Description
Get our FREE Newsletter at https://www.PrometheanAction.com — In this June 13, 2026 Promethean Action weekly class, Bruce Director argues that a new revolution in science requires rejecting today’s reductionist paradigm—mathematics → physics → biology → cognition—and returning to the creative breakthroughs of figures like Kepler. Using Kepler’s Harmony of the World, he reviews elliptical planetary motion and Kepler’s laws, then explores Kepler’s claim that the solar system is organized by harmonic (musical) principles perceptible by the intellect. Director connects geometric congruence on planes versus spheres to harmonic ordering in nature, demonstrates musical ratios and the Pythagorean comma, and contrasts chant with polyphony to show how well-tempered tuning enables higher composition. Examples from Bach and Beethoven illustrate musical “geometry” and resolution of dissonance. He concludes with a “creative paradigm” grounded in creativity, human art and science, life, and abiotic processes.
What Mathematics Can Learn From Classical Music by Bruce Director Fidelio Magazine Winter 1994
https://archive.schillerinstitute.com/fidelio_archive/1994/fidv03n04-1994Wi/fidv03n04-1994Wi_037-what_mathematics_can_learn_from.pdf
Beethoven String Quartet No. 15 Op. 132 Amadeus Quartet 1st Movement
https://www.youtube.com/watch?v=-nz0_co9KNc
J.S. Bach Es ist genug BWV 60.5 Gächinger Kantorei
https://www.youtube.com/watch?v=OYopaW1ImPQ
00:00 Class Intro and Stakes
02:05 Kepler and New Science
04:52 Reductionism Under Fire
06:31 Limits of Math and Physics
10:17 Life Mind and AI
14:35 Kepler Laws Review
18:57 Third Law and Harmony
24:31 Harmony as Congruence
30:34 Platonic Solids and Orbits
32:19 Music of the Spheres
37:04 String Ratios and Comma
42:42 Mars Orbital Fifth
44:37 Planetary Interval Pairs
46:09 Asteroid Belt Discord
52:13 Polyphony And Prayer
57:38 Tempering The Comma
01:01:14 Keyboard Interval Geometry
01:08:05 Spiral Of Keys
01:11:23 Bach Dissonance Resolves
01:14:40 Beethoven Half Step World
01:24:34 Creative Paradigm Wrap Up