Sacred geometry and cymatics
One big 'keystone moment' for me was when I realized that cymatic resonance patterns are directly related to the geometric figures descended from Hebrew gnosticism and the Egyptian mystery school (commonly known as 'sacred geometry'). If you are not familiar with cymatics, this refers to the study of resonance patterns on plates sprinkled with powder.
The following image shows a comparison of the cymatic pattern produced by the first and fifth harmonic partials (a musical major third / minor sixth) with the geometrical figure known as Metatron's cube (Hebrew Star of David). When the two are overlaid, it is easy to see the correspondence between the physical and mathematical representations.
Such vibratory pattern are naturally recursive or fractal, coherently nesting the same figure inside themselves. This phenomena is a natural result of overlapping harmonic waves. In this case, the inside cube and corresponding Metatron's cube is actually the square root of the outer cube.
I think that sacred geometry was seen as sacred by the ancients because it occurs naturally in all harmonic waves, occurring not only in sound and music but also coherent light (such as laser and star light), atoms and even the event horizons of black holes. In fact, harmonics are the prime ordering principle and foundation of quantum physics, explaining everything from flowers to human consciousness as the musical geometry of harmonic interference just like this.
to visualize the principle of what I mean..
and with commentary explaining this:
wave interference of overlapping and condensing waves at the quatntum scale makes this whole ball of wax possible.
Concerning this, I just received some very interesting papers by physicist Peter Rowlands that proposes a quantum language grammar for encoding intelligence in holographic space using resonance principles. I think things are looking up for Science to finally arrive at a better understanding of Nature's simplicity. Still, there's no telling how long it will take for it to get into the schools and inform the broader society