Does the Cosmos Resonate—or Not?

Why the most harmonious universe could also be the most unstable—and why cosmic order seems to favor irrationality.

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Human beings have always admired the cosmos for its elegance. From the graceful orbits of the planets to the silent symmetry of the spiral galaxies, the night sky radiates harmony. For centuries, philosophers, scientists, and mystics alike have tried to reduce this harmony to something concrete: a note, a number, a formula.

Two such numbers, the octave and the golden section, have emerged as symbols of universal order. Both occur in music, art, mathematics, and architecture. Both are praised for their aesthetic appeal and cosmic significance. And recent scientific work points to something even more fascinating—and paradoxical.

The Octave and the Golden Section

The octave, the musical doubling of a frequency (2:1), is familiar and pleasing to the ear. Play a low C on the piano and then a C one octave higher and the sound resonates. It feels stable and harmonious. But in nature, and especially in the mechanics of the heavens, as we shall see, the same resonance turns out to be a source of chaos.

In contrast, the golden section or ratio—approximately 1.618 or φ (phi)—seems to be more obscure. It’s praised as the most irrational number, which means that it’s the most difficult to approximate with fractions.¹ But in the dynamic systems found in everything from planetary motion to the heartbeat² to the human gait³, the golden ratio has a stabilizing rather than a disruptive effect.

For the ancient Greeks, the heavens were musical. Pythagoras believed that the planets sang the “music of the spheres” as they danced. In his work Harmonices Mundi [The Harmony of the world],⁴ Johannes Kepler detailed correspondences between the planetary orbits and the musical intervals. He saw divine harmony in the proportions of the solar system. He was especially fascinated by the harmonious relationships between the orbits. Saturn and Jupiter, for example, with orbital periods of about 30 and 12 years respectively, orbit the sun in a ratio of 2:5 (close to a double octave).

Planetary Resonance and Earthquakes

Today, however, we know that solar systems, including our own, are fragile.⁵ Orbital harmonies can lead to chaotic behavior. The superposition of resonances—especially simple resonances such as 2:1—can actually cause instability. Jack Wisdom even calculated that the entire solar system has a Lyapunov time (a measure of how quickly small differences lead to chaos) of only five million years.⁶

This tension between harmony and chaos doesn’t only apply to planets. Researchers analyzed earthquake data from over sixty years and made a surprising discovery: earthquakes measuring 7+ on the Richter scale cluster around certain orbital constellations with Jupiter.⁷

Using NASA planetary ephemerides and extensive chi-square tests, the team discovered a surprising correlation: the probability of a strong earthquake increases significantly when Earth and Jupiter are at angles of approximately 45° and 135° to each other—not at the intuitively expected positions of exactly 0° or 180°. These configurations do not form obvious resonances such as octaves but appear to exert a pulsating tidal effect that temporarily destabilizes tectonic systems and triggers large seismic events.

Anti-resonance and Refusal

In dynamic systems (including planetary orbits and forced oscillators), the golden ratio, as the most irrational ratio, has the special property of avoiding resonance with almost everything: it simply cannot be harmonized with other frequencies. In systems dominated by resonance, this makes φ a kind of “anti-resonance number.”

In mathematics, this property is known as Diophantine incommensurability. Physicists in the twentieth century, particularly using the so-called KAM theory,⁸ showed that systems with golden ratios tend to form quasi-periodic, stable tracks that are immune to the chaos generated by neighboring resonances. And in physics, frequency modulations based on the golden ratio often lead to minimal Lyapunov exponents, indicating high stability over long periods of time. This property also occurs in other disciplines, such as musical instrument making ⁹ and neural oscillations.¹⁰ Steiner describes incommensurability as something that brings life to an otherwise rigid system.¹¹

Ultimately, what we call harmony could be a double agent. The resonances that sound beautiful to our ears—the octaves, the perfect ratios—are often the fault lines of instability in the cosmos. Meanwhile, the golden middle, with its refusal to conform neatly to anything, whispers secrets of a deeper order. Irrationality, not symmetry, is what quietly holds these systems together. Where resonance causes chaos, φ deflects it, not through superiority, but by slipping between the cracks of predictability. Does the universe perhaps entrust its deepest stability not to what conforms but to what refuses to conform?

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Translation Joshua Kelberman

1. Heinrich Müller, “Physics of Irrational Numbers,” Progress in Physics 18, no. 2 (October 2022): 103–109.
2. Ertan Yetkin, “The Cardiac Cycle and Diastolic Duration in Healthy Adults: Verifying Golden Ratio?” Indian Heart Journal 77, no. 2 (2025): 130.
3. Marco Iosa, Giovanni Morone, and Stefano Paolucci, “Golden Gait: An Optimization Theory Perspective on Human and Humanoid Walking,” Frontiers in Neurorobotics 11 (December 19, 2017): article 69.
4. Johannes Kepler, Harmonices Mundi [The Harmony of the world] (Linz: Johann Planck, 1619).
5. A. C. Petit, G. Pichierri, M. Goldberg, and A. Morbidelli, “Dynamical Evolution of Planetary Systems,” in Handbook of Exoplanets, edited by Hans J. Deeg and Juan A. Belmonte (Cham, Germany: Springer, 2025).
6. Jack Wisdom, “The Origin of the Kirkwood Gaps: A Mapping for Asteroidal Motion Near the 3/1 Commensurability,” Astronomical Journal 87, no. 3 (1982): 577–593.
7. E. W. Holt and E. Newman, “Tidal Triggering of Magnitude 7+ Earthquakes by Jupiter,” arXiv preprint arXiv:2508.07064 (2025).
8. Kolmogorov–Arnold–Moser (KAM) theorem: Andrej N. Kolmogorov (1954); Vladimir I. Arnold (1963); Jürgen Moser (1962).
9. B. Patrick Daley and Justin Goldston, The Harmonic Color Wheel: A Journey Through Universal Harmony, The SydTek University Stacks 27 (n.p.: SydTek University Stacks, 2025).
10. Barbara Pletzer, Hubert Kerschbaum, and Wolfgang Klimesch, “When Frequencies Never Synchronize: The Golden Mean and the Resting EEG,” Brain Research 1335 (2010): 91–102.
11. Rudolf Steiner, Interdisciplinary Astronomy: Third Scientific Course, CW 323 (Hudson, NY: SteinerBooks, 2020), especially lecture in Stuttgart, Jan. 4,  1921; see also, The Book of Revelation and the Work of the Priest, CW 346 (Forest Row, East Sussex: Rudolf Steiner Press, 1999), lecture in Dornach, Sept. 15, 1924.