Spock treats knowledge as geometry. Concepts are points in high-dimensional space, and reasoning is navigation through that space. This isn't just a metaphor—it's a mathematical framework with remarkable properties.
Why random vectors in 512+ dimensions are almost orthogonal, enabling collision-free concept representation without coordination.
Truth as a direction, not a boolean. How partial truths, uncertainty, and evidence accumulation emerge from vector alignment.
The three fundamental operations—Add, Bind, Negate—and how they compose to represent complex knowledge structures.
Reasoning as navigation: how the Plan and Solve verbs find paths through conceptual space toward goals.
How theories create local contexts, overlay mechanics, and geometric merge strategies for version control.
DSL-In/DSL-Out principle: every computation is traceable, replayable, and auditable.
| Concept | Mathematical Basis | Practical Implication |
|---|---|---|
| Quasi-orthogonality | Johnson-Lindenstrauss lemma: random projections preserve distances | Concepts can be generated without global coordination |
| Measure concentration | In high-D, most volume is near the surface of hyperspheres | Normalized vectors have stable, predictable norms |
| Cosine similarity | cos(θ) = ⟨a,b⟩ / (‖a‖·‖b‖) measures directional alignment | Truth degrees are angles, not discrete values |
| Superposition | Vector addition creates weighted mixtures | Evidence from multiple sources accumulates naturally |
| Binding | Hadamard product creates dissimilar, reversible combinations | Relationships can be encoded and decoded |
Spock AGISystem2 bridges the gap between neural flexibility and symbolic rigor. Unlike pure neural networks (black boxes) or pure symbolic systems (brittle logic), Spock provides: