Theory of Colours (book)

Theory of Colours (original German title, Zur Farbenlehre) is a book by Johann Wolfgang von Goethe published in 1810. It contains some of the earliest published descriptions of phenomena such as coloured shadows, refraction, and chromatic aberration.

Its influence extends primarily to the art world, especially among the Pre-Raphaelites. J. M. W. Turner studied it comprehensively, and referenced it in the titles of several paintings (Bockemuhl, 1991 ). Wassily Kandinsky considered Goethe's theory "one of the most important works."

Although Goethe's work was never well received by physicists, a number of philosophers and physicists have been known to have concerned themselves with it, including Arthur Schopenhauer, Kurt Gödel, Werner Heisenberg, Ludwig Wittgenstein, and Hermann von Helmholtz. Mitchell Feigenbaum had even convinced himself that 'Goethe had been right about colour!' (Ribe & Steinle, 2002 ).

In his book, Goethe provides a general exposition of how colour is perceived in a variety of circumstances, and considers Isaac Newton's observations to be special cases. Goethe's concern was not so much with the analytic measurement of colour phenomenon, as with the qualities of how phenomena are perceived. Science has come to understand the distinction between the optical spectrum, as observed by Newton, and the phenomenon of human colour perception as presented by Goethe.

Goethe's theory
It is hard to present Goethe's "theory", since he refrains from setting up any actual theory; "its intention is to portray rather than explain" (Scientific Studies ). For Goethe, "the highest is to understand that all fact is really theory. The blue of the sky reveals to us the basic law of color. Search nothing beyond the phenomena, they themselves are the theory."

"The crux of his color theory is its experiential source: rather than impose theoretical statements, Goethe sought to allow light and color to be displayed in an ordered series of experiments that readers could experience for themselves." (Seamon, 1998 ). As such, he would reject both the wave and particle theories because they are conceptually inferred and not directly perceived by the human senses. According to Goethe, "Newton's error... was trusting math over the sensations of his eye.""

- Jonah Lehrer

Goethe outlines his method in the essay, The experiment as mediator between subject and object (1772). It underscores his experiential standpoint. "The human being himself, to the extent that he makes sound use of his senses, is the most exact physical apparatus that can exist." (Goethe, Scientific Studies )

Historical background


In 1740, Louis Bertrand Castel published a criticism of Newton's spectral description of prismatic colour, where he observed that the colours of white light split by a prism depended on the distance from the prism, and that Newton was looking at a special case; an argument which Goethe later developed.

It was in the 1780s when Goethe was asked to return a prism which had been on loan from the Privy Councillor Buettner in Jena. As he did so, he paused to take a look through the prism – and what he saw led him to a comprehensive study of light phenomena, culminating in The Theory of Colours.

"Along with the rest of the world I was convinced that all the colours are contained in the light; no one had ever told me anything different, and I had never found the least cause to doubt it, because I had no further interest in the subject."

- Goethe

At the time, it was already known that the prismatic phenomenon is a process of splitting up the colourless (white) light into colours. Newton's theory stated that colourless light already contains the seven colours within itself – and when we direct this light through a prism, the prism separates what is already there in the light – the seven colours into which it is analyzed.

Goethe's reasoning
Goethe reasoned: In such way the phenomena are interpreted, but this is not the primal or complete phenomenon. A look through the prism shows that we do not see white areas split evenly into seven colours. Rather, we see colours at some edge or border-line.

"If we let light pass through the space of the room, we get a white circle on the screen... Put a prism in the way of the body of light that is going through there – the cylinder of light is diverted (Figure I), but what appears in the first place is not the series of seven colours at all, only a reddish colour at the lower edge, passing over into yellow, and at the upper edge a blue passing over into greenish shades. In the middle it stays white.

The colours therefore, to begin with, make their appearance purely and simply as phenomena at the border between light and dark. This is the original, the primary phenomenon. We are no longer seeing the original phenomenon when by reducing the circle in size we get a continuous sequence of colours. The latter phenomenon only arises when we take so small a circle that the colours extend inward from the edges to the middle. They then overlap in the middle and form what we call a continuous spectrum, while with the larger circle the colours formed at the edges stay as they are. This is the primal phenomenon. Colours arise at the borders, where light and dark flow together."

- Steiner, 1919

Goethe therefore concluded that the spectrum is a compound phenomenon. Colour arises at light-dark boundaries, and where the yellow-red and blue-violet edges overlap, you get green.

Experiments with turbid media
Goethe's studies of colour began with subjective experiments which examined the effects of turbid media on the perception of light and dark. He observed that light seen through a turbid medium appears yellow, and darkness seen through an illuminated medium appears blue.

"The highest degree of light, such as that of the sun... is for the most part colourless. This light, however, seen through a medium but very slightly thickened, appears to us yellow. If the density of such a medium be increased, or if its volume become greater, we shall see the light gradually assume a yellow-red hue, which at last deepens to a ruby colour.

If on the other hand darkness is seen through a semi-transparent medium, which is itself illumined by a light striking on it, a blue colour appears: this becomes lighter and paler as the density of the medium is increased, but on the contrary appears darker and deeper the more transparent the medium becomes: in the least degree of dimness short of absolute transparence, always supposing a perfectly colourless medium, this deep blue approaches the most beautiful violet."

- Goethe

Starting from these observations, he began numerous experiments, observing the effects of darkening and lightening on the perception of colour in many different circumstances.

Darkness and light
For Goethe, light is "the simplest most undivided most homogenous being that we know. Confronting it is the darkness" (Letter to Jacobi). Unlike his contemporaries, Goethe didn't see darkness as an absence of light, but rather as polar to and interacting with light; colour resulted from this interaction of light and shadow.

"...they maintained that shade is a part of light. It sounds absurd when I express it; but so it is: for they said that colours, which are shadow and the result of shade, are light itself."

- Johann Eckermann

Based on his experiments with turbid media, Goethe characterized colour as arising from the dynamic interplay of darkness and light. The editor of the Kurschner edition of Goethe's works gives the following analogy:

"Modern natural science sees darkness as a complete nothingness. According to this view, the light which streams into a dark space has no resistance from the darkness to overcome. Goethe pictures to himself that light and darkness relate to each other like the north and south pole of a magnet. The darkness can weaken the light in its working power. Conversely, the light can limit the energy of the darkness. In both cases color arises."

- Steiner, 1897

Goethe writes:

"Yellow is a light which has been dampened by darkness

Blue is a darkness weakened by the light."

Boundary conditions


When viewed through a prism, the orientation of a light-dark boundary with respect to the prism is significant. With white above a dark boundary, we observe the light extending a blue-violet edge into the dark area; whereas dark above a light boundary results in a red-yellow edge extending into the light area.

Goethe was intrigued by this difference. He felt that this arising of colour at light-dark boundaries was fundamental to the creation of the spectrum (which he considered to be a compound phenomenon).

Light and dark spectra


Since the colour phenomenon relies on the adjacency of light and dark, there are two ways to produce a spectrum: with a light beam in a dark room, and with a dark beam (i.e. a shadow) in a light room.

Goethe recorded the sequence of colours projected at various distances from a prism for both cases (see Plate IV, Theory of Colours). In both cases, he found that the yellow and blue edges remain closest to the side which is light, and red and violet edges remain closest to the side which is dark. At a certain distance, these edges overlap. When these edges overlap in a light spectrum, green results; when they overlap in a dark spectrum, magenta results.

With a light spectrum, coming out of the prism, one sees a shaft of light surrounded by dark. We find yellow-red colours along the top edge, and blue-violet colours along the bottom edge. The spectrum with green in the middle arises only where the blue-violet edges overlap the yellow-red edges.

With a dark spectrum (i.e. a shadow surrounded by light), we find violet-blue along the top edge, and red-yellow along the bottom edge – where these edges overlap, we find magenta.

Goethe's colour wheel
"When the eye sees a colour it is immediately excited and it is its nature, spontaneously and of necessity, at once to produce another, which with the original colour, comprehends the whole chromatic scale."

- Goethe, Theory of Colours

Goethe anticipated Ewald Hering's Opponent process theory by proposing a symmetric colour wheel. He writes, "The chromatic circle... [is] arranged in a general way according to the natural order... for the colours diametrically opposed to each other in this diagram are those which reciprocally evoke each other in the eye. Thus, yellow demands violet; orange, blue; red, green; and vice versa: thus... all intermediate gradations reciprocally evoke each other; the simpler colour demanding the compound, and vice versa. (Goethe, Theory of Colours ).

Goethe also expressed his understanding of the light and dark spectra in including magenta in his colour wheel. Whereas for Newton - magenta was an 'extraspectral' colour - for Goethe, magenta was a natural result of violet and red being mixed in a dark spectrum (see top of colour wheel) - just as green resulted from the mixing of blue and yellow in the light spectrum (bottom of colour wheel).

"For Newton, only spectral colors could count as fundamental. By contrast, Goethe's more empirical approach led him to recognize the essential role of (nonspectral) magenta in a complete color circle, a role that it still has in all modern color systems." (Ribe & Steinle, 2002

Newton and Goethe
Due to their different approaches to a common subject, many misunderstandings have arisen between Newton's mathematical understanding of optics, and Goethe's experiential approach.

Because Newton understands white light to be composed of individual colours, and Goethe sees colour arising from the interaction of light and dark, they come to different conclusions on the question: is the optical spectrum a primary or a compound phenomenon?

For Newton, all the colours already exist in white light, and the prism merely fans them out according to their refrangability. Goethe sought to show that, as a turbid medium, the prism was an integral factor in the arising of colour.

"Whereas Newton observed the colour spectrum cast on a wall at a fixed distance away from the prism, Goethe observed the cast spectrum on a white card which was progressively moved away from the prism... As the card was moved away, the projected image elongated, gradually assuming an elliptical shape, and the coloured images became larger, finally merging at the centre to produce green. Moving the card farther led to the increase in the size of the image, until finally the spectrum described by Newton in the Opticks was produced... The image cast by the refracted beam was not fixed, but rather developed with increasing distance from the prism. Consequently, Goethe saw the particular distance chosen by Newton to prove the second proposition of the Opticks as capriciously imposed."

Whereas Newton narrowed the beam of light in order to isolate the phenomenon, Goethe observed that with a wider aperture, there was no spectrum. He saw only reddish-yellow edges and blue-cyan edges with white between them, and the spectrum arose only where these edges came close enough to overlap. For him, the spectrum could be explained by the simpler phenomena of colour arising from the interaction of light and dark edges.

Newton explains "the fact that all the colors appear only when the prism is at a certain distance from the screen, whereas the middle otherwise is white... [by saying] the more strongly diverted lights from the upper part of the image and the more weakly diverted ones from the lower part fall together in the middle and mix into white. The colors appear only at the edges because there none of the more strongly diverted parts of the light from above can fall into the most weakly diverted parts of the light, and none of the more weakly diverted ones from below can fall into the most strongly diverted ones." (Steiner, 1897 )

Table of differences
As a catalogue of observations, Goethe's experiments are useful data for understanding the complexities of human colour perception. Whereas Newton sought to develop a mathematical model for the behaviour of light, Goethe focused on exploring how colour is perceived in a wide array of conditions.

Goethe's reification of darkness has caused almost all of modern physics to reject Goethe's theory. Both Newton and Huygens defined darkness as an absence of light. Young and Fresnel combined Newton's particle theory with Huygen's wave theory to show that colour is the visible manifestation of light's wavelength. Physicists today attribute both a corpuscular and undulatory character to light, which is the content of the so-called Wave–particle duality. Curiously, since the crux of Goethe's theory is tied to what is experiential, he would reject both the wave and particle theories since they are conceptually inferred and not directly perceived by the human senses.

History and Influence
The original German edition of this book is comprised of three sections: i) a didactic section in which Goethe presents his own observations, ii) a polemic section in which he makes his case against Newton, and iii) a historical section.

From its publication in 1810, the book was controversial for its stance against Newton. So much so, that when Charles Eastlake translated the text into English in 1840, he omitted the content of Goethe's polemic against Newton.

"Significantly (and regrettably), only the 'Didactic' colour observations appear in Eastlake's translation. In his preface, Eastlake explains that he deleted the historical and entoptic parts of the book because they 'lacked scientific interest', and censored Goethe's polemic because the 'violence of his objections' against Newton would prevent readers from fairly judging Goethe's color observations." (Bruce MacEvoy, Handprint.com, 2008)

Influence on the Arts
After being translated into English by Charles Eastlake in 1840, this theory became widely adopted by the art world - especially among the Pre-Raphaelites. J. M. W. Turner studied it comprehensively, and referenced it in the titles of several paintings (Bockemuhl, 1991 ).

Wassily Kandinsky considered Goethe's theory "one of the most important works."

Influence on Latin American Flags
During a party in Weimar in the winter of 1785, Goethe had a late-night conversation on his theory of primary colours with the South American revolutionary Francisco de Miranda. This conversation inspired Miranda, as he later recounted, in his designing the yellow, blue and red flag of Gran Colombia, from which the present national flags of Colombia, Venezuela and Ecuador are derived. (See Flag of Colombia).

Reception by Scientists
Although the accuracy of Goethe's observations does not admit a great deal of criticism, his theory's failure to demonstrate significant predictive validity eventually rendered it scientifically irrelevant.

"Goethe's colour theory has in many ways borne fruit in art, physiology and aesthetics. But victory, and hence influence on the research of the following century, has been Newton's."

- Werner Heisenberg, 1952

Much controversy stems from two different ways of investigating light and colour. Goethe was not interested in Newton's analytic treatment of colour - but he presented an excellent rational description of the phenomenon of human colour perception. It is as such a collection of colour observations that we must view this book.

"Most of Goethe's explanations of color have been thoroughly demolished, but no criticism has been leveled at his reports of the facts to be observed; nor should any be. This book can lead the reader through a demonstration course not only in subjectively produced colors (after images, light and dark adaptation, irradiation, colored shadows, and pressure phosphenes), but also in physical phenomena detectable qualitatively by observation of color (absorption, scattering, refraction, diffraction, polarization, and interference). A reader who attempts to follow the logic of Goethe's explanations and who attempts to compare them with the currently accepted views might, even with the advantage of 1970 sophistication, become convinced that Goethe's theory, or at least a part of it, has been dismissed too quickly."

- Judd, 1970

"As Feigenbaum understood them, Goethe's ideas had true science in them. They were hard and empirical. Over and over again, Goethe emphasized the repeatability of his experiments. It was the perception of colour, to Goethe, that was universal and objective. What scientific evidence was there for a definable real-world quality of redness independent of our perception?"

- James Gleick

Current Status
Developments in understanding how the brain interprets colours, such as colour constancy and Edwin Land's retinex theory bear striking similarities to Goethe's theory (Ribe & Steinle, 2002 ).

A modern treatment of the book is given by Dennis L. Sepper in the book, Goethe contra Newton: Polemics and the Project for a New Science of Color (Cambridge University Press, 2003).

Quotations
"As to what I have done as a poet... I take no pride in it... but that in my century I am the only person who knows the truth in the difficult science of colours – of that, I say, I am not a little proud, and here I have a consciousness of a superiority to many."

- Johann Eckermann

"[Goethe] delivered in full measure what was promised by the title of his excellent work: data toward a theory of colour. They are important, complete, and significant data, rich material for a future theory of colour. He has not, however, undertaken to furnish the theory itself; hence, as he himself remarks and admits on page xxxix of the introduction, he has not furnished us with a real explanation of the essential nature of colour, but really postulates it as a phenomenon, and merely tells us how it originates, not what it is."

- Schopenhauer

"Goethe's theory of the origin of the spectrum isn't a theory of its origin that has proved unsatisfactory; it is really not a theory at all. Nothing can be predicted by means of it. It is, rather, a vague schematic outline, of the sort we find in James's psychology. There is no experimentum crucis for Goethe's theory of colour."

- Wittgenstein

"Can you lend me the Theory of Colours for a few weeks? It is an important work. His last things are insipid."

- Ludwig van Beethoven

"Should your glance on mornings lovely Lift to drink the heaven's blue Or when sun, veiled by sirocco, Royal red sinks out of view - Give to Nature praise and honor. Blithe of heart and sound of eye, Knowing for the world of colour Where its broad foundations lie."

- Goethe

On the catalytic moment
"Aber wie verwundert war ich, als die durch's Prisma angeschaute weiße Wand nach wie vor weiß blieb, daß nur da, wo ein Dunkles dran stieß, sich eine mehr oder weniger entschiedene Farbe zeigte, daß zuletzt die Fensterstäbe am allerlebhaftesten farbig erschienen, indessen am lichtgrauen Himmel draußen keine Spur von Färbung zu sehen war. Es bedurfte keiner langen Überlegung, so erkannte ich, daß eine Gränze nothwendig sey, um Farben hervorzubringen, und ich sprach wie durch einen Instinct sogleich vor mich laut aus, daß die Newtonische Lehre falsch sey.

But I was astonished, as I looked at a white wall through the prism, how it stayed white! That only there where it came upon some darkened area, it showed more or less some colour, then at last, around the window sill all the colours shone, in the light grey sky outside there was no colour to be seen. It didn't take long before I knew here was something significant about colour to be brought forth, and I spoke as through an instinct out loud, that the Newtonian teachings were false. [rough translation by user: johnrpenner]"

- Goethe

Alternative (improved) translation:

But how amazed I was when the white wall I was looking at through the prism remained white: that a more or less definite colour appeared only where a dark surface or edge adjoined the white one; and that the liveliest colours appeared on the window-bars, though there was not a trace of color to be seen in the pale grey sky. It didn't take me long to realise that colors are only produced where there is a border or boundary, and I immediately exclaimed out loud, as if instinctively, that Newton's theory [of colour] was false. (translation by Paul Carline, 16/03/2010)