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 = 4(π^2)r / t2

Centripetal force: P = am = 4(π^2)mr / 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- r1^3 / r2^3 = t1^2 / t2^2 may be written also r1^3 / t1^2 = r2^3 / t2^2 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 4(π^2)m, and a gathering of the constant product 4(π^2)c under a new symbol, for which we choose the letter f. In this way we arrive at: 4(π^2)mr / t2 = 4(π^2)cm / 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 (r^3) 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 (t^2). 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 - r1^3 / r2^3 = t1^2 / t2^2 assumes the form- r1^3 / r2^3 = (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): rJ^3 / rE^3 = (tJ / tE) / (tE / tJ) Let us now see what meaning we can attach to the two expressions tJ / tE and tE / tJ.

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: tJ / tE = 12 / 1 To find the analogous expression for the reciprocal ratio: tE / tJ = 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: rJ3 / rE3 = (tJ / tE) / (tE / tJ) = 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