c20p44

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.).

 * * * 

c20p63

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.

c20p81

(c) KEPLER AND THE ‘MUSIC OF THE SPHERES’

c20p98

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.

c20p5

Let our first object of observation be man himself in so far as he illustrates a polarity of the second order.

c20p90

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,

c20p25

In a science which knows how to deal with movement as an event of absolute dynamic reality, the Copernican aspect loses its significance as the only valid aspect of our cosmic system. For its application as a means of describing the dynamic happenings within this system presupposes the acceptance of Einstein’s relativistic conception of motion. Indeed, for the building up of a picture of the dynamic structure of our system, the Copernican view-point is inadequate.

c20p45

(b) HEARING AS DEED

c20p64

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.

c20p82

‘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.’