Signature of the Celestial Spheres
Discovering Order in the Solar System
by Hartmut Warm
In Hartmut Warm's magnum opus, "Signature of the Celestial Spheres", the author - 'a civil engineer and independent researcher in astronomy, geometry and the history of harmonics and musical aesthetics' - takes up the challenge laid down 400 years ago by Johannes Kepler, the 17th century mathematician and astronomer, in his book Harmonices Mundi (Harmonies of the World) for: "...as many of you as will chance to read this book ... come, be vigorous and either tear up one of the harmonies which have everywhere been related to one another, change it for another one, and test whether you will come close to the astronomy laid down in Chapter IV; or else argue rationally whether you can build something better ... and overthrow either partly or wholly the arrangement which I have applied...". Kepler had attempted to find a relationship between measurements of the planetary orbits expressed as ratios, the geometry of regular solids (the Platonic solids and his own discovery of 4 regular star polyhedra) and musical intervals which are themselves a ratio of frequencies.
Kepler certainly made some progress in this endeavour but he was not happy with the accuracy to which he could make the correlations and thus, the challenge that until the work of Hartmut Warm has not been taken up. Hartmut takes the reader on an expedition across the solar system, enumerating and exploring all likely spatial and temporal parameters of the wandering stars in order to find patterns in the ratios of these measurements that would correspond to the worlds of geometry and music. Mercifully, the bulk of the mathematics is presented in extensive appendices so as not to interrupt and distract from the main flow of the exposition. Certainly in the present age there is a much more complete picture of the solar system, very powerful mathematical algorithms for predicting its configurations, readily available precise measurements of all its aspects and the possibility, by the use of computers, of exploring the movements of the planets for long periods of time in the past and into the future. All being of distinct advantage to the present-day researcher compared with Kepler in his age. Given this, it would seem highly probable that if there were any correspondences to be found then a mind diligent enough and using the tools and information now available should be able to find them. It seems that Hartmut has done just that and that we should be grateful to Kepler for having initially recognised the possibility and for raising the challenge. Hartmut finds correspondences by a number of different means. There are the ratios between the semi-minor axes (a fundamental parameter of an ellipse) of the planetary orbits, which correlate with musical intervals. There are the various devices developed by Hartmut for depicting the geometries of the relative motions of the planets either from a helio-centric viewpoint or from the viewpoint of particular planets and especially in relation to periodically repeating events such as conjunctions and oppositions. Thus in the interplay of Venus and Earth we have a pentagram traced out around the sun which comes to completion every 8 years but not quite perfectly so that after this time the next pentagram is rotated at 2.4 degrees to the previous and so in this way rotating completely around the sun in 1194.6 years. In the dance of the planets Jupiter and Uranus there is the creation of a giant hexagram around the sun over a period of 82.87 years. In many of the constructions, three or more planets are involved. For example the consideration of the successive positions of Venus and Jupiter at the times of Venus /Uranus conjunctions leads to an almost perfect 20-pointed star figure being drawn across the heavens and in the same way plotting the positions of Earth and Jupiter at Venus/Uranus conjunctions draws a 30-pointed star which can be seen as the synthesis of the numbers 5 and 6 from the Venus/Earth pentagram and the Jupiter/Uranus hexagram. In plotting the 'double conjunctions' of Venus at Venus/Jupiter and Venus/Neptune i.e. by drawing lines between the positions of Venus at conjunctions with Jupiter and with Neptune as they occur in sequence over a period of 379.14 years, there results a geometry not unlike that of a rose window created by a medieval master craftsman. A different but similarly spectacular construction results from plotting the 'double conjunctions' of Venus at Venus/Saturn and Venus/Neptune over a period of 809.46 years. Surprisingly there are even beautiful geometric correspondences observed involving the individual periods of rotation of the planets. If one considers each planet to possess an arrow starting at its centre and pointing outwards through its equator then knowing the rotational period for each, one can determine how often the direction of these imaginary arrows are aligned in parallel - these moments being referred to as 'rotation synods'. Thus in a method analogous to those involving the planetary conjunctions we have for example the plotting of the successive positions of Venus at Sun/Mercury rotation synods, which draws a slowly rotating pentagon through the firmament or as Harmut puts it, "The queen of heaven appears to enjoy embellishing her pentagrams with corresponding pentagons". Plotting the successive positions of the Moon (one of the 'ancient' planets) at Sun/Mercury rotation synods produces a slowly rotating 10-pointed star or double pentagram. The examples here are but a few of the wonders revealed in this book. Signature of the Celestial Spheres is filled to the brim with a bountiful plethora of dazzling stars, flowers and other breath-taking geometrical splendours all being rendered in space by the heavenly bodies of our solar system through their sometimes complex relations. This collection includes 16 magnificent colour plates. Hartmut manages to relate these geometries and the musical proportions discovered with the corresponding characters of the planets which are approached with a reverential feeling and dealt with in a respectful and appreciative manner and not as if they are just big spheres of matter flying through the space-time continuum as is prevalent today in the popular view. We start to see the planets as more like beings and the solar system more like a vast community with the discovered correspondences being but indications of influences from a higher realm. However, the author does not shy from the task of addressing whether in fact these amazing geometries and correspondences are not just something that can reasonably be expected to arise through chance.
The book includes stochastic analyses to determine the probabilities of the observed coincidences arising if, for example, the planets were randomly distributed in their orbits. The probabilities are shown to be very low indeed. It seems that the present structure of the solar system is not something that has simply come about by chance and the author contends that higher powers have played and may still be playing a guiding role. The climax of the book, not to give too much away, brings together all of the relationships discovered into a cohesive and glorious whole that more than does justice to the task of answering the challenge set so long ago by Johannes Kepler.
Perhaps just as Kepler was himself living at the dawn of a new age of materialistic science, now at this time with the Venus/Earth pentagram having completed a 180 degree rotation in the 600 years since the start of the consciousness soul age, thus portending a great and imminent cultural shift, we can begin to hope that through the new insights and efforts inspired and assisted by the likes of Hartmut's stupendous achievements, we will be able to raise science and human understanding to a new, higher octave.
Publisher: Rudolf Steiner Press
Dimensions: 15.6 x 23.2 x 3cm
Weight: 921 grammes