Man or Matter Part 28

If one sets in the path of a luminous cone a gla.s.s-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 s.p.a.ce 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 relations.h.i.+ps 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 quant.i.tative 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 a.s.sumption 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 s.p.a.ce 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 partic.i.p.ation 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 pa.s.ses through a transparent body of prismatic shape. For his a.s.sumption 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 s.p.a.ce 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 pa.s.ses 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-s.p.a.ce - influenced by the shape of the prism - and the surrounding Dark-s.p.a.ce.

Accordingly, we shall study these two parts of the process separately.

As an aid to distinguis.h.i.+ng 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 s.p.a.ce 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 pa.s.sing through the prism, let us remember that it is a characteristic of an ordinary light-beam to direct itself through s.p.a.ce 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 pa.s.sage 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 s.p.a.ce 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 Trubung 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 diminis.h.i.+ng steadily. Hence our visual ray, meeting conditions quite similar to those occurring when we look across the light-filled atmosphere into universal s.p.a.ce, 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 s.p.a.ce 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, pa.s.sing freely across the colours as if carried by them into the infinite. On the blue-violet side, s.p.a.ce 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 s.p.a.ce-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, s.h.i.+ning 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 s.p.a.ce 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 s.p.a.ce.

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 acc.u.mulation 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, a.s.sumes, 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 G.o.d'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 G.o.ds; 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 ill.u.s.trated 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 nouris.h.i.+ng man's ethical being and at the same time furnis.h.i.+ng 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.