Johannes Kepler: Harmonia Mundi

Johannes Kepler 1571-1630

During his lifetime of investigations into planetary motion, Johannes Kepler discovered simple numerical relationships between the planetary orbits which exhibited harmonic frequencies which matched those of the musical scale. He was intensely interested in Pythagorean number theory and the geometry of the simple solid figures, the tetrahedron, cube, octahedron, icosahedron and dodecahedron. Analysing planetary position data observed and collated by Tycho Brahe, he found that the golden section, phi, and the square roots and cubes of simple whole numbers permeated the relationships of orbital periods, distance and eccentricity ratios. Convinced he had discovered direct evidence of the Creator’s hand in the apparent  perfection of the cosmos, he devoted much of his life to unravelling the interwoven geometrical relationships of the solar system.

DISCLAIMER: This blog does not take any position regarding concepts of ‘Intelligent design’ or ‘creationism’ . Instead it seeks knowledge using reason and data and follows where they lead.

The laws he discovered governing planetary motion hold up very well for the inner planets as measured and calculated by modern sytems such as the JPL ephemeris.

Kepler’s laws are:

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.^[1]
3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Although these three laws are all that mainstream astronomy and modern astrophysics eventually distilled from Keplers work, there is much more to tell, and it reveals the reason only a fraction of his work is acknowledged by the mainstream as belonging to modern science.

Kepler didn’t just find the laws of nature governing individual planetary orbits. He discovered rules governing the relationships between the orbits of the planets of the inner solar system, and the ‘consonances and compensations’ built into their orbital eccentricities and inter-related timings. Rules that now turn out to relate to the recently discovered feedbacks that tie the motion of the planets directly to the variation in the main source of energy at the heart of the system, The Sun.

Kepler intuited this necessity of planetary-solar mutual influence within a holistic paradigm in the epilogue of his meisterwerk ‘Harmonia Mundi’ – The Harmonies of the World. He understood that just as the sun effected the planetary motion,  the sun had to be affected by that motion, so that the whole system could work in harmony.

For as the sun rotating into itself moves all the planets by means of the form emitted from itself … And the movements of the planets around the sun at their centre and the discourses of ratiocinations are so interwoven and bound together that, unless the Earth, our domicile, measured out the annual circle … never would human ratiocination have worked its way to the true intervals of the planets and to see the other things dependent from them, never would it have constituted astronomy.

If as the Earth breathes forth clouds, so the sun black smoke? If as the Earth is moistened and grows under showers, so the sun shines with those combusted spots, while clear flamelets sparkle in all its fiery body.

Still it is not easy for dwellers on the Earth to conjecture what sort of sight is present in the sun, what eyes there are, or what other instinct there is for percieving those [planetary] angles even without eyes, and for evaluating the harmonies of the movements entering into the antechamber of the mind by whatever doorway, and finally what mind there is in the sun.

kepler was drawing an analogy between the effect of planetary conjunctions as seen from Earth on the mind (ratiocinations) and dispositions of the human psyche and their effect on the sun.

In trying to fathom the numerical relationships he observed in the planetary motions, Kepler worked to understand fundamental geometrical relationships, discovering the ‘Kepler triangle’.

This united two of the basic geometrical features of the inner solar system using the golden section – phi and Pythagoras’ theorum.

This leads to the reconciliation of the circle and square – almost. There is an error of 0.1%, about the same quantity as the sun’s decadal variability. More detail at the Wiki page.
On consideration of  his discoveries regarding the planets hidden ratios and harmonies Kepler said;

Geometry has two great treasures: one the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio [ the golden section]. The first we may compare to a measure of gold; the second we may name a precious jewel.

And it’s saying things like this that led to the exclusion of much of his work from the corpus of science. A man of his times, he was part scientist, part mystic, and part-time jobbing astrologer. By the time Isaac Newton became president of the Royal Society 85 years later, the great science institution of its time, there was an effort underway to purge the natural sciences and especially astronomy and celestial mechanics of renaissance concepts of a fusion between science, art and religion. So those parts of Keplers work which related to Pythagorean number theory and the relationship of celestial motions to the harmonies of the musical scale were rejected as mysticism for composers to muse upon, and those parts which used the golden section and the five solid crystal forms were dismissed as ‘mere artifice’, for artists and engravers to design patterns and proportions with.

Geometry was giving way to abstract mathematics. By the time the enlightenment period took full hold, with its emphases on taxonomy and the standardisation of measurement and a more militant stance against the intrusion of religious ideas onto the ground of science, Kepler’s deeper insights into the mysteries of the solar system were lost to view. They were torn asunder by the division of ‘categories’,  harmony and ratio hidden in the linear fixation of metrification: Kepler’s alchemical golden section transmuted to the leaden and dead-handed Astronomical Unit.

In the next part in this series, we will see how the ratios Kepler discovered were found to be the same as those involved in the cyclicity of the occurrence of solar flares and CME’s by Theodor Landscheidt in the 1980’s, confirming the other element of the unifying whole Kepler correctly intuited.