Relationship between geometry and wave interference

Excluding my formal math training, I approach geometry from the perspective of music perception and visualization. As I came to learn, perception is related to a reflected first-derivative "spatial" Gaussian curve, which in polar coordinates describes the structure of our brain (and leaves, continental formations, et-cetera). This is my Interference function, which I derive unconventionally through a symmetrical balance of squared harmonics and a Fibonacci estimator equation.

This apple-like curve is the pattern that harmonic interference makes between two orthogonal coherent standing wave sources, such as a musical tone or a laser beam. When two standing waves phase-shift against each other, they create geometry -- that is, harmonic (crystals) when they align with resonance points and anti-harmonic (quasi-crystals) when they align with damping points. So, crystalline structures (12-fold Platonic and Archimedean) are resonant structures produced by harmonic convergence or alignment of standing waves. Quasi-crystalline structures (5-fold Fibonacci, Lucas and other irrational golden ratio spaces) are non-resonant or silent spaces (gaps) between harmonic structure. Harmonic is spatial while anti-harmonic is temporal, yet they both coexist together in spacetime.

When I look at any geometrical shape, I try to imagine the wave interference pattern that it represents. An egg, for instance, is a quasi-crystal and thus acts as a temporal container to protect the spatial development of the harmonic crystal (life form) in its spherical yolk. In musical terms, the shell is dissonant (heavily damped) while the yolk is consonant (highly resonant).

When I look at the Thorsteinn 5-fold FANG system (discussed in earlier posts), I see a quiet temporal space that exists between harmonic structure but that supports its development. In short, infinity supports the finite. From a mythological perspective, this becomes Atlas (phi-damping) holding up the world through the mighty Pillars of Hercules (pi-resonance). Consider that in a harmonic dodecahedron the 5-fold geometry related to the golden ratio is squeezed out of the faces to the infinite edges. The edges define the area of the faces and the volume inside, but are themselves infinite.

For instance, consider wave partials 5 and 7 are harmonics in a standing wave. As coherent standing waves form in everything from the atomic level up, partials 5 and 7 always intersect each other on the cosine (even / female) component of the fundamental frequency. Specifically, they intersect in 12 locations per period with 2 additional tangent contacts. Without going into a longer explanation, the wave can be dampened or crystallized by applying pressure (like transforming coal into a diamond). When we do this, it follows an axial alignment along golden ratio angles, thus matching the Fatty and Skinny primitives in your FANG system. This pressurized realignment process warps the wave oscillation into a coherent standing wave, damping out fractional Fibonacci waves, fusing the tangent anti-nodes and allowing whole number harmonic wave partials to form "sympathetically." As it applies to partials 5 and 7, they crystallize into the geometry of a dodecahedron or its dual. In the same way, adding or subtracting other partials and applying various pressures will create other geometry. The Rhombic Triacontahedron used as a primitive in the FANG system would have a great deal of damping pressure on it, for instance, and would not resonate well as a chamber. A nano-structure in this form would not reflect certain waves.

All of this is consistent with Bohmian physics which states that the Universe is a quantum hologram and that it enfolds into life, starting with our brain, which is then described by holonomic brain theory (Karl Pribram). That is, everything is an interference pattern of EM energy projected through the quantum chromodynamic (QCD) lattice, materializing as physical resonant geometries inside this spatial container. Perception is then a recreation of the outside hologram within the inner hologram of our brain/lattice which we recognize through a one-to-one geometric (or phase shift) pattern matching process. Only Nature can recognize itself.