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PARERGA AND PARALIPOMENA: SHORT PHILOSOPHICAL ESSAYS |
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[b]CHAPTER 7: On the Theory of Colours[/b]
§ 103
As the indifference of my contemporaries could not possibly shake my firm belief in the truth and importance of my theory of colour, I wrote and published it twice, in German in 1816 and in Latin in 1830 in the third volume of the Scriptores ophthalmologiei minores of J. Radius. As, however, this total lack of interest leaves me little hope, at my age, of living to see a second edition of these essays, I will here note down the few remarks I still have to make on the subject.
Whoever undertakes to discover the cause of a given effect will, if he goes to work in the proper way, begin by thoroughly investigating the effect itself, as the data for discovering the cause can be drawn only from the effect and this alone gives the direction and clue to his discovery of the cause. Nevertheless, this has not been done by any of those who prior to me enunciated theories of colour. I t was not only Newton who proceeded to look for the cause without having any precise knowledge of the effect to be explained, but his predecessors had also done the same thing. Even Goethe, who examined and explained the effect, the given phenomenon, the sensation in the eye, certainly much more thoroughly than did the others, still did not go far enough in this direction, otherwise he could not have failed to light upon my truths which are the root of all theory of colour and contain the grounds and basis of his own. Thus I cannot except even him when I say that all prior to me, from the most ancient to the most modern times, were concerned only with investigating what modification either the surface of a body or light must undergo, whether through analysis into its component parts or through cloudiness or other obscuration, in order to exhibit colour, in other words, to stimulate in our eye that thoroughly characteristic and specific sensation which cannot be defined at all, but can be demonstrated only through the senses. But instead of this, the correct and methodical way is obviously to turn first to this sensation to see whether we may not be able to find out from its more specific nature and from the conformity to law of its phenomena, what here takes place physiologically. For in the first place, we have a thorough and precise knowledge of the effect as that which is given. In any case, this must also furnish the data for investigating the cause as that which is sought, in other words, the external stimulus here which acts on our eye and produces that physiological occurrence. Thus for every possible modification of a given effect, it must be possible to demonstrate a modifiability of its cause exactly corresponding to that effect. Further, where the modifications of the effect are not separated from one another by sharp lines of demarcation, such lines should not be drawn in the cause; but here too the same gradualness of the transitions must take place. Finally, where the effect shows contrasts, that is, admits of a complete reversal of its mode and manner, then the conditions for this must also lie in the nature of the assumed cause, and so on. The application of these general principles to the theory of colour can easily be made. Everyone acquainted with the facts will at once see that my theory which considers colour only in itself, in other words, as a given specific sensation in the eye, already furnishes data a priori for judging the theories of Newton and Goethe concerning the objective aspect of colour, or the external causes that stimulate such a sensation in the eye. But on closer examination, he will find that, from the standpoint of my theory, everything is in favour of Goethe's and against Newton's.
To give here to those acquainted with the facts just one proof of what has been said, I will explain in a few words how the correctness of Goethe's primary physical phenomenon already follows a priori from my physiological theory. If colour in itself, that is to say, in the eye, is the qualitatively halved, and thus only partially stimulated, nervous activity of the retina, then its external cause must be a diminished light, yet one that is diminished in quite a special way. This cause must have the peculiar quality of imparting to every colour precisely as much light as it does darkness or cloudiness ([x]) to the physiological opposite and complement of that colour. But this can happen in a sure and certain way that satisfies all cases only if the cause of the brightness in a given colour is precisely the cause of what is shady or dark in the complement of that colour. Now this requirement is perfectly satisfied by the partition of opacity that is inserted between light and darkness, since, under opposite illumination, it always produces two colours which are physiologically complementary and turn out differently according to the degree of thickness and density of this opacity. Together, however, they will always make up white, that is, the full activity of the retina. Accordingly, with the maximum tenuity of opacity, these colours will be yellow and violet; with increasing density, they will change into orange and blue; and finally, with still greater density, they become red and green. This last, however, cannot really be demonstrated in this simple way, although the sky at sunset feebly exhibits it. Finally, if the opacity is complete, that is to say, becomes so dense as to be impervious to light, then, with light falling on it, white appears and with light placed behind it, we have darkness or black. This method of considering the problem will be found discussed in detail in §11 of my Latin essay on the theory of colours.
It is clear from this that, if Goethe had himself discovered my physiological colour theory which is fundamental and essential, in it he would have had a solid support for his basic physical view. Moreover, he would not have fallen into the error of absolutely denying the possibility to produce white from colours, a fact that is testified by experience, although always in the sense of my theory, never in that of Newton's. But although Goethe had made a most complete collection of the materials for the physiological theory of colours, it was not granted to him to discover the theory itself, which, however, as something fundamental, is really the main point. Yet this can be explained from the nature of his mind; thus for this he was too objective. Madame George Sand is reported as having said somewhere: chacun ales defauts de ses vertus. [1] It is precisely the astonishing objectivity of his mind, everywhere stamping his works with the mark of genius, which stood in his way where it was of value and prevented him from going back to the subject, in this case the perceiving eye itself, in order to seize here the final threads on which hangs the whole phenomenon of the world of colour. On the other hand, coming from Kant's school, I was prepared and trained for satisfying this demand in the best way. And so a year after withdrawing from Goethe's personal influence, I was able to discover the true, fundamental, and irrefutable theory of colour. Goethe's propensity was for understanding and interpreting everything purely objectively; but with this he was then conscious of having done his part and was quite incapable of seeing beyond this. Thus in his theory of colours we sometimes find a mere description where we expect an explanation. And so the last attainable thing here seemed to him to be a correct and complete explanation of the objective course of events. Accordingly, the most general and important truth of his whole theory of colours is a plain objective fact that he himself quite rightly calls primary phenomenon. With this he regarded everything as done; a correct' thus it is' was for him always the final goal; he had no craving for a 'thus it must be'. Indeed he could even scoff:
[quote]Then, the philosopher steps in And shows, no otherwise it could have been. [2][/quote]
Now instead of this, he was of course just a poet and not a philosopher; that is to say, he was not animated by, or possessed of, an ambition to get to the ultimate grounds and innermost relation and connection of things in the way we wish. But for this very reason, he had to leave me the best harvest as gleanings, for the most important information and explanation in regard to the essential nature of colour, the ultimate satisfaction and the key to all that Goethe teaches, are to be found alone in my work. Accordingly, after I have deduced, as briefly mentioned, his primary phenomenon from my theory, it no longer merits this name. For it is not, as he assumed, something absolutely given and for ever withdrawn from all explanation; on the contrary, it is only the cause, such as is required in consequence of my theory, for producing the effect and thus for halving the activity of the retina. The only primary phenomenon in the proper sense is that organic ability of the retina to let its nervous activity appear in two qualitatively opposite halves, sometimes equal and sometimes unequal, and to throw them successively into relief. Here, of course, we must stop, since from this point at best only final causes can be seen, just as in physiology we generally come across this. And so possibly through colour we have one more method of distinguishing and recognizing things.
In addition, my theory of colours has over all others the great advantage of giving an account of the peculiar nature of the impression of every colour and of making this known to us as a definite numerical fraction of the retina's full activity, which is then either + or -. In this way, we learn to understand the specific difference of colours and the peculiar nature of each. Newton's theory, on the other hand, leaves entirely unexplained that specific difference and peculiar effect of each colour, since, according to it, colour is just a qualitas occulta (colorifica) [3] of the seven homogeneous lights. Accordingly, it gives each of these seven colours a name and then leaves it at that; and Goethe, on his part, is content to divide colours into warm and cold, leaving the rest to his aesthetic observations. Therefore only in my work do we obtain between the true nature of every colour and its sensation a connection which has hitherto always been missed.
Finally, for my theory of colours I may claim yet another peculiar though superficial advantage. Thus with all newly discovered truths, possibly without exception, it is soon found that something very similar has already been said and that it required only a single step in order to reach them. Indeed, it is even found sometimes that the truth had been positively expressed, yet had escaped notice because such expression had been made without emphasis. For the author himself had not recognized its value and grasped how rich in results it would be, a circumstance that prevented him from properly working it out. In such cases, therefore, one had, if not the plant, at any rate the seed. Now my colour theory is a fortunate exception to this. Never has it occurred to anyone anywhere to regard colour, this really objective phenomenon, as the retina's halved activity and accordingly to assign to each individual colour its difinite numerical fraction that makes up unity with the fraction of another colour, such unity representing white. Indeed, these fractions are so positively obvious, that Professor Rosas who wanted to claim them as his own, introduced them as absolutely self-evident in his Handbuch der Augenheilkunde, volume i, § 535, and also p. 308.
But the obvious correctness of the fractions laid down by me is certainly very useful for the facts of the case, for in spite of all their certainty, it would nevertheless be difficult really to establish them. It might perhaps be effected in the following way. Let us procure perfectly black and perfectly white sands and mix them in six proportions, each exactly corresponding in darkness to one of the six principal colours. The result must then be that the ratio of black sand to white in the case of each colour corresponds to the numerical fraction I have assigned to that colour. For example, if we were to take three parts of white sand and one of black to form a grey corresponding in darkness to yellow, then a grey corresponding to violet would require a mixture of the two sands in exactly the opposite proportion; green and red, on the other hand, would require equal proportions of the two sands. However, the difficulty arises here of determining which grey corresponds in darkness to each colour. This could be decided by our observing the colour close to the grey through a prism in order to see what relation of brightness to darkness each bears to the other in refraction. If in this respect they are both alike, then the refraction cannot possibly give any colour phenomenon.
Our test of the purity of a given colour, whether for example this particular yellow is exactly so, or has a tinge of green, or even of orange, has reference to the precise accuracy of the fraction that is expressed by that colour. But the fact that we are able to judge this purely arithmetical relation from mere feeling is proved by music whose harmony rests on the much greater and more complex numerical relations of simultaneous vibrations, but whose tones we judge extremely accurately, and yet arithmetically, purely by ear. Just as the seven tones of the scale are distinguished from countless others that are possibly to be found between them through the rational nature of their vibration numbers, so also are the six colours that are given names of their own distinguished from countless others lying between them merely by the rational and simple nature of the fraction of the retina's activity which manifests itself in them. Just as I test the accuracy of a tone, when tuning an instrument, by striking its fifth or octave, so do I test the purity of any given colour by producing its physiological spectrum whose colour is often easier to judge than is the given colour itself. Thus, for example, I have inferred that the green of grass has a marked tinge of yellow merely from the fact that the red of its spectrum has a strong touch of violet.
§ 104
After Buffon had discovered the phenomenon of physiological colours on which the whole of my theory is based, it was interpreted and explained by Father Scherffer in his Abhandlung von den zufalligen Farben, Vienna, 1765, in accordance with the Newtonian theory. As this explanation of the facts is found repeated in many works and even in Cuvier's Anatomie comparee (lec. 12, art. I), I will here expressly refute it and indeed reduce it ad absurdum. It starts by saying that, fatigued by a long contemplation of a colour, the eye loses its susceptibility to homogeneous light-rays of this kind. It then experiences a sensation of white that is afterwards intuitively perceived only to the exclusion of just those homogeneous rays of colour. And so the eye no longer sees this as white, but experiences instead a product of the other six homogeneous rays which, together with that first colour, constitute white; and hence this product is now said to be the colour that appears as a physiological spectrum. But now ex suppositis [4] this explanation of the facts can be seen to be absurd. For after looking at violet, the eye perceives on a white (or better still grey) surface a yellow spectrum. Now this yellow had to be the product of the other six homogeneous lights that remained after the separation of violet; and so had to be composed of red, orange, yellow, green, blue, and indigo; a fine mixture for obtaining yellow! These will give a muddy sort of colour and nothing else. Moreover, if yellow is itself a homogeneous light, how could it then be the result of that mixture? But by itself alone one homogeneous light is absolutely the required colour of the other, such colour following it physiologically as spectrum, just as yellow is of violet, blue of orange, red of green, and vice versa; this simple fact already overthrows Scherffer's explanation; for it shows that what the eye sees on the white surface after looking continuously at a colour is anything but a combination of the six remaining homogeneous lights; on the contrary, it is always only one of them, for example yellow, after violet has been intuitively perceived.
Besides, there are many other facts that are at variance with Scherffer's explanation. For example at the very outset, it is not true that, by continuously looking at the first colour, the eye becomes insensitive thereto, and indeed to the extent of being no longer able to perceive it afterwards even in the white. For it sees that first colour quite distinctly up to the very moment when it turns therefrom to the white. Further, it is well known from experience that we see physiological colours most distinctly and easily early in the morning immediately after we have woken up. But it is just at that time, as the result of a long rest, that the eye is at its maximum strength and is, therefore, least likely to become fatigued through continuously looking for several seconds at a colour and to become dull and deadened to the point of being insensitive thereto. Moreover, there is the awkward fact that, to see physiological colours, we certainly do not need to look at a white surface; for this any colourless surface is suitable, a grey one being the best, but even a black will do. In fact, we see the physiological colour even with our eyes shut! Buffon had already stated this and Scherffer himself admits it in § 17 of his above-mentioned work. Now here we have a case where, as soon as a false theory has reached a definite point, nature stands right in its path and gives it the lie. It is here that Scherffer becomes very nonplussed and admits to finding the greatest difficulty. Yet instead of being puzzled at his theory which can never be consistent, he seizes on all kinds of wretched and absurd hypotheses, wriggles pathetically, and ultimately drops the matter.
I will here mention yet another fact that is only rarely observed because it too furnishes an argument against Scherffer's theory in that according to this it is absolutely unintelligible; but also because it deserves to be shown by a special brief discussion to be consistent with my theory. Thus if there are on a large coloured surface some smaller colourless spots, these will no longer remain colourless when the physiological spectrum that is required by the coloured surface subsequently appears. On the contrary, they will appear in the colour of the whole surface which existed in the first instance, although they have not been in any way affected by its complement. For example, from looking at a green wall with small grey windows, there follows, as spectrum, a red wall with green not grey windows. According to my theory, we have to explain this by saying that, after a definite qualitative half of its activity was brought about on the whole of the retina by the coloured surface, some small spots were nevertheless excluded from that excitation. With the cessation of the external stimulus, the complement of that half of the retina's activity which was excited by it, subsequently appears as spectrum. The spots that were excluded from that stimulus then take over in sympathy that qualitative half of the retina's activity which existed in the first instance. For now they imitate, as it were, what was done previously by the whole of the remaining part of the retina, whereas they alone were excluded from this by the failure of the stimulus to appear in their case. Consequently, they afterwards went through the exercise, so to speak.
Finally, if anyone wishes to raise a difficulty by saying that, when we look at a multicoloured surface, the retina's activity is, according to my theory, distributed simultaneously in a hundred places in very different proportions, let him reflect that, when we listen to the harmony of a large orchestra, or to the rapid runs of a virtuoso, the ear-drum and auditory nerve are moved now in simultaneous vibrations and then in those that most rapidly succeed one another, according to different numerical ratios. The intelligence arithmetically grasps and assesses all these; it receives the aesthetic effect from them and at once notices every deviation from the mathematical accuracy of a tone. He will then see that I have not credited with too much the far more perfect sense of sight.
§ 105
It is only through my theory that full justice has been done to the essentially subjective nature of colour, although the sense of this is already expressed in the old proverb des gouts et des couleurs il ne faut disputer. [5] But what Kant says about aesthetic judgement or the judgement of taste here applies to colour, namely that it is indeed only subjective and yet, like one that is objective, claims to receive the assent of all those who are normally constituted. If we did not have a subjective anticipation of the six principal colours which gives us an a priori standard for them, we should have no judgement concerning the purity of a given colour; for its designation would then be merely conventional through a name of its own, as is actually the case with many fashionable colours. Accordingly, we should be incapable of understanding many things, for instance what Goethe says of true red, that it is the red of carmine, not the ordinary scarlet that is yellowish-red; whereas this is now very easy for us to understand and is then clear to all.
To this essentially subjective nature of colour is ultimately due the extreme readiness with which chemical colours change. Sometimes this goes so far that only an exceedingly small change, or one that cannot even be detected, in the properties of the object in which the colour is inherent, corresponds to a total change of that colour. For example, sulphide of mercury obtained by fusing together mercury and sulphur is black (just as is a similar combination of lead with sulphur). Only after it has been sublimated, does it assume the well-known fiery-red colour; and yet through this sublimation it is not possible to detect a chemical change. Red mercuric oxide, when merely warmed, becomes dark brown and yellow nitrate of mercury becomes red. A well-known Chinese cosmetic comes to us on little pieces of pasteboard and is then dark green; when touched with a wet finger, it instantly turns to a bright red. Even the turning red of crabs through boiling is relevant to the point in question; also the sudden turning of many leaves from green to red at the first frost, and the turning red of apples on the side that gets the sunlight. This is attributed to a more vigorous deoxidation of that side in the same way that some plants have the stem and the whole framework of the leaf in bright red, but the parenchyma in green; also in general the diversity of colours of many petals. In other cases, we can show the chemical difference that is indicated by the colour to be very small, for example when tincture of litmus or violets changes colour through the slightest trace of oxidation or alkalization. In all this, we now see that, in the chemical sense, the eye is the most sensitive reagent, for it instantly shows us not only the smallest traceable changes of the mixture, but even those that no other reagent can indicate. On this incomparable sensitiveness of the eye depends generally the possibility of chemical colours, which in itself is still wholly unexplained. Through Goethe, on the other hand, we have at last arrived at a correct insight into physical colours, despite the fact that Newton's much advertised and false theory rendered this more difficult. Physical colours are related to chemical exactly as magnetism that is produced by galvanic apparatus, and is to that extent intelligible from its immediate cause, is to the magnetism that is fixed in steel and iron ores. The former gives a temporary magnetism which lasts only through a complex set of circumstances and ceases to exist as soon as these disappear; the latter, on the other hand, is inherent in a body, unalterable, and till now unexplained. It is just bewitched, like an enchanted prince. Now the same holds good of the chemical colour of a body.
§ 106
In my theory I have shown that even the production of white from colours rests exclusively on a physiological basis, since it occurs only by the fact that a pair of colours and hence two which are complementary, in other words, two into which the retina's activity is halved and separated, are again brought together. Now this can happen only if the two external causes that stimulate in the eye each of the two colours act simultaneously on one and the same spot of the retina. I have mentioned several ways of bringing this about; the easiest and simplest is when we allow the violet of the prismatic spectrum to fall on yellow paper. But in so far as we will not rest content with merely prismatic colours, we shall succeed best by uniting a transparent with a reflected colour, for example by allowing light to fall through a reddish-yellow glass on to a mirror of blue glass. The expression 'complementary colours' has truth and meaning only in so far as it is understood in the physiological sense; otherwise it has none at all.
Goethe has wrongly denied the possibility of producing white from colours generally; but this was because Newton had stated it from a false argument and in a false sense. If it were true in the Newtonian sense, or if Newton's theory in general were correct, then, in the first place, every combination of two of the fundamental colours assumed by him would inevitably give us at once a colour brighter than each of them separately, since the combination of two homogeneous parts of the white light that is divided into these would already be a step back towards the restoration of that white light. But this is not for one moment the case. Thus if we bring together in pairs the three colours which are fundamental in the chemical sense and of which all the rest are composed, then blue and red give us violet that is darker than either of these; blue and yellow give green that is indeed much darker than the latter, although it is somewhat brighter than the former; yellow and red give orange that is brighter than the latter but darker than the former. Already one sees here a really adequate refutation of Newton's theory.
But the real, effective, conclusive, and inescapable refutation thereof is the achromatic refractor; and precisely on this account Newton very consistently regarded such a thing as impossible. Thus if white light consists of seven kinds of light each of which has a different colour and at the same time a different refrangibility, then the degree of refraction and the colour of the light are of necessity inseparably associated. Thus where light is refracted, it must also appear coloured, however much the refraction be varied and complicated and drawn apart; only so long as not all the seven rays are again completely brought together into a heap and thus, according to Newton's theory, white is recomposed, all effect of refraction then at the same time being ended and so everything again back in its place. Now when the invention of achromatism revealed the very opposite of this result, the Newtonians in their embarrassment seized on an explanation that, with Goethe, we feel tempted to regard as senseless verbiage; for with the best will in the world, it is very difficult to attribute to it even an intelligible meaning, that is, something that can to a certain extent be represented in intuitive perception. Thus besides the colour-refraction, there is said to occur a colour-dispersion different therefrom; and by this is to be understood the distance of the separate coloured lights from one another, their dispersion, which is the most direct cause of the lengthening of the spectrum. But ex hypothesi [6] this is the effect of the different refrangibility of those coloured rays. Now if this so-called dispersion, that is, the lengthening of the spectrum and thus of the sun's image after refraction, is due to the fact that light consists of different coloured lights each of which has by its nature a different refrangibility, in other words, is refracted at a different angle, then this definite refrangibility of each light must always and everywhere adhere to it as an essential quality. Therefore the separate homogeneous light must be refracted always in the same way just as it is coloured always in the same way. For Newton's homogeneous light-ray and its colour are absolutely one and the same; it is simply a coloured ray and nothing else. Hence where there is a light-ray, there also is its colour; and where there is colour, there too is its ray. If ex hypothesi it lies in the nature of every such differently coloured ray to be refracted at a different angle, then its colour will also accompany it into this and every angle; consequently the different colours must make their appearance at every refraction. And so to attribute any meaning and sense to the Newtonians' favourite explanation that' two different kinds of refracting medium can refract light with equal intensity but disperse colours in a different degree', we must assume that, while crown-glass and flint-glass refract light as a whole and thus white light with equal intensity, yet the parts whereof this very whole through and through consists are refracted differently by flint-glass from the way in which they are by crown-glass and thus alter their refrangibility. A hard nut to crack! Moreover, they must change their refrangibility in such a way that, with the use of flint-glass, the most refrangible rays acquire an even greater refrangibility, whereas the least refrangible assume one that is even smaller; and therefore that this flint-glass increases the refrangibility of certain rays and at the same time diminishes that of certain others and that nevertheless the whole, which consists of these rays alone, retains its previous refrangibility. Despite all this, that dogma, which is so difficult to understand, is still held in universal esteem and respect; and even at the present day we can see from the optical writings of all nations how seriously people speak of the difference between refraction and dispersion. Now let us return to truth!
The immediate and essential cause of the achromatism that is brought about by means of the combination of the convex lens from crown-glass, and of the concave lens from flint-glass, is without doubt entirely physiological. Thus it is the production of the retina's full activity on those places that are affected by physical colours, since here two colours, certainly not seven, namely two which together make up that activity, are brought on to each other; and so a pair of colours is again united. Objectively or physically this is brought about in the following way. Through a refraction that occurs twice in the opposite sense (by means of concave and convex lenses), there results the opposite colour-phenomenon, namely a yellowish-red border with yellow fringe, on the one hand, and a blue border with violet fringe, on the other. But this refraction, occurring twice in the opposite sense, at the same time brings those two coloured margins over each other in such a way that the blue border covers the yellowish-red, and the violet fringe the yellow; and so these two physiological pairs of colours, namely one of 1/3 and 2/3 and the other of 1/4 and 3/4 of the retina's full activity, are again united; consequently, colourlessness or achromatism is also re-established. This, then, is the direct cause of achromatism.
But what is the remoter cause? Thus as the required dioptric result, namely a surplus of refraction that remains colourless, is brought about by the fact that the flint-glass, acting in the opposite sense, is able to neutralize with a considerably smaller refraction the colour-phenomenon of the crown-glass through an, opposite phenomenon that is just as broad, since its own colour borders and fringes are originally considerably broader than those of the crown-glass, the question then arises how it is that two different kinds of refracting media with equal refraction give us such a very different width of colour-phenomenon. A very adequate account of this can be given according to Goethe's theory, if we go into this more fully and thus more clearly than did he himself. His deduction of the prismatic colour-phenomenon from his first principle that he calls primary phenomenon, is perfectly correct. The only thing is that he did not go far enough into details, whereas without a certain amount of precise examination, it is impossible to do justice to such things. He quite correctly explains the coloured border-phenomenon that accompanies refraction from a secondary image accompanying the main one that is displaced by refraction. But he did not specifically state the position and mode of acting of this secondary image and did not make this clear by a sketch. In fact, he speaks throughout of only one secondary image and the result is that we have to assume that not merely the light or luminous image, but also the darkness surrounding it undergoes a refraction. I must, therefore, supplement his facts in order to show how that varied breadth of the coloured border-phenomenon really arises with equal refraction but different refracting substances, a phenomenon that the Newtonians describe by the senseless expression of a difference of refraction and dispersion.
First of all, a word or two on the origin of these secondary images that accompany the main image during refraction. Natura non facit saltus; [7] this is the law of the continuity of all changes by virtue of which no transition in nature occurs suddenly and abruptly whether in space, or time, or in the degree of any quality or property. Now when light enters and again emerges from a prism, it is twice diverted suddenly from its straight path. Are we then to assume that this occurs with such abruptness and sharpness that the light does not suffer even the slightest blending with the surrounding darkness, but, wheeling right across this at large angles, preserves its edges most distinctly and sharply, so that it emerges with unalloyed purity and remains wholly intact? Is it not more natural to assume that, in the first as well as the second refraction, a very small part of this mass of light does not take up the new alignment rapidly enough and so becomes somewhat detached and now, as it were, remembering as an afterthought the path just forsaken, accompanies the main image as a secondary one that floats somewhat over it after one refraction and somewhat under it after the other? In fact in this connection, we could think of the polarization of light by means of a mirror that reflects back one part of it and lets through another.
The following figure shows more particularly how, in accordance with Goethe's fundamental law, the four prismatic colours arise from the effect of those two secondary images that fall off with prismatic refraction. It is those four colours alone and not seven that really exist.
[x]
This figure represents a disc of white paper, some four inches in diameter, stuck on to a dull black paper, as it appears in nature and not according to Newtonian fictions, when looked at through a prism at a distance of about three yards. Now anyone who wants to know what we are talking about must convince himself of this by personal inspection. By holding the prism in front of his eyes and first approaching and then moving away from the disc, he will almost immediately perceive the two secondary images. He will see how they follow his movements and deviate more or less from the main image, and how they shift over each other. Prismatic experiments generally may be made in two different ways; either so that refraction precedes reflection, or vice versa. The former happens when the sun's image passes through the prism on to the wall; the latter occurs when we look at a white image through a prism. This method is not only less troublesome to carry out, but also shows much more clearly the actual phenomenon because here the effect of refraction directly reaches the eye. Thus we have the advantage of receiving the effect at first hand, whereas with the other method we obtain it only at second hand, after reflection from the wall has occurred. A second advantage is that the light comes from an object that is close to us, sharply defined, and not dazzling. Therefore the white disc here described shows quite distinctly the two secondary images which accompany it and which have been brought about by a refraction that occurs twice and shifts it upwards. The secondary image, resulting from the first refraction that occurs when the light enters the prism, trails behind and therefore remains with its extreme edge in darkness and covered thereby. The other secondary image, however, resulting with the second refraction and thus when the light emerges from the prism, moves forward rapidly and thus is drawn over the darkness. But the manner of acting of both extends, although more feebly, to that part of the main image which is weakened by their loss; and so only that part of it which remains covered by both secondary images and thus retains its full light, appears white. On the other hand, where one secondary image alone contends with the darkness, or the main image that is somewhat weakened by the loss of this secondary image is already impaired by the darkness, colours result, and moreover in accordance with Goethe's law. Consequently, we see violet occur on the upper part where one secondary image alone advancing rapidly is drawn over the black surface; but under it we see blue where the main image, nevertheless weakened by the loss, is operating. On the lower part of the image, however, where the individual secondary image remains in darkness, yellowish-red appears; but over this we have yellow where the weakened main image already shines through. In the same way, the rising sun, at first covered by the denser lower atmosphere, appears yellowish-red and is yellow only when it has reached the more rarefied atmosphere.
Now if we have really grasped and understood this, we shall not find it difficult to see, at any rate in a general way, why with the same refraction of light some refracting media, like flint-glass, give the phenomenon of a wider coloured edge, whilst others, like crown-glass, give one that is narrower; or, in the language of the Newtonians, what gives rise to the lack of uniformity in light refraction and colour dispersion. Thus refraction is the distance of the main image from its line of incidence; dispersion, on the other hand, is the distance of the two secondary images from the main image which occurs here. But now we find this accidental property existing in varying degrees in different kinds of light-refracting substances. Accordingly, two transparent bodies can have the same power of refraction; in other words, the image passing through them is deflected an equal amount from its line of incidence. Nevertheless, the secondary images that cause the colour-phenomenon, may deviate from the main image more with refraction through one body than with that through another.
Now to compare this account of the facts with the Newtonian explanation of the phenomenon which has been so often repeated and is analysed above, I select the expression of the latter which is given in the following words in the Munchner Gelehrte Anzeigen of 27 October 1836, after the philosophical transactions: 'Different transparent substances refract the various homogeneous lights in very unequal proportion; 8 so that the spectrum produced by different refracting media, and moreover in similar circumstances, acquires a very different extension.' If the lengthening of the spectrum were the result of the unequal refrangibility of the homogeneous lights themselves, it would necessarily have proved to be everywhere in accordance with the degree of refraction. Therefore only in consequence of the greater refractive power of a medium could there arise a greater lengthening of the image. Now if this is not the case, but of two media having equal refractive power, one gives a longer and the other a shorter spectrum, this proves that the lengthening of the spectrum is not the direct effect of refraction, but merely that of an accident accompanying refraction. Now the secondary images here arising are such an accident; these may very well deviate more or less from the main image with equal refraction, according to the nature of the refracting substance.
Ought we not to suppose that considerations of this sort would inevitably open the eyes of the Newtonians? We should indeed, if we did not yet know how great and formidable is the influence which is exercised on branches of knowledge and in fact on all intellectual attainments by the will, that is, by tendencies and inclinations and, to speak more precisely, by evil tendencies. In 1840 Eastlake, the English painter and Keeper of the National Gallery, produced such an excellent translation of Goethe's colour theory that it was a perfect reproduction of the original; it can be read and in fact understood more easily than the original. We must now see how Brewster reacts to it when writing a criticism of it in the Edinburgh Review. His behaviour is not unlike that of a tigress
ON THE THEORY OF COLOURS 195 into whose lair a man enters for the purpose of seizing her cubs. Is this like the tone of calm and certain conviction in face of a great man's error? On the contrary, it is the tone of an intellectual bad conscience which suspects with alarm that the other party is right and is resolved to defend, [x], [9] now as a national possession the pseudo-science that is thoughtlessly accepted without investigation. By adhering to it, one is already compromised. And so if Newton's colour theory is regarded by Englishmen as a national affair, a good French translation of Goethe's work would be highly desirable; for we may certainly hope to see justice done by the French learned world who to this extent are neutral, although even here there are sometimes amusing instances of their partiality for the Newtonian colour theory. For example, in the Journal des savans, April 1836, Biot relates with cordial approbation how Arago prepared very cunning experiments in order to ascertain whether the seven homogeneous lights do have perhaps an unequal velocity of propagation, so that from the variable fixed stars that are now nearer, now more distant, red or violet light arrives first and thus the star appears to assume different colours in succession. But fortunately in the end he had discovered that this was not so. Sancta simplicitas! [10] A pretty exhibition is given also by M. Becquerel who in a memoire presente a l' academie des sciences, 13 June 1842, chants afresh the same old tune as if it were something new: si l' on refracte un faisceau (sic) de rayons solaires a travers un prisme de flint-glass, et qu'on recoive sur un carton blanc l'image oblongue refractee, on distingue ASSEZ NETTEMENT (here is a qualm of conscience) sept sortes de couleurs, ou sept parties de l'image qui sont colorees chacune a peu pres de la meme teinte: ces couleurs sont: le rouge, l'orange, le jaune, le vert, le bleu, l'indigo (this mixture of 3/4 black with 1/4 blue is said to be found in light!) et le violet, cette derniere etant celle des rayons les plus refrangibles. [11] As M. Becquerel still has the effrontery to chant so fearlessly and frankly this piece from the Newtonian credo thirty-two years after the appearance of Goethe's colour theory, we might feel tempted to declare to him assez nettement: 'Either you are blind or are lying.' But then we should be doing him an injustice, for it is merely a case of M. Becquerel preferring to believe Newton rather than the evidence of his own two eyes. This is the effect of Newtonian superstition.
But so far as the Germans are concerned, their judgement of Goethe's colour theory is in keeping with the expectations we must have from a nation that could for thirty years praise Hegel as the greatest of all thinkers and sages, that scribbler of nonsense and absolutely hollow philosophaster, who is devoid of mind and merit. In fact, they all join in the chorus to such an extent that the whole of Europe echoes with the noise. I know quite well that desipere est juris gentium, [12] in other words, that everyone has the right to judge in accordance with his intellect and his wishes. But in return for this, he will have to put up with being criticized for his opinions by the generations to come and in advance by his own; for there is still a Nemesis even here.
§ 107
At the close of these supplementary remarks on chromatology, I will quote a few interesting facts which serve to corroborate Goethe's fundamental law of physical colours, but which he himself did not notice.
If in a dark room we discharge the electricity of a conductor into a vacuum glass tube, this electric light appears as a very beautiful violet. Here as with blue flames, the light itself is at the same time the cloudy medium. For there is no essential difference whether the illuminated dimness or cloudiness, through which we peer into the dark, casts into our eye its own or reflected light. But since this electric light is here exceedingly faint and feeble, it gives rise to violet, wholly in accordance with Goethe's theory, instead of blue being produced even by the feeblest flame such as that of methylated spirit, sulphur, and so on.
A common everyday proof of Goethe's theory which was overlooked by him, is that many bottles filled with red wine or dark beer, after standing for a long time in a cellar, often undergo a noticeable cloudiness of the glass through a deposit on the inside. In consequence of this, they then appear bright blue when the light falls on them, and likewise when we hold something black behind them after they have been emptied. With light that shines through, on the other hand, they show the colour of the liquid or, when empty, that of the glass.
The coloured rings that appear when we firmly press together with our fingers two pieces of polished plate-glass or even polished convex glasses, may be explained in the following way. Glass is not without elasticity; and so with that strong compression the surface to some extent gives and is flattened. For a moment, therefore, it loses its perfect smoothness and evenness, whereby a gradually increasing cloudiness results. And so here too we have a cloudy medium and the different degrees of its cloudiness, with partially incident partially transmitted light, give rise to the coloured rings. If we release the pressure from the glass, its former condition is at once restored by the elasticity and the rings disappear. Newton placed a lens on a glass plate; and so the rings are called Newtonian. The present-day undulation theory bases its calculation of the oscillation-numbers of the colours on the curvature of this lens and on the space between it and its tangent. Here it assumes the air in that intervening space to be a medium different from glass and accordingly assumes refraction and homogeneous lights. All this is quite incredible. (See the description of the facts in Ule's Die Natur, 30 June 1859, no. 26.) For this it is not necessary to have a lens at all; two pieces of plate-glass pressed with the fingers give the best result and the longer we press them in different places, the better the result. Here there is no intervening space at all with its layer of air, for they are stuck together pneumatically. (We must previously breathe on them.) In the same way, the colours of soap-bubbles are the effect of varying local cloudinesses of this semi-transparent material; likewise the colours of a layer of turpentine, old window-panes that have become dull, and so on.
Goethe had the true objective insight into the nature of things, a view that is given up entirely to this. Newton was a mere mathematician, always anxious to measure and calculate, and taking as the basis of this purpose a theory that was pieced together from the superficially understood phenomenon. This is the truth; and you can make what faces you like!
Here the greater public may be informed of one more article with which I have filled the two sides of my sheet in the album that was published by the city of Frankfurt and deposited in their library on the occasion of the centenary of Goethe's birth in 1849. The introduction to it refers to the very impressive ceremonies with which the day was publicly celebrated in that city.
[b]THE FRANKFURT GOETHE-ALBUM[/b]
No garlanded monuments, nor the firing of salutes, nor the ringing of bells, let alone banquets and speeches, can suffice to atone for the grievous and revolting injustice and wrong suffered by Goethe in connection with his theory of colours. For instead of its perfect truth and excellence meeting with just and well-merited approbation, it is generally regarded as an abortive attempt. Professional men merely laugh at it, as was recently expressed in a periodical; in fact, they look upon it as a weakness of the great man which is to be treated with indulgence and covered with oblivion. This unprecedented injustice and unheard-of perversion of all truth became possible only by the fact that an apathetic, indolent, and indifferent public, devoid of all power of judgement and therefore easily imposed on in this matter, renounced all investigation and examination of their own, however easy these might be even without previous knowledge, in order to leave such matters to the 'professional men', that is, to those who pursue a branch of knowledge not for its own sake, but for the purpose of reward. And this public now allows itself to be impressed by such men with their peremptory utterances and serious countenances. Now if it was its intention not to judge for itself but, like little children, to let itself be guided by authority, then that of the greatest man, whom along with Kant the nation boasts, should certainly have carried more weight than that of many thousands of such men of the trade put together, and especially in a matter that he had made his chief concern throughout the whole of his life. Now as regards the decision of these professional men, the plain unvarnished truth is that they were heartily ashamed of themselves when it came to light that they had not only allowed themselves to be hoaxed by the palpably false, but for over a hundred years without any inquiries and investigations of their own had revered, taught, and propagated it in blind faith and with devoted admiration, until at last an old poet had come along to teach them something better. After this humiliation which they could not get over, they then grew callous, as is usual with transgressors, arrogantly refused subsequent information, and, by obstinately sticking for over forty years to the obviously false and even absurd, discovered and proved to be such, have gained a respite, it is true, but have increased their guilt a hundredfold. For veritatem laborare nimis saepe, extingui nunquam, [13] as Livy has said. The day of disillusionment is at hand and must come; and what then? Then 'we gladly assume what airs we can.' (Egmont, Act III, Sc. 2.)
In those German states that possess academies of learning, the ministers of public instruction placed in charge thereof could show most nobly and sincerely their veneration for Goethe which undoubtedly exists, by giving such academies the task of furnishing within a fixed time a thorough and detailed investigation and critique of Goethe's colour theory together with their decision as regards its opposition to Newton's. Perhaps those highly placed officials might hear my voice and, as it appeals for justice to our most illustrious dead, they might gratify it without first consulting those who, by their inexcusable silence, are themselves accessories to the crime. This is the surest way to remove from Goethe that unmerited ignominy. It would then no longer be a case of disposing of the matter with peremptory utterances and serious faces; nor would the audacious pretence ever again be allowed a hearing that here it was a question not of judgement, but of lengthy calculations. On the contrary, the heads of corporations would see themselves faced with the alternative of either giving truth the palm, or of most seriously compromising themselves. And so under the influence of such thumbscrews, we may hope for something from them and, on the other hand, need not have the least fear. When examined seriously and honestly, Newton's chimeras obviously do not exist at all, but are merely seven prismatic colours, invented in favour of the tonic sol-fa; thus the red that is not one; the simple primary green that appears in the clearest manner before our eyes, quite naively and openly, as a mixture of blue and yellow; but in particular, the monstrosity of homogeneous lights of dark and even indigo colour which are to be found concealed in clear pure sunlight; and, moreover, their different refrangibility to which any pair of achromatic opera glasses will give the lie. Now I ask, how could such fictions be right in face of Goethe's clear and simple truth and of his explanation of all physical colour phenomena which has been reduced to one great natural law? Everywhere and in all possible circumstances nature furnishes staunch and impartial evidence in favour of that law. We might just as well be afraid of seeing the refutation of one multiplied by one! Qui non Libere veritatem pronuntiat, proditor veritatis est. [14]
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[b]Notes:[/b]
1 ['Everyone has the failings of his virtues.']
2 [Faust, Pt. II, Bayard Taylor's translation.]
3 ['An occult (colour-stimulating) quality'.] 4 ['From the assumptions'; 'from the premisses'.]
5 ['One must not argue about tastes and colours.']
6 ['According to the assumption'.]
7 ['Nature makes no jumps.' (Law of continuity first laid down by Aristotle.)]
8 Yet the sum of these, namely white light, in equal proportion! I add this as a supplement.
9 ['Tooth and nail'.]
10 ['Sacred simplicity'. (Said to have been uttered by Johann Hus at the stake as a peasant in blind belief cast a piece of wood into the flames.)]
11 ['If we refract a pencil of solar rays through a prism of flint-glass and receive on a white card the oblong refracted image, we distinguish clearly enough seven kinds of colours or seven parts of the image each of which is coloured with approximately the same tint. These colours are red, orange, yellow, green, blue, indigo, and violet; the last being that of the most refrangible rays.'
12 ['To be foolish and unwise is man's right.']
13 [' Only too often is truth hard-pressed, but she can never be destroyed.']
14 ['Whoever does not freely and frankly acknowledge the truth is a betrayer thereof.']
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