliant, more saturated and bright, than you ever saw on your computer screen or painted canvas. These colours are pure, genuine, absolute, as Goethe said. But what about ordinary, darker and softer colours, such as olive green, brown and grey? You may have noted that there is no place for grey within the system of ideal colours. A perfect grey surface equally reflects all sorts of light, only to less degree than a white surface does. Goethe made prismatic observations including grey surfaces in the designs. He pointed out that the peculiarity of grey is that it contributes both light and darkness. It can play the role of white as well as the role of black in the images. Let us look at how it turns out visually.
You recognize the boundary spectra, but the colours look slightly different. Where grey has the role of black, it contributes an amount of whiteness. Where it has the role of white, it contributes an amount of blackness, to the boundary colours. We may explore the issue with the help of the spectral integrator, described above. As a matter of fact, this is very illustrative. As long as we move the slits in the horisontal direction, we are essentially in the realm of wavelengths. We may, however, include the intensity dimension, by projecting the full spectrum slightly above the prisms, like this.
Doing this we regulate the amount of light passing through the thin prisms. Then the direct light (in this case green) will contain a certain amount of full spectrum, i.e. whiteness, and the complementary field (purple) will be correspondingly darker, by loosing intensity.
THE DARKNESS OF EARTH-COLOURS
Goethe was of course well aware that paint, based on pigments found in nature, brings with it quite appreciable amounts of darkness, relative to the corresponding ideal colours. These rather belong to the sky - as in this watercolour, where he lets the sky illustrate the inverted spectrum yellow-purple-turquoise.
However, he acknowledged that the system of boundary colours showed a general pattern, valid for colour appearance in all natural phenomena. For instance the yellow boundary spectrum reminds us of the colour change of the setting sun, running from white, via yellow and orange to dark red.
In his "Farbenlehre" Goethe preferred to refer to sunset as a fundamental colour phenomenon, rather than the artificial prismatic boundary spectrum. The sun-image shows a more gradual change of hue in correlation with a more profound darkening.
When it comes to the lovely flower petals, their brilliant colours are mostly due to a strong absorption band at various positions within the visual range. Hence their reflectances are quite like ideal colours.
For the painter it i good to be aware of these "chromatic rules" since they should be used in harmony with the established rules for the treatment of light and shadow in natural situations, with material objects. For the skilful imitation of this on canvas, the artist needs to use less pure, even black, pigments.
CONCLUSION
So - in conclusion - there are many more similarities between qualitative colour apperance and objective physical conditions than the series of rainbow-colours, mostly referred to.
Why didn't Newton and his followers pay due attention to this? Well, Newton, in his time, was working with a beam of sunlight in a dark chamber and with the primary aim to come to grips with the disturbing chromatic aberrations in optical instruments. It never crossed his mind that darkness could have a decisive role for pigment based object colours.
Goethe happened to begin by studying black and white pictures under ordinary daylight conditions. For him light belongs to the visual process by which things and their properties become visible for us.
The observation that colours exclusively appear at the border between black and white areas indicates that colour is a contrast phenomenon, where light an dark play equally important roles. This became evident for him, in his approach to the issue of colour. And since his aim was a general understanding of colour, he took the structural features of the prismatic spectra seriously.
When it comes to describing the physical conditions governing the multiplicity of colours in natural situations, Goethe was intuitively right in bringing up the issue of boundary colours.
I will explore this a bit futher in a forthcoming lecture: The system of ideal colours"
APPENDIX: LECTURE NOTES
1) Goethe enthusiastically presented his findings in Beiträge zur Optik (aug. 1791).
2) He later on describes the disappointment he felt, when nobody seemed to understand what he had found so remarkable. You find the text in "Konfession des Verfassers" at the end of "Materialen zur Geschichte der Farbenlehre", in his big work "Zur Farbenlehre" 1810.
3) In the above diagrams n illustrating seeing the boundary spectra when looking through a prism at a white surface with a black square on it a I have kept the line of sight fixed and instead moved the screen stepwise downwards. In reality it would be the observer who redirects his line of sight (= his intention of observation) towards a point closer to the boundary of the black area. Observe that, when seeing, you are not looking at the optical image projected on the retina. You are looking at the outer world, finding out how it is constituted, by help of the retinal image. Thinking about the eye as a camera is deceptive! The technological analogy is in some respects useful, but the reality of vision is much more complex.
I characterize what happens when illumination is reflected from a surface or passes through a translucent medium, as a modulation of the state of the light. This modulation is in general described in terms of spectral energy distribution (or photon density) but in this particular case (ideal colours) it is only the spectral composition that is influenced, i.e. light being exchanged with darkness at certain frequencies within the visible range. This is the essential point with ideal colours that they do not modulate the intensity level, as most materials do in practice, due to impurities etc.
4) Concerning the Spectral Colour Integrator. Karl Miescher, in Basle, once constructed and used one, which was later on taken over by a research group at Oslo university (Holtsmark et al) where I had the pleasure of using it for some experimental investigations in 1976-77.
The small, hobby-version setup, here described, I made already around 1966 at the Physical institute, Stockholm University.
5) Goethe didn't speak of "ideal colours". His own terms: reine, ursprüngliche Farben (Ankündigung, Beiträge 1791).
6) Goethe was primarily caught by the primary boundary spectra - the yellow and the blue one. They are in a sense absolute. The secondary "mixed" spectra have infinite variations, according to the width of the white or black stripe.
7) The prismatic spectra have a very marked structure, lifting forth six distinctive qualities: yellow, red, violet, cyan, purple, green. But with the spectral integrator you can produce smooth transitions, e.g. yellow, via various orange hues, to rubi-red. (The six marked types of hue rather reveal the simple tri-chromaticity of our retinal receptor system.) Goethe wanted to emphasize this continuity character of colour: how easily momentary colours transform over into each other - giving rise to a continuous, dynamic hue circle.
As a matter of fact, you can construct a hue circle with ideal colours, where all hues have stronger saturation than the corresponding hue within the RGB triangle. You take the inverted spectrum from blue, violet,purples,red,orange, yellow. And then by mixing turkois and yellow-green you construct a series of green hues. I show you this in the trichromaticity diagram.
8) Goethe's choice of "Urphenomen" fell on turbid media ("Trübe"). The reddening sun being a typical example. The rainbow is not suitable for this role, because it is a rather complex phenomenon; it doesn't have the simplicity and generality that could be demanded of a Primary phenomenon.
9) It is the place and width of the dark band in an ideal colour spectrum that signifyes the particular colour. The rest of the spectrum is unmodified, i.e. same as for the initial unmodified white light.
10) Newton may have thought that the hue, experienced when you send a beam of light of a selected wavelength into the eye, is unconditionally caused by this particular sort of light. He then overlooked the fact that the absense of all other wavelengths is a necessary condition. The different sorts of light are physically independent (do not interact to create new sorts, or extinguish each other, nor take up place, can simutaneously occupy the same spot in space) but they are not formally independent (each sort has a specific place in the given series of sorts/wavelengths). It is not a question of "parallel light universes", one for each sort.
11) Goethe tells, he could'nt find a suitable room to serve as dark chamber, so he had to start by looking through the prism in an ordinary daylight situation. And the first he saw was that a white wall didn't show any colours, when regarded through the prism. So white doesn't unconditionally produce a colour spectrum. The specific physical/spatial conditions must necessarily be taken into account, as cause of colour appearance (cause, in a more general sense than mechanical). So it is wrong to think that colours belong to light per se, as Newton seemed to have thought, from what he proposed in Opticks.
12) In "Beiträge zu Optik" Goethe gives us the following characterization of light:
Das Licht hingegen können wir uns niemals in abstracto denken, sondern wir werden es gewahr als die Wirkung eines bestimmten Gegenstandes, der sich in dem Raume befindet und durch eben diese Wirkung andere Gegenstände sichtbar macht. §23
He pays attention to the light source, rather than light as a "something" in space. Like Newton, he deliberately puts the question of the nature of light aside for the moment.
13) It is interesting that you may regard the issue of colour perception both from the point of view of light - the light reaching the eye - and from the point of view of matter - the coloured objects you see, by help of this light.
The latter is more difficult to handle theoretically (or rather: technologically), because you must find out how the perceptual system manages to separate the two factors: relating to the spectral energy distribution of the initial light, respectively the material's power to modify this spectral distribution. The latter being "the colour of the object".
As a physicist you manage this by a two-step measuring process, in the definition of reflectance and transmittance as ratios (at a suitable number of wavelengths) between the intensity of outcoming and incident light.
As a living organism, developed through evolution, you rather use som kind of AI-algorithm, processing the enormous amount of data from the surrounding world, as it is normally, since long, constituted and experienced. Perception as an ongoing process.