Ideometrics¶

The formal science of measuring, comparing, and composing ideas.

Ideometrics is the branch of RTSG that treats ideas as geometric objects with measurable properties — position, mass, velocity, dimension, and synergy. It provides the mathematical substrate for IdeaRank, intelligence fingerprinting, cognitive assembly theory, and the Intelligence Arena.

Core Thesis¶

An idea is not an atomic unit. It is a structured object in the concept graph — a node with:

• Position in the 8D intelligence space
• Dimensionality dim(n) — how many I-vector dimensions it activates
• Mass — how many other nodes it connects to (weighted by relation strength)
• Velocity — rate of change in the collective consciousness graph over time
• Synergy — the additional value produced when combined with other ideas

Ideometrics provides formal operations on these objects: composition, projection, comparison, ranking, and fingerprinting.

Key Definitions¶

Idea Node¶

A node n in the RTSG concept graph G = (V, E, W) where: - V = all concepts in the domain - E = relations between concepts (first-class objects, not mere pointers) - W: E → ℝ = relation weights (synergy coefficients)

Entity Dimensionality¶

The number of I-vector dimensions that node n activates above threshold θ_k. A concept like "free will" activates linguistic (I_L), logical (I_M), interpersonal (I_P), and interoceptive (I_IE) dimensions — dim ≥ 4. A pure calculation activates only I_M — dim = 1.

Pedagogical implication: A dim = 1 concept requires single-modality instruction. A dim ≥ 5 concept requires simultaneous activation of all relevant I-vector dimensions.

Node Value Metric¶

Value is a function of where n sits in the concept graph (its IdeaRank score) and how it activates the 8D I-space. Nodes in the top layer of IdeaRank that activate many dimensions simultaneously are the most valuable — they are the ideas that connect everything.

Idea Composition¶

Given two ideas n₁, n₂ with I-vectors I(n₁) and I(n₂):

where S(n₁, n₂) = synergy tensor contribution from the cross-dimensional activation. The synergy is non-zero when n₁ and n₂ activate complementary dimensions — the combination produces something neither has alone.

Cognitive Assembly Value¶

A well-formed cognitive assembly is always worth more than the sum of its parts. Equality holds only for uncorrelated, non-synergistic components. This is Theorem 4 of RTSG, derived from the SynergyTensor structure.

Complexity Measures¶

Basic English Complexity Ratio (Niko hypothesis)¶

How many Basic English words are needed to express the same document D? More words needed = deeper idea = higher Kolmogorov complexity. This approximates K(D) without requiring a universal Turing machine.

Properties: - Pure tautology: complexity = 1.0 (already in basic form) - Simple fact: complexity ≈ 1.2–1.5 - Technical concept: complexity ≈ 2–4 - Deep original theory: complexity ≈ 5–10+

The RTSG framework itself has a Basic English complexity ratio of approximately 7–9 depending on which section. This places it in the same range as general relativity (~8) and quantum field theory (~9).

Kolmogorov Depth¶

The true complexity measure is K(D) — the length of the shortest program that outputs D. The Basic English ratio is a computable approximation. The IdeaRank depth of the top-layer nodes that constitute D is another approximation.

The Collective Consciousness Graph¶

The union of all RTSG graphs across all agents in a network:

Properties: - Density grows with the number of agents and connections - Frontier = nodes that exist in few agent graphs (novel ideas) - Core = nodes that exist in many agent graphs (consensus knowledge) - IdeaRank on G_collective identifies the most cross-dimensionally connected ideas in the entire network

The wiki is the current implementation of G_collective for the RTSG BuildNet.

Temporal Ideometrics¶

Ideas have temporal properties:

Intellectual dating: Given corpus C(ξ), the temporal position of ξ in intellectual history is recoverable from the IdeaRank distribution of the corpus against G_collective at different time periods.

Velocity: An idea's velocity in G_collective = its rate of adoption (how fast other nodes start referencing it). High-velocity ideas = paradigm shifts. Low-velocity = incremental advances.

Prediction: Ideas in the top layer of IdeaRank with high dim(n) and currently low velocity are the most valuable targets — they have maximum inherent value but have not yet diffused through G_collective. These are the ideas to publish.

Applications¶