Exegesis Volume 5 Issue #5 From: Janice & Dennis Subject: Kepler's cosmology
Exegesis Digest Fri, 04 Feb 2000

Date: Wed, 2 Feb 2000 10:10:06 +1300
From: Janice & Dennis
To: Exegesis
Subject: Kepler's cosmology
 

Copernicus began "his first astronomical treatise, the Commentariolus" with this report: "Our ancestors assumed a large number of celestial spheres for a special reason: to explain the apparent motion of the planets by the principle of regularity. For they thought it altogether absurd that a heavenly body should not always move with uniform velocity in a perfect circle." (2, p202)

We ought to wonder if this confusion between the circle archetype and the sphere was tacit, or deliberate. Regardless, both are here located in a central position in the ancient cosmic paradigm. God's perfect forms. Trans-cultural, too. In China, heaven (macrocosm) was the circle, earth (microcosm) the dot in the centre. Oriental gongs sometimes have the symbol painted on their circumference and centre, with the sound symbolising the cosmic resonance. The mysterious relation between cosmic order and symmetry and earthly disorder and chaos is the perennial focus for human enquiry into how the world works. Large-scale cosmic symmetry-breaking in the early history of the universe is currently the focus for cosmologists, but apart from the obvious sphere at genesis, I am unaware of any relevant actual findings. We might expect a subsequent binary division, opening an infinite similar series. But if the number archetypes are that primal, triadic and tetradic divisions could also be concurrent. More productive than theorising such remote history is likely to be analysis of current large-scale symmetries. Astrology maps the most evident in the local cosmos, but astrologers tend to merely recite the mantra in preference to learning how their system maps collective reality. Kepler wasn't content with such roboticism. He was that rare astrologer who was more interested in what was really going on.

"Kepler's search for scientific truth continually reflected the mysticism of a deeply religious man. Beginning in the year 1595, Kepler started gathering together his scattered thoughts about the Copernican system. He was influenced by the work of Hipparchus, Plato, St. Augustine, Nicholas of Cusa, and especially by the writings of Pythagoras, the ancient Greek philosopher. Pythagoras and his followers believed that the true nature of all things was number, and that all relationships could therefore be expressed mathematically. This view, of course, was very much in line with Kepler's own thinking. As the years passed, he continued to be driven by this Pythagorean idea that "numbers govern the world"." (1, p29)

Kepler had been inspired by this perception from Copernicus: "We find in this arrangement a marvellous symmetry of the world and a harmony in the relationship of the motion and size of the orbits, such as one cannot find elsewhere." Nowadays, cosmology has returned to the perception of cosmic symmetry, but the focus is remote in time and space, being mainly on the origin of the universe, and its general features. Astrologers need to retain focus on the unique qualities of local space/time, and unique frames of reference for human experience. Nobody experiences the origin of the universe, and any relevant knowledge that ensues from this wild goose chase by various theoretical physicists will need to be demonstrated. [Even when/if they nail the goose, it'll probably remain mythical.] "Two manifestations especially of this heavenly motion were thought by Kepler to be sure signs of God's great harmonic structure. One of these was the so-called "aspects" used by astrologers. By "aspect", astrologers meant the particular angle that one planet formed with another in the zodiac, or the band of sky across which the planets moved against the constellations of stars. Some angles.. were far more meaningful than others. Some astrologers were convinced that there were "good" and "bad" aspects, and that their effects were surely felt in the lives of human beings. Kepler did not hold with this, preferring simply to believe that certain aspects, or angles, were more indicative of world harmony than others. The other heavenly phenomenon which Kepler was concerned with was the speeds at which the planets travelled." (1, p46)

Kepler's eureka moment was based on the ratio of the orbits of Jupiter and Saturn, but it proceeded to unfold the revelation that harmonic relations between all the orbits could be found in a similar manner. Thus the famous model of the solar system reproduced in many histories of science as a picture of a 3-dimensional construction, where the 5 `regular solids' lie between the 6 planets. First Kepler had inserted the equilateral triangle between Jupiter and Saturn, and it seemed to fit. So he tried a square between Mars and Jupiter, a pentagon between Earth and Mars, a hexagon between Venus and Earth, etc., but the fit was not close enough. Then he realised he ought to try the 3-dimensional equivalents: "One can construct any number of regular polygons in a two-dimensional plane; but one can only construct a limited number of regular solids in three-dimensional space. These `perfect solids', of which all faces are identical, are (1) the tetrahedron (pyramid) bounded by four equilateral triangles (2) the cube (3) the octahedron (eight equilateral triangles) (4) the dodecahedron (twelve pentagons) and (5) the icosahedron (twenty equilateral triangles). They were also called the "Pythagorean" of "Platonic" solids. Being perfectly symmetrical, each can be inscribed into a sphere, so that all of its vertices (corners) lie on the surface of the sphere. Similarly, each can be circumscribed around a sphere, so that the sphere touches every face in its centre. It is a curious fact that, inherent in the nature of three-dimensional space, that (as Euclid proved) the number of regular solids is limited to these five forms. Whatever shape you choose as a face, no other perfectly symmetrical solid can be constructed except these five. Other combinations just cannot be fitted together. So there existed only five perfect solids - and five intervals between the planets! It was impossible to believe that this should be by chance, and not by divine arrangement. It provided the complete answer to the question why there were just six planets "and not twenty or a hundred". And it also answered the question why the distances between the orbits were as they were. They had to be spaced in such a manner that the five solids could be exactly fitted into the intervals, as an invisible skeleton or frame. And lo, they fitted! Or at least, they seemed to fit, more or less." (2, p249/50/51)

How well any model fits is a matter of opinion. Intellectual fashion trends dictate the extent to which any model is considered to match reality. This question of whether the map fits the territory is paradigmatic; normally not considered by the vast majority of members of any society, who merely subscribe to the received opinion of those deemed to be accepted experts. Newton's laws provided a better fit than Kepler's, we are taught, yet they include them, so some reasonable correspondence ought to be acknowledged. Seems to me that most natural forms have little correspondence with mathematical structures, so a reasonably close approximation has merit.

The relevance for us here is that the structure of the solar system is harmonic, and produces natural time cycles. Astrology, as a coded system for interpreting experiential qualities of time, evolved partly via projection of models onto the heavens, and partly via collective empirical learning of how well the interpretations matched reality. So we need to understand how astrology, in the form we have inherited it, decodes the archetypal structure of both the planetary orbits and the underlying system.

"Kepler also speculated on what the force could be that kept the planets speeding on their way around the sun. The old idea had been that they were carried around by angels or some other divine beings. But Kepler suggested that there must be some propelling force - some "vigour" as he called it - emanating from the sun like the spokes of a giant wheel. Thus Kepler, nearly seven decades before Isaac Newton saw the traditional apple fall from the tree at Woolsthorpe, anticipated that great English scientist's thoughts about gravitation." (1, p36)

Koestler says the more distant planets not only have longer orbits, they also travel slower - giving the example of Saturn's circuit being twice as long as Jupiter's, but it takes two and a half times as long a time to complete that distance. "Nobody before Kepler had asked the question why this should be so, as nobody before him had asked why there are just six planets.. Kepler's answer was, that there must be a force emanating from the sun which drives the planets round their orbits. The outer planets move slower because this driving force diminishes in ratio to distance "as does the force of light". It would be difficult to over-estimate the revolutionary significance of this proposal. For the first time since antiquity, an attempt was made not only to describe heavenly motions in geometrical terms, but to assign them a physical cause. We have arrived at the point where astronomy and physics meet again, after a divorce which lasted for two thousand years. This reunion of the two halves of the split mind produced explosive results. It led to Kepler's three Laws, the pillars on which Newton built the modern universe." (2, p258)

"Again we are in the fortunate position of being able to watch, as in a slow-motion film, how Kepler was led to taking that decisive step. In the key passage from the Mysterium Cosmographicum which follows... "If we want to get closer to the truth and establish some correspondence in the proportions [between the distances and velocities of the planets] then we must choose between these two assumptions: either the souls which move the planets are the less active the farther the planet is removed from the sun, or there exists only one moving soul in the centre of all the orbits, that is the sun, which drives the planet the more vigorously the closer the planet is, but whose force is quasi-exhausted when acting on the outer planets because of the long distance and the weakening of the force which it entails."" (2, p258/9)

Many years later "Kepler made, in the second edition, the following notes: ll(ii). That such souls do not exist I have proved in my Astronomia Nova. (iii). If we substitute for the word 'soul' the word 'force' then we get just the principle which underlies my physics of the skies in the Astronomia Nova.... For once I firmly believed that the motive force of a planet was a soul. . . . Yet as I reflected that this cause of motion diminishes in proportion to distance, just as the light of the sun diminishes in proportion to distance from the sun, I came to the conclusion that this force must be something substantial - 'substantial' not in the literal sense but . . . in the same manner as we say that light is something substantial, meaning by this an unsubstantial entity emanating from a substantial body."" (2, p259)

"We are witnessing the hesitant emergence of the modern concepts of "forces" and "radiating energies" which are both material and non-material, and, generally speaking, as ambiguous and bewildering as the mystical concepts which they have come to replace. As we watch the working of the mind of Kepler (or Paracelsus, Gilbert, Descartes) we are made to realize the fallacy of the belief that at some point between the Renaissance and the Enlightenment, man shook off the "superstitions of medieval religion" like a puppy getting out of the water, and started on the bright new road of Science. Inside these minds, we find no abrupt break with the past, but a gradual transformation of the symbols of their cosmic experience - from anima motrix into vis matrix, moving spirit into moving force, mythological imagery into mathematical hieroglyphics-a transformation which never was, and, one hopes, never will be entirely completed." (2, p259)

In his book "Kepler", the novelist John Banville won the 1981 Guardian fiction prize in Britain with his dramatisation of parts of Kepler's life. A section of the book reproduces entire letters of Kepler's. Included is one to his powerful friend at court, the Bavarian chancellor von Hohenburg, at Christmas 1606, which reveals Kepler's cosmology...

"Having lately completed my Astronomia nova, and looking forward to a year or two of much needed rest & recuperation, here I am now launching out again, with renewed fervour, upon those studies of world harmony, which I interrupted seven years ago in order to clear away the little task of founding a new astronomy! Since, as believe, the mind from the first contains within it the basic & essential forms of reality ... I foresee a work divided into five parts, to correspond to the five planetary intervals, while the number of chapters in each part will be based upon the signifying quantities of each of the five regular or Platonic solids which, according to my Mysterium, may be fitted into these intervals. ...I have taken as my motto that phrase from Copernicus, in which he speaks of the marvellous symmetry of the world, and the harmony in the relationships of the motion & size of the planetary orbits. I ask, in what does this symmetry consist? How is it that man can perceive these relationships? The latter question is, I think, quickly solved - I have given the answer just a moment ago. The soul contains in its own inner nature the pure harmonies as prototypes or paradigms of the harmonies perceptible to the senses. And since these pure harmonies are a matter of proportion, there must be present figures which can be compared with each other: these I take to be the circle and those parts of circles, which result when arcs are cut off from them. The circle, then, is something which occurs only in the mind: the circle which we draw with a compass is only an inexact representation of an idea which the mind carried as really existing in itself. In this I take issue strenuously with Aristotle, who holds that the mind is a tabula rasa upon which sense perceptions write. This is wrong, wrong. The mind learns all mathematical ideas & figures out of itself; by empirical signs it only remembers what it knows already. Mathematical ideas are the essence of the soul. Of itself, the mind conceives equidistance from a point, and out of that makes a picture for itself of a circle, without any sense perceptions whatever. ...Geometry was not received through the eyes: it was already there inside."

It is interesting to see the astrologer/scientist adopting the rather feisty stance that our pattern recognition of basic primal symmetries (archetypes) is innate rather than learned. Both, perhaps, would be more reasonable. [This line of reasoning would be more persuasive if the Pythagorean solids all appeared in natural forms, but I have seen no evidence that the more complex ones do.] Still, the assumption that humans, and animals, use their brains to model their environment remains widely held in science, almost to the point of having become common sense.

If, then, the psyche has evolved to mirror the cosmic structure of the environment, it would be unsurprising to find archetypes of nature manifesting synchronously within as without. Astrology, as a decoding system, ought then to be seen as a (flawed) cultural device for interpreting the local cosmic environment. Since the way the world works is reliably constant, psychic structure and those environmental structures that the horoscope depicts can be expected to have a durable correspondence. Kepler clearly intuited this, and his efforts to discover the fundamental symmetries of the solar system proceeded therefrom. Our own efforts in this list can be guided by his.

(1) "Johannes Kepler and Planetary Motion", DC Knight, 1962. (2) "The Sleepwalkers", A Koestler, 1959.

Dennis Frank

End of Exegesis Digest Volume 5 Issue 5

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