Goethe vs. Newton

(Added 18.1.2024)

I have decided to add some background remarks to this study on rainbows from Goethe's point of view, which I started as a blog in 2010.

Johann Wolfgang von Goethe can be characterized as an early phenomenologist in his studies of nature. I will discuss the controversy between Newton and Goethe, their different approaches to prismatic color phenomena and also the sources to which Goethe owed his way of doing science.

I am not suggesting that modern physical science is wrong. From a phenomenological perspective, physical science as physics is correct and a logical and appropriate continuation of what was developed as light theory in the beginning of the seventeenth century, followed by wave theories of light and electromagnetism, all the way up to modern quantum electrodynamics (QED). I am trying to show however, that what Newton presented as evidence for his theory on white sun light being composed of all the colors of the spectrum, can be questioned or even refuted and this was exactly what Goethe did, a hundred years after Newton. This is appropriate because it is still thought that Newton was right in maintaining that his observations were correct despite objections from his contemporaries.

Today we understand that the visible spectrum is that part of the continuous band of electromagnetic radiation that is visible to the human eye. In physics then, this part of electromagnetic radiation is called light. Moreover, in physics it is understood that the spectrum which Newton observed with his prism, and which can be seen by anyone in every prism experiment today, is not the theoretical spectrum of modern wave theory. The visual spectrum is now understood to be a mixture of multiple theoretical wavelengths of electromagnetic radiation. When we talk about the visual spectrum, we talk in terms of colors. When talking about the 'theoretical spectrum', we talk about wavelengths of electromagnetic radiation or light quanta in quantum language. The visual colors in a spectrum are composed of different combinations of electromagnetic radiation wavelengths. Also, the visual spectrum does not contain all the spectral colors that human visual organization can distinguish. Colors such as aniline red for example, is absent in a single visual spectrum because it is thought to be a mixture of different wavelengths, a mixture not found in a continuous spectrum. Colors containing only one wavelength are called monochromatic colors.

How this talk about colors and wavelengths is problematic or crucial to our topic, that I shall discuss in the following.

 Newton's  way of approaching the question

The first astronomical telescopes at the beginning of seventeenth century were impractical long refractor telescopes that, instead of giving pinpoint images of distant stars, gave blurry images with colorful fringes owing to chromatic aberration. Newton had invented an ingenious telescope design using a reflecting mirror which had no color aberration, and this he wanted to present to the Royal Society with his new theory of light.

It was this pinpoint image of a star that Newton had in mind when he arranged his first experiment with a prism, letting sunlight shine through a small hole in his window shutter. When he placed a prism in the way of this narrow beam of light, it produced the familiar continuous oblong spectrum on the opposite wall.

 

Newton not only gave the distinguished Royal Society a telescope that had no chromatic aberration, he also gave them a theory according to which refracting telescopes had to have this undesirable flaw. It was, accordinng to Newton, due to the fact that in a lens telescope, different colors inherent in white light were refracted to their focal points at different distances from the lens, causing the colored fringes. Likewise, as white light is separated into colors in a prism, this must also happen in lenses.

However, by choosing a pinpoint light source, Newton failed to see, that he had dramatically limited the overall phenomenon he was supposed to explain. He thus came to understand the continuous spectrum as the primary phenomenon in a prism, which according to Goethe, it was not.

 

In many popular physics books the formation of a spectrum in a prism is illustrated in a manner which differs from the actual visible phenomenon:

What is ”illustrated” is Newton's theory (white light is dissolved into the colors of a rainbow), instead of that which could be seen by the observer. The obvious aim is to make the observer see the phenomenon according to the theory – that is, to ”see” the theory and not the actual phenomenon.

 

Here we have pictured white light entering the prism and what can be seen behind the prism as light widens to form a continuous colored spectrum (screen is placed in the plane of the illustration paper). Immediately after light exists the prism we see a beam of white light with colors only at its borders. The colored borders get wider and the white area in between narrower as the distance from the prism increases. Only at a certain distance from the prism the spectrum comes to resemble the complete continuous spectrum illustrated in physics text books. 

The partial 'unfinished' spectrum, that included white light is known as boundary, or edge spectrum. Although physics books avoid mentioning it in this context (it is crucial in physics to determine the complete spectrum before the presentation of the edge spectrum), it is a familiar phenomenon for the physicists and its explanation is considered uncomplicated and simple. In the circles underneath the spectrum is illustrated what can be seen on the screens set at right angles (blue vertical lines) to the gradually widening spectrum.

 

Physicist's explanation of the white area behind the prism: White light is shone through a prism on a screen S. Each vertical row of letters on the screen marks a monochromatic spectrum produced by a single ray of white light incident on the prism from the left. This is the theoretical spectrum that physics talks about, when using the language of ray optics. It is a simplified ray optical translation from the language of different wavelengths of electromagnetic radiation. The uppermost ray of white light is resolved into colors behind the prism, red on top (R), then yellow under it (Y), then green (G), then blue (B) and finally at bottom the color violet (V). The next ray of white light, just under the first one, is refracted a bit lower forming similar sequence of colors a bit lower than the first one, and so on. Colors from different rays of white light will therefore overlap each other on the screen. A horizontal row, where all the letters (colors) are present, produces white light again. The visual color at every point in the spectrum on the screen is produced from various monochromatic lights originating from different rays of white light on the left.

Thus goes the reasoning. It is problematic because the theoretical spectrum is nowhere to be seen. It is unobservable. It is understandable only by the theoretical reasoning with wavelengths of electromagnetic radiation. This way of explaining the appearance of white in the middle of the spectrum is done by virtue of the theory itself. And here exactly lies the problematic. In the physical explanation of the visual spectrum one ends up denying the reality of the visual spectrum by taking the same observational phenomenon (the visual spectrum) as a theoretical starting point.

Newton had maintained that his experiments show by observation, ”as a fact” that white light consists of colored lights, which are separated by the prism in refraction. His argumentation for the theory is based on observation. If observation shows something else, then the theory may not be validated by these experiments. Newton is well aware of this and that is why white light after the refraction is problematic and he does not mention it. When it is mentioned and explained by his followers, it is done so by virtue of the theory, not by observation of facts. One cannot use the theory of ”white light being composed of colored lights” to explain the white area in spectra, because precisely these experiments were supposed to prove the theory valid in the first place, and this by observation.

 

Newton's ”experimentum crucis”. By rotating the prism on the left on its axis Newton could let one color at a time pass along a fixed path through the hole in the second screen. Once this color passed through the second prism, it according to Newton, retained its color and would not produce a new complete spectrum.

In the circles is shown what is actually seen when one looks through the second prism towards the light source (upper circles) and what one sees on the last screen (right) when different colors are passed through the second prism.

The experimentum crucis was criticized already in Newton's time by other scientists. Newton responded to this criticism with annoyance, explaining that the meaning of his experiment was not understood or it was simply not done right. All the conclusions he makes are, according to him, drawn straight from the ”observational facts” of the experiment. He stresses the point that he does not make hypothesis. He just reports the observations he has made. As it happens, the main objections against Newton have been precisely about the hypothetical nature of his theory, that Newton did in fact hypothesize, and that the experimentum crucis gave little if any evidence for his hypothesis – that white sun light is composed of all the colors of the spectrum, and that different spectral colors have different amount of refrangibility.

When giving a lecture for the society of natural philosophy in Helsinki on these experiments in the nineties, I noticed that the participants were at first puzzled by the questions the experiments rise. A gentleman finally said that he would do the experiments with a slit instead of a prism. No white areas there. Problem solved!

This is a typical answer from physicists when confronted with Goethe's objections. Modern physics does not need any experiments with prisms or colors. Quantum electrodynamics handles the problem quite well without any such oddities. Why then does the same physics still maintain that white sunlight is composed of all the colored lights in a spectrum? Does it follow from observations or is it the theory again?

 

                               Refrangibility or edge color formation?

Newton explains his idea of ”refrangibility” with the experiment above. On a black background he paints a deep blue square and a red square. Looking at them through a prism he observes that the blue square has shifted down while the red square has remained intact. From this he concludes that blue light has a stronger refrangibility than red light (it is refracted more down than red light).

 

Goethe re-examines Newton's experiment by placing two white squares (quadrangles here in our drawing) by side of the blue and red ones. As he looks at them through a prism he sees that all four squares have identical edge color seams at top and bottom. In the white squares the edge colors are distinct and vivid. When the edge colors are formed of dark blue or red light, they are more or less discernible when they are intensified or extinguished by the color they are made of. In case of the blue square the red and yellow edge colors at top are barely noticeable on black background and it gives the impression that here the to of the blue square has dropped down. Blue and violet edge colors at bottom seem to continue the blue square downwards, so that the whole square seems to have moved down.

Red square on the other hand seems to stay in its place since the red and yellow edge colors just disappear in the red color of the square at top. At bottom blue and violet edge colors are extinguished as they are formed from red light.

Newton should actually have used violet color instead of dark blue for the first square in order to prove his point more vigorously, since violet color is refracted even more than blue color. Why did he use the dark blue color then? He used it because if he had used violet color the edge color seams would have been clearly visible. Newton must have experimented with both and seen that using violet color contradicts his theory but precisely with a deep blue color the edge colors are most difficult to see.

 

                          Refrangibility or edge color fromation? What do you think?

Goethe dismissed Newton's idea that the continuous spectrum was a primary phenomenon. He argued that boundary or edge spectral colors are the primary phenomena in a prism and that the continuous spectrum is formed as a secondary phenomenon when the colors yellow and cyan blue overlap in the middle and mix. Prismatic colors need the boundary or border between light and darkness to appear. For Goethe colors of the spectrum can not be derived from light alone. Darkness is equally needed. Light and darkness mix at the border with another and colors arise.

According to Goethe also atmospheric colors are formed in the interaction between light and darkness. A setting Sun (light), when still somewhat high in the sky and seen through a turbid medium, (the dusty atmosphere), has almost white, yellowish color, orange when seen lower and sometimes even dark ruby red color when seen at the horizon. Looking towards the horizon we are looking through a thicker layer of turbid dusty atmosphere than when looking straight up. Similarly, when seeing the blue of the sky, we are looking through the same turbid atmosphere (lit by the Sun from the side) at the darkness of the black space behind. When looking straight up from a high altitude, the turbid lit medium between us and the dark space is thin, therefore making the sky dark blue or dark violet. When looking toward the horizon we are looking at the dark space through a thick layer of turbid medium and therefore the sky there looks light blue or even white. 

These color phenomena Goethe called Ur-Phänomen or primordial phenomena in the atmosphere. There yellow and red colors appear when looking at light through a turbid medium, blue and violet when looking at darkness through the same turbid medium. Light and darkness mix with another. ”Colors are the sufferings of light and darkness.”

This is an explanation of atmospheric color phenomena, differing from the well known physical theory of light scattering. Still, from a phenomenological point of view, it is just as adequate, and consistent in its logic as the physical explanation is on its part.

 

Edge color formation when looking at different examples of borders between white and black surfaces through a prism, as presented by Goethe.

 

When the white area between the dark ones is large enough, the result is two sets of border or edge colors; red and yellow above, blue and violet underneath. By narrowing the white area, the yellow from the upper edge colors and blue from the lower edge colors mix and they form green. The result is a continuous spectrum, observed by Newton.

In Goethe's opinion, to say that white sunlight is composed of all the colors of a spectrum is just as absurd as saying that darkness is composed of all the colors of a spectrum. And then Goethe ”makes spectral colors out of darkness” by looking through a prism at an image having a narrow black horizontal line between two white areas. The result is a negative spectrum, having complementary colors compared to a normal spectrum – cyan blue above, then aniline red, and yellow at bottom. Goethe's intention was not, of course, to produce colors from black alone, but merely to show that having a black line on a white background is a complementary case compared to having a white line on a black background, and the result seen through a prism is also a complementary spectrum.

Since a physicist readily admits that this aniline red, which is not seen in a normal continuous spectrum, is a mixture of the colors red and violet (or the mixture of wavelengths corresponding these colors), it is odd that it is not seen that the color green in a normal spectrum is a mixture of the colors blue and yellow (when speaking in terms of color). It is even more odd, since the color green is actually seen as a mixture of different wave lengths of electromagnetic radiation. Aniline red and green are complementary colors having a similar origin in the mixing of different prismatic edge colors.

 

When asked about Goethe's theory of colors, a physicist often says it is nonsense. And in a way he is right. From the point of view of physics Goethe's ideas make no sense. But then one misses the point. Goethe's way of approaching nature is pure phenomenology. It is not intended to be modern physics. It's aim is to follow the observable phenomena and this is the basis for the objectivity of his method. In the case of experiments with prisms, what is factually observable, is colors appearing at the borders of light and darkness, depending on the arrangement of light and dark and the position of the prism. This is the starting point of a phenomenological study of prismatic colors. From a phenomenological point of view darkness (black) plays an equally important role in the appearance of colors as does light (white).

Goethe had developed his method by following phenomena, engaging with them intensively and extensively, letting them tell their story without imposing his own hesitated ideas and theories upon them. He then began to understand that phenomena of certain kind always appeared when certain conditions or circumstances were met. He understood that circumstances were not something external to the phenomenon, but actually an integral part of it. A phenomenon for Goethe was not just something occurring outside a human being, but something continuing its presence in his consciousness as meaning. ”Search nothing beyond the phenomena, they themselves are the theory.”

But where did Goethe get the idea that prismatic and atmospheric colors were the joint products of light and darkness?

 

In his comprehensive work; Zur Farbenlehre, Goethe also included a history of studies on color. There one finds that he had aquainted himself thoroughly with color science all the way from antiquity, through the middle ages, to Kepler, Descartes etc. The idea that light and darkness both play a major role in the formation of natural phenomena was already known for instance in ancient Greece, Middle East and Egypt. Goethe was well aware of this, so the idea itself must not have been new to him when he glanced through the prism for the first time. One cannot say, however, that Goethe used this idea as a theoretical hypothesis behind his obsevational work. What it provided was an open mind towards observable reality, a non discriminative and impartial attitude towards all sense experience.

 

Martin Heidegger, existentialist and a phenomenologist, had raised the interest of modern scholars toward the thinking of ancient creek philosophers from a totally new perspective. From the study of beings, pursued by metaphysics from antiquity to modern times, Heidegger set the crucial question in way that he understood it was meant by pre-Socratic philosophers. That is - what is being in itself? Being without beings!

Heidegger refers to Parmenides and to his poem On Nature, where Parmenides learns from the Goddess of Night the two ways to knowledge. The way of gods – aletheia, and the way of mortal humans – doxa. The way of gods is to know that everything is one. The way of mortals is knowledge about sensible things and this is always knowledge about opposites in nature phenomena.

 

In the writings of Alcmaeon of Croton (5^th century BC) one can find an description of the two ways of knowledge, that of aletheia and doxa:

“About invisible things, about divine things only gods have a precise knowledge. But inasmuch as one can infer from the evidence of things of humans (viz. perceived by the senses), most of them go in pairs. Thus by sight we distinguish white from black and the large from the small, by ears a good word from a bad word, by smell a pleasant odor from a disgusting one, by taste sweet from bitter, and by touch smooth from rough.”

The above quotation is from prof. Andrei Lebedev's article: Alcmaeon of Croton on Human Knowledge, the Seasons of Life, and Isonomia: A New Reading of B 1 DK and Two Additional Fragments from Turba Philosophorum and Aristotle.

According to Lebedev, Alcmaeon inferred that the duality of all sensiblia reflects the dualistic nature of all sensible things, i.e. that all bodies are composed of opposite elements or 'dynameis'. This way of understanding the difference between human and divine knowledge was typical for archaic Greek philosophy. Lebedev adds that apart from Alcmaeon, it is found in Xenophanes, Parmenides, and Heraclitus: ”The duality of all sensible phenomena was commonplace in archaic Greek metaphysics and physics. In Heraclitus, exactly as in Parmenides, superior divine knowledge is “knowing all things as one”, and inferior human knowledge is concerned with opposites.”

 

Also Aristotle (384-322 BC) talks about opposites in his book on Physics. All understanding and knowing in every field of study depends on knowing the first principles (arche) and causes (aitia). He points out that all former philosophers make first principles out of contrary opposites. They can not be derived from each other or anything else, and everything is to be derived from them.

Aristotle broadens this archaic view of opposites his first book on physics by saying :

”If there exists anything divine, good and worthy of achieving, we say that there also exists a contrary opposite to this, and also that which wants and wills this opposite according to its nature.”

When Goethe says that prismatic colors appear as a result of the interaction between light and darkness, we need not go any further to see that natural science in ancient Greece and its philosophy is the place to look for – which of course, most propably, owed its ideas to even more ancient peoples and cultures.

                          Image: NASA, Webb's First Deep Field (NIRCam Image) 

Where do we as modern human beings need Goethe and his way of doing science? If modern physics is right, what is the point of all this? 

 The point of our journey with Goethe is the same as with all human endeavors for understanding reality. These endeavors can take different routes. Physics is a route that paints a certain kind of picture of the reality around us - a physical picture. On this physical route to reality we are being told that what we see, hear, smell, taste and so on, is not to be trusted as a means to an ultimate reality. In the end it can only be reached by a calculative, theorizing intellect. 

 A phenomenological route to reality on the other hand, is exactly interested with that which appears, and how it all is experienced as meaning in our consciousness. Defining all reality with theoretical, mathematical and physical thinking alone is an indication of a hopelessly narrow understanding of human capabilities and modes of being. The question of reality is still an open book – a mystery if you will. Both for physicists and phenomenologists alike. 

So, from here, let us begin our study of rainbows – from a Goethean point of view.