This webpage documents a comprehensive symbolic harmonic system that integrates elements of numerology, geometry, quantum physics, and modular mathematics. The system is inspired by and expands upon the works of Bruce Cathie, Buckminster Fuller (Synergetics), and ancient harmonic traditions. It combines numeric patterns, geometric structures, and constant derivations to reveal an elegant repeating structure at the heart of physical reality.
Central to this system is a model of closest-packing of spheres, described by Buckminster Fuller's Synergetic formula:
Spheres(n, f) = 2 × n × f² + 2
This formula gives a discrete count of sphere layers. These values are then analyzed under modular harmonic conditions (e.g., mod 144) to find cyclical behaviors and harmonics.
Constants were constructed symbolically from ratios of harmonic pairs (e.g., 5/2 and 2/5), producing self-similar structures within the numeric system.
| Constant | Expression | Meaning & Relevance |
|---|---|---|
| 2.9 | ((1/(n×5/2)) + (1/(n×2/5))) × n | Geometric scaling constant used to rebuild harmonic sphere values |
| 0.16 | (1/(n×5/2)) / (1/(n×2/5)) | Dimensionless number linked to energy ratios, notably eV (1.6×10⁻¹⁹ J) |
| 7.25 | ((1/(n×5/2)) + (1/(n×2/5))) / (1/(n×5/2)) | Produces the same value whether evaluated symbolically or through sphere transformations |
| 2.2667 | ((1/(n×5/3)) + (1/(n×3/5))) × n | Rational ratio (34/15) that harmonizes with 2.9 and 7.25 |
| 137.252 | Derived from inverse of a symbolic e-expression | Close to fine-structure constant inverse (137.036) |
| 0.01854 | From factorial expressions involving Euler's number | Links thermodynamics, pressure conversion, and symbolic physics |
Values from sphere packing and constants are passed through modular reductions against key harmonic bases:
The numerological constants are used to reverse-engineer sphere values:
Sphere = 290 = 100 × 2.9 = 40 × 7.25 = 127.9 × 2.2667
This reconstruction shows that different constants in the system map to the same physical values through symbolic resonance, reinforcing the system's internal logic and potential natural origin.
Some constants from this system closely resemble those found in physics:
| User Constant | Resonant Quantity | Match |
|---|---|---|
| 432 | A4 tuning (Hz) | Exact match |
| 137.252 | Fine-structure inverse α⁻¹ ≈ 137.036 | +0.16% deviation |
| 0.16 | Electron volt in Joules (1.6×10⁻¹⁹) | Unit-linked |
| 2.9 | Euler's number (e ≈ 2.718) | Symbolic echo (~6.6% offset) |
| 144 | Geometric and musical base (12²) | Structural harmonic |
This framework opens many possible directions:
The ultimate aim is to present a coherent and beautiful language where number, geometry, and resonance unify across physical and metaphysical domains.