Collaboration Day 1

Goethe's theory of colours

Johann Wolfgang von Goethe is the most famous of all those who have opposed Newton’s theory of light and colours. He fought hard not only against Newton, but also against Newton’s followers, throwing at them accusations and insults which he categorically felt were conspicuously warranted. Surely enough, his undisguised contempt was fully reciprocated, and it has remained so for two hundred years now. Goethe studied colours for more than forty years, and his particular way of analysing and reasoning has been much discussed, especially by philosophers. His massive book Zur Farbenlehre (Theory of colours) was published in 1810, and—like Newton’s Opticks—is still in publication today. If Goethe was/is loathed and ridiculed by physicists, he was/is also praised and appreciated by many others. These days his views on colours experience a new resurgence, which gives one an eerie feeling—considering Goethe’s prediction that his work will be rightfully acknowledged in the year 2000.

Then how is Goethe’s theory of colours seen today? That’s truly hard to say. Although many have talked favourably about Goethe’s understanding of colour phenomena, very few have dared to proclaim that he was right and Newton was wrong. In fact I do not believe that anyone has asserted that publicly, yet. Instead, every person who undertook the task of writing about Goethe’s foray into the nature of colour (and there have been many, many of them) has diplomatically abstained from taking a definitive stance against Newton’s theory. After all that would reveal, in the eyes of the thinkers of modern society, a certain naivety and ignorance of the soundness and rational power of scientific investigation. And no one wants to risk that, no one in academic circles, at least. See, on this subject, what the philosopher Dennis Sepper has to say in his book Goethe contra Newton:

Newton’s partial success, compounded by subsequent deformations of his theories in the course of the 18th century optics, created a situation that justified Goethe’s criticisms and his attempts to lay a new foundation grounded upon a more scrupulous regard for articulating the proper approaches to the phenomena of color. Yet to argue that Goethe’s Farbenlehre and his polemics have been largely misunderstood is not to argue that they are unproblematic or simply right. I have come to believe that Goethe has an ampler conception of science than Newton, that he has a sounder notion of what an empirical methodology requires and a firmer grasp on the epistemological and philosophical issues involved; however, in the competition for scientific achievement Newton must take the palm of victory. (I do not, by the way, expect that everyone who reads this book will agree with my assessment of Goethe, but I do think most will understand that these claims are not groundless.) Although Goethe is not as amathematical as people think, he nevertheless did not resolve the question of how mathematical conception and calculation are to be reconciled with seeing and experiencing the appearances, and thus despite his intention to present an all-encompassing science of color—and not a merely qualitative science (whatever that might be), as some enthusiasts have claimed—we must conclude that, even on his own terms, he failed to realize this project. 

Nevertheless, it appears that one prominent mathematical physicist has come closest, thus far, to declaring an unabated allegiance to Goethe, but even that example is quite inconclusive (for he merely declared that “Goethe had been right about colour”). 

From a personal perspective Goethe’s theory of colours is fundamentally wrong. What I found surprisingly correct in his work, however, is his explanation of the real causes for the apparent displacement of blue-coloured objects in subjective prismatic experiments. On the other hand, I found surprisingly odd his modificationist views of the spectral colours, considering how close he came (through his experiments) to the correct explanation. Another disconcerting aspect of the Goethe-Newton saga was the extremely poor arguments used by physicists in ‘explaining away’ the anomalies in prismatic experiments presented by Goethe. Furthermore, I also found greatly disturbing the completely unwarranted complications of the main issues in the debate between Goethe’s commentators and Newton’s followers. The principal culprits in the unnecessary chaos that was created have been, unsurprisingly, the philosophers who have found that there is an inevitable necessity of their epistemological-syllogistic expertise to resolve a dispute between two theories both wanting. I will talk in detail about all these issues later.

Goethe began his own investigation into the nature of colours after observing that a white wall remained white when he looked at it through a prism. He wrote about this event the following:

Like everyone in the world I was convinced that all the colours 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 colours from the perspective of physics, I read in some compendium or other the customary 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 coloured 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 colour appear…It did not take much deliberation for me to recognize that a boundary is necessary to produce colours, and I immediately said to myself, as if by instinct, that the Newtonian teaching is false.

This episode, especially Goethe’s conclusion based solely on this observation, has been heavily criticised and derided by Newtonians. Even those who have defended Goethe’s work on the origin of colours have (wisely, it seems) refrained from attempting to back up Goethe on his ‘white wall’ conclusion. Sepper, for instance, writes about this episode in Goethe contra Newton:

He [Goethe] appears to have committed an incredible blunder at the outset of his physical studies of color by rejecting Isaac Newton’s theory of white light and colors as demonstrably false. A few casual observations with a prism appear to have settled his opinion: Observing that a white wall viewed through a prism remains white, and that colors appear only where there are contrasts of dark and light, he concluded that the notion that white light is separated into the various colors that compose it was wrong. Yet the phenomena he observed were not unknown to Newton, and so it seems that his insight amounted to nothing more than a misunderstanding of the theory. Although not a few scientists, both friends and strangers, tried to put him right, in person and in print, Goethe nevertheless held fast to his belief and continued his studies outside the traditional framework of optics and color science.

It is interesting the rather non-committing use of words like “he appears” and “it seems”, Sepper uses. Why those terms, Dennis? Are you doubting the validity of the explanation with which scientists have refuted Goethe’s conclusion?

I have tried for a long time to engage in a debate with physicists about the validity of the conventional understanding of light and colours (of which the ‘white wall’ episode would have been a definite topic), without any success. As a consequence I’ve had to rely only on the superficial ‘explanations’ I managed to find—for, on this topic, there is an incredible drought of detailed scientific explanations out there. Indeed, what I have invariably found are short comments followed by absolute assertions that Newton was right and Goethe was wrong. The explanations I managed to get ranged from “the violet and red parts of the spectrum come from different parts...” to the two most elaborate I will cite below.

What Goethe saw is perfectly explicable on Newtonian principles. Had the light passing through his prism come from a point-source, as in a camera obscura, and so been effectively a single ray, he would have seen the phenomenon he expected, a ray of white light dispersed into a sheet of coloured bands. When many rays pass through the prism together, as when it is held up to a window, the spectra produced by the dispersal of the individual rays overlap and reconstitute the original white effect. Only when the source is limited or interrupted... will the rays along its edge be able to produce a spectrum that is not overlaid by any others and so remains separately visible to the observer. Goethe tells us that he soon came to hear this explanation from ‘a nearby physicist’—possibly J. H. Voigt, Wiedenburg’s successor as professor of mathematics in Jena—whom he felt he ought to consult in view of his own lack of experience in these matters, but ‘whatever objections I made... whatever display I made of my experiments and convictions, I heard nothing but his initial credo and had to tolerate being told that experiments in the camera obscura were much more suitable for acquiring a true view of the phenomena’.  (Goethe—Nicholas Boyle)

It’s hard to imagine that no one ever explained to Goethe why the white wall still appeared white when viewed through the prism, and why it was perfectly consistent with Newton’s conception of differential refrangibility. The explanation can basically be read directly off of Newton’s 1665 drawing, or by simply reversing the directions in the basic projection schematic, as shown below. According to Newton, every ray of light emanating from the white wall consists of a mixture of all the spectral colors, but only the red component of the upper ray is refracted into the ray entering Goethe’s eye, and only the violet component of the lower ray is refracted into that ray. (The other components of the upper and lower rays are refracted at different angles, and hence do not emerge from the prism along that particular ray leading to the eye.) In effect, the final ray of white light entering Goethe’s eye is composed of all the spectral colors gathered from different points on the wall. It might seem miraculous that it should work out this way – until we realize that it’s just the reversal of the original experiment, the one that projected the spectrum of colors onto the wall.

The two explanations are expressed rather differently, but the process is the same: The image the observer will get, according to Newton’s disciples, will simply be a single ray of white light—hence no colours. It seems that this explanation is compelling enough to clarify the ‘white wall’ observation and to conclude that Goethe was wrong and Newton was right. But the situation is nowhere near as simple, and certainly not compelling enough. I am amazed that Goethe, or one of his defenders, did not reply to that explanation with the following: If that explanation is correct, and if what the observer sees is a single ray of white light, then another prism (placed in the path of the ray of white light, like in the figure below) should disperse that ray of light into a full spectrum! This is indeed what the observer should expect, in the context of the accepted theoretical understanding and of the given explanation.

Nevertheless, if you perform this simple experiment nothing will change! The observer will still not see any colours. Then what could Newton’s defenders say about this observational fact?

As I said, the ‘white wall’ situation is nowhere near as simple and it is not compelling enough to so easily declare Newton a winner. In fact I can think up a way of defending (from a Newtonian perspective) even the two prisms set-up I have given above, to which I have also developed yet another way of defending Goethe’s conclusion—which reinforces what I said about the difficulty of comprehensively solving the ‘white wall’ mystery. This is just one of the reasons for my trying to engage physicists into a proper debate. The most important reason for my trying, however, is the fact that there is a way of understanding all prismatic experiments—although, naturally, there is also a necessary price to pay in the process. It will all become evident later, but for now let us return to the main discussion.

A most interesting offshoot of the accepted ‘explanation’ for the ‘white wall’ observation is perfectly illustrated by an elaboration of the situation described by the author of the paragraph (and drawing) I cited earlier.

Of course, this also explains (in Newtonian terms) why Goethe saw colors near boundaries. If, for example, we darken the part of the wall where the violet and blue components originate, then the ray entering the eye will no longer be white. Indeed, we could make the wall appear red by darkening or blocking all except the rays coming from the wall at the angle that refracts red light through the prism. (This is reminiscent of diffraction gratings.) So, not only does Newtonian theory account for Goethe’s observations, it immediately suggests new phenomena, and ways of manipulating the elements of the experiment to produce specified results. This interesting explanation, although perhaps not intuitively obvious (as it obviously wasn’t to Goethe), follows mathematically from Newton’s conception of light and differential refrangibility.

What do you think about what is asserted above? Keeping in mind what we have discussed so far, consider what colour the observer will see if he darkens the wall right below where the violet component is supposed to come from. With the prism oriented as in the drawing he would see red. What about if he darkened the wall right above where the red component comes from? In that case he’d see violet. Ah, but the author of the above meant completely the opposite, didn’t he? He certainly meant that the wall should be darkened above the violet, and below the red. He’d just forgotten to specify. OK, then what about if the observer, clumsily, darkens the wall below the red just where the violet originates? And vice-versa, above violet where red originates? What about if the observer, even more clumsily, darkens the wall above and below, covering both points where the red and violet components originate? What about above and below where the rest of the colours originate? And so on, and so forth.

Goethe’s ‘white wall’ observation, as well as most of the other contentious observations in the saga of light-colour debate, is not compellingly explainable in Newtonian terms because Newton’s theory of light and colours (in its current form) is deficient. Something, some vital thing, is missing, and for as long as that thing will remain missing there will continue to be a Lucas or a Goethe crying foul. Goethe, however, did not merely believe that Newton’s theory was deficient—he was convinced that the theory was fundamentally wrong. He also believed that he had the proofs, to that end. He developed and conducted a large number of experiments (most of them subjective prismatic experiments), which were designed to demonstrate the inability of Newton’s theory to explain their observational facts. Goethe’s experiments have created a kind of cult following among those interested in the nature of light and colours, and have even managed to sway the attention of physicists away from the principal factors that affect the results of prismatic experiments. To see what I mean I will cite below from a number of authors who have undertaken the task of explaining Goethe’s understanding of colour. Some of these authors are philosophers, while others are physicists, and I have no doubt that—in view of what we’ve discussed thus far—you’ll find the conclusions of these authors very interesting.

A short note of clarification

This post, as well as the previous two and the next dozen or so that will follow it, have been written almost a decade ago, and they used to be part of a website and a blog (called jaccuse.info and newjaccuse.info, respectively) which I discontinued just before the end of last year. Now I am putting them back online, and before doing it I had decided to leave them by and large as they were originally conceived. That inevitably means that they will contain some lost or obsolete references and perhaps many broken links within. But that is not even of a mild concern to my mind, and it shouldn't be to anyone else's either. Moreover, I had also decided to not publish the entire content of my former sites, which is likely to result in some missing coherence as a whole, at times. Nonetheless, having thought about these issues I had also decided that in certain situations I ought to bend the rules I made, and one of those situations has arisen now. 

I am referring to the so-called issue of Goethe's 'white wall' observation. This is an issue that really drives me absolutely mad, when Newtonians are quick to explain 'away' Goethe's apparently gross misunderstanding. Take as a perfect example just the last paragraph above, in red. Now let me tell you that the guy who wrote it (and whose name I never cared to mention) has to be some thing of a physics and mathematics Grand Master of sorts--judging only by his massive website of that kind, which he's been most likely running ever since probably the very first Atari must have been dropped into this modern world. And for that I, the infidel, can only say "Kudos, dude!" Nevertheless, as from the point of order that we are discussing here the guy is very much a most ordinary, mediocre specimen of dudes. Not that he realises that at any given time, of course. (But, after all, how could he, come to think of it, when what he does is merely repeating what legions of others have been saying for more than 200 years to all those who may, or who indeed have, had the incredible audacity and nerve to question anything that none other than Sir Isaac Newton had chosen to bestow upon humanity as a perennial legacy and gift.)And then I certainly cannot feel any calmer either when I see yet another simpleton declaring that

What Goethe saw is perfectly explicable on Newtonian principles. Had the light passing through his prism come from a point-source, as in a camera obscura, and so been effectively a single ray, he would have seen the phenomenon he expected, a ray of white light dispersed into a sheet of coloured bands. 

Say what, dude, are you kidding me?! What camera obscura have you ever seen in which a 'single ray of light' was ever shone? How do you dare to even contemplate the thought, let alone throw it straight in the face of a man who had dedicated (for no other reason than perhaps his personal love for truth and his unquenchable thirst for knowledge) 40 years of his life to that noblest of the most noble human causes. 

But this is all I will say here, now. Nevertheless, let me assure you that the 'white wall' subject will play one of the leading roles in the development of my unfolding saga. For now though I'll bid you goodbye.