Front matter (continued 9)

Many examples of the activity of the force-spheres represented by the three exterior planets are to be found also in nature external to man. From the realm of plant life we may take the woody and bark-like formation of the trees as representing the operation of Saturn-forces. Similarly, all that goes on in the organizing of the single leaf, and particularly in the organization of the countless separate leaves which make up the foliage of a tree into a unified whole, the characteristic crown of a tree, is an example of the work of Jupiter. Both activities are assisted by the force of Mars, which directs them from the cosmic periphery toward the single physical object.

Between the two groups of astral force operating in this manner, the Sun acts as a mediating element through its double function of supporting the activity of the three lower planets by means of its heat and of conveying to the earth, through its light, the forces of the three higher planets. In the human microcosm the Sun-forces accomplish a corresponding task by means of the influences which radiate from the heart through the body along the paths taken by the blood.

*

In what follows we shall point to a group of phenomena which show the astral interconnexion between earth and universe; we owe our knowledge of them to Rudolf Steiner. It is due to him, also, that experimental research into the relevant facts became possible. They concern the reflexion of the various planetary movements, observable in the sky, in the behaviour of certain mineral substances of the earth.

In connexion with our discussion of electricity (Chapter XIII) we spoke of the special function of the metals as bearers of the 'mercurial' quality (in the alchemical sense of the term). As one of the characteristics which reveal this function we mentioned the peculiar capacity of metals to behave as 'solid fluids'. This exceptional place among the mineral substances of the earth, the metals owe to their close association with the extra-terrestrial astral forces of the world. In this field, too, modern spiritual investigation has recovered something which was known to people of old - that among the metals there are seven which have a distinctive character, for each stands in a special relation to one of the seven planets (that is, the planetary force-spheres) of our cosmic system. This is shown in the following table:

As compared with these seven, the other metals are products of combinations of various planetary forces. A comparison of the role of Saturn as the outermost planet of our cosmic system with the role played by its metal, lead, as a final product of radioactive disintegration, leads one to conceive of the radioactive sphere of the earth as being related especially to the planets outside the orbit of Saturn, namely, Uranus, Neptune, Pluto.

Thanks to the work of L. Kolisko who, in following Rudolf Steiner's indications, observed for many years the behaviour of the seven metals singly and in combination by submitting their salts to certain capillary effects, we know to-day that the" earth bears in her womb substances whose dynamic condition follows exactly the events in the planetary realm of the universe.⁸

*

The picture of the universe which has thus arisen before our mind's eye is a startling one only so long as we keep comparing it with its heliocentric predecessor. How wrong it would be to regard it as something inconceivable for the modern mind, is shown by the fact that the modern physiologist has already been driven to form quite a similar picture of the human organism, as far as it concerns glandular action in this organism. His observations have taught him to distinguish between the gland as a spatially limited physical organ and the gland as a functional sphere, and to conceive of the latter as the essential gland. Seen thus, 'the spatial and temporal dimensions of each gland are equal to those of the entire organism' (A. Carrel). In this way we come to see the human organism as a realm of interpenetrating spheres of distinctive physiological activities. Each of these activities is anchored somewhere in the physical body by the anatomically discernible gland-body, and the latter's relationship to the functional sphere is such that a gland's 'physiological individuality is far more comprehensive than its anatomical individuality'.

We need only translate this statement into its macrocosmic counterpart to obtain another statement which expresses fittingly the relationship of the visible body of a planet to the functional (astral) sphere indicated by its orbit. Then we shall say that 'a planet's astral individuality is far more comprehensive than its astronomical individuality'.

It should be observed that the step we have here taken, by using a conception obtained through microcosmic observation to help us to find the answer to a question put to us by the macrocosm, complies with one of the fundamentals of our method of research, namely, to allow 'the heavens to explain the earth, and the earth the heavens' (R. St.).

(b) HEARING AS DEED

In the introductory part of the last chapter we said that we have the right to employ results of investigation carried out by higher faculties of spiritual perception without contradicting our principle of seeking to understand the phenomenal world by reading it, provided our doing so helps to enhance our own reading activity, and provided it can be shown that the acquisition of the higher faculties of perception is a direct continuation of the training we have to apply to our mind and senses to make them capable of such reading. As regards the forces of astral character, the first of these two conditions has been fulfilled by the observations we have already worked through in this chapter. We have still to show that the second condition is equally fulfilled.

The faculty of the mind which permits direct investigation of the astral realm was called (spiritual) Inspiration by Rudolf Steiner, who thereby restored to this term, also, its proper meaning. We have already indicated that this faculty resides in the sense of hearing in the same way that the faculty of Imagination - as we have found - resides in the sense of seeing. In order to understand why it is this particular sense which comes into consideration here, we have to consider that the phenomena through which the astral world manifests most directly are all of a rhythmic nature. Now, the sense through which our soul penetrates with direct experience into some outer rhythmic activity is the sense of hearing, our aural perceptions being conveyed by certain rhythmic movements of the air. In what follows we shall see how the study of both the outer acoustic phenomena and our own psycho-physical make-up in the region of the acoustic sense, leads to an understanding of the nature of Inspiration and of how it can be trained.

*

Among all our sense-perceptions, sound is unique in making itself perceptible in two quite different ways - via the ear as a direct sense experience and via the eye (potentially also via the senses of touch and movement) in the form of certain mechanical movements, such as those of a string or a tuning fork. Hence the world-spectator, as soon as he began to investigate acoustic phenomena scientifically, found himself in a unique position. In all other fields of perception, with the exception of the purely mechanical processes, the transition to non-stereoscopic colourless observation had the effect that the world-content of the naive consciousness simply ceased to exist, leaving the ensuing hiatus to be filled in by a pattern of imagined kinematic happenings - for example, colour by 'ether'-vibrations, heat by molecular movements. Not so in the sphere of acoustics. For here a part of the entire event, on account of its genuine kinetic character, remains a content of actual observation.

In consequence, the science of acoustics became for the scientific mind of man a model of the required division between the 'subjective' (that is, for scientific considerations non-existent) and the 'objective' (that is, the purely kinematic) part of observation. The field of aural perception seemed to justify the procedure of collecting a mass of phenomena, stripped of all that is experienced by man's soul in meeting them, and of assembling them under a purely abstract concept, 'sound'.

Professor Heisenberg, in his lecture (quoted at the beginning of Chapter II) on the way in which the scientific interrogation of nature has deliberately limited itself, draws attention to the fact that a full knowledge of the science of optics in its present form might be acquired merely through theoretical study by one born blind, yet without his ever getting to know what light is. Heisenberg could, of course, have said the same of the science of acoustics in regard to one born deaf. But we can go a step further by asking how far a deaf and a blind person could get towards establishing the respective science. The answer must be that, whereas the person lacking sight would not of himself be in a position to establish a science of optics, it would be well within the scope of the deaf man to establish a science of acoustics. For all the processes essential to a physical acoustics are accessible to the eye and other senses.

In order to make our experience of hearing a finger-post pointing the way to an understanding of the faculty of Inspiration innate in man, we must first of all seek to transform acoustics from a 'deaf into a 'hearing' science, just as Goethe turned the theory of colour from a colour-blind into a colour-seeing science.

*

Following our procedure in the case of optics, we select from the total field of acoustic phenomena a defined realm specially suited to our purpose. As it was then the spectrum, so it will be now the so-called quality of sound, or tone-colour.

By this term in acoustics is understood a property possessed by sound apart from pitch and volume, and dependent on the nature of the source from which a tone is derived. It is the tone-colour by which the tone of a violin, for instance, is distinguished from a tone of equal intensity and pitch produced by a flute. Similarly, two musical instruments of the same kind are distinguished from each other by tone-colour.

Tone-colour plays a specially significant part in human and animal voices. Not only has each individual voice its unique colour, but the colour varies in one and the same person or animal, according to the prevailing mood. Moreover, by uttering the various vowels of his language, man is able to impart varying colour to the sounds of his speech. For the difference we experience when a tone is sung on the vowel 'a' or the vowel 'e', etc., derives from the particular colour given by the vowel to that tone.

Among the discoveries of the last century in the realm of acoustics, there is one which especially helped to establish a purely kinematic conception of sound. Helmholtz showed that tones which to our ears seem to have a clear and definite pitch may be split up by a series of resonators into a number of different tones, each of them sounding at a different pitch. The lowest of these has the pitch which our ears attach to the entire tone. Thus in any ordinary tone there may be distinguished a 'fundamental' tone and a series of 'overtones'. Helmholtz further showed that the particular series of overtones into which a tone can be resolved is responsible for the colour of that tone as a whole. Naturally, this meant for the prevailing mode of thinking that the experience of the colour of a tone had to be interpreted as the effect of a kind of acoustical adding together of a number of single tone perceptions (very much as Newton had interpreted 'white' light as the outcome of an optical adding together of a certain number of single colour perceptions).

The picture becomes different if we apply to the aural experience Goethe's theorem that, in so far as we are deluded, it is not by our senses but by our own reasoning. For we then realize that sounds never occur of themselves without some tone-colour, whilst physically 'pure' tones - those that represent simple harmonic motions - exist only as an artificial laboratory product. The colour of a tone, therefore, is an integral part of it, and must not be conceived of as an additional attribute resulting from a summing up of a number of colourless tone experiences.

Further, if we compare our experiences of the two kinds of tone, they tell us that through the quality or colour of the natural tone something of a soul-nature, pleasant or unpleasant, speaks to us, whereas 'pure' tones have a soulless character.

Resolving normal tones by Helmholtz's method (useful as it is for certain purposes) amounts to something like dissecting a living, ensouled organism into its members; only the parts of the corpse

remain in our hands.

*

Having thus established that the psychic content of aural experience forms an integral part of the tone-phenomenon as such, we must seek to understand how the kinetic process which is indispensable for its appearance comes to be the vehicle for the manifestation of 'soul' in the manner described.

To this end we must first of all heed the fact that the movement which mediates aural sensation is one of alternating expansion and contraction. Expressed in the language of the four Elements, this means that the air thus set in vibration approaches alternately the condition of the watery element beneath it and of the element of fire (heat) above it. Thus, in a regular rhythm, the air comes near the border of its ponderable existence. Purely physical considerations make us realize that this entails another rhythmic occurrence in the realm of heat. For with each expansion of the air heat is absorbed by it and thereby rendered space-bound, while with every contraction of the air heat is set free and returns to its indigenous condition - that is, it becomes free from spatial limitations.

This picture of the complete happenings during an acoustic event enables us to understand how such a process can be the vehicle for conveying certain astral impulses in such a way that, when met by them, we grow aware of them in the form of a direct sensation. Taking as a model the expression 'transparent' for the perviousness of a substance to light, we may say that the air, when in a state of acoustic vibration, becomes 'trans-audient' for astral impulses, and that the nature of these vibrations determines which particular impulses are let through.

What we have here found to be the true role of the kinetic part of the acoustic process applies equally to sounds which are emitted by living beings, and to those that arise when lifeless material is set mechanically in motion, as in the case of ordinary noises or the musical production of tone. There is only this difference: in the first instance the vibrations of the sound-producing organs have their origin in the activity of the astral part of the living being, and it is this activity which comes to the recipient's direct experience in the form of aural impressions; in the second instance the air, by being brought externally into a state of vibration, exerts a kind of suction on the astral realm which pervades the air, with the result that parts of this realm become physically audible. For we are constantly surrounded by supersensible sounds, and the state of motion of the air determines which of them become perceptible to us in our present state of consciousness.

At this point our mind turns to a happening in the macrotelluric sphere of the earth, already considered in another connexion, which now assumes the significance of an ur-phenomenon revealing the astral generation of sound. This is the thunder-storm, constituted for our external perception by the two events: lightning and thunder.

Remembering what we have found earlier (Chapter X) to be the nature of lightning, we are now in a position to say: a supraterrestrial astral impulse obtains control of the earth's etheric and physical spheres of force in such a way that etheric substance is thrown into the condition of space-bound physical matter. This substance is converted by stages from the state of light and heat via that of air into the liquid and, in certain cases, into the solid state (hail). To this we now add that, while in lightning the first effect of the etheric-physical interference of the astral impulse appears before our eyes, our ears give us direct awareness of this impulse in the form of thunder. It is this fact which accounts for the awe-inspiring character of thunderstorms.

*

The picture we have thus received of the outer part of the acoustic process has a counterpart in the processes inside the organ of hearing. Hearing, like seeing, depends upon the co-operation of both poles of the human organism-nerve and blood. In the case of hearing, however, they play a reversed role. In the eye, the primary effect of light-impressions is on the nervous part; a secondary response to them comes from the blood organization. In the ear, the receptive organ for the astral impulses pressing in upon it is a part which belongs to the body's limb system, while it is the nervous organization which functions as the organ of response. For in the ear the sound-waves are first of all taken over by the so-called ossicles, three small bones in the middle ear which, when examined with the Goethean eye, appear to be a complete metamorphosis of ah arm or a leg. They are instrumental in transferring the outer acoustic movements to the fluid contained in the inner ear, whence these are communicated to the entire fluid system of the body and lastly to the muscular system.⁹ We shall speak of this in detail later on. Let it be stated here that the peculiar role played by the larynx in hearing, already referred to by us in Chapter XVI, is one of the symptoms which tells of the participation of the muscular system in the internal acoustic process.

Psychologically, the difference between ear and eye is that aural perceptions work much more directly on the human will - that is, on the part of our astral organization connected with the limb system. Whereas eye-impressions stimulate us in the first place to think, ear-impressions stimulate us to ... dance. The whole art of dancing, from its original sacred character up to its degenerate modern forms, is based upon the limb system being the recipient of acoustic impressions.

In order to understand how the muscles respond to the outer astral impulses which reach us through our ear, we must first understand what happens in the muscles when our will makes use of them for bodily motion. In this case, too, the muscular system is the organ through which certain astral impulses, this time arising out of the body's own astral member, come to expression. Moreover, the movement of the muscles, though not outwardly perceptible, is quite similar to acoustic movements outside the body. For whenever a muscle is caused to alter its length, it will perform some kind of vibration - a vibration characterized even by a definite pitch, which differs in different people. Since throughout life our body is never entirely without movement, we are thus in a constant state of inward sounding. The muscular system is capable of this vibration because during the body's initial period of growth the bones increase in length to a much greater extent than do the sinews and muscles. Hence the latter arrive at a condition of elastic tension not unlike that of the strings of a musical instrument.¹⁰

In the case of bodily movement, therefore, the muscles are tone-producers, whereas in acoustic perceptions they are tone-receivers. What, then, is it that prevents an acoustic perception from actually setting the limbs in motion, and, instead, enables our sentient being to take hold of the astral impulse invading our muscles?

This impediment comes from the contribution made by the nervous system to the auditory process. In order to understand the nature of this contribution we must remember the role played by the blood in seeing. It was found by us to consist in the bringing about of that state of equilibrium without which we should experience light merely as a pain-producing agent. Similarly, the perception of sound requires the presence of a certain state of equilibrium between the nerve-system and the limb-system. In this case, however, a lack of equilibrium would result not in pain, but in ecstasy. For if acoustic impressions played directly into our limb-system, with nothing to hold them in check, every tone we encounter would compel us to an outward manifestation of astral activity. We should become part of the tone-process itself, forced to transform it by the volitional part of our astral organization into spatial movement. That this does not happen is because the participation of the nervous system serves to damp down the potential ecstasy. Hence it is more or less left to the sentient part of the astral organization - that is, the part free from the physical body - to partake in the astral processes underlying the tone occurrences.

*

Our discussion has reached a point where we are able to answer a question which first arose in the course of our study of the four ethers, and which arises here anew.

In studying the chemical or sound ether we were faced with the fact that part of the etheric realm, although in itself accessible to the spiritual part of the sense of sight, offers supersensible experience comparable to the perception of sound. Conversely, we are now met by the fact that it is spiritual hearing which gives access to the immediate perception of a realm of forces which is not only the source of acoustic phenomena, but the origin of all that manifests in nature in the form of sulphurous, saline and mercurial events, such as the world of colours, electricity, magnetism, the manifold rhythmic occurrences on the earth (both taken as a whole .and in single organisms), etc. - all of which are taken hold of by quite other senses than that of hearing.

At our first encounter with this problem we remarked that in the supersensible no such sharp distinctions exist between different sense-spheres as are found in body-bound sense-perception. At the same time we remembered that even in physical perception we are inclined to attach acoustic attributes to colours and optical attributes to tones. In fact, it was precisely an instance of this kind of experience, namely, our conception of tone-colour, which gave us our lead in discussing the acoustic sphere in general. Our picture of the particular interaction of the two polar bodily systems in the acts of seeing and hearing now enables us to understand more clearly how these two spheres of perception overlap in man. For we have seen how the system which in seeing is the receiving organ, works in hearing as the responding one, and vice versa. As a result, optical impressions are accompanied by dim sensations of sound, and aural impressions by dim sensations of colour.

What we are thus dimly aware of in physical sense activity, becomes definite experience when the supersensible part of the senses concerned can work unfettered by the bodily organ. Clear testimony of this is again given to us by Traherne in a poem entitled Dumnesse. This poem contains an account of Traherne's recollection of the significant fact that the transition from the cosmic to the earthly condition of his consciousness was caused by his learning to speak. The following is a passage from the description of the impressions which were his before his soul was overcome by this change:

'Then did I dwell within a World of Light Distinct and Seperat from all Mens Sight, Where I did feel strange Thoughts, and such Things see That were, or seemd, only reveald to Me ...

'... A Pulpit in my Mind A Temple, and a Teacher I did find, With a large Text to comment on. No Ear, But Eys them selvs were all the Hearers there. And evry Stone, and Evry Star a Tongue, And evry Gale of Wind a Curious Song.'¹¹

*

We have obtained a sufficiently clear picture of the organization of our sense of hearing to see where the way lies that leads from hearing with the ears of the body to hearing with the ears of the spirit, that is, to the inspirative perception of the astral world.

In the psycho-physical condition which is characteristic of our present day-consciousness, the participation of our astral organization in any happenings of the outer astral world depends on our corporeal motor system being stimulated by the acoustic motions of the air, or of some other suitable medium contacting our body. For it is only in this way that our astral organization is brought into the sympathetic vibrations necessary for perceiving outer astral happenings. In order that astral events other than those manifesting acoustically may become accessible to our consciousness, our own astral being must become capable of vibrating in tune with them, just as if we were hearing them - that is, we must be able to rouse our astral forces to an activity similar to that of hearing, yet without any physical stimulus. The way to this consists in training ourselves to experience the deeds and sufferings of nature as if they were the deeds and sufferings of a beloved friend.

It is thus that we shall learn to hear the soul of the universe directly speaking to us, as Lorenzo divined it, when his love for Jessica made him feel in love with all the world, and he exclaimed:

'There's not the smallest orb which thou behold'st But in his motion like an angel sings, Still quiring to the young-eyed cherubim, - Such harmony is in immortal souls. But whilst this muddy vesture of decay Doth grossly close it in, we cannot hear it.'

(c) KEPLER AND THE 'MUSIC OF THE SPHERES'

'One must choose one's saints .. . and so I have chosen mine, and before all others, Kepler. In my ante-room he has ever a niche of his own, with his bust in it.'

This opinion of Goethe's must surprise us in view of the fact that Kepler was the discoverer of the three laws called after him, one of which is supposed to have laid the foundation for Newton's mechanical conception of the universe. In what follows it will be shown how wrong it is to see in Kepler a forerunner of the mechanistic conception of the world; how near, in reality, his world-picture is to the one to which we are led by working along Goetheanistic lines; and how right therefore Goethe was in his judgment on Kepler.

Goethe possessed a sensitive organ for the historical appropriateness of human ideas. As an illustration of this it may be mentioned how he reacted when someone suggested to him that Joachim Jungius - an outstanding German thinker, contemporary of Bacon, Van Helmont, etc. - had anticipated his idea of the metamorphosis of the plant. This remark worried Goethe, not because he could not endure the thought of being anticipated (see his treatment of K. F. Wolff), but because this would have run counter to the meaning of man's historical development as he saw it. 'Why do I regard as essential the question whether Jungius conceived the idea of metamorphosis as we know it? My answer is, that it is most significant in the history of the sciences, when a penetrating and vitalizing maxim comes to be uttered. Therefore it is not only of importance that Jungius has not expressed this maxim; but it is of highest significance that he was positively unable to express it - as we boldly assert.'¹²

For the same reason Goethe knew it would be historically unjustified to expect that Kepler could have conceived an aspect of the universe implicit in his own conception of nature. Hence it did not disturb him in his admiration for Kepler, that through him the Copernican aspect of the universe had become finally established in the modern mind - that is, an aspect which, as we have seen, is invalid as a means of forming a truly dynamic conception of the world.

In forming his picture of the universe, it is true, Copernicus was concerned with nothing but the spatial movements of the luminous entities discernible in the sky, without any regard to their actual nature and dynamic interrelationships. Hence his world-picture - as befits the spectator-form of human consciousness which was coming to birth in his own time - is a purely kinematic one. As such it has validity for a certain sphere of human observation.

When Kepler, against the hopes of his forerunner and friend, Tycho Brahe, accepted the heliocentric standpoint and made it the basis of his observations, he did so out of his understanding of what was the truth for his own time. Kepler's ideal was to seek after knowledge through pure observation. In this respect Goethe took him as his model. Kepler's discoveries were a proof that man's searching mind is given insight into great truths at any stage of its development, provided it keeps to the virtue of practising pure observation.

It has been the error of Newton and his successors up to our own day, to try to conceive the world dynamically within the limits of their spectator-consciousness and thus to form a dynamic interpretation of the universe based on its heliocentric aspect. This was just as repellent to Goethe as Kepler's attitude was attractive.

But by so sharply distinguishing between Newton and Kepler, do we not do injustice to the fact that, as the world believes, Kepler's third law is the parent of Newton's law of gravitation? The following will show that this belief is founded on an illusory conception of the kind we met before. As we shall see, Kepler's discovery, when treated in a Keplerian way, instead of leading to Newton, is found to be in full agreement with the very world-picture to which our own observations have led us.

*

It is an established conviction of the mathematical scientist that, once an observed regularity in nature has been expressed as a mathematical equation, this equation may be transformed in any mathematically valid way, and the resulting formula will still apply to some existing fact in the world. On innumerable occasions this principle has been used in the expectation of providing further insight into the secrets of nature. We came across a typical instance of this in discussing the basic theorem of kinematics and dynamics (Chapter VIII). Another example is Newton's treatment of Kepler's third law, or - more precisely - the way in which Newton's law of gravitation has been held to confirm Kepler's observations, and vice versa,

It will be our task to analyse the Kepler-Newton case on the very lines of our treatment of the two parallelogram theorems. This analysis will give us insight into a truth which we have to regard as one of the basic maxims of the new science. It says that whether a given formula, derived mathematically from one that was first read from nature, still expresses some fact of nature, cannot be decided by pure mathematical logic, but only by testing it against truly observable phenomena.

Through Kepler's third law a certain relation is expressed between the spatial dimensions of the different planetary spheres and the time needed by the relevant planet to circle once round the circumference of its own sphere. It says: 'The squares of the periodic times of the planets are always in the same proportion as the cubes of their mean distances from the sun.' In mathematical symbols this reads: t₁² / t₂² = r₁³ / r₂³ We shall see later how Kepler arrived at this law. The point is that there is nothing in it which is not accessible to pure observation. Spatial distances and lengths of time are measured and the results compared. Nothing, for instance, is said about the dynamic cause of the movements. The assertion is restricted - and this is true also of the first and second law - to a purely kinematic content, and so precisely to what the earthly onlooker can apprehend. Now it is said that Kepler's third law is a necessary consequence of Newton's law of gravitation, and that - since it is based on pure observation - it therefore establishes the truth of Newton's conception. In this assertion we encounter a misconception exactly like the one in the statement that the theorem of the parallelogram of forces follows by logical necessity from the theorem of the parallelogram of velocities. For:

(a) The law of gravitation itself derives from Newton's formula for the centripetal force acting at a point which moves along a circle, this formula being itself the result of an amplification of the formula for centripetal acceleration by the factor 'mass' (as if the latter were a pure number):

Centripetal acceleration: a = 4ϲr / t²

Centripetal force: P = am = 4ϲmr / t²

(b) The formula for centripetal acceleration - and the concept of such acceleration itself - is the result of splitting circular movement into two rectilinear movements, one in the direction of the tangent, the other in the direction of the radius, and of regarding it - by a mode of reasoning typical of spectator-thinking - as composed of the two. This procedure, however, useful as it may be for the purpose of calculation, is contrary to observation. For, as we have pointed out earlier, observation tells us that all original movement - and what can be more original than the movements of the planetary bodies - is curvilinear. No insight into the dynamic reality of cosmic movement, therefore, can ever be gained by handling it mathematically in this way.

(c) The transformation of Kepler's formula which is necessary in order to give it a form representing the nucleus of Newton's formula, is one which, though mathematically justified, deprives Kepler's formula of any significance as expression of an observed fact. The following analysis will show this.

Kepler's formula- r₁³ / r₂³ = t₁² / t₂² may be written also r₁³ / t₁² = r₂³ / t₂² and this again in the generalized form: r³ / t² = c. Obviously, by each of these steps we diminish the reality-value of the formula. In its original form, we find spatial extension compared with spatial extension, and temporal extension with temporal extension. Each of the two comparisons is a fully concrete one, because we compare entities of like nature, and only then test the ratios of the two - that is, two pure numbers against each other - to find that they are identical. To compare a spatial and a temporal magnitude, as is done by the formula in its second form, requires already a certain degree of abstraction. Still, it is all spectator's work, and for the spectator time is conceivable and measurable only as a rate of spatial displacement. Hence the constant number c, by representing the ratio between the spatial extension of the realm inside a planet's orbit and the time needed by it to perform one round on this orbit - a ratio which is the same for all planets - represents a definite structural element of our cosmic system.

By this last operation our equation has now achieved a form which requires only one more transformation to bring it into line with Newton's formula. Instead of writing: r³ / t² = c we write: r / t² = c (1 / r²) All that now remains to be done amounts to an amplification of this equation by the factor 4ϲm, and a gathering of the constant product 4ϲc under a new symbol, for which we choose the letter f. In this way we arrive at: 4ϲmr / t² = 4ϲcm / r² and finally: P = ... = fm / r² which is the expression of the gravitational pull believed to be exerted by the sun on the various planetary bodies. Nothing can be said against this procedure from the point of view

of mathematical logic. For the latter the equation r / t² = c (1 / r²) is still an expression of Kepler's observation. Not so for a logic which tries to keep in touch with concrete reality. For what meaning, relevant to the phenomenal universe as it manifests in space and time to physical perception, is there in stating - as the equation in this form does - that: the ratio between a planet's distance from the sun and the square of its period is always proportional to the reciprocal value of the area lying inside its orbit?

*

Once we have rid ourselves of the false conception that Kepler's law implies Newton's interpretation of the physical universe as a dynamic entity ruled by gravity, and gravity alone, we are free to ask what this law can tell us about the nature of the universe if in examining it we try to remain true to Kepler's own approach.

To behave in a Keplerian (and thus in a Goethean) fashion regarding a mathematical formula which expresses an observed fact of nature, does not mean that to submit such a formula to algebraic transformation is altogether impermissible. All we have to make sure of is that the transformation is required by the observed facts themselves: for instance, by the need for an even clearer manifestation of their ideal content. Such is indeed the case with the equation which embodies Kepler's third law. We said that in its original form this equation contains a concrete statement because it expresses comparisons between spatial extensions, on the one hand, and between temporal extensions, on the other. Now, in the form in which the spatial magnitudes occur, they express something which is directly conceivable. The third power of a spatial distance (r³) represents the measure of a volume in three-dimensional space. The same cannot be said of the temporal magnitudes on the other side of the equation (t²). For our conception of time forbids us to connect any concrete idea with 'squared time'. We are therefore called upon to find out what form we can give this side of the equation so as to express the time-factor in a manner which is in accord with our conception of time, that is, in linear form.¹³ This form readily suggests itself if we consider that we have here to do with a ratio of squares. For such a ratio may be resolved into a ratio of two simple ratios.

In this way the equation - r₁³ / r₂³ = t₁² / t₂² assumes the form- r₁³ / r₂³ = (t₁ / t₂) / (t₂ / t₁) The right-hand side of the equation is now constituted by the double ratio of the linear values of the periods of two planets, and this is something with which we can connect a quite concrete idea.

To see this, let us choose the periods of two definite planets - say, Earth and Jupiter. For these the equation assumes the following form ('J' and 'E' indicating 'Jupiter' and 'Earth' respectively): r_J³ / r_E³ = (t_J / t_E) / (t_E / t_J) Let us now see what meaning we can attach to the two expressions t_J / t_E and t_E / t_J.

During one rotation of Jupiter round the sun the earth circles 12 times round it. This we are wont to express by saying that Jupiter needs 12 earth-years for one rotation; in symbols: t_J / t_E = 12 / 1 To find the analogous expression for the reciprocal ratio: t_E / t_J = 1 / 12 we must obviously form the concept 'Jupiter-year', which covers one rotation of Jupiter, just as the concept 'earth-year' covers one rotation of the earth (always round the sun). Measured in this time-scale, the earth needs for one of her rotations 1 / 12 of a Jupiter-year.

With the help of these concepts we are now able to express the double ratio of the planetary periods in the following simplified way. If we suppose the measuring of the two planetary periods to be carried out not by the same time-scale, but each by the time-scale of the other, the formula becomes: r_J³ / r_E³ = (t_J / t_E) / (t_E / t_J) = period of Jupiter measured in Earth-years / period of Earth measured in Jupiter-years. Interpreted in this manner, Kepler's third law discloses an intimate interrelatedness of each planet to all the others as co-members of the same cosmic whole. For the equation now tells us that the solar times of the various planets are regulated in such a way that for any two of them the ratio of these times, measured in their mutual time-units, is the same as the ratio of the spaces swept out by their (solar) orbits.

Further, by having the various times of its members thus tuned to one another, our cosmic system shows itself to be ordered on a principle which is essentially musical. To see this, we need only recall that the musical value of a given tone is determined by its relation to other tones, whether they sound together in a chord, or in succession as melody. A 'C' alone is musically undefined. It receives its character from its interval-relation to some other tone, say, 'G', together with which it forms a Fifth. As the lower tone of this interval, 'C' bears a definite character; and so does 'G' as the upper tone.

Now we know that each interval represents a definite ratio between the periodicities of its two tones. In the case of the Fifth the ratio is 2:3 (in the natural scale). This means that the lower tone receives its character from being related to the upper tone by the ratio 2:3. Similarly, the upper tone receives its character from the ratio 3:2. The specific character of an interval arising out of the merging of its two tones, therefore, is determined by the ratio of their ratios. In the case of the Fifth this is 4:9. It is this ratio, therefore, which underlies our experience of a Fifth.

The cosmic factor corresponding to the periodicity of the single tone in music is the orbital period of the single planet. To the musical interval formed by two tones corresponds the double ratio of the periods of any two planets. Regarded thus, Kepler's law can be expressed as follows: The spatial ordering of our planetary system is determined by the interval-relation in which the different planets stand to each other.

By thus unlocking the ideal content hidden in Kepler's third law, we are at the same time enabled to do justice to the way in which he himself announced his discovery. In textbooks and encyclopaedias it is usually said that the discovery of the third law was the surprising result of Kepler's fantastic attempt to prove by external observation what was once taught in the school of Pythagoras, namely, that (in Wordsworth's language):

'By one pervading spirit Of tones and numbers all things are controlled.'

Actually, Kepler's great work, Harmonices Mundi, in the last part of which he announces his third law, is entirely devoted to proving the truth of the Pythagorean doctrine that the universe is ordered according to the laws of music. This doctrine sprang from the gift of spiritual hearing still possessed by Pythagoras, by which he could perceive the harmonies of the spheres. It was the aim of his school to keep this faculty alive as long as possible, and with its aid to establish a communicable world-conception. The Pythagorean teaching became the foundation of all later cosmological thinking, right up to the age which was destined to bring to birth the spectator-relationship of man's consciousness with the world. Thus it was left to Copernicus to give mankind the first truly non-Pythagorean picture of the universe.

When Kepler declared himself in favour of the heliocentric aspect, as indicated by Copernicus, he acknowledged that the universe had grown dumb for man's inner ear. Yet, besides his strong impulse to meet the true needs of his time, there were inner voices telling him of secrets that were hidden behind the veil woven by man's physical perceptions. One of these secrets was the musical order of the world. Such knowledge, however, could not induce him to turn to older world-conceptions in his search for truth. He had no need of them, because there was yet another voice in him which told him that the spiritual order of the world must somehow manifest itself in the body of the world as it lay open to physical perception. Just as a musical instrument, if it is to be a perfect means of bringing forth music, must bear in its build the very laws of music, so must the body of the universe, as the instrument on which the harmonies of the spheres play their spiritual music, bear in its proportions a reflexion of these harmonies. Kepler was sure that investigation of the world's body, provided it was carried out by means of pure observation, must needs lead to a re-establishment of the ancient truth in a form appropriate to the modern mind. Thus Kepler, guided by an ancient spiritual conception of the world, could devote himself to confirming its truth by the most up-to-date methods of research. That his search was not in vain, our examination of the third law has shown.

One thing, however, remains surprising - that Kepler announced his discovery in the form in which it has henceforth engraved itself in the modern mind, while refraining from that analysis of it which we have applied to it here. Yet, in this respect also Kepler proves to have remained true to himself. There is, on the one hand, the form in which Kepler pronounced his discovery; there is, on the other, the context in which he made this pronouncement. We have already pointed out that the third law forms part of Kepler's comprehensive work, Harmonices Mundi. To the modern critic's understanding it appears there like an erratic block. For Kepler this was different. While publishing his discovery in precisely the form in which it is conceived by a mind bent on pure observation, he gave it a setting by which he left no doubt as to his own conception of its ideal content. And as a warning to the future reader not to overlook the message conveyed by this arrangement, he introduced the section of his book which contains the announcement of the law, with the mysterious words about himself: 'I have stolen the golden vessels of the Egyptians from which to furnish for my God a holy shrine far from Egypt's confines.'

^{1 We must here distinguish sensation from feeling proper, in which sensation and motion merge in mercurial balance.}

^{2 Note how for Ruskin the gulf which for the onlooker-consciousness lies between subject and object is bridged here - as it was for Goethe in his representation of the physico-moral effect of colour.}

^{3 De motu animalium and Theoria mediceorum planetarum ex causis physicis deducta.}

^{4 Knowledge of this biological rhythm is still preserved among native peoples to-day and leads them to take account of the phases of the moon in their treatment of plants. A cosmic nature-wisdom of this kind has been reopened for us in modern form by Rudolf Steiner, and has since found widespread practical application in agriculture. See L. Kolisko, The Moon and Plant Growth.}

^{5 In the order of names given above we follow the ancient usage for the two planets nearest to the sun, not the reversed order in which they are used to-day. This is necessary in a cosmology which aspires at a qualitative understanding of the universe, in view of the qualities represented by these names. Note also the absence of the three most distant planets, Uranus, Neptune and Pluto. They are not to be considered as parts of the indigenous astral structure of our cosmic system - any more than radioactivity is an original feature of the earth.}

^{6 Note the 'Venus' character of Ruskin's description of the plant's state of florescence quoted above (p. 336).}

^{7 As to the time-scale of the processes brought about by Mercury and Venus respectively, experience shows that they reveal the cosmic rhythms less clearly than those for which the Moon-activity is responsible. The same is found at the opposite pole. There it is the Saturn - generated processes which show the cosmic rhythm more conspicuously than those engendered by Jupiter and Mars. To learn to recognize rhythmic events in nature and man as reflexions of corresponding planetary rhythms is one of the tasks which future scientific research has to tackle. A practical example of this kind will appear in the further course of this chapter.}

^{8 See L. Kolisko: Working of the Stars in Earthly Substances, and other publications by the same author.}

^{9 The close connexion between the ear and the motor system of the body is shown in another way by the fact that part of the ear serves as an organ for the sense of balance.}

^{10 The muscle-tone can be made audible by the following means. In a room guarded against noise, press the thumbs lightly upon the ears and tense the muscles of the hands and arms - say by pressure of the fingers against the palms or by contracting the muscle of the upper arms. If this is done repeatedly, the muscle-tone will be heard after some practice with increasing distinctness. It is easily distinguished from the sound of the circulating blood as it is much higher. (As an example: the author's muscular pitch, not a particularly high one, has a frequency of approx. 630 per sec., which puts it between Treble D sharp and E.)}

^{11 Compare also the beginning of Traherne's poem Wonder, quoted in Chapter VI (p. 110), where he says that everything he saw 'did with me talk'.}

^{12 For the particular reasons by which Goethe justifies his assertion, see his essay Leben und Verdienste des Doktor Joachim Jungius.}

^{13 The natural question why Kepler himself did not take this step, will be answered later on.}

CHAPTER XXI

Know Thyself

Our inquiries have led us to a picture of man as a sensible-supersensible organism composed of three dynamic aggregates - physical, etheric, astral. As three rungs of a spiritual ladder they point to a fourth, which represents that particular power in man by which he distinguishes himself from all other beings in nature. For what makes man differ from all these is that he is not only fitted, as they are, with a once-for-all given mode of spiritual-physical existence peculiar to himself, but that he is endowed with the possibility of transforming his existence by dint of his free will - that indeed his manhood is based on this capacity for self-willed Becoming.

To this fourth principle in man we can give no better name than that which every human being can apply to himself alone and to no other, and which no other can apply to him. This is the name, I. In truth, we describe man in his entirety only if we ascribe to him, in addition to a physical, etheric and astral body, the possession of an I (Ego).

Naturally, our previous studies have afforded many opportunities for observing the nature and mode of activity of the I. Still, at the conclusion of these studies it is not redundant to form a concise picture of this part of man's being, with particular regard to how it works within the three other principles as its sheaths. For in modern psychology, not excluding the branch of it where efforts are made to penetrate into deeper regions of man's being, nothing is less well understood than the true nature of man's egoity.

*

In order to recognize the peculiar function of the I in man, we must first be clear as to how he differs from the other kingdoms of nature, and how they differ from one another with respect to the mode of action of the physical, etheric and astral forces.

The beings of all the kingdoms of nature are endowed with an aggregate of physical forces in the form of a material body subject to gravity. The same cannot be said of the etheric forces. Only where life is present as an inherent principle - that is, in plant, animal and man - is ether at work in the form of an individual etheric organization, while the mineral is formed by the universal ether from outside. Where life prevails, we are met by the phenomena of birth and death. When a living organism comes to birth, an individual ether-body is formed out of the general etheric substance of the universe.¹ The death of such an organism consists in the separation of the etheric from the physical body and the dissolution of both in their respective mother-realms. So long as an organism is alive, its form is maintained by the ether-body present in it.

Our studies have shown that the plant is not devoid of the operation of astral forces. In the plant's life-cycle this comes to clearest expression in its florescence. But it is a working of the astral forces from outside, very much as the ether works on the mineral. As a symptom of this fact we may recall the dependence of the plant on the various outer astronomical rhythms.

It is only in animal and man that we find the astral forces working in the form of separate astral bodies. This accounts for their capacity for sensation and volition. Besides the alternation of birth and death, they experience the rhythm of sleeping and waking. Sleep occurs when the astral body leaves the physical and etheric bodies in order to expand into its planetary mother-sphere, whence it gathers new energy. During this time its action on the physical-etheric aggregate remaining upon earth is similar to that of the astral cosmos upon the plant.

Again, in the animal kingdom the ego-principle works as an external force in the form of various group-soul activities which control and regulate the life of the different animal species. It is in the group-ego of the species that we have to look for the source of the wisdom-filled instincts which we meet in the single animals.

Only in man does the ego-principle enter as an individual entity into the single physico-etheric-astral organism. Here, however, the succession of stages we have outlined comes to a conclusion. For with the appearance of the I as an individual principle, the preceding evolutionary process - or, more correctly, the involutionary process - begins to be reversed. In moving up from one kingdom to the next, we find always one more dynamic principle appearing in a state of separation from its mother-sphere; this continues to the point where the I, through uniting itself with a thus emancipated physico-etheric-astral organism, arrives at the stage of self-consciousness. Once this stage has been reached, however, it falls to the I to reverse the process of isolation, temporarily sanctioned by the cosmos for the sake of man.

That it is not in the nature of the I to leave its sheaths in the condition in which it finds them when entering them at the beginning of life, can be seen from the activities it performs in them during the first period after birth. Indeed, in man's early childhood we meet a number of events in which we can perceive something like ur-deeds of the I. They are the acquisition of the faculties of walking, speaking and thinking. What we shall here say about them has, in essentials, already been touched upon in earlier pages. Here, however, we are putting it forward in a new light.

Once again we find our attention directed to the threefold structure of man's physical organism. For the faculty of upright walking is a result of the I's activity in the limb-system of the body; the acquisition of speech takes place in the rhythmic system; and thinking is a faculty based on the nerve-system. Consequently, each of the three achievements comes to pass at a different level of consciousness-sleeping, dreaming, waking. All through the struggle of erecting the body against the pull of gravity, the child is entirely unaware of the activities of his own I. In the course of acquiring speech he gains a dim awareness, as though in dream, of his efforts. Some capacity of thinking has to unfold before the first glimmer of true self-consciousness is kindled. (Note that the word 'I' is the only one that is not added to the child's vocabulary by way of imitation. Otherwise he would, as some mentally inhibited children do, call all other people 'I' and himself 'you'.)

This picture of the three ur-deeds of the I can now be amplified in the following way. We know that the region of the bodily limbs is that in which physical, etheric and astral forces interpenetrate most deeply. Consequently, the I can here press forward most powerfully into the physical body and on into the dynamic sphere to which the body is subject. Here the I is active in a way that is 'magic' in the highest degree. Moreover, there is no other action for which the I receives so little stimulus from outside. For, in comparison, the activity that leads to the acquisition of speech is much more of the nature of a reaction to stimuli coming from outside - the sounds reaching the child from his environment. And it is also with the first words of the language that the first thoughts enter the child's mind. Nothing of the kind happens at the first stage. On the contrary: everything that confronts the I here is of the nature of an obstacle that is to be overcome.

There is no learning to speak without the hearing of uttered sounds. As these sounds approach the human being they set the astral body in movement, as we have seen. The movements of the astral body flow towards the larynx, where they are seized by the I; through their help the I imbues the larynx with the faculty of producing these sounds itself. Here, therefore, the I is active essentially within the astral body which has received its stimulus from outside. In order to understand what impels the I to such action, we must remember the role played by speech in human life: without speech there would be no community among human individuals on earth.

An illustration of what the I accomplishes as it enters upon the third stage is provided by the following episode, actually observed. Whilst all the members of a family were sitting at table taking their soup, the youngest member suddenly cried out: 'Daddy spoon ... mummy spoon. ... ' (everyone in turn spoon) ' ... all spoon!' At this moment, from merely designating single objects by names learnt through imitation, the child's consciousness had awakened to connective thinking. That this achievement was a cause of inner satisfaction could be heard in the joyful crescendo with which these ejaculations were made.

We know that the presence of waking consciousness within the nerves-and-senses organism rests upon the fact that the connexion between physical body and etheric body is there the most external of all. But precisely because this is so, the etheric body is dominated very strongly by the forces to which the physical head owes its formation. This, too, is not fundamentally new to us. What can now be added is that, in consequence, the physical brain and the part of the etheric body belonging to it - the etheric brain - assume a function comparable with that of a mirror, the physical organ representing the reflecting mass and the etheric organ its metallic gloss. When, within the head, the etheric body reflects back the impressions received from the astral body, the I becomes aware of them in the form of mental images (the 'ideas' of the onlooker-philosopher). It is also by way of such reflexion that the I first grows aware of itself - but as nothing more than an image among images. Here, therefore, it is itself least active.

If, once again, we compare the three happenings of learning to walk, to speak and to think, we find ourselves faced with the remarkable fact that the progressive lighting up of consciousness from one stage to the next, goes hand in hand with a retrogression in the activity of the I itself. At the first stage, where the I knows least of itself, it is alive in the most direct sense out of its own being; at the second stage, where it is in the dreaming state, it receives the impetus of action through the astral body; at the third stage, where the I wakens to clear self-consciousness, it assumes merely the role of onlooker at the pictures moving within the etheric body.

Compare with this the paths to higher faculties of knowledge, Imagination and Inspiration, as we learnt to know them in our previous studies. The comparison shows that exactly the same forces come into play at the beginning of life, when the I endeavours to descend from its pre-earthly, cosmic environment to its earthly existence, as have to be made use of for the ascending of the I from earthly to cosmic consciousness. Only, as is natural, the sequence of steps is reversed. For on the upward way the first deed of the I is that which leads to a wakening in the etheric world: it is a learning to set in motion the etheric forces in the region of the head in such a way that the usual isolation of this part of the etheric body is overcome. Regarded thus, the activity of the I at this stage reveals a striking similarity to the activity applied in the earliest period of childhood at the opposite pole of the organism. To be capable of imaginative sight actually means to be able to move about in etheric space by means of the etheric limbs of the eyes just as one moves about in physical space by means of the physical limbs.

Similarly, the acquisition of Inspiration is a resuming on a higher level of the activity exercised by the I with the help of the astral body when learning to speak. And here, too, the functions are reversed. For while the child is stimulated by the spoken sounds he hears to bring his own organ of speech into corresponding movements, and so gradually learns to produce speech, the acquisition of Inspiration, as we have seen, depends on learning to bring the supersensible forces of the speech-organ into movement in such a way that these forces become the organ for hearing the supersensible language of the universe.

Our knowledge of the threefold structure of man's organism leads us to seek, besides the stages of Imagination and Inspiration, a third stage which is as much germinally present in the body's region of movement, as the two others are in the regions of thought and speech. After what we have learnt in regard to these three, we may assume that the path leading to this third stage consists in producing a condition of wide-awake, tranquil contemplation in the very region where the I is wont to unfold its highest degree of initiative on the lowest level of consciousness.

In an elementary manner this attitude of soul was practised by us when, in our earlier studies, we endeavoured to become inner observers of the activity of our own limbs, with the aim of discovering the origin of our concept of mass. It was in this way that a line of observation opened up to us which led to the recognition of the physical substances of the earth as congealed spiritual functions or, we may say, congealed utterances of cosmic will.

Cosmic Will, however, does not work into our existence only in such a way that, in the form of old and therefore rigid Will, it puts up resistance against the young will-power of the I, so that in overcoming this resistance the I may waken to self-activity. Cosmic Will is also present in us in an active form. We point here to the penetration by the higher powers of the universe into the forming of the destiny of humanity and of individual man. And here Rudolf Steiner has shown that to a man who succeeds in becoming a completely objective observer of his own existence while actively functioning within it (as in an elementary way we endeavoured to become observers of our limb actions while engaged in performing them) the world begins to reveal itself as an arena of the activities of divine-spiritual Beings, whose reality and acts he is now able to apprehend through inner awareness. Herewith a third stage of man's faculty of cognition is added to the stages of Imagination and Inspiration. When Rudolf Steiner chose for it the word Intuition he applied this word, also, in its truest meaning.

*

While through Imagination man comes to know of his ether-body as part of his make-up, and correspondingly through Inspiration of his astral body, and thereby recognizes himself as participant in the supersensible forces of the universe, it is through Intuition that he grows into full awareness of his I as a spirit-being among spirit-beings -

God-begotten, God-companioned, for ever God-ward striving.

^{1 The word 'body' is here used in a sense no different from our earlier use of it, when in connexion with our study of combustion (Chapter XI) we referred to the 'warmth-body' as a characteristic of the higher animals and man. Such a warmth-body is nothing else but the warmth-ether part of an ether-body. To use the word body for aggregations of etheric or astral forces is legitimate if one considers the fact that the physical body also is really a purely dynamic entity, that is, a certain aggregate of forces more or less self-contained.}