Note, in this respect, the principle of the mirror as another instance of the fact that the interplay between light and an illumined surface can have on the visual ray an effect similar to that of external space. For the optical processes which occur on the surface of a mirror are such that, whilst taking place on a two-dimensional plane, they evoke in our consciousness pictures of exactly the same nature as if we were looking through the mirror into the space behind it.

*

The value of our picture of the colour-polarity is shown further if we observe how natural phenomena based on the same kind of polarity in other realms of nature fit in with it. We remember that one of Goethe's starting-points in his investigation of the riddle of colour was the observation that of the totality of colours one part is experienced as 'warm' and the other as 'cold'. Now we can go further and say that the colours of the spherical pole are experienced as cold, those of the radial pole as warm. This corresponds precisely to the polarity of snow-formation and volcanic activity. The former, being the spherically directed process, requires physically low temperatures; the latter, being the radially directed process, requires high temperatures. Here, once more, we see with what objectivity the human senses register the facts of the outer world.

Another realm of phenomena based on a similar polar order is that of electricity. When we studied the negative and positive poles of the vacuum tube, with regard to the polar distribution of radius and sphere, our attention was drawn to the colours appearing on the two electrodes - red at the (positive) anode, blue at the (negative) cathode. Again we find a coincidence with the natural order of the colours.

Note how the qualitative dynamic method employed here brings into direct view the relationship between light and electricity, while it precludes the mistake of tracing light processes to those of electricity, as modern science does. Nor are electric processes 'explained' from this point of view merely as variations of light processes. Rather is the relation between light and electricity seen to be based on the fact that all polarities arising perceptibly in nature are creations of the same primeval polarity, that of Levity and Gravity. The interplay of Levity and Gravity can take on many different forms which are distinguished essentially by differences in cosmic age. Thus the colour-polarity in its primal form, made manifest by the heavens, differs as much from the corresponding polarity shown by the vacuum tube, as does the lightning in the heights from the electric spark.

*

With the aid of what we have learnt here concerning outer light-processes we shall turn once more to the activity of our own inner light.

We may expect by now that our eye is fitted with two modes of seeing activity, polar to each other, and that the way in which they come into operation depends on whether the interplay of positive and negative density outside the eye leads to the appearance of the blue-violet or of the yellow-red side of the colour-scale. Such a polarity in the activity of the eye can indeed be established. Along with it goes a significant functional difference between the two eyes (not unlike that shown of the two hands).

To observe this we need simply to compare the two eyes of a person in a photograph by covering alternately the right and the left half of the face. Nearly always it will be found that the right eye looks out clearly into the world with an active expression, and the left eye with a much gentler one, almost held back. Artists are well aware of this asymmetry, as of others in the human countenance, and are careful to depict it. An outstanding example is Raphael's Sistine Madonna, where in the eyes and whole countenance both of Mother and Child this asymmetry can be studied in a specially impressive way.

Inner observation leads to a corresponding experience. A convenient method is to exercise the two eyes in complete darkness, in the following way. One eye is made to look actively into the space in front of it, as if it would pierce the darkness with its visual ray, while the activity of the other eye is held back, so that its gaze rests only superficially, as it were, on the darkness in front of it. Experience shows that most people find it natural to give the active note to the right eye, and the passive note to the left.

Once one has grown conscious of this natural difference between the two eyes, it is quite easily detected while one is looking normally into the light-filled environment. We thereby realize that for the two eyes to act differently in this way is the usual thing.

As an instance where this fact is well observed and effectively made use of, that of shooting may be mentioned here, especially shooting at flying game. Those who train in this sport learn to make a completely different use of the two eyes in sighting the target. The naturally more active eye - only once in about fifty cases is it the left - is called by them the 'master-eye'. Whilst the less actively gazing eye is usually employed for surveying the field as a whole into which the target is expected to enter, the master-eye is used for making active contact with the target itself ('throwing' oneself on the target 'through' the eye).

One further observation may be added. If one looks with rested eyes and in very faint daylight (perhaps in the early morning on awakening) at a white surface, while opening and closing the eyes alternately, then the white surface looks faintly reddish to the 'master-eye', and faintly bluish to the other.

*

Following the lines of our treatment of after-images in the last chapter, we will next inquire into the anatomical and physiological basis of the two opposite sight-activities. In the previous instance we found this in the polarity of nerve and blood. This time we must look for it in a certain twofold structure of the eye itself. We shall best perceive this by watching the 'becoming' of the eye, thus again following a method first shown by Goethe.

Fig. 11 shows the human eye in different stages of its embryonic formation. The eye is clearly seen to consist of two parts essentially different in origin. Growing out from the interior of the embryonic organism is a structure that is gradually pushed in, and in its further development becomes the entire posterior part of the eye, destined to carry its life-imbued functions. A second independent part grows towards this from outside; this is at first a mere thickening of the embryonic skin formation, but later it loosens itself and presses forward into the interior of the cup-shaped structure. It is gradually enclosed by this, and evolves finally into that part of the finished eye which embodies the optical apparatus functioning according to purely physical laws.

This series of forms shows that in the embryonic formation of the eye we are confronted with two processes, one of spherical, and the other of radial orientation. Consequently the two parts of the eye are differentiated in such a way that the posterior part, which has grown forth radially from the embryonic organism, as the life-filled element represents the sulphur-pole of the total eye, while the anterior part, with its much more crystalline nature, having grown spherically towards the organism, represents the eye's salt-pole.

Closer inspection into the connexion of the two visual activities of the eye with its basic corporeal parts reveals that here, at the outermost boundary of the human organism, we encounter once more that peculiar reversal of functions which we have already several times met in various realms of nature. For the anterior part of the eye - its salt-pole - which has come into being through a spherically directed formative process, seems to be the one through which we exercise the perceptive activity streaming out radially from the eye, whilst the posterior part - the eye's sulphur-pole - which has come into being through radially directed formative action, serves that form of seeing which is more receptive and is carried out in a plane-wise manner.

Considerations of this kind, and they alone, enable us also to draw true comparisons between the different sense-organs. Take the organ of hearing. Usually the ear is assumed to fill the same role in the field of hearing as does the eye in the field of seeing. In fact the ear corresponds to only one half of the eye; the other half must be looked for in the larynx. In other words, the two parts of the eye are represented in the realm of hearing by two separate organs, ear and larynx. Speaking from the aspect of metamorphosis, the vital part of our eye may be regarded as our 'light-ear'; the crystalline part, as our 'light-larynx'. In order to come consciously to a perception of sight we must 'listen' to the 'deeds and sufferings' of light, while at the same time we meet them with the help of the 'speaking' of our inner light. Something similar holds good for hearing. In fact, observation reveals that we take in no impression of hearing unless we accompany it with an activity of our larynx, even though a silent one. The significance of this fact for the total function of hearing will occupy us more fully later.

*

Our insight into the polar nature of visual activity will enable us now to link the external interplay of Light and Dark - to which the physical colours owe their existence - to that play of forces which we ourselves set in motion when our eye meets the world of colours in their polar differentiation.

We established earlier that in the cold colours the role of darkness belongs to the pole of levity or negative density, and the role of lightness to the pole of gravity or positive density, whereas in the case of the warm colours the roles are reversed. Let us now unite with this the insight we have meanwhile gained into the two kinds of activity in seeing - the receptive, 'left-eyed' and the radiating, 'right-eyed' - which mediate to us the experience of the positive or negative density of space spread out before our eyes. Taking together the results of outer and inner observation, we can express the polarity ruling in the realm of colour as follows.

If lightness and darkness as elements of colour, meet us in such a way that lightness, by reason of its positive density, calls forth 'left-eyed' activity, and darkness, by reason of its negative density, 'right-eyed' activity, then our soul receives the impression of the colour blue and colours related to blue. If lightness and darkness meet us so that we see the former in a 'right-eyed', and the latter in a 'left-eyed' way, then we experience this as the presence of yellow and the colours related to it.

The reason why we usually fail to observe the different kinds of interplay of the two modes of seeing, when we perceive one or other of the two categories of colour, is because in ordinary sight both eyes exercise each of the two activities without our becoming aware which is the leading one in a particular eye. If, however, one has come to a real experience of the inner polarity of the visual act, one needs only a little practice to realize the distinction. For example, if one looks at the blue sky, notably at noon-time, on the side away from the sun, or at the morning or evening sky, shining yellow and red, one quickly becomes conscious of how our eyes take hold of the particular contribution which Light and Dark make to one or other of the two colour appearances.

*

In the natural course of our argument we had to keep at first to the appearance of colours as they come freely before us in space. The results we have obtained, however, hold good equally well for the permanent tints of material objects, as the following example will show.

A fact known to science is that red and blue surface colours, when illumined by light of steadily diminishing intensity, are seen to reverse their normal ratio of brightness. This phenomenon can be seen in nature, if, for instance, one observes a bed of blue and red flowers in the fading evening light and compares the impression with that which the same flowers make in bright daylight. If the phenomenon is reproduced artificially, the actual transition from one state to the other can be clearly observed. The easiest way is to place a red and a blue surface side by side under an electric light whose intensity can be gradually lessened by means of a sliding resistance. Here, as much as in the natural phenomenon, our reason finds it difficult to acknowledge that the surface gleaming in a whitish sheen should be the one which ordinarily appears as darkling blue, and that the one disappearing into darkness should be the surface which normally presents itself as radiant red.

This riddle is readily solved if we apply what we have learnt about the particular shares of lightness and darkness in these two colours, and if we link this up with the respective forms of seeing exercised by our two eyes. To the dim light, clearly, our eyes will respond more with the 'left-eyed' than with the 'right-eyed' form of vision. Now we know that it is 'left-eyed' vision which is roused by the lightness-component in blue and the darkness-component in red. It is only to be expected, therefore, that these elements should become conspicuous when in the dim light our seeing is mainly 'left-eyed'. This solution of the problem makes us realize further, that the laws which Goethe first found for the coming into appearance of colours freely hovering in space are indeed applicable to the fixed material colours as well.

1 It will be well to remember here the discussion of our experience of temperature through the sense of warmth in Chapter VIII (p. 134f.).

2 Along these lines the true solution of the problem of the so-called coloured shadows will be found, Goethe studied this without finding, however, a satisfactory answer.

CHAPTER XVII

Optics of the Doer

Three basic concepts form the foundation for the present-day scientific description of a vast field of optical phenomena, among them the occurrence of the spectral colours as a result of light passing through a transparent medium of prismatic shape. They are: 'optical refraction', 'light-ray', and 'light-velocity' - the latter two serving to explain the first. In a science of optics which seeks its foundation in the intercourse between man's own visual activity and the doings and sufferings of light, these three concepts must needs undergo a decisive change, both in their meaning and in their value for the description of the relevant optical phenomena. For they are all purely kinematic concepts typical of the onlooker-way of conceiving things - concepts, that is, to which nothing corresponds in the realm of the actual phenomena.

Our next task, therefore, will be, where possible, to fill these concepts with new meaning, or else to replace them by other concepts read from the actual phenomena. Once this is done the way will be free for the development of the picture of the spectrum phenomenon which is in true accord with the Goethean conception of Light and Colour.

*

The first to be brought in this sense under our examination is the concept of the 'light-ray'.

In present-day optics this concept signifies a geometrical line of infinitely small width drawn, as it were, by the light in space, while the cone or cylinder of light actually filling the space is described as being composed of innumerable such rays. In the same way the object producing or reflecting light is thought of as composed of innumerable single points from which the light-rays emerge. All descriptions of optical processes are based upon this conception.

Obviously, we cannot be satisfied with such a reduction of wholes into single geometrically describable parts, followed by a reassembling of these parts into a whole. For in reality we have to do with realms of space uniformly filled with light, whether conical or cylindrical in form, which arise through certain boundaries being set to the light. In optical research we have therefore always to do with pictures, spatially bounded. Thus what comes before our consciousness is determined equally by the light calling forth the picture, and by the unlit space bordering it.

Remembering the results of our earlier study, we must say further of such a light-filled realm that it lacks the quality of visibility and therefore has no colour, not even white. Goethe and other 'readers', such as Reid and Ruskin, tried continually to visualize what such a light-filled space represents in reality. Hence they directed their attention first to those spheres where light manifests its form-creative activity, as in the moulding of the organ of sight in animal or man, or in the creation of the many forms of the plant kingdom - and only then gave their mind to the purely physical light-phenomena. Let us use the same method to form a picture of a light-filled space, and to connect this with the ideas we have previously gained on the co-operation in space of levity and gravity.

Suppose we have two similar plant-seeds in germ; and let one lie in a space filled with light, the other in an unlit space. From the different behaviour of the two seeds we can observe certain differences between the two regions of space. We note that within the light-filled region the spiritual archetype of the plant belonging to the seed is helped to manifest itself physically in space, whereas in the dark region it receives no such aid. For in the latter the physical plant, even if it grows, does not develop its proper forms. This tells us, in accordance with what we have learnt earlier, that in the two cases there is a different relation of space to the cosmically distant, all-embracing plane. Thus inside and outside the light-region there exists a quite different relation of levity and gravity - and this relation changes abruptly at the boundaries of the region. (This fact will be of especial importance for us when we come to examine the arising of colours at the boundary of Light and Dark, when light passes through a prism.)

*

After having replaced the customary concept of the light-bundle composed of single rays by the conception of two dynamically polar realms of space bordering each other, we turn to the examination of what is going on dynamically inside these realms. This will help us to gain a proper concept of the propagation of light through space.

In an age when the existence of a measurable light-velocity seems to belong to the realm of facts long since experimentally proved; when science has begun to measure the universe, using the magnitude of this velocity as a constant, valid for the whole cosmos; and when entire branches of science have been founded on results thus gained, it is not easy, and yet it cannot be avoided, to proclaim that neither has an actual velocity of light ever been measured, nor can light as such ever be made subject to such measurement by optical means - and that, moreover, light, by its very nature, forbids us to conceive of it as possessing any finite velocity.

With the last assertion we do not mean to say that there is nothing going on in connexion with the appearance of optical phenomena to which the concept of a finite velocity is applicable. Only, what is propagated in this way is not the entity we comprise under the concept of 'light'. Our next task, therefore, will be to create a proper distinction between what moves and what does not move spatially when light is active in the physical world. Once more an historical retrospect will help us to establish our own standpoint with regard to the existing theories.

The first to think of light as possessing a finite velocity was Galileo, who also made the first, though unsuccessful, attempt to measure it. Equally unsuccessful were attempts of a similar nature made soon afterwards by members of the Accademia del Cimento. In both cases the obvious procedure was to produce regular flashes of light and to try to measure the time which elapsed between their production and their observation by some more or less distant observer. Still, the conviction of the existence of such a velocity was so deeply ingrained in the minds of men that, when later observations succeeded in establishing a finite magnitude for what seemed to be the rate of the light's movement through space, these observations were hailed much more as the quantitative value of this movement than as proof of its existence, which was already taken for granted.

A clear indication of man's state of mind in regard to this question is given in the following passage from Huygens's famous Traité de la Lumière, by which the world was first made acquainted with the concept of light as a sort of undulatory movement.

'One cannot doubt that light consists in the movement of a certain substance. For if one considers its production one finds that here on the earth it is chiefly produced by fire and flame, which without doubt contain bodies in rapid motion, for they dissolve and melt numberless other bodies. Or, if one considers its effects, one sees that light collected, for instance, by a concave mirror has the power to heat like fire, i.e. to separate the parts of the bodies; this assuredly points to movement, at least in true philosophy in which one traces all natural activity to mechanical causes. In my opinion one must do this, or quite give up all hope of ever grasping anything in physics.'

In these words of Huygens it must strike us how he first provides an explanation for a series of phenomena as if this explanation were induced from the phenomena themselves. After he has drawn quite definite conclusions from it, he then derives its necessity from quite other principles - namely, from a certain method of thinking, accepting this as it is, unquestioned and unalterably established. We are here confronted with an 'unlogic' characteristic of human thinking during its state of isolation from the dynamic substratum of the world of the senses, an unlogic which one encounters repeatedly in scientific argumentation once one has grown aware of it. In circles of modern thinkers where such awareness prevails (and they are growing rapidly to-day) the term 'proof of a foregone conclusion' has been coined to describe this fact.1

'Proof of a foregone conclusion' is indeed the verdict at which one arrives in respect of all the observations concerned with the velocity of light - whether of existing phenomena detectable in the sky or of terrestrial phenomena produced artificially - if one studies them with the attitude of mind represented by the child in Hans Andersen's story. In view of the seriousness of the matter it will not be out of place if we discuss them here as briefly as possible, one by one.2

The relevant observations fall into two categories: observations of certain astronomical facts from which the existence of a finite velocity of light and its magnitude as an absolute property of it has been inferred; and terrestrial experiments which permitted direct observation of a process of propagation connected with the establishment of light in space resulting in the measurement of its speed. To the latter category belong the experiments of Fizeau (1849) and Foucault (1850) as well as the Michelson-Morley experiment with its implications for Einstein's Theory of Relativity. The former category is represented by Roemer's observations of certain apparent irregularities in the times of revolution of one of Jupiter's moons (1676), and by Bradley's investigation into the reason for the apparent rhythmic changes of the positions of the fixed stars (1728).

We shall start with the terrestrial observations, because in their case alone is the entire path of the light surveyable, and what is measured therefore is something appertaining with certainty to every point of the space which spreads between the source of the light and the observer. For this reason textbooks quite rightly say that only the results drawn from these terrestrial observations have the value of empirically observed facts. (The interpretation given to these facts is another question.)

Now, it is a common feature of all these experiments that by necessity they are based on an arrangement whereby a light-beam can be made to appear and disappear alternately. In this respect there is no difference between the first primitive attempts made by Galileo and the Academicians, and the ingeniously devised experiments of the later observers, whether they operate with a toothed wheel or a rotating mirror. It is always a flash of light - and how could it be otherwise? - which is produced at certain regular intervals and used for determining the speed of propagation.

Evidently what in all these cases is measured is the speed with which a beam of light establishes itself in space. Of what happens within the beam, once it is established, these observations tell nothing at all. The proof they are held to give of the existence of a finite speed of light, as such, is a 'proof of a foregone conclusion'. All they tell us is that the beam's front, at the moment when this beam is first established, travels through space with a finite velocity and that the rate of this movement is such and such. And they tell us nothing at all about other regions of the cosmos.

That we have to do in these observations with the speed of the light-front only, and not of the light itself, is a fact fully acknowledged by modern physical optics. Since Lord Rayleigh first discussed this matter in the eighties of the last century, physicists have learnt to distinguish between the 'wave-velocity' of the light itself and the velocity of an 'impressed peculiarity', the so-called 'group-velocity', and it has been acknowledged that only the latter has been, and can be, directly measured. There is no possibility of inferring from it the value of the 'wave-velocity' unless one has a complete knowledge of the properties of the medium through which the 'groups' travel. Nevertheless, the modern mind allows itself to be convinced that light possesses a finite velocity and that this has been established by actual measurement. We feel reminded here of Eddington's comment on Newton's famous observations: 'Such is the glamour of a historical experiment.' (Chapter XIV.)3

Let us now turn to Roemer and Bradley. In a certain sense Roemer's observations and even those of Bradley rank together with the terrestrial measurements. For Roemer used as optical signals the appearance and disappearance of one of Jupiter's moons in the course of its revolution round the planet; thus he worked with light-flashes, as the experimental investigations do. Hence, also, his measurements were concerned - as optical science acknowledges - with group-velocity only. In fact, even Bradley's observations, although he was the only one who operated with continuous light-phenomena, are exposed to the charge that they give information of the group-velocity of light, and not of its wave-velocity. However, we shall ignore these limitations in both cases, because there are quite other factors which invalidate the proofs they are held to give, and to gain a clear insight into these factors is of special importance for us.

Roemer observed a difference in the length of time during which a certain moon of Jupiter was occulted by the planet's body, and found that this difference underwent regular changes coincident with the changes in the earth's position in relation to Jupiter and the sun. Seen from the sun, the earth is once a year in conjunction with Jupiter, once in opposition to it. It seemed obvious to explain the time-lag in the moon's reappearance, when the earth was on the far side of the sun, by the time the light from the moon needed to cover the distance marked by the two extreme positions of the earth - that is, a distance equal to the diameter of the earth's orbit. On dividing the observed interval of time by the accepted value of this distance, Roemer obtained for the velocity of light a figure not far from the one found later by terrestrial measurements.

We can here leave out of account the fact that Roemer's reasoning is based on the assumption that the Copernican conception of the relative movements of the members of our solar system is the valid conception, an assumption which, as later considerations will show, cannot be upheld in a science which strives for a truly dynamic understanding of the world. For the change of aspect which becomes necessary in this way does not invalidate Roemer's observation as such; it rules out only the customary interpretation of it. Freed from all hypothetical by-thought, Roemer's observation tells us, first, that the time taken by a flash of light travelling from a cosmic light-source to reach the earth varies to a measurable extent, and, secondly, that this difference is bound up with the yearly changes of the earth's position in relation to the sun and the relevant planetary body.

We leave equally out of account the fact that our considerations of the nature of space in Chapter XII render it impermissible to conceive of cosmic space as something 'across' which light (or any other entity) can be regarded as travelling this or that distance in this or that time. What matters to us here is the validity of the conclusions drawn from Roemer's discovery within the framework of thought in which they were made.

Boiled down to its purely empirical content, Roemer's observation tells us solely and simply that within the earth's cosmic orbit light-flashes travel with a certain measurable speed. To regard this information as automatically valid, firstly for light which is continuously present, and secondly for everywhere in the universe, rests again on nothing but a foregone conclusion.

Precisely the same criticism applies to Bradley's observation, and to an even higher degree. What Bradley discovered is the fact that the apparent direction in which we see a fixed star is dependent on the direction in which the earth moves relatively to the star, a phenomenon known under the name of 'aberration of light'. This phenomenon is frequently brought to students' understanding by means of the following or some similar analogy.

Imagine that a machine-gun in a fixed position has sent its projectile right across a railway-carriage so that both the latter's walls are pierced. If the train is at rest, the position of the gun could be determined by sighting through the shot-holes made by the entrance and exit of the bullet. If, however, the train is moving at high speed, it will have advanced a certain distance during the time taken by the projectile to cross the carriage, and the point of exit will be nearer the rear of the carriage than in the previous case. Let us now think of an observer in the train who, while ignorant of the train's movement, undertook to determine the gun's position by considering the direction of the line connecting the two holes. He would necessarily locate the gun in a position which, compared with its true position, would seem to have shifted by some distance in the direction of the train's motion. On the other hand, given the speed of the train, the angle which the line connecting the two holes forms with the true direction of the course of the projectile - the so-called angle of aberration - provides a measure of the speed of the projectile.

Under the foregone conclusion that light itself has a definite velocity, and that this velocity is the same throughout the universe, Bradley's observation of the aberration of the stars seemed indeed to make it possible to calculate this velocity from the knowledge of the earth's own speed and the angle of aberration. This angle could be established by comparing the different directions into which a telescope has to be turned at different times of the year in order to focus a particular star. But what does Bradley's observation tell us, once we exclude all foregone conclusions?

As the above analogy helps towards an understanding of the concept of aberration, it will be helpful also to determine the limits up to which we are allowed to draw valid conclusions from the supposed occurrence itself. A mind which is free from all preconceived ideas will not ignore the fact that the projectile, by being forced to pierce the wall of the carriage, suffers a considerable diminution of its speed. The projectile, therefore, passes through the carriage with a speed different from its speed outside. Since, however, it is the speed from hole to hole which determines the angle of aberration, no conclusion can be drawn from the latter as to the original velocity of the projectile. Let us assume the imaginary case that the projectile was shot forth from the gun with infinite velocity, and that the slowing-down effect of the wall was great enough to produce a finite speed of the usual magnitude, then the effect on the position of the exit hole would be precisely the same as if the projectile had moved all the time ' with this speed and not been slowed down at all.

Seeing things in this light, the scientific Andersen child in us is roused to exclaim: 'But all that Bradley's observation informs us of , with certainty is a finite velocity of the optical process going on inside the telescope!' Indeed, if someone should claim with good reason (as we shall do later on) that light's own velocity is infinite, and (as we shall not do) that the dynamic situation set up in the telescope had the effect of slowing down the light to the measured velocity - there is nothing in Bradley's observation which could disprove these assertions.

*

Having thus disposed of the false conclusions drawn by a kinematically orientated thinking from the various observations and measurements of the velocity which appears in connexion with light, we can carry on our own studies undisturbed. Two observations stand before us representing empirically established facts: one, that in so far as a finite velocity has been measured or calculated from other observations, nothing is known about the existence or magnitude of such a velocity except within the boundaries of the dynamic realm constituted by the earth's presence in the universe; the other, that this velocity is a 'group'-velocity, that is, the velocity of the front of a light-beam in process of establishment. Let us see what these two facts have to tell us when we regard them as letters of the 'word' which light inscribes into the phenomenal world as an indication of its own nature.

Taking the last-named fact first, we shall make use of the following comparison to help us realize how little we are justified in drawing from observations of the front speed of a light-beam any conclusions concerning the kinematic conditions prevailing in the interior of the beam itself. Imagine the process of constructing a tunnel, with all the efforts and time needed for cutting its passage through the resisting rock. When the tunnel is finished the activities necessary to its production are at an end. Whereas these continue for a limited time only, they leave behind them permanent traces in the existence of the tunnel, which one can describe dynamically as a definite alteration in the local conditions of the earth's gravity. Now, it would occur to no one to ascribe to the tunnel itself, as a lasting quality, the speed with which it had been constructed. Yet something similar happens when, after observing the velocity required by light to lay hold on space, this velocity is then attributed to the light as a quality of its own. It was reserved for a mode of thought that could form no concept of the real dynamic of Light and Dark, to draw conclusions as to the qualities of light from experiences obtained through observing its original spreading out into space.

To speak of an independently existing space within which light could move forward like a physical body, is, after what we have learnt about space, altogether forbidden. For space in its relevant structure is itself but a result of a particular co-ordination of levity and gravity or, in other words, of Light and Dark. What we found earlier about the qualities of the two polar spaces now leads us to conceive of them as representative of two limiting conditions of velocity: absolute contraction representing zero velocity; absolute expansion, infinite velocity (each in its own way a state of 'rest'). Thus any motion with finite velocity is a mean between these two extremes, and as such the result of a particular co-ordination of levity and gravity. This makes it evident that to speak of a velocity taking its course in space, whether with reference to light or to a physical body in motion, is something entirely unreal.

Let us now see what we are really told by the number 186,000 miles a second, as the measure of the speed with which a light-impulse establishes itself spatially. In the preceding chapter we learnt that the earth's field of gravity offers a definite resistance to our visual ray. What is true for the inner light holds good equally for the outer light. Using an image from another dynamic stratum of nature we can say that light, while appearing within the field of gravity, 'rubs' itself on this. On the magnitude of this friction depends the velocity with which a light-impulse establishes itself in the medium of the resisting gravity. Whereas light itself as a manifestation of levity possesses infinite velocity, this is forced down to the known finite measure by the resistance of the earth's field of gravity. Thus the speed of light which has been measured by observers such as Fizeau and Foucault reveals itself as a function of the gravitational constant of the earth, and hence has validity for this sphere only.1 The same is true for Roemer's and Bradley's observations, none of which, after what we have stated earlier, contradicts this result. On the contrary, seen from this viewpoint, Roemer's discovery of the light's travelling with finite speed within the cosmic realm marked by the earth's orbit provides an important insight into the dynamic conditions of this realm.

*

Among the experiments undertaken with the aim of establishing the properties of the propagation of light by direct measurements, quoted earlier, we mentioned the Michelson-Morley experiment as having a special bearing on Einstein's conceptual edifice. It is the one which has formed the foundation of that (earlier) part of Einstein's theory which he himself called the Special Theory of Relativity. Let us see what becomes of this foundation - and with it the conceptual edifice erected upon it - when we examine it against the background of what we have found to be the true nature of the so-called velocity of light.

It is generally known that modern ideas of light seemed to call for something (Huygens's 'certain substance') to act as bearer of the movement attributed to light. This led to the conception of an imponderable agency capable of certain movements, and to denote this agency the Greek word ether was borrowed. (How this word can be used again to-day in conformity with its actual significance will be shown in the further course of our discussions.) Nevertheless, all endeavours to find in the existence of such an ether a means of explaining wide fields of natural phenomena were disappointed. For the more exact concepts one tried to form of the characteristics of this ether, the greater the contradictions became.

One such decisive contradiction arose when optical means were used to discover whether the ether was something absolutely at rest in space, through which physical bodies moved freely, or whether it shared in their movement. Experiments made by Fizeau with running water seemed to prove the one view, those of Michelson and Morley, involving the movement of the earth, the other view. In the celebrated Michelson-Morley experiment the velocity of light was shown to be the same, in whatever direction, relative to the earth's own motion, it was measured. This apparent proof of the absolute constancy of light-velocity - which seemed, however, to contradict other observations - induced Einstein to do away with the whole assumption of a bearer of the movement underlying light, whether the bearer were supposed to be at rest or itself in motion. Instead, he divested the concepts of space and time, from which that of velocity is usually derived, of the absoluteness hitherto attributed to them, with the result that in his theory time has come to be conceived as part of a four-dimensional 'space-time continuum'.

In reality the Michelson-Morley experiment presents no problem requiring such labours as those of Einstein for its solution. For by this experiment nothing is proved beyond what can in any event be known - namely, that the velocity of the propagation of a light-impulse is constant in all directions, so long as the measuring is confined to regions where the density of terrestrial space is more or less the same. With the realization of this truth, however, Einstein's Special Theory loses its entire foundation. All that remains to be said about it is that it was a splendid endeavour to solve a problem which, rightly considered, does not exist.1

*

Now that we have realized that it is inadmissible to speak of light as consisting of single rays, or to ascribe to it a finite velocity, the concept of the refraction of light, as understood by optics to-day and employed for the explanation of the spectrum, also becomes untenable. Let us find out what we must put in its place.

The phenomenon which led the onlooker-consciousness to form the idea of optical refraction has been known since early times. It

consists in the fact, surprising at first sight, that an object, such as a coin, which lies at the bottom of a vessel hidden from an observer by the rim, becomes visible when the vessel is filled with water. Modern optics has explained this by assuming that from the separate points of the floor of the vessel light-rays go out to all sides, one ray falling in the direction of the eye of the observer. Hence, because of the positions of eye and intercepting rim there are a number of points from which no rays can reach the eye. One such point is represented by the coin (P in Fig. 12a). Now if the vessel is filled with water, light-rays emerging from it are held to be refracted, so that rays from the points hitherto invisible also meet the eye, which is still in its original position. The eye itself is not conscious of this 'break' in the light-rays, because it is accustomed to 'project' all light impressions rectilinearly out into space (Fig. 12b.). Hence, it sees P in the position of P'. This is thought to be the origin of the impression that the whole bottom of the vessel is raised.

This kind of explanation is quite in line with the peculiarity of the onlooker-consciousness, noted earlier, to attribute an optical illusion to the eye's way of working, while charging the mind with the task of clearing up the illusion. In reality it is just the reverse. Since the intellect can form no other idea of the act of seeing than that this is a passive process taking place solely within the eye, it falls, itself, into illusion. How great is this illusion we see from the fact that the intellect is finally obliged to make the eye somehow or other 'project' into space the impressions it receives - a process lacking any concrete dynamic content.

Once more, it is not our task to replace this way of 'explaining' the phenomenon by any other, but rather to combine the phenomenon given here with others of kindred nature so that the theory contained in them can be read from them direct. One other such phenomenon is that of so-called apparent optical depth, which an observer encounters when looking through transparent media of varying optical density. What connects the two is the fact that the rate of the alteration of depth, and the rate of change of the direction of light, are the same for the same media.

In present-day optics this phenomenon is explained with reference to the former. In proceeding like this, optical science makes the very mistake which Goethe condemned in Newton, saying that a complicated phenomenon was made the basis, and the simpler derived from the complex. For of these two phenomena, the simpler, since it is independent of any secondary condition, is the one showing that our experience of depth is dependent on the density of the optical medium. The latter phenomenon we met once before, though without reference to its quantitative side, when in looking at a landscape we found how our experiences of depth change in conformity with alterations in atmospheric conditions. This, then, served to make us aware that the way we apprehend things optically is the result of an interplay between our visual ray and the medium outside us which it meets.

It is exactly the same when we look through a vessel filled with water and see the bottom of it as if raised in level. This is in no sense an optical illusion; it is the result of what takes place objectively and dynamically within the medium, when our eye-ray passes through it. Only our intellect is under an illusion when, in the case of the coin becoming visible at the bottom of the vessel, it deals with the coin as if it were a point from which an individual ray of light went out.. .. etc., instead of conceiving the phenomenon of the raising of the vessel's bottom as one indivisible whole, wherein the coin serves only to link our attention to it.

*

Having thus cleared away the kinematic interpretation of the coin-in-the-bowl phenomenon, we may pass on to discuss the optical effect through which the so-called law of refraction was first established in science. Instead of picturing to ourselves, as is usually done, light-rays which are shifted away from or towards the perpendicular at the border-plane between two media of different optical properties, we shall rather build up the picture as light itself designs it into space.

We have seen that our inner light, as well as the outer light, suffers a certain hindrance in passing through a physical medium - even such as the earth's gravity-field. Whilst we may not describe this retardation, as is usually done, in terms of a smaller velocity of light itself within the denser medium, we may rightly say that density has the effect of lessening the intensity of the light. (It is the time required for the initial establishment of a light-filled realm which is greater within such a medium than outside it.) Now by its very nature the intensity of light cannot be measured in spatial terms. Yet there is a phenomenon by which the decrease of the inner intensity of the light becomes spatially apparent and thus spatially measurable. It consists in the alteration undergone by the aperture of a cone of light when passing from one optical medium to another.

If one sets in the path of a luminous cone a glass-walled trough filled with water, then, if both water and surrounding air are slightly clouded, the cone is seen to make a more acute angle within the water than outside it (Fig. 13). Here in an external phenomenon we meet the same weakening in the light's tendency to expand that we recognized in the shortening of our experience of depth on looking through a dense medium. Obviously, we expect the externally observable narrowing of the light-cone and the subjectively experienced change of optical depth to show the same ratio.

In order to compare the rate of expansion of a luminous cone inside and outside water, we must measure by how much less the width of the cone increases within the water than it does outside. (To be comparable, the measurements must be based upon the same distances on the edge of the cone, because this is the length of the way the light actually travels.) In Fig. 13 this is shown by the two distances, a-b and a'-b'. Their ratio is the same as that by which the bottom of a vessel appears to be raised when the vessel is filled with water (4:3).



Thus by means of pure observation we have arrived at nothing less than what is known to physical optics as Snell's Law of Refraction. This law was itself the result of pure observation, but was clothed in a conceptual form devoid of reality. In this form it states that a ray of light in transition between two media of different densities is refracted at their boundary surface so that the ratio of the angle which is formed by the ray in either medium with a line at right angles to the boundary surface is such that the quotient of the sines of both angles is for these media a constant factor. In symbols sin / sin = c.

It will be clear to the reader familiar with trigonometry that this ratio of the two sines is nothing else but the ratio of the two distances which served us as a measure for the respective apertures of the cone. But whereas the measurement of these two distances is concerned with something quite real (since they express an actual dynamic alteration of the light), the measuring of the angle between the ray of light and the perpendicular is founded on nothing real. It is now clear that the concept of the ray, as it figures in the usual picture of refraction, is in reality the boundary between the luminous space and its surroundings. Evidently the concept of the perpendicular on the boundary between the two media is in itself a complete abstraction, since nothing happens dynamically in its direction.

To a normal human understanding it is incomprehensible why a ray of light should be related to an external geometrical line, as stated by the law of refraction in its usual form. Physical optics, in order to explain refraction, had therefore to resort to light-bundles spatially diffused, and by use of sundry purely kinematic concepts, to read into these light-bundles certain processes of motion, which are not in the least shown by the phenomenon itself. In contrast to this, the idea that the boundary of a luminous cone is spatially displaced when its expansion is hindered by an optical medium of some density, and that the measure of this displacement is equal to the shortening of depth which we experience in looking through this medium, is directly evident, since all its elements are taken from observation.

*

From what we have here found we may expect that in order to explain the numerical relationships between natural phenomena (with which science in the past has been solely concerned), we by no means require the artificial theories to which the onlooker in man, confined as he is to abstract thinking, has been unavoidably driven. Indeed, to an observer who trains himself on the lines indicated in this book, even the quantitative secrets of nature will become objects of intuitive judgment, just as Goethe, by developing this organ of understanding, first found access to nature's qualitative secrets. (The change in our conception of number which this entails will be shown at a later stage of our discussions.)

1 Compare with this our account in Chapter X of the rise of the atomistic-kinematic interpretation of heat.

2 The following critical study leaves, of course, completely untouched our recognition of the devotion which guided the respective observers in their work, and of the ingenuity with which some of their observations were devised and carried out.

3 The assumption is that the wave-velocity differs from the group-velocity, if at all, by a negligible amount.

4 Once this is realized there can be no doubt that with the aid of an adequate mathematical calculus (which would have to be established on a realistic understanding of the respective properties of the fields of force coming into play) it will become possible to derive by calculation the speed of the establishment of light within physical space from the gravitational constant of the earth.

5 The grounds of Einstein's General Theory were dealt with in our earlier discussions.

CHAPTER XVIII

The Spectrum as a Script of the Spirit

The realization that Newton's explanation of the spectrum fails to meet the facts prompted Goethe to engage in all those studies which made him the founder of a modern optics based on intuitive participation in the phenomena. In spite of all that he achieved, however, he never reached a real solution of the riddle of the colour-phenomenon produced when light passes through a transparent body of prismatic shape. For his assumption of certain 'double images', which are supposed to appear as a result of the optical displacement of the boundaries between the Light-filled and the Dark-filled parts of space and the mutual superposition of which he believed to be responsible for the appearance of the respective colours, does not solve the problem.1

What hindered Goethe in this field was his limited insight into the nature of the two distinct kinds of forces which, as we have noted in the course of our own inquiries, correspond to his concepts of Licht and Finsternis.

With the aid of this distinction - which we have indeed established through a consistent application of Goethe's method - we shall now be able to develop precisely that insight into the coming-into-being of the spectral colours which Goethe sought.2

*

Dynamically, the process of the formation of the spectrum by light that passes through a prism divides into two clearly distinguishable parts. The first consists in the influence which the light undergoes inside the prism as a result of the latter's special shape, the other, in what happens outside the prism at the boundary between the Light-space - influenced by the shape of the prism - and the surrounding Dark-space. Accordingly, we shall study these two parts of the process separately.

As an aid to distinguishing clearly one process from the other, we shall suppose the prism experiment to be so arranged that the light area is larger than the width of the prism, which will then lie completely within it. We shall further suppose the dimensions of the whole to be such that the part observable on the screen represents only a portion of the total light-realm situated between the boundaries of the prism. The result is that the screen depicts a light-phenomenon in which there is no trace of colour. For normal eyesight, the phenomenon on the screen differs in no way from what it would be if no prism intervened in the path of the light.

These two seemingly identical light-phenomena reveal at once their inner dynamic difference if we narrow the field of light from either side by introducing into it an object capable of casting shadow. If there is no prism we see simply a black shadow move into the illumined area on the screen, no matter from which side the narrowing comes. If, however, the light has come through a prism (arranged as described above) certain colours appear on the boundary between the regions of light and shadow, and these differ according to the side from which the darkening is effected. The same part of the light area may thus be made to display either the colours of the blue pole of the colour-scale, or those of the yellow pole. This shows that the inner dynamic condition of the light-realm is altered in some way by being exposed to an optically resistant medium of prismatic shape. If we are to find the cause and nature of this alteration we must revert to the prism itself, and inquire what effect it has on light in the part of space occupied by it. By proceeding in this way we follow Goethe's model: first, to keep the two border-phenomena separate, and, secondly, not to ascribe to the light itself what is in fact due to certain boundary conditions.

In order to realize what happens to the light in passing through the prism, let us remember that it is a characteristic of an ordinary light-beam to direct itself through space in a straight line if not interfered with, and to illuminate equally any cross-section of the area it fills. Both these features are altered when the light is exposed to a transparent medium of prismatic shape - that is, to an optically resistant medium so shaped that the length of the light's passage through it changes from one side of the beam to the other, being least at the so-called refracting edge of the prism, greatest at the base opposite to that. The dimming effect of the medium, therefore, has a different magnitude at each point of the width of the beam. Obviously, the ratio between levity and gravity inside such a light-realm, instead of being constant, varies from one side to the other. The result is a transverse dynamic impulse which acts from that part of the light-realm where the weakening influence of the prism is least towards the part where it is strongest (see long arrow in Plate C, Fig. i).3 This impulse manifests in the deflection of the light from its original course. Apart from this, nothing is noticeable in the light itself when caught by an observation screen, the reason being that the transverse impulse now immanent in the light-realm has no effect on the reflecting surface.

The situation changes when the light-realm is narrowed down from one side or the other - in other words, when an abrupt change of the field-conditions, that is, a sudden leap from light to dark or from dark to light, is introduced within this realm. In this case, clearly, the effect of the transverse field-gradient on such a leap will be different, depending on the relation between the directions of the two (see small arrows in Fig. i). Our eyes witness to this difference by seeing the colours of the blue pole of the colour-scale appear when the field-gradient is directed towards the leap (a), and the colours of the yellow pole when the gradient is directed away from it (b).

For our further investigation it is very important to observe how the colours spread when they emerge at the edge of the shadow-casting object thus introduced into the light-realm from the one side or the other. Figs, ii and iii on Plate C show, closely enough for our purpose, the position of the colour-bearing areas in each case, with the dotted line indicating the direction which the light would have at the place of origin of the colours if there were no object interfering with its free expansion.4 We observe a distinct difference in the widening out of the two colour-areas on both sides of the original direction of the light: in each case the angle which the boundary of the colour-area forms with this direction is smaller on the side of the colours nearest the light-realm (blue and yellow respectively) than on the opposite side (violet and red).

Remembering what we have learnt about the dynamic characteristics of the two colour-poles, we are now in a position to state the following. When a light-area subject to a lateral gradient is narrowed down, so that the gradient is directed towards the narrowing object, colours arise in which the interaction between the two polarically opposite forms of density is such that positive density makes for lightness, and negative density for darkness. Whereas, when the border is so situated that the gradient is directed away from it, the interaction is such that positive density makes for darkness, and negative density for lightness. Further, the fact that on both occasions the darkness element in the colour-band increases in the outward direction tells us that in this direction there is on the blue-violet side a gradual decrease in positive, and increase in negative, density, while on the opposite side we find just the reverse. We note again that both processes occupy a considerable part of the space originally outside the boundaries of the light-area - that is, at the violet end the part towards which the light-beam is deflected, and at the red end the part from which it turns away.

The visual ray, when penetrating actively into the two colour-phenomena thus described, receives evidence of a dynamic happening which may be expressed as follows.

Where the transverse impulse, which is due to the varying degree of Trübung in the light-realm, is directed towards the latter's edge, the intermingling of the Dark-ingredient and the Light-ingredient, contained in that realm, is such that Dark follows Light along its already existing gradient, thereby diminishing steadily. Hence our visual ray, meeting conditions quite similar to those occurring when we look across the light-filled atmosphere into universal space, notifies us of the presence of the blue-violet colour-pole. If, on the other hand, the edge is in the wake of the transverse impulse, then a kind of dynamic vacuum arises in that part of space from which the beam is deflected, with the effect that the Dark-ingredient, imprinted on the light within the prism, is drawn into this vacuum by following a kind of suctional influence. Consequently Dark and Light here come to oppose one another, and the former, on its way out of the light-area, gains in relative strength. On this side our visual ray meets conditions resembling those which occur when we look across the darkening atmosphere into the sun. Accordingly our optical experience tells us of the presence of the yellow-red colour-pole.

From our description of the two kinds of dynamic co-ordination of positive and negative density at the two ends of the spectrum it follows that the spatial conditions prevailing at one end must be quite different from those at the other. To see this by way of actual perception is indeed not difficult. In fact, if we believe that we see both ends of the spectrum lying, as it were, flatly on the surface of the observation screen, this is merely an illusion due to our superficial way of using our eyes. If we gaze with our visual ray (activated in the manner previously described) into the two sides of the spectrum, while turning our eyes alternately in one or other direction, we soon notice that the colours of the yellow-red rise towards the eye so as to give the impression of protruding almost corporeally from the surface of the screen. We feel: Density obtains here in a state of fiery radiation. When turning to the other side we feel our visual ray, instead of being as before caught up in the colours, passing freely across the colours as if carried by them into the infinite. On the blue-violet side, space itself seems to fluoresce mysteriously5. Following Goethe's conception of the physical-moral effect of colours, we may describe the experience received thus from the two poles of the spectrum by saying that an 'other-worldly' character belongs to the colours of the blue-violet pole; an 'earthly' character to those of the yellow-red; while that of green, which appears when both sides are made to overlap, witnesses to its mediating nature between the two.

*

In our endeavour to view the fundamental experiment of Newtonian optics with the eyes of Goethe we have been led from the wide expanse of the earth's sunlit periphery into the confines of the darkened experimental chamber. With the aid of the results gained from studying the artificially produced spectrum phenomenon, we shall now return to our original field of observation in order to study the same phenomenon in nature. There it meets us in the form of the rainbow, which we shall now be able to read as a chapter in the great book of nature.

From what we have learnt already we can say at once that the rainbow must represent some sort of border-phenomenon, thus pointing to the existence of a boundary between two space-regions of differing illumination. Our question therefore must be: what is the light-image whose boundary comes to coloured manifestation in the phenomenon of the rainbow? There can be no doubt that the image is that of the sun-disk, shining in the sky. When we see a rainbow, what we are really looking at is the edge of an image of the sun-disk, caught and reflected, owing to favourable conditions, in the atmosphere. (Observe in this respect that the whole area inside the rainbow is always considerably brighter than the space outside.)

Once we realize this to be the true nature of the rainbow, the peculiar order of its colours begins to speak a significant language. The essential point to observe is that the blue-violet part of the spectrum lies on the inner side of the rainbow-arch - the side immediately adjoining the outer rim of the sun-image - while the yellow-red part lies on the outer side of the arch - the side turned away from the sun-image. What can we learn from this about the distribution of positive and negative density inside and outside the realm occupied by the sun-disk itself in the cosmos?

We remember that along the gradient from blue to violet, negative density (Light) increases and positive density (Dark) decreases, while from yellow to red it is just the reverse-positive density increases and negative density decreases. The rainbow therefore indicates a steady increase of Dark towards the outer rim, and of Light towards the inner. Evidently, what the optical image of the sun in the atmosphere thus reveals concerning the gradation of the ratio between Light and Dark in the radial direction, is an attribute of the entire light-realm which stretches from the sun to that image. And again, the attribute of this realm is but an effect of the dynamic relation between the sun itself and the surrounding cosmic space.

The rainbow thus becomes a script to us in which we read the remarkable fact that the region occupied by the sun in the cosmos is a region of negative density, in relation to which the region surrounding the sun is one of positive density. Far from being an accumulation of ponderable matter in a state of extremely high temperature, as science supposes, the sun represents the very opposite of ponderability. (It would be beyond the scope of this book to show how in the light of this fact one learns to re-read the various solar phenomena known to science.)

Once we realize this, our judgment of all that our terrestrially devised optical instruments, such as the telescope and spectroscope, tell us about the nature of the sun and its surroundings, will change accordingly. For it becomes clear that for the interpretation of solar phenomena shown by these instruments we cannot properly use concepts derived from observations within the earth's realm of positive density.

To compare adequately solar and terrestrial phenomena, we must keep in mind that they are in every respect polar opposites. For instance, the fact that the spectroscope reveals phenomena in the sun's light which are strikingly similar to others occurring when earthly matter is first caused to emit light - that is, brought near the upper border of its ponderable existence - and then studied spectroscopically, should not impose on us the illusion that the sun consists of matter in this same condition. On the contrary, the similarity should tell us that imponderable substance, while on its way between sun and earth to ponderable existence, assumes, at the point of transition, aspects exactly like those revealed by ponderable substance at the corresponding point in its upward transformation.

What we observe, when we study the sun through a spectroscope, is not the sun itself, but the conditions obtaining in this border-region, where imponderable substance enters the earth-realm.

The rainbow, directly we learn to see it as the border-phenomenon that it is, tells us something of itself which revives in modern form a conception held generally in former ages, when it was seen as a mediator between the cosmic-divine and the earthly-human worlds. Thus the Bible speaks of it as a symbol of God's reconciliation with the human race after the great Flood. Thus the Greeks beheld it when they saw it as the bridge of Iris, messenger of the Gods; and similarly the Germanic mythology speaks of it as the pathway along which the souls of the fallen warriors draw near to Valhalla. By recovering this old conception in a new and scientifically grounded form we are enabled also to rectify the misunderstanding from which the ancient bridge-conception of the rainbow has suffered in later days, when tradition had begun to replace direct insight into the truth.

When with the rise of man's onlooker-relation to the world of the senses, the rainbow could appear to him only as a form flattened against the sky, people began to think that the ancient picture of it as a bridge had been derived from its likeness to the latter's arched form. Representations of the rainbow from these times indeed show supersensible beings, such as the souls of the dead, moving upwards and downwards along the two halves of the arch. It is not in this abstract way that ancient man formed his cosmic imagery. What was seen going on between the upper and nether worlds when a rainbow appeared in the heights of the atmosphere was no traffic over the arch, but an interplay across the rainbow between the realm of levity, glimmering down in the rainbow's violet border, and the realm of gravity glowing up from the red. And this is how we have now learnt to see it again.

*

At one point in our optical studies (page 259) we referred to some words of Ruskin in which he deplored the influence exerted on the soul-life of modern man by the world-conception of science. He illustrated this by showing how much less inspiration a man trained in the science of optics receives from the sight of a rainbow than does a 'simple peasant'. One lesson of our studies is that training in optics, if it proceeds on Goethean lines, has no such detrimental effect. There is, however, a further problem, outside Ruskin's scope, which we are now able to approach in the same healthy way.

Ruskin distinguishes between three possible stages in man's relation to the world of the senses. The first stage he calls that of 'inactive reverie'; the second - in a certain respect more advanced - that of 'useful thought', the stage of scientifically awakened man to whom all things disintegrate into countable and nothing but countable parts. Beyond this, Ruskin conceives of a third, still higher stage, in which man becomes capable of raising himself through 'higher contemplation' into an artistic-ethical relation to the content of the sense-world. Now, in the way Ruskin represents the second and third stages they seem to be exclusive of one another. That was as far as he could go, in his own day. Natural observation along Goethean lines leads to a form of higher contemplation which unites the second and third stages by nourishing man's ethical being and at the same time furnishing him with useful knowledge-knowledge, that is, which enables him to improve the conditions of the human race on the earth. The following is an example of the practical possibilities that open up in the field we are discussing if we apply the knowledge gained through our new approach to the forces working in nature.

We shall speak here of a task of experimental research which was mentioned by Rudolf Steiner in connexion with the renewal of natural science.

Rudolf Steiner felt the need for pioneers who, by advancing along the paths opened up by Goethe, would press forward into the realm of undiscovered phenomena on the upper border of nature, and this prompted him to give to those who were ready to listen various pointers towards new ways of experimental research. In so far as practical results have already been reached along these lines, they lie in the fields of biology and physiology (and of chemistry, in a certain respect) rather than in that of physics. Now, among the indications given in this latter field, and not yet worked out, there is one which deals with a way, unknown to-day, of influencing the spectrum by the magnet.

The possibility of a magnetic influence on the spectrum is, in itself, not unknown to modern physics. It was the Dutchman, Zeeman, who first observed a change in the appearance of certain spectral lines as a result of light passing through a magnetic field. This discovery, however, is in two respects typical of modern science. The Zeeman effect consists in the splitting up of certain spectral lines into other lines - hence, of a breaking up of a whole into parts. And by seemingly providing a decisive confirmation of contemporary views concerning the electromagnetic nature of light, Zeeman's discovery has formed one of the milestones in the progress of modern physical thought - with the usual result that an enlargement of man's knowledge of the behaviour of natural forces has served to entangle his conception of nature still more deeply in illusion.

Apart from the fact that our own way of combining observation and thought guards us against drawing theoretical conclusions from Zeeman's discovery, Rudolf Steiner's indication opens up the prospect of achieving quite practical results, opposite in character to those of the Zeeman effect. For in contradistinction to the use of a magnetic field for splitting the spectrum, Rudolf Steiner has made us aware of the possibility of uniting into a higher synthesis parts of the spectrum which normally appear in separated form. His indication points to nothing less than a leading over of the optically produced spectrum from its usual linear form, with two boundaries on either side, into a closed circular form, and of doing this by an adequate application - as yet undiscovered - of magnetic force. Further, according to his statement, the point where the two ends of the spectrum meet will prove to be a fountain-head of certain higher natural forces which otherwise are not directly accessible.

In order to understand how this is possible, we must remember that in two respects the spectrum is not a complete phenomenon. There is, to begin with, the fact that the colour-band visible on the observation screen is only apparently confined to the surface of the screen. For, as we have seen, because of the differing co-ordination of levity and gravity at the two ends of the spectrum, the conditions of space prevailing at each are polarically opposite. Negative space opens up spherically behind the blue-violet colours on one side, while positive space, filled by the radially shining yellow-red colours, arises on the other. So we see that what we found earlier for the two poles of magnetism and electricity holds good also for the spectrum. That is, the two processes bringing about the relevant phenomena are not confined to the part of space which these phenomena seem to occupy; for the whole positive and negative realms of the universe share in them. Hence the spectrum, though apparently bounded at its two ends, proves by its very nature to be part of a greater whole.

Once before we were led to recognize - though from a different aspect - that the spectrum is a phenomenon which, when rightly viewed, calls for a certain completion. In following Goethe's initial observations we realized that the known spectrum, extending from red via green to violet, has a counterpart extending from violet via peach-blossom to red. The reader may have wondered why we never returned to this other spectrum, in spite of the role it played in making Goethe aware of Newton's error. The reason was that in order to gain the understanding we needed of the spectrum, we had to observe the two border-phenomena independently - that is, without regard to their relative positions. Moreover, with ordinary optical means it is possible to produce only one type of spectrum at a time, so that each is left in need of being complemented by the other. In order to have both together in finite space, as part of one and the same phenomenon, space itself must be dynamically transformed in such a way that the continuation of the finite spectral band running through infinity enters into the finite as well.

Our understanding of magnetism as a specific representation of the polarity of the second order enables us to comprehend, at least in principle, how magnetism might influence - not light itself, as present-day physics erroneously believes - but the secondary polarity of the spectral colours formed out of the primary polarity Light and Dark. To see this in all necessary detail is a task of the future, beyond the scope of this book. We have here to continue our account of Rudolf Steiner's statement by communicating what he indicated concerning the particular nature of the new source of force which would appear in the normally infinite part of the spectrum, if this were brought into the region of the finite.

In order to understand the significance of this indication we must turn our attention to parts of the ordinary spectrum, well known in themselves, which we have purposely left out of our study so far. These are the regions of the ultra-violet and the infra-red, invisible in themselves, but forming part of the spectrum as a whole. The ultraviolet manifests through chemical effects, the infra-red through thermal effects. We have left them out of our considerations because these regions of the spectrum differ from the visible part not only quantitatively, as present-day science believes, but qualitatively also, and in a fundamental way. We must regard them as dynamic realms of particularly extreme spherical and radial activities. As such they represent metamorphoses, in the Goethean sense, of the levity-gravity interaction represented by the optically visible part of the spectrum. In this way the spectrum discloses a threefold differentiation of that region of force, which up to now we have called simply levity, into activities producing chemical, optical and thermal effects.

So far physical investigation is able to lead us, but no further. If, however, we let nature herself speak to us, while holding this differentiated concept of levity in mind, she tells us that beyond the three metamorphoses envisaged so far, there must be a fourth.

Let us remember that it was certain phenomena of life which first made us aware of the existence of a realm of forces with the attributes of anti-gravity, and that these forces revealed themselves first as creators of form. Now it is obvious that warmth, light and chemical energy, though they all play an essential part in living organisms, could never by themselves bring about that 'catching from chaos, carbon, water, lime and what not and fastening them into a given form' which Ruskin describes as the activity of the spirit in the plant. In order to be in this sense an instrument of the spirit active in nature, levity must be capable of yet another metamorphosis into an activity which controls the other three, so that through their action, definitely shaped organic structures may come into being.

The reason why this fourth and highest metamorphosis of Light does not appear in the ordinary spectrum is because it is of too spiritual a quality to be caught by the optical apparatus. In nature herself a creative life-process requires always the presence of a germ already imbued with life. And so, in order to call this fourth metamorphosis of Light into the spectrum, stronger means are needed than the mere optical transformation of light-filled spaces. This stronger agent, according to Rudolf Steiner, is magnetism. With the aid of this it will be possible to organize together round a common spatial centre that part of the activity of levity which escapes the optical instrument and thus remains cosmic, and that part which appears by itself in terrestrial space.

Once this is practically carried out, we may expect a complete colour-circle to appear as already divined by Goethe. The full circle consists of twelve discernible colours, with the Goethean peach-blossom diametrically opposite the green. It is in this region of the peach-blossom that - again according to Rudolf Steiner - we shall find a source of actively working life-forces, springing from the fourth metamorphosis of levity. Such is the prospect for research work guided on the new lines.

POSTSCRIPT

The fact of our having disclosed here one of Rudolf Steiner's indications concerning as yet undetected possibilities of scientific research, makes it necessary to deal with an objection which may be raised, particularly by some readers who already know this indication through their own relation to Rudolf Steiner's work. They may object to a discussion of the subject in a publication such as this, feeling it dangerous to hand over to the world information which in the economic battles of to-day might be used in a sense contrary to the social-moral aims to which the work of Rudolf Steiner was dedicated.

In reply it may be said that all we have gone through in this book has shown that concrete knowledge of the world cannot be gained without a certain ethical effort by the seeker. Therefore, anyone who receives such knowledge with a passive attitude of soul will find it meaningless, and will be quite unable to turn it to practical account. We may therefore rest assured that the solution of the problem related here, as of any other experimental task set by Rudolf Steiner, will contain in itself a guarantee that no use will be made of it detrimental to the true progress of mankind.

On the other hand, the present world-situation, which to so high a degree is determined by the vast liberation of the sub-physical forces of the earth, makes one feel it is essential not to close the considerations of the fields of knowledge dealt with in these chapters, without a hint at the practical possibilities which arise from a continuation of Goethe's strivings in this field.

1 See, in Rudolf Steiner's edition of Goethe's scientific writings, his footnote to Goethe's criticism of Nuguet's theory of the spectrum in the historical part of the Farbenlehre (Vol. IV, p. 248, in Kürschner's edition).

2 It is obvious that the reader who wishes to appreciate fully the significance of the observations described in the following paragraphs, must, as in previous cases, carry out these observations himself.

3 In this and the two following diagrams the light-realm has been represented as being less wide than the space obtained by the prism. To avoid unnecessary complexity the colours which, in such a case, actually appear at the border of the light-realm where it emerges from the prism are not shown in any of the diagrams.

4 This direction can be established with sufficient exactitude by holding a very thin object right in front of the prism and marking with a stretched thread the direction which leads from the object to its shadow on the screen. The colour-producing edge must then be introduced from either side so that it just touches the thread.

5 The difference in character of the various parts of the spectrum, as described above, comes out particularly impressively if for capturing the colour-phenomenon one uses instead of a flat white surface, a clear crystal of not too small size, or else a cluster of crystals - moving it slowly along the coloured band from one end to the other. (I am indebted to Fr. Julius, teacher of Natural Science at the Free School in The Hague, for this suggestion.)

PART III

Towards a New Cosmosophy

CHAPTER XIX

The Country in which Man is not a Stranger

I question not my Corporeal or Vegetative Eye any more than I question a window concerning sight. I look through it and not with it. WILLIAM BLAKE.