Why Does Spock Work?

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.

Core Theory Pages

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Hyperdimensional Computing

Why random vectors in 512+ dimensions are almost orthogonal, enabling collision-free concept representation without coordination.

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The Geometry of Truth

Truth as a direction, not a boolean. How partial truths, uncertainty, and evidence accumulation emerge from vector alignment.

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Vector Symbolic Operations

The three fundamental operations—Add, Bind, Negate—and how they compose to represent complex knowledge structures.

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Semantic Gradient Descent

Reasoning as navigation: how the Plan and Solve verbs find paths through conceptual space toward goals.

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Theories as Subspaces

How theories create local contexts, overlay mechanics, and geometric merge strategies for version control.

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Native Explainability

DSL-In/DSL-Out principle: every computation is traceable, replayable, and auditable.

The Central Insight

The Miracle of High Dimensionality: In spaces with 512+ dimensions, randomly generated vectors are almost certainly orthogonal to each other. This means you can create millions of distinct concepts without any coordination—just generate random vectors, and they're guaranteed to be unique.
Quasi-Orthogonality in High Dimensions 2D Space Vectors often overlap (high correlation) Add dimensions 512D Space Vectors nearly orthogonal (correlation ≈ 0) P(|correlation| > 0.2) < 0.003% for random 512D vectors

Quick Navigation

Mathematical Foundations

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

Why This Matters for AGI

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:

References