The K-Matrix: Intelligence Dimensions¶
Overview¶
The K-Matrix is RTSG's framework for modeling intelligence as a multi-dimensional tensor rather than a single scalar (IQ). It maps cognitive capability across 8 Gardner dimensions, their 10 compound products, and identifies 3 dimensional holes.
Gardner Dimensions¶
The 8 base dimensions, derived from Howard Gardner's multiple intelligences theory and extended by RTSG:
| Dim | Name | Symbol | Status | Knowledge Graph Nodes |
|---|---|---|---|---|
| 1 | Spatial | \(d_S\) | Active | 31 |
| 2 | Linguistic | \(d_L\) | Active | 2,008 |
| 3 | Logical-Mathematical | \(d_M\) | Active | 2,141 |
| 4 | Bodily-Kinesthetic | \(d_B\) | Active | 1 |
| 5 | Musical | \(d_\mu\) | Hole | 0 |
| 6 | Interpersonal | \(d_I\) | Hole | 0 |
| 7 | Intrapersonal | \(d_\iota\) | Hole | 0 |
| 8 | Naturalistic | \(d_N\) | Active | 22 |
The dominance of Linguistic (2,008) and Logical-Mathematical (2,141) reflects the knowledge graph's current bias toward formal/analytical content. The 3 holes are topological features — their absence shapes the structure.
The K-Matrix Tensor¶
For an individual, the K-Matrix is:
where \(K_{ij}\) represents the coherence between dimensions \(i\) and \(j\). The diagonal \(K_{ii}\) is raw aptitude in dimension \(i\); the off-diagonal \(K_{ij}\) measures cross-dimensional integration.
The K-score is the spectral radius:
This captures the dominant mode of intelligence — the direction in which cognitive energy concentrates most.
Compound Dimensions¶
Taking tensor products of active dimension pairs yields 10 compound dimensions:
| Compound | Formula | Interpretation |
|---|---|---|
| Spatial × Linguistic | \(d_S \otimes d_L\) | Visual storytelling, spatial metaphor |
| Spatial × Logical-Math | \(d_S \otimes d_M\) | Geometric reasoning, topology |
| Spatial × Bodily | \(d_S \otimes d_B\) | Proprioceptive navigation, dance |
| Spatial × Naturalistic | \(d_S \otimes d_N\) | Ecological mapping, terrain sense |
| Linguistic × Logical-Math | \(d_L \otimes d_M\) | Formal proof, mathematical writing |
| Linguistic × Bodily | \(d_L \otimes d_B\) | Embodied metaphor, sign language |
| Linguistic × Naturalistic | \(d_L \otimes d_N\) | Nature writing, taxonomy |
| Logical-Math × Bodily | \(d_M \otimes d_B\) | Algorithmic movement, martial arts |
| Logical-Math × Naturalistic | \(d_M \otimes d_N\) | Mathematical biology, ecology models |
| Bodily × Naturalistic | \(d_B \otimes d_N\) | Survival skills, animal movement |
These live in the knowledge graph as nodes with dimensional_product relations to their parents.
Dimensional Holes¶
The 3 missing dimensions create topological holes in the knowledge graph:
The holes represent structural silence — what the graph does not say. In Grothendieck filter language, the holes are the negative space of the identity filter.
Filling these holes requires:
- Musical (\(d_\mu\)): Rhythm, harmony, temporal pattern recognition
- Interpersonal (\(d_I\)): Social cognition, empathy, theory of mind
- Intrapersonal (\(d_\iota\)): Self-knowledge, metacognition, introspection
Cross-Federation Links¶
The strongest bridge in the knowledge graph:
This massive cross-federation explains why RTSG naturally produces mathematical writing — the two dominant dimensions are deeply entangled.
Connection to Fugue¶
The Fugue methodology (chess + martial arts + cognition) operates primarily in the compound dimension \(d_M \otimes d_B\) (Logical-Mathematical × Bodily-Kinesthetic), with Fugue's shape-first evaluation adding \(d_S\) (Spatial). The full Fugue K-vector is: