'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 ...

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.

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.

What strikes us first in this respect is the plant's dependence on the succession of the seasons. These in turn are an outcome of the changing mutual positions of earth and sun. That which forms part of the individual organism in higher living beings is located in the cosmic surroundings of the plant. In fact, it is our planetary system which provides the forces that stir the etheric and physical forces of the earth to their various interactions, thus bringing about all the manifold secondary polarities.

As the originator of the secondary polarities in earthly nature the astral realm must undoubtedly itself be structured polarically, one part of it forming the cause of all the happenings by which levity is brought into interaction with gravity, the other of all the happenings by which gravity is brought into interaction with levity. There must be a further part which is responsible for the establishment of the 'mercurial' mean between the two poles of the secondary polarity. This leads us to a threefold aspect of the astral realm.

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.).

 * * * 

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.

'... 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

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:

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.