c20p99 chapter_20_text

c20p99

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 4Ï2m, and a gathering of the constant product 4Ï2c under a new symbol, for which we choose the letter f. In this way we arrive at:
4Ï2mr / t2 = 4Ï2cm / 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

c20p6 chapter_20_text

c20p6

When studying man’s nature with the idea of understanding the genesis of his onlooker-consciousness, it will be remembered, we had to examine the ordering of his consciousness into waking, dreaming and sleeping in the different members of his organism. We recognized three different organic systems, the sensory-nerve system, the rhythmic system and the metabolic-limb system, as the bodily foundation of three different soul activities. These are the thought-forming activity which belongs to waking consciousness; the feeling activity which belongs to dream consciousness; and the willing activity which belongs to sleep consciousness. We then saw in these three systems representatives of the three alchemical functions – ‘sulphurous’ in the metabolic, ‘saline’ in the nervous, ‘mercurial’ in the mediating rhythmic system.

c20p100 chapter_20_text

c20p100

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?

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c20p26 chapter_20_text

c20p26

This statement must not be taken to deny all justification to the heliocentric view-point. There is, after all, the fact that the orbits which the heavenly bodies appear to follow when viewed in this way, assume a particular geometrical character which cannot be accidental. And more than that, when the heliocentric aspect is seen in its true setting, it forms (as will be shown later) an extremely revealing part of the script which tells us of the nature of the astral forces. All that is required is that the heliocentric picture be taken for what it is, namely, a purely kinematic aspect of the true dynamic ordering of our cosmic system, which in itself calls for quite other means of conceptual representation.

c20p46 chapter_20_text

c20p46

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.

c20p65 chapter_20_text

c20p65

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.

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c20p83 chapter_20_text

c20p83

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.

c20p102 chapter_20_text

c20p102

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.

c20p7 chapter_20_text

c20p7

Regarded thus, man’s nature reveals itself as being endowed with a physical organization, and an etheric organization, which are brought into different relationships by being acted upon by a third organization consisting of forces of the kind here to be studied. At his lower pole these forces co-ordinate the ether and physical organizations in a manner corresponding to the function of the ‘sulphur’-pole of the alchemical triad. Here, therefore, the warmth-ether takes the lead and acts in such a way that the higher kinds of ether are able to come to expression in material processes of the body. At the upper pole corresponding forces co-ordinate the physical and ether organizations in a way characteristic of the ‘salt’-pole. This gives the lead to the life-ether, so that the physical organism provides the foundation for the activity of the ether-forces without, however, being actually penetrated by them (at least after completion of the embryonic and first post-embryonic development). As a result, consciousness lights up in this part of the body. The rhythmic sphere, being the ‘mercurial’ middle, is distinguished by an alternation of the two conditions described. With each diastole it becomes more akin to the pole below, and with each systole more akin to the pole above. Here, therefore, the lighting up of consciousness is only partial.

c20p101 chapter_20_text

c20p101

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.