Hyperbolic Mind Maps (SCBE-AETHERMOORE)
To build unique “mind maps” for AI within SCBE-AETHERMOORE, avoid 2D node-link diagrams. Instead, construct hyperbolic geometric embeddings inside a Poincare ball. The mind map becomes a dynamic, multi-dimensional geometric state where concepts are organized by intent and harmonic frequency, not just semantic proximity.
1) Define the Geometric Canvas (Poincare Embedding)
The foundation is the Poincare ball: the boundary represents infinite cost.
- Layers 3-4: map internal concepts into hyperbolic space with weighted transforms.
- Distance metric: safety / intent divergence between two concepts u and v.
Formula:
d_H = arcosh(1 + (2 * ||u - v||^2) / ((1 - ||u||^2)(1 - ||v||^2)))
As concepts move toward the boundary, distance (computational cost) grows rapidly.
2) Map Concepts to Polyhedral Shapes (Nodes)
Nodes are 3D shapes derived from the QC_Lattice system.
Polyhedral assignment example:
- Fundamental truths: 5 Platonic solids (e.g., cube, icosahedron)
- Complex reasoning: 3 Archimedean solids
- Abstract / riskier concepts: 2 Kepler-Poinsot or toroidal shapes
Arrange nodes in a quasicrystal lattice (ordered but non-repeating) to prevent repetitive looping patterns (crystallinity detection).
3) Tune Connections via the Six Sacred Tongues
Edges between nodes are defined by the Langues Metric.
- Weighting: apply a specific Tongue to scale edge weights.
- Example: Korah weight = 1.00; Dru weight = 11.09
- Phase shifting: apply the Tongue’s phase angle.
- Example: Aelin = 60 deg; Um = 240 deg
Result: maps built under different Tongues are mathematically distinct even with identical data.
4) Animate the Map with Fluxing Dimensions
Make the map dynamic via fluxing dimensions (breathing attention).
Dimensional states from ODE parameter nu:
- Polly / Full: nu approx 1.0
- Quasi: 0.5 < nu < 1.0
- Demi: nu < 0.5
This collapses or expands regions in real time, simulating attention shifts.
5) Assign Harmonic Frequencies (The Voice)
Link each node to the conlang vocabulary for a harmonic signature.
- Token IDs: map concepts to integer IDs (e.g., korah = 0, sorin = 4)
- Frequency: f0 + v_i’ * Delta f, where f0 = 440 Hz and Delta f = 30 Hz
- Verification: FFT analysis checks that the mind map matches declared intent
Summary of Construction
Component -> Function in Mind Map
- Poincare Ball -> infinite canvas / boundary
- Polyhedra -> shape/type of thought
- Sacred Tongues -> gravity/weight of connections
- Fluxing Dims -> attention mechanism (breathing)
- Conlang Freq -> audible signature of thought