Harmony of the spheres: star polygons in space
Connect the positions of two planets over years and symmetrical star figures appear. Venus and Earth draw a fivefold rosette.
That the universe is tuned like a musical instrument is one of humanity’s oldest ideas. According to legend, Pythagoras could hear the music of the spheres. Plato carried the discovery attributed to him, that consonances correspond to simple ratios, over to the structure of the cosmos.
Kepler
At the beginning of the modern age Johannes Kepler gave this idea a new foundation. In his Harmony of the World (Harmonices Mundi, 1619) he tried to use the planetary laws he had discovered to show that the motions of the planets follow ratios corresponding to musical intervals. For him geometry, music and astronomy were at heart one, and what holds the world together were geometric archetypes, thoughts of God.
Earlier, Kepler had supposed that the distances of the six known planets were determined by the five Platonic solids, an idea he published in 1596 and, despite the discrepancies, still defended in a new edition in 1621. Why the five perfect solids fascinated him so much that he wanted to transfer them to the universe is answered by the geometry of gap-free filling of space. Long after Kepler, Schelling, Goethe, Hermann Hesse and many others took up the idea in philosophy and poetry, and Hans Kayser held it to be scientifically valid. Today’s science, however, hardly takes the harmony of the spheres in the solar system seriously and sees Kepler’s ideas rather as a beautiful dream.
Hartmut Warm
The engineer and programmer Hartmut Warm has revived Kepler’s idea in a new form. He studied not the distances between the orbits but the patterns of motion of pairs of planets over long periods. Connect the positions of two planets with a line at regular intervals and astonishingly symmetrical figures appear. In them Warm found geometric forms and, transferred to acoustics, intervals such as the third, fourth and fifth. His work is called Die Signatur der Sphären (The signature of the spheres).
Lines between two planets on simplified circular orbits, drawn over eight revolutions of the outer planet. Venus and Earth (the default) give a fivefold rosette, because 8 Earth years are almost exactly 13 Venus years.
The rosette of Venus and Earth is the best-known example: eight Earth years correspond almost exactly to thirteen orbits of Venus, and the five conjunctions in that time lie on the points of a pentagram. This is a real order that anyone can check in the sky, and it follows from a single ratio. The number of points is always the difference of the revolutions, here 13 − 8 = 5. That 5, 8 and 13 are consecutive Fibonacci numbers is a pretty bonus (see The pentagram and the golden ratio). Whether the planets were drawn into this ratio by their gravity, as the moons of Jupiter were into theirs (see Resonances), is disputed, however. Most celestial mechanicians regard 8 : 13 as a chance approximation, not a true resonance. Whether one wants to see the harmony of the spheres of the Pythagoreans in such patterns is a matter of interpretation. At most they are linked with the tetractys by the pentagram, which on this website also appears among the start figures of the tetractys. No causal connection is known.
Sources and further reading
Sources
- Plato, Republic X 616b to 617d (the sirens on the spheres)
- Johannes Kepler, Mysterium cosmographicum, Tübingen 1596, 2nd ed. Frankfurt 1621
- Johannes Kepler, Harmonices mundi libri V, Linz 1619, book V
Further reading
- Hartmut Warm, Die Signatur der Sphären. Von der Ordnung im Sonnensystem, Hamburg 2001