Popular Science Monthly/Volume 17/July 1880/Goethe's Farbenlehre: Theory of Colors II

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By Professor JOHN TYNDALL, F. R. S.


ONE hole Goethe did find in Newton's armor, through which he incessantly worried the Englishman with his lance. Newton had committed himself to the doctrine that refraction without color was impossible. He therefore thought that the object-glasses of telescopes must for ever remain imperfect, achromatism and refraction being incompatible. This inference was proved by Dollond to be wrong.[2] With the same mean refraction, flint-glass produces a longer and richer spectrum than crown-glass. By diminishing the refracting angle of the flint-glass prism, its spectrum may be made equal in length to that of the crown-glass. Causing two such prisms to refract in opposite directions, the colors may be neutralized, while a considerable residue of refraction continues in favor of the crown. Similar combinations are possible in the case of lenses; and hence, as Dollond showed, the possibility of producing a compound achromatic lens. Here, as elsewhere, Goethe proves himself master of the experimental conditions. It is the power of interpretation that he lacks. He flaunts this error regarding achromatism incessantly in the face of Newton and his followers. But the error, which was a real one, leaves Newton's theory of colors perfectly unimpaired.

Newton's account of his first experiment with the prism is for ever memorable. “To perform my late promise to you,” he writes to Oldenburg, “I shall without further ceremony acquaint you that in the year 1666 (at which time I applied myself to the grinding of optick-glasses of other figures than spherical) I procured me a triangular glass prism, to try therewith the celebrated phenomena of colors. And in order thereto, having darkened my chamber, and made a small hole in my window-shuts, to let in a convenient quantity of the sun's light, I placed my prism at its entrance, that it might be thereby refracted to the opposite wall. It was at first a very pleasing divertisement, to view the vivid and intense colors produced thereby; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblong form, which, according to the received laws of refractions, I expected should have been circular. They were terminated at the sides with straight lines, but at the ends the decay of light was so gradual that it was difficult to determine justly what was their figure, yet they seemed semicircular.

"Comparing the length of this colored spectrum with its breadth, I found it about five times greater; a disproportion so extravagant that it excited me to a more than ordinary curiosity of examining from whence it might proceed." This curiosity Newton gratified by instituting a series of experimental questions, the answers to which left no doubt upon his mind that the elongation of his spectrum was due to the fact "that light is not similar or homogeneal, but consists of difform rays, some of which are more refrangible than others; so that, without any difference in their incidence on the same medium, some shall be more refracted than others; and therefore that, according to their particular degrees of refrangibility, they were transmitted through the prism to divers parts of the opposite wall. When," continues Newton, "I understood this, I left off my aforesaid glass-works; for I saw that the perfection of telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of optick authors, as because that light itself is an heterogeneous mixture of differently refrangible rays; so that were a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which, having the same incidence upon the same medium, are apt to suffer a different refraction."

Goethe harped on this string without cessation. "The Newtonian doctrine," he says, "was really dead the moment achromatism was discovered. Gifted men, our own Klügel, for example, felt this, but expressed themselves in an undecided way. On the other hand, the school which had been long accustomed to support, patch up, and glue their intellects to the views of Newton, had surgeons at hand to embalm the corpse, so that even after death, in the manner of the Egyptians, it should preside, at the banquets of the natural philosophers."

In dealing with the chromatic aberration of lenses, Goethe proves himself to be less heedful than usual as an experimenter. With the clearest perception of principles, Newton had taken two pieces of cardboard, the one colored a deep red, the other a deep blue. Around those cards he had wound fine black silk, so that the silk formed a series of separate fine dark lines upon the two colored surfaces. He might have drawn black lines over the red and blue, but the silk lines were finer than any that he could draw. Illuminating both surfaces, he placed a lens so as to cast an image of the surfaces upon a white screen. The result was that, when the dark lines were sharply defined upon the red, they were undefined upon the blue; and that, when, by moving the screen, they were rendered distinct upon the blue, they were indistinct upon the red. A distance of an inch and a half separated the focus of red rays from the focus of blue rays, the latter being nearer to the lens than the former. Goethe appears to have attempted a repetition of this experiment; at all events he flatly contradicts Newton, ascribing his result not to the testimony of his bodily eyes, but to that of the prejudiced eyes of his mind. Goethe always saw the dark lines best defined upon the brighter color. It was to him purely a matter of contrast, and not of different refrangibility. He argues caustically that Newton proves too much; for, were he correct, not only would a dioptric telescope be impossible, but, presented to our naked eyes, differently colored objects must appear utterly confusing. Let a house, he says, be supposed to stand in full sunshine; let the roof-tiles be red, the walls yellow, with blue curtains behind the open windows, while a lady with a violet dress steps out of the door. Let us look at the whole from a point in front of the house. The tiles we will suppose appear distinct, but on turning to the lady we should find both the form and the folds of her dress undefined. We must move forward to see her distinctly, and then the red tiles would appear nebulous. And so with regard to the other objects, we must move to and fro in order to see them clearly if Newton's pretended second experiment were correct. Goethe seems to have forgotten that the human eye is not a rigid lens, and that it is able to adjust itself promptly and without difficulty to differences of distance enormously greater than that due to the different refrangibility of the differently colored rays.

Newton's theory of colors, it may be remarked, is really less a "theory" than a direct presentation of facts. Given the accepted definition of refraction, it is a matter of fact, and not of theoretic inference, that white light is not "homogeneal," but composed of differently refrangible rays. The demonstration is ocular and complete. Having palpably decomposed the white light into its constituent colors, Newton recompounded these colors to white light. Both the analysis and the synthesis are matters of fact. The so-called "theory of light and colors" is in this respect very different from the corpuscular theory of light. Newton's explanation of color stands where it is, whether we accept the corpuscular or the undulatory theory; and it stands because it is at bottom not a theory but a body of fact, to which theory must bow or disappear. Newton himself pointed out that his views of colors were entirely independent of his belief in the "corporiety" of light.

After refraction-colors Goethe turns to those produced by diffraction; and, as far as the phenomena are concerned, he deals very exhaustively with the colors of thin plates. He studies the colors of Newton's rings both by reflected and transmitted light. He states the conditions under which this class of colors is produced, and illustrates the conditions by special cases. He presses together flat surfaces of glass, observes the flaws in crystals and in ice, refers to the iridescences of oil on water, to those of soap-bubbles, and to the varying colors of tempered steel. He is always rich in facts. But, when he comes to deal with physical theory, the poverty and confusion of his otherwise transcendent mind become conspicuous. His turbid media entangle him everywhere, leading him captive and committing him to almost incredible delusions. The colors of tempered steel, he says, and kindred phenomena, may perhaps be quite conveniently deduced from the action of turbid media. Polished steel powerfully reflects light, and the coloring produced by heating may be regarded as a feeble turbidity, which, acted upon by the polished surface behind, produces a bright yellow. As the turbidity augments, this color becomes dense, until finally it exhibits an intense ruby-red. Supposing this color to reach its greatest proximity to darkness, the turbidity continuing to augment as before, we shall have behind the turbid medium a dark background, which appears first violet, then dark blue, and finally light blue, thus completing the cycle of the phenomena. The mind that could offer such an explanation as this must be qualitatively different from that of the natural philosopher.

The words "quite conveniently deduced," which I have italicized in the last paragraph, are also used by Goethe in another place. When the results of his experiments on prismatic colors had to be condensed into one commanding inference, he enunciated it thus: "Und so lassen sich die Farben bei Gelegenheit der Refraction aus der Lehre von den trüben Mitteln gar bequem ableiten." This is the crown of his edifice, and it seems a feeble ending to so much preparation. Kingsley once suggested to Lewes that Goethe might have had a vague feeling that his conclusions were not sound, and that he felt the jealousy incident to imperfect conviction. The ring of conscious demonstration, as it is understood by the man of science, is hardly to be found in the words "gar bequem ableiten." They fall flaccid upon the ear in comparison with the mind-compelling Q. E. D. of Newton.

Throughout the first 350 pages of his work, wherein he develops and expounds his own theory, Goethe restrains himself with due dignity. Here and there, there is a rumble of discontent against Newton, but there is no sustained ill-temper or denunciation. After, however, having unfolded his own views, he comes to what he calls the "unmasking of the theory of Newton." Here Goethe deliberately forsakes the path of calm, objective research, and delivers himself over to the guidance of his emotions. He immediately accuses Newton of misusing, as an advocate, his method of exposition. He goes over the propositions in Newton's "Optics" one by one, and makes even the individual words of the propositions the objects of criticism. He passes on to Newton's experimental proofs, invoking, as he does so, the complete attention of his readers, if they would be freed to all eternity from the slavery of a doctrine which has imposed upon the world for a hundred years. It might be thought that Goethe had given himself but little trouble to understand the theorems of Newton and the experiments on which they were based. But it would be unjust to charge the poet with any want of diligence in this respect. He repeated Newton's experiments, and in almost every case obtained his results. But he complained of their incompleteness and lack of logical force. What appears to us as the very perfection of Newton's art, and absolutely essential to the purity of the experiments, was regarded by Goethe as needless complication and mere torturing of the light. He spared no pains in making himself master of Newton's data, but he lacked the power of penetrating either their particular significance, or of estimating the force and value of experimental evidence generally.

He will not, he says, shock his readers at the outset by the utterance of a paradox, but he can not withhold the assertion that by experiment nothing can really be proved. Phenomena may be observed and classified; experiments may be accurately executed, and made thus to represent a certain circle of human knowledge; but deductions must be drawn by every man for himself. Opinions of things belong to the individual, and we know only too well that conviction does not depend upon insight, but upon will that man can only assimilate that which is in accordance with his nature, and to which he can yield assent. In knowledge, as in action, says Goethe, prejudice decides all, and prejudice, as its name indicates, is judgment prior to investigation. It is an affirmation or a negation of what corresponds, or is opposed to our own nature. It is the cheerful activity of our living being in its pursuit of truth or of falsehood, as the case may be—of all, in short, with which we feel ourselves to be in harmony.

There can be no doubt that Goethe, in thus philosophizing, dipped his bucket into the well of profound self-knowledge. He was obviously stung to the quick by the neglect of the physicists. He had been the idol of the world, and, accustomed as he was to the incense of praise, he felt sorely that any class of men should treat what he thought important with indifference or contempt. He had, it must be admitted, some ground for skepticism as to the rectitude of scientific judgments, seeing that his researches on morphology met at first no response, though they were afterward lauded by scientific men. His anger against Newton incorporates itself in sharp and bitter sarcasm. Through the whole of Newton's experiments, he says, there runs a display of pedantic accuracy, but how the matter really stands, with Newton's gift of observation, and with his experimental aptitudes, every man possessing eyes and senses may make himself aware. It may, he says, be boldly asked, Where can the man be found, possessing the extraordinary gifts of Newton, who would suffer himself to be deluded by such a hocus pocus if he had not in the first instance willfully deceived himself? Only those who know the strength of self-deception, and the extent to which it sometimes trenches on dishonesty, are in a condition to explain the conduct of Newton, and of Newton's school. "To support his unnatural theory," he continues, "Newton heaps experiment on experiment, fiction upon fiction, seeking to dazzle where he can not convince."

It may be that Goethe is correct in affirming that the will and prejudice of the individual are all-influential. We must, however, add the qualifying words, "as far as the individual is concerned." For in science there exists, apart from the individual, objective truth; and the fate of Goethe's own theory, though commended to us by so great a name, illustrates how, in the progress of humanity, the individual, if he err, is left stranded and forgotten—truth, independent of the individual, being more and more grafted on to that tree of knowledge which is the property of the human race.

The imagined ruin of Newton's theory did not satisfy Goethe's desire for completeness. He would explore the ground of Newton's error, and show how it was that one so highly gifted could employ his gifts for the enunciation and diffusion of such unmitigated nonsense. It was impossible to solve the riddle on purely intellectual grounds. Scientific enigmas, he says, are often only capable of ethical solution, and with this maxim in his mind he applies himself, in the second volume of the "Farbenlehre," to the examination of "Newton's Persönlichkeit." He seeks to connect him with, or rather to detach him from, the general character of the English nation that sturdy and competent race which prizes above all things the freedom of individual action. Newton was born in a storm-tossed time—none, indeed, more pregnant in the history of the world. He was a year old when Charles I. was beheaded, and he lived to see the First George upon the throne. The shock of parties was in his ears, changes of ministries, parliaments, and armies were occurring before his eyes while the throne itself, instead of passing on by inheritance, was taken possession of by a stranger. What, asks Goethe, are we to think of a man who could put aside the claims, seductions, and passions incident to such a time, for the purpose of tranquilly following out his bias as an investigator?

So singular a character arrests the poet's attention. He had laid down his theory of colors; he must add to it a theory of Newton. The great German is here at home, and Newton could probably no more have gone into these disquisitions regarding character than Goethe could have developed the physical theories of Newton. He prefaces his sketch of his rival's character by reflections and considerations regarding character in general. Every living thing, down to the worm that wriggles when trod upon, has a character of its own. In this sense even the weak and cowardly have characters, for they will give up the honor and fame which most men prize highest, so that they may vegetate in safety and comfort. But the word character is usually applied to the case of an individual with great qualities, who pursues his object undeviatingly, and without permitting either difficulty or danger to deflect him from his course.

"Although here, as in other cases," says Goethe, "it is the exuberant (Ueberschwängliche) that impresses the imagination, it must not be imagined that this attribute has anything to do with moral feeling. The main foundation of the moral law is a good will,[3] which, in accordance with its own nature, is anxious only for the right. The main foundation of character is a strong will, without reference to right or wrong, good or bad, truth or error. It is that quality which every party prizes in its members. A good will cherishes freedom, it has reference to the inner man and to ethical aims. The strong will belongs to nature and has reference to the outer world—to action. And, inasmuch as the strong will in this world is swayed and limited by the conditions of life, it may almost be assumed as certain that it is only by accident that the exercise of a strong will and of moral rectitude find themselves in harmony with each other." In determining Newton's position in the series of human characters, Goethe helps himself to images borrowed from the physical cohesion of matter. Thus, he says, we have strong, firm, compact, elastic, flexible, rigid or obstinate, and viscous characters. Newton's character he places under the head of rigid or obstinate, and his theory of colors Goethe pronounces to be a petrified aperçu.

Newton's assertion of his theory and his unwavering adherence to it to the end of his life Goethe ascribes straight off to moral obliquity on Newton's part. In the heat of our discussion, he says, we have even ascribed to him a certain dishonesty. Man, he says, is subject to error, but when errors form a series, which is followed pertinaciously, the erring individual becomes false to himself and to others. Nevertheless, reason and conscience will not yield their rights. We may belie them, but they are not deceived. It is not too much to say that, the more moral and rational a man is, the greater will be his tendency to lie when he falls into error, and the vaster will be that error when he makes up his mind to persist in it.

This is all intended to throw light upon Newton, but, when Goethe passes from Newton himself to his followers, the small amount of reserve which he exhibited when dealing with the master entirely disappears. He mocks their blunders as having not even the merit of originality. He heaps scorn on Newton's imitators. The expression of even a truth, he says, loses grace in repetition, while the repetition of a blunder is impertinent and ridiculous. To liberate one's self from an error is difficult, sometimes indeed impossible for even the strongest and most gifted minds. But to take up the error of another, and persist in it with stiff-necked obstinacy, is a proof of poor qualities. The obstinacy of a man of originality when he errs may make us angry, but the stupidity of the copyist irritates and renders us miserable. And, if in our strife with Newton we have sometimes passed the bounds of moderation, the whole blame is to be laid upon the school of which Newton was the head, whose incompetence is proportional to its arrogance, whose laziness is proportional to its self-sufficiency, and whose virulence and love of persecution hold each other in perfect equilibrium.

There is a great deal more invective of this kind; but you will probably, and not without sadness, consider this enough. Invective may be a sharp weapon, but over-use blunts its edge. Even when the denunciation is just and true, it is an error of art to indulge in it too long. We not only incur the risk of becoming vapid, but of actually inverting the force of reprobation which we seek to rouse, and of bringing it back by recoil upon ourselves. At suitable intervals, separated from each other by periods of dignified reserve, invective may become a real power of the tongue or pen. But indulged in constantly it degenerates into scolding, and then, instead of being regarded as a proof of strength, it is accepted, even in the case of a Goethe, as an evidence of weakness and lack of self-control.

If it were possible to receive upon a mirror Goethe's ethical image of Newton and to reflect it back upon its author, then, as regards vehement persistence in wrong thinking, the image would accurately coincide with Goethe himself. It may be said that we can only solve the character of another by the observation of our own. This is true; but in the portraiture of character we are not at liberty to mix together subject and object as Goethe mixed himself with Newton. So much for the purely ethical picture. On the scientific side something more is to be said. I do not know whether psychologists have sufficiently taken into account that, as regards intellectual endowment, vast wealth may coexist with extreme poverty. I do not mean to give utterance here to the truism that the field of culture is so large that the most gifted can master only a portion of it. This would be the case supposing the individual at starting to be, as regards natural capacity and potentiality, rounded like a sphere. Something more radical is here referred to. There are individuals who at starting are not spheres, but hemispheres; or, at least, spheres with a segment sliced away full-orbed on one side, but flat upon the other. Such incompleteness of the mental organization no education can repair. Now, the field of science is sufficiently large, and its studies sufficiently varied, to bring to light in the same individual antitheses of endowment like that here indicated.

So far as science is a work of ordering and classification, so far as it consists in the discovery of analogies and resemblances which escape the common eye—of the fundamental identity which often exists among apparently diverse and unrelated things—so far, in short, as it is observational, descriptive, and imaginative, Goethe, had he chosen to make his culture exclusively scientific, might have been without a master, perhaps even without a rival. The instincts and capacities of the poet lend themselves freely to the natural history sciences. But, when we have to deal with stringently physical and mechanical conceptions, such instincts and capacities are out of place. It was in this region of mechanical conceptions that Goethe failed. It was on this side that his sphere of capacity was sliced away. He probably was not the only great man who possessed a spirit thus antithetically mixed. Aristotle himself was a mighty classifier, but not a stringent physical reasoner. And, had Newton attempted to produce a "Faust," the poverty of his intellect on the poetic and dramatic side might have been rendered equally manifest. But here, if not always, Newton abstained from attempting that for which he had no capacity, while the exuberance of Goethe's nature caused him to undertake a task for which he had neither ordination nor vocation, and in the attempted execution of which his deficiencies became revealed.

One task among many—one defeat amid a hundred triumphs. But any recognition on my part of Goethe's achievements in other realms of intellectual action would, I fear, be regarded as impertinent. You remember the story of the First Napoleon when the Austrian plenipotentiary, in arranging a treaty of peace, began by formally recognizing the French Republic. "Efface that," said the First Consul; "the French Republic is like the sun; he is blind who fails to recognize it." And were I to speak of recognizing Goethe's merits, my effacement would be equally well deserved. "Goethe's life," says Carlyle, "if we examine it, is well represented in that emblem of a solar day. Beautifully rose our summer sun, gorgeous in the red, fervid east, scattering the specters and sickly damps, of both of which there were enough to scatter; strong, benignant in his noonday clearness, walking triumphant through the upper realms—and now mark also how he sets! ‘So stirbt ein Held’; so dies a hero!"

Two grander illustrations of the aphorism "To err is human" can hardly be pointed out in history than Newton and Goethe. For Newton went astray not only as regards the question of achromatism, but also as regards a vastly larger question touching the nature of light. But though as errors they fall into the same category, the mistake of Newton was qualitatively different from that of Goethe. Newton erred in adopting a wrong mechanical conception in his theory of light, but in doing so he never for a moment quitted the ground of strict scientific method. Goethe erred in seeking to ingraft in his "Farbenlehre" methods altogether foreign to physics on to the treatment of a purely physical theme.

We frequently hear protests made against the cold mechanical mode of dealing with aesthetic phenomena employed by scientific men. The dissection by Newton of the light to which the world owes all its visible beauty and splendor seemed to Goethe a desecration. We find, even in our own day, the endeavor of Helmholtz to arrive at the principles of harmony and discord in music resented as an intrusion of the scientific intellect into a region which ought to be sacred to the human heart. But all this opposition and antagonism has for its essential cause the incompleteness of those with whom it originates. The feelings and aims with which Newton and Goethe respectively approached Nature were radically different, but they had an equal warrant in the constitution of man. As regards our tastes and tendencies, our pleasures and pains, physical and mental, our action and passion, our sorrows, sympathies, and joys, we are the heirs of all the ages that preceded us; and, of the human nature thus handed down, poetry is an element just as much as science. The emotions of man are older than his understanding, and the poet who brightens, purifies, and exalts these emotions, may claim a position in the world at least as high and as well-assured as that of the man of science. They minister to different but to equally permanent needs of human nature; and the incompleteness of which I complain consists in the endeavor on the part of either to exclude the other. There is no fear that the man of science can ever destroy the glory of the lilies of the field; there is no hope that the poet can ever successfully contend against our right to examine, in accordance with scientific method, the agent to which the lily owes its glory. There is no necessary encroachment of the one field upon the other. Nature embraces them both, and man, when he is complete, will exhibit as large a toleration.

  1. A discourse delivered in the Royal Institution of Great Britain, on Friday evening, March 19, 1880.
  2. Dollond was the son of a Huguenot. Up to 1752 he was a silk-weaver at Spitalfields; he afterward became an optician.
  3. I have rendered Goethe's "gute Wille" by good will; his "Wollen," which he contrasts with "Wille," I have rendered by strong will.