j.w. von goethe's "zur farbenlehre"
Theory of Colours by Johann Wolfgang von Goethe is without a doubt the most passionate "color theory" book ever written. The German writer and bureaucrat Johann Wolfgang von Goethe (pronounced "GUR-ta", 1749-1832), most famous for his poem Faust and novel Sorrows of Young Werther, spent almost two decades of his maturity developing this remarkable meditation on color a compendium of personal speculation and homebaked demonstrations with prisms, colored papers and staged lighting, mixed with anecdotal color observations from artists and naturalists of the era all published in 1810 as Zur Farbenlehre ("On Chromatics"). Because this text was (and still is!) often commended to artists for entirely specious reasons, and at the same time is a major secular document in the "culture war" against modern science, I present here a careful and lengthy review.
This English translation (the only one currently available) was published in 1840 by the Victorian art historian Charles Eastlake. It highlights the oddly divided agenda of Goethe's project. The original German text begins with Zur Farbenlehre, an extensive collection of didactic color observations and conjectures that explores the nature of color in perception, the physical world and art. There follows Unmasking Newton's Theory, a polemical screed against Isaac Newton's Opticks (which Goethe called an "old nest of rats and owls"), and the Historical Part, a review of previous color theories with a commentary that includes yet more attacks on Newton's methods and character. (An appendix on the Entoptic Colors visible in polarized light was added in 1820.)
Significantly (and regrettably), only the "didactic" material appears 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's color theory would prevent readers from fairly judging Goethe's theory of color.
It is grossly misleading to rely on a translation that amputates roughly half the content from the book that Goethe considered the greatest achievement of his life and, in subsequent editions, protected from abridgement (specifically, suggestions that he delete the polemic). To remedy this, I have studied the complete German text, in the belief that any evaluation of Goethe's "color theory" must take into account the gross errors of insight and judgment on display in the polemical and historical parts. (Citations to Eastlake's translation are referenced by paragraph number only; citations to deleted parts of Goethe's book state both the book/section title and paragraph number.)
The core message of Zur Farbenlehre is that the Opticks (1704) contained both factual errors and moral flaws; both arose from a rationalist world view that Goethe radically rejects.
What was the factual dispute? Newton empirically refuted the belief, common among naturalists of the 17th century, that the sun's "white" light was pure, homogeneous and fundamental (or "primitive"). Using prismatic refraction of a single shaft of sunlight, he showed that "white" light actually contains at least seven hues, whose individual colors were otherwise unchanged by manipulation with lenses or filters but which could be reassembled to form "white" light again. These various hues were, therefore, equally "primary" or irreducible colors, and Newton showed how they could create all other colors in nature though various geometrically weighted combinations of two or more spectral hues or pigment mixtures.
In rebuttal, Goethe reasserted the ancient theory, commonly attributed to Aristotle and inherited from medieval optics and early Baroque naturalists, that color results when light comingles with dark. He lists as the basic tenets of this position that "white" light is simple and homogenous (he calls sunlight the "Urlicht" or original light); that colors are caused by the "shadowing" or darkening of this white light; that it was therefore absurd to conclude that light could be reassembled from darkness; and that there are not seven but only two "primary" colors yellow and blue that emerge first from the light and dark mixture ("Instead of An Epilogue", Unmasking Newton's Theory). These points comprise what I'll call the factual disagreement with Newton.
The Aristotelian dogma was affirmed by long tradition, and was still defended by a minority of influential artists and naturalists at the turn of the 19th century. The German Neoclassical painter Anton Raffael Mengs (1728-1779) had been a vigorous advocate, and many of the Neoclassical artists whom Goethe consulted in the 1790's (such as Heinrich Meyer and Angelika Kauffmann) accepted the Aristotelian light/dark framework as well. It was defended by the 18th century French academics that Goethe praises in his historical review, and even by some 19th century British scientists. This is the basis for Goethe's baffling optimism (e.g., ¶173, ¶727) that his book would rally contemporary scientists to rediscover the empirical and mathematical support for an ancient Greek dogma.
In Goethe's view, Newton erred in these factual matters primarily because he mistook a secondary phenomenon for a primordial cause:
The worst that can happen to physical science as well as to many other kinds of knowledge is that men should treat a secondary phenomenon as a primordial one, and (since it is impossible to derive the original fact from the secondary state) seek to explain what is in reality the cause by an effect made to usurp its place. (¶175, cf. ¶718)
This factual dispute is somewhat muddled by the fact that the ancient theory is metaphorically correct! Color really is created by the partial "darkening" or absorption of "white" light by matter. The mechanism of this darkening was precisely described by Newton as "nothing but a Disposition to reflect [or absorb] this or that sort of Rays more copiously than the rest." Colors result because some of "primary" colors of light are absorbed or darkened more than others; the purest (most saturated) hues appear when the "white" light spectrum is pared down to a single homogenous color band of the spectrum, producing colors that are also much dimmer (darker) than the original "white" light (diagram, below).
competing physical explanations of color
(left) the Newtonian theory, based on the selective absorptance of spectral "primaries" (wavelengths); (right) the Aristotelian theory, based on the occult "mixture" of pure white light with pure darkness
But this explanation depends on the fact that "colored rays" are in the light to begin with. The Aristotelian theory rejected that claim, but was not specific about the mixture process that allowed the two light and dark primitives to produce all colors it could only observe (correctly) that colored light was always darker than the original "white" light.
Although Newton conducted various physical manipulations of light, he was careful to point out that the stimulus is perceived as color only through attributes of mind: "The Rays to speak properly are not coloured. ... [Colours] in the Rays ... are nothing but their Dispositions to propagate this or that motion into the Sensorium; and in the Sensorium they are Sensations of those Motions under the Forms of Colours." Thus, Newton was first to make the important distinction between the physical aspect of color (its angle of refraction, or refrangibility, when passed through a transparent medium) and the sensory phenomenon of color (a response to refrangibility by the perceiving mind). Naturalists of the 18th century further emphasized the importance of mind in color experience through the study of a variety of "subjective" color effects, particularly afterimages and strongly colored shadows, a research tradition that Newton's view clearly supports.
In contrast, Goethe adhered to the Aristotelian theory which asserted that color is created by material substances only. This forced its advocates to define any immaterial prismatic or rainbow colors as "illusory" or "false" colors, a remarkably explicit example of how this intellectual position used disparagement to avoid theoretical embarrassment. As I'll describe later, it was the inability of the Aristotelian theory to explain exactly how colors arise in materials, and why color should appear in certain circumstances as "illusory", that primarily attracted Goethe's attention and forms the bulk of his "didactic" or empirical color observations.
But Goethe was not really motivated by a factual dispute: he saw something more ominous at stake. This is the real source of his "violent" opposition to Newton.
Goethe was convinced that Newton's experimental methods and geometrical models of color mixture were a kind of falsehood machine, a delusional maze, an insane and malign procedure for fabricating nonsense that caused many scientists of his time literally to abandon their senses. For Goethe, the sensory experience of color was the fundamental basis for his science, and sensory experience was equivalent to reality:
[Higher rules and laws] ... are not to be made intelligible to the understanding by words and hypotheses alone, but at the same time by real phenomena to the senses. We call these primordial phenomena because nothing appreciable to the senses lies beyond them. (¶175)
Even when such a primordial phenomenon is arrived at, the evil is that we still refuse to recognize it as such, that we still aim at something beyond, although it would become us to confess that we are arrived at the limits of experimental knowledge. ... Important elementary facts are a worthier basis for further operations than insulated cases, opinions and hypotheses. (¶727)
Here Goethe is not just saying that Newton carelessly mislaid a few facts. He is asserting that sense data form the ultimate limit to human inquiry about the world, if not the ground of reality itself; and he is accusing Newton of systematically ignoring perceptual facts in favor of abstractions and concepts that we can only imagine or talk about. For Goethe, it is our lived experience as directly reported by our senses that is the necessary basis for insight. As a result, he avoids any reference to optics or light "rays", as these concepts drag in the abstract scaffolding of mathematics and physics that he called "a scientific coffin". This is his moral disagreement with Newton, and it is at the core of his indignant, ad hominem polemic.
In the section titled "Newton's personality" (Historical Part), Goethe describes Newton as a man "without passion, without longings", whose organ of perception was mathematics and who therefore experienced geometrical ideas as tangible reality. (In the Conversations With Eckermann [February 18, 1829], he compared Newton and his abstractions to a child who looks behind a mirror, expecting to find the reflected objects there.) In effect, abstract thinking is interpreted by Goethe as a kind of mental defect. Newton's "rigid character" hastily seized on the wrong phenomena, those "illusory" color perceptions, then methodically constructed a theory around them by ignoring inconvenient facts or denying their implications.
To support these accusations, Goethe calls out dozens of specific examples from the definitions and prism experiments of Newton's Opticks, analyzing them step by step and sometimes word by word though (as Goethe admits) he discusses limited excerpts from Book I of the Opticks only. He attempts to convince us that Newton arbitrarily required only certain experiments to be done in a certain way, because this allowed Newton to push his erroneous preconceptions into his theory and to mislead readers with an inaccurate or tendentious interpretation of his experimental results:
We can compare the Newtonian method to a stage set painted in perspective, which must be seen from only one viewpoint to make the lines convergent and convincing. Newton and his disciples do not want the viewer to step a little to one side and view the scene as a whole. (Unmasking Newton's Theory, ¶74).
All these points create a portrait of Newton as an outright liar and charlatan, which was enough in Goethe's mind to justify the self righteous invective against him:
Only someone who knows the power of self deception, and knows that it has a very close relation to dishonesty itself, will be able to explain the method of Newton and his followers. (Unmasking Newton's Theory, ¶45)
Thus, the core dispute for Goethe has less to do with color than with science as a whole. After all, facts are usually enough to refute a factually incorrect theory. But Newton had by then become the personification of the kind of science that was dominant by the end of the 18th century. By attacking Newton, Goethe was attacking modern science more generally, primarily in order to defend a very different world view and a very different approach to natural phenomena.
Newton's Philosophiae Naturalis Principia Mathematica ("The Mathematical Principles of Natural Philosophy", 1687), is considered the greatest single work of the Scientific Revolution. The essential premise of the book is that diverse natural phenomena can be explained as the action of a fundamental natural property acting within a universal geometrical (mathematical) regularity. Newton's famous dictum, "I make no hypotheses" simply means that science should describe the widest variety of phenomena using the fewest possible concepts. Newton illustrated this approach by showing that a single unseen force acting at a distance between material bodies (gravity) could explain the motion of planets and comets and the movement of everyday objects such as falling weights and pendulums. This paved the way for advances in physics, astronomy and engineering across the 18th century that culminated in the Industrial Revolution. Newton's Opticks occupies a different but equally important place in the history of science, as a demonstration of the experimental method to test and refine theory.
In contrast to Newton's abstract mathematical methodology and experimental methods, Goethe advocated an intuitive and analogical analysis of conscious experience, a holistic method that proceeds by first bringing all the perceptual phenomena together, ordering them in a series of perceptual priority or importance, and then perceiving directly in this ordered pattern a basic experiential truth. As Goethe says, "we bring the phenomena together as a whole, and have arranged them so that everyone is obliged to consider them in their true order and in their proper proportions." (Unmasking Newton's Theory, ¶1)
The key to this holistic method is Goethe's claim that the causes of perceptual experiences reveal themselves to us via the similarities between one perceptual experience or appearance and another. In effect, we recognize a common cause across diverse phenomena in the same way we perceive a Hapsburg family connection in the prominence of a chin:
In examining every appearance of Nature, but especially in examining an important and striking one, ... we should look round through all of nature to see where something similar, something that has affinity to it, appears: for it is only by combining analogies that we gradually arrive at a whole that speaks for itself and requires no further explanation. (¶228)
This approach is exemplified in the watercolor Color Magnet (right), painted after a long evening discussion with the poet Friedrich Schiller about the "polarity" of color the observed tendency of one color to produce its opposing or complementary color through a form of contrast. The premise is: if color expresses a kind of polarity, and magnets display a kind of polarity, then perhaps there is a phenomenal "attractiveness" that underlies the behavior of both magnets and colors. The short vertical bars (far right of the diagram) represent the primordial yellow/red and cyan/violet refraction fringes that Goethe considered to be the basic phenomena (as described below); the curved bars (far left of the diagram) which are drawn to resemble the curve of iron filings across the opposing poles of two magnets show the mixtures that result when "attracting" fringes are paired to produce the "union" mixture green (below) and the "deepening" extraspectral mixture purpur (above). These combinations in turn create Newton's spectrum (horizontal bar, bottom) and the extraspectral purples (horizontal bar, top). Linking all mixtures together end to end, just as several bar magnets can be linked together in a row, produces the central vertical bar, the double circumference of the hue circle. (A missing point is that, just as identical magnetic charges repel each other, reversing one of the primoridal color bars would mix violet with yellow and red with cyan, resulting in gray or colorless mixtures.) There is an almost mystical simplemindedness in this pursuit of patterns, resemblances and associations, but it is the essence of the Goethean analysis of natural phenomena.
Unfortunately, Goethe's antagonism to abstract theories has been obscured by the English translation title: Farbenlehre simply means "chromatics," with no "theory" implied, just as Sprachlehre means "grammar" and not "theory of speech". Given Goethe's vital sensitivity to language, it is not irrelevant to note that the root meaning of lehre is "lesson," "teaching" or "learning from experience". In the same way that a language grammar simply describes the patterns in language that is developed by listening to how language is spoken, Goethe wanted to develop a holistic "color grammar" that describes the patterns in color that is deduced by looking at how color behaves. He presents learnings from color experience not a theory of colors extracted from color experiments. This makes his book an important precursor to German phenomenology. All these complexities have disappeared from the truncated English version of the book.
Where, ultimately, does the Goethean method lead? How can we tell if the analogical insights of his holistic inquiry are correct or illusory? On this key point, Goethe has nothing to offer except the prerogatives of spiritual genius. As he asserted many years later, one simply sees the correct interpretation of the phenomena, or one is a lesser form of man:
Nature understands no jesting; she is always true, always serious, always severe; she is always right, and the errors and faults are those of man. The man incapable of appreciating her she despises; and only to the apt, the pure, and the true does she resign herself, and reveal her secrets. The Understanding will not reach her; man must be capable of elevating himself to the highest Reason, to come into contact with the Divinity, which manifests itself in the primordial phenomena, which dwells behind them, and from which they proceed. (Conversations With Eckermann, February 13, 1829)
The appeal to a superior intellect, unclouded sensory presence and higher moral character packed into the phrase "the apt, the pure and the true" represents the culminating vantage of Goethe's "moral" dispute with Newton. I conclude this review on the implications of that tonic triad.
So let's turn to the "color theory" itself. In the "didactic" part of Zur Farbenlehre (which is also titled "Zur Farbenlehre"), Goethe's specific ambition was to provide a comprehensive explanation of how the color producing light/dark mixtures occur in two different situations:
(1) the many subjective color effects that appear to arise entirely in the eye chromatic induction (simultaneous color contrasts, studied systematically by Chevreul a few decades later), complementary shadow colors produced when two different light sources (such as a candle and the sky) cast separate shadows from a single object, and both positive (dazzling) and negative (habituated) afterimages which had all been studied and reported by late 18th century naturalists in the decades before Goethe wrote his book; and
(2) the many objective color effects that seem to have nothing to do with a prism diffraction, interference, iridescence, opalescence and color changes in translucent or chemically transformed materials.
Goethe's "magnetic" conception of color relationships
from a watercolor by Goethe (1798)
The easiest way to experience the force of the subjective color effects is through complementary colored shadows. This was probabaly the subjective color phenomenon most clearly described by 18th century naturalists. A vertical opaque object is set up so that the separate shadows from two different light sources are cast against a screen or wall behind it: the shadow of each light is illuminated by the other light. (For best results, the light sources should be placed at distances so that the shadows cast by the two light sources are of approximately equal depth or darkness.) One of the lights must be white and the other light colored. The classic 18th century method combined the shadow of candlelight with the shadow cast by the afternoon sky, but a red light is typically easy to procure and produces the more striking effect.
When both lights are turned on, the shadow cast by the white light is illuminated by the red light, and appears red. However the shadow cast by the red light, which is illuminated by the white light, does not appear white but rather the complementary color of red, which is green (image, right). In the same way a green light will produce a red complementary shadow, an orange light a cyan shadow, and a cyan light an orange shadow, and a yellow light a blue violet shadow. (The common demonstration in the 18th century used a candle to provide a "yellow" light and the sky, through a window, to provide the "white" light; a blue light does not produce a convincing yellow shadow, because yellow is a high contrast color that does not appear in darkness.)
complementary green shadow produced by red and white lights
How does Goethe interpret these pretty effects in the Farbenlehre? Perhaps the most striking of his complementary color examples is the peculiar afterimage that occurred when Goethe, Germany's most celebrated womanizer, stared too long at a comely serving wench who was standing in the sunlit doorway of a rathskeller (¶52-¶53 of Theory of Colours). In the afterimage that appeared when he looked at a dark wall, he saw her emerald bodice turn scarlet, her black hair become luminous, and her pale skin turn dark (Goethe's faded watercolor, right). Though amusing, the anecdote illustrates Goethe's method of finding analogous patterns or phenomena in the experience of desire as itself the expression of deeper life impulses.
Goethe's infers, from the opposing change in the afterimage colors, a "desire" or effort toward compensation, balance or "filling in the blank" that is induced when a strong color stimulus is encountered by the eye in a situation where color is missing (shadow) or has been withdrawn (afterimage). This leads Goethe to infer an "eye animism" or innate desire in the eye to produce color on its own:
The colours which we see on objects are not qualities entirely strange to the eye; the organ is not thus merely habituated to the impression; no, it is always predisposed to produce colour of itself, and experiences a sensation of delight if something analogous to its own nature is offered from without. (¶760)
The evidence of "physiological" or materially inexplicable color phenomena demonstrated to Goethe the "vital sensitivity" of the eye, the importance of "delight" in its behavior, and its active role in shaping experience.
The second step is to associate this vital sensitivity with other, more significant life processes. For him, color is a sensual, passionate, vital experience that occurs through an "attraction" between the eye and light that is analogous to the attraction between Goethe and the buxom maiden. This attraction, as a precursor to love and childbirth, is in turn part of the cycle of all life, so that the vitality of color perception is actually part of a single grand, dynamic pattern of attractions and repulsions, the flux of opposites akin to life and death, that animates the entire physical world:
To divide the united, to unite the divided, is the life of nature; this is the eternal systole and diastole, the eternal collapsion and expansion, the inspiration and expiration of the world in which we move. (¶739)
Thus, darkness is not merely the absence of light, as described by Newton: it is the polar opposite of light, forming with light the dynamic antagonism that produces all color experience.
And having traced the universal importance of this dynamic antagonism, Goethe can apply it to other problems of subjective perception. The "antagonism" between complementary colors such as red and green, or yellow and blue, results from the dynamic response of the eye to the presence or privation of light. Privation produces the compensatory colors in the afterimage of the girl's skin and bodice, and this compensatory process, acting on all visible hues, produces the disposition of opposing hues around the hue circle (which Goethe calls the "colorific circle"):
These [complementary color] phenomena are of the greatest importance, since they direct our attention to the laws of vision, and are a necessary preparation for the future observation of colors. They show that the eye especially demands completeness [Totalität], and seeks to eke out the colorific circle in itself. (¶60)
This analogical process of connecting beautiful women and "eye animism" to the cycles of nature clarifies what Goethe found objectionable in Newton's supposed lack of passion or desire, his preference for geometry and mathematics over sensual life. For Goethe, the young woman, not refrangibilities, is the reality, and his visual response to her, in the afterimage created by his arousal, was part of the "primordial" desire and longing that animates every aspect of the world. In this way, Goethe provides the link between subjective color effects and the light/dark coloring of materials that was absent from the traditional Aristotelian account.
In his many "subjective" examples of eye animism, Goethe is basically weaving a poetic gloss around phenomena that were already well known to naturalists of his time. When he attempts an explanation for the physical or "objective" causes of color, things get murkier.
Through a variety of examples, Goethe reduces the physical causes of color to:
the "clouding" or "shadowing" of white light by semitransparent media such as water, sheets of parchment or the atmosphere;
the "displacement" or "bending" of object images produced in transparent media such as lenses, prisms and water; or
the "doubling" of images observed in the penumbra of shadows cast by the sun or by laminated materials (such as the front and back of a mirror or a sheet of colored glass, or in mica and soap bubbles).
Goethe uses these phenomena as analogical evidence for "the doctrine of semitransparent mediums and double images" (¶299, ¶691): color is fundamentally associated with some kind of clouding (darkening), doubling or displacement of an image. But the key attribute of an image is its nature as a color area surrounded by a contrasting ground, or a figure outlined by an edge. Therefore color to the extent it has an external, physical origin results from the blending of edges or boundaries between dark and light. Edges are both the essential element of an image (separating one color area from another), and the primordial cause of color appearance:
[When viewed through a prism], we have found all unbroken surfaces, large or small, to be colourless, yet at the outlines or boundaries [edges], where the surface is relieved upon a darker or lighter object, we observe a coloured appearance. Outline, as well as surface, is necessary to constitute a figure or circmscribed object. We therefore express the leading fact thus: circumscribed objects must be displaced by refraction in order to exhibit an appearance of colour. (¶197-198)
But how exactly does a singular edge produce a color mixture? To answer that question Goethe refers to a key observation from Aristotle and Leonardo da Vinci. This is the changing appearance of smoke, which is bluish when seen in front of a dark background and reddish when seen against light (¶160), a contrast described by Baroque color theorists as light obscured and darkness illuminated. A second group of examples comprise color changes produced by thickening. Thus, thickening a piece of parchment or amber makes the light it transmits redder; water as it deepens becomes bluer. These opposing effects seem to demonstrate that the effects of edge displacements occur because (1) the light/dark polarity acts spatially, depending on whether dark is located in front of or behind the light; and (2) various forms of repetition, blurring or gradation of the edge will alter the proportions of dark to light that are mixed.
a girl in afterimage colors
watercolor by Goethe, c.1810
Goethe summarizes these "primordial" effects in the colors produced when simple black and white patterns are viewed through a prism. He describes as objectively different the two situations in which colored fringes appear along the edges of a beam of light passed through a prism, or around the edges of printed black/white patterns viewed through a prism, even though optically these are identical effects. (His concern seems to be to link subjective and objective color effects.) Both procedures create colored fringes on opposite sides of the image of the white or black area yellow/red on one side, cyan/violet on the other (diagram, right).
However the variation in the hue of each fringe is only a secondary smearing of the edge image by the prism: in Goethe's view the fundamental or primary phenomenon is expressed in the chromatic "polarity" between the attributes YELLOW and BLUE. By the same analogic analysis illustrated with the "color magnets" (above), Goethe attributes much more than a simple hue contrast to this chromatic antagonism labeling the polarity "magnetically", with positive and negative signs, and assigning to it a remarkable range of sensory, emotional and chemical correlates (¶696):
Considered from a general point of view, colour is determined towards one of two sides. It thus presents a contrast which we call a polarity, and which we may fitly designate by the expressions plus and minus.
(I indicate where Goethe is describing the action of this primordial polarity, rather than the presence of a color sensation, by writing the hue labels YELLOW and BLUE in capital letters.)
In keeping with the smoke effects described above, Goethe assigns a spatial relationship to this polarity. The colors in the YELLOW (+) pole, which include yellow, orange and red, are created by overlaying increasing amounts of dark on or in front of light; the colors in the BLUE () pole, which include cyan, blue and violet, are produced by overlaying increasing amounts of light on or in front of dark (¶145¶151).
Next, by viewing through a prism increasingly narrow bands of white paper on a black background, Goethe demonstrates that the two fringes gradually overlap, so that the opposing YELLOW/BLUE yellow and cyan fringes mix in the center to create green (¶214) the "union" of the YELLOW/BLUE visual polarity. And by reversing the procedure, and placing black bands of paper over a white background, the fringe positions are reversed, overlapping violet and red to produce a "deepening", "intensification" or "augmentation" of the BLUE/YELLOW polarity as "purpur" ("a red that contains no part of yellow or blue", cf. ¶215 and diagrams below). These two mixtures complete the hue circle.
Goethe is not explicit about what his terms union or augmentation mean, perceptually or physically. He does suggest that green is merely the mixture or muddling of the light/dark attributes, while purpur represents their intensification to the point where the YELLOW/BLUE polarity disappears or fuses. He frequently refers to purpur as the acme or purest state of color, yet he does not elevate the purpur/green contrast to an explanatory role equivalent to YELLOW/BLUE. This is significant, given that nearly all of the subjective color changes observed in afterimages or in chromatic induction (simultaneous contrast, successive contrast and colored shadows) produce contrasts between red and green, not between yellow and blue.
As Goethe reveals in the deleted "Historical Part" of Theory of Colours, these pretty, yellow and blue prism fringes had been described by the Jesuit Cartesian Louis Bertrand Castel in 1740, and were of course familiar since the 16th century as the chromatic aberration encountered as a vexing flaw in the earliest optical instruments.
Newton's spectrum out of Goethe's primordial fringes
the YELLOW and BLUE fringes appear immediately after the light leaves the prism; the complete spectrum appears only at some distance from the prism
Castel had used these fringes polemically (and in a sarcastic and "violent" tone very similar to Goethe's) to show that Newton had been distracted by a mere "ghostly magic". Goethe's innovation was to add the complementary "dark" spectrum which appears in the fringes at the shadow edges of a bar or pencil placed across the beam of light before it is refracted by the prism to demonstrate the origin of the "dyer's primaries" yellow, blue and purpur that describe subtractive (material) color mixtures.
In either version, Goethe (like Castel) pointed out that the edge fringes appear in the refracted beam just after it emerges from the prism and much before the complete spectrum is visible (photo, above). And while the YELLOW/BLUE fringes appear immediately along any contrasted edge viewed through a prism, the spectral colors only appear when the refracted light beam is projected at a sufficient distance, or when the white band viewed through the prism is sufficiently narrow. These observations supported Goethe's accusation that Newton requires evidence to be disregarded, or only looked at in a certain way.
As a parlor trick and as a schematic (diagram, below), this simple demonstration was one of the most persistent arguments used against the Newtonian theory of multiple "primary" colors by all 18th century defenders of the ancient light/dark theory. It was persuasive to many intelligent people for over a century after Newton published the Opticks. And it was the primary evidence Goethe offers to prove that Newton's spectrum is only a "secondary" phenomenon. So it is important to understand why Newton described it correctly, and why Goethe's objections to that explanation are wrong. Let's examine how Goethe reported the basic observation.
"light" and "dark" spectral mixtures from Goethe's "primordial" fringes
adapted from Plate IV, Figures 1 and 2 and ¶214-¶216 of "Zur Farbenlehre" (1810)
First, note that there is an unexplained inconsistency (marked by ?, above) when the fringes overlap so far that violet mixes with yellow. This produces a yellow mixture in the "dark" spectrum but a violet mixture in the "light" spectrum. Since the YELLOW hues are produced by dark over light, and the BLUE hues by light over dark, this color ambiguously results from a double layer of light (or dark) sandwiched between two layers of dark (or light)! This is a logical puzzle that Goethe never attempts to address.
Worse, if we simply extend the beams of light much farther, it's obvious that the YELLOW and BLUE fringes must eventually overlap the dark (or light) on the opposite side, and red eventually mix with violet in the middle. This implies some distinctive color mixtures would appear at an even greater distance, but this is a possibility that Goethe explicitly avoids exploring.
Indeed, Goethe left these "?" areas colored gray when the diagrams were first printed as Plate 5 and Plate 6 of his Beiträge zur Optik ("Essays on Optics") in 1792, but later colored it in (as shown above) as a way to minimize it. So he was at first aware of this inconsistency then attempted to suppress it.
In his Plate IV, Goethe portrays these mixtures in their "objective" form, as the physical distance of the image from the prism in relation to the width of the light beam, but he repeats the demonstration in the "subjective" form, as the visual width (angular size) of black/white bands viewed through the prism. These demonstrations are summarized in the images below (and the original photos are posted here.)
Goethe's primordial fringes and the spatial frequency of edges
Photographs of (left panel) white bars on black background and (right panel) black bars on white background; bars viewed at an angular size of 2° (top row), 30 minutes or 1/2° (middle row) and 15 minutes (bottom row). Each image shows a single bar against the background (left column) and alternating white/black bars of equal width (right column). Colors desaturated due to image flare.
Surprisingly, we see that Goethe fabricates the appearance of the "light" fringes at a great distance (or small angular size): the "yellow" band in the spectrum never really disappears, as his diagram mandates it should; the "violet" band is also still present (at the top), but is now too faint to be visible. And at an even greater distance (the smallest visual frequency (15') appears at a viewing distance of 10 meters or so), the "dark" black on white pattern degrades into alternating magenta/green bars of equal width the same red and green colors that Goethe observed in diffraction or interference effects (his catoptrical colors and paroptical colors). But the geometry explicit in Plate IV requires that the "yellow" or "violet" part of the spectrum must continue to expand relative to the total width of the refracted light beam at greater distances. Goethe did not step far enough back to view higher spatial frequencies, and he did not read the later sections of the Opticks where Newton attributes these interference colors to the "spacing of fits" (differing wavelengths) of specific spectral hues. Because he simply ignored these complications, or was not careful enough to observe them in the first place, Goethe did not have to explain them.
Newton's explanation for these fringes, which combines additive mixture with the differing "refrangibilities" of different spectral hues, is carefully laid out in the Opticks (Book I, Part II, Proposition viii) a passage that Goethe either did not read, could not understand, or chose to ignore. The explanation consists of two parts: the additive mixture of light, and the differing angles of refraction of the spectral hues.
YELLOW and BLUE fringes produced by chromatic aberration along black/white edges
YELLOW varies from yellow to red through the increasing mixture of dark over light; BLUE varies from cyan to violet through the increasing mixture of dark under light; after Goethe (1810)
The role of additive light mixture in the explanation is easier to grasp if you start with the demonstration of converging beams of monochromatic or "pure color" lights, for example, the three "primary" colored lights (red, green and blue violet) that are arranged to make an overlapping pattern on a gray surface (diagram, right). Where red and green light overlap, the mixture is yellow; where green and blue violet light overlap the mixture is cyan; where red and blue violet overlap the mixture is magenta; and where all three overlap, the result is white light, exactly as Newton described.
To add refrangibility to the problem, simply think of the different hues of a prism spectrum as six diverging beams of colored light, all shining through the same aperture (which represents the prism), but each angled away from the others to mimic the fanning out of hues that appears due to differences in the "refrangibilities" or angles of refraction (diagram, below). Note that each unique hue is represented by a beam of parallel light rays: the original solar light consists of approximately parallel light rays of all wavelengths, and each wavelength is refracted at exactly the same angle no matter what part of the prism it passes through. (In an actual solar spectrum there is a separate beam for each of the hundreds of visible wavelengths, so six beams is a clarifying simplification.)
Goethe's primordial fringes from the additive mixture of colored lights
Additive mixtures always brighten as more light is added, but they also become more desaturated (paler or whiter) as the mixed hues are more dissimilar. So close to the prism, where more and more of the colored beams overlap, we find paler, brighter additive light mixtures: this creates the central beam of "white" light. However, as the diagram shows, the "red" and "violet" wavelengths emerge first from this overlap with the other monochromatic beams. This is why Goethe's YELLOW/BLUE fringes (in their darkest "red" and "violet" form) appear immediately along the sides of the refracted image.
In contrast, the beam of pure "green" light near the prism is completely whitened by the combination of "red" and "violet" light overlapped with it, and farther from the prism it mixes with "blue" beam of light to make "cyan", and with the "orange" to make "yellow", so it is actually disguised within YELLOW/BLUE fringes. It is only when we move still farther from the prism that the overlap with desaturating colors is finally reduced enough so that the "green" light can emerge in the center of the spectrum. And in this disposition the spectral hues remain, no matter how far from the prism they are observed.
Thus, in Goethe's key counterargument to Newton, we find evidence of his disregard for the explanations offered by Newton, his slipshod approach to color research, and his bias to overlook facts that contradicted his theory. And these can stand for the dozens of superficial and even hilarious errors, conjectures and outright fabrications that appear when Goethe attempts to link color to physical phenomena.
Among these: he confuses afterimages with Gegenschein or with electrical discharges from a kite (which mariners knew as "St. Elmo's fire"; ¶30), confuses shadow parallax with diffraction or refraction (¶366-428), confuses image flare with retinal undulations (¶98). His "double image" explanation of refraction effects is both feeble and inconclusive (¶218-¶242), and his discussion of the "augmentation", "culmination" and "fluctuation" of colors is merely incomprehensible. He claims that "the yellow and yellow red affect the acids, the blue and blue red the alkalis" (¶492) though these color relationships are not at all chemically consistent; and that "metals, when slightly oxidated, at first appear white" (¶497), omitting that iron oxidizes directly into red, silver into black and copper into either red or black or, as Goethe claims, into blue (¶515). He asserts that the image of the sun passed through a square aperture nevertheless appears round because "we might rather consider the splendour of the sun, or any light, as an infinite specular multiplication of the circumscribed luminous image" (¶402). His few genuinely insightful or interesting color observations are buried under a tedious heap of mythical, uninformed or impressionistic color anecdotes about the view of the moon from a balloon, the color effects of opals, or the blue light emitted by rotting wood. There are dozens of paragraphs (¶758¶832) on the "moral" (psychological) effect of colors (scarlet is especially pleasing to "impetuous, robust, uneducated men"; vivid colors are especially attractive to children and savages). He offers the sky as an example of how blue is produced by light over dark (sunlight over space), but does not address the obvious counterexamples of medieval blue stained glass, or blue ice, which are produced by light shining through (from behind) the darkened material.
additive mixtures in overlapping beams of colored light
Because of these embarrassing muddles, the claim for Goethe's color authority among artists largely hangs on a single icon the Farbenkreis or "colorific circle" (¶50 and Plate I, Figure 3 of Theory of Colours; diagram, right). Much of Goethe's explanation for the color circle is based on the "eye animism" that appears in complementary afterimage and shadow colors (¶39-¶80). Yet, as both John Gage and Martin Kemp point out, complementary color phenomena had been independently described several times by 18th century naturalists such as Comte de Buffon, Ignaz Schiffermüller, Moses Harris, George Palmer and Count Rumford in the 60 years before Goethe began his own color explorations, so he is not the source for these observations. And indeed all circular arrangements of hues, including Goethe's, are based on Newton's original hue circle, which Newton contrived as the only geometrical solution to describe the perceptual facts. Much of this literature Goethe knew when he published his first essays on color in 1792, but his polemical inspirations (from Castel in particular) and his borrowings from 18th century naturalists have been lost with the deleted "Historical Part". Instead, Goethe is today habitually given priority for the traditional (and inaccurate) three complementary contrasts of yellow/violet, orange/blue and red/green (cf. ¶60, ¶612, ¶810).
Even here, Goethe is misread by his modern advocates. His gelbrote ("yellow red") does not mean "orange" but red that is, "yellowish red" or scarlet. Goethe says this color can produce "an intolerably powerful impression" that he equates with spectral "red" refraction fringes and with the pigments vermilion and minium (red lead oxide, cf. ¶774-¶775). And his term purpur (inconsistently rendered "red", "pure red" or "bright red" in Eastlake's translation) does not mean a spectral "red" but what we would today call magenta or red violet, because Goethe specifically equates it with the brilliant hue of a Roman cardinal's carmine dyed robes, the color extracted from the shellfish dye murex, and the color produced by overlapping opposite ends of the spectrum (cf. ¶215, ¶704 and Goethe's Plate IV, above).
Goethe's conception of complementary colors
from "Theory of Colours" (1840), Plate I Figure 3 and ¶612
Finally, it is instructive to compare Goethe's researches with those by his contemporary, the charismatic and mystical German Romantic painter Philipp Otto Runge (1777-1810). I can't do justice to Runge's talent here, but his intellect and personality made him the most influential painter of the early 19th century German Romantic movement. He counted among his friends many of the leading painters, poets, philosophers and scientists of the time. He was also deeply committed to color research, and (like Goethe) had studied the scientific and artistic color literature all the way back to the Greeks and Leonardo, discussed it extensively with his wide circle of acquaintances, and conducted his own color mixing experiments. He summarized his thoughts in several remarkably original and passionate essays, including his most famous work, Die Farbenkugel (The Color Sphere), published in 1810 with a speculative preface by the reknowned Danish naturalist Henrik Steffens. Runge shared his color ideas in letters to Goethe written from 1803 onwards, but died of tuberculosis the same year Die Farbenkugel was published. In magnanimous tribute, Goethe reprinted a key letter from Runge at the end of Zur Farbenlehre, but unfortunately this letter is also deleted from Eastlake's translation. (You can find it reprinted in The Art of Arts by Anita Albus.)
The crux here is the very different outcomes from the very similar researches and speculations of these two men. Runge rejected the Aristotelian theory, made splendid use of complementary colors and optical color mixing in his own paintings, and used his color sphere to define pleasing or discordant complementary color combinations exactly as Michel-Eugène Chevreul would do with his color hemisphere almost 30 years later. In contrast, as Eastlake writes in his preface, "in the portion expressly devoted to the aesthetic application of the doctrine, the author [Goethe] seems to have made but an inadequate use of his own principles."
As Goethe himself proudly declares, "my draft color theory is inherently polemical" (Unmasking Newton's Theory, ¶1). But by becoming combative Goethe commits the very faults he attributed to Newton. He interprets only certain observations in a certain way, confuses cause and effect, and omits or misinterprets conflicting evidence in pursuit of his tendentious and erroneous preconceptions. The early 19th century scientists who reviewed Goethe's book almost unanimously dismissed it as the result of his peculiar methods the English naturalist Thomas Young called it "a striking example of the perversion of the human faculties," and a Continental reviewer summarized it as "a tissue of ingenious and obstinate error".
What explains Goethe's willful and antagonistic obsession with color? His English biographer Nicholas Boyle explains that throughout the 1790's Goethe was struggling through what we would today call a midlife crisis grief over lost youth in Italy, the limitations of domesticity, boredom in his daily bureaucratic responsibilities, anguish at the violence of the French Revolution and Napoleonic tyranny, and revulsion toward the spiritually empty world view that Rationalist science seemed to advocate and industrial practice was beginning to make real. Boyle explains that Goethe's subjective approach allowed him to project his personal conflicts into his study of color and his horror of abstract science onto Newton; his Farbenlehre was to be a liberating and life enhancing new "poetry of the spirit". This emotional turmoil infused his emphasis on color "antagonisms" and color symbolism (another area where Runge and Neoclassical artists led the way), and his ideas did significantly influence 19th century German philosophers such as Georg Friedrich Hegel and Arthur Schopenhauer. But its impact on scientists and on the practical outlook of artists has been inconsequential.
It has been fashionable, ever since Eastlake published his amputated translation, to perform yet more amputation on top of that to cut away Goethe's light/dark theory, naive prism demonstrations and gibberish physical color explanations in order to justify a charitable gloss on his "insightful" or "prophetic" color observations. The subjective color contrasts which Goethe borrowed from the 18th century scientific literature remain well established facts of color vision, and these also are brought to Goethe's defense. True, goes this argument, Newton's physical account of color was integrated with the perceptual trichromatic theory of color vision as a highly successful explanation of retinal nerve impulses and of all the physical ways that color is produced by an external light or material stimulus. But many subjective color effects can only be explained in terms of the color psychology imposed on the nerve impulses, and cannot be predicted from the light stimulus alone, and this position is often attributed to Goethe, even though he expressly states that the eye simply mimics the dynamic principles found in the external world. Goethe is even said to be vindicated in the two color contrasts yellow/blue and red/green that inform Evald Hering's theory of unique hues and that are fundamental to most modern models of color perception.
I strongly reject this view, because it requires a biased interpretation of a mutilated edition of the book Goethe wrote. It credits Goethe for color observations painstakingly developed by his predecessors or successors, and portrays Goethe as a visionary and innovator within a scientific tradition that he actually resisted "violently". I can think of no other case, on any topic in any literature, where posthumous reputation is premised on such a blatant program of censorship, misreading and misattribution.
But there is a more important issue. When Goethe's book is read as a whole, the intellectual "debate" between Newtonian color science and Goethean color poetry remarkably foreshadows the contest between evolution and Creationism (aka "Intelligent Design") and with uncanny parallels in the details. The same rhetorical tactics used today by Creationists against evolutionary biology (ignoring or misconstruing evidence, selective citation, reasoning from false premises, fabricating explanations to suit preconceptions, "what if" counterarguments, and hostile ad hominem rhetoric) were used by the Cartesians and by Goethe against Newtonian physics. The same spiritual accusations made today by the Creationists against evolution or cosmology more generally (that it is imaginary, that it is "only a theory", that it is soulless, that it ignores the evidence of our senses, that we can't actually "see it" happen) were made by Castel and Goethe against Newton's "ghostly" refrangibilities.
Indeed, Goethe's jeering jeremiad against Newton apparently originated (by his account) in a single event in 1791 that has the savor of a religious revelation:
Like everyone in the world I was convinced that all the colors were contained in light; I had never been told otherwise, and I had never had the slightest reason for doubting it, since I had taken no further interest in the matter. ... As I was now thinking about approaching colors from the perspective of physics, I read in some compendium or other the customary [Newtonian] account, and, since I could not derive anything for my purposes from the theory as it stood there, I undertook at least to see the phenomena for myself. ... At that very moment I was in a room that had been painted completely white; I expected, mindful of the Newtonian theory as I placed the prism before my eyes, to see the light that comes from there to my eye split up into so many colored lights. How astonished I was, then, when the white wall, observed through the prism, remained white just as before; that only there, where darkness adjoined on it, did a more or less determinate color appear. ... It did not take much deliberation for me to recognize that a boundary is necessary to produce colors, and I immediately said to myself, as if by instinct, that the Newtonian teaching is false. (J.W. Goethe, Werke [Hamburger Ausgabe], Vol.14 p.259).
And over three decades later, in a spirit of religious self righteousness, Goethe disparaged the objections raised against his theory by a friend who had, at Goethe's insistence, made some color observations of his own and had come to doubt Goethe's explanations:
"With your idea of colored light [Goethe replied], you belong to the fourteenth century, and with all the rest you are in the very abyss of dialectics. ... My Zur Farbenlehre, he continued, fares just the same as the Christian religion. It seems for a while as if there were faithful disciples; but very soon they fall off and form a new sect. You are a heretic like the rest, for you are not the first that has apostatized." ... When I went to him, and told him that he should have my objections in writing for a closer examination, and that the only reason he did not agree with me lay in the clumsiness of my verbal statement, he could not help, with a half-laugh and a half-sneer, throwing in my teeth at the very doorway something about heretics and heresy. (Conversations With Eckermann, February 19, 1829)
Near the end of his life, all the many rational objections to his theory could draw from Goethe nothing more than a zealot's condescension, again in Eckermann's account:
"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."
When we read Zur Farbenlehre as a whole, as Goethe intended we would, and consider the book in the context of Goethe's life, as Goethe quotably insisted we should, it becomes quite clear that Goethe was not an impartial scientist or an inquisitive observer of natural phenomena. He was fundamentally the polemicist for an elitist world view that is directly opposed to the conduct of science and the consensus, collaborative work of rational inquiry. His book about color is the work of a self proclaimed prophet, not the study of a painter or a scientist, and for that reason it offers neither practical artistic guidance nor a valid scientific theory. It presents instead a fascinating case study of intellectual error.
The antirationalist rejection of the scientific project, which fundamentally comes down to the feeling that there is more to life than science can explain, or that there is something sinister in the direction that science is taking humanity, is an extraordinarily enduring divide in modern intellectual history. Indeed, since Goethe's era it has only widened into the "two cultures" described by Sir Charles Snow in 1959 and played out in the politicized "culture wars" of today, and it is rehashed in the contemporary academic literature by the holdouts who offer Goethe as the model of "a new science" or "an alternative way to conduct scientific inquiry". We obscure our understanding of this dislocation by attributing it exclusively to religious belief, or by suggesting that science is at bottom only a subjective endeavor.
Goethe observed that it takes a great man to exemplify a great error. An informed, uncensored study of Goethe and his place in the scientific debate of his times might help us better understand the origins of antirationalism and its role in modern cultural debates. Meanwhile, oblivious to the grossly censored and misinterpreted transmission of Goethe's true gospel, many authors today still treat him as the quotable old testament of "color theory" or the Jeremiah of a new vision of science. But these are only ritual displays of intellectual inquiry, and as I've taken pains to show, ritual is never inquiry enough.
The complete German text of Zur Farbenlehre (useful to evaluate Eastlake's translation), along with many of Goethe's earlier writings on color, are available at the Farben-Welten web site.
The remarkably negative Continental reaction to Newton's empirical rather than "theoretical" approach to science, due primarily to his refutation of the physical theories of both Aristotle and René Descartes, is nicely summarized in The Newtonian Moment: Isaac Newton and the Making of Modern Culture by Mordechai Feingold (New York Public Library: 2004).
For Goethe as the model for a "new" or "alternative" science, see for example Arthur Zajonc, "Goethe's theory of color and scientific intuition," American Journal of Physics (44:4), April 1979; or physicist Henri Bortoft's The Wholeness of Nature: Goethe's Way Toward a Science of Conscious Participation in Nature (Lindsfarne Books, 1996).
For a sympathetic but critical reading of Goethe's project contra Newton (by a philosopher), see Goethe Contra Newton by Dennis Sepper (Cambridge University Press, 2003).
Kevin Brown's Zur Farbenlehre is a careful and thoughtful exploration of the many (and sometimes ironic) similarities and contrasts between Newton's and Goethe's approaches to color.